Thermal-Hydraulic Phenomena - February 20, 2001


                Official Transcript of Proceedings


Title:                    Advisory Committee on Reactor Safeguards
                               Thermal-Hydraulic Phenomena Subcommittee

Docket Number:  (not applicable)

Location:                 Rockville, Maryland

Date:                     Tuesday, February 20, 2001

Work Order No.: NRC-076                               Pages 1-292

                   NEAL R. GROSS AND CO., INC.
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                             FEBRUARY 20, 2001
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                            ROCKVILLE, MARYLAND
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                       The Subcommittee met at the Nuclear
           Regulatory Commission, Two White Flint North, Room
           T2B3, 11545 Rockville Pike, at 8:30 a.m., Dr. Graham
           B. Wallis, Chairman, presiding.
                 GRAHAM B. WALLIS           Chairman
                 THOMAS S. KRESS            Member
                 DANA A. POWERS             Member
                 WILLIAM J. SHACK           Member
                 Virgil Schrock
                 Novak Zuber
                 Paul Boehnert
                 Ralph Caruso
                 Ralph Landry
                 Joe Staudemeyer
           ALSO PRESENT:
                 Jack Haugh
                 Mark Paulsen
                 G. Swindelhurst
                        AGENDA ITEM                        PAGE
           Introduction by Chairman Wallis. . . . . . . . . . 4
           RETRAN-3D T/H, R. Landry, NRR. . . . . . . . . . . 8
           EPRI Presentation
             G. Swindelhurst, Duke Energy . . . . . . . . . .54
             M. Paulsen, CSA. . . . . . . . . . . . . . . . .92
           NRR Staff Presentation: Status of T/H Code . . . 282
             Review Submittals, R. Landry
           Subcommittee Caucus
             Follow-on Items from this Meeting
             Future Actions
             Committee Action
           Adjournment. . . . . . . . . . . . . . . . . . . 292
                                                    (8:30 a.m.)
                       CHAIRMAN WALLIS:  The meeting will now
           come to order.  This is a meeting of the ACRS
           Subcommittee on Thermal-Hydraulic Phenomena.  I am
           Graham Wallis, the Chairman of the Subcommittee.
                       ACRS members in attendance are Doctors
           Thomas Kress, Dana Powers and William Shack.  ACRS
           consultants in attendance are Messers Virgil Schrock
           and Novak Zuber, who also have PhDs.
                       The purpose of this meeting is for the
           Subcommittee to continue its review of the Electric
           Power Research Institute RETRAN-3D thermal-hydraulic
           transient analysis code and discuss the status of the
           NRC staff's pending reviews of industry thermal-
           hydraulic codes.
                       The Subcommittee will gather information,
           analyze relevant issues and facts, and formulate
           proposed positions and actions, as appropriate, for
           deliberation by the full Committee.
                       Mr. Paul Boehnert is the cognizant ACRS
           Staff Engineer for this meeting.  
                       The rules for participation in today's
           meeting have been announced as part of the notice of
           this meeting previously published in the Federal
           Register on January 30, 2001.
                       Portions of the meeting may be closed to
           the public, as necessary, to discuss information
           considered proprietary to Electric Power Research
           Institute.  I would ask EPRI to point out if that is
           the case at anytime.
                       A transcript of this meeting is being
           kept, and the open portions of this transcript will be
           made available as stated in the Federal Register
           notice.  It is requested that speakers first identify
           themselves and speak with sufficient clarity and
           volume so that they can be readily heard.  
                       We have received no written comments or
           requests for time to make oral statements from members
           of the public.
                       Now I am going to do what I almost never
           do at these meetings, and that's make some preliminary
                       There is a history to this story.  About
           two years ago we received some documents from EPRI
           describing their code RETRAN-3D and, having read these
           documents, I made a presentation to the ACRS which was
           concerned with some problems with the momentum
           equations and their formulation and use.
                       EPRI met with us after that, still almost
           two years ago, but we never had any technical
           discussion or resolution of the issues at that time. 
           Since then, there's been an exchange of RAIs and
           responses between the staff and EPRI, and the staff
           has prepared an SER.  I'm not quite sure if it is
           drafted at this time or final, but the ACRS itself
           hasn't been directly involved in this issue since
           1999.  So this is our chance to really get to grips
           with it.
                       I suggest there are three questions or
           maybe six.  There are three questions, and each one of
           them raises another one that goes with it.
                       The first one is:  What are the
           formulations of these equations?  Let's clarify. 
           Let's get the information straight so we know exactly
           what is going on.  It's a fact finding question.
                       Related to that is the question that goes
           along with it, which is:  Are they valid, and under
           what circumstances and with what kind of
           approximations or whatever?
                       The next question is:  How are these
           formulations used?  How do they actually apply to the
           real life nodes, control volumes and whatever in
           reactor systems?  The question that goes along with
           that is:  Are these methods of use valid?  What's the
           basis for validity, and what's perhaps the limitations
           and so on?
                       The third question is:  How does the
           overall code work using these particular methods? 
           Going along with that is the question:  What's the
           basis for validation of this code?  
                       I separate these questions, because it's
           conceivable that the formulations contain
           approximations, even errors, maybe used in a way which
           is difficult or can be qualified in some way, but
           there is a claim still made that, nonetheless, the
           code works, because there's some measure of working
           which is applied to the code.
                       The other thing I wish to say is I can't
           imagine how we would spend all day on these issues,
           and I actually have a plan to leave at three o'clock. 
           Originally, we were going to have about an hour
           presentation, and I didn't expect that we would spend
           all day on these matters.  Let's see how it goes.
                       I'm not sure just how EPRI is going to
           prepare, but if you prepared -- if you can address the
           three questions that I posed in the order that they
           were posed, that would help me anyway.
                       So I'm sorry to take the time of the
           Subcommittee, and now I will call upon Dr. Ralph
           Landry who is bursting with enthusiasm to give his
           view on this matter.
                       DR. LANDRY:  Thank you, Mr. Chairman.  I
           don't know if I should say bursting with enthusiasm to
           get the view known, but I'll try to get it known.  I
           think in our presentation and in our SER we do, in a
           sense, address some of the questions and our views of
           the answers to some of your questions.
                       First, what I'd like to do is very quickly
           go over the topics that we are going to cover and a
           quick rundown of some of the milestones, just to
           refresh the new members of the subcommittee on what we
           have done with this code, because it has been for
           quite a period of time.
                       So I'd like to get a highlight of the
           milestones, talk a little bit about the staff approach
           to the review, the evaluation of some of the aspects
           of RETRAN-3D which we did in the evaluation, which
           includes momentum equation, 5-equation model, critical
           flow model, and down the list talk a little bit about
           using RETRAN-3D in a RETRAN-02 mode.
                       One of the concerns that was raised by the
           applicant was that they would like to have permission
           to use RETRAN-3D in substitute for RETRAN-02, and I'll
           have some remarks on that, because you can't exactly
           substitute the code.  There are changes that cannot go
           back in time to the old code.
                       I would like to touch briefly on the
           conditions on use.  The former versions of the code
           had an extensive number of revision conditions on use. 
           We have reviewed some of those, and we have added
           more.  Then the conclusions of the staff.
                       (Slide change)
                       DR. LANDRY:  Very quickly, as the Chairman
           said, about two years ago, approaching three years
           ago, we received the request to review RETRAN-3D.  We
           received the code itself and  documentation in
           September of 1998.  In December of that year we issued
           our acceptance for review of the material.
                       We met with the Subcommittee in December
           of '98, March, May, July of '99, March 2000 and again
           now in 2001, a lot of meetings that we've held with
           the Subcommittee.  There was a meeting with the full
           Committee, as the Chairman pointed out, at which time
           he expressed his concerns with some of the material in
           the documentation.
                       The staff has met with EPRI on a lot of
           times, and we prepared our SER in December of 2000.
                       (Slide change)
                       DR. LANDRY:  The approach that we took to
           this review is, as we have said several times, in the
           past we used a lot of contractor support in reviewing
           codes.  This was one of the first codes in a long time
           in which we assembled a staff group to do the review
           without relying on contractors.
                       We assembled a group of four, which a
           former member of the Subcommittee referred to as "the
           Gang of Four," to perform the review, people with
           expertise in thermal-hydraulics, kinetics, numerics,
           that could look at the code and do a review.
                       Originally, we had planned on
           concentrating on only the differences between RETRAN-
           3D and RETRAN-02.  However, fundamental problems that
           were pointed out caused us to go back and start
           looking at the basis in the code itself, some of the
           fundamentals which we had not planned on reviewing.
                       We exercised the code extensively.  We
           made many, many, many computer runs using models which
           we obtained from the applicant, models which we put
           together, attempts to break the code, to find where
           the code could fail and where it had shortcomings.
                       We looked at the conditions and
           limitations on the previously approved versions of the
           code.  We identified additional conditions and
           limitations, and we put together a long list of
           conditions on use of RETRAN-3D as RETRAN-02
           substitute.  I'll go into some of those a little later
           in this presentation.
                       (Slide change)
                       DR. LANDRY:  Okay.  One of the first
           problems we ran into in looking at extensive concerns
           with the code was with the momentum equation.  Some of
           these problems, as Dr. Zuber has pointed out, go all
           the way back to 1974, and with the RELAP3 and RELAP4
           codes from which RETRAN derived.  In fact, I believe
           some of them even go back all the way to the FLASH
                       Some of the points of concern that the
           staff raised, and these are all delineated and
           discussed further in the SER:  We were concerned with
           the attempt at rigor in the derivation of the momentum
           equation.  A lot of effort is spent on a derivation,
           forms, terms that are not really in RETRAN-3D itself.
                       We have problems with the notation that
           was used in the derivation in the text. The
           documentation goes through an indicial notation, then
           goes into a non-standard notation.  So that when we
           thought we understood an equation on one page, we
           encounter the equation on another page and, because of
           the change in notation, it's a totally different
           equation.  We have to sit down and try to figure out
           what in the world we are looking at on the next page.
                       There are typographical errors.  Sometimes
           we weren't sure if we were seeing typographical errors
           or changes in notation.  
                       Distributed descriptions occurred in the
           text.  Descriptions of the equations spanned sections
           and chapters in the documentation.  There wasn't one
           concise description and derivation.
                       Nomenclature is missing.  Sometimes terms
           are defined within the text.  When we have found a
           term in an equation we didn't understand, we didn't
           know if it was a change in notation, a typographical
           error, or if we had to go back and start reading text
           to find what the term meant, because it wasn't in the
           nomenclature list.
                       DR. SCHROCK:  Excuse me, Ralph.  On slide
           3 you had an item "acceptance of RETRAN-3D for
           review."  It seems to me that so much of the effort --
           it's just wheel spinning here -- could have been
           avoided if you had stepped up to the plate and said at
           that time, this list of things renders this submittal
           inadequate for NRC review at this time.
                       I think that's what you were driving for
           in your revision of the standard review plan and in
           the reg guide supporting it.  So I think you've got to
           address that issue at some time.  When are you going
           to do that?
                       DR. LANDRY:  Well, some of these problems
           -- Let me back up.  We have to understand what the
           acceptance for review process is, in the first place. 
           If it's a mini-review to see that there is enough
           material there to begin a review, then you won't find
           these kind of problems until you go into the text in
           depth and start finding the problems.
                       If you want to say an acceptance review
           means that everything is absolutely correct in the
           text, then you have done the review at the same time. 
           The acceptance review process which we envisioned was
           one in which we would look at the documentation and
           say, yes, this documentation has enough material,
           covers all the topics that it should cover, and we can
           begin the in depth review of the material.
                       That was our initial goal in doing an
           acceptance review. 
                       DR. SCHROCK:  Well, when I reviewed it, I
           could have said after the first two hours that this is
           not a document that describes a code that can be
                       DR. ZUBER:  Zuber.  Let me add, I
           completely agree with Virgil.  If a code has errors,
           which should be really at the junior level, that code
           should not ever be reviewed for the reason that this
           is not acceptable, period, and not really go for two
           years, which we have been now and God knows how long.
                       I think that doesn't do credit to NRC.  It
           doesn't do credit to the technology.  Basic errors in
           the code which on the junior level can be detected
           should not be even accepted.
                       DR. LANDRY:  In our writing of the SRP,
           which has a lot of information and based on our
           experience in this review, I think that in the future
           we are going to do a greater review of material before
           we accept it; whereas, at this point we just looked
           through, said okay, there's enough material here we
           can start a review.
                       We were coming off of an experience with
           a previous design submittal in which we were reviewing
           an SB LOCA code, which is -- the documentation was
           less than a quarter of an inch thick.  We said,
           obviously, this isn't adequate to do a review of the
                       So we needed to do a review of the
           material first to see if there's enough material to
           review before we could accept it, and that was the
           mindset that got us into this position; and as we then
           got into the review in depth, we've started learning
           more and more of errors in it and that perhaps this
           should have been done in a different way.
                       CHAIRMAN WALLIS:  Maybe it would help if
           you had someone like Professor Schrock review the code
           and say just what he said, that after sort of an hour
           reading he could tell you that, you know, this ship is
           headed for an iceberg, let's not let it happen.
                       DR. LANDRY:  I think we have learned a lot
           from this experience and learned how we have to do
                       DR. ZUBER:  Just one more comment.  You
           see, you get into a position.  If you accept it for
           review and after sometime you cannot really approve
           it, you are being accused or put in a position it
           costs so much money to go to NRC, and then you get the
           lawyers on your back.
                       What you should really do, stop in the
           beginning and say this is not acceptable, go back. 
           You save them money, but if they want to waste their
           money, that's their own prerogative.  But they should
           not waste your time.
                       DR. LANDRY:  We agree with you, Novak.  We
           have learned a lot from this.  
                       Okay, I think I was down to the last step. 
           In looking through the derivations of the momentum
           equation, we also found that there were missing steps. 
           Where there had been a great deal of detail lavished
           on the initial phases of the derivation, the
           derivation became very sparse, and very great leaps
           were taken at the end.
                       (Slide change)
                       DR. LANDRY:  In our review we determined
           that the so called "vector momentum equation" really
           isn't.  The equation that is in the material is a
           scalar equation of motion.  It is projected on a
           vector momentum along a control volume dependent
           direction.  It's really not a vector momentum
                       We found a number of errors, some of which
           you corrected.
                       CHAIRMAN WALLIS:  You concluded that it
           was a projection of a vector momentum equation?
                       DR. LANDRY:  We viewed it as that it's a
           projection of vector momentum along a --
                       CHAIRMAN WALLIS:  Because it appears to be
           a strange hybrid, which isn't really projection of a
           vector momentum equation.  It isn't energy
           conservation, and it isn't recognizable based.
                       DR. LANDRY:  That's what we are trying to
           say.  It's not --
                       CHAIRMAN WALLIS:  But you said something
           there which I don't think is --
                       DR. LANDRY:  Well, I was trying to shorten
           up a statement. 
                       CHAIRMAN WALLIS:  -- is true.
                       DR. STAUDEMEYER:  Joe Staudemeyer, NRC
           staff.  If you look at the derivation, it really is a
           projection of a vector momentum equation along a
           direction that depends on what the volume is on the
           direction of volume that it's in.  So --
                       CHAIRMAN WALLIS:  Well, that's what it
           claims to be.
                       DR. STAUDEMEYER:  And you can work out all
           the terms, and it does work out that it's that.  But
           then you end up with 20 terms left over that don't --
                       CHAIRMAN WALLIS:  Okay.  Well, we are
           going to get into that with EPRI, I guess.  I think
           that all of us have great difficulty projecting
           several of these terms in a direction which makes any
           direct link between a vector momentum equation and the
           equation that actually appears.
                       DR. STAUDEMEYER:  Yes.  Well, there are
           some other assumptions I have to go into to get it,
                       DR. LANDRY:  Okay.  In the review we
           pointed out a number of errors.  I know the Chairman
           had pointed out a number of errors and a lot of
           information on the momentum equation also.  Some of
           these overlap.  We haven't gone back to see if we have
           a one to one correspondence, but I'm sure some  of
           this overlaps with what the Chairman has pointed out
                       We found that there is a cosine term
           missing from a vector dot product in going from
           equation 236 to equation 237.  We pointed out where
           this would be easily seen if one tries to solve this
           equation for a bend in a pipe.
                       We said that it was mathematically
           possible to eliminate the cosine term from the
           pressure difference term if a constant pressure is
           assumed in the cell, but then the cosine term has to
           appear somewhere else.  It has to be moved to the Floc
           term, projection of nonuniform normal wall forces.
                       The EPRI staff told us that this was going
           to be evaluated based on empirical information and
           empirical data.  The staff is anxiously awaiting to
           see the source of that information.  We are not aware
           of any such information.  We would very much like to
           see it.
                       We have said that the equation for
           mechanical energy conservation cannot be derived from
           the equation of motion.  Therefore, you cannot show
           that your mechanical energy is being conserved.
                       We said that pipe configuration with a TEE
           split or two parts coming together, such as a jet
           pump, results in a non-zero pressure difference that
           is dependent on the area of the exit path or paths. 
           The EPRI staff agreed with this, and has gone back and
           fixed the information.
                       We have looked at an attempt at a
           derivation called the "Porsching Paper."  According to
           the staff's view is that the paper is irrelevant.  We
           said it's irrelevant, because the paper does not
           appear to have any mathematical errors, but the
           definitions and restrictions on control volumes that
           are required to be consistent with the mean value
           theorem makes the paper irrelevant.
                       Pressures and flows in RETRAN are defined
           in a control volume with specified functional
           dependencies.  The integrals in the paper should be
           evaluated with the RETRAN-3D assumed function
           dependence for pressure and flow.  In our view, the
           paper doesn't pertain to the derivation.
                       I'm sure EPRI is going to want to respond
           to that a little later also.
                       (Slide change)
                       DR. LANDRY:  We looked at the 5-equation
           non-equilibrium model.  This is a topic that caused us
           quite a bit of concern during the review.
                       Part-way -- A year into the review, part-
           way into the review, we found out that there was a
           fundamental change in the code which we weren't aware
           of.  That was being in the works at the time the code
           was submitted.  
                       This caused us a great deal of
           consternation.  Finally, the material was submitted. 
           We came back in our review and said that this model
           has not been assessed properly and, therefore, is not
           acceptable for use.
                       Licensees who wish to use the 5-equation
           non-equilibrium model have to provide separate
           effects, integral systems effects assessment over the
           full range of conditions that are to be encountered
           for which the model is applied.
                       Assessment of uncertainties --
                       DR. ZUBER:  Every time you get an
           applicant, you will have to do another review.
                       DR. LANDRY:  That is correct.
                       DR. ZUBER:  Well, that's a waste of money
           and waste of time.  In a sense, you have to review,
           but not at this level.  This should be the level of
           code acceptance, and then you apply to a given plant. 
           That's another story, but this is really the basic
           equation, the basic model.  If you have to do this for
           every applicant, it takes your time.  It costs money,
           and it costs them money, and I'm really surprised that
           they didn't address this problem.
                       DR. LANDRY:  This was -- In the original
           phase of the review, our understanding was that the
           code was being submitted so that we could review the
           code, as we have with a number of other industry
           codes, and say that the code is approved for use and,
           as long as it's used within the constraints, we don't
           have to review the submittal.  But -- Let me finish,
                       Back in the RETRAN-02 days, RETRAN-02 was
           approved, but there were 39 conditions and limitations
           on use, which meant virtually everybody who used the
           code had to come in with a justification assessment
           and support why that code is applicable for their
                       We thought we were getting out of that
           mode.  However, we can't.  We are still in that mode
           with RETRAN-3D, because of our view of the assessment. 
           When the code is used, it still must be heavily
           supported for every application, and yes, we agree
           with you.
                       DR. ZUBER:  That really surprises me, that
           the industry complains for money, and yet really that
           puts NRC in the position that they have to do it.
                       DR. LANDRY:  The code has to be assessed
           properly for the application.  If it's not done
           generically, then it has to be done for each specific
                       DR. ZUBER:  Well, this approach really
           makes -- four separate effects.  You can really put
           the burden not on the co-developer but on the
           applicant.  I mean, that's the philosophy, I mean, if
           you follow logically this approach.
                       DR. LANDRY:  You are going to hear me say
           that throughout this presentation.
                       DR. ZUBER:  Good.
                       CHAIRMAN WALLIS:  Well, what happens when
           the applicant, say Maine Yankee which doesn't exist
           anymore -- we'll pick someone -- comes up, wants to
           use RETRAN, and their engineers look at it and say,
           gee whiz, we can't figure out this momentum equation? 
           Is it their responsibility to defend it?
                       DR. LANDRY:  The defense of a methodology
           used in a licensing application is put on the
           applicant, the licensee.  The licensee --
                       CHAIRMAN WALLIS:  But do they have to
           defend something in the code which they didn't
                       DR. LANDRY:  The licensee is responsible
           for everything that is submitted on their application.
                       CHAIRMAN WALLIS:  So they have to go over
           the same terrain again maybe.
                       DR. LANDRY:  If material is not correct.
                       CHAIRMAN WALLIS:  It's an awfully wasteful
           and inefficient process.  
                       DR. LANDRY:  If the material is not
           correct or not done adequately, then the burden is
           placed on the licensee.
                       CHAIRMAN WALLIS:  I guess that's the theme
           that the ACRS keeps trying to sing that no one has
           listened to.  If you do the job right the first time,
           it saves one hell of a lot of wasted energy and money.
                       DR. LANDRY:  We're not going to disagree
           with you.
                       CHAIRMAN WALLIS:  What's wrong with that
           statement?  We've said that before, and we get all
           this gripe about, well, it's too much effort to do it
           right and, no, no.  
                       DR. ZUBER:  Limited resources, too much
           money, and it ends up they to minimize any effort. 
           I'm sorry.
                       DR. LANDRY:  We don't disagree with you.
                       CHAIRMAN WALLIS:  Let's move on.
                       DR. LANDRY:  This is why we like to do --
           let's call them topical type reviews, because we can
           review a material one time and then, when it's
           applied, all we have to do is see that it's applied
           properly.  It saves everybody.
                       CHAIRMAN WALLIS:  Well, it's like the
           homework.  If everything is right, you just check it
           out and give them an A, and that's the end of it, and
           it's five minutes work.
                       DR. LANDRY:  I wish I had people like you
           in school.  Do you give multiple choice quizzes?
                       CHAIRMAN WALLIS:  The interesting part is,
           if it's a better derivation than the professor's, then
           you have to think about it.
                       DR. SCHROCK:  Doesn't it seem reasonable
           that, if you are unable to approve something as a
           generic tool for general applications, maybe a minor
           exception here and there, but for general
           applications, if you are not able to do that, then why
           don't you ask what is the function of such an
           approval?  What does it accomplish for anybody?
                       DR. LANDRY:  When we look at a new
           methodology, new model, that's one of the things we
           look at.  Back on another code that we reviewed
           recently when we talked about replacing one of the
           transfer correlations, we were looking at what is the
           benefit.  It's a newer equation --
                       DR. SCHROCK:  I'm not talking about
           details at that level, but the conclusion is that the
           code is basically unacceptable for -- I guess you've
           identified something like 40 different situations, and
           if it's going to be used for those situations, then
           additional -- significant additional work will have to
           be done.
                       So you really haven't produced anything
           that's useful either to the industry or to the
           regulators, it seems to me.  You've --
                       DR. LANDRY;  Well, one of the bottom lines
           we are going to get to in this is that, while there
           are a great many conditions and limitations on use and
           a great many things that the applicant must do when
           using this code, the code is an improvement over
                       It is numerically improved.  It is more
           robust.  But -- and then we get into the "buts," all
           the things that must be done.  So, yes, it is an
           improvement, but it's not perfect especially in that
           it's not totally supported in its assessment
                       This has been an ongoing discussion.
                       DR. ZUBER:  But that is where I see the
           kind of trouble recently is you try always to put
           everything in that one basket.  One is the
           formulation, the basic equations, and this is, I
           think, question one that Graham had.
                       The second one is what kind of
           validations.  I think you should separate those, and
           on the first level the equations, the formulations,
           then the constitutive equations.  Then you will go
           back into validations.  Don't try to kind of jump from
           one to the other, I think.  Focus on one.  If it's
           acceptable, then look at the validation, but putting
           them together -- and this is what industry does -- is
           at least confusing.
                       CHAIRMAN WALLIS:  I think you also have to
           decide when you review is this sort of a series of
           filters, and if you filter the fundamental formulation
           and, if it doesn't pass that filter, do you go any
           further or do you sort of go on to start looking at
           assessment and stuff with loft, no matter what
           happened in the previous filters.  
                       I think that's something you guys have to
           think about in the process.  That is a sort of series
           of steps with yes/no and, if there's a no, you don't
           go any further or do you have some yes/maybes.  How
           are you going to do that?
                       DR. LANDRY;  That's a difficulty.  As you
           come down through a particular model, is this -- does
           it look valid, what they have done?  Is it assessed? 
           If you come out no, do we stop altogether or do we go
           to the next stage and say, okay, the next model. Okay,
           we've a yes here.  This one we have a yes.  This one,
           you have to go back and support or you put a
           limitation.  We keep doing down the list --
                       CHAIRMAN WALLIS:  How many of those are
           necessary, and to what degree is the thing.  You have
           to ask yourselves pretty carefully.
                       DR. LANDRY:  That is a very difficult
           question, because that really doesn't show up until
           you start assessing against things like an integral
           system or full size data where you can say the 
           overall package does a bad job or the overall package
           does a good job, but it could do a better job if this
           was fixed.
                       DR. ZUBER:  Let me say, I think, if I may
           be direct, there you are really going on a kind of a
           tangent.  You used the word model.  What does it mean? 
           Does it mean the formulation, which is also model, or
           does it mean the constitutive relations, and that's
           all similar.  And don't put those things together.
                       The first thing is, is the formulation
           correct?  Are the equations correct?  If they are,
           then you proceed to the next one.  Then you look at
           the model.  If you question the model, you go to the
           validation.  There is a kind of a hierarchal approach,
           how you look at these problems.  But don't take
           immediately model, because you don't know -- at least,
           I don't know what you are really addressing.
                       So look at the formulation equations.  If
           they pass, fine.  If not, send it back to the student. 
           Go back then to the constitutive equations.  If they
           are acceptable, fine.  If not, what is the validation.
                       CHAIRMAN WALLIS:  Well, there is also the
           question of what you mean by correct.  I mean, there
           are errors that reveal a fundamental misunderstanding,
           and there are errors which are more in the form of you
           can't solve this thing exactly, so you make some
           assumptions, but you've got to be clear what they are,
           and those aren't exactly errors.  Correctness, I
           think, has to be qualified.
                       You are not looking for something which is
           exact.  We are looking for something which is
           plausible and doesn't contain real errors, which sort
           of exaggerate some fundamental misunderstanding and
           produce a ludicrous answer under some circumstances,
           that sort of thing.
                       DR. LANDRY:  I think to follow that up and
           back up just a second to the momentum equation as an
           example, in the derivation -- Now we've argued about
           it.  We've heard the Chairman's views on it, the views
           of the Committee, the views of the consultants, our
           views.  We've been in a long debate with the
                       I think the bottom line to this as an
           example is that this was an attempt at a rigorous
           derivation of a momentum equation for use in a
           computer code.  Fundamentally, you can't get to that
           point the way it's been done.
                       A far more productive method, and one
           which we pointed out to the applicant at one point,
           would be to tell us what is in the code.  What are the
           terms?  What do the terms mean?  Why is it acceptable? 
           Why is it valid?  
                       Rather than trying to do a rigorous
           derivation from basic principles, which you can't get
           to because of all the assumptions you have to make,
           tell us what's in the code, and tell us why it's
                       This would have been a far more productive
                       CHAIRMAN WALLIS:  Well, I assume what's in
           the code is what's written down in the equation.  Is
           there something different between the equations and
           the code?
                       DR. LANDRY:  What's in the documentation
           can't be in the code, and that's not the way it has
           been derived.
                       CHAIRMAN WALLIS:  Well, see, that's yet
           another mystery that I didn't raise in my questions,
           is what's actually in the code.
                       DR. LANDRY:  And that's what I'm getting
           to, that tell us exactly what's in the code.  Tell us
           what the terms are.  Tell us what the terms mean, and
           tell us why it is valid.
                       CHAIRMAN WALLIS:  Doesn't the code come
           with some kind of code documentation which says that
           these lines in the code formulate the momentum
           equation, and these lines have the momentum fluxes,
           these are how the terms are evaluated?  I would think
           that has to be, as just quality assurance in  code
                       DR. LANDRY:  Well, some codes are better
           than others at that.  Some codes have a great deal of
           comment in them.  Some do not.  
                       CHAIRMAN WALLIS:  Well, I think you should
           require enough comment so that you can read the code.
                       DR. KRESS:  Do you do that with codes, go
           through line by line?
                       DR. LANDRY:  No.
                       DR. KRESS:  You normally don't do that, do
                       DR. LANDRY:  No.
                       CHAIRMAN WALLIS:  I do, when a student
           writes me something that purports to be the right way
           to do something.  I mean, that's how I learned how to
           program a computer, was by figuring out what the
           students were doing.
                       DR. KRESS:  What you generally have is
           this is the finite difference form of the equation
           that we coded in the codes.  You usually have that
                       DR. LANDRY:  Right.  That is in the
           manuals.  We can say, okay, that's done right.  We
           assume that they've gone from this to the code itself.
                       CHAIRMAN WALLIS:  Because, well, if there
           are typos of the type we've seen in some of the
           documentation, there should be -- you would expect
           typos in the code, too.
                       DR. LANDRY:  We've had this discussion
           before for years, and no, we don't go line by line in
           the code.
                       CHAIRMAN WALLIS:  I think you should.  At
           least, if you don't, you should threaten to, and you
           should perhaps do it from time to time in a small bit,
           bite sizes.
                       DR. LANDRY:  I think our management would
           like to discuss resources.  
                       CHAIRMAN WALLIS:  Oh, don't give me that
           nonsense.  If it's the right thing to do, it has to be
                       DR. LANDRY:  Anyway, this is an example of
           how we've tried to interact and say what you should be
           doing to make this job right, and we just disagree
           with the approach that's been taken.
                       DR. SCHROCK;  Code people have developed
           standard procedures for validating codes.  They use
           different words to describe the different parts of the
           process.  There are, in fact, codes available that
           will check that programming.
                       I never hear about those things having
           been applied in this arena, and I wonder why not.  And
           it's not that it isn't known to industry.  
                       I served on a review committee concerning
           the NPRs that went into this in great detail at
           General Atomic, and it was very clear that industrial
           representatives were on top of this.  But it doesn't
           come here.  Why is that?
                       DR. LANDRY:  Well, there is almost a loss
           of corporate memory going on.  This began -- and you
           were involved in it, if I remember right, Virgil --
           back '78-'79, even before Paul was with the
           Subcommittee.  I think Andy Bates was with the
           Subcommittee, and Milt Plessett was the Chairman then.
                       We've got into a long debate, and this
           began out in Idaho Falls at a meeting, a long debate
           over what do the terms validation, verification
           assessment mean, and after about six months finally
           arrived at definitions, which we started using as we
           went through the code development work for a number of
                       Now we are going back, and we have a new
           crop coming in, and we seem to have lost our
           understanding of what those terms meant.
                       CHAIRMAN WALLIS:  One of those words means
           that the code as written reflects equations as
           formulated.  That's one  of those words, verification.
                       DR. SCHROCK:  That says that the equations
           you meant to program are, in fact, in the program.
                       DR. LANDRY:  Validation says that, yes,
           it's performing the function it was intended to
           perform.  An assessment is that the code is performing
           at this level overall.  
                       DR. SCHROCK;  But there are available
           recognized methods, computerized, to check that
           verification step.  Have those ever been applied to a
           code like RETRAN?
                       DR. LANDRY:  Not that I'm aware of.
                       MR. CARUSO:  Dr. Schrock, this is Ralph
           Caruso from the staff.  I think that's actually quite
           a good idea.  I'm just going to give an observation.
                       It's my observation that -- I'm thinking
           back to some people that I know in Europe who used to
           work with RELAP, and I do believe that they tried to
           use one of these tools about ten years ago, and they
           were not successful.
                       I believe it had to do with the same
           reason -- same reasons that we have problems with
           compilers trying to optimize codes; and when you try
           to optimize some of these codes with those optimizers,
           they don't work very well because of the way the codes
           are structured, because they were designed to run
           originally on very small memory machines, and people
           were very creative in how they did the coding.  So
           that the logic checkers get confused.  They don't
           understand what's going on.
                       DR. SCHROCK;  I think what you are saying
           is it's a matter of getting caught up in obsolescence. 
           The actual programming is so old that the modern
           techniques can't recognize what it's all about.
                       MR. CARUSO:  I do believe I heard an
           argument about this similar to this about ten years
           ago, but one of the reasons I believe -- A lot of the
           people who are doing code development now are updating
           the codes.  They are restructuring them.  Research
           here is doing that with TRAC-G, so that it will be
           able to be maintained better and also to be optimized
           better and maybe even make it amenable to these logic
           checker programs.
                       I don't know if RETRAN-3D was restructured
           with that in mind, but that's certainly something that
           we would like to keep in mind in the future.
                       DR. ZUBER:  Well, I think this will be a
           good field for Research to contribute.  If the method
           is not available, a contribution to NRR would be to
           develop such a method instead of doing some other
           things which are really irrelevant.
                       CHAIRMAN WALLIS:  Let's move on.
                       (Slide change)
                       DR. LANDRY:  Okay.  Another area of our
           review, another topic we would like to bring up, was
           the critical flow model.  Three critical flow models
           are included in RETRAN-3D:  Extended Henry/Fauske;
           Moody; and Isoenthalpic Expansion/Homogeneous
                       DR. SCHROCK:  That one I pointed out in my
           report, that isoenthalpic expansion is a misnomer for
           what it actually does.
                       CHAIRMAN WALLIS:  Let's just point out,
           Ralph, you had this set of slides before this
           Subcommittee before.
                       DR. LANDRY:  Some of this, I may have.
                       CHAIRMAN WALLIS:  So I don't want to go
           through it all again.
                       DR. LANDRY:  Okay.  These are points we
           brought out --
                       CHAIRMAN WALLIS:  We would like to focus
           on --
                       DR. LANDRY:  -- in the SER.
                       CHAIRMAN WALLIS:  We would really like to
           focus on what EPRI has as a response to our concerns,
           and we have had a discussion with you about this
                       DR. LANDRY:  Did you want to cover at all
           the drift flux, Chexal-Lellouche?  
                       (Slide change)
                       DR. LANDRY:  Chexal-Lellouche is --
                       CHAIRMAN WALLIS:  We didn't really get so
           far.  You see, we got hung up by asking questions of
           EPRI to which they did not respond in our first
           encounter with them, and then I thought what we were
           trying to do today was to reach, if possible, some
           consensus on those matters.
                       DR. LANDRY:  Okay.  I was trying to just--
                       CHAIRMAN WALLIS:  And you are helpful, but
           we have been through all this before with the
           Subcommittee, not quite the same membership, but you
           had a meeting with us a month ago or something where
           you went through this.
                       DR. LANDRY:  Okay.  I'll let the members
           just read through then.  Basically, our conclusion is
           that overall Chexal-Lellouche is accurate, but the
           user must be careful and use it within the range of
           validity and for the proper fluid.  You cannot use
           Chexal-Lellouche for air-water parameters for steam
           water calculations.
                       DR. SCHROCK:  What are they left to do if,
           in fact, they find that they are operating outside the
                       DR. LANDRY:  Then they have to come up
           with a database or a different methodology.  
                       CHAIRMAN WALLIS:  That's one of your
           restrictions that you have.
                       DR. LANDRY:  Right.
                       DR. ZUBER:  I think, if this is correct,
           I think those equations are not applicable to this,
           and you should stick to it.
                       DR. LANDRY:  Yes, that's what we've said,
           unless they can prove it.  
                       (Slide change)
                       DR. LANDRY:  Boron transport, I think we
           have already discussed, the technology --
                       CHAIRMAN WALLIS:  The interesting thing
           with boron transport -- excuse me -- is that if you
           have a code that's validated in terms of peak clad
           temperature for LOCAs, then --
                       DR. LANDRY:  This code can't be used for
                       CHAIRMAN WALLIS:  -- it can't be used just
           without any testing or validation or assessment for
           boron transport.  It's a different problem.
                       DR. LANDRY:  And this code is not used for
                       CHAIRMAN WALLIS:  Right.  Thank you.
                       (Slide change)
                       DR. LANDRY:  Let's see. Neutron kinetics,
           we've gone through in great detail with you.  We
           showed you our calculations.  The only problem there
           is we felt a little rub would --
                       CHAIRMAN WALLIS:  Did you want the ACRS to
           give as much attention to the neutron kinetics as it
           did to the momentum equation?
                       DR. LANDRY:  No.  
                       (Slide change)
                       DR. LANDRY:  Code assessment:  We had a
           lot of problems.  We've pointed this out throughout
           the review, that the bulk of the assessment -- This
           gets back to what we were just talking about a few
           minutes ago.  The bulk of the assessment is based on
           plant calculations performed by utilities.  A lot of
           the figures don't include who did them, what code
           version they even used.
                       CHAIRMAN WALLIS:  There are options in the
           code, aren't there?
                       DR. LANDRY:  What options were used.  So
           that the assessment models do not explicitly --
           approved in the SER will be either the responsibility
           of the licensee or the applicant.
                       The bottom line is each applicant of
           RETRAN-3D will have to submit a valid approach to
           assessment which we think should include a PIRT.
                       (Slide change)
                       DR. LANDRY:  Code use:  Code, as we've
           discussed a number of times, is highly dependent upon
           the user.  We've pointed out throughout the discussion
           problems in use of the code.
                       DR. ZUBER:  That really concerns me,
           because as time goes by people who have some
           experience and knowledge who are away, the memory is
           gone, and you have people who are not experienced
           working under pressure of being efficient and pushing
           the limits.
                       I think this is really a topic which NRC
           should really consider.
                       DR. LANDRY:  That's why in our SER we've
           said that there has to be a statement, a certification
           of the ability, the training, the background, the
           experience of the analyst who has used the code, one
           that a submittal is sent in.
                       DR. ZUBER:  That applies to NRC also.  
                       DR. LANDRY:  It's harder to regulate
                       (Slide change)
                       DR. LANDRY:  RETRAN-3D in a RETRAN-02
           mode:  I'd like to spend just a minute on this one. 
           This was a topic that came up.  I don't know if we've
           discussed this at length with the Subcommittee.  But
           the request was made to approve use of RETRAN-3D as a
           RETRAN-02 substitute by utilities that have RETRAN-02.
                       We looked at this and said there are a
           number of areas where RETRAN-3D is an improvement over
           02, improvements that cannot be backed out.  Implicit
           numerical solution, time step lock improvements,
           improved water property tables are good, and these are
           improvements in the code to make the code more robust. 
           We would not want to back off from those.
                       There are a number of items that we point
           out in the SER that can be used in using RETRAN-3D in
           an 02 mode, and there are a number of models which we
           point out, a number of options which the analyst
           cannot use, that they are not permitted to be used for
           RETRAN-3D as a RETRAN-02 substitute.
                       One of the big ones, again, is Chexal-
           Lellouche that we were just talking about a minute
                       DR. SCHROCK:  What is the 3-D neutronics? 
           What's the reason for that one being excluded?
                       DR. LANDRY:  Because 02 does not have 3-D
           neutronics.  RETRAN-02 is point kinetics, and -- or 1-
           D, 1-D kinetics.  There are significant differences
           between 3-D and 1-D kinetics, and we've said that you
           cannot use the 3-D kinetics.
                       DR. SCHROCK:  Yes, I get it.
                       DR. LANDRY:  The bottom line is that
           organizations that have been approved for using
           RETRAN-02 can use 3-D in an 02 mode without additional
           NRC approval, as long as they stay within the
           constraints of the SER.  However, if they go outside
           of those constraints, they then have to have
           individual approval for use of 3-D.
                       This is quite a restriction, because this
           says that a utility, an entity who has not been
           approved for use of RETRAN-02 cannot come and say,
           okay, now we're using RETRAN-3D, but we're using it as
           RETRAN-02, is that okay.  We are saying, no, it's not
           okay.  You're not approved for use of RETRAN-02.  How
           can you use 3-D in a substitute mode?
                       This case has come up, by the way, and we
           asked that utility an identical RAI:  Enclosed are the
           45 conditions on use on RETRAN-3d; show you compliance
           with each and every one of them.  When they get to
           this one, they can't.
                       (Slide change)
                       DR. LANDRY:  Conditions on use:  RETRAN-02
           had 39 conditions on use.  Ten of those still apply to
           RETRAN-3D.  In addition, we have added six more which
           are rather restrictive.
                       DR. ZUBER:  I thought you just mentioned
           45 conditions.
                       DR. LANDRY:  There are 45 total for
           conditions on use which we address in the SER.
                       DR. ZUBER:  And on RETRAN-02 there were
                       DR. LANDRY:  Right.
                       DR. ZUBER:  So this is not a progression. 
           This is retrograding.
                       DR. LANDRY:  Well, some of those 39 no
           longer apply.  
                       CHAIRMAN WALLIS:  Now when you've got
           these conditions on use, it seems to me that they have
           something to do with the importance of doing it right,
           to getting a valid answer for nuclear safety purposes;
           and if the problem with the momentum equation has an
           effect on nuclear safety, then one has a real
           justification for saying you've got to do something
           about that.
                       I don't see how these conditions are tired
           in with some sort of leverage on the important
           question of nuclear safety, and you can put on
           conditions, but really you have to focus on those
           parts of the things you are nervous about or uncertain
           about or are not quite right somewhere and what effect
           they have on regulation and so on.
                       I get the impression that people have sort
           neglected the momentum equations in the past, because
           there's been some kind of corporate belief that it
           didn't matter anyway.   That, seems to me, a very
           dangerous line to take.
                       So then it becomes -- You don't question
           it; you don't make a condition on it.  You don't think
           about it.  You've got to tie in -- If you're nervous
           about some term in the momentum equation, it would
           seem that when you are thinking ahead to realistic
           codes that someone then has to say, okay, suppose it's
           twice as big or something and suppose you're uncertain
           about how big this term is, what effect does it have? 
           What leverage does it have on the kinds of answers
           we're likely to get in our code prediction?  
                       That, I think, is going to happen in the
           future, isn't it?  So the conditions -- I'm making a
           speech, I suppose, but these conditions have to be
           related to the actual use to answer safety questions.
                       DR. LANDRY:  Right.  When individual
           applications come in, that needs to be addressed.
                       CHAIRMAN WALLIS:  And those will be
           different, depending on the question.  And if you come
           up with a new reactor design or some new concern like
           boron dilution or something --
                       DR. LANDRY:  That's correct.  It will be
           different for each application, each use of the code.
                       CHAIRMAN WALLIS:  And you may actually
           find when you look at some of these applications that
           you need other kinds of conditions.  That's the
           sensitivity of the answer to something you hadn't
           realized before.
                       DR. LANDRY:  That's correct.  Just because
           something has not been pointed out in this review does
           not mean in an individual application review an
           additional condition cannot surface.
                       CHAIRMAN WALLIS:  Well, BWR, of course, is
           an interesting one, because as you upgrade the power,
           you may be pushing some of those envelopes.
                       DR. LANDRY:  Right.  
                       CHAIRMAN WALLIS:  We haven't really
           studied that yet enough to know how important the
           resurgence might be.
                       DR. LANDRY:  That's right.
                       DR. ZUBER:  Let me just make -- follow on
           what Graham said.  What is missing from this approach,
           the NRC and the industry after 20 years or 25 years,
           really, they didn't establish really the importance of
           some factors or elements, when you can really neglect
           something and when you must take it into account and,
           if you don't have to take into account, you are
           justified to not use it, then you had a good -- to
           defend it.  But then you have to address what is
           important, and this was really never done.
                       I think this could really improve the
           efficiency of a regulatory agency, and I think this is
           what research should do.  This will also cut the cost
           of approval by the industry.  I think this is a field
           which really -- and therefore, it should be done in
           this -- you know, that regulation.
                       DR. LANDRY:  I think the attempt at a PIRT
           is an initial step at that, and I realize -- another
           concern that you've expressed before -- that we have
           to understand for individual events what are the
           overriding effects, what are the critical effects for
           a particular event, and which are unimportant, and are
           there certain effects taking place that mask
           everything else happening.  That hasn't been done.
                       CHAIRMAN WALLIS:  That's what we call sort
           of concluding the loop.  You put experts in the room. 
           They give you the PIRT.  That's just the first step,
           and you have to go through the whole questions of
           making sure that, if something is of high importance,
           that it's actually evaluated and someone checks.  But,
           yes, indeed, you have a good enough evaluation to meet
           some criteria.
                       DR. LANDRY:  Okay.  We have pointed in the
           conditions on use also that anytime that an auxiliary
           calculation is performed, an auxiliary code, that
           there has to be an assessment showing that there is a
           consistency in going from RETRAN-3D to that auxiliary
           calculation, such as DNB.
                       As I said earlier, we have to have a
           statement on the user's experience and qualification
           with the code, and assessment of the code for models
           and correlations not specifically approved must be
           submitted by the licensee or the applicant.
                       (Slide change)
                       DR. LANDRY:  Our conclusions in the SER
           are that RETRAN-3D is a significant advancement in the
           analysis tools base for licensees.
                       CHAIRMAN WALLIS:  Did it significantly
           advance the momentum equation?  Well, we are here
           today because of the momentum equation.
                       DR. LANDRY:  I know.  No, I would go back
           to what I said earlier.  The formulation that is
           given, the derivation that is given, in our view,
           should not be in there.  It's much more productive to
           say --
                       DR. ZUBER: Let me say -- I mean, this is
           passing the word.  What does it mean, it should not be
           there?  If the derivation is incorrect, call it
           incorrect and call a spade a spade.  It's irrelevant
           -- Well, you may take the -- but these equations are
           in the code.  No, you cannot have it both ways.
                       DR. LANDRY:  This is what I meant earlier. 
           The code equations, the formulation that is in the
           code should be explained and why that formulation is
           correct, not the derivation that is given.
                       The code lacks sufficient assessment in
           places and places a burden on the applicants to
           justify the code use.  Code used in the RETRAN-02 mode
           can be used in the RETRAN-02 mode, provided it's
           justified, and we have outlined what that takes.
                       One thing that the RETRAN Maintenance
           Group has done that we are very encouraged by and that
           we agree with very strongly is that a peer review
           process has been put in place.  We were told back in
           November that the RETRAN Maintenance Group has taken
           the step of -- It's not legislated to anybody using
           the code, but the members are encouraged to submit
           their material to their peer review process before
           it's submitted to the NRC.
                       This would alleviate a number of the staff
           concerns over user experience, over nodalization
           selection, over option selection, because the RETRAN
           Maintenance Group would look at this, the experienced
           people, and say, yes, this has been a valid approach
           that has been taken to the analysis.  We feel that
           that is a very encouraging step.
                       We have said that Chexal-Lellouche drift
           flux model is an improvement, but it has to be used
           cautiously.  You can't use it outside --
                       DR. SCHROCK:  Why do you think it's an
                       DR. LANDRY:  It seems to give good results
           for certain ranges of a void fraction.  There are some
           ranges of void fraction where it does not.
                       DR. SCHROCK:  And do you think it's not
           possible to do that with phenomenologically based
                       DR. LANDRY:  Yes, it should be.  But this
           is a heavily supported correlation.  It has a great
           deal of --
                       DR. SCHROCK:  Well, it has a lot of
           politics behind it, but for you to make the statement
           that it's an improvement, an improvement compared to
           what and on what --
                       CHAIRMAN WALLIS:  This is the model that
           uses a bubbly flow model to model annular flow?
                       DR. LANDRY:  That's correct.  But that --
           And we point that that's not good.
                       DR. ZUBER:  A droplet, a mist flow.
                       DR. LANDRY:  Yes.  We've pointed out in 
           annular, an annular mist flow -- we pointed out in the
           SER that the correlation underpredicts.
                       DR. ZUBER:  Okay.  Now let me ask you. 
           What about the type where you have the perforations?
           Is it there you have a void fraction maybe of .3 or
           .4, but do you consider this applicable or not?  Let
           me help you.  It would not be applicable.
                       The reason is -- I wrote a memo to -- my
           last memo to you to tell you why the thing is not
           applicable, not only for this equation but the other
                       There are data in the literature which you
           could use and test your models, and the applicants,
           especially Lellouche, never used it to my knowledge,
           and that equation has absolutely no physical meaning. 
           It's a hodge podge of everything, and it cannot be
           applied -- -- cannot be applied to mist flow, to
           droplet flow.
                       CHAIRMAN WALLIS:  It's a big recipe with
           quite a big database.
                       MR. STAUDEMEYER:  This is Joe Staudemeyer,
           Reactor Systems Branch.  The statement that it's an
           improvement is based on void fraction predictions in
           BWR channels, which is its biggest place of
                       If you look at the Chexal-Lellouche
           results compared to previous RETRAN correlations, it's
           much better at predicting void fraction in BWR
                       DR. SCHROCK:  So it is compared against
           the previous correlation in RETRAN.  But other things
           are available that were not compared.  So I think your
           statement is misleading.  
                       DR. LANDRY:  I think you have to read the
           whole text in the SER.  I tried to condense the SER in
           these slides.
                       DR. SCHROCK:  Well, I've read the SER, and
           I find it, frankly, to be very much more flattering to
           the code than it deserves, despite the criticisms.
                       DR. ZUBER:  And I agree with Virgil.
                       CHAIRMAN WALLIS:  There seems to be two
           discussions going on today.  One is with you, and one
           which we are going to get to with EPRI, which I think
           is going to be on a different plane altogether.
                       DR. SCHROCK;  But this may be our only
                       DR. LANDRY:  We have also said that final
           acceptance of RETRAN-3D for licensing basis
           calculations depends on successful adherence to
           conditions and limitations on use discussed in the
                       CHAIRMAN WALLIS:  Now is this SER a final
                       DR. LANDRY:  No SER can be final-final. 
           At this point --
                       CHAIRMAN WALLIS:  It's not labeled Draft.
                       DR. LANDRY:  It's not labeled Draft.  At
           this point we've given it --
                       CHAIRMAN WALLIS:  So EPRI has it?
                       DR. LANDRY:  EPRI has it.
                       CHAIRMAN WALLIS:  And if the ACRS had some
           concerns about, let us say, the momentum equation,
           that might irrelevant of the regulatory process?
                       DR. LANDRY:  No, it might be relevant, and
           if material comes out that necessitates a supplement
           or addendum to our SER, then we can write one.  We're
           not restricted to this is the last word.
                       CHAIRMAN WALLIS:  Well, I guess what
           concerns me is that I think we are going to find that
           our discussion with EPRI is somehow of a different
           nature than yours.  We are going to go after where
           this equation comes from, what does this term mean,
           not common sense because all you have to do is bend
           the pipe this way and you get an absurd answer or
           something like that.  That's the kind of thing we are
           going to do.
                       The process you've been through, it's not
           clear to me brings that sort of thing out.  We seem to
           be doing something different here, and I'm not sure
           how the sort of thing we are going to be doing relates
           to the formal regulatory process of coming up with an
                       Maybe we'll come back to you with that at
           the end of the day.  Unless we've gained some time, I
           think you're through, Ralph.  Thank you very much.
                       Should we move on?  Can we move on with
           EPRI?  I would like to say that we are here today
           because of concerns about formulation of momentum
           equations, and really the sooner we can get to that,
           the better.  
                       I'm not sure what EPRI has in mind, but
           last time we never got to it, and our advice, as much
           as we could get through in a short time with e-mails
           and so on, to EPRI was explain the responses to RAIs
           which resolve the questions which ACRS had and not go
           through a lot of stuff which we've already been
           through before about the code and industry and uses
           and things, which are not part of our discussion.  
                       I'm not quite sure what you have in mind
           for this presentation.
                       MR. SWINDELHURST:  My name is Greg
           Swindelhurst.  I'm the Chairman of the RETRAN
           Maintenance Group, which is the group which are the
           main users of RETRAN, both domestically and
                       I'm going to give a very short
           presentation which does respond to some of the
           questions which came up during Ralph Landry's
           discussion, but we realize what you really want to get
           to, and we will get to that quickly.
                       (Slide change)
                       MR. SWINDELHURST:  I will not repeat the
           items which the NRC has adequately covered, but there
           are a few things which need some emphasis, and that is
           that we have worked for over two years with the NRC
           staff to go through their issues, their concerns, and
           those have been resolved.
                       I'm not saying that they have been
           resolved in a positive, successful way that everybody
           is happy with, but they have been resolved to the
           extent that perhaps things have happened like certain
           models have been withdrawn from review, because we
           realized they did not have an adequate validation
                       We've resolved some things in the form of
           errors which have been identified, which have been
                       CHAIRMAN WALLIS:  Now there are two code
           errors.  That says code.  That's not documentation. 
           It's actually something in the code itself?
                       MR. SWINDELHURST:  Right.  I'm referring
           to two code errors.  
                       Now there's also been numerous
           documentation problems which we are cleaning up and
           correcting.  We've issued change pages to the NRC
           staff along the way, and that will all take place, and
           when we --
                       DR. SCHROCK:  Can you tell me where I
           could read about these two code errors?
                       MR. SWINDELHURST:  I think Ralph already
           had them on his previous slide.
                       CHAIRMAN WALLIS:  They are not responsive
           to the ACRS concerns.
                       MR. SWINDELHURST:  Yes, they are.
                       CHAIRMAN WALLIS:  Well, I don't think so,
           because as far as I can see, the new documentation is
           the same as the old.  There is one thing which has to
           do with resolving something through an angle.  Is that
           one of the ones you meant?
                       MR. SWINDELHURST:  We will cover these in
           detail in a minute, but --
                       CHAIRMAN WALLIS:  Okay, we'll get to
                       MR. SWINDELHURST:  -- I think the staff
           and ourselves agree there have been two code errors
           that -- They are Fortran errors which have been
           corrected.  There's been a lot of equation and --
                       CHAIRMAN WALLIS:  If they were Fortran
           errors, that's fine.
                       (Slide change)
                       MR. SWINDELHURST:  Okay.  I would also
           like to point out, as Ralph mentioned, a lot of the
           issues remain to be addressed by the applicant
           submitting in the future an application of this code.
                       DR. ZUBER:  You are really confusing me. 
           You said everything was resolved between EPRI and NRR. 
           The problem is that we just heard that NRR said that
           RETRAN -- I mean the formulation is irrelevant,
           because it was incorrect.  How did you want to answer
                       MR. SWINDELHURST:  I think --
                       DR. ZUBER:  That's not an error.  This is
           the basic questions.  Do you agree with that statement
           they make?  If yes, why?  If no, again why?
                       MR. SWINDELHURST:  Okay.  The review
           process results in the NRC asking us questions which
           we respond to, and then the SER is written with
           certain conditions and limitations on the use of the
           code.  When I say that we've resolved it, what I mean
           is we've gone through that process, and we reached
           this  point in the review where an SER has been
           issued, and we understand how we are permitted to use
           this code in the future.
                       Now a lot of the issues are carrying over
           to the applicant in the area of validation, licensing
           of new RETRAN-3D models, things of that sort.
                       DR. ZUBER:  But wait.  You are really
           dancing around the point, using this expression.  if
           the code -- If I understood Ralph, they detected some
           incorrect -- or errors in the formulation, and for
           this reason they said it's not applicable or
           irrelevant.  Do you agree with that statement, yes or
                       MR. SWINDELHURST:  We do not.
                       DR. ZUBER:  Are you going to address it?
                       MR. SWINDELHURST:  Yes.
                       DR. ZUBER:  Today?
                       MR. SWINDELHURST:  Yes.
                       DR. ZUBER:  Okay.
                       MR. SWINDELHURST:  We may not address it
           to your satisfaction, but we will address it.  We
           think that these code equations are suitable for the
           intended use of this code.
                       DR. ZUBER:  Again, suitable --  It's a
           very elastic word.  It may be suitable for something
           and not suitable for others.
                       CHAIRMAN WALLIS:  Can we get to it when we
           actually look at an equation and find out if it's
           suitable?  I might point out that the ACRS has
           deliberately been a spectator.  We are not involved in
           producing SERs.  The staff does that.
                       We don't do the RAI process.  So we've
           been spectators up to now, and now we're coming in
           again and saying do we like what we see.
                       MR. STAUDEMEYER:  We understand that, but
           we are also of the opinion that your comments have
           been heard by the NRC staff, and they have been
           forwarded to us through the RAI process, and that's
           the way that we respond to things.  That's just --
           That's nor NRR works.
                       CHAIRMAN WALLIS:  Yes, that is the
           process.  Right.  I agree.
                       (Slide change)
                       MR. SWINDELHURST:  I'm skipping one slide,
           because we've covered it adequately.  On this slide I
           would like to just emphasize a couple of things,
           although Ralph has gone through this adequately.
                       We do have this RETRAN-02 mode.  We do
           have any of the new models, not the RETRAN-02 mode. 
           Maybe the validation hasn't been adequate.  The future
           applicants are going to have to come in and justify
           that to the staff's satisfaction.  We fully agree with
                       It's a fully acceptable way to move
           forward with the use of this code for licensing
           applications.  This is nothing new, this third bullet
           here.  Any organization using a code like a thermal-
           hydraulic is obligated to come explain to the NRC and
           document and show that they are skilled and capable of
           using this code, and we fully agree that that process
           ought to continue in the future.
                       CHAIRMAN WALLIS:  But it says here,
           "Organizations without NRC-approved models."  So the
           implication you have is that the models in RETRAN have
           been approved and do not need to be reviewed again?
                       MR. SWINDELHURST:  Some of the models
           have, and some of them have not.  The ones which have
           not are called out in the conditions of the SER.
                       CHAIRMAN WALLIS:  So if we look at -- So
           something like equation 2.3-4 -- this is a momentum
           equation or subsequent things -- Your impression is
           that NRC has given these derivations its blessing?
                       MR. SWINDELHURST:  I would say NRC has
           given the use of this code, including those equations
           as they end up in the coding -- Yes.
                       CHAIRMAN WALLIS:  And so, if an
           undergraduate student read this equation and submitted
           it to me in homework and I gave him a D, and he said,
           no, it's got NRC blessing, would that be a true
           statement by the student?
                       MR. SWINDELHURST:  I guess that would
           depend on what his intended application of that
           equation was.
                       DR. ZUBER:  Now let me say, you just
           remind me of something, the difference between science
           and technology and politics and law.  In science and
           technology, the word is mean is technology is either
           correct or is incorrect, and what you are saying
           there, it depends how you end up with the thing.
                       MR. SWINDELHURST:  Certainly.  
                       DR. ZUBER:  The question is not if it's
           wrong.  Even for a junior, it cannot be fashionable.
                       MR. SWINDELHURST:  Just as a simple
           example, you know, we are clearly stating that this
           code should not be used for doing large brick LOCA
           calculations.  We agree to that, because these
           equations are not suitable for that application.
                       They may very well, and we maintain they
           are suitable for a lot of other applications where the
           phenomena are less complex and the event that you are
           simulating is less dynamic.
                       DR. ZUBER:  The simplest example is the
           flow to a straight pipe, and what I keep seeing here
           in the memo which was sent by Lance Agee, I think, the
           error there is -- I mean, on the junior level.
                       MR. SWINDELHURST:  Well, we'll cover that
           in the next --
                       CHAIRMAN WALLIS:  I think your claim is
           that, even if there should be errors, it doesn't
           matter for the applications you have in mind.
                       MR. SWINDELHURST:  I don't think we would
           call them errors.  I think they are approximations
           that are used to put the equations in a form they can
           be solved in a computer for this type of an
                       CHAIRMAN WALLIS:  Well, that's
           interesting, because if you look at what happens in
           politics, our late President was accused of lying
           about something which many people may have considered
           to be minor, and then he did a lot of things which
           were valid policies.  But half the political body in
           Washington seems to condemn him for this incorrect,
           invalid statement he made right up front.  That
           somehow for them cast a shadow over everything else.
                       I think what you are saying is it doesn't
           matter, because for the purposes we have in mind,
           everything is okay.  Is that your viewpoint?
                       MR. SWINDELHURST:  We would claim it's not
           an error.  It's the way the equation is being
           formulated for this application.
                       CHAIRMAN WALLIS:  But if it were that
           these equations had errors in them which were of a
           really fundamental nature --
                       DR. SCHROCK:  The problem I have is the
           presentation has this pretense of rigor.  The errors
           are there, and then you emerge from that with a claim
           that these are approximations.  They are never
           introduced as approximations.  They are simply errors,
           sometimes even defended as not being errors.
                       Then the bottom line is that you say,
           well, the equations are okay, because they are, in
           fact, engineering approximations.  But this has never
           been shown that they are satisfactory approximations,
           what is being approximated, that  indeed the
           approximation is satisfactory for all applications
           that have been approved.
                       MR. SWINDELHURST:  I think we understand
           the comment that the documentation hasn't met your
           needs, and we understand --
                       DR. ZUBER:  The basic need of -- you
           expect from a junior.  
                       CHAIRMAN WALLIS:  Now you cannot write
           statements which just are not correct and get
           validity, really, it seems to me.  It's very dangerous
           to make statements about momentum balances which just
           are not true and then to expect credibility in the
           rest of the document.  That's where we are.
                       Now the NRC, it may be, operates in a
           different way, but that's the puzzle we have anyway. 
           So we're going to get to that.
                       MR. SWINDELHURST:  We're going to get to
                       DR. ZUBER:  Just one -- Think about
           intervenor going in front of television and showing
           your equations, and he is a professor somewhere.  He
           says, look, I would have flunked a junior if he gave
           me this solution.  Then you say NRC and industry
           license safety calculations based on these errors. 
           What would this do to the industry?  
                       MR. SWINDELHURST:  We don't think we are
           in that situation.
                       DR. ZUBER:  You may well be.
                       MR. SWINDELHURST:  I understand, but --
                       DR. ZUBER:  You may well be, and let me
           say you will be there.
                       CHAIRMAN WALLIS:  But if you were there,
           it would be a serious matter, would it not be?  That's
           what's baffled me about this whole thing, is that, you
           know, you've had two years to respond to what seem to
           me just very trivial things, and you come back with
           not really seeming to understand the issue.  
                       We'll get to that, I'm sure, but I think
           you as a sort of manager, a responsible person, ought
           to wonder about whether this matters and whether you
           can really go forward with the statements you are
           making when somebody, as Dr. Zuber said, could make
           those kind of claims against you.  It is a sort of
           Achilles heel which I wouldn't want to have.
                       DR. ZUBER:  This is going to kill this
                       CHAIRMAN WALLIS:  No, it isn't going to
           kill the industry.  I mean, the last thing we want to
           do is kill the industry because of something so
                       DR. ZUBER:  Foolish things kill big
                       CHAIRMAN WALLIS:  Okay.  Well, I guess we
           have to move on.  I think we have to say something to
           you, because you are a responsible person, really.  I
           don't know if the buck stops with you, but it stops
           with somebody.
                       MR. SWINDELHURST:  I think you're right.
                       CHAIRMAN WALLIS:  Does it stop with you?
                       MR. SWINDELHURST:  It certainly does in
           terms of what we do --
                       CHAIRMAN WALLIS:  The buck stops with you?
                       MR. SWINDELHURST:  -- and my company doing
           this type of work.  We have to be sure it's correct
           and accurate for the intended purposes.  There's no
           doubt.  We're the licensee.  The licensee is
                       DR. ZUBER:  I also think it's the
           responsibility of NRR to accept or discard such an
                       DR. KRESS:  On your fourth point, before
           we take that, if there are things in RETRAN-3D that
           are -- we say are fundamentally wrong with the
           momentum equation, it's very likely that those are in
           RETRAN-02 also.  Does that put into question the use
           of RETRAN-02?
                       If it puts in question the use of RETRAN-
           3D, would it also put into question use of RETRAN-02?
                       MR. SWINDELHURST:  Most of what we are
           talking about is also applicable to RETRAN-02 and,
           when we find an error in the RETRAN-3D, we go
           backwards and see if the same error s in RETRAN-02. 
           If it is, we get that fixed also.
                       DR. KRESS:  And do you have to reapply for
           approval of that part -- those changes?  Is there a
                       MR. SWINDELHURST:  No.  No, if there's an
           error correction, the NRC staff allows us to correct
           errors without re-review.
                       DR. KRESS:  Okay.  That probably answers
           my question.
                       (Slide change)
                       MR. SWINDELHURST:  I would like to just
           bring in a topic which may not seem like it's directly
           applicable, but we believe it is.
                       As you are aware, the staff has issued
           this draft guide 1096 for comment within the industry. 
           We are expecting that this will run through -- The
           comment process will be issued, and it will require
           more technical justification for future submittals of,
           you know, realistic or best estimate, whatever
           terminology you prefer, codes and applications in this
           thermal-hydraulics area.   That's a fact, and that's
           perfectly okay.  
                       As Ralph also mentioned, we think these
           requirements ought to be commensurate with the
           significance of the application.  If the application
           is a relatively simple transient where the phenomena
           are mild and all of us would agree to that, then they
           should not be a lot of required validation testing,
           because there shouldn't be any concern of the need for
                       CHAIRMAN WALLIS:  That is an awkward -- I
           essentially agree with that, but this is all done, I
           think, in the public view, and you have to be
           sensitive to the view of the community, and that
           includes people like undergraduate students.  If they
           read something in the document which their professor
           has just corrected as wrong in their homework, then
           that's going to demolish a lot of their faith in
           what's going on in this industry, isn't it?
                       I mean, it's not just a question of the
           requirements being commensurate with this, a game
           played between you and the NRC.  At some level I think
           you have to be concerned with a wider audience. 
           That's where, I think, you fall down here.
                       I agree that it may well be that, as I
           found with TMI, analyzing it myself, mass and energy
           balances is most of the story for most transients, and
           who cares about momentum equations.  Well, if you can
           show that, that's great.  But if you claim that you've
           got a derivation where the term so and so means
           something and the term something means something, and
           it doesn't mean something, then that cannot be
           excused, I think, just by making the statement in line
           3 here.
                       I agree with line 3, but I think there is
           a wider audience out there.  It includes your own
                       MR. SWINDELHURST:  I realize that.  I
           think we realize that there is a wider audience and
           that --
                       CHAIRMAN WALLIS:  Industrial engineers and
           NRC staff and everybody.
                       MR. SWINDELHURST:  I understand.
                       DR. ZUBER:  See, underlining what Graham
           said is you are going for exactness.  I mean
           responsibility.  You have a good derivation, basic
           principles, etcetera, etcetera, and you come with
           something which is not so.  
                       You could really simplify the problem
           which you can defend and be more efficient, and then
           if something cannot be applied, then you have to
           develop a rigor.  What you have here is something, a
           mish-mash.  I mean exactness or basic principles,
           which they are not and something, then which is very
           difficult to apply long running.
                       It's not really an efficient way to do
           this analysis.
                       CHAIRMAN WALLIS:  But you could say that
           no one knows how to solve this problem.  So we make
           the only thing we know how to do, which is to analyze
           it as a series of straight pipes, whatever it is, and
           then say, look, we've got some data that show that for
           our purposes that's okay.
                       MR. SWINDELHURST:  I think that's exactly
           what we're doing.  Okay?
                       CHAIRMAN WALLIS:  But it's this -- Well,
           we'll see when we get to it.  Okay.
                       MR. SWINDELHURST:  And we've never gotten
           into that in this discussion, is to what extent does
           it make a difference?  To what extent do you get
           acceptable answers at the end of this?  That's where
           we are, and we've been there for 20 years using this
           code in that way.
                       Okay.  The last item here I just want to
           mention is, you know, we did talk a lot about best
           estimate/realistic, and that's kind of the looking
           forward way of doing licensing type analyses perhaps,
           but we've still got this traditional conservative way
           which is the way things are done now, and we need to
           -- the industry needs to make certain that that option
           is still recognized as being a valid and useful way to
           continue to do this work in the future.
                       DR. SCHROCK:  That is a problem, I think. 
           Seems to me that industry should want to get away from
           that crutch in the long term.  I don't understand why
           you have this strong desire to preserve it.
                       In the shorter term you don't want to go
           through required relicensing processes to continue to
           qualify operating plants.  That's understandable.  But
           you should expect a normal transition, and that normal
           transition might even be as long as 20 years.  I don't
           know.  But you should at some point in the future
           stand up and say, yeah, we're proud of the fact that
           we began an industry which was based on pretty shaky
           engineering calculations.  We did it very
           conservatively.  We went through a transition in which
           we believe we have better calculations, and we can,
           therefore, up-rate the power on our plants.  But
           indefinitely into the future, we demand the right to
           license power plants according to 1971 technology. 
           That's stupid.
                       MR. SWINDELHURST:  I think that the
           evolution you are talking about probably is going to
           occur.  You know, it may take 20 years.  Who knows? 
           But --
                       DR. SCHROCK:  It won't occur in 20 years
           the way we are moving.
                       MR. SWINDELHURST:  Well, this is rather
           new, though, this transition to realistic or best
                       DR. SCHROCK:  No, it goes back 13 years. 
           What do you mean, it's new?
                       MR. SWINDELHURST:  For the non-LOCA stuff,
           it's relatively new, and the reason, in my opinion,
           that it hasn't been moving that way faster is because
           there hasn't been a need to do it.
                       As you mentioned, with up-ratings or other
           things that come along, there may, in fact, be a need
           to do it, and then it will be forced through another
                       DR. ZUBER:  And if you wait for 20 years,
           you won't have this industry.
                       CHAIRMAN WALLIS:  Well, it's coming back.
                       DR. ZUBER:  Not following this work.  This
           will kill it.
                       (Slide change)
                       MR. SWINDELHURST:  Okay.  Just a few more
           comments here.  
                       The NRC has mentioned, as Ralph has, that
           there's a concern of an absence of user guidelines. 
           We don't share that perspective.  We think there's
           adequate documentation and understanding within
           organizations as to what it takes to use a code like
           this to build models, to submit topic reports to the
           NRC to get approval to do this type of licensing work,
           and we do not share their opinion that there's an
           absence of information available to do this.
                       CHAIRMAN WALLIS:  Well, I'm not a user,
           but I must say, when I looked at your RAI reply, which
           we are going to get to about how you model, say, the
           lower plenum, I hadn't a clue what was going on and
           how anything you told me there related to what I would
           stick into your momentum equation in order to have a
                       So I struggled.  I had sleepless nights,
           and I still couldn't figure out what was going on.  So
           at least this user didn't understand how to use the
           code for a geometry other than the very simple ones
           showed in your examples.
                       MR. SWINDELHURST:  We will have to work on
           that then, and we are prepared to talk about that as
                       There has also been expressed concern
           about inexperienced users or maybe even experienced
           users misusing this code.  That's true of any code. 
           You've got to have code experience.  You've got to
           know what you're doing.
                       This is a highly technical code.  Ralph
           has mentioned that there's a lot of options and a lot
           of different ways users can model a plant, model a
           particular analysis.  That's one of the reasons why,
           just because we are not starting this, we're not
           embarking on a new program here -- this is 20 years of
           organizations using codes like this -- it's very
           difficult to retool and standardize and do everything
           the same way.
                       There's lots of different plant designs
           out there, and different organizations do things
           different ways.  And because of that and because the
           organizations are not choosing to retool and start all
           over with standard methods, it is necessary for us to
           get to this step, which may not be desirable and may
           not be efficient, of individual organizations needing
           to validate, assess their models independently.  
                       There's really no other choice on this
           point.  That's where we are, and that's what we are
           going to have to do, and we accept that.  
                       Ralph mentioned peer review.  This is a
           brand new thing.  We've been waiting for the SER to
           come out so we could start communicating this.  We
           think it's a good thing.  We have unanimous support
           within the RETRAN user group that this is something
           people ought to consider doing.
                       Then again, it's still optional, and we
           will definitely encourage people, especially new
           users, to make use of this.  It makes sense, and
           especially with the incentive from Reactor Systems
           Branch that this is something they would think is
           worthwhile.  It would be good for an applicant to do
           it in terms of their future deliberations with the NRC
                       CHAIRMAN WALLIS:  I would hope that some
           of those peers are like some of the people you see on
           this side of the table today who have come with a sort
           of basis of knowledge but not -- they're not so tied
           up with the code, they have anything at stake in it or
           anything, and they don't know the history.  So they
           can ask the questions which maybe haven't been asked
           before and things like that.
                       MR. SWINDELHURST:  Okay.  We really have
           attempted to answer your questions, and the questions
           we've attempted to answer is what we see in the RAIs. 
           We are certainly going to try to answer your questions
                       We also realize that it's very likely we
           will not be able to reach an agreement that we are all
           happy with in terms of your questions being --
                       CHAIRMAN WALLIS:  I was going to ask you
           what you hoped would come out of this meeting today. 
           What's your expected result?
                       MR. SWINDELHURST:  I was hoping that we
           would be able to answer your questions maybe better
           than we have in the past, and maybe to characterize
           our perspective that the equations are suitable for
           the intended purposes.
                       Yes, there's approximations that need to
           be made along the way.  There's engineering judgments
           that need to be made along the way.  But the end
           result of that in terms of using this code for the
           types of analyses we do with this code, non-LOCA
           analyses, that it's a suitable framework for doing
           these analyses.
                       CHAIRMAN WALLIS:  If we were -- You know,
           we are all competent professional technical people,
           and these are relatively straightforward matters.  It
           would seem that you ought to be open for a consensus.
                       MR. SWINDELHURST:  I think that's a nice
           thing to hope for, but I would say, based on where we
           are, we're not really expecting that.
                       DR. ZUBER:  You are here where you were
           two years ago, the same position.  Reading this memo
           from Agee, I didn't see much difference of what we saw
           two years ago.
                       CHAIRMAN WALLIS:  So what's happened?  You
           have helped us -- You helped me.  You've been more
           explicit about some of the things in your
           documentation.  That helps me to know what it is you
           are saying, but not perhaps to understand why you are
           saying it; because the basic problems seem to be still
           the same.
                       You've clarified.  So I think there's
           better information.  But that may just reinforce our
           areas of disagreement.
                       MR. SWINDELHURST:  That may be true.
                       CHAIRMAN WALLIS:  We'll see about that
                       MR. SWINDELHURST:  But we'll give it a
           try, and we'll see how it works.
                       CHAIRMAN WALLIS:  For all of our sakes,
           the best thing that could come out of here today would
           be all agreed that, yes, this written down is a good
           momentum equation.  The way it's resolved is fine, and
           so on and so on and so on, check off these things, and
           say let's go home and open a bottle of champagne or
                       MR. SWINDELHURST:  Just for example, let's
           say somebody is not happy unless it's a three-
           dimensional code, and I don't mean 3-D neutronics.  I
           mean the whole code, the whole thing is three-
                       If that's somebody's expectations of
           what's necessary here, then certainly we are not going
           to get there.
                       CHAIRMAN WALLIS:  No.  My level of review
           is the same -- I got to put it bluntly -- is the same
           as the level of review I would give to an
           undergraduate homework in flow mechanics.  And if we
           can't agree on that, I'm astonished and flabbergasted
           and bamboozled and vexed and -- you know, I could go
           on for a whole torrent.  It's very strange.
                       DR. ZUBER:  Okay.  Graham, you gave us the
           most optimistic, desirable solution.  The other one is
           for the industry to admit, yes, there is an error.  We
           are aware.  We didn't correct it for two years, but we
           shall now evaluate case by case the effect and do
           sensitivity analysis, and then give us how you are
           going to do it.  
                       Then let me guess it's wrong.  What you
           really want is to smother something which doesn't
           smell too good and use all these elastic words.  I
           think this is not good for the industry at all, and
           for a regulatory agency.
                       CHAIRMAN WALLIS:  Well, it may be or may
           not be.  Got to be careful what words we use.
                       DR. ZUBER:  For me or they?
                       CHAIRMAN WALLIS:  Well, they have to be
           careful, too.  Maybe you don't have to be careful.
                       DR. SCHROCK;  In my mind, the operative
           word here is formally.  You've formally addressed ACRS
           concerns, but you've not addressed ACRS concerns in
           spirit.  You've dealt with the regulatory process in
           a way that you perceive as meeting the requirements of
           the regulatory process, but you've not had deep
           concern about the technical issues which have been
           raised here.
                       MR. SWINDELHURST:  I think we've had deep
           reflection on all the technical issues raised here,
           and we've gone back and considered each one.
                       DR. SCHROCK:  For one, I don't see that
           you have.
                       CHAIRMAN WALLIS:  Well, this is going to
           be embarrassing, because I mean, if we get someone up
           there and we look at this equation and the claim that
           say the pressure drop is balanced by the frictional
           forces when all the other terms are out of this
           momentum equation, well, that isn't true.
                       We can pull the whole thing apart, and we
           can look at all these statements.  That's going to be
           very embarrassing to go through.  Are we going to go
           through that sort of thing?
                       MR. SWINDELHURST:  To the extent you want
           to go through it, I believe we will go through it.
                       CHAIRMAN WALLIS:  Well, if you don't
           resolve it, I guess we are going to be under some
           obligation to write our opinion.
                       MR. SWINDELHURST:  That's right, and --
                       CHAIRMAN WALLIS:  And if there's no
           response from you that helps to clarify things, it's
           going to be the opinion we get from reading the
           documentation, which is the same -- at least from my
           point of view, the same opinion I had before.  And in
           a way, it's reinforced, because the strange features
           are now clearer.
                       MR. SWINDELHURST:  Well, let's give it a
           chance, and maybe there will be some --
                       CHAIRMAN WALLIS:  Well, I'm giving you a
           chance.  You know, I'd love to feel that I was wrong
           and discover that I was wrong.
                       DR. ZUBER:  I'd like to have a bottle of
                       MR. SWINDELHURST:  We believe that your
           concerns are generally generic to other codes like 
           this code, and I believe you've shared that opinion.
                       CHAIRMAN WALLIS:  That is -- Yes, that is
           a niggling thing, isn't it?  That's true.
                       DR. SCHROCK:  It's true, but it doesn't
           help RETRAN-3D.
                       CHAIRMAN WALLIS:  No, it doesn't help.
                       MR. SWINDELHURST:  I'm not saying -- I'm
           just saying that this is the way the industry uses
           codes like this, and not all codes do things this way,
           but a lot do.
                       DR. ZUBER:  You see, but the difference is
           you are addressing problems which we had 30 years ago,
           25 years ago.  Now you get into the edge of the
           regulations, and again has changed.  The environment
           has changed, and you cannot use the same argument --
           alibi, one used 20 years ago when you hear much of
           conservatism, which are now going to decrease and,
           therefore, all these codes which were applicable for
           a previous era are not good for a time and era which
           is coming now.
                       MR. SWINDELHURST:  I agree with you.  When
           you start decreasing the conservatisms, the importance
           of accurate modeling becomes even more--
                       DR. ZUBER:  Even more so.  Even more so.
                       CHAIRMAN WALLIS:  Go ahead.
                       DR. ZUBER:  One was able to live under
           those -- with these errors, because we had a large
           conservatism, which we didn't have to have, had we
           done it correctly.  Now when we want to decrease it,
           we have to do it correctly.  I think this is the
           problem which neither the industry nor NRR, NRC, has
           addressed, as far as I have seen today.
                       MR. SWINDELHURST:  Well, I think we're
           seeing that in the draft guide that came out.  That's
           exactly what it's speaking to, and we recognize that.
                       DR. ZUBER:  But I don't see this reflected
           in the code developments and code analysis.  That's my
                       CHAIRMAN WALLIS:  I'd like to say
           something in praise of EPRI.  You do realize that
           there are generically applicable difficulties,
           particularly with the momentum equations in codes.  I
           think EPRI realizes that or your contractors do.
                       So an effort was made to provide different
           justifications, and I think that's praiseworthy.  It's
           good.  It's just that we have some difficulties with
           what you have now done.  I think it's good that you've
           faced up to the fact there was a problem there.
                       MR. SWINDELHURST:  Well, we certainly got
           concerns we have to respond to, and we're trying to do
           that, and I think a lot of it --
                       CHAIRMAN WALLIS:  No.  I mean you faced up
           to a problem that probably is generic in a whole batch
           of codes and tried to better than they have.  I think
           that's a good thing to try to do.
                       (Slide change)
                       MR. SWINDELHURST:  Okay.  We have -- EPRI
           has had an independent derivation of the RETRAN
           momentum equation, as it's been labeled, by Dr. Thomas
           Porsching.  He is with us here today.
                       CHAIRMAN WALLIS:  If someone will explain
           that to me, because the equation I saw Dr. Porsching
           derive is not the same as the RETRAN momentum
                       MR. SWINDELHURST:  We'll be prepared to
           speak about that.
                       CHAIRMAN WALLIS:  Okay.
                       DR. SCHROCK:  But you also have the fact
           that NRR has said that it's irrelevant to the issues
           that it's examined.  So what's the purpose of the
           bullet on this slide?
                       MR. SWINDELHURST:  Well, obviously, we
           don't agree with that.  So I guess we would like to
           take an opportunity today to have our side of that
                       We would like to clearly point out that we
           are calling it a momentum equation.  It's sort of a
           perhaps mislabeling of this equation, and we just want
           to admit up front that we recognize that.  It's more
           directly a flow equation.
                       CHAIRMAN WALLIS:  But you call it a
           momentum equation, and all your derivations say it's
           based on some general microscopic momentum balance.
           And I agree.  It does look more like a flow equation,
           but that's not the claim that's made in any of your
                       DR. ZUBER:  Let me say, I have a problem. 
           I mean, I know momentum mass energy.  I never knew a
           flow equation.  What is that?
                       MR. SWINDELHURST:  We will cover that in
           the next --
                       DR. ZUBER:  Well, no.  What you are really
           doing -- Are you developing new physics or what?
                       MR. SWINDELHURST:  I think the reason we
           are making this acknowledgment, which we've made in
           the past, is that momentum equation means a very
           specific thing.
                       DR. ZUBER:  Momentum.  
                       MR. SWINDELHURST:  And the way it's used
           to term the equation in this code and the derivation
           of it is somewhat loose with that terminology.  
                       CHAIRMAN WALLIS:  So we are going to get
           into that after the break, I guess.
                       MR. SWINDELHURST:  Correct.  
                       (Slide change)
                       MR. SWINDELHURST:  Just repeating one
           thing.  You know, we believe that this equation is
           suitable for this application.  The whole code, the
           use of the code, all the features is up to the user to
           defend it.  He has to deal with the SER we have, the
           conditions and limitations we have.
                       If more assessment work is done as
           requested by the staff, that is the logical, normal
           next step in the process when trying to use this code
           for an application.  We accept all that.
                       CHAIRMAN WALLIS:  And he has to be able to
           figure out how to use it, too.
                       MR. SWINDELHURST:  Certainly.
                       CHAIRMAN WALLIS:  So that's sort of my
           second question.  First question is:  Are the methods
           valid?  What are they, and are they valid?  The second
           one is:  How do you use it?  That's another question.
                       MR. SWINDELHURST:  And this is the way
           it's always been.  It's always --
                       CHAIRMAN WALLIS:  If it's not clear how to
           use it, then you can't very well make it the
           responsibility of the user.
                       MR. SWINDELHURST:  We don't believe we
           have that problem with documentation.
                       CHAIRMAN WALLIS:  It's like driving a car
           where steering wheel isn't connected to the front end. 
           It's rather awkward to ask the user to be responsible
           or that.
                       DR. POWERS:  In fairness, Graham, I mean,
           don't they have several hundred users of this code,
           and it's been used by a lot of people?
                       CHAIRMAN WALLIS:  Apparently.
                       MR. SWINDELHURST:  Tens of users.
                       DR. POWERS:  Tens of users, okay.
                       CHAIRMAN WALLIS:  Okay.  So you're going
           to explain to us how the equation applies to, say,
           that plenum model and --
                       MR. SWINDELHURST:  Certainly.
                       CHAIRMAN WALLIS:  Okay.  Thank you. 
                       MR. SWINDELHURST:  And just the last
           point:  When we shift in the future to the best
           estimate/realistic, we realize that's a different
           world, and there will be different rules we'll be
           playing by when we are doing best estimate plus
           uncertainty type analyses.
                       CHAIRMAN WALLIS:  I go back to Dr. Powers'
           point, though, and it may be that a lot of people are
           using this thing.  But how are they using it, if it's
           not clear how to use it?  Maybe you can explain that
           to us.  But if it isn't clear, if our view is that it
           isn't clear, and you can't tell me how to explain it,
           then it's baffling.
                       MR. SWINDELHURST:  I think the explanation
           is that there has been hundreds and hundreds of people
           who have learned how to use this code in various
           organizations, and they learn it from the
           documentation.  They learn it from training sessions. 
           They learn it from mentoring, from people who have
           gone before them.
                       When they need help, they go to the
           vendor, and it's a community of code users who -- just
           like any other code.
                       CHAIRMAN WALLIS:  So you are going to
           essentially tell us.  We're going to come in as naive
           code users and say we can't figure out how to evaluate
           the momentum flux at this end of this box, and --
                       DR. POWERS:  I am not sure that that's the
           right standard to apply.  I guess that's what I'm
           driving at, is that at least in a lot of the codes
           that I get associated with, they aren't this mature,
           and the documentation is spotty at best.  But they
           become -- The codes get internationally used because
           of this -- what you call it -- mentoring or training
           sessions or group exercises calculating individual
           problems, that there is a tremendous -- Like many
           engineering disciplines, there's a great deal of oral
           lore associated with how to use and how not to use the
                       So I think I don't see a need to come in
           and say is this documentation such that, if I am an
           obstinate and recalcitrant user, I can find flaws in
           its explanations and dream up examples that are where
           it's just not going to work following this.
                       I mean, I think that's an unfair standard
           to apply to this.  I think you have to have a much
           more liberal standard applying to the logic, because
           there is so much of this, and that's not unusual.  I
           mean, all the codes I'm associated with are that.
                       DR. ZUBER:  This is my problem I always
           had with code users and the documentation.  Really,
           they don't really look what's in the document.  They
           don't understand, and very often they just put it on
           the computer and then run it and fiddle around. 
                       I think then they show good agreement with
           some experiments by adjusting some coefficients
           without really acquiring -- I mean inquiring is it
           applicable, can I use it, when can I not use it.  I
           think this is my problem, one of the problems with
           this code.
                       MR. SWINDELHURST:  Let me just give an
           example of that as how a user would use this code. 
           First you have to go to your plant model.  Okay? 
           You've looked at other people's plant models.  You
           know what they did.  You look at your plant design. 
           You adopt the good ideas, and you have to do some
           initial -- some new type of work.
                       You go to your plant model.  You go
           through the code manuals.  You select every option in
           the code based on what other options are recommended,
           what other people are using, what works best to invoke
           the right equations, right options, right
                       You build all your model.  Then you have
           to validate it against something, and we do usually
           use plant data.  A lot of work is done by the code
           developer and by some contractors looking at, you
           know, scale data.
                       We use plant data, and then you have to go
           play this all in front of the NRC in the form of a
           submittal saying this is how we use this code, all
           these options turned on.  And if we do some knob
           turning or some dialing in on something, that is laid
           out as part of the submittal:  We adjusted this
           parameter, because it didn't match plant response. 
           And that's part of your modeling.  Okay?
                       CHAIRMAN WALLIS:  But in setting up this
           model, someone has to look at this noding and say
           here's some W's defined here and here, and they have
           to be somehow put into a structure which then the
           equation uses.
                       Maybe you can help us later on to explain
           how various W's are related to what's in the equation
           when someone is actually doing the noding and so on. 
           That would help us a lot.
                       MR. SWINDELHURST:  But these activities
           have been routinely done by many, many people, and it
           isn't as big a mystery as --
                       CHAIRMAN WALLIS:  Well, many people
           followed Hitler.  I mean, there's no excuse because
           many people did something that it's all right.
                       DR. ZUBER:  That's a problem, really.
                       CHAIRMAN WALLIS:  That's the sort of naive
           attitude we have, being outsiders to this business.
                       Are we going to get to see Dr. Paulsen
           after the break?
                       MR. SWINDELHURST:  Yes.  We've got Dr.
           Paulsen coming up next.  He's got a presentation, plus
           he's prepared to answer anything you want to ask. 
           We've got Dr. Thomas Porsching here to discuss his
           development, if you have any interest in that.  Jack
           Haugh is here as EPRI management.
                       CHAIRMAN WALLIS:  Good.  That will be very
                       I think what we would like to do is we
           would like to look at only two or three equations and
           their derivation and understand it, and also
           understand how it's related to some of those weird
           shaped nodes.  Maybe that's all we need to know.
           So it shouldn't take very long.
                       MR. SWINDELHURST:  I think we're perfectly
           willing to follow your lead as to what you want to
                       CHAIRMAN WALLIS:  That would be great, and
           it would sort of follow what you send as a response to
           the RAIs.  So we've had a chance to look at all this
           before.  We're pretty well prepared.  It's not as if
           you had to explain everything.
                       So perhaps we can get most of that or all
           of it done this morning.  Good, thank you.  So we'll
           take a break until quarter of eleven -- Sorry, before
           I use this gavel, it's going to a break, 15 minutes
           until 10:30.
                       (Whereupon, the foregoing matter went off
           the record at 10:15 a.m. and went back on the record
           at 10:30 a.m.)
                       CHAIRMAN WALLIS:  We are now going to hear
           a presentation from Mark Paulsen.
                       MR. BOEHNERT:  Mark, I'm assuming this is
           going to be open.  There is no proprietary information
                       DR. PAULSEN:  This is open, yes.  
                       What we hope to cover today is to address
           some of the concerns that have been raised about the
           momentum equation, the formulation of the momentum
           equation, address also some of the issues relative to
           how we apply the RETRAN equations to complex geometry. 
           What do the users have to do when they want to model
           a three-dimensional plant using these simplified
                       DR. KRESS:  Can you orient me as to what
           CSA is and how you fit into the --
                       DR. PAULSEN:  CSA -- We are a consulting
           firm that is the developer -- We have been involved in
           the development of RETRAN.  We also do the maintenance
           portion of the work for RETRAN, and we provide user
           support and training.
                       DR. ZUBER:  Where are you located?
                       DR. PAULSEN:  We are located in Idaho
                       CHAIRMAN WALLIS:  Now RETRAN actually
           appeared about 20 years ago.
                       DR. PAULSEN:  RETRAN actually began
           probably in about the late Seventies.
                       CHAIRMAN WALLIS:  There was a report from
           whatever the embodiment then was of Idaho Falls.
                       DR. PAULSEN:  Yes.  It began at Energy
           Incorporated.  It was a spin-off from the RELAP-4
           code, and it was designed specifically to provide
           utilities a tool to analyze Chapter 15 transients,
           because at that point in time utilities were relying
           solely upon industry.
                       CHAIRMAN WALLIS:  I think what we found in
           the original documentation that you submitted with
           RETRAN in 1998 was almost exactly the same as EG&G or
           whoever they were had submitted in their report in
           1980.  Very, very similar.
                       DR. PAULSEN:  For which one now?
                       CHAIRMAN WALLIS:  The documentation we
           first read two years ago, two and a half years ago.
                       DR. PAULSEN:  Oh, okay, the original
                       CHAIRMAN WALLIS:  Was exactly the same for
           RETRAN as in the report that is now 20 years old from
           Idaho Falls.
                       DR. PAULSEN:  Yes.  It was an EI report.
                       CHAIRMAN WALLIS:  Right.
                       DR. PAULSEN:  That's right.  Okay.
                       DR. ZUBER:  This shows the genetic
                       CHAIRMAN WALLIS:  Yes, of the genes.
                       DR. SCHROCK:  Let's see.  You are going to
           clarify Mr. Swindelhurst's comment about the vagary of
           the terminology momentum equation and flow equation?
                       DR. PAULSEN:  I hope to.
                       DR. SCHROCK:  Good.  Okay.
                       DR. PAULSEN:  And the approach I have
           taken was I went back and looked at some of the
           concerns that have been raised in the previous ACRS
           meetings and looked at the RAIs that we had been
           issued by the staff and tried to put together a
           cohesive story that starts at the top and goes to the
                       So I'm not following the order of the RAI
           questions.  I'm trying to start at the top and make a
           cohesive story.  Now if you have questions as we go,
           I'm sure you're not bashful, and you will ask
                       So we may not even get to the RAI
           question, if we can get things resolved up at the top.
                       DR. SCHROCK:  Does the 2 mean a second
           round of questions?
                       DR. PAULSEN:  That's correct.  This round
           of questions dealt primarily with the staff's trying
           to direct -- or to relay the ACRS concerns about the
           momentum equation.  So there's a lot of overlap in
           these RAI2 questions with what the ACRS concerns were
           on the momentum equation.
                       Most of the concern has arisen on how we
           use the one-dimensional momentum equation.  We start
           with a 1-D equation, and then we develop what we use
           as our flow equation, and we are going to try and talk
           about that, point out the definitions and some of the
           assumptions we make.
                       So while we are doing this, we hope we can
           address your concerns.  I hope you don't get the
           feeling that we've been trying to avoid your concerns
           for two years.  We have actively been trying to
           resolve them.
                       CHAIRMAN WALLIS:  We have no feelings at
                       DR. PAULSEN:  Okay.  What this has led to
           is the fact that we have -- In responding to the
           request for additional information, we have attempted
           to make the documentation more usable, more accurate,
           and we have also identified several code errors which
           we'll talk about, and we have  corrected them.
                       (Slide change)
                       DR. PAULSEN:  So as we go through the
           development of the RETRAN-3D flow equation, first of
           all, I'm going to start with some general comments to
           try and point out where we are going with all of this,
           so that we don't put equations down on the board
           before we actually know where we are trying to go, and
           maybe that will help clarify things.
                       Then we also want to list, as many as
           possible anyway, our definitions in the assumptions
           that we make.  We will then go through the case where
           we actually start with a constant area channel, start
           with the momentum equation, and derive our flow
           equation, and then go through later how we apply that
           to variable area channels and then for situations
           where we may have more connections than just a simple
           straight piece of pipe --
                       CHAIRMAN WALLIS:  Now your constant area
           channel you are going to show us is that bend to --
                       DR. PAULSEN:  That's right.
                       CHAIRMAN WALLIS:  That originally had a
           variable area, because in the first document we saw it
           had an AEK and an AK plus one, which was different.
                       DR. PAULSEN:  That's right.
                       CHAIRMAN WALLIS:  And now it seems to have
           fallen back to being constant area.
                       DR. PAULSEN:  For this initial development
                       CHAIRMAN WALLIS:  Then it fell back to a
           more special case?
                       DR. PAULSEN:  This is a constant area.
                       CHAIRMAN WALLIS:  Later it gets
                       DR. PAULSEN:  That's correct.
                       CHAIRMAN WALLIS:  To be a variable area?
                       DR. PAULSEN:  That's right, and it's
           really with the abrupt area change --
                       CHAIRMAN WALLIS:  Without an area change
           at all, just a tube with different areas on the end. 
           Are you going to list that one?
                       DR. PAULSEN:  Basically, we'll go through
           three developments, one where we start with a constant
           area.  Then we'll go to one where there is an abrupt
           area change --
                       CHAIRMAN WALLIS:  Why abrupt?  In a
           variable area it doesn't have to be abrupt.  I'm just
           pointing out that in the original documentation what
           you now have as a constant area channel was a variable
           area channel.
                       DR. PAULSEN:  That's correct.
                       CHAIRMAN WALLIS:  And for some reason it's
           fallen back, maybe --
                       DR. PAULSEN:  Because in -- There was a
           lot of confusion about those figures that led to --
           and really, that figure was used to develop a constant
           area equation.
                       CHAIRMAN WALLIS:  But if your equation is
           right, it should apply to a variable area channel
           without a sudden change of area.
                       DR. PAULSEN:  Well, we'll talk about that
           as we go.  Okay?
                       Then we are going to look at complex
           geometries on how we actually apply these One-D
           equations, what kind of assumptions do users have to
           make, what are some of the sensitivities, and how do
           they apply them?  Where do you break a model up to
           start applying these equations?
                       We will also identify where some of this
           guidance is available for users.  There is actually
           documentation available that directs users on how to
           do some of this nodalization.
                       (Slide change)
                       CHAIRMAN WALLIS:  What does this first
           statement mean?  
                       DR. PAULSEN:  That it's fundamentally one-
                       CHAIRMAN WALLIS:  What does it mean?  What
           do you mean by that?  I want to see what he says it
                       DR. PAULSEN:  We are starting with a one-D
           momentum equation.
                       CHAIRMAN WALLIS:  What does that mean?
                       DR. PAULSEN:  We are not going to account
           for any momentum in the transverse direction.
                       CHAIRMAN WALLIS:  So you mean it's a
           momentum equation resolved in one direction?
                       DR. PAULSEN:  In one direction.  That's
                       CHAIRMAN WALLIS:  So when I -- I want to
           be clear about this.  I don't want to criticize
           something which is different. 
                       You are saying this is the resolution of
           momentum fluxes, forces of momentum changes in one
                       DR. PAULSEN:  Yes, and we'll see --
                       CHAIRMAN WALLIS:  And when you get to a
           bend, you are going to explain how a bend can be one-
           dimensional and things like that?
                       DR. PAULSEN:  We'll talk about that.
                       CHAIRMAN WALLIS:  Okay.  I just want to be
                       DR. SHACK:  You're saying more, though,
           right?  You're saying the flows are all one-
           dimensional, too.  There are no transverse flows --
                       DR. PAULSEN:  That's true.  That's true.
                       CHAIRMAN WALLIS:  Your averaging works in
           a one-dimensional sense?
                       DR. PAULSEN:  That's correct.
                       CHAIRMAN WALLIS:  Right.
                       DR. ZUBER:  What do you mean by flow
                       DR. PAULSEN:  An equation of motion.
                       DR. ZUBER:  You conserve three things in
           thermal-hydraulics.  It's momentum, energy and mass. 
           You don't conserve the flow.  If this is the
           conservation equation, then it's the momentum
                       You see, this kind of elastic --
                       CHAIRMAN WALLIS:  Well, I think -- Let's
           clarify.  What you are going to do is you are going to
           manipulate this momentum equation resolved in one
           direction in some way until it looks like something
           else, which isn't quite recognizable as a momentum
           equation --
                       DR. PAULSEN:  That's correct.
                       CHAIRMAN WALLIS:  -- and you call that a
           flow equation.  Is that what you're doing?
                       DR. PAULSEN:  That's correct.
                       DR. ZUBER:  Am I correct to understand
           that, even up in your new conservation equation --
                       CHAIRMAN WALLIS:  No.  They are going to
           do some manipulation to get something which isn't
           immediately recognizable as a momentum equation but
           came from the momentum equation.  That's what I
           understand you are going to show us.
                       DR. PAULSEN:  That is correct.
                       DR. ZUBER:  They may write new textbooks.
                       DR. PAULSEN:  Okay.  I think one of the
           areas where we've probably introduced some confusion
           in the past was, as pointed out, maybe trying to be
           too rigorous with the implication that there was more
           fundamental physics behind the code than really there
                       We are not really trying to do anything in
           three dimensions.  There's a lot of development where
           we've emphasized the vector momentum equation. 
           Really, it's a scalar equation, but we carry some
           vector information along.  We'll show the purpose of
           that in a few minutes.
                       CHAIRMAN WALLIS:  But you have an example
           which is a 90-degree bend.  
                       DR. PAULSEN:  That's correct.
                       CHAIRMAN WALLIS:  And that isn't in your
           list here, is it, but it's an example in your --
                       DR. PAULSEN:  Places where we really
           recommend -- where we would recommend angle
           information be used.
                       CHAIRMAN WALLIS:  Yes, but you are showing
           how to use it for a 90-degree bend in your
                       DR. PAULSEN:  That's right.
                       CHAIRMAN WALLIS:  So I think we ought to
           look at that example.
                       DR. PAULSEN:  And I have an example -- I
           have some discussion of 90-degree bends and what level
           of detail you go into when you are modeling.
                       Basically, by carrying some of this angle
           information along, you can get a more correct
           representation of the momentum flux in some of these
           areas where you've got multi-dimensional pieces coming
                       Where we really don't recommend using --
           We're not trying to use angles to represent three-
           dimensional flow patterns in downcomers or lower
           plenums.  We admit that right up front.  And in most
           models -- One of the examples we gave was the elbow
           which Dr. Wallis pointed out.  That was simply
           supposed to be there to represent the effects of the
                       We don't recommend users model individual
           elbows.  In practice, users are going to lump straight
           sections of pipe and elbows into one section.
                       CHAIRMAN WALLIS:  But you have an example
           in your first response to the RAIs where you have the
           cold leg and the downcomer.  There's a node that spans
           both of them.  That looks awfully like an elbow to me.
                       DR. PAULSEN:  And we'll talk about that. 
           There's an example that --
                       CHAIRMAN WALLIS:  I think we need to talk
           about that.
                       DR. PAULSEN:  Yes.  Then we don't use the
           angle information to simulate every turn in the piping
                       CHAIRMAN WALLIS:  You do not?
                       DR. PAULSEN:  We do not.
                       DR. SCHROCK:  What do you do to simulate?
                       DR. PAULSEN:  Pardon me?
                       DR. SCHROCK:  What do you do to simulate
           the turns in the piping?
                       DR. PAULSEN:  Those we generally account
           for with loss coefficients.
                       CHAIRMAN WALLIS:  Your claim in one of
           your documents is that the friction on the wall is
           balanced by the pressure drop in that situation.  
                       DR. PAULSEN:  That's right.
                       CHAIRMAN WALLIS:  And that that comes from
           a momentum equation?
                       DR. PAULSEN:  Basically, I think when we
           get through our momentum -- I keep wanting to call it
           momentum equation.  Pardon me.  It's years of
           incorrect training.
                       CHAIRMAN WALLIS:  But you told us where it
           comes from.  It's your principle you're using.
                       DR. PAULSEN:  That's right, and I'll
           probably be calling it the momentum equation, but what
           we are referring to is the One-D or the scalar
           equation is what we actually get to.
                       CHAIRMAN WALLIS:  Well, I guess we'll get
           to that, but your claim is that the momentum -- the
           overall momentum balance simply have a bend in the
           pipe with no momentum change and stuff that goes
           around.  Frictional forces are balanced by the
           pressure drop in the momentum balance.
                       DR. PAULSEN:  What we end up --
                       CHAIRMAN WALLIS:  That's not -- I need to
           question you about that, because I don't think that's
                       DR. PAULSEN:  Because basically, what we
           end up with when we get our equation, if we drop the
           time derivative term and we look at just the terms on
           the righthand side of the equation, it looks like the
           mechanical energy equation.
                       CHAIRMAN WALLIS:  No, it doesn't.  
                       DR. PAULSEN:  It's very similar.  We have
           the Bernoulli terms --
                       DR. ZUBER:  Wait, wait, wait, wait, wait. 
           Do you know how the Bernoulli equation is derived?
                       DR. PAULSEN:  Yes.  Bernoulli -- It's a
           mechanical energy equation.
                       DR. ZUBER:  Okay.  How do you derive the
           Bernoulli equation?
                       DR. PAULSEN:  Well, I don't think that
           really is relevant here, because --
                       DR. ZUBER:  No, it is.
                       DR. PAULSEN:  -- we're talking about the
           momentum equation.
                       DR. ZUBER:  No, exactly, because you said
           that, when you drop the storage terms, the equations
           are like the energy equations.  Then you brought in
           the Bernoulli equations.  Graham said no.  I said no. 
           You tell me -- I'm questioning you how are you
           deriving the Bernoulli equation?
                       DR. PAULSEN:  Well, let's wait until we
           see what the equations are.
                       CHAIRMAN WALLIS:  I'd like to see it,
           Novak.  I'd like to see the equations.
                       DR. PAULSEN:  Let's look at the equations
                       DR. ZUBER:  He does not know --
                       CHAIRMAN WALLIS:  I think that may become
           clear later on.  We'll find out.  I don't think we --
                       (Slide change)
                       DR. PAULSEN;  Okay.  We are going to start
           with the illustration of the momentum cell shows an
           elbow, and the primary reason for showing this elbow
           is just so that we keep track of some of the effects
           of the vector information on the flow into the
           momentum cell, because we used that in some of our
           components -- for instance, T's in plenums, as we'll
           see toward the end of this discussion.
                       As I mentioned previously, we don't
           recommend using angles in every elbow or change in
           direction in the piping network.  What we'll see is,
           if you include an angle for an elbow, you're going to
           see a pressure change there as a result of that angle,
           but as soon as you get around a bend where you've put
           in an angle, the pressure goes back the same.  It's a
           recoverable loss. 
                       So the only place it really affects the
           pressure is locally where you have included that angle
                       (Slide change)
                       DR. PAULSEN:  So at this point, here we
           have our momentum cell.  Basically, our momentum cell
           overlaps two mass and energy cells.  So here we have
           an upstream mass and energy cell and a downstream mass
           and energy cell, which we refer to as control volumes.
                       Now this momentum cell -- you might refer
           to it as a control volume also.  But in RETRAN
           terminology, control volumes are mass and energy
           cells, and we'll call this a momentum cell or
                       CHAIRMAN WALLIS:  Then let's look at this: 
           Ak user supplied down there, and you have Ak+1 user
           supplied.  So that would make me think they could be
           different, and they were in your original derivation.
                       DR. PAULSEN:  That's correct.
                       CHAIRMAN WALLIS:  Yet in your equation you
           make them the same.  Why is that?
                       DR. PAULSEN:  Because we are going to use
           this to develop a uniform area flow equation.
                       CHAIRMAN WALLIS:  Yes, but your RETRAN
           equation has different areas in it.
                       DR. PAULSEN:  And we'll get to that as we
           develop --
                       CHAIRMAN WALLIS:  No, but please, if you
           are going to say you've got a general equation with
           two areas in it, it should apply to this shape, too,
           shouldn't it?  Yes?
                       DR. PAULSEN:  If we have two areas?
                       CHAIRMAN WALLIS:  If Ak and Ak+1 are not
           equal, your equation has Ak and Ak+1 different, your
           general RETRAN equation.  Right?  So it should apply
           to this.
                       DR. PAULSEN:  That's the one where we
           assume -- after we've gone through the development of
           having an area change.
                       CHAIRMAN WALLIS:  What you call the RETRAN
           equation -- right? -- has Ak+1 and Ak in it.  Right? 
           What you call the RETRAN equation?
                       DR. PAULSEN:  Is that on the next slide?
                       CHAIRMAN WALLIS:  Wherever it appears, it
           has an Ak and an Ak+1, which are different.  Right?
                       DR. PAULSEN:  They may or may not be
                       CHAIRMAN WALLIS:  They could be different
           in this figure, right?  And your equation -- The
           RETRAN equation, which you want us to believe, has an
           Ak and an Ak+1 which are different in it, in general.
                       DR. PAULSEN:  Yes.
                       CHAIRMAN WALLIS:  It doesn't have a step
           change or anything, and you originally had a
           derivation for this shape in which the Ak and the Ak+1
           were different, and for some reason you've fallen back
           to Ak, and I think the reason is you couldn't get rid
           of the Ak's and the Ak+1s multiplying the pressures. 
           So you just said we won't do it, because we don't know
           how to do it.  We'll just forget it.
                       DR. PAULSEN:  That goes with part of this
           development --
                       CHAIRMAN WALLIS:  In your original
           derivation, when we get to the part, the pressures on
           the ends multiplied different areas.  Right?
                       DR. PAULSEN:  They have an area for the
           node upstream and the node --
                       CHAIRMAN WALLIS:  Well, we'll back to that
           when you do your derivation.  But I'm just pointing
                       Another question I have to ask you:  This
           bend could be a 90 degree bend or 180 degree end or
           any kind of bend?  Still works?
                       DR. PAULSEN:  In actual practice in RETRAN
           the bends are usually limited to 90 degrees.
                       CHAIRMAN WALLIS:  This equation
           development, this theory, would apply to any kind of
           a bend in a pipe of constant area.  Right?  Okay.  So
           if I give you a picture of an 180 degree bend, you can
           tell me how it applies to that?
                       DR. PAULSEN:  A what now?
                       CHAIRMAN WALLIS:  180 degrees, and 360
           degree bend, your pipe comes along, goes to loop and
           goes off, you will show me how this equation applies
           to that?  It's a general bend?  Can we get into that
           sort of discussion?
                       DR. PAULSEN:  Well, let's get the slides
           up, and then we'll get the equations up --
                       CHAIRMAN WALLIS:  Can we do that?  Is that
                       DR. PAULSEN:  Okay.
                       DR. KRESS:  Before you take that one off,
           how is it you know exactly where to place the momentum
           cell with respect to the two mass and energy cells?
                       DR. PAULSEN:  to the mass and energy
           cells?  In practice, where users generally put
           junctions is what we would call this, the momentum
           cell, is where there are changes in geometry.
                       CHAIRMAN WALLIS:  It's sort of in the
           middle.  It's a convenient place.
                       DR. PAULSEN:  Right.  And in some cases,
           depending on the type of transient, if you want to get
           spatial resolution, then you may add more nodes where
           you don't have geometry changes.  But most places
           you'll see junctions will be, say, where the cold leg
           connects to the downcomer, a surge line comes off of
           the cold leg.
                       DR. KRESS:  So the junction would be where
           1 is on that.
                       DR. PAULSEN:  That's right.
                       CHAIRMAN WALLIS:  They tend to be mass and
           energy cell junctions, but the momentum cell is
           something else.  Was that your question, how do you
           locate the momentum cell?
                       DR. KRESS:  Yes.  You know, you could just
           place it -- You could leave the junction where you had
           it, but you seem to -- like you have some freedom to
           locate the momentum cell.
                       DR. PAULSEN:  That's right.
                       DR. KRESS:  I just wondered what rationale
           was used to place it anywhere when you go to divide up
           your circuit into those cells.  Like, for example, one
           might look at an actual bend and say let's make the
           angle phi to 1 the same for the inlet and exit between
           those two.  That would be one choice, for example.
                       DR. PAULSEN:  Right.
                       DR. KRESS:  That might help you in how you
           derive the equation.  But I don't know what the
           rationale was.
                       DR. PAULSEN:  Okay.  It's basically where
           you have area changes, and then in some cases where
           you have long sections of piping you may put in
           additional nodes just to get additional spatial
           resolution so that you come closer to approximating
           the difference equations.
                       CHAIRMAN WALLIS:  And this phi i -- you
           are going to resolve in the direction of phi i?
                       DR. PAULSEN:  Yes, of this --
                       CHAIRMAN WALLIS:  Now I notice when you
           have, say, the downcomer picture, your face at the end
           of the cold leg is parallel to the upstream face phi
           k or something.  Well, I know that phi is upsized
                       DR. PAULSEN:  That's right.
                       CHAIRMAN WALLIS:  Which kind are they?
                       DR. PAULSEN:  These are phis.  All of
           these are phis, I think.
                       CHAIRMAN WALLIS:  So that phi i could be
           parallel to phi k in some cases or parallel to phi
                       DR. PAULSEN:  That's correct.
                       CHAIRMAN WALLIS:  It's not necessarily
           halfway between it -- somewhere, anywhere.
                       DR. PAULSEN:  That's correct.  Somewhere.
                       DR. KRESS:  That was my question, yes.
                       CHAIRMAN WALLIS:  It's an arbitrary angle. 
                       DR. PAULSEN:  But in actual practice,
           these either will be the same angle or in general 90
                       CHAIRMAN WALLIS:  I noticed that with the
           bend.  You had it the same at one end and different at
                       DR. PAULSEN:  That's right.
                       CHAIRMAN WALLIS:  Okay.  So it's not
           defined to be halfway between or anything special. 
           It's anywhere.
                       DR. PAULSEN:  That's right.
                       CHAIRMAN WALLIS:  Okay.
                       DR. PAULSEN:  And one of the reasons that
           I think historically that this staggered mesh was used
           was because flows were needed to obtain the mass and
           energy balance on these control volumes and, by
           overlapping this flow equation, the flow was
           calculated at that location.  That was the rationale.
                       CHAIRMAN WALLIS:  Your CFD was the same
           thing in many cases.
                       DR. PAULSEN:  Yes.
                       CHAIRMAN WALLIS:  Then you have to do some
           interpolation or upwinding or various different rules
           which you go into in your effects.
                       DR. PAULSEN:  Right.  But in reality, when
           you start looking at a model, we would never -- Well,
           I can't say that.  In plant models where people are
           modeling reactor systems for Chapter 15 analyses, you
           wouldn't see someone modeling an elbow this way.  An
           elbow would be lumped into a long section of piping.
                       DR. KRESS:  Your L where you have one-half
           L, where is it on this?
                       DR. PAULSEN:  These are geometric
           properties.  This would be the flow length of this
           control volume.  So, basically, our momentum cell
           covers half the length of the upstream volume and half
           the length of the downstream volume.
                       DR. KRESS:  So that does fix where you
           place this momentum cell?
                       DR. PAULSEN:  That's right.
                       CHAIRMAN WALLIS:  So it's a little
           problematic if the volumes are of changeable area.
                       DR. PAULSEN:  That's right.  In fact, if
           you have something like a nozzle -- and this really
           gets into comparing with experimental data.  If you
           are going to look at comparing a nozzle, then you are
           going to have to put in some kind of representative
           geometry that is representative of the section
           spatially that you are --
                       CHAIRMAN WALLIS:  Right.  I think in the
           reactor you try to choose these things so that they
           are essentially constant area on both sides of the
                       DR. PAULSEN:  That's correct.
                       DR. SCHROCK:  You don't show the forces on
           the diagram, the gravitational force, for example.
                       DR. PAULSEN:  That's right.  This is just
           basically geometric information.
                       CHAIRMAN WALLIS:  -- forces downwind?
                       DR. SCHROCK:  That is what I'm commenting
           on.  How do these -- What's the justification of the
           balance without specifying more clearly what these f's
                       DR. PAULSEN:  Okay.  
                       DR. SCHROCK:  I mean, the f gravitational
           passes through the center of mass.
                       DR. PAULSEN:  That's correct.
                       DR. SCHROCK:  How does it align with other
                       DR. PAULSEN:  Okay.  
                       DR. SCHROCK:  And how does that become a
           one-dimensional equation?  They are in different
                       DR. PAULSEN:  Okay.  That we'll show on
           the next slide.  Maybe you've already looked at the
                       CHAIRMAN WALLIS:  You need to get there,
           but we need to understand this.
                       DR. SCHROCK:  Oh, yes.  That's what I'm
           looking at, in fact, is the next slide.
                       DR. PAULSEN:  Okay.  And one thing worth
           noting before we move to that equation is that, with
           this momentum cell, we are going to have terms where
           we have momentum that moves across this boundary and
           the downstream boundary.  So there will be velocities
           at these two surfaces, and these velocities in a
           straight piece of pipe will align with the normal
           vector for the REA, but in general they can be at some
           other velocity -- or other direction.
                       DR. KRESS:  Is this intended for a single
           fluid or two-phase fluid?
                       DR. PAULSEN:  The momentum equation or
           this flow equation looks at the mixture of fluid.
                       DR. KRESS:  As if it were one fluid?
                       DR. PAULSEN:  As if it were one fluid. 
           Then there's a separate equation that actually
           calculates the velocity difference, if there happens
           to be two-phase.
                       DR. ZUBER:  It is a two-phase mixture, not
           a single phase.  It's a two-phase mixture.
                       DR. PAULSEN:  It can be, yes.  If you have
           two-phase conditions, it will be a two-phase mixture.
                       DR. ZUBER:  I think this was a question. 
           You have a two-phase mixture going out the densities,
           and then you have another equation where you have the
           difference in velocities.
                       DR. PAULSEN:  That's correct.  This is
           basically the mixture equation.
                       DR. ZUBER:  Mixture equation.
                       CHAIRMAN WALLIS:  Now this pressure you
           talk about -- what is that, this p-i -- or pk?  What
           is pk?
                       DR. PAULSEN:  Well, maybe that will come
           out on the next slide, but we do have pressures that
           are defined for the mass and energy cells.  So we will
           have a pressure, a representative pressure, for our
           upstream mass and energy cell and a different pressure
           for our downstream mass and energy cell.
                       DR. ZUBER:  And they act where?
                       DR. PAULSEN:  They act where?
                       DR. ZUBER:  Where does the pressure act?
                       DR. PAULSEN:  Well, let me put the next
           slide up, and I'll leave this one out for just a
                       (Slide change)
                       DR. PAULSEN:  Because we have -- First of
           all, this is just kind of introductory material to
           show how the equations are closed.  We have the mass
           and energy cells where we actually do a mass and
           energy balance.  So we will have total mass in those
           cells, and we will have total energy, and then based
           on water properties, we have a pressure equation
           estate where for our fixed control volume, given the
           mass and energy in a node, we can calculate the
                       DR. KRESS:  Now the energy that's in that
           thing includes the energy that's due to friction --
           You account for that energy in another equation that
           adds in the friction.
                       DR. PAULSEN:  That's right.  In fact, we
           have -- In RETRAN-3D we use an internal energy
           equation, and in general the viscose terms, the
           dissipation terms, are small compared to the others. 
           So we've currently neglected that viscose dissipation
           in the energy equation, but it includes the convective
           terms in and out of the volume, heat addition from
           various either heat conductors or decay heat.
                       So we, in effect, do our internal energy
           balance to come up with our internal energy and mass,
           and then we have a pressure for that control volume. 
           That pressure, we assume -- Well, let's go on here for
           just a minute.
                       DR. KRESS: Well, it's an equilibrium
                       DR. PAULSEN:  For the three-equation model
           it is equilibrium, and we have the pressure as a
           function of total mass and total energy.  When we go
           to our five-equation model which has -- constrains
           nonequilibrium, it's developed primarily for
           applications in BWRs where you have subcooled boiling.
                       One phase is constrained at saturation, if
           we have two-phase conditions, that being the vapor
           phase.  The liquid phase can then be subcooled or
           superheated, and this pressure equation estate then
           changes so that our pressure is a function of our
           total mass, total energy, and then our vapor mass
           that's in the volume.
                       So depending on the governing equations,
           this pressure equation estate can change.  If we have
           noncondensables in the system, it can also change. 
           But for the simple case, our pressure is determined by
           the mass and energy for the simple three-equation
                       DR. SCHROCK:  So one-phase is constrained
           to be equilibrium, and the other is not?
                       DR. PAULSEN:  That's right.
                       DR. KRESS:  So for noncompressible fluids
           that are flowing adiabatically, your pressure becomes
           a constant, a constant area?
                       DR. PAULSEN:  It should effectively do
           that.  Right now we would actually do a separate mass
           and energy balance for each node and, if the specific
           volume and specific internal energy don't change, then
           we should end up with the same pressure.
                       DR. KRESS:  That's why I was asking what
           you did with the friction term?
                       DR. PAULSEN:  Okay.  
                       DR. KRESS:  Never mind. Go on.
                       DR. ZUBER:  Can you explain those terms on
           the righthand side?
                       DR. PAULSEN:  I think you ought to explain
           every one.
                       DR. PAULSEN:  Yes.  Okay.  So this --
           We've talked a little bit about the momentum cell
           geometry where we are using a staggered mesh.  What we
           are hoping to get from this place we're starting is an
           equation that will allow us to calculate flow at the
           boundary between those mass and energy cells.
                       So we have our time rated change of
           momentum for the momentum cell volume averaged over
           the momentum cell volume, and then at this point we
           have the, in effect, momentum that's being transferred
           through the flow surfaces, the ends of --
                       CHAIRMAN WALLIS:  So assuming they are
           parallel to the -- the surface is perpendicular to the
           velocity there?
                       DR. PAULSEN:  The assumption that we have
           here is that this area is the normal area.  It's
                       CHAIRMAN WALLIS:  Forces normal to the
                       DR. PAULSEN:  Right.
                       CHAIRMAN WALLIS:  Because in some earlier
           derivation of this, you had some a-primes and all
                       DR. PAULSEN:  Well, you pointed out there
           were some errors in there, and we agreed that there
           were some problems there.  
                       So at this point in this --
                       CHAIRMAN WALLIS:  -- flow rate out of j?
                       DR. PAULSEN:  That's right.  This ends up
           being the velocity that's the normal component of the
           velocity.  This would then be the true velocity
           crossing that surface, which may or may not be normal. 
           For most applications in RETRAN, it will be.
                       Then we have our forces.  This is our wall
           force that's parallel to the wall, our viscose
           friction term.  This is a term which --
                       DR. SCHROCK:  I asked you about the forces
           in the diagram.  You're writing single forces here now
           in this balance relationship.  Where are these forces
           in this diagram?
                       DR. PAULSEN:  Okay.  This force will be
           parallel to the wall.
                       DR. SCHROCK:  Well, the wall isn't
           everywhere parallel.
                       DR. PAULSEN:  At any point along the wall,
           it will --
                       DR. SCHROCK:  But this is an equation for
           the control volume.
                       DR. PAULSEN:  Yes.  Basically --
                       DR. SCHROCK:  So you don't get it by
           taking the point differential equations and
           integrating over the volumes.  You have an ad hoc
           equation, and you're trying to explain your way out of
           the terms in the ad hoc equation.
                       Now what I'm asking you to do is show a
           force diagram.
                       DR. PAULSEN:  And basically --
                       DR. SCHROCK:  You've shown a control
           diagram.  Now show a force diagram.
                       DR. PAULSEN:  And basically, these wall
           forces are, like you said, ad hoc models.
                       CHAIRMAN WALLIS:  They are frictional
           sheer stresses on the wall, but then it's the integral
           of all that over the whole volume.
                       DR. PAULSEN:  That's right.  And basically
           we'll apply something like a Moody model where we know
           the length of the flow path.  We will use that --
                       CHAIRMAN WALLIS:  Moody doesn't tell you
           that.  If you have, say, a -- I'm going to give you
           this 180 day bend in a little while.  But if you look
           at the sheer stresses on a 180 degree bend, you find
           their resultant is in the direction which is right
           angles to the end faces of the bend.  It's completely
           orthogonal to the pressure forces on the ends.
                       I mean, the pressure drop in the pipe is
           not the same as a momentum balance for a pipe.  The
           Moody -- except for a straight pipe.
                       DR. PAULSEN:  That's right.
                       CHAIRMAN WALLIS:  Not the same thing.  So
           it is obscure, what your Fs are here.
                       DR. PAULSEN:  And basically, what we are
           trying to show here -- and I appreciate your point
           about where those forces are applied.  When we end up
           doing our next operation, we are going to have some
           kind of a scaler term for our friction.
                       CHAIRMAN WALLIS:  Well, this isn't scaler
                       DR. PAULSEN:  It's not scaler yet.
                       CHAIRMAN WALLIS:  One-dimensional.  It's
           a misnomer?  Okay.  I'm sorry, because I thought
           that's what you were talking about.
                       So this F tilde is the integral of all the
           sheer stresses on the wall over the area?
                       DR. PAULSEN:  Yes.
                       CHAIRMAN WALLIS:  Whatever direction it
           happens to be.
                       DR. PAULSEN:  That's right.  It's
           uncalculable but general.
                       CHAIRMAN WALLIS:  It's a big arrow, the
           resultant force from all due to friction.  Okay.
                       DR. PAULSEN:  And these forces are normal
           sheer forces that you will see when you have changes
           in geometry were obstacles in your flow pattern
           somewhere in here.
                       CHAIRMAN WALLIS:  That's the same thing as
           integral PBS, isn't it?  What's different about it?
                       DR. PAULSEN:  These may be from internal.
                       CHAIRMAN WALLIS:  Same thing.  Surfaces,
           whatever the surface is, wiggles, squiggles.
                       DR. KRESS:  Yes, that's what bothered me.
                       CHAIRMAN WALLIS:  There's nothing
           different about Floc.  Right?
                       DR. PAULSEN: Floc is --
                       CHAIRMAN WALLIS:  The sheer stress of
           pressure.  right?
                       DR. PAULSEN:  It's another viscose loss
                       CHAIRMAN WALLIS:  Well, I think that's
           where there's a misleading thing.  You see, now you're
           going to an energy balance when this is a momentum
           balance.  Floc, it seems to me, is either incorporated
           in FF or in integral feed --
                       DR. PAULSEN:  Let me tell you where we are
           trying to get to.
                       CHAIRMAN WALLIS:  I know where you're
           trying to get to.
                       DR. PAULSEN:  All right.  Now we're trying
           to get to somewhere that looks like --
                       DR. ZUBER:  The Bernoulli equation.
                       DR. PAULSEN:  -- the Bernoulli equation.
                       CHAIRMAN WALLIS:  You are trying to fudge
           your way to Bernoulli's equation.  Right?  And we're
           just trying to keep you honest.
                       DR. PAULSEN:  That's fine.  
                       CHAIRMAN WALLIS:  But if you go back to
           fundamentals, which you do -- I mean, you try to
           establish the fundamentals, because you do a lot of
           hairy math later on -- there's only the integral of
           the sheer stress tensor with the surface and the
           integral of the normal stress, if you want to break it
           out from the sheer stress.  That's all.
                       The only thing the surface does to the
           flow is via sheer stress and normal stress integrated
           over it.  There are two forces, and really one, if you
           put them together.
                       DR. PAULSEN:  That's right.  
                       CHAIRMAN WALLIS:  So this -- I think what
           you are doing -- What I find throughout all your
           derivations, you sort of mix up these ideas of energy
           losses with momentum, and Floc really doesn't have any
           business in the momentum equation.
                       DR. PAULSEN:  Okay.  
                       CHAIRMAN WALLIS:  That's what confused me.
                       DR. PAULSEN:  So maybe we would be better
           off taking this out and then letting it appear when we
           actually apply mechanical energy --
                       CHAIRMAN WALLIS:  Maybe if we work
           together, we can come up with something.
                       DR. PAULSEN:  Yes, I can see where you're
           coming from.  And some of this is historical.
                       CHAIRMAN WALLIS:  Yes, I know, but some of
           it is because people didn't understand properly in the
           first place.
                       DR. PAULSEN:  And some of what was
           understood by the people that have gone by the wayside
           and retired wasn't documented, and so we're trying to
           reconstruct history and maybe leaving out some steps.
                       DR. ZUBER:  Well, why did you have to
           reconstruct?  You can start from correct formulation
           and forget about history.  It's almost like going to
           the Neanderthals to derive something.  
                       DR. PAULSEN:  Okay.  The next term that we
           have here is just from additional things that are very
           complicated that we can't really model at a
           fundamental level, things like pumps and turbines.
                       CHAIRMAN WALLIS:  Electromagnetic forces?
                       DR. PAULSEN:  That's right.  We know that
           there's going to be some additional forces, and then
           we have the body force term, the gravity.
                       DR. SCHROCK:  You put secondary flows in
           that category?  I mean, in this geometry you induce a
           secondary flow.
                       DR. PAULSEN:  That's right.
                       DR. SCHROCK;  It's not specifically
           thought about.
                       DR. PAULSEN:  No.  If the secondary flows
           are an important part, then that's a limitation.
                       CHAIRMAN WALLIS:  It wold appear in Ffw.
                       DR. SCHROCK:  That is where that would 
           show up.
                       CHAIRMAN WALLIS:  It captures it all.
                       DR. SCHROCK:  Yes.
                       CHAIRMAN WALLIS:  So this is momentum
           equation.  It has to be resolved in some direction.
                       DR. ZUBER:  Wait, wait, wait.  What is
           this Stot for the pressure?
                       DR. PAULSEN:  The what now?
                       CHAIRMAN WALLIS:  Stot?
                       DR. ZUBER:  That last term.
                       DR. PAULSEN:  This one?
                       CHAIRMAN WALLIS:  Stot.
                       DR. PAULSEN:  This is for the total
           surface area.
                       CHAIRMAN WALLIS:  That's a new
           development.  You used to have it over the ends, and
           now you are going to -- This is a completely new
           development in your theory?
                       DR. PAULSEN:  That's right.  
                       DR. ZUBER:  Well, how do you differentiate
           the second term -- I mean the Ffw from this integral
                       DR. PAULSEN:  These are viscose forces. 
           They've been separated out from the pressure terms.
                       DR. SHACK:  The sheer and the normal you
           can resolve.  It's Floc and the integral of p that
           become confusing.
                       CHAIRMAN WALLIS:  The sheer you can't
           resolve or amend.
                       DR. SHACK:  Well, but you can get an
           integral result.  You can calculate it.
                       DR. KRESS:  You can apply an integral
           equation that's derived or based on the data or
           derived some other way.
                       DR. ZUBER:  What you are really deriving
           are new dynamics.
                       CHAIRMAN WALLIS:  Well, that's
           interesting.  Let's go ahead.  
                       DR. KRESS:  I'm still confused about that
           last term.
                       DR. ZUBER:  That's the point.
                       DR. KRESS:  Because what I view that as is
           the effect on the momentum in changing direction.
                       DR. PAULSEN:  That's what that is.
                       DR. KRESS:  And it seems to me like in a
           one-dimensional equation, you don't have that, because
           your direction is along the stream line, and that's
           what confused me.
                       DR. PAULSEN:  Do you have some insight,
                       DR. PORSCHING:  Well, first of all, that
           equation is -- It's a misnomer.  At this point it's a
           three-dimensional lumped equation that you've gotten
           by taking a --
                       CHAIRMAN WALLIS:  Sir, could you get to
           the microphone and identify yourself for the record?
                       DR. PORSCHING:  Sure.  I am sorry.  I am
           Tom Porsching.  I'm an Americus Professor of
           Mathematics from the University of Pittsburgh.
                       Just by way of insertion here,
           introduction, I was asked a year and a half or so ago
           by EPRI to examine the equations of motion and fluid
           dynamics and see if there was a rational way to derive
           a scalar balance or a scalar relationship of the type
           that is used, as it turns out, in the RETRAN equation. 
           So that's my role.  That's a role I've played in this,
           and just recently received from Mark four or five days
           ago copies of these slides.
                       So I haven't had a real chance to digest
           them, but I notice that the equation that he is
           discussing right now is an evolved version of what you
           could get by taking the Navier-Stokes equations or, if
           you want to lump the viscose terms in a term such as
           that Ffw term, the Euler equations, and integrating
           them over a control volume.
                       The term that you see at the very end
           there, that pndS term over Stot, can be derived, can
           result from the first relationship that I mentioned by
           viewing the pressure gradient term that shows up in
           the Euler equations as really a tensor, a divergence
           of a tensor where the tensor is, in fact, the identity
                       That allows you, after you've done the
           integration over the volume, to use the divergence
           theorem to convert that to a pressure -- to an
           integral over a surface.
                       CHAIRMAN WALLIS:  There's no need to do
           that.  This is simply an overall force balance, and
           it's straightforward.
                       DR. PORSCHING:  Well, maybe.  That's my
           view.  That's the way I view it.
                       CHAIRMAN WALLIS:  You would need no
           Navier-Stokes equations to do this.  The thing which
           is confusing to us, I think, is when we first saw
           this, Bert, Stuart and Lightfoot was involved, and
           Bert, Stuart and Lightfoot make it quite clear that
           they've got pressures over the end areas, and they've
           got a pressure and an S.  That's what you wrote in
           your first documentation that we reviewed.
                       Now we've got something different.
                       DR. ZUBER:  Well, but they have the same
           result.  They have the same result.
                       CHAIRMAN WALLIS:  Well, this, I think, is
           a different story than we saw, because you're invoking
           Bert Stuart and Lightfoot.  You're not invoking
           something that everybody believes.  You're invoking
           something new.
                       DR. ZUBER:  But more than that.  They are
           developing something completely new, because last time
           they obtained relations which are completely different
           from the Bert, Stuart and Lightfoot.
                       CHAIRMAN WALLIS:  That's what is so
                       DR. ZUBER:  It's interesting, wrong,
           amusing or sad.
                       CHAIRMAN WALLIS:  Maybe it's all of the
                       DR. KRESS:  Well, the only place I would
           need that last term, it seems to me like, is if I'm
           trying to determine the response of the pipe to the
           flow and, you know, trying to get the support forces. 
           When I'm looking at the flow itself, I don't need that
                       DR. PAULSEN:  That's right.
                       CHAIRMAN WALLIS:  You don't need that
           term?  The pressure drop between the ends that
           accelerates the flow.
                       DR. KRESS:  Oh, I thought that was in one
           of the other terms.  
                       DR. PAULSEN:  It's included in this term. 
           It's part of this term.
                       DR. KRESS:  I do need that term then, if
           that's what it is.
                       CHAIRMAN WALLIS:  But we'll buy this as
           long as we understand what we're looking at.  But this
           is so obvious, as long as we are clear about what we
           mean, I think we can go on.  
                       DR. PAULSEN:  I think the part of the term
           that you were talking about is going to be the
           integral over this surface area.
                       CHAIRMAN WALLIS:  That's Bert, Stuart and
           Lightfoot have.
                       DR. SCHROCK:  I'm afraid anybody reading
           the record of this meeting would be very confused by
           the composite of the statements that have just been
                       You admitted when I suggested that it's an
           ad hoc equation that, yes, indeed it is an ad hoc
           equation.  Dr. Porsching stood up and told us it's not
           a one-dimensional equation; it's a three-dimensional
           integral representation of a three-dimensional
           situation; and in fact, it is derivable from first
           principles.  But if that is the case, then it's
           incumbent on you to show us how that happens.  How is
           it derived from first principles?
                       So I think the sequence of things that I
           heard in the last five minutes are absolutely self-
                       DR. PAULSEN:  You want this equation
                       CHAIRMAN WALLIS:  This is just momentum
           and force balance.  I think we can move on, as long as
           we are clear what you mean.  Stot is the integral over
           the whole surface, which is the ends and the walls of
           the pipe.
                       DR. PAULSEN:  That's correct, and --
                       CHAIRMAN WALLIS:  And the sheer stress --
           resultant of the sheer stresses is f-squiggle, and we
           can forget about Floc and Fp.  Right?  So we've got
           sheer stresses, pressure forces, gravity, momentum
           fluxes, and they are balanced or not balanced.  If
           they are not balanced, there's got to be an
           acceleration by Newton.  We're not going to question
                       DR. PAULSEN:  Right.
                       CHAIRMAN WALLIS:  So what's the problem? 
           Can we go on?  
                       DR. PAULSEN:  Sure.
                       CHAIRMAN WALLIS:  But now this is going to
           be resolved to make it one-dimensional?
                       DR. PAULSEN:   I hope so.
                       CHAIRMAN WALLIS:  Okay, let's resolve it. 
           You're going to resolve every term in one direction? 
           Are you going to resolve the momentum fluxes in that
                       DR. PAULSEN:  Yes.  And I'm going to have
           to apologize here.  I think your hard copies are
           correct, but when I printed these slides, the Greek
           characters disappeared. So your slides are going to be
           correct --
                       CHAIRMAN WALLIS:  So this says the change
           of the momentum in the I directional, the p to
           whatever you call it -- end direction, whatever.  It's
           the psi direction, right?
                       DR. PAULSEN:  That's right.
                       CHAIRMAN WALLIS:  Is equal to the change
           in momentum flux in that psi direction.  I notice here
           Ak+1 instead of Ak.  So Ak, I think, is different from
           Ak.  You're going to make it the same for some reason?
                       DR. PAULSEN:  At this point --
                       CHAIRMAN WALLIS:  No reason it has to be
           the same.
                       DR. PAULSEN:  At this point, we are doing
           it for a uniform area.
                       CHAIRMAN WALLIS:  No, you're not.  You've
           got Ak+1 that's different from --
                       DR. PAULSEN:  That's right.  That's simply
           to show that where it came from is from the downstream
                       CHAIRMAN WALLIS:  Well, I think you're
           hiding from the fact that if you put in an Ak+1, you
           can't make it go away, you know.  That's what you said
           before.  Dr. Porsching's paper has an A1, n A2 and A0,
           three different areas.  You only have one.  And if you
           use his equation, you get a different answer than you
           get by generalizing your equation.
                       So we have a problem with that. But
           anyway, this is resolved in the direction m, right?
                       DR. PAULSEN:  That's right.
                       CHAIRMAN WALLIS:  And that Fw is some
           resolution of the forces from the wall sheer stresses
           in that direction.
                       DR. PAULSEN:  That's right, or along the
                       DR. PAULSEN:  And the Tg is resolved as
                       DR. PAULSEN:  The what?
                       CHAIRMAN WALLIS:  The g is resolved as
           well?  Should be, right?
                       DR. PAULSEN:  That's right.
                       DR. ZUBER:  What is that delta-p, sub-p?
                       DR. PAULSEN:  Was it this term, Dr. Zuber? 
           It's the pump.  Yes, it's just a source term that gets
           added for volumes that have pumps.
                       So here we have the momentum coming in,
           and this will be the momentum going out the other end. 
           What we have effectively done at this point is dot
           this equation then with the junction normal vector to
           make this a scalar equation.
                       DR. KRESS:  But you don't know that angle
           in general.
                       DR. PAULSEN:  That angle is input.
                       CHAIRMAN WALLIS:  You're free to chose it.
                       DR. PAULSEN:  The user would input that
           angle in his input description.
                       DR. KRESS:  Well, if you are going to then
           take the -- invoke the divergence theory, then doesn't
           that fix that angle for you?  
                       CHAIRMAN WALLIS:  You're getting too
           complicated for me, Tom.
                       DR. KRESS:  Well, the divergence theory
           fixes the point at which the mean value -- I mean the
           mean value theory.  It fixes -- When you invoke the
           mean value theory, that fixes that point and that
                       CHAIRMAN WALLIS:  But you can resolve in
           any direction.  Now this next statement is really
           weird:  "Pressure assumed uniform."  How can you have
           a pressure difference if it's assumed uniform?
                       DR. PAULSEN:  Within each of the control
           volumes --
                       CHAIRMAN WALLIS:  Now you get into a sort
           of a logical --
                       DR. PAULSEN:  This upstream side and the
           downstream side, we're assuming that we have one
           pressure and that it's uniform in --
                       DR. ZUBER:  Well, what difference is that
                       CHAIRMAN WALLIS:  So you're assuming
           something incredibly unphysical.  Right?  In order to
           get on with the problem?
                       DR. PAULSEN:  Well, we really don't know
           the pressure distribution --
                       DR. ZUBER:  Hold on.  Hold on.  What is --
           You mean where you have the arrow in the middle?
                       DR. PAULSEN:  This arrow?
                       DR. ZUBER:  Yes.  You have a pressure
                       DR. PAULSEN:  That's right.
                       CHAIRMAN WALLIS:  You got into something
           absurd here.  Your flow goes around the bend.  The
           bend is like a turbine bucket, and the pressure on the
           outside of the bend is different from the pressure on
           the inside, and that's why it turns.  If you are going
           to assume it's uniform pressure, it's got to go
                       So the whole idea is contrary to physics.
                       DR. ZUBER:  Look, Graham, you see that
           middle point, middle dotted line.  It has a pressure
                       CHAIRMAN WALLIS:  That's right.  I guess
           he has that.
                       DR. ZUBER:  He has.  I mean, this is like
           you have a supersonic flow.
                       CHAIRMAN WALLIS:  But also he assumes the
           pressure on the inside of the bend and the outside are
           the same.  So there's no force to turn the flow to the
           right.  There's nothing that stops the flow from going
           straight up in the air there.
                       DR. PAULSEN:  Except we know that the flow
           has to go through our junction, and we've defined
           those angles.
                       DR. ZUBER:  That is unbelievable.
                       DR. PAULSEN:  It's the pressure balance
           that -- pressure drop balance that really drives the
                       CHAIRMAN WALLIS:  But you see, you -- But
           you're using a momentum balance.  So you've got to
           keep track of forces and directions.  
                       DR. ZUBER:  You know, if you really follow
           fluid dynamics, if you have a pressure discontinuity
           across an interface normal to the flow -- I usually
           call it shock or something -- then you have a velocity
                       DR. PAULSEN:  yes.
                       DR. ZUBER:  And this is what I get.  
                       CHAIRMAN WALLIS:  -- because in the
           original documentation you had a pressure on the
           bottom area and the top area which were the Pk and the
           Pk+1.  All the books do it.  
                       DR. PAULSEN:  And if you do the mean value
           theorem or apply the mean value theorem, you can get
           the pressure at that --
                       CHAIRMAN WALLIS:  You take everything as
           mean.  You lose some of the physics, because the only
           reason it goes around the bend is because the pressure
           is bigger on one side than the other, and taking the
           mean pressure doesn't capture that at all.
                       DR. PAULSEN:  We know that we can make
           fluid flow by using the Bernoulli equation where we're
           just looking at --
                       CHAIRMAN WALLIS:  That's not what we are
           talking about here.
                       DR. PAULSEN:  That's where we're trying to
           get to.
                       CHAIRMAN WALLIS:  Why don't you just use
           it then?  I mean, giving a bogus derivation of
           Bernoulli equation is worst than just invoking it, if
           it's bogus.  Now maybe it's good.  I don't know yet. 
           We are obviously having some difficulty with it.  So
                       DR. PAULSEN:  One of the differences is
           what we have for our time derivative, but the steady
           state form of the equation looks a lot like the --
                       CHAIRMAN WALLIS:  So your equation -- I'm
           going to give you this right angle bend there. 
           There's a 180 degree bend, and you can tell me how
           your forces work for that, if you like.  Would you
           want to do that, because I claim that the momentum
           fluxes are in one direction, the net wall sheer
           stresses in the other.  What's the momentum?  What's
           the direction of momentum?  It's in this direction.
                       DR. PAULSEN:  In RETRAN the momentum will
           be in the direction of whatever you define the
           junction angle to be. 
                       CHAIRMAN WALLIS:  But you're not looking
           at pressure forces on the ends anymore.  It doesn't
           matter what the orientation at the ends is?  It's
           irrelevant?  Seems to me, the orientation of the ends
           in terms of pressure is irrelevant in your model.
                       DR. PAULSEN:  The orientation of the ends
           has to be normal -- or perpendicular to the walls of
           the pipe.
                       CHAIRMAN WALLIS:  Okay.  How does that --
           Just put another coil in the pipe.  Doesn't make any
           difference to your equation.  A little bit more curl
           or something doesn't make any difference.  Yet the
           pressure is acting on a different surface.
                       DR. PAULSEN:  We will definitely get
           different flows in a situation like that if you model
           the actual flow lengths and then the losses that you
           would normally get through a form loss type term.  
                       CHAIRMAN WALLIS:  Well, would it be
           appropriate for you to take my 180 degree pipe and
           show us the Fs and the forces and the momentum fluxes
           and so on?  Would it be appropriate?  He's got
           something you can draw with here.
                       DR. PAULSEN:  Well, I think what we ought
           to do is maybe look at the equation we end up with.
                       CHAIRMAN WALLIS:  But I'm just saying that
           your model should apply to any bend, and you're going
           to resolve it in some direction.  I think, if you look
           at 180 degree pipe, you'll find that the momentum
           fluxes and the pressures that are orthoganol to the
           friction forces in the momentum change.
                       Since yours is general, it ought to apply
           to that, oughtn't it?  I'm just trying to clarify it. 
           if it's general, you've got that thing at the top
           there.  Just put the arrows for the momentum fluxes in
                       DR. PAULSEN:  Are these control volumes or
           is this a momentum cell?
                       CHAIRMAN WALLIS:  It's a momentum cell. 
           Put in the momentum fluxes as you would have them
           going in the ends there.  Maybe you'll be right. 
           Maybe we'll be convinced here.  I don't know.  
                       We need one that works.  Get the one that
           works.  This is government.
                       DR. PAULSEN:  Let's see if this works.
                       CHAIRMAN WALLIS:  You've got momentum
           fluxes coming in there.  Right?  And then going out
           there.  Where is the -- what's the average momentum? 
           It's an incompressible flow, and let's say A1=A2. 
           What's the average momentum in the pipe?  What's its
                       DR. PAULSEN:  Is this -- Okay, so this is
           our momentum cell?
                       CHAIRMAN WALLIS:  Yes, the whole thing is
           a momentum cell.
                       DR. PAULSEN:  At some point we have to
           assign an angle for this thing.
                       CHAIRMAN WALLIS:  Well, let's do that
           later, because we would solve for the overall thing. 
           What is the direction of the overall momentum in the
           pipe there?  It's horizontal, isn't it?  Okay, so it's
                       DR. PAULSEN:  Yes.
                       CHAIRMAN WALLIS:  So it's horizontal.  Now
           what's the direction of the net sheer stresses on the
           wall?  By symmetry, it's also horizontal.
                       DR. PAULSEN:  Right.
                       CHAIRMAN WALLIS:  So your FFW is
           horizontal.  How can that, in the momentum balance,
           balance the pressures at the end which are vertical,
           which you claimed it does.  You said that Moody --
           pressure drop in the pipe is balanced by the sheer
           stress, you said, in the trivial case.  Yet they are
           in opposite direction.  How does it happen?
                       DR. PAULSEN:  Basically, what we have done
           is made this one dimensional so that, in effect, we
           have a straight pipe.
                       CHAIRMAN WALLIS:  You straightened it out.
                       DR. PAULSEN:  That's right.
                       DR. KRESS:  Or another way to say it is
           you've resolved all these things along the stream
                       DR. PAULSEN:  That's right.
                       CHAIRMAN WALLIS:  You had to resolve each
           little bit around the whole thing, but when you
           resolve the whole thing, you've got absurdities.  if
           you take that loop at the bottom there, you've got
           even more absurdities.  You've got that there's no
           change in momentum flux, and the pressures are all --
           There's nothing to accelerate the flow, but we know it
           isn't true.
                       DR. PAULSEN:  That's right.
                       CHAIRMAN WALLIS:  So you haven't done the
           momentum balance, it seems to me.  You've done an
           integration of little pieces of momentum or something
           or you've done a Bernoulli type flow, which is also
           historic with RELAP and all that.
                       DR. PAULSEN:  That's right.
                       CHAIRMAN WALLIS:  But you've really
           confused us by this kind of hybrid, which is neither
           fish nor fowl.  It seems to be a mixture of the two.
                       DR. ZUBER:  Graham, it's violating
           everything we have learned in fluid dynamics.
                       CHAIRMAN WALLIS:  Well, not necessarily.
                       DR. ZUBER:  Graham, look,  they develop a
           discontinuity of pressure -- how can this be?  If  you
           have a discontinuity in pressure, you must have then
           a discontinuity in velocities.
                       DR. PAULSEN:  If you look at any code, and
           they can assume node-wise pressure --
                       DR. ZUBER:  Forget code.  Don't try
           everybody is cheating, therefore I can cheat also. 
           That's another argument here.
                       DR. PAULSEN:  No, that's something that
           comes with difference equations.
                       DR. ZUBER:  No, no, no.
                       DR. KRESS:  It's a finite difference
                       DR. ZUBER:  No.  They assume the same
           pressure, you see, at the entrance, and then a
           different at the exit.  The discontinuity occurs in
           the middle, and you have a pressure jump in the
           middle.  You have to have that independence in
           velocity.  Those are called the jump conditions.
                       CHAIRMAN WALLIS:  You have a real problem
           mathematically to relate the integral of pressure
           around a surface to the integral of pressures
           throughout a volume.  There's a real -- It's not as if
           you've got a gradient of pressure or anything.
                       The volume integral of pressure is a
           different animal from the surface integral of
           pressure, and yet you are saying your volume integral
           of pressure you used for your code in the thermal-
           dynamics can somehow be borrowed and immediately
           transported into some surface integral of pressure,
           which is the kind of thing that the Porsching
           influence has led you to, because the other one didn't
           work out very well.  But you just have another
           mathematical problem then, I think, when you do that.
                       It may be that, if you really acknowledge
           these and really say, well, we made that assumption
           because that's the only thing we knew how to do, then
           Novak can get as blue in the face as he likes, but at
           least you've said that's what we've done.
                       DR. ZUBER:  Oh, no.  I agree.  If they
           would say, Graham, this was wrong; the effect of this
           error is such and such, and it took us many
           calculations to show that this is not the important
                       The problem I have here, they don't want
           to acknowledge candidly the wrong formulation, the
           wrong results, and I don't agree that they have done
           sufficient sensitivity calculations.
                       CHAIRMAN WALLIS:  The difficulty, Novak,
           is that the code has some formulation in it, and all
           this story has developed and ways to try to justify
           what someone has put in the code for reasons which the
           present users may not even believe.
                       DR. ZUBER:  Well, the trouble is then you
           have to say to the public we have really codes we have
           to believe in that you flunk a junior student on that.
                       CHAIRMAN WALLIS:  Well, let's see now.  I
           don't know.  Do you see the problem I have with the
           180 degree bend?
                       DR. PAULSEN:  Yes.
                       CHAIRMAN WALLIS:  It's that the forces are
           in different directions, and I don't know how you
           resolve them in any direction to get your equation. 
           That's all.   Maybe you can think about that after
           lunch or something.
                       DR. SCHROCK:  It seems to me that that
           problem is present for any degree of bend, isn't it?
                       CHAIRMAN WALLIS:  Anything except a spring
                       DR. SCHROCK:  The fact that the forces
           that are described in these what I'm calling ad hoc
           equations are simply not in the same direction. 
           Therefore, it's a little difficult to understand how
           they can represent a force balance.
                       DR. PAULSEN:  And in fact, we may be
           better off just saying that we are doing it for a
           straight piece of pipe and elbows are handled --
                       CHAIRMAN WALLIS:  You could use what I
           call the two-pipe plus junction model, which is what
           you almost do.
                       DR. PAULSEN:  That's what we've attempted,
                       CHAIRMAN WALLIS:  But you haven't, because
           you've tried to then resolve it.  You've got the
           vector thing mixed up.  Two-part plus junction model
           works if the pipes are in any -- Here's a pipe. 
           Here's a junction.  Here's not a pipe.  Doesn't matter
           where it is, as long as you've got that, but you've
           confused everything by calling it a vector equation
           and resolving it.
                       DR. PAULSEN:  I think I see where you are
           coming from now.
                       CHAIRMAN WALLIS:  It's taken a long time.
                       DR. PAULSEN:  Well, some of it is, I think
           -- Well, yes.
                       CHAIRMAN WALLIS:  California is a long way
           from New England.  I know that.
                       DR. PAULSEN:  Well, some of it may have
           helped if we could have worked with --
                       CHAIRMAN WALLIS:  Well, you've got a
           Californian here, too.  
                       DR. PAULSEN:  Things have been kind of
           indirect, I guess.
                       DR. ZUBER:  Two years ago, I mean, we
           discussed some of these things.
                       MR. BOEHNERT:  What's this got to do with
                       CHAIRMAN WALLIS:  Well, that's why it
           takes a long time.  I mean time and distance.  No, I
           don't think we want anymore comparisons like that.
                       DR. PAULSEN:  The next step in the
           development is based on the assumption that we have
           spatially uniform pressures.
                       CHAIRMAN WALLIS:  Yes, but then you
           shouldn't be doing this hairy -- You've cast this
           hairy surface integral when you've already assumed the
           problem away by having it uniform is really strange.
                       DR. ZUBER:  Well, it's wrong.  It's not
           strange.  It's wrong, because if you do that and you
           have -- discontinuity, and that's not physics.  
                       DR. PAULSEN:  Well, with the finite
           difference codes there is always pressure differences
           in each node.
                       CHAIRMAN WALLIS:  What you are doing --
           Okay, you're going -- you're doing this whole
           integral, and essentially you are getting some sort of
           a surface average pressure over the entire surface.
                       DR. PAULSEN:  Yes.
                       CHAIRMAN WALLIS:  That's essentially what
           you are doing, and I'm saying mathematically that is
           not the same thing as some volume integral of
           pressure, which is what you use in your thermal-
           dynamics.  So there's a sleight of hand at a different
           level going on here.  
                       DR. PAULSEN:  In the thermal-dynamics we
           only know mass and energy on a global basis.
                       CHAIRMAN WALLIS:  But you know a thermal-
           dynamic pressure.
                       DR. PAULSEN:  Pardon me?
                       CHAIRMAN WALLIS:  You know a thermal-
           dynamic pressure.
                       DR. PAULSEN:  That's right.
                       CHAIRMAN WALLIS:  So when a flow goes
           around a bend, it goes around because the pressure on
           one side is greater than the pressure on the other,
           and an average pressure of thermal-dynamics -- we will
           never reflect that.  Never.
                       DR. PAULSEN:  Okay.
                       DR. ZUBER:  Okay.  Do you agree with the
           statement that Ralph made that this derivation is
                       DR. PAULSEN:  Well, I think we can show by
           comparison with simple experiments, simple thought
           problems that the resulting equations reproduce
           reality.  We can actually do comparisons of
           expansions, contractions, T's where we actually
           reproduce reality.
                       DR. SHACK :  Well, and you can't apply
           your equations to a straight pipe.
                       DR. PAULSEN:  That's right.  
                       CHAIRMAN WALLIS:  And I think what happens
           in RELAP, though it's very difficult to get them to
           say that, but every time that people come up with a --
           They've come up with the RELAP documentation.  All
           they do is analyze a straight pipe.  
                       Then they say, well, here's a straight
           pipe, a straight pipe, a straight pipe.  A bend turns
           out to be a sequence of straight pipes, but they never
           tell you that up front, we're going to model
           everything as a straight pipe.
                       DR. ZUBER:  Graham, it is not even that. 
           They cannot even apply to a straight pipe, and we
           shall come to it, because what you have in this
           handout, it doesn't apply to a straight pipe.  It goes
           contrary to whatever we have in Bert, Stuart &
           Lightfoot.  Your results here --
                       CHAIRMAN WALLIS:  Well, let's do this
           integral over the areas.  I guess we're going to have
           to do it.  What you essentially come down to is this
           Pk, Pk+1 times Ak.  
                       DR. PAULSEN:  That's right.
                       CHAIRMAN WALLIS:  And the Pk is really a
           definition of a pressure over an entire area composed
           of the pipe and the end, which does not include the
           junction.  It's that whole surface of whatever it is
           that wiggles and squiggles and everything which does
           not include the junction.
                       DR. PAULSEN:  Yes.
                       CHAIRMAN WALLIS:  Because it's a very
           funny pressure.  It's some sort of average pressure
           over all the surface there.
                       DR. ZUBER:  But Ak is a surface normal to
           the --
                       CHAIRMAN WALLIS:  Well, in Porsching A is
           A0.  It's different, and that's what I was pointing
           out to you earlier, that if you take the Porsching
           equation with an A0 there, then your equation -- it
           looks different.  Your pressure difference multiplies
           an A0.  When you divide it through by it, it's not the
           same as Ak.  
                       DR. PAULSEN:  Right.
                       CHAIRMAN WALLIS:  So his equation is not
           the same as yours, even if you believe this.  But this
           Pk and Pk+1 are not the same as the Pk that are in Bert,
           Stuart and Lightfoot, which are on the ends of the
           pipe.  They are an average over the whole wall and the
           end, coming all the way back to this.
                       DR. ZUBER:  See, but Graham, it is
           integrated over one normal area, k, which assumes that
           Ak and Ak+1 are equal.  
                       CHAIRMAN WALLIS:  Well, it's the junction
           area, really.  In Porsching's paper it's an A0, which
           is like a middle of the pipe, not the ends at all.
                       DR. ZUBER:  But you don't know what that
           A0 is.
                       DR. PAULSEN:  And then this uniform pipe--
                       CHAIRMAN WALLIS:  Doesn't have to be
           uniform.  All that needs to be is the area of the
           junction that cuts the middle of your picture. 
           Doesn't have to be uniform pipe for the Porsching
           approach.  But then you can't divide through by Ak and
           get your answer, because A0 isn't the same as Ak.  
                       So even if you believe Porsching and even
           if you are willing to say Pk, Pk+1 equals the same
           pressures as the sum dynamic pressures, you still have
           a problem with the areas being --
                       DR. SHACK:  Well, no.  Porsching is
           rigorous.  It's just that you don't know where the P
           is evaluated.  I mean, it's a mean value over some
           portion of the surface.  There exists a point at which
           that statement is true.
                       DR. ZUBER:  No, it is not, because here's
           the equation, and here are uses, and we can't bring it
                       CHAIRMAN WALLIS:  There's another
           Porsching paper, though, a more recent one, which
           seems to realize that there's a problem here, and it
           sort of works for a straight pipe and it works for a
           pipe with a slight bend in it, but you have a problem
           when you have big bends because of the surface
                       So there's a learning process going on
           here which is fascinating to watch.  It's a difficult
           problem.  I think what you have to do is face up to
                       I wrote a tutorial on the momentum
           equation.  I guess you haven't seen it.  Here's the
           momentum equation.  Here's why it's very difficult to
           use and, therefore, you have to make assumptions and
           so on, and these are the kind of things people have
                       I think that would be a much better
           presentation than this sort of attempt to do something
           rigorous that gets people a little hot under the
           collar, because they say, how can you do that?
                       DR. PAULSEN:  But in general, where we are
           trying to go is to something that looks like the
           Bernoulli equation.
                       DR. ZUBER:  Well, then you could have
           started with Bernoulli.  Let me ask you something. 
           Are you familiar with a book by Ginsberg, this book?
                       DR. PAULSEN:  No.
                       DR. ZUBER:  It was translated by NASA 30
           years ago, and he deals with this problem.  It's the
           best book I saw on this approach, and I would strongly
           advise you, go and read it, and also, too, NRC.
                       CHAIRMAN WALLIS:  So if this were
           Porsching, you would have Ak and Ak+1 instead of Ak in
           there, and you would have -- They are still resolved
           in some direction psi?
                       DR. PAULSEN:  Yes.
                       CHAIRMAN WALLIS:  And then you would have
           A0 in there, and A0 depends on what psi is.  You
           change psi, you change A0.  Is that right?
                       DR. PAULSEN:  Yes.  They go together.  So
           this ends up being our scalar equation where this is
           our time rated change of momentum in our momentum
                       Then we use some definitions, a geometry
           term.  This ends up being the volume of the momentum
           cell where it's just based on half the length of the
           upstream and the downstream volumes.
                       CHAIRMAN WALLIS:  But those were in
           different directions.  
                       DR. PAULSEN:  What's that?
                       CHAIRMAN WALLIS:  Those are in different
           directions.  When the cell -- Now it's a bend.  Those
           L's are in different directions.  So don't the momenta
           have to be resolved in some way?  And you seem to be
           resolving the momentum flux and not resolving anything
           else.  The momentum has to be resolved in the two
           pipes.   You got two pipes here, right?
                       DR. PAULSEN:  We have two pipes.
                       CHAIRMAN WALLIS:  And you got to resolve
           that momentum.  Have you?
                       DR. PAULSEN:  Well, we think we have.
                       CHAIRMAN WALLIS:  See, you can't do it
           that way in general.  
                       DR. PAULSEN:  Well, let me take a look at
           this next step then.
                       (Slide change)
                       DR. PAULSEN:  Basically, what we've done
           then is defined that time rated change of momentum to
           be basically a flow term.  There was a geometry term
           factored out.
                       CHAIRMAN WALLIS:  It's like a pipe.
                       DR. PAULSEN:  That's right.
                       CHAIRMAN WALLIS:  You've got two pipes is
           what you've really got.  
                       DR. PAULSEN:  It is two pipes.  That's
                       DR. ZUBER:  But the same area.
                       DR. PAULSEN:  Two pipes here with the same
                       CHAIRMAN WALLIS:  They don't have to have
           the same.
                       DR. PAULSEN:  That's right.  
                       CHAIRMAN WALLIS:  You get an L over A or
           something, whatever it is.  
                       DR. PAULSEN:  That's right.
                       DR. ZUBER:  But then they would not get 
           the pressure.  
                       CHAIRMAN WALLIS:  See, and when you -- The
           thing I find difficult is what am I looking at?  The
           RETRAN flow equation, when it appears later, has an
           Ak2 and it has an Ak12 in there.
                       DR. PAULSEN:  That's right.
                       CHAIRMAN WALLIS:  Which is simply written
           down.  Now if you are going to derive it, you better
           have a pipe which has a different area in and out
           rather than just generalizing something without any
                       DR. PAULSEN:  Okay.  That's the next step.
                       CHAIRMAN WALLIS:  If you look at
           Porsching, it shouldn't be Ak+12 anyway.  It should be
           Ak+1A0, even if you believe Porsching.  So you can't
           just say it's a pipe of constant area and then write
           down an equation with no explanation for a pipe with
           bearing area.
                       DR. PAULSEN:  Well, the next step is to

           try and show you how we have come up with the equation
           for --
                       CHAIRMAN WALLIS:  The way you've done that
           is with two pipes which are straight.
                       DR. PAULSEN:  Two straight pipes and
           connect them with the mechanical energy equation.
                       CHAIRMAN WALLIS:  So you are essentially
           saying we're going to take any old bend of any shape--
                       DR. PAULSEN:  That's right.
                       CHAIRMAN WALLIS:  -- and model it as two
           straight pipes.
                       DR. PAULSEN:  That's right.
                       CHAIRMAN WALLIS:  Or any shape of any kind
                       DR. PAULSEN:  That's right.
                       CHAIRMAN WALLIS:  Like a cobra that
           swallowed a pig, and it's got a big bulge in the
           middle --
                       DR. PAULSEN:  That's right.
                       CHAIRMAN WALLIS:  But he still treats it
           as a straight pipe.
                       DR. PAULSEN:  That's correct.
                       CHAIRMAN WALLIS:  So I think that's what
           you've done.
                       DR. PAULSEN:  Yes, it is.
                       CHAIRMAN WALLIS:  All this other stuff is
           very misleading.
                       DR. SCHROCK:  Was this last equation one
           that you can put a number on in the EPRI report,
           RETRAN report?
                       DR. PAULSEN:  I am not sure if I've got
           the latest copy that was mailed.
                       DR. ZUBER:  I think it's 236 or something
           like that.
                       DR. PAULSEN:  Must be about 2.3.
                       CHAIRMAN WALLIS:  2.3.10 is in revision 5.
                       DR. PAULSEN:  It's more like 10.  Twenty-
           six is the one after we get some of the area change.
                       DR. ZUBER:  You are right.
                       CHAIRMAN WALLIS:  It's 2.3.10 in 5. 
           There's 5(b) where it's somewhere else.  In version
           5(b) it's 2.3.10.
                       You see, you write down the average
           momentum of cell is All k over 2 plus All k plus 1
           over 2 times W. Well, that's not resolved in any
           direction.  Okay.  
                       (Slide change)
                       DR. PAULSEN:  So what we have come up with
           then is a scalar equation of motion.
                       CHAIRMAN WALLIS:  Wall forces disappear.
                       DR. PAULSEN:  We have the pressure force
           in effect and the --
                       CHAIRMAN WALLIS:  You see, the problem
           with wall forces disappears -- we know that the sort
           of token bucket turns the flow because of a wall
           force.  You can't make it disappear.  Even someone who
           knows no math at all will tell you the force on the
           wall becomes as a momentum balance.  Don't need to
           know any math at all.
                       DR. KRESS:  But momentum is made up of
           direction and mass times velocity.  So wall forces
           generally only affect the direction.  If you're
           talking about integrating along a stream line, I think
           those wall forces just sort of change the direction,
           and you don't really need them.
                       CHAIRMAN WALLIS:  As long as you don't
           have things like changes of area.
                       DR. KRESS:  That's right.
                       DR. PAULSEN:  And that's basically what's
           being done, is integrating along the stream line.
                       CHAIRMAN WALLIS:  See, you don't use that
           rationale at all.
                       DR. KRESS:  If you had started with that
           rationale, I think we would have a lot less trouble.
                       DR. PAULSEN:  Okay.  
                       CHAIRMAN WALLIS:  See, I don't know what
           we are doing here.  Are we helping you to devise an
           acceptable rationale?
                       DR. PAULSEN:  Well, I think we're coming
           to understand maybe where your problems are.
                       CHAIRMAN WALLIS:  I thought they were
           obvious two years ago, but nobody listened.  
                       DR. PAULSEN:  I think we've covered them
           in a little more depth now, and I think --
                       CHAIRMAN WALLIS:  You went back to the
           same sort of thing.  Except for the Porsching
           rationale, you really have the same.
                       DR. ZUBER:  Since you see where we are
           coming from, you know where you are going to?  I'm
           quite serious.  I mean, you see our problems,
           basically dynamics.  Hopefully, you said you have that
           equation you agreed to.  Now where are you going?
                       DR. PAULSEN:  Well, that's not my
           decision.  That's up to EPRI, but I think we can relay
           word that we now understand your concerns, and maybe
           be able to come up with a resolution.
                       DR. ZUBER:  See, what they said about this
           -- This was obvious two years ago.  For whatever
           reason, arrogance or ignorance, you never addressed
           it, and now it's facing us straight, and you are
           putting kind of a burden on NRR.  We are becoming
           critical, and you are just writing --
                       DR. PAULSEN:  Well --
                       CHAIRMAN WALLIS:  That's very unfortunate.
                       DR. ZUBER:  It is really sad and very
           inefficient way of using money and time.
                       DR. PAULSEN:  Well, we tried to work with
           the staff, and I think their intention was to try and
           relay your concerns.
                       DR. ZUBER:  Well, you were here at the
                       DR. PAULSEN:  And our intentions were to
           try and resolve those concerns, and somehow between
           the two of us we didn't.
                       CHAIRMAN WALLIS:  I was wondering if we
           could go to the next one before lunch, just to get it
           out of the way.
                       DR. SHACK:  I still have one problem, even
           with this equation.  That is your momentum term is
           really a V.NC, and you've lost the V.NC and replaced
           it with the V-Normal.
                       DR. PAULSEN:  This equation?
                       DR. SHACK:  Yes.
                       DR. PAULSEN:  Okay.
                       DR. SHACK:  If you just go back a step, go
           back to 11 or go back to 9 -- 
                       DR. PAULSEN:  Is it on 11 or is it 9?
                       DR. SHACK:  Well, try 9, because that
           shows the dot product.  Okay, now how does V-dot-n-phi
           end up as V-normal?  So it's V-dot-n-phi on this graph
                       DR. PAULSEN:  On this graph?
                       DR. SHACK:  No, no, on the lefthand side
           of the equation, V-dot-n-phi.  Now go to 11, and it's
           just V.  You've lost the dot product.
                       CHAIRMAN WALLIS:  Right.  He hasn't
           resolved the momentum.
                       DR. SHACK:  You haven't resolved the
                       CHAIRMAN WALLIS:  No, he hasn't.  
                       DR. SHACK:  You better stick to a straight
                       CHAIRMAN WALLIS:  That's what I was
           saying.  With two straight pipes, he's got his L1 and
           L2.  He doesn't resolve them in any way. 
                       Now there is a problem.  I guess we can't
           leave it alone.  This W that you have here resolved --
           W is a scalar.
                       DR. SCHROCK:  That's right.
                       CHAIRMAN WALLIS:  So when you start
           resolving W, as we'll see if we get to it at the flow
           around the bend, you get into real problems.  I think
           we totally disagree with your momentum flux terms and
           even the simple thing of your example of flow around
           the bend.
                       DR. SHACK:  But his W-phi is just V
           multiplied by Row A.  Then he divides by Row A.
                       CHAIRMAN WALLIS:  Yes, but you see, when
           you look at his flow around the bend, the momentum
           term in there doesn't fit any of the patterns.  It's
           something else.  So maybe you have to have lunch
           first, but we are going to get to that, I think, too.
                       So there's a danger in saying W resolved
           in the direction, because W is a scalar quantity.  You
           have to be very careful about it.  I think it's
           possible to do it, but you have to be damn careful
           that you know what you are doing -- what you mean by
           it, because it's not a physical quantity.  It's
           something you've artificially contrived.
                       DR. PAULSEN:  One of the things that we
           have corrected was that there was an error in the
           momentum flux term that Dr. Wallis pointed out --
                       CHAIRMAN WALLIS:  This was the cosine of
                       DR. PAULSEN:  There was a missing cosine
           or an extra cosine.  There was an extra cosine, and
           that has been corrected.
                       DR. SHACK;  So you got rid of one, and you
           lost another one.  
                       DR. PAULSEN:  And as we have mentioned,
           we've had Dr. Porsching review this, and --
                       CHAIRMAN WALLIS:  That's very interesting. 
            I found that interesting to read.  But of course,
           there is a long history of fluid mechanics and
           attempts to deal with this sort of problem.  So either
           there's a revolutionary insight or -- May be, but
           strange it comes out of the blue.
                       I think what the difficulty with the first
           Porsching paper was that the kinds of averaging to get
           the pressures somehow got confused.  Pk, Pk+1, in yours
           weren't the same as in his, and all that.  I think you
           have tried to resolve that now.
                       DR. PAULSEN:  I think so.
                       DR. ZUBER:  Did you say tried?
                       CHAIRMAN WALLIS:  Tried to, yes.  I said
           tried to.
                       DR. PAULSEN:  And this was basically the
           incorrect term where this -- we basically had that Pk
           resolved in that psi direction squared.  As a result
           of that, we have looked at what effect that might have
           on users in the field using the code.
                       We filed a trouble report probably about
           two years ago that identified that to users, and we
           went back and looked at how that error might effect
           situations.  As it ended up, it was probably
           fortuitous, but most user models have angles of zero
           or 90 degrees where that error doesn't actually show
                       CHAIRMAN WALLIS:  I think, when we get to
           -- I think this afternoon we should look at sort of
           your bend model and your downcomer and so on.  I think
           I still have real troubles with your angles, because
           you have sort of momentum, if it's going out in this
           direction, it's resolved -- disappears, because it's
           in the Y direction and not the X direction; whereas,
           in reality the momentum in the whole thing has to be
           accelerated somehow.
                       So we have some problems with angles of 90
                       Can we very quickly look at the abrupt
           area change, because I want -- Your original figure
           was better than the new one, because it actually
           showed the sort of discontinuity, implying that these
           were long pipes.
                       DR. PAULSEN:  That these are?
                       CHAIRMAN WALLIS:  This sort of model of
           one-dimensionalizing this problem only works if the
           pipes are long.
                       DR. PAULSEN:  That's right.
                       CHAIRMAN WALLIS:  And then there's a
           junction in between.  So it's what I call the two-
           pipe-plus-junction model.
                       DR. PAULSEN:  That's right.
                       CHAIRMAN WALLIS:  And you use a straight
           pipe theory, which everyone can agree on, for each
           pipe.  So we don't need to go over the equations. 
           Then you do some -- You say the pressure drop is given
           by some sort of empirical thing.  Then you eliminate
           the pressures, and this is two pipe plus junction
                       DR. PAULSEN:  That's correct.
                       CHAIRMAN WALLIS:  It's simply saying that
           everything is straight pipe and junction; putting two
           pipes and a junction together is just a generalization
           of something more fundamental.
                       DR. PAULSEN:  That's correct.
                       CHAIRMAN WALLIS:  But then you say you're
           going to resolve these Ws in the psi direction.  You
           don't do that for the straight pipe, and you can't do
           it now.
                       DR. PAULSEN:  Well, that's the junction. 
                       CHAIRMAN WALLIS:  You can't do it now.
                       DR. PAULSEN:  Do we say that?  
                       CHAIRMAN WALLIS:  Yes.  Your slide number
           20 has the Ws in the psi direction, and that's
           inappropriate for the two pipe plus junction model. 
                       DR. PAULSEN:  Basically, for straight
           pieces of pipe.
                       CHAIRMAN WALLIS:  No, that's the only
           thing you are analyzing, is two straight pieces of
                       DR. PAULSEN:  Yes, that's right.
                       CHAIRMAN WALLIS:  And if you start --
                       DR. PAULSEN:  These will be the same.
                       CHAIRMAN WALLIS:  If you start resolving
           in the psi direction, you get the wrong answer.  You
           don't get Bernoulli's equation.  You've got to get
           these squared over two.  You don't get it, if you
           start resolving in a psi direction.
                       In fact, if you start saying that -- Say,
           if it's a momentum balance in the X direction,
           anything in the Y direction gets thrown away, you get
           the wrong answer.  
                       DR. PAULSEN:  For the straight piece of
           pipe, this would end up being -- All angles would be
           the same.
                       CHAIRMAN WALLIS:  So you've got two pipes
                       DR. PAULSEN:  That's right.
                       CHAIRMAN WALLIS:  And you are now going to
           resolve -- You are mixing up two ideas of the bend and
           the two pipes.  Two pipes can be joined with a
           junction, but these squareds are the P squareds in
           those pipes and not resolved in any way whatsoever.  
                       DR. PAULSEN:  The what now?
                       CHAIRMAN WALLIS:  Two pipes like this.
                       DR. PAULSEN:  Okay.
                       CHAIRMAN WALLIS:  You analyze this one. 
           You analyze that one.  You analyze the junction.  You
           eliminate the pressure drops of the junction.  You get
           the pressures at the end.  You end up with P squared. 
           You don't end up with Wk, Wk over Ak2, WK-phi.  You
           end up with P2 here and P2 there, and not resolved
                       That's why you need Bernoulli's, because
           you are going to take that final thing there with the
           W2 over 2, combine it with the first two terms, and
           show that it looks like Bernoulli's equation for a
           last list system.
                       DR. PAULSEN:  That's right.  
                       CHAIRMAN WALLIS:  That won't happen if you
           have a psi in there.  
                       DR. PAULSEN:  That's right.
                       CHAIRMAN WALLIS:  You've got to have a W2
                       DR. PAULSEN:  These cases, that psi would
           all be the same angle.
                       CHAIRMAN WALLIS:  Shouldn't be there.
                       DR. PAULSEN:  Yes.
                       CHAIRMAN WALLIS:  No, it shouldn't be
           there at all.  If you have flow coming in and going
           out at different angles, you don't resolve those terms
           for the two pipe model.
                       DR. PAULSEN:  Okay.  
                       CHAIRMAN WALLIS:  Think about it.  Just do
           it.  So you've somehow mixed up your idea that you are
           resolving momentum with something like this, which
           really is a flow equation --
                       DR. PAULSEN:  Yes.
                       CHAIRMAN WALLIS:  -- which is blessed by
           the NRC since time immemorial, because they didn't
           know what else to do, but it didn't have the psi in
                       DR. PAULSEN:  That's right.
                       CHAIRMAN WALLIS:  And in trying to do
           something better, I think you've produced something
           which logically doesn't make sense anymore.
                       DR. PAULSEN:  And as we'll see maybe after
           lunch, there are several places where we use angles,
           and --
                       CHAIRMAN WALLIS:  Well, maybe after lunch
           we should look at that bend model where you actually
           take -- you lead us through, and you actually develop
           the momentum in and out, and you have this strange
           thing, the Wx is W over 2 and Wy is W over 2, all that
           stuff.  Can you lead us through that?
                       DR. PAULSEN:  Which case is that now?
                       CHAIRMAN WALLIS:  That's the simple bend
           which we had as an example, sort of the first thing I
           tried to understand, this one here in the documents to
           RAIs, momentum cells for an example elbow. And you
           have statements such as W-4Y is a half-something or
           other and all these things.  You have things about W2
           being a half-W-3.  W2y being half-w-3, all those
           things.  Can you lead us through that?
                       DR. PAULSEN:  Okay.  Where are we heading
           with that, I guess?
                       CHAIRMAN WALLIS:  I think with that, it
           shows a fundamental misunderstanding of how to
           evaluate these momentum flux terms.  But maybe you can
           convince us. 
                       You see, the difficulty I have is you may
           be doing something using a different logic from what
           we are used to, and we are trying to figure out what
           that logic is.  It may first appear to be wrong.  It
           may be that, when we follow your logic, we say, well,
           maybe if you think in this way, which may be unusual,
           one could justify it or something.
                       DR. PAULSEN:  Where there's an assumption
           made that's not apparent.  
                       CHAIRMAN WALLIS:  Right.
                       DR. PAULSEN:  Okay.  I don't have a slide
           on that.
                       CHAIRMAN WALLIS:  I think you ought to
           think about this over lunch, this psi thing with the
           two, because I think we are -- ACRS might accept the
           two pipe plus junction model if that's the only thing
           anyone knows how to do, and you got to get on with the
           problem, realizing that it contains assumptions.  But
           this sort of mixture of things where it doesn't really
           make sense, and there are statements that, you know,
           say that the pressure drop is balanced by the friction
           and all the other terms disappear is not true, if
           you're just making a momentum balance.  But it is true
           if you're making a stream line.
                       DR. PAULSEN:  That's right.
                       CHAIRMAN WALLIS:  So it's those kind of
           untrue statements that bother us.  The answer may be
           something which is usable.
                       DR. PAULSEN:  Okay.  
                       CHAIRMAN WALLIS:  So is it time to break
           for lunch?
                       DR. PAULSEN:  And the stream line argument
           kind of carries over into the complex geometry
                       CHAIRMAN WALLIS:  But you've got to be
           careful.  You know, when stream lines get mixed up,
           they are no longer stream lines.
                       DR. PAULSEN:  That's right.
                       CHAIRMAN WALLIS:  They don't follow a
           stream line.  So you can get bogus answers by trying
           to follow a stream line.  But I think we'll all agree
           that there isn't a simple answer to this momentum
           balance problem when you try to write a code, and
           you've done -- You've made a valiant attempt.
                       DR. PAULSEN:  Okay.  More after lunch.
                       CHAIRMAN WALLIS:  So we will adjourn until
           one o'clock.  We'll have a break, a recess until one
           o'clock.  Thank you very much.  
                       (Whereupon, the foregoing matter went off
           the record at 11:57 a.m.)
                                A-F-T-E-R-N-O-O-N   S-E-S-S-I-O-N
                                                    (1:00 p.m.)
                       CHAIRMAN WALLIS:  We will come back into
           session and continue our discussion of the RETRAN-3D
           code.  We have a request from Jack Haugh of EPRI to
           make a statement at this time.
                       MR. HAUGH:  Thank you, Dr. Wallis.  I
           appreciate that.  Again, for everyone, my name is Jack
           Haugh.  I'm the Area Manager, which is EPRI-speak for
           program manager for a variety of areas, including most
           of the safety work, and the RETRAN work rolls up to me
           in a managerial sense.
                       I think my remarks were intended to say,
           well, I always like after a couple of hours of
           discussion going on to kind of say where are we in all
           of this?  I think the message I would like to convey
           is severalfold.
                       The first is that, regarding RETRAN
           itself, as has been pointed out, this code was
           developed as an offshoot or a derivative from older
           RELAP versions and so on, and there is historical
           material in the code development and documentation,
           and there are equations written and so on.
                       Clearly, the results of the in depth
           considered review by the ACRS, for example, has
           demonstrated that there are places where the approach
           taken to try and derive a set of equations that can be
           used has its shortcomings.
                       There have been points raised, exceptions
           noted, etcetera, to point out that it doesn't quite do
           the job that it needs to do, and that there is a
           seeming rigor or academic rigor to it that is, in
           reality, not really there.
                       Had we to do this all over again, 20 years
           ago, knowing what we know now and thanks in great part
           to the critiques and the study given by the ACRS, it
           would have been done differently.  
                       I think -- You know, I heard some comments
           before dealing with the momentum equation.  According
           to Graham, it's a very difficult thing to do, that we
           have made, I think he said, a noble attempt.  Novak
           said an heroic attempt, which I must say heroism is
           wonderful, but I don't know.  
                       If it gets you into trouble in the end,
           maybe it's not so smart, but the bottom line is, you
           know, I think your observations had, had you started
           with something more simple -- you know, go to friend
           Bernoulli, make a few statements that you're
           connecting a bunch of linear segments -- Assuming you
           have a straight pipe, you accommodate some of these
           things like the bends and the separation around the
           bends and the awkwardness with pressures and so on. 
           You take a loss term in there, and you try and just
           fit it in there, and you come up with this quasi-
           empirical sort of thing which you tune to the plant
           and which you utilize or demonstrate its applicability
           to your own minds by how you match the plant
           conditions.  What else needs to be said?
                       All right.  Now --
                       DR. ZUBER:  Sensitivity analysis.
                       MR. HAUGH:  I beg your pardon?
                       DR. ZUBER:  Sensitivity analysis.
                       MR. HAUGH;  Yes.  I mean, that's always an
           important thing, because you need to know the range of
           applicability of things.
                       CHAIRMAN WALLIS:  There is something else
           that needs to be said.  I've said it this morning. 
           There's a public out there watching.  It's not just
           you and the plant and the NRC that are in this.  There
           is a theater as well of public opinion.
                       So it has -- you have to say things in a
           way which is not going to give people qualms.
                       MR. HAUGH:  Yes.  Well, we certainly
           appreciate that, and I can assure both the committee
           and the public that that is certainly always our
           intent as EPRI.
                       Now at this point now it becomes where do
           we go from here, having said what I just did.  I had
           thought that, rather than belaboring the point by my
           assuring you that we understand the message that has
           been given to us, that continued working our way the
           equations and finding the exceptions or the confusions
           and so on is perhaps not the best utilization of your
           time this afternoon, nor is it mine.
                       CHAIRMAN WALLIS:  Well, there is one thing
           I would like to do, though.  I would like to look at
           this bend example, because it seems to show -- You
           know, it's actually how you use something.  It's not
           just a derivation.
                       MR. HAUGH:  If you wish, we would be very
                       CHAIRMAN WALLIS:  I have some problem with
           even if you believe the equation, how do you use it
           the way you use it.  So I think we need to do --
           That's the second part of my thing.
                       First, you have to establish the
           equations.  Then you have to sort of show that they
           can be used in a sensible way, and then you have to
           show that they give good results for a plant.
                       MR. HAUGH:  Yes.  And that is where, from
           my perspective, I would like to see the discussion
           ultimately move today.  That is to say, we finally
           come up with some formulation that we believe works
           and can be utilized in a computer code and can be
           utilized to replicate the plant transients within
           ranges of applicability, and that if those ranges are
           understood by the users -- and we take pains to be
           sure that they do understand those ranges of
           applicability -- that the demonstrations that we can
           match the plant data are very important, a very
           important consideration to see that the tool is useful
           for its purported purposes.  
                       That's all I would like to leave you with
           at the moment, and hope that we can get onto that
           first presentation that the Chairman has asked for,
           and then to what we have done by way of validation.
                       CHAIRMAN WALLIS:  So we've already --
           Perhaps you are suggesting -- We forget the first
           question I asked, which is what equations you are
           using and are the derivations valid.  We've already
           been over that terrain.  You don't want to go over it
                       MR. HAUGH:  Yes.  I think, you know, it's
           been made quite clear today that there are
                       CHAIRMAN WALLIS:  Right.  And now we've
           got to look at how they are used.  I think the bend is
           an example.  I would personally like to see how you
           propose to use them for something like this, you know,
           the downcomer and the lower plenum, because that was
           all that we got response to the RAI is this is how we
           set up the cells.  
                       I couldn't figure out in any way how you
           write a momentum equation for those cells as set up. 
           If we could get some guidance and if you are ready to
           do that --
                       MR. HAUGH;  Well, I'll ask Mark to come up
           here.  I'm not sure to what degree of completeness he
           has that laid out, but we'll ask him to do so.
                       CHAIRMAN WALLIS:  If it's not completed
           here and then you want to come before the full
           committee next week, we are going to have to say that
           we still have a lot of unresolved issues, and it might
           make more sense for you and us to agree that these are
           the unresolved issues, and then for us to meet as a
           subcommittee so before we go to the full committee
           with all that's implied there and letters to the
           Commission and all that stuff, we actually have some
           better understanding of what you think in the final
           version of things is sort of an acceptable
           presentation before that committee.  I think we need
           to do that.
                       MR. HAUGH:  Well, perhaps that is the
           better way to proceed at this point.
                       CHAIRMAN WALLIS:  It would really be
           premature to go next week with something which is
           still -- it still has all these unresolved issues in
           it, which I don't think we are going to resolve fully
                       DR. ZUBER:  I am gratified that you
           recognize our concerns.  The only questions I have is
           what are you going to do about it?  
                       MR. HAUGH:  The first thing is, if we can
           agree that the code does work and does do its job
           properly -- Well, perhaps before shaking your head no,
           you'll let me finish.  Okay?  Body language speaks
           reams, Novak.  
                       DR. ZUBER:  Look, I want for you to be
                       MR. HAUGH:  I know you do very much, and
           we certainly appreciate that.
                       If it is simply a matter that the
           derivations, again, purport a degree of rigor and
           correctness that is not there, there are easy ways to
           alert all of our users to this fact.  The RETRAN
           newsletter can carry that in depth.
                       If it is necessary to revise the code
           manuals, that can be done.  But I wouldn't make an ad
           hoc commitment to do so at the moment.  It depends on
           the nature of the need.
                       CHAIRMAN WALLIS:  Well, maybe it will show
           up.  It will be clearer to you when we look at
           something like this bend.  Here you are saying, okay,
           we can accept this equation as being usable, let's use
                       MR. HAUGH:  Yes.
                       CHAIRMAN WALLIS:  Then when we use it for
           the bend, you seem to get results which are very
           peculiar; and if it doesn't work for this simple bend
           -- results look really peculiar for that bend -- how
           can we sort of say that this is now going to be good
           for other geometries.  So maybe we need to --
                       MR. HAUGH:  Well, I appreciate the nature
           of the comment and, hopefully, we are going to be able
           to address that to your satisfaction this afternoon.
                       CHAIRMAN WALLIS:  So even if we accept the
           equation, then the way it's used seems to raise some
           other questions.
                       MR. HAUGH:  Yes.  I appreciate that.
                       CHAIRMAN WALLIS:  I don't think we are
           ready to move on to the question of does the code as
           a whole fit some plant data or something, because that
           could be for lots of other reasons, that someone has
           tweaked this or chosen this.  You know, there are
           options in the code to make things work. 
                       That's a big whole other --
                       MR. HAUGH:  Well, let's take this in the
           next step, as you have proposed, and let's go from
           there.  Upon completion of that, perhaps we'll know
           whether it's advisable to proceed to the full
                       CHAIRMAN WALLIS:  I don't think we're
           going to be ready for the full committee.  I don't
           think this subcommittee will know what to write.  I'm
           not sure you will know what to say.
                       DR. SCHROCK:  I'd like to just address a
           point that came up earlier today that I think is one
           that you need to pay attention to.  That is this idea
           that these codes have to be in the hands of experts,
           people who know what they are and what they do and how
           to make them function correctly in their application.
                       The difficulty that you have with the
           group of people that are out there that know how to
           run these codes is that they have been oversold. 
           That's my experience in talking with many of them.
                       They have been oversold on the rigor
           that's in the code, and so many of them really believe
           -- I mean sincerely believe that they learn physics by
           operating these codes.  
                       That's a dangerous situation.  That's a
           dangerous situation.  
                       MR. HAUGH:  Well, if there are
           misperceptions of that sort, we'll do our best to
           disabuse them of that.
                       DR. SCHROCK:  I don't know if you
           recognized that.
                       MR. HAUGH:  I appreciate the nature of
           your comment, certainly.
                       DR. SCHROCK:  All right.
                       MR. HAUGH:  With that, I'll ask Mark to
           come back and resume his presentation, but to focus it
           on the matter raised by Dr. Wallis.
                       CHAIRMAN WALLIS:  Thank you.  That was
           very helpful.  Thank you.
                       DR. PAULSEN:  The point I was thinking
           about resume this discussion was starting at the point
           where we have what we call our RETRAN flow equation
           and then discuss how it's applied to more complex
                       CHAIRMAN WALLIS:  I'd like to see it
           applied to simple geometry first.
                       DR. PAULSEN:  A simple geometry?
                       CHAIRMAN WALLIS:  Like this bend here or
           the T, because this business of I's and J's, you can
           just get lost in generalities.  But if you would show
           us how it works for this sort of thing -- I have real
           problems with that and, unless I get an answer, I'm
           going to have to write it up in some form to form some
           other record, which we don't want it to be.
                       The same thing with the T, the treatment
           of the T is very strange from a momentum balance point
           of view, too, and it's a simple thing.  I think it's
           much better to do these examples than it is to go into
           something where you have some generalized math, which
           -- it's hard to get hold of.
                       DR. PAULSEN:  Okay.  so the T -- You're
           looking at the newer write-up, I believe.
                       CHAIRMAN WALLIS:  Whatever your latest
           version of the bend is.
                       DR. PAULSEN:  Okay.  Which revision, I
                       CHAIRMAN WALLIS:  This is revision 5.
                       DR. PAULSEN:  Revision 5?  Okay.
                       CHAIRMAN WALLIS:  I think the answer is
           the same as in revision 1.  No, I think you've got a
           factor of root 2 in there.
                       DR. PAULSEN:  There was an error in the
           first one where we were missing a cosine.
                       CHAIRMAN WALLIS:  You changed the other
           root 2 in there.  Right.  So either version you could
           look at and explain to us how you get the terms and
           what's going on.
                       Are you prepared to do that?  Do you have
           transparencies of --
                       DR. PAULSEN:  Okay.  I don't have
           transparencies of that example.  I do have a sample
           problem where we actually ran an angle.  That might
           address your question.  Shall we take that approach
           and then --
                       CHAIRMAN WALLIS:  No.  I mean, I have
           questions about how W-2X is a half-W-2 and things like
           that.  I mean very simple questions.  If you can
           remember the problem, maybe you can answer that.
                       DR. PAULSEN:  Basically -- Let me just put
           this elbow up.
                       CHAIRMAN WALLIS:  I thought you would have
           this ready, because I -- Maybe I responded to Lance
           Agee and said you guys should come with transparencies
           of all the RAI answers.  I know that message got
           through.  I don't know quite who reads the messages.
                       DR. PAULSEN:  I didn't bring
           transparencies for that T example, but basically --
           Let's start here.  I think I'm losing my battery.
                       CHAIRMAN WALLIS:  You see, the problem is,
           when I made the presentation two years ago, I had a
           detailed critique of the bend, the T and the Y.  I
           have problems with terms in all of those and, unless
           there's some sort of answer, those difficulties will
           remain, and they shouldn't remain.
                       DR. PAULSEN:  My impression of your
           critique of the Y initially was the fact that we were
           missing a -- that, basically, there was an error in
           what we had.
                       CHAIRMAN WALLIS:  I think I had about six
           critiques of the Y.  
                       DR. PAULSEN:  I mean of the elbow.
                       CHAIRMAN WALLIS:  Oh, the elbow, yes.
                       DR. PAULSEN:  For the elbow.
                       CHAIRMAN WALLIS:  Well, let's look at the
           example you actually work out, this one here.
                       DR. PAULSEN:  Okay.  So we'll just go back
                       CHAIRMAN WALLIS:  You can get started on
                       DR. PAULSEN:  Is he going to make a Vu-
                       CHAIRMAN WALLIS:  Well, yes, he is, but
           you might get started on it.  So we have W1 and W2 and
           W3 defined at the edges of mass balance.
                       DR. PAULSEN:   Can you hold that up?  I'm
           just trying to remember --
                       CHAIRMAN WALLIS:  You don't have a
           nodalization.  You could take the one that Ralph has
           given you there.  So the 1, 2, 3s are the boundaries
           of mass and energy cells, and then the 1-circle, 2-
           circle are the boundary of the momentum cell.
                       DR. PAULSEN:  That's correct.
                       CHAIRMAN WALLIS:  Right?
                       DR. PAULSEN:  That's right.
                       CHAIRMAN WALLIS:  And you have to decide
           what your W1 and W2 bar are, because they are in your
           momentum equation?
                       DR. PAULSEN:  That's correct, and they
           happen to be the -- Then if we were looking at this
           momentum equation at this point here, we have a
           boundary in the way this is drawn at that these two
                       So at those points we need to know those
                       CHAIRMAN WALLIS:  Right.  So I think what
           you do is you say W1 bar is a half-W1 plus W2.  It's
           sort of an interpolation of --
                       DR. PAULSEN:  That's correct.
                       CHAIRMAN WALLIS:  Then you suddenly say
           it's equal to W2.  So you're assuming some sort of--
                       DR. PAULSEN:  That's at steady state, I
                       CHAIRMAN WALLIS:  But it isn't steady
           state.  The whole thing is a transient analysis.
                       DR. PAULSEN:  This was just a steady state
                       CHAIRMAN WALLIS:  No.  This is the example
           of a transient -- Okay.  Well, that's what really
           confused me, because you seemed to invoke the steady
           state all the time.  But, really, you are showing us
           how to do a transient.
                       DR. PAULSEN:  That's correct, and --
                       CHAIRMAN WALLIS:  So what you put in your
           transient is a half-W1 plus W2.  It's not W2.
                       DR. PAULSEN:  That's correct.  We put in
           the one-half, and the specific case we were looking at
           was a steady state.
                       CHAIRMAN WALLIS:  That's very misleading. 
           I think you don't -- Well, but the whole purpose is to
           develop a dynamic transient equation, and it's very
           misleading if you suddenly invoke steady state, which
           is not valid in a transient.
                       So we should take this to be half-W1 plus
           W2?  All right.
                       DR. PAULSEN:  Yes.  And in fact, the way
           -- We need a model, and you can call it interpolation
           or whatever.  You need something to get the boundary
           velocities or flows at these --
                       CHAIRMAN WALLIS:  Okay.  So let's say
           you've got W1, W2 and half-W1 plus W2 going in.  Right?
                       DR. PAULSEN:  Right.  So for this one we
           just do -- There's actually a model where we can
           either use a donor cell approach or --
                       CHAIRMAN WALLIS:  But you used the half-
                       DR. PAULSEN:  And that example uses the
           half.  So it would use the average --
                       CHAIRMAN WALLIS:  So what goes in as a
           halfW1 plus W2?  Could you write that on there or
           something so we can see what we are doing?
                       DR. PAULSEN:  Okay.  
                       CHAIRMAN WALLIS:  So that's called W2,
           that one there.
                       DR. PAULSEN:  This one here?
                       CHAIRMAN WALLIS:  All right.  And W1 is
           what goes in, and at your point at the momentum cell
           it's a half-W1 plus W2, that lefthand thing.  Okay. 
           That's going in.  
                       Now we need to know -- Now you say W1 psi
           is W1x.  What does that mean?  It would be 1-bar-x. 
           You're saying that psi is in the x direction.
                       DR. PAULSEN:  That's in the direction of
           this angle.
                       CHAIRMAN WALLIS:  So you are making a
           momentum balance in x direction?
                       DR. PAULSEN:  That's right.  
                       CHAIRMAN WALLIS:  Now for coming out you
           say W2x-bar, that's coming out of that 45 degree thing
                       DR. PAULSEN:  That's right.
                       CHAIRMAN WALLIS:  W2x-bar is a half-W2. 
           Where did that come from?
                       DR. PAULSEN:  It would also be half of
           this other flow.
                       CHAIRMAN WALLIS:  Well, is the idea that
           it's a half of W2 in x direction plus W3 in x
           direction, and there is no W3?
                       DR. PAULSEN:  That's correct.
                       CHAIRMAN WALLIS:  But you can't resolve
           flow rates that way.  The flow rate across that is a
           1/2W2 plus W3, same way as for the other, because
           flows are continuous.  They don't -- When it goes
           around the bend, flows are conserved.  
                       DR. PAULSEN:  The flows are conserved. 
           That's right.
                       CHAIRMAN WALLIS:  You don't conserve just
           the x direction of the flow.  You can't say that W2-
           bar is a 1/2W2x.  It doesn't mean anything.  You can't
           average the x direction velocities flow rates in a
           pipe.  The flow is continuous.  It goes around the
           bend.  All of W2 goes around the bend, not half of it.
                       DR. PAULSEN:  That's right.  
                       CHAIRMAN WALLIS:  So how does W2x get to
           be 1/2W2?
                       DR. PAULSEN:  In fact, I think what we end
           up here is that this flow will be oriented in this
           direction, and it will end up being equal to the
           steady state -- for the steady state --
                       CHAIRMAN WALLIS:  But you say W2x is a
           1/2W2, and W2y is 1/2W2.  So that, to me, says half the
           flow is going in the x direction and half of it is
           going in the y direction.  You've got a statement
           here:  W2x-bar is a 1/2W2 at that boundary.  I'm trying
           to understand what it means.
                       DR. PAULSEN:  Which equation is that that
           you are looking at?
                       CHAIRMAN WALLIS:  It's in the middle of
           page II-93.  You've got the same edition that I have,
           Revision 5, an non-numbered equation, the fourth one
           down:  W2x-bar is a 1/2W2.  
                       So you are explaining how to use the code. 
           That's why we are going into this, and I don't
           understand that statement at all.  Then W2y-bar is a
           1/2W2 is the next line.  
                       What it seems to say is that the flow in
           the x direction is half the total flow.  A flow in the
           y direction is a half the total flow.  Is that what it
                       DR. PAULSEN:  Yes.  
                       CHAIRMAN WALLIS:  But that doesn't make
           any sense.  If you draw a boundary in the y direction,
           you've got the whole flow going across it, and equally
           true for the x direction.  You can't resolve flow
           rates in x and y directions.  You just cannot do it. 
           It's non-physical.  Flow rates across any section in
           that pipe are the same.
                       DR. SHACK:  But these are his closure
           relations, not his conservation equation.
                       CHAIRMAN WALLIS:  They are what he is
           going to put into his equation to use.
                       DR. SHACK:  He's going to eventually end
           up conserving mass, but at the moment he's not doing
                       CHAIRMAN WALLIS:  No.  He's using -- These
           are the terms that go into the momentum equation, this
                       DR. SHACK:  Right.  But he's calculating
           them from his closure relations, not from a
           conservation relation.
                       CHAIRMAN WALLIS:  But what do they mean? 
           Where are they coming from?
                       DR. PAULSEN:  It is simply an average. 
           It's an interpolation.
                       CHAIRMAN WALLIS:  But you can't average --
           W doesn't have components.  So you can't average x
           direction component of a scalar.
                       DR. KRESS:  I thought they come about
           because it's a 45 degree angle and --
                       CHAIRMAN WALLIS:  That comes later.
                       DR. KRESS:  -- and that gives it one-half.
                       CHAIRMAN WALLIS:  No, there's a 1 over
           root-2 that comes later for that.
                       DR. KRESS:  Oh, there's another one?  
                       CHAIRMAN WALLIS:  Yes.
                       DR. SHACK:  But if you go back to this 3-
           28, those are his closure relations.   Those come from
                       CHAIRMAN WALLIS:  I'm saying it doesn't
           make any sense.
                       DR. SHACK:  Don't ask if it makes sense. 
           Just follow the rules and see where you end up.  Give
           him a chance.
                       CHAIRMAN WALLIS:  No, but what does the
           rule mean?
                       DR. SHACK:  He defines the closure rules. 
           Let him do that.
                       DR. ZUBER:  What does it physically mean?
                       CHAIRMAN WALLIS:  It doesn't mean
                       DR. SHACK:  It means he's saying the
           velocity is the average of the -- you know, the in and
           out velocities.
                       CHAIRMAN WALLIS:  It's not.  It's not a
           velocity.  It's a flow rate.
                       DR. SHACK:  Well, the quantity.
                       CHAIRMAN WALLIS:  But he's saying it's the
           component of a flow rate in an x direction, which I
           say doesn't exist.  Flow rates don't have components.
                       DR. SHACK:  Just think of it as a
           variable, and he's averaging the variable.
                       CHAIRMAN WALLIS:  You can define any
           variable.  It means nothing.
                       DR. SHACK:  But you know, we're doing
           mathematics here now.  You know, we've got a quantity
           that's varying.  So we know what it knows, and we have
           to find -- interpolate a value somewhere else.
                       CHAIRMAN WALLIS:  No, because we are going
           to use it in a momentum equation.  It's got to mean
                       DR. SHACK:  Ah.  When he uses it in a
           momentum equation, it means something.  But the
           equation he is writing down now is simply how he is
           going to interpolate these discrete values.
                       CHAIRMAN WALLIS:  What you are telling me
           is you understand the logic that he's using, albeit it
           may be unphysical.  Right.
                       DR. SHACK:  Yes.  You know, it's the sort
           of thing you would do in a mathematical thing when
           I've got discrete quantities and I need to get a value
                       CHAIRMAN WALLIS:  But I'm saying that I
           don't know what then W2x is.  If you are going to
           average something, you better tell me what it is.
                       DR. SHACK:  Well, in this case it's just
           a variable.  You know, when he goes to his momentum
           equation or he goes to his conservation equation, he
           had better end up conserving mass.
                       CHAIRMAN WALLIS:  This has nothing to do
           with conserving mass.
                       DR. SHACK:  No, this doesn't.  This is an
           interpolation scheme.
                       CHAIRMAN WALLIS:  So let's go back to
           where we were.  We've got W2x is 1/2W2, and let's then
           explain that in terms of interpolation scheme.
                       DR. PAULSEN:  Okay.  I'm trying to get my
           diagram here to match.  
                       CHAIRMAN WALLIS:  W2-bar is across the 45
           degree.  Right?
                       DR. PAULSEN:  That's right.
                       CHAIRMAN WALLIS:  And W2 is coming in
           there, and W3 is going out the bottom, and I'm asking
           what W2x-bar is.  
                       DR. PAULSEN:  Okay.  The model that we
           have used, there's either the donor or the average,
           and you've picked the average.
                       CHAIRMAN WALLIS:  Right.  You picked the
                       DR. PAULSEN:  Yes, that's right.  I'm
           sorry.  So for this particular case, what we would
           call the flow that's normal to that surface --
                       CHAIRMAN WALLIS:  In the x direction.
                       DR. PAULSEN:  -- in the x direction is
           going to be basically -- well, it will be 1/2W2.  Is
           that what we've got?
                       CHAIRMAN WALLIS:  Yes, 1/2W2 you say it
           is.  Right.  Why is not 1/2W2 plus --
                       DR. PAULSEN:  It's 1/2W3x, but W3x is equal
           to zero.  The W2x back at the ranch is W2, because it's
           in that direction.  W3x is zero, because it's straight
           down.  So when you do the average, you get half.
                       CHAIRMAN WALLIS:  But in the momentum
           equation we need to know the mass flux across the
           area.  We don't need to know some strange Wx.  
                       DR. SHACK:  At the moment he's just
           interpolating.  He's not doing momentum yet.
                       CHAIRMAN WALLIS:  No, but he is going to.
                       DR. SHACK:  Yes, when he does momentum,
           then nail him momentum, but at the moment let him
                       CHAIRMAN WALLIS:  Well, let's say now --
           My critique would be you can't resolve flow rates in
           x and y direction.  So what you are doing is something
           fantastic rather than representing physics.
                       DR. PAULSEN:  Okay.  
                       CHAIRMAN WALLIS:  I mean, you could do it
           if that's the rules you are going to play by,
           according to Dr. Shack, but it's a very funny game.
                       DR. PAULSEN:  And what we are doing is
           trying to resolve things in the x and y directions.
                       CHAIRMAN WALLIS:  Yes, I understand that's
           what you must have been thinking you were doing. 
                       DR. PAULSEN:  So the flow in the x
           direction for this particular surface would just be
           1/2 of W2.
                       CHAIRMAN WALLIS:  And in the y direction
           it's 1/2W2.
                       DR. PAULSEN:  In the y direction it's
                       CHAIRMAN WALLIS:  What does flow in the x
           direction mean, though?  How do you define a flow in
           the x direction?
                       DR. PAULSEN:  That's going to be what we
           take to be the velocity divided by the density.
                       CHAIRMAN WALLIS:  Times some area?
                       DR. PAULSEN:  Times an area.
                       CHAIRMAN WALLIS:  But then it would be a
           root-2, wouldn't it, if it's a velocity?
                       DR. PAULSEN:  It's a what now?
                       CHAIRMAN WALLIS:  The square root of 2, if
           it's a velocity, rather than a half.
                       DR. PAULSEN:  The half is simply the
           averaging scheme that was developed.  If we use a
           donor approach, then it's just the upstream turn.
                       CHAIRMAN WALLIS:  Let me say this.  In
           steady flow W2 = W3 --
                       DR. PAULSEN:  That's correct.
                       CHAIRMAN WALLIS:  -- equals W1-bar equals
           W2-bar, all the same.  Right?  
                       DR. PAULSEN:  That's right.
                       CHAIRMAN WALLIS:  So W2-bar better be W2,
           and then its x component is 1/2W2?
                       DR. PAULSEN:  This term?  The x component
           at this location will be half.
                       CHAIRMAN WALLIS:  All the Ws are equal.
                       DR. SHACK:  Part of the problem is he
           thinks of W sometimes as a mass flow rate and
           sometimes it's a velocity.
                       CHAIRMAN WALLIS:  But it's neither in this
           sense.  It can't be either.  The flow rate is W across
           that surface. The x direction velocity is x over root
           two.  It's not a half.
                       If you are using a mass balance, the flow
           rate over there is the total flow rate, not half of
           it.  So when we get to the momentum equation, I guess
           we'll see that.    
                       So when you get down to the bottom of the
           page, you are going to take W2 over 2, which is your
           Wx-bar, divided by A2, and you are going to multiply
           it by the velocity it takes with it, which is W2 over
                       I guess we would agree that the velocity
           component resolved is 1 over root two, but I would
           maintain, if you are going to make a momentum balance,
           you've got to multiply it by the whole flow rate, not
           the flow rate in some direction.  I mean, your whole
           momentum equation was the flow rate times component of
           velocity, not flow rate component times component of
           velocity.  So that half shouldn't be there.  
                       The problem I have with this is that there
           seems to be a fundamental conceptual mistake in a very
           simple example, and this presumably is in all the more
           complicated geometries, too, to some degree, but even
           more difficult to figure out because they are more
                       If you are giving the user advice to do
           this for this simple bend, then I don't understand how
           we can believe the advice for a more complicated
           geometry.  This doesn't make sense.
                       DR. PAULSEN:  The point is that we don't
           really use this in modeling RETRAN.
                       CHAIRMAN WALLIS:  Well, why do you present
           it then?
                       DR. PAULSEN:  Well, that's a good
                       DR. ZUBER:  Well, how do you use it?
                       DR. PAULSEN:  It was going to be an
           illustrative example to show simply that, once you go
           around the bend, you get the pressure back.  You will
           see an increase in pressure as you go into the bend
           and, once you are around the bend --
                       CHAIRMAN WALLIS:  That won't wash.  I
           mean, the user has to write a momentum equation for
           this cell, 1-2.  Right?  It has to be there somehow. 
           So what does RETRAN use for the momentum equation, the
           actual equation used for that cell?
                       DR. PAULSEN:  For this cell?  In most
           cases, if the user does not input angles, he is simply
           going to use that momentum equation -- that flow
           equation that we looked at earlier.
                       CHAIRMAN WALLIS:  So there won't be any 2
           or root two in there?
                       DR. PAULSEN:  Unless he puts in an angle.
                       CHAIRMAN WALLIS:  So you are making it
           arbitrary whether or not there is a factor of 1/22? 
           Could be there or not there, depending on what the
           user chooses to do?  
                       DR. SHACK:  Well, I think what he's saying
           is that, by the time he gets to the end of the elbow,
           it won't make any difference whether he modeled it as
           an elbow or as a straight pipe --
                       CHAIRMAN WALLIS:  If you get to the end of
           the elbow.  But you might not.  You might discharge
           into a container.
                       DR. SHACK:  If he had that geometry, you
           would do something different.  But if he's just doing
           an elbow versus a straight pipe --
                       CHAIRMAN WALLIS:  You see the problem I
           have.  You have a fundamental equation, one is to
           believe can be used.  You use it for something like
           this half an elbow, and it doesn't make sense.
                       DR. PAULSEN:  Okay.  I guess the point we
           were trying to show here was that once you get around
           the elbow, everything comes back, that since it's a
           recoverable loss, and you really don't need to include
           the detail of elbows in loops.
                       CHAIRMAN WALLIS:  I don't think that's
           necessarily true, because then you would have to use
           your y component of momentum or something on the other
           side of it.
                       DR. PAULSEN:  That's right, and it ends up
           canceling out.
                       DR. SHACK:  He's got his momentum equation
           3-37-C to show his pressure drop in the first -- you
           know, as he coming through there in the first part. 
           Then he is going to get a pressure recovery when he
           computes pre-3 minus T-1.
                       CHAIRMAN WALLIS:  That's not really
           kosher.  I mean, you can say we calculated this whole
           thing wrong up to 2, and we make the same error in
           reverse from 2 to 3.  So the error is irrelevant. 
           That's -- I don't think that is really respectable.
                       Now maybe if you went around in a complete
           circle, you might find the errors build up instead of
                       DR. PAULSEN:  Well, I guess it looks like
           maybe that we haven't addressed the issue here on the
           elbow example.  We'll have to go back and look at that
                       CHAIRMAN WALLIS:  I think it's really
           fundamental.  This is supposed to illustrate the use
           of an equation, and doesn't reinforce the equation at
                       DR. ZUBER:  And then if you cannot explain
           the simplest case, how can one believe -- at least,
           how could I believe or Graham or anybody else -- then
           you got a more complicated case.
                       CHAIRMAN WALLIS:  What would be on the
           lefthand side if it were a transient?  You have a d by
           T of something with a L1 and L2 in there?
                       DR. PAULSEN:  That's right.
                       CHAIRMAN WALLIS:  Then you would have Dr.
           Shack's problem, that the L1 and L2 are not in the
           same direction; are they resolved in some way?  That's
           not explained either.
                       DR. PAULSEN:  Yes.
                       CHAIRMAN WALLIS:  So it seems to me that
           you can't explain this simple thing.  How should the
           user use it for something more complicated?  
                       DR. PAULSEN:  Well, let's go on and look
           at some of the more detailed cases.
                       DR. ZUBER:  This is the simplest detailed
           case, and you cannot explain why --
                       CHAIRMAN WALLIS:  We can look at the T,
           too.  I mean, the T has this peculiar one-fourth of W1
           minus W22 in it.  If you make W2 zero, you find
           Bernoulli's equation has a quarter in it.  Now
           Bernoulli's equation doesn't have a quarter in it.
                       So again -- I mean, I don't want to go
           into all these details, but I've found that in writing
           my review of this stuff, I was writing page after page
           of stuff saying that this doesn't make sense.
                       DR. PAULSEN:  Okay.  It sounds like we
           still have something to do with the elbows.  
                       CHAIRMAN WALLIS:  You must have a
           reasonable excuse for the equation you are using, and
           you must have a reasonable exposition of how it
           applies to some simple geometries that doesn't appear
           to have some logical disconnects in it.  Then I think
           it's acceptable.
                       DR. PAULSEN:  Okay.  The point that I
           would like to make at this point is the fact that
           initially we started out trying to show rigor and
           including the angles, and that was probably a mistake;
           because we don't really use angles in a code.
                       CHAIRMAN WALLIS:  But even so, if you are
           going to use the two pipe plus junction model, how
           does it apply to a bend?  Still the same issue.  How
           does it apply to the downcomer?  
                       DR. PAULSEN:  That's right.  
                       CHAIRMAN WALLIS:  You're just going to say
           there's two straight pipes and a junction up there? 
           Maybe there is there, but I don't see any two straight
           pipes here.  I see a bend.  So I don't know how to
           define my two straight pipes.
                       DR. PAULSEN:  Basically, it does use a
           straight pipe model, a two straight pipe model.  
                       CHAIRMAN WALLIS:  But it isn't, because
           it's got this root 2 --
                       DR. PAULSEN:  And that comes from the
           angle piece that we normally would not include.
                       CHAIRMAN WALLIS:  See, the genuine -- If
           you model this as two straight pipes, you wouldn't
           have the factor 2 or the factor root 2 in there at
           all.  That's my contention.  If you simply took two
           straight -- Excuse me -- with a 45 degree bend like
           that and said the bend is a junction, you wouldn't
           have any of those root 2s and 2s in there.
                       DR. PAULSEN:  That's right.  Because
           normally we would model an elbow as a node -- straight
           node that way and a node in that direction.
                       CHAIRMAN WALLIS:  Right.  And there
           wouldn't be any of these 2, root 2s and stuff.
                       DR. PAULSEN:  No.  There's none of the
           root 2s.
                       CHAIRMAN WALLIS:  So you have an equation
           which differs from the other one by a factor of --
           what, 2.8 or something?  Well, in that case we should
           do sensitivity studies to see when the factors vary
           between half and 4 or something.  Does it make a
           difference or something?
                       DR. PAULSEN:  Right.
                       CHAIRMAN WALLIS:  And it may well be that
           what you've just said is that when you are really
           worried about a circuit, everything sort of washes out
           in the end anyway, and random fluxes don't matter
           because what you lose here, you gain there may well be
                       DR. PAULSEN:  In this particular case,
           most applications where we have elbows would not use
           that 45 degree angle.  We would do something either
           like that nodalization or something like that
                       CHAIRMAN WALLIS:  So I guess we get back
           to Ralph Landry's point, that what's in the code and
           how it's actually used is different from the
           exposition in the documentation, and the code seems to
           work, and the documentation in that context is
                       DR. PAULSEN:  And I guess maybe what we
           need to do is focus on that.  There are --
                       CHAIRMAN WALLIS:  But you see the problem
           I have.  I'm coming from the outside.  I'm like the
           naive sophomore student trying to understand this,
           because my professor says go and figure out what they
           are doing with this bend.  I come back, and I say,
           prof, I just can't figure out what they are doing. 
           And that's not good.
                       DR. SCHROCK:  Do I understand you put a
           loss coefficient in when you do what you've shown
                       DR. PAULSEN:  Yes.  In something like this
           there would be a loss coefficient.  
                       CHAIRMAN WALLIS:  And there is no pressure
           from the wall.  There's no force from the wall.
                       DR. PAULSEN:  No.
                       CHAIRMAN WALLIS:  So there's nothing to
           turn the flow to the other direction.  There is no
           force in the x direction to turn it around the bend?
                       DR. PAULSEN:  In this case?
                       CHAIRMAN WALLIS:  There's no force from
           the wall.
                       DR. PAULSEN:  Just the pressure difference
           that we would see.
                       DR. SCHROCK:  So that is strictly modeling
           straight pipe -- stringing together straight pipes to
           represent the actual geometry.
                       DR. PAULSEN:  That's correct.  
                       CHAIRMAN WALLIS:  Maybe you better go back
           and say that's just what you are doing.  
                       DR. PAULSEN:  That's probably the best
                       CHAIRMAN WALLIS:  And make all the excuses
           -- Well, don't make excuses.  This is engineering.  We
           understand engineering approximations.  We understand
           you do the best you can do, and that you test to see
           if it works, and we would buy that.  
                       We cannot buy what appears to be logical,
           sort of non sequiturs.  So you see, I have a problem
           not just at the formulation of the equations but in
           the examples showing how they are used.  If that's not
           the way you really use them, then you need to show us
           examples of how you do really use them.
                       DR. PAULSEN:  And that is kind of where I
           was headed.
                       CHAIRMAN WALLIS:  And that's where I had
           a problem with the T, because the T seemed to me to
           give some funny results, but maybe it's okay for
           nuclear safety.
                       DR. PAULSEN:  Well, I've got some examples
           of a T where we might need to include some of the
           effects of angles.
                       DR. SCHROCK:  There is also the downcomer.
                       DR. PAULSEN:  Yes.  Shall we just skip
           over the 1-D stuff.  I think you probably --
                       CHAIRMAN WALLIS:  Well, yeah, I guess we
           can.  We're going to spend a lot of time -- The T is
           not 1-D, because it comes in one way and goes out the
                       DR. PAULSEN:  Right.  
                       CHAIRMAN WALLIS:  And you have this
           mysterious magnitude of the volume sent at the flow,
           and you have again this mysterious W1x, W1y.  Stuff is
           coming in in this direction, but it seems to have a
           component in that direction even though it's all going
           in this direction.
                       DR. SCHROCK:  Then there's issues of flow
           -- or phase separation in Ts.
                       DR. PAULSEN:  That's right, and none of
           that is really handled.  That all has to be done with
           sensitivity studies or constitutive models.
                       CHAIRMAN WALLIS:  Frankly, everybody knows
           you cannot model a T with a simple momentum balance. 
           You cannot do it.  
                       DR. PAULSEN:  And basically, what we have
           -- the form that we have after responding to one of
           the NRC questions is a form that pretty much maintains
           the Bernoulli had the p plus rho-v, one-half rho-v.
                       CHAIRMAN WALLIS:  What you need to do is 
           you need to do experiments.  You need to define some
           empirical coefficients reflecting how much it's like
           Bernoulli and how much it's like momentum and
           capturing that, and then you have to have coefficients
           that come from experiments.  You energy loss depends
           not just on one flow rate but the ratio of the flow
           rates and things like that.
                       When you have flow going all the around
           the bend instead of carrying on, the pressure recovery
           is quite different from when it was going straight on. 
           It's not a simple problem.
                       DR. PAULSEN:  And the real problem during
           an application is that those flow patterns can change,
           and the relative magnitudes can change.  So you have
           to try and capture something that bounds the --
                       CHAIRMAN WALLIS:  But there's nothing of
           bounding in your -- You see, your example is presented
           as if this is right, and if you had  qualified is and
           said that in reality it's doing something like this
           and in order to get on with the problem we make this
           assumption which we think is bounding or something,
           that would, I think, help a great deal.  When you just
           put it down as if it's right --
                       DR. PAULSEN:  I understand your concern
                       CHAIRMAN WALLIS:  -- then this psi thing
           is sometimes x and sometimes y.  I thought it was some
           intermediate angle in the bend somewhere.  
                       I would think it needs to be fixed up. 
           Otherwise, we may have to write a critique based on
           what we see.  It's all we've got to go on.
                       DR. SHACK:  Who are you going to believe,
           your eyes or what you hear?
                       DR. ZUBER:  Well, my advice would be
           really to go and go through the entire document and
           really address point by point.  State your
           assumptions, the equations, and proceed from there. 
           This is really arm waving -- really arm waving.
                       CHAIRMAN WALLIS:  You are still
           constrained to what's really in the code, and that's
           where we still have a bit of a mystery as to what it
           really does with these things.
                       DR. PAULSEN:  And I guess that was kind of
           the purpose of going over these next few slides, is
           that --
                       CHAIRMAN WALLIS:  But these are much more
           complicated things.  So I have difficulty.
                       DR. PAULSEN:  These will be some arm
                       CHAIRMAN WALLIS:  You lose me in this arm
           waving completely, because it gets even -- it
           obfuscates the issues even more.  Which one did you
           want to go into?
                       DR. PAULSEN:  Well, let's just kind of go
           through this quickly and see if --
                       CHAIRMAN WALLIS:  Did you want to go
           through 29 and 30?  Okay, that's fine.  
                       (Slide change)
                       DR. PAULSEN:  One of the things that we
           have to do in RETRAN is we've got our flow equation
           which basically looks like the Bernoulli equation, and
           it came from 1-D information.  We don't have anymore
           information than that, and now we have to try and
           model a complex system where we've actually got some
           3-D geometry and some different flow paths.
                       So what we have to do is use a number of
           approximations on how we apply that equation then to
           these three-dimensional geometries.  There's a whole
           volume of RETRAN documentation that's devoted to
           setting up a model for a plant that provides specific
           guidance for how do I model a plenum, what do I have
           to consider, how do I calculate a length, how do I
           calculate diameters when I've got these weird geometry
                       That's all discussed in the modeling
           guidelines for RETRAN-2.  Now that document hasn't
           been rewritten for RETRAN-3D, because what is given
           there is equally applicable to RETRAN-3D in terms of
           how you set up nodalization and how you set up your
           input parameters for that flow equation.
                       So, basically, that modeling guideline
           provides us with some general rule as to how we would
           define the input.  In many instances, it will provide
           alternate methods for calculating some of that input
                       One of the things that is required,
           though, is that we typically require some sensitivity
           studies, because we are doing approximations.
                       CHAIRMAN WALLIS:  Well, you responded to
           that by the next slide, 30.  That's a question, was
           one of the RAIs:  How do you model these kinds of
                       DR. PAULSEN:  That's right.
                       CHAIRMAN WALLIS:  And frankly, I looked at
           the tables, and I couldn't understand what any of the
           terms in those tables meant.  So I was left none the
           wiser than I was before as a result of the response to
           this RAI.
                       DR. PAULSEN:  There was also some -- a
           reference to this modeling guidelines document --
                       CHAIRMAN WALLIS:  And if you had said,
           look, here is the node, let's say the downcomer to low
           plenum.  Let's say we've got this complicated thing we
           have to model.  We are going to use the RETRAN
           momentum equation in some form.  This is how we
           evaluate Pk, Pk+1, Wk, Wk psi, and this is the final
           equation we come up with; this is how we get the Ls,
           you know -- None of that is in this reply.  So I have
           no idea.
                       DR. PAULSEN:  Okay.  for that information
           we actually referred to this modeling guideline
           document.  It's NP-18.50, volume 5.
                       CHAIRMAN WALLIS:  See, you're replying  to
           an RAI or I guess it's also one we stirred the staff
           up to ask this question.  The Table 1, Table 2 didn't
           help at all.  I don't know what you are talking about. 
           There are junctions which are labeled 1 and 2, and
           there are junctions which are labeled 2-circle and so
                       DR. PAULSEN:  Okay.  The circled
           quantities are the volumes.  
                       CHAIRMAN WALLIS:  But they seem to be the
           same.  There's no distinction between the two kinds of
           junction.  Then I couldn't understand these 1/2W2s and
           1/2W3s.  They seem to be something like the halves
           that you have in the bend.
                       DR. PAULSEN:  They are.
                       CHAIRMAN WALLIS:  Then you get this
           quarter-W32.  Well, so these have the same strange
           features that we didn't like about the bend.
                       DR. PAULSEN:  Those are those boundary
           flows that you need at the momentum cell boundary.
                       CHAIRMAN WALLIS:  So I guess, to be happy,
           it will be nice to see how you did it.  When you've
           got, say, the lower plenum -- Look at the lower plenum
           downcomer.  We've got four boundaries to the outside
           world.  We've got 2 and 3 and 4 and 5.  How do you get
           away with two pressures, P1 and P2 when you've got
           four boundaries to the outside world?
                       DR. PAULSEN:  Okay.  Let's put that slide
           up here for just a minute.
                       (Slide change)
                       DR. PAULSEN:  That may be confusing where
           we actually have these two flows shown.  But basically
           in this case, when we write the momentum equation or
           our flow equation, it would actually be written for
           just this one junction, and then we actually have to
           have a boundary rho vA at this surface and one at this
           surface of the momentum equation.
                       CHAIRMAN WALLIS:  So is it they are in the
           same direction at 2 and 3?  So what happens to 4 and
           5 then?
                       DR. PAULSEN:  Four and 5 are factored into
           this boundary condition here.  They are factored into
           this flow with this boundary.
                       CHAIRMAN WALLIS:  There isn't any flow at
           that boundary, is there?
                       DR. PAULSEN:  That's the rho vA on this
                       CHAIRMAN WALLIS:  I understand there's no
           flow going into the bottom of the lower plenum.
                       DR. PAULSEN:  What's that now?
                       CHAIRMAN WALLIS:  No flow coming out that
           bottom line across there.
                       DR. PAULSEN:  At this one?
                       CHAIRMAN WALLIS:  Yes.  Is that flow
           coming out of there?
                       DR. PAULSEN:  What this boundary is is the
           net.  It's sort of an average based on the conditions
           in these junctions, and I think --
                       DR. ZUBER:  How do you determine that?
                       DR. PAULSEN:  I have an example that
                       CHAIRMAN WALLIS:  Your momentum equation
           is assuming it is coming in at 2-circle and going out
           to 3-circle? 
                       DR. PAULSEN:  The 2-circle.
                       CHAIRMAN WALLIS:  That's the inlet Wk, and
           the Wk+1 is --
                       DR. PAULSEN:  And then there will be a
           boundary on this surface, yes.  There will be a
           surface flow on this surface.
                       CHAIRMAN WALLIS:  And then what do the
           other flows do, the W4, W5?
                       DR. PAULSEN:  These W4s and W5s are
           actually used to -- It's actually W3, 4 and 5 are used
           to calculate this value.
                       CHAIRMAN WALLIS:  See, if I were to use
           Bernoulli, I would use it from 2-circle up into the
           core.  It's going from 2-circle up to W4, W5.  It's
           turning the corner.  
                       DR. PAULSEN:  That's right.
                       CHAIRMAN WALLIS:  It's not going from 2
           into the lower plenum, is it?  You seem to say that
           the inlet is at 2 and the outlet is at 3, and the rest
           of it is --
                       DR. PAULSEN:  What we should do is, when
           we start looking at a momentum cell, it's really this
           part that we have written for.
                       CHAIRMAN WALLIS:  You shaded it, right?
                       DR. PAULSEN:  The shaded part.
                       CHAIRMAN WALLIS:  And the in is the top,
           and the out is the bottom?
                       DR. PAULSEN:  That's correct.
                       CHAIRMAN WALLIS:  That's a very funny
                       DR. PAULSEN:  And we don't have those
           explicitly included.  They are included in that
           surface flow.
                       CHAIRMAN WALLIS:  I guess, if we looked at
           the details of this equation, if you developed it for
           us, we would have a whole lot of questions about it
           probably.  It would be nice to see it, though.
                       DR. PAULSEN:  What we still apply here is
           that two pipe equation.
                       CHAIRMAN WALLIS:  I can't see two pipes. 
           The two pipes are from 2 down to W3 and from W3 down
           to the lower plenum?  That flat thing is a pipe going
                       DR. PAULSEN:  This is the lower plenum.
                       CHAIRMAN WALLIS:  That flat thing is a
           pipe oriented downwards?
                       DR. PAULSEN:  That's half -- Yes, half the
           lower plenum.  
                       CHAIRMAN WALLIS:  And that's a good model
           of that part of the system?  See, the key thing is
           it's coming in W3 and going out at W4, W5.  The pipe
           should be horizontal or something to connect between
           W3 and W4, W5, shouldn't it?
                       DR. PAULSEN:  Some of this has to do with
           the level of nodalization, but in this simple
           nodalization this is the way that pipe would be
                       DR. SCHROCK:  Does that vertical leg on
           that thing represent the entire downcomer or some
           section of it?
                       DR. PAULSEN:  In a very simple model, this
           could be the whole downcomer.  In some cases, the
           downcomer may be nodalized vertically.
                       DR. SCHROCK:  No, no.  I'm not concerned
           with vertical nodalization but as it represents the
           entire downcomer?
                       DR. PAULSEN:  In a lot of cases it is
           modeled with one downcomer.  In some cases, models
           will have multiple downcomer volumes, depending on the
           type of transient that is being modeled.
                       CHAIRMAN WALLIS:  So what I'm supposed to
           do is take some of these terms in Table 1 and Table 2
           and just substitute them into your equation 5, which
           is your RETRAN momentum equation, and that's going to
           be a momentum equation for that shaded volume?
                       DR. PAULSEN:  That's correct.
                       CHAIRMAN WALLIS:  Well, there aren't
           enough terms.  I think sort of a commencing argument,
           you have to complete the loop.  You have to say,
           right, we are going to show you how to evaluate P1,
           P2, Ak, Ak+1, all the things that appear in that
           equation, because it's not transparent in any way at
                       I wouldn't have a clue how to evaluate Ak,
                       DR. PAULSEN:  And I think some of the
           problem is because we haven't given the preliminaries
           on how that's done, and we have referred just to that
           modeling guidelines where all that information exists.
                       CHAIRMAN WALLIS:  Seems to me, this is
           very important.
                       DR. ZUBER:  But that was for another code.
                       DR. PAULSEN:  What's that?
                       DR. ZUBER:  That was for another code, not
           for this one.
                       DR. PAULSEN:  Those terms are unchanged. 
           The mixture momentum equation is unchanged.  You model
           the nodalization the same way.
                       CHAIRMAN WALLIS:  This is for what code?
                       DR. PAULSEN:  RETRAN-2.  It was the
           predecessor to RETRAN-3D.  So that we basically have
           the same momentum equation formulation.
                       DR. ZUBER:  I have a problem.  Really,
           throughout your presentation you use basically --
           basically.  I prefer something more definite.  
                       DR. PAULSEN:  The momentum equation is the
           same.  The mixture momentum equation is the same.
                       CHAIRMAN WALLIS:  If I had to write a
           review of this today, I would write that the
           description in this reply to this RAI is completely
                       DR. PAULSEN:  Well, yes.  And I think part
           of the problem is that we relied on what was in the
           modeling guidelines without specifically including
           some of that.
                       CHAIRMAN WALLIS:  Well, maybe there is a
           good option, but it just isn't here.
                       DR. PAULSEN:  Yes.  I think --
                       DR. SCHROCK:  I have a sort of simple
           question.  In talking about pipes, elbows, etcetera,
           we finally ended with a conclusion that what the code
           actually does is calculate flows in straight pipe
           segments and then puts loss coefficients for the
           junctions between those.
                       DR. PAULSEN:  That's right.
                       DR. SCHROCK:  That's what is programmed
           into the code.  Now you are talking about this more
           complex system.  You've got this set of variables
           defined on the board.  It seems incomplete to include
           flow into and out of the lower part of the lower
           plenum, but what isn't clear to me is are you showing
           us something that is actually programmed into the code
           or is it again a situation where you are trying to
           illustrate in principle what you think the code does,
           but the code has actually got equations that are not
           from this?  Which is it?
                       DR. PAULSEN:  Trying to illustrate what
           the code does.  This is not hard wired into the
                       DR. SCHROCK:  And what does user
           guidelines in choosing nodalization mean for these
           complex geometries?  What is the user actually doing
           that influences what the code calculates?  That's one
                       The other question is what are the
           equations that are programmed into the code?
                       DR. PAULSEN:  Okay.  Basically, the
           equation that's programmed is that equation with the
           area change included in it.  So it has momentum flux
           terms.  It has the form loss terms, the pressure
           gradient on the righthand side.  The lefthand side has
           a thing that's factored out that is called geometric
           inertia.  It's basically the L over A, and that's
           multiplied times --
                       DR. ZUBER:  What is the L for this?  You
           have a volume.
                       DR. PAULSEN:  Okay.  That's the next step
           in this discussion, is what the L is.  For the 1-D
           case that we've talked about, the L and the A are just
           geometric terms.  They are the geometric length and
           the geometric flow area.
                       CHAIRMAN WALLIS:  What are the Ps?  The Ps
           and 2 and 3 or 2 and 4?  What are the Ps?
                       DR. PAULSEN:  The Ps in this case are at
           2 and 3.
                       CHAIRMAN WALLIS:  That's absolutely naive. 
           The pressure that pushes this up around it is between
           2 and 4.  Three is irrelevant.  Three is just a token
           bucket.  The pressure that accelerates this flow is
           between 2 and 4.  
                       DR. PAULSEN:  And if sum those equations,
           you can show that, too.
                       CHAIRMAN WALLIS:  Oh, you sum them?  
                       DR. PAULSEN:  No, if you were to.
                       CHAIRMAN WALLIS:  This is one equation. 
           You have one equation for that entire shaded area.
                       DR. PAULSEN:  We have one equation for
           this path.
                       CHAIRMAN WALLIS:  I would put the
                       DR. PAULSEN:  And we have another equation
           for this path.
                       CHAIRMAN WALLIS:  It's a shaded -- I
           understood that 2-circle is a volume for mass
           conservation, and 3-circle is the lower plenum.  2-
           circle is the downcomer.  Take half the downcomer and
           half the lower plenum, make a momentum cell.
                       DR. PAULSEN:  For this path.
                       CHAIRMAN WALLIS:  It is not divided at
           all.  It's one equation for that whole shaded thing. 
           Right?  One equation for that whole shaded thing in
           the middle.
                       DR. PAULSEN:  For this?
                       CHAIRMAN WALLIS:  Yes.  One equation, one
           RETRAN equation for that whole shaded thing.
                       DR. PAULSEN:  That's right, and that's for
                       CHAIRMAN WALLIS:  And now you are telling
           me it is subdivided in some way.
                       DR. PAULSEN:  No.  This one equation that
           we've just talked about is for this flow from the
           downcomer to the lower plenum.
                       CHAIRMAN WALLIS:  And that's between 2 and
           3.  In terms of pressures it's the top surface and the
           bottom surface.
                       DR. PAULSEN:  That's right.
                       CHAIRMAN WALLIS:  It's driving the flow.
                       DR. PAULSEN:  Two and 3, and then we write
           another equation for junction 4 and another one for
           junction 5, and basically this equation looks at the
           pressure between 3 and 4, and this other one would
           look between 3 and 5.  
                       CHAIRMAN WALLIS:  So the fact that the
           flow is coming out at 4 and 5 doesn't figure out
           somehow in your momentum, though in the bend we had
           going in and coming out.  That coming out is somehow
           different from the coming out at 3.
                       DR. PAULSEN:  That's right.  
                       CHAIRMAN WALLIS:  So I'm trying to figure
           out what the two pipe model is saying.  It's saying
           that there is actually a pipe between -- this flat
           thing, this disk-like thing is a pipe between the top
           and the bottom, and the flow is coming in and going
                       DR. PAULSEN:  Right.
                       DR. SCHROCK:  I can't read the subscripts
           on it, but on the last picture right there you've got
           a W, looks like 2 going down.
                       DR. PAULSEN:  This one here?
                       DR. SCHROCK:  That one.  The flow going
           into the horizontal surface on the top of that flat
           segment, going down there; on the other side, it's
           going up.  One of them is out of the downcomer. The
           other one is into the downcomer.  How do you square
           that with the other picture?
                       DR. PAULSEN:  That's basically -- This may
           be misleading by including these, and it appears that
           maybe it is, because this is the situation we have
           where we have the downcomer flow and then the core and
           bypass flow or two core flows.
                       For this particular momentum cell, we only
           worry about that case, and these flows --
                       DR. SCHROCK:  5 is bypass flow?
                       DR. PAULSEN:  It could be core bypass. 
           It's just one of the parallel paths through the core
           at this point or it may be another core channel.  But
           we would write one equation for this path, and then
           another equation for this middle path, and it would
           probably be less confusing if we had left those flows
           off, and then a similar equation --
                       DR. SCHROCK:  Or put them in the middle. 
           I mean, the downcomer is modeled as one pipe.
                       CHAIRMAN WALLIS:  No, there are two
           downcomers.  One is going up; one is coming down. 
           There's two different cells for the downcomer.
                       DR. SCHROCK:  What?
                       CHAIRMAN WALLIS:  Two and 5 are different.
                       DR. PAULSEN:  Yes.  This would be a core
           channel, and it may be a bypass or a second core
                       DR. SCHROCK:  Well, it's not the
                       DR. ZUBER:  No, the downcomer would just
           be one on the left.
                       DR. PAULSEN:  Just the 2 is the downcomer.
                       DR. SCHROCK:  2 is the whole downcomer,
           and you do that as one pipe.  Then the upflows are in
           the core and in a bypass.  You make it look in this
           picture as though 5 is into the downcomer.
                       DR. PAULSEN:  At this flow?
                       DR. SCHROCK:  Well, I mean your picture --
           it just geometrically looks like a part of the
           downcomer, and that's not what you mean.
                       DR. PAULSEN:  No.  No, this isn't part of
           the downcomer.  This flows both --
                       CHAIRMAN WALLIS:  Well, I think all this
           illustrates that we need more explanation.  It may
           well be that the whole thing you've put together has
           a kind of modular structure, which at some level makes
           sense, but it's difficult to figure out what it is.  
                       DR. PAULSEN:  And I think we have
           sometimes difficulty seeing the forest for the trees,
           because maybe we are too close.  I don't know, but the
                       DR. ZUBER:  The trees -- The forest
           doesn't make any difference.  No, really.  I can see
           that you have two pipes and you connect them.  If it's
           a pipe flow here, you really approximate the whole
           downcomer by horizontal pipe.  Right?
                       DR. PAULSEN:  By a vertical pipe, in this
           case.  Yes.
                       DR. ZUBER:  Downcomer.  Then in the lower
           plenum it's another pipe.
                       CHAIRMAN WALLIS:  It's a vertical pipe.
                       DR. ZUBER:  No, the horizontal --
                       CHAIRMAN WALLIS:  It's a vertical pipe. 
           I think the lower plenum is a vertical pipe.  Its
           horizontal momentum isn't --
                       DR. ZUBER:  Well, what determines this
           horizontal line?  Where is it?
                       DR. PAULSEN:  This one?  That's just half
           of this normal volume.
                       DR. ZUBER:  Well, can it be three-
           quarters, five-fifths?
                       DR. PAULSEN:  No.  It's half.
                       DR. ZUBER:  Why?
                       DR. PAULSEN:  That's just the way the code
           is formulated, is that you get half of --
                       DR. ZUBER:  No.  Look, the code doesn't
           formulate anything.  It's you who formulate the code,
           and you tell the code what to do.
                       DR. PAULSEN:  Let's back up to the
           inertia, because that's really where -- There's some
           of these terms that you input for these things that
           really aren't 1-D, and it's really not the length. 
           Maybe that's what you are getting at.
                       DR. ZUBER:  I would like to see what are
           you doing.
                       DR. PAULSEN:  I think that's maybe what
           you are getting at.
                       DR. SCHROCK;  If you were just dealing
           with steady state, the net flow across that horizontal
           surface would be zero, and if would have no impact on
           the rest of your equations.  But you are dealing with
           a transient.  So you have to account for accumulation
           and depletion in that volume.
                       The only way to do that is to account for
           the inflows and the outflows through that horizontal
           surface.  You're not doing that.
                       DR. PAULSEN:  I think that's what we are,
           and I'll show you in a slide.
                       CHAIRMAN WALLIS:  But the pressures --
           You're saying the pressures on the end, the top and
           bottom, determine the flow, but there is a pressure on
           that other boundary there going to W4, W5, which is
           not the same as either of the other two pressures.  It
           doesn't seem to appear in there at all.  There's a
           pressure across that boundary where W4, W5 come out
           that affects the balance on that box.  No, the bottom
           thing.  Look at that shaded thing there.
                       DR. PAULSEN:  This one here?
                       CHAIRMAN WALLIS:  Your two pipe equation
           says everything is going from 2 to 3.  That's where we
           evaluate P1 and P2.
                       DR. PAULSEN:  That's right.
                       CHAIRMAN WALLIS:  There's a pressure
           across that top there that doesn't appear in the
           equation at all.  
                       DR. PAULSEN:  Across this one?
                       CHAIRMAN WALLIS:  Right.
                       DR. PAULSEN:  Right.  Now where we only
           use that simplified momentum equation, we only have
           coupling with one upstream volume --
                       CHAIRMAN WALLIS:  So physically it doesn't
           make any sense.
                       DR. PAULSEN:  -- and one downstream
                       CHAIRMAN WALLIS:  --  post-balanced the
           pressure across there has got to come into the
           balance.  Right?
                       DR. PAULSEN:  So the flow equation we
           write is simply for this pressure, this pressure.
                       CHAIRMAN WALLIS:  Well, I think it would
           be good if you could go through and actually derive
           the answer for this problem, all the way through to
           the final equation, showing how you evaluate the Ls
           and the As.
                       DR. PAULSEN:  That's sort of what I've got
           outlined here.
                       DR. SCHROCK:  Is there a version of this
           slide somewhere where you can read the subscripts?  I
           can't read them -- the one that's up there.
                       DR. PAULSEN:  The one that's up there?  
                       DR. SCHROCK:  Where can I find that where
           I can read the subscripts?
                       CHAIRMAN WALLIS:  They are lost in the
                       DR. PAULSEN:  It's in the RAI and it's an
                       DR. SCHROCK:  Is it legible there?
                       DR. PAULSEN:  It should be.
                       CHAIRMAN WALLIS:  When it's FAX'ed, it's
           not legible.    Well, it's fascinating, because if
           you've done this, you've done something which is very
                       DR. PAULSEN:  Well, the users do this all
           the time.  So they've done the challenging work.
                       DR. ZUBER:  Are you implying they are
           doing it correctly?
                       DR. PAULSEN:  Pardon me?
                       DR. ZUBER:  Are you implying they are
           doing it correctly?
                       DR. PAULSEN:  I think they have
           demonstrated in most cases that they are.
                       CHAIRMAN WALLIS:  This is a discussion of
           length here?
                       DR. PAULSEN:  Yes.  That's what this deals
                       DR. SCHROCK:  See, all of this that you
           are telling us seems to me to govern the choice of
           equations that are going to describe the system, but
           those equations have already been programmed into
           RETRAN.  What I'm having difficulty understanding is
           how your user guidelines on nodalization can influence
           what has been programmed.  I don't see that there is
           any way that it can do that unless you are going to
           tell us that there are a number of different things
           that are programmed and that the user chooses among
           various options.
                       DR. PAULSEN:  For the most case, the user
           will use the compressible form of the momentum
           equation that has the momentum flux terms, and then
           there will be area changes on the upstream and
           downstream volume for these kinds of geometries.  So
           there is basically an equation that's programmed that
           they use the same equation, and their input then will
           affect various terms in that equation.
                       As I mentioned, one of the primary terms
           in this equation is the inertia.  For one-D
           components, it's a geometric inertia.  For these 3-D
           components, it's something else.
                       In effect, if you imagine where you have
           flow coming into a downcomer, the flow first has to
           kind of wrap around the downcomer and then turn and go
           down.  So what the user has to do in determining the
           inertia then is to estimate via some engineering
           judgment or hand waving -- it's not an exact
           calculation -- be able to calculate what that flow
           path might be in determining what the geometric
           inertia is.
                       CHAIRMAN WALLIS:  Some kind of average
           length of a stream line or something?
                       DR. PAULSEN:  That's one way of doing it. 
           One of the complications you run into there is that
           stream lines may change during the transient.
                       CHAIRMAN WALLIS:  See, in the Porsching
           paper it says it's volume divided by area, which I
           don't think is really the right answer.  I convinced
           myself, if I had a pipe that went around a complete
           circle, that the momentum in that pipe is zero,
           because everything balances, and it can be a long
           circle.  If I take a pipe and bend it in a circle,
           that circle has no momentum in it, if it's a steady
           flow or incompressible flow.
                       DR. PAULSEN:  Okay.  
                       CHAIRMAN WALLIS:  If you are following the
           length all the way around, that makes sense.
                       DR. PAULSEN:  So you follow, in effect,
           the flow path of the stream lines.
                       CHAIRMAN WALLIS:  That's different from
           looking at the entire momentum, because the actual
           momentum added up is zero.
                       DR. PAULSEN:  Right.  
                       DR. ZUBER:  Do you contend that this code
           is a best estimate code or what?
                       DR. PAULSEN:  A best estimate?  In some
           senses, yes.  There aren't an awful lot of
           conservatisms built into the code itself.
                       DR. ZUBER:  There are?
                       DR. PAULSEN:  There aren't.  One area --
           You know, there may be a model here or there like a
           critical flow model that's a conservative form of the
           model, but because of the way that model is used--
                       CHAIRMAN WALLIS:  So you showed a picture
           here.  The answer is it's the length, the average
           length of a stream line or something, and there is
           some rationale for that?
                       DR. PAULSEN:  That's right.  So you have
           to kind of visualize what the flow path might be.
                       CHAIRMAN WALLIS:  Does it matter if it's
           fatter at one end than the other?
                       DR. PAULSEN:  Yes, it does, if you want to
           account for all of those effects.  Basically, in the
           user guidelines it spells out whether you've got
           parallel paths that you've got lumped into your
           junction or whether you have serial paths.
                       CHAIRMAN WALLIS:  Okay.  So you could walk
           us through, if you had the time, how you actually
           calculate L and A for those three geometries you just
           showed us?
                       DR. PAULSEN:  That's right.  Basically,
           all I wanted to point out was that there are not
           rigorously developed equations for how you do it but
           some rationale for how you actually calculate those.
                       CHAIRMAN WALLIS:  See, the concern I have
           is I couldn't understand what you say, and I still
           don't.  But maybe a user gets enough training that he
           or she can do it.  If it's so much up to the user, the
           users might choose all kinds of different Ls and As,
           depending on their own preference.  So you get all
           different answers to the same problem, depending on
           who happened to use the code.
                       DR. PAULSEN:  Well, and in fact, that's
           why you have to do some sensitivity studies to find
           out where the sensitivities are in the model.  You
           know, some -- Inertia on some junctions may not affect
           this solution --
                       CHAIRMAN WALLIS:  Does this mean that the
           NRC has to review how a particular user has chosen to
           work out these things and provide some kind of
           validation of it every time?
                       DR. PAULSEN:  There are a lot of
           guidelines that people routinely follow and standard
           sensitivity analyses that people do. A lot of things
           that are common in models, although they are not
           exactly the same, but people learn from previous use.
                       For instance, a report for a particular
           transient may identify that there's a particular
           inertia that is sensitive.  So you may have to use
           some kind of a more representative inertia in a
           particular area for a given kind of transient.
                       CHAIRMAN WALLIS:  So there's a whole lot
           of evolution of how to use the code which we don't
           know about, which is why it works today, because
           people have learned.  You don't just blindly follow
           some guideline, that you have to do something special
           with this particular node and with that node.  
                       So all of that is missing when we simply
           look at some documentation.
                       DR. PAULSEN:  Yes.  A lot of that
           information is like in Volume 5.
                       CHAIRMAN WALLIS:  But we need to know
           that.  I think, if we are going to make a judgment, we
           have to know that, and we can't just base it on our
           assurance that this 30 years of experience, therefore,
           has to be good.
                       DR. PAULSEN:  I can appreciate that.  
                       CHAIRMAN WALLIS:  Sorry, Novak, you had a
                       DR. ZUBER:  I agree completely with you. 
           But it is distressing that the code which we developed
           years ago, 20 years, 30 years ago, I realize to be
           poor, and we wanted to do something better.  Now you
           are developing a best estimate code which essentially
           has the same shortcomings as those codes of 20 years
           ago and 30 years ago.
                       And we are really not -- to say, look,
           this is how it is done and this is what it's for.  You
           have kind of an arm waving argument, and you passed it
           back to NRC and to the customer, and this is not a
           good way to evaluate safety.
                       CHAIRMAN WALLIS:  But it may not -- You
           know, it's evolved.  So there may not be equations
           that describe the workings of your knee, but your knee
           has evolved until it works.  So something like that is
           happening here with this code.
                       DR. ZUBER:  Well, the thing is -- the
           simplest thing, look at the downcomer -- Even for the
           pipes, on the straight pipes we have problems.  There
           were problems you were not able to explain.  With the
           downcomers, it's purely arm waving.
                       DR. PAULSEN:  There is no doubt about
           these three-dimensional geometries.  They --
                       DR. ZUBER:  -- if it was just the elbow,
           I mean, that Graham brought up.  That's a simple one. 
           I can always make it more complicated and say I cannot
           solve it, and we have to agree on that.
                       DR. PAULSEN:  One of the points I would
           like to make, though, is the fact that elbows normally
           aren't modeled.  In a model you may have something
           that looks like an elbow where the hotleg or the
           coldleg connects to the downcomer, where the hotleg
           leaves the upper plenum.  
                       You may have a T where the surge line
           connects.  I've got some examples that kind of show
           the types of pressure differences we see there by
           including these momentum effects, and then an example
           of what it does to a typical Chapter 15 transient that
           might kind of give you a flavor for what's going on.
                       CHAIRMAN WALLIS:  How much stuff do we
           have to look at to go through all that?
                       DR. PAULSEN:  There's just a little bit. 
           I don't want to spend a lot of time, because I think
           we understand where your concerns are.
                       Basically, I just wanted to point out that
           when you go to this three-dimensional, modeling the
           three-dimensional components,t here's some guidance in
           terms of rules, but there is nothing absolute.  There
           is nothing as definitive as the equation for the 1-D
           or for the straight pipe.
                       CHAIRMAN WALLIS:  So the staff in
           evaluating a code like this would be quite within
           their purview and all that to say we think that L
           should be twice as long for this node; let's try it
           and see what happens.  
                       DR. PAULSEN:  And I think past reviews
           have done things like that.  Past reviews have done
           things like that or asked what's the sensitivity in
           this particular loss coefficient or inertia.
                       DR. ZUBER:  Had you done the thing
           correctly two years ago, we would not have this
           discussion.  If you had addressed all the concerns and
           then even using the same equations addressed the
           sensitivity of each term, and probably you could get
           some of these problems to rest.  Now it is just plan
           arm waving.
                       DR. PAULSEN:  When it comes to coming from
           the downcomer into the lower plenum, then the inertia
           terms and the flow length terms, you have to kind of
           visualize what the flow --
                       CHAIRMAN WALLIS:  You see, that's the
           problem I had, because you told me it was coming in
           and going out into the lower plenum.  So you in was at
           the top, and your out was at the bottom.
                       Now you are saying your in is at the top
           and your out is at the top again.  That's a different
           model from what you just described.
                       DR. PAULSEN:  This is how we would
           calculate the inertia.  We actually -- For the inertia
           we actually look at that path.
                       CHAIRMAN WALLIS:  But your two pipe thing
           -- you just explained to me it comes in at the top and
           it goes into the lower plenum.  That's the in and the
           out.  Now your in and out is a different in and out. 
           It can't be both.
                       DR. PAULSEN:  Yes, I see what your concern
                       CHAIRMAN WALLIS:  Yes.  It's a very simple
           concern.  I mean, my seven-year-old grandson would
           probably have the same concern.  
                       DR. ZUBER:  Let me ask you, how do you
           determine that it is one-half of your downcomer? 
           Again, why not one-third or one-fifth?
                       DR. PAULSEN:  Oh, it isn't.  For a
           situation like this, it isn't one-half.  For a
           situation like this, the user has to look at how he's
           got his model nodalized.  If he's got one node, then
           he has to kind of look at what the flow path might be
           through the hardware.  
                       In fact, normally, this flow length is
           going to be much longer than the one-half.
                       DR. ZUBER:  Okay.  Then let me ask you: 
           Did you do a sensitivity analysis on that to see what
           is the --
                       DR. PAULSEN:  Users do these kinds of
           sensitivity --
                       DR. ZUBER:  No.  Look, users -- I am not
           talking to the users.  I am merely talking, did you? 
           I have concerns about your approach and assumptions,
           and then you want to defend it.  And my question is
           you tried to explain how you determine -- My question
           is did you perform some analyses, calculations, or
           take twice that length, half that length and see what
           is the effect?
                       DR. PAULSEN:  Those are pretty common
           things that we do when we do analysis.
                       DR. ZUBER:  Well, the question is -- My
           question is did you, and what is the effect; and if
           you did it, then where I can read it?
                       DR. PAULSEN:  Okay.  We haven't run any
           specific analyses right now that we could point a
           finger to, but --
                       DR. ZUBER:  You answered the question. 
           You see, the problem we have is you have these
           assumptions you cannot really defend.  You always say
           this was done 30 years ago, this was approved, and
           then you explain something and you don't run the
           sensitivity analysis.
                       DR. PAULSEN:  For a specific application,
           these sensitivity studies are run quite often.
                       DR. ZUBER:  See, but you want to have a
           code approved, and this is something which is
           questioned in the analysis.  You have two pipes.  You
           want to model a very complicated -- my own guess is an
           engineer would be, okay, I should then run L to see
           what is the effect, and if the effect is important, I
           would address it.  If it's not important, I would say,
           Zuber, shut up, I have done it and here is the result. 
           And you didn't do it.
                       CHAIRMAN WALLIS:  Well, I just wonder --
                       DR. PAULSEN:  This term will vary,
           depending on the kind of transient you are having.
                       CHAIRMAN WALLIS:  I'm wondering where we
           could be.  I mean, we could simply say that as ACRS we
           appreciate there's a 30 year law of how to interpret
           all these things so that they work, and there is no
           way that we can possibly penetrate this tribal
           knowledge by simply saying we don't really have much
           to say.
                       DR. SHACK;  Well, we've passed a lot of
           other codes that had the same problems.
                       CHAIRMAN WALLIS:  And that's part of the
                       DR. KRESS:  That is exactly the
                       DR. ZUBER:  Wait, wait just a moment. 
           Wait, wait, wait.  No, you have to answer  your
           question.  These codes were designed to address one
           problem, where we have quite a different era.  We had
           quite a bit of conservatism.  Now we are getting into
           the regulations.  That conservatism is going to
           decrease.  We have to have better codes.
                       What I hear from this presentation and
           previous, we won't have them.  We don't have them, and
           the worst irritation to me is you don't even
           appreciate what this will mean to this technology.
                       This intervenor could really run rings 
           around the NRC in the analysis like that, and I hope
           it doesn't come.  But --
                       CHAIRMAN WALLIS:  I think we have to say
           that there is no way we can penetrate the lore, l-o-r-
           e, of 30 years.  But we can look at something like an
           example of following a flow around a bend and say does
           this establish credibility.  That's about the only
           level the ACRS can penetrate to, because there is so
           much other stuff that you have to sort of been in the
           business for years to --
                       DR. ZUBER:  But, Graham, but the point is
           that first simple thing you cannot really even get a
           positive answer to it, and the question is then -- my
           judgment would be have a letter, list the concerns,
           and it's up to the NRR to make a decision.
                       DR. SCHROCK:  I am still struggling with
           the problem of the simplest technical communication
           here.  We have something on the projector there at the
           moment which is unclear, unexplained, and it's being
           talked about as though we all understand what it
                       I don't think we have the same
           understanding of it.  I certainly don't understand
           what you mean by that picture.  Have you divided the
           downcomer into four segments, and you are showing what
           projects onto the -- Here you got a --
                       DR. PAULSEN:  That's right.
                       DR. SCHROCK:  -- cut through the thing,
           and now it's projecting down into a vertical view of
           the lower plenum, and --
                       DR. PAULSEN:  That's right.
                       DR. SCHROCK: -- you are showing the flow
           which is in that one-fourth of the whole downcomer?
                       DR. PAULSEN:  That's correct.  It would be
           flow coming down --
                       DR. SCHROCK:  Did others understand that?
                       DR. PAULSEN:  -- down this portion of the
           downcomer.  So it would be --
                       DR. SCHROCK:  But the whole downcomer is
           represented as one pipe.  
                       DR. PAULSEN:  That's right.  And so if
           you've represented this as one pipe and you've got
           four parallel paths that you have -- in this case,
           they might be symmetric parallel paths.  So there are
           guidance on how you would combine inertias for these
           four parallel paths for one effective path.
                       DR. ZUBER:  Which you evaluate the
           sensitivity of, how you calculated.
                       DR. PAULSEN:  That's the recommendation,
           is that we do sensitivity studies on these.
                       DR. ZUBER:  And you didn't do them yet,
           did you?
                       DR. PAULSEN:  I'm trying to point out that
           those sensitivity studies are model-specific.  We have
           done sensitivity studies on a number of models, but
           the sensitivities may be different when you move to a
           different model.
                       DR. ZUBER:  What you mean, model?  It's
           the same equations or what?
                       DR. PAULSEN:  The level of nodalization.
                       CHAIRMAN WALLIS:  I am going to backtrack
           to this morning when I showed you a 180 degree bend,
           and I wondered if it was fair to do that.  But it
           seems to me, you are showing it to me now in something
           you prepared before I showed it to you.  I had a lot
           of trouble figuring out how the size and he momentum
           fluxes and things applied to a 180 degree bend, and I
           think that's still a problem.
                       You know, that equation doesn't clearly
           apply to something like this picture, and this isn't
           two pipes.  So I'm not quite sure what you are showing
           me.  Do you claim that your RETRAN equation works for
           this sort of a --
                       DR. SCHROCK:  He is going to show you how
           to calculate the equivalent pipe through the lower
                       DR. PAULSEN:  That's right.
                       DR. SCHROCK:  By looking at this flow
                       CHAIRMAN WALLIS:  It's the length of that
                       DR. ZUBER:  Yes.  That pipe can be
                       DR. PAULSEN:  It's the length of this flow
                       CHAIRMAN WALLIS:  And the pressures are at
           the top of each side and all that, and clearly the
           momentum balance doesn't work, but you have sort of
           imagined that if it were straight, it would work out
           this way.
                       DR. ZUBER:  Let me ask you something.  I'm
           sorry.  What kind of guidance -- What kind of peer
           review groups you had in conducting this?
                       DR. PAULSEN:  In doing this?  
                       DR. ZUBER:  I mean developing this RELAP
           -- or RETRAN-3D.
                       DR. PAULSEN:  This portion of the code
           really is not new.  This modeling technique has been
           used and is a carryover from RELAP-4.
                       DR. ZUBER:  And RELAP3.
                       DR. PAULSEN:  And in some cases -- The
           momentum flux terms, no, but these inertia terms are
           carryovers from RELAP3.  The other systems' codes do
           this type --
                       DR. ZUBER:  The problem is this was a
           different requirement, different environment, and you
           are developing code that should be used for the next
           ten years when you have increase of power, decrease of
                       CHAIRMAN WALLIS:  That's why we need lots
           of assessment if it is going to be used.
                       DR. ZUBER:  Well, I don't see it here, but
           in doing even this most trivial one, just to see what
           is the effect of that length, and you leave it to the
           user to the NRR to calculate it.
                       DR. PAULSEN:  All I'm trying to say is
           there is no way we can do one sensitivity study on an
           inertia in a given model and give blanket coverage of
           what the --
                       DR. ZUBER:  No, just for your intellectual
           -- Granted, I mean, it will take twice as long, three
           times as short, and see what the result is.
                       DR. PAULSEN:  We have done those in years
           past on numbers of cases when we were doing loft and
           semi-scale experiments, when we were doing plant
           transients to look at responses.  Those are the kinds
           of things that we do and that we tell users to do, is
           to look at the sensitivities of those terms.
                       DR. SCHROCK;  But what do you do about
           phase separation in this imagined u-bend representing
           the plenum?
                       DR. PAULSEN:  The case that we've shown
           here would be for a case with no phase separation. 
           You know, if you start getting phase separation or
           your flow pattern changes significantly, then that
           inertia can change during the transient, and then
           that's another sensitivity that you are going to have
           to consider.
                       DR. SCHROCK;  Well, of course, it's the
           inertia that causes the phase separation.  
                       CHAIRMAN WALLIS:  So check several of
           those works for a 180 degree bend like that?  
                       DR. PAULSEN:  In most cases, we wouldn't
           apply that down here.
                       CHAIRMAN WALLIS:  Well, you've got to use
                       DR. SCHROCK:  But in some cases, you
                       DR. PAULSEN:  For the transient, Chapter
           15 transient analyses that we typically use RETRAN
           for, we wouldn't encounter that kind of a situation. 
           That would be more of a small break.
                       CHAIRMAN WALLIS:  I think we know where we
           are now with all this, and we're not quite sure where
           we are going.  I think, since some of us are leaving
           at three, we ought to have a discussion between us and
           you folks and NRR about where we want to go from here.
                       DR. PAULSEN:  I guess I have one question. 
           That's if this last information kind of completes the
           picture or if there's still something missing?  
                       CHAIRMAN WALLIS:  Well, what you've sort
           of done is I think that you've assured me, and I
           believe it, that people have worked with these things,
           whatever their weaknesses, for 30 years, and they have
           evolved a lore and a way of learning how you have to
           fix things up so that all these things work out for
           the kind of problems they have been solving.
                       I think you do have a real problem with
           documentation as it is, establishing credibility of
           the methods for anyone except someone who is one of
           those people familiar with this 30 year lore.  I think
           that is a real problem when you face the intellectual
           community, professors at universities, the students in
           universities, the engineers out there who become
           engineers who see this stuff and say, gee whiz, I
           don't want to be part of that because it doesn't make
           sense to me, I'll go and get a different job, all that
           kind of stuff.
                       That's where the problem is.  That's where
           we have the problem, but we are not sure that we are
           in the position -- NRR can evaluate the lore and say
           we believe that's fine, we understand there's been a
           big learning experience.
                       We have much more difficulty with that. 
           But we can evaluate much more readily the worked
           examples, the justification for the equations, and I
           think that's where you fall down.  It's not a
           convincing story.
                       I wonder what you wanted to do about that
           in terms of fixing it up, and do you really want to go
           before the full committee next week where some of
           these questions may come up again in exactly the same
           form. I 'm not quite sure -- I don't think they are
           resolved, really, are they?
                       DR. PAULSEN:  I don't think all of them
           are, no.  Before we move from here, I guess, if we
           were to revise the documentation to kind of point
           users in the direction of how you model more complex
           geometry with some of the illustrations that I've just
           presented, and then refer them to modeling guidelines,
           do you think that would be an improvement and address
           some --
                       CHAIRMAN WALLIS:  That would certainly
           convey much more information which would be helpful. 
           It might give us the same qualms about the momentum
           balance, because we would look at these complex
           geometries and say, gee whiz, the same way we do for
           the simple ones.  
                       DR. PAULSEN:  But at least put together
           the picture of how the whole plant would be modeled
           and how the pieces go together.
                       CHAIRMAN WALLIS:  Well, of course, that is
           the engineering problem you address.  My critique of
           all these codes is they launch into Navier-Stokes
           equations, blah, blah, blah.  They should define the
           problem first and say this is what we need to do, and
           these are the kind of assumptions we may have to make,
           because these are the variables we are dealing with
           and these are the things that matter; this is why we
           are going to do it.
                       Developing sort of equations in a vacuum
           and then saying, we think they apply, is just not
           quite perhaps the way to do it.  I don't know how much
           you want to rewrite.
                       I think we have a real concern with SERs
           being issued before the documentation has been fixed
                       DR. PAULSEN:  Okay.  And I guess we have
           taken the position that we have told the Commission
           that we are going to make particular revisions.
                       CHAIRMAN WALLIS:  See, we have told the
           Commission that there appear to be basic errors in
           these momentum balances, and you have told the
           Commission they are out to lunch, they are fine,
           everything is great about these momentum balances, and
           we are going to show them it's all right.
                       That was about the dialogue that was
           presented at the beginning of today, and I don't think
           we are much further ahead there.  We still have the
           same reservation.  The only thing that we are doubtful
           about is, well, in spite of all that, is this still a
           good code.
                       DR. PAULSEN:  Okay.  But I think we have
           come to -- at least that the equations that we are
           using in the code seem to predict the physics
           reasonably well in terms of expansions --
                       DR. ZUBER:  I didn't see that.  I didn't
           see it.
                       DR. PAULSEN:  Okay.
                       DR. ZUBER:  It seems convincing.  You were
           not able to explain the simple examples.  When I asked
           you how you did out of the Bernoulli equations, you
           were not able to see the difference between the
           Bernoulli equations and the momentum equations.  It's
           an ad hoc approach, and if you use this approach, and
           it's up to you to say up front this is what we did
           and, therefore, we have done this and this and this
           sensitivity analysis to address this and this and
           these questions, and I didn't see that either.
                       This is my summary.
                       CHAIRMAN WALLIS:  So we may end up, if we
           have this meeting next week, about where we are now. 
           I'm not quite sure how we would come out.
                       DR. KRESS:  I can't see much of a
           possibility of us coming out in the full committee any
           different than where we are right now.
                       DR. SHACK:  What are our questions?  I
           mean, is it how do you nodalize a three-dimensional
           flow for a one-dimensional code?  When we approved S-
           RELAP last time, it didn't bother us then.  
                       DR. ZUBER:  It is a little different
           environment.  We did this approach 30 years ago,
           because we addressed a different problem.  Now you are
           decreasing the -- you want to obtain better, more
           efficient blend, and they should do it.  But they
           should really correct the approach.
                       I won't do the same approach with the same
           shortcoming by decreasing the margin of safety, and
           that's a problem I see.  Otherwise, I wouldn't be
           complaining, because we have enough margin.  But this
           code is going to be used for the next 15 years, and in
           15 years you can imagine how much the margin will be
           reduced, and this is the problem which ACRS has to
                       CHAIRMAN WALLIS:  Well, we were careful in
           RELAP.  We said that this is -- we don't disagree with
           the staff, because the staff is in a box.  It's
           approved RELAP for other purposes; they can't very
           well turn it down for Siemens.  That was the kind of
           thing.  We were in the box.  But then we had a lot of
           qualifications in saying the documentation had all of
           these errors and things we point out before and, when
           this is done for a best estimate code, that's got to
           be fixed.
                       DR. SHACK:  Let's separate best estimate
           codes -- You know, there we had the explicit
           requirement to evaluate uncertainties, and that
           includes all uncertainties, whether it's, you know,
           how do you nodalize a three-dimensional problem into
           a one-dimensional problem.  But as I say, to suddenly
           at this point bring up how do you nodalize a three-
           dimensional solution into a one-dimensional problem,
           as though,  you know, we've been doing it for --
                       CHAIRMAN WALLIS:  I don't think it's
           unfair at all, and we are members of the public
           looking in at how things are done, and if it's been
           done this way for 20 years and it still doesn't make
           sense to us, we have every right to say it doesn't
           make sense to us.  There must be some mysterious lore
           practiced by this industry which makes it work.  We
           have every right to say that.
                       DR. ZUBER:  And as technical men, it was
           all right to go to the public at technical meetings.
                       CHAIRMAN WALLIS:  But we don't want to
           give the public the wrong impression.
                       DR. ZUBER:  Okay, fine.  But don't --
                       CHAIRMAN WALLIS:  We don't want to give
           them the impression that, because there are all these
           things that you wouldn't accept in undergraduate
           homework, the whole structure that's evolved over 30
           years is hopeless.  We don't want to give that
                       DR. ZUBER:  No, you can leave it,  because
           you have quite a bit of conservatism.  I mean, you can
           always argue that point.  But now we are going to
           decrease it, and we should.  But then you should do it
           correctly.  I think this is the change of environment. 
           This is what the ACRS has to consider.
                       On the other hand, I'm not concerned with
           the 3D.  I'm really concerned with the other momentum
           equations and --
                       CHAIRMAN WALLIS:  There are bigger
           questions, though.  It's this working entirely in this
           regulatory environment that bothers me.  I go back to
           the question of the student.  If I have students
           working on fluid mechanics and they start to say I
           want to be a nuclear engineer, and they start to look
           at this stuff, if all they see is this sort of
           documentation, I think you turn them off, because they
           wouldn't see all the other stuff which is the 30 years
           of experience that it works.  I don't want that to
                       DR. ZUBER:  There is something worse. 
           Sometimes when I read reports like this, I feel sorry
           that I have put my technical life in this technology.
                       CHAIRMAN WALLIS:  Well, I have trouble
           sleeping sometimes, and that shouldn't happen.
                       DR. SCHROCK:  I'd like to point out that
           in this last little bit of discussion here, you,
           Graham, were saying, well, we can maybe accept a lot
           of this fuzziness, but when we go on to best estimate
           codes, Bill made a comment about best estimate codes
           which implied to me that you didn't hear what Mr.
           Paulsen had to say about what he views this code as
                       He says it's best estimate.
                       CHAIRMAN WALLIS:  It's the best they could
                       DR. SHACK:  You know, people have
           different meanings to the meaning best estimate.
                       DR. KRESS:  He meant there were no
           purposeful conservatisms in that.
                       DR. SHACK:  But from the NRC's point of
           view, a best estimate code means one where you
           explicitly address all the uncertainties.
                       DR. SCHROCK;  It means one that is going
           to be submitted under the new rules and required
           uncertainty evaluation, precisely.  
                       CHAIRMAN WALLIS:  Well, I admire your
           struggling with the problem.  It's a difficult one,
           and you may have got something which works for the 
           kind of things we've done up to now in nuclear safety. 
           But I can't get over the business of just looking at
           this thing that, if it were on undergraduate homework,
           I wouldn't like to see that kind of an answer.  That
           shouldn't happen, and I can't reconcile these things.
                       DR. PAULSEN:  We'll go back and reexamine
                       CHAIRMAN WALLIS:  Do you guys want to come
           in next week?  What are you going to say?
                       DR. PAULSEN:  Jack?
                       CHAIRMAN WALLIS:  Usually, we give someone
           advice about how you should present yourselves to the
           full committee.  Is there a hurry? You've taken two
           years.  Do we have to rush to judgment next week?
                       MR. HAUGH:  Certainly, the schedule is
           yours to set.  I mean, if this is locked in concrete
           beyond --
                       CHAIRMAN WALLIS:  No, there was another
           presentation on water hammer where the EPRI presenters
           decided they didn't like the critique they had had,
           and they wanted to go back and work on it and come
           back with something better.  That happened a month or
           two ago.  You don't have to meet this schedule.
                       MR. HAUGH:  Well, perhaps we could
           reconsider that date, as you are suggesting, but
           there's a question of just, you know, how much work
           can be done in any one given time, and that's going to
           be a question of trying to define exactly what we need
           to bring back to you, and that would determine the
           length of time needed.
                       We can't, in the space of a week or so,
           completely re-derive everything, reformulate all the
           documentation, etcetera, etcetera.  So I mean, there
           has to be some specificity as to what would be needed.
                       CHAIRMAN WALLIS:  That's not realistic for
           you to reformulate everything in a week.
                       MR. HAUGH:  Yes.  That's what I'm saying.
                       CHAIRMAN WALLIS:  So in a week, we would
           have to write a judgment based on what we see, and if
           we felt so moved to, we might write a detailed
           critique of all these twos and root twos and lack of
           forces on bends and stuff, and put it all in writing
           as the report next week.  I just wonder if you want to
           see that happen, if we have to critique what we've
           got.  I'm not sure that gets anybody any benefit.
                       MR. HAUGH:  I think I would agree with you
           on that statement, certainly.
                       CHAIRMAN WALLIS:  But if it gets no one
           any benefit, why are we doing it?
                       MR. HAUGH:  Right.  
                       CHAIRMAN WALLIS:  Well, I think you
           perhaps need to think about it in the next day or two
           or something.
                       DR. KRESS:  Keep in mind, you don't lose
           anything at all by delaying it and not showing up. 
           There's nothing you lose except a little time.
                       CHAIRMAN WALLIS:  Well, he's sensitive
           that Dana is no longer the Chair.  We don't have this
           person keeping us on track all the time, we have to do
           things on time.
                       DR. POWERS:  If they choose not to come
           before the full committee, all that would happen would
           be that the subcommittee Chairman would give a summary
           of what their status was on things, which to my mind
           is -- I apologize that I've been over meeting with the
           Commission, so I haven't heard everything, but that
           there is -- you are on a path, closer pathway to
           resolution than I've ever seen before.
                       CHAIRMAN WALLIS:  I think we could say
           that we had a very good meeting, that now we
           understand each other.  Now we think EPRI understands
           the concerns, and we believe that they understand them
           well enough that there's hope that they address them
                       That would be what we would say, something
           like that.  We would hope we would be able to say
           that, because you've been far more responsive in this
           meeting than the last time we had a meeting with EPRI,
           and we are not on some treadmill that says next week
           we have to do what was on the schedule.
                       MR. HAUGH:  Okay.  To have complementarity
           in terms of the good feelings on leaving the meeting,
           we would like to request an opportunity to present at
           least one more piece of information here.
                       It shows when you make these different
           cases and ways of doing it, does it really make a
           difference or not?  And perhaps that's something that
           needs to be considered as well in terms of crafting
           what it is that we would be expected to do by whatever
           time.   We would appreciate your indulgence on that.
                       CHAIRMAN WALLIS:  That is useful
           information, too.
                       MR. HAUGH:  Okay.  Thank you.
                       CHAIRMAN WALLIS:  Do you want to say that
                       DR. PAULSEN:  There are just a couple of
           quick slides that I'd like to show, just for
           illustrative purposes on what some of the effects
           might be.
                       I think this was the reason we got caught
           in the trap of trying to carry the vector information
           along, which did nothing but add confusion.  For a
           situation like this where we have a coldleg and a
           pressurizer with a surge line, if we have a situation
           where we don't account for the effects of angles, in
           this particular case where we have no angles, if we
           were to input a pressure of 2200 in the pressurizer,
           our pressurizer in the hotleg would end up being 2205,
           which is less than the hydrostatic head for that
           particular path.
                       When we actually put in the angle effect
           in this junction, it in effect knocks out this
           velocity head upstream so that it doesn't affect this
           piece that goes off at 90 degrees.
                       CHAIRMAN WALLIS:  But if it were a true
           Bernoulli, it might affect it.
                       DR. PAULSEN:  If there were some flow,
                       CHAIRMAN WALLIS:  And of course, in this
           case you might have flow coming from two and one, and
           I had a problem with that T when you had your W1, W2. 
           Two actually could be negative, and I didn't quite
           understand how you handled that.
                       DR. PAULSEN:  So this is just an example
           showing at steady state where these angular effects in
           some cases need to be included to get the right
           pressure distribution.
                       CHAIRMAN WALLIS:  It indicates to me,
           though, that you got to be careful, because the delta
           p, the difference in the pressure here, is 5 and 26.
                       DR. PAULSEN:  That's right.
                       CHAIRMAN WALLIS:  Depending on what
           assumptions you make.  That's a big change.
                       DR. PAULSEN:  That's right.  But it's only
           at local pressure.  But in the case where we specify
           the pressure in the pressurizer, this could give us 20
           psi wrong in the rest of the system.
                       DR. PAULSEN:  It's the delta P that drives
           the flow and, if it's five times as big, you might get
           a flow in the surge line which is wrong by a factor of
           two and  half or something.  That might make a
           difference to the transient.
                       DR. PAULSEN:  That's right.
                       CHAIRMAN WALLIS:  So there are cases.  We
           were a bit concerned about these dP 600, 1000 type
           things where the pressure, hydrostatic balances
           throughout these different bathtubs that Novak talks
           about makes a difference to whether the water goes
           this way or that way.  You have to get your delta Ps
           right more accurately than perhaps you do in some of
           these things where there's a big hole and everything--
                       DR. PAULSEN:  Where you don't have as
           large forcing function, those hydrostatic heads there
           are what drive the system.  That's right.
                       DR. SHACK;  Now let me just understand
           this a little bit better.  In the case one you sort of
           arbitrarily set the angles to zero.
                       DR. PAULSEN:  This is if we neglect all of
           the angle information and just treat everything as
           straight pipes.  Then in effect, this pipe is going to
           be, you know, downstream of this pipe.  So it's going
           to see the velocity term upstream from this piece,
           which will then --
                       CHAIRMAN WALLIS:  Turn around the corner?
                       DR. PAULSEN:  Yes.  It makes it think it's
           going around the corner, where it is really not.  So
                       CHAIRMAN WALLIS:  But the two pipe model
           would do that to you, because a two pipe model is
           energy conservation, and Bernoulli would do that,
           wouldn't it?
                       DR. PAULSEN:  This is a case -- I probably
           didn't give enough conditions.  This is the steady
           state case where we have no flow in the surge line. 
           So that's something I missed.
                       So I just want to point this out, that
           there are some cases where you really need to account
           for some of these --
                       CHAIRMAN WALLIS:  What I did with your T
           was I said what happens if W2 is zero.  That's where
           I got my V2 over 4.
                       DR. PAULSEN:  Oh, that one?  
                       CHAIRMAN WALLIS:  And I couldn't see how
           I took this V2 over 4 and the other and compared it
           with Bernoulli.
                       DR. PAULSEN:  Okay.  
                       CHAIRMAN WALLIS:  So I think you are
           illustrating that there might be -- it might be
           important if you do this right.
                       DR. PAULSEN:  Right.  This just happens to
           be something that looks like an elbow where we have
           actually included -- This is horizontal.  So it's
           laying at a plane.  So we don't have any gravity. 
           We've turned off all the friction, and we have a
           uniform pipe, no heating.
                       So you can see that we have a uniform
           pressure until we hit this bend, and then it looks
           sort of like a stagnation point.
                       CHAIRMAN WALLIS:  Right.
                       DR. PAULSEN:  So the pressure elevates. 
           But as soon as you get around the bend, that
           recoverable pieces come back.
                       CHAIRMAN WALLIS:  What this would do,
           though, is it would squirt flow out and prevent flow
           coming in, so that it would rob the corner of mass,
           wouldn't it?  It would unofficially rob the corner of
           mass, because these pressure differences would then
           drive a change in flow if you put this into the code. 
           So it would rob that corner of mass.
                       DR. PAULSEN:  I'm not sure it would really
           have any effect unless you had some other connections.
                       CHAIRMAN WALLIS:  It would calculate a
                       DR. PAULSEN:  Yes.  
                       CHAIRMAN WALLIS:  Probably.  
                       DR. SCHROCK:  In that picture, you have
           the junction 21, junction 21 and -2 in your little
           tables, but in the picture you have a 19 and no 20.
                       DR. PAULSEN:  These angles would be for
           20.  This is 20. This would be 20, 21.  So these would
           be these two, this path, and this one and two then
           would be the hotleg path.  So that's a 20.
                       CHAIRMAN WALLIS:  Well, this is why for
           some of these T junctions RES is actually doing
           research and measuring some of these things.  
                       DR. PAULSEN:  We are actually --
                       CHAIRMAN WALLIS:  That would be the way to
           resolve some of these questions.  
                       DR. PAULSEN:  And we actually have some
           people in Switzerland that are using the code to
           actually try and compare with some data for T's.  So,
           hopefully, we'll have some data in the -- or some
           actual comparisons with data to help justify use of
           the code for T's.  
                       This is an example where we took just a
           simple PWR transient model.  It was a single loop
           model, and generally users don't model a lot of this
           angular information.  They would even model this as a
           straight pipe, this as a straight pipe, and then they
           will angle differences down here.
                       So what I've got is a case where we have
           zero angles and then the case where we have actually
           put in the 90 degree turn here, and then have these
           two junctions 180 degrees away from this junction.
                       Basically, the results of this case are
           that, when you do that -- provide that information, it
           doesn't change anything in the system except where the
           angle changes.  So we would see a change in the
           downcomer, a change in the upper plenum, and a change
           in the lower plenum pressure. 
                       So case one listed here are the base cases
           with no angles, and then case two was where we have
           included the effects of angles.
                       CHAIRMAN WALLIS:  Probably means the
           momentum flux terms are small.
                       DR. PAULSEN:  And that's what the next
           slides show, is that, you know, at most this affects
           pressures by a psi or two.  It's probably not going to
           -- and based on that, I would say it's not going to
           change the transient much, but I've cheated.  We
           already ran that.
                       CHAIRMAN WALLIS:  I think you should say
           that right up front.  You should say there are
           difficulties with modeling momentum equation.  You
           have to make some assumptions to get on with it. 
           We've tried various assumptions.  They make this kind
           of difference, and this is what's in the code, and
           that's why.  
                       DR. PAULSEN:  I think we're seeing --
                       CHAIRMAN WALLIS:  This sort of pseudo-
           academic stuff is not doing much help.
                       DR. PAULSEN:  That's right.  And
           basically, you can see that this is the two cases for
           a typical transient, and this happens to be the surge
           line flow for a typical Chapter 15 analysis.
                       Basically, there was no difference in the
           surge line flow.  There was really no difference
           anywhere except in the upper plenum pressures where we
           had about a psi or two that were different, and
           there's just an offset in the pressure that tracks
           through the transient.
                       I think, if you look at the slides, one of
           them, there's a slight difference, but in effect these
           momentum flux terms which for at least this case don't
           have much significant --
                       CHAIRMAN WALLIS:  The academic reviewer 
           looking at these things tends to regard it as being
           basically immoral to do a full momentum balance.
                       DR. PAULSEN:  Well, and there are
           situations where momentum flux may be more important. 
           So you want to make sure it's right.
                       CHAIRMAN WALLIS:  But in reality, it
           doesn't matter.  It's only a small sin.  
                       DR. PAULSEN:  I guess I'm going to skip
           over the RAI questions.  I think I wanted to go to
           this last slide, because this kind of summarizes what
           we've tried to do.
                       We've actually, from my personal point of
           view, tried to make a conscientious effort to address
           your concerns, but I think we were missing the target,
           and I think now --
                       CHAIRMAN WALLIS:  I think our conclusion,
           looking at your replies, was you don't understand what
           we're talking about.
                       DR. PAULSEN:  So we've made -- We have
           made some code revisions and error corrections where
           we identified those, and we've tried to evaluate the
           error corrections on what impact they might have, and
           we've attempted to revise the documentation so it's
           more complete.
                       I think maybe we have identified some
           areas where we could use some further change.  But the
           plan was that we would issue a new code at the end of
           this review process that would have the updates that
           had come about as a result of the review, correcting
           errors and those kinds of revisions, as well as
           distributing new documentation with it that would
           resolve the problems.
                       I think that's still the plan.
                       CHAIRMAN WALLIS:  It would really be
           appropriate for us to see some new documentation  and
           comment on that, because that's the end of the story,
           isn't it?  It's difficult to comment now when you are
           still in the process of changing it.
                       DR. ZUBER:  Especially after this meeting,
           you may consider to revise the documentation.  I would
           really advise you to do this.
                       CHAIRMAN WALLIS:  It is a moving target. 
           I mean, if I look back at the responses to RAIs and I
           look at your new derivation with the Porschingesque
           integral with the divergence and all that, that's
           completely different rationale than we had before.
                       DR. PAULSEN:  Some of this has been as a
           result of our dialogue with the staff, trying to, I
           guess, address their concerns, too.  So it's been kind
           of an evolving thing.
                       CHAIRMAN WALLIS:  I think that the effort
           by Dr. Porsching to introduce some rigor was a good
           thing, but it seems to sometimes -- You know, you got
           to be careful then that the definitions of
           mathematical terms he has are not quite the same as
           yours.  You may give the appearance of being on the
           same track, but when you look in details, it turns out
           his equation isn't the same as yours.
                       So again, you got to be careful about
           jumping to conclusions here.
                       DR. ZUBER:  Graham, I would like to go on
           the record that his equation on page 8 where he has
           two parts, horizontal connected, is incorrect, and it
           does not agree with the standard equation which is in
           Bert, Stuart and Lightfoot.
                       Although I appreciated reading it,
           somebody on the divergence and the main integral
           theorem, I was really surprised that she didn't put
           the section from Bert and Stuart and Lightfoot to
           compare is results with the standard.  I think that
           analysis was wrong.
                       CHAIRMAN WALLIS:  My conclusion is that
           probably you don't want to come next week unless you
           are determined to do so.
                       DR. PAULSEN:  Well, I don't think that we
           would have anything to gain.
                       CHAIRMAN WALLIS:  If you do, I don't quite
           know what you would come with.  You've condensed this
           story.  Which part of it would you tell us, and --
                       DR. PAULSEN:  Well, I think what we would
           probably want to be able to do is to revise the
           development of the equations.  Did you want to
           comment, Jack?
                       MR. HAUGH:  This is Jack Haugh speaking
           again for EPRI.
                       I think, given all that has transpired, it
           would be inappropriate to push this next week, but
           again I believe we've been given very broad guidance
           and suggestions as to the nature of the problem, and
           this could become a very protracted business in terms
           of, you know, how long this all takes to have a
           pleasant meeting of the minds when this is all over
           with, with the ACRS.
                       So it would be helpful to us to have as
           complete a set of things to come back with.  I think
           that's not unfair to ask of the committee to assist us
           in that fashion.  
                       I really don't want to get into a never-
           ending process of, okay, now go after this, and now go
           after that, etcetera, etcetera.  
                       DR. ZUBER:  It's too bad that you were not
           here two years ago to make this statement.  We
           probably would not even have this discussion today.
                       MR. HAUGH:  Well, like the Bible, they
           save the good wine until last.  Okay?  
                       DR. ZUBER:  Oh.  My advise:  You should
           really look at this book by Ginsberg.
                       MR. HAUGH:  Yes.  Well, we'll endeavor --
                       DR. ZUBER:  I think you will get quite a
           bit of guidance on what it is and how to deal with
           these things.
                       MR. HAUGH:  And perhaps offline afterwards
           you might help me on the title as best you recall it,
                       DR. PAULSEN:  That was by  Ginsberg?
                       DR. ZUBER:  Ginsberg.  It was translated
           in the early Seventies.  I had a copy, but somebody
           borrowed it, and I don't have it.  But to my judgment,
           this is probably the best document which summarized
           this kind of approach, and you can take some ideas
           from that book.
                       DR. PAULSEN:  Thank you.
                       CHAIRMAN WALLIS:  I think we've got to be
           careful about us participating too closely in
           development of your documentation.  We could simply
           stand back and say you do whatever you believe is
           right, and we'll critique it and, if we don't like it,
           we'll say so.  
                       I hope it isn't that you are doing this in
           response to what we said.  I mean, if there is
           something that we've unearthed which you believe to be
           not the best you could do, then you should change it,
           not just because we said so.
                       DR. ZUBER:  Graham, just something.  You
           have a good write-up in your --
                       CHAIRMAN WALLIS:  I've got a tremendous
                       DR. ZUBER:  Wait, wait, wait.  That's one.
           You have your --
                       CHAIRMAN WALLIS:  Oh, the --
                       DR. ZUBER:  The tutorial.  
                       CHAIRMAN WALLIS:  -- tutorial on the
           momentum equation.
                       DR. ZUBER:  And then you had something
           right in your concerns.   I think this should really
           be -- or could be of great help to them.  I don't know
           whether this is appropriate or not, but --
                       CHAIRMAN WALLIS:  Well, we can talk about
           that.  But again, I'm not in the business of
           developing your documentation.
                       DR. PAULSEN:  Well, I can appreciate that,
                       MR. BOEHNERT:  I did have a question, I
           guess, for the staff.  That is, they have issued an
           SER.  So where does this all sit, given the SER being
                       MR. LANDRY:  We will wait and see what is
           done with the documentation by EPRI, and we will
           review that material.  We are not adverse to issuing 
           a supplement or addendum to our SER.  
                       CHAIRMAN WALLIS:  So I think the progress
           we've made over two years is that it's taken us
           actually meeting face to face, which hasn't happened
           for two years, to realize that probably neither of us
           is completely off the wall, and there's something that
           has to be worked out.
                       DR. PAULSEN:  I agree.
                       CHAIRMAN WALLIS:  But this should have
           happened the first day perhaps, if we had any sense.
                       What else do we need to say?  Ralph, do
           you have something to say at this point to help us
           finish up?
                       MR. LANDRY:  No.  I think this has been a
           good process.  We've been trying to get through a
           process like this for over two years now, and I think
           that in a lot of ways we've been talking past each
           other, meaning us and the applicant.
                       Finally, I think we've come to an
           understanding of one another and are moving toward
           resolution, at least being able to issue an addendum
           to an SER that says all of these criticisms or some of
           these criticisms can go away as long as we have the
           proper understanding of the code and its use.
                       CHAIRMAN WALLIS:  Well, that may not be
           our point of view.
                       MR. LANDRY:  We do have a feeling that
           they have made improvements in the RETRAN family of
           codes by going to RETRAN-3D.  We have not been happy
           with the course that they have taken in this
           particular matter.
                       I think, if this gets cleared up, that we
           will have a much better position to take on the code.
                       CHAIRMAN WALLIS:  I think we have to have
           a discussion among the ACRS about what are the
           criteria for acceptability, and your criteria would
           seem to be that the code as written, programmed and
           tried out, evaluated, assessed, works for reactor
           transients, and that's the thing that really matters. 
           And ACRS would have to say, well, is it all that
           matters?  How important is it that it have some good
           justification in terms of the kind of theory that most
           professional people understand.
                       So I think we are going to have to discuss
           among ourselves what weight we give to these various
           things in terms of the way we would evaluate the code.
                       MR. LANDRY:  I'm not saying that we don't
           feel that there has to be some justification either. 
           One of the things that I suggested this morning in
           talking, and have continued throughout this review, to
           say is the applicant should explain what is in the
           code and why it is acceptable or why it is -- they
           should justify it.  
                       What's in the code?  Why does it work, and
           why should we accept it?  That's almost a minimum
           level of justification that needs to prepared for any
                       DR. ZUBER:  Ralph, I think the minimum
           should be that we cannot license actually the code
           which has errors which are junior.  I think this is a
           bad policy for the NRC.  
                       With the first level, I would say does it
           violate a knowledge of a junior; and if it violates --
                       CHAIRMAN WALLIS:  Ralph, you had something
           you wanted to present about code review in general?
           But this is really a RETRAN meeting.  Do we need to go
           into that or should we just take it home and read it? 
           It lets us know where we are with the review of these. 
           Do we need to go into that?
                       MR. LANDRY:  No.  This was simply --
                       CHAIRMAN WALLIS:  It's simply just a
                       MR. LANDRY:  This was placed on the
           schedule, and --
                       CHAIRMAN WALLIS:  Well, it simply a list
           of where we are.
                       MR. LANDRY:  -- you can take it home and
           read it.  All it basically says is where we are with
           the codes that we have in-house today under review,
           and what do we anticipate coming in.
                       We anticipate RELAP5 Realistic LOCA, and
           we anticipate W-COBRA TRAC Realistic small break LOCA
           this springtime.  And we anticipate sometime in the
           future TRAC-G for BWR Realistic LOCA.
                       So that's really more to apprise the
           committee on what we have, what we expect to have, so
           that for both of us we can plan what our interactions
           and workloads are going to be in the future.
                       We do understand the comments and concerns
           that you expressed on S-RELAP5, Appendix K.  We have
           discussed those with that applicant, and are prepared
           to push ahead in the review on S-RELAP5 Large Break
           LOCA, and what is expected of that material.
                       We hope that the Westinghouse people, who
           were sitting in that subcommittee meeting, also
           understand the concerns and, when they come in with
           their W-COBRA TRAC Realistic Small Break, they will
           take to heart those same concerns.
                       CHAIRMAN WALLIS:  We would hope that when
           all this is through that a method is established for
           making this whole process much more efficient.  We
           don't have to take so long to review things which
           eventually get fixed up.  
                       Things would come in without elements of
           the documentation that we even have to question.  That
           would be a wonderful world.
                       MR. LANDRY:  It would for us also, and
           this process has been a learning process from the
           RETRAN to S-RELAP5, and now into the Realistic LOCA
           space.  It's been a learning process, and we
           understand your concerns.  We share many of those
           concerns, and I think we are making progress with
                       CHAIRMAN WALLIS:  Do my colleagues have
           any wisdom?  I'd like comments from the consultants.
                       DR. SCHROCK:  At this moment?
                       CHAIRMAN WALLIS:  Well, you are going to
           write something on your way home or something, so we
           have something to go on fairly quickly?  I think we
           have all said a lot today, and I'm not sure -- unless
           there is something you want to add which you didn't
           say earlier or I didn't hear earlier.
                       DR. SCHROCK:  I don't think that I would
           -- I mean, in my mind it's fairly complex, and it is
           going to take a little time to write it down.  But
           I'll get it to you promptly.
                       DR. POWERS:  I would appreciate it, Virgil
           and Novak both.  In the morning you both brought up
           topics where you thought Research ought to be
           providing support to Ralph and his people.
                       You, Virgil, mentioned codes for doing
           logic checking as a tool.  Novak, I can't quite
           remember what it was.
                       DR. ZUBER:  Oh, I have quite a few.  I can
           send it again.  I wrote it in my last memo to Graham.
                       CHAIRMAN WALLIS:  I asked him to address
           that question at lunchtime.
                       DR. ZUBER:  There are many things they
           could do that should help NRR and the industry.
                       DR. POWERS:  Anything that would provide
           tools to make the processes either higher quality or
           higher efficiency --
                       DR. ZUBER:  Efficiency, efficiency.
                       DR. POWERS: -- and I think we should --
           Well, I think quality, too.
                       DR. ZUBER:  Well, together, together.
                       DR. POWERS:  I think we need to factor
           that into our long range thinking about where the
           research program is going.
                       DR. ZUBER:  Had they used quality, we
           would not hear this discussion for two years.  They
           could have saved money, and they would have saved
                       DR. POWERS:  One of the questions -- It
           may not be arising here, but one of the questions that
           continues to perturb me in this general area -- It's
           a philosophical question.  It's one I asked you
           sometime ago.
                       Within the realm of physical chemistry,
           there is something known by various names, but it's
           basically the Poisson ultimate equation for finding
           the activity of an ion in solution.
                       It is manifestly absolutely impossible
           wrong in its technical formulation.  It's an incorrect
           use of supra position.  It is hailed as one of the
           triumphs of physical chemistry.  Everybody knows it
           can't possibly be correct.  It just works very, very
                       I keep coming back and wondering,
           especially as we move into this best estimate case,
           what do we do about that case?  
                       CHAIRMAN WALLIS:  That's quite different,
           I think, from the momentum equation.
                       DR. POWERS:  We are talking about supra
           position in electrostatics.  It is as fundamental a
           thing as I could think of.
                       DR. KRESS:  You are saying this is an
           analog, that we have these momentum equations that
           appear manifestly wrong in many respects, and yet when
           we compare with the data, it doesn't seem to make any
           difference.  You get good results.
                       DR. POWERS:  Here I think you can compare
           to the data, and the momentum terms are small, and you
           get good comparisons.  
                       DR. KRESS:  I don't think that's ever been
           shown, though.
                       DR. POWERS:  In the Poisson case, that's
           not the case.  The terms are huge.  
                       DR. KRESS:  The terms are huge, and you
           still get the right answer.
                       DR. POWERS:  And in fact, it's the other
           way around.  They are so huge that supra position
           itself gets wiped out.
                       CHAIRMAN WALLIS:  Here we have -- You
           know, thousands of homework problems have been solved
           using these momentum equations, and we know which of
           these are acceptable answers.  There's also kinds of
           engineering experience with them.
                       So I think it's at a different level
           altogether from what you are referring to.
                       DR. POWERS:  Well, I would be willing to
           bet that there have been more homework problems solved
           in supra position of electrostatics than thermal-
           hydraulics by several orders of magnitude.
                       CHAIRMAN WALLIS:  Well, we could debate
           that sometime, not here.  
                       DR. POWERS:  I mean, it seems to me -- It
           seems to me that, as we move to best estimate codes,
           you pretty soon have to confront this, that if you've
           got a complex set of equations by Messers Navier and
           Stokes, I suppose, that cannot be solved, and so
           people throw terms away and do high handed things
           because it fits the data.
                       CHAIRMAN WALLIS:  Yes.  Yes.
                       DR. POWERS:  And you can't -- I mean, I
           don't know what the answer to this question is.  I
           mean, it has perturbed the physical chemists for a
           long time, but it was fully 80 years after the
           Poisson-Bothman equation was first used before
           somebody could come up with something that was
           rigorous that reproduced things to equivalent
           exactness and, having done that, everybody proceeded
           to ignore it and went right back to using the Poisson-
           Bothman equation.
                       CHAIRMAN WALLIS:  I think the basic
           question is how good is good enough is the question we
           have in reactor safety.  How safe is safe enough?  How
           good is good enough in terms of momentum equation?
                       DR. POWERS:  Well, or how do you know when
           it's good enough.  I mean, you know -- I mean, I would
           classify much of what we look at here as irrational
           proximations.  That is, it's not like a finite
           difference equation.  You know, you can't -- you are
           not starting from fundamental partial differential
                       You know, when somebody does an
           idealization of a three-D geometry into a one-D
           geometry, you know, how do you quantify the error in
           that.  You know, beyond engineering judgment, you
           know, seems to me you are kind of hard pressed for a
           better solution.
                       Now if somebody goes out and CFDs it to
           death --
                       DR. ZUBER:  I think a problematic match,
           kind of a complex level.  I would start from the
           simplest.  If I mean something which I know has been
           working since, let's say, my junior year, the people
           before and people after, and it's a standard approach,
           I would expect this approach will be applicable -- And
           I think if it's not applicable of what the reactor is
           using, it's not applicable to the simple approach, I
           cannot defend it.
                       I could defend things, for example, if
           something is very complex.  I think this is addressing
           -- you will get it next week.  If this code is so
           complex and we know something is wrong in there, and
           it still works, then the question should be asked.
                       I'm very sad that NRC and the industry did
           not themselves, why is he talking; and there must be
           a reason why, and try to find it.  They  could
           simplify it, they could defend these things, and it
           would be efficient.  This is one thing which was not
                       This approach, again, is not going to do
           it either.  But this is something which needs to be
           done in the next two years.
                       DR. POWERS:  But certainly something that
           Professor Wallis has mentioned as a direction that the
           industry and the NRC together might want to pursue is
           why do these things work, even when they have high
           handed and --
                       CHAIRMAN WALLIS:  Actually, it's in an
           ACRS letter signed by the previous Chair, I think.  We
           know where the buck stops.
                       DR. POWERS:  He very often signs like
                       CHAIRMAN WALLIS:  So I am going to close
           this meeting.  I think we have achieved some things,
           and I do look forward to a resolution of all of these
           to the point where everyone thinks that we've said
           enough and the product is good enough.
                       So I am going to close the meeting now.
           Thank you.
                       (Whereupon, the foregoing matter went off
           the record at 3:10 p.m.)


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