Thermal-Hydraulic Phenomena - February 20, 2001
Official Transcript of Proceedings
NUCLEAR REGULATORY COMMISSION
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.
Court Reporters and Transcribers
1323 Rhode Island Avenue, N.W.
Washington, D.C. 20005
(202) 234-4433 UNITED STATES OF AMERICA
NUCLEAR REGULATORY COMMISSION
+ + + + +
ADVISORY COMMITTEE ON REACTOR SAFEGUARDS
(ACRS)
THERMAL-HYDRAULIC PHENOMENA SUBCOMMITTEE
+ + + + +
TUESDAY
FEBRUARY 20, 2001
+ + + + +
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.
COMMITTEE MEMBERS:
GRAHAM B. WALLIS Chairman
THOMAS S. KRESS Member
DANA A. POWERS Member
WILLIAM J. SHACK Member
CONSULTANTS:
Virgil Schrock
Novak Zuber
ACRS STAFF PRESENT:
Paul Boehnert
Ralph Caruso
Ralph Landry
Joe Staudemeyer
ALSO PRESENT:
Jack Haugh
Mark Paulsen
G. Swindelhurst
I-N-D-E-X
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
P-R-O-C-E-E-D-I-N-G-S
(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
remarks.
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
code.
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
defended.
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
code.
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
things.
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
equation.
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,
too.
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
also.
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,
Novak.
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
application.
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
application.
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
originate?
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
RETRAN-02.
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
validation.
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
applicant.
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
valid.
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
documentation.
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
you?
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
documented.
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
done.
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
years.
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
Equilibrium.
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
before.
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
database?
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
LOCA.
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
LOCA.
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
ourselves.
(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
ago.
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
39.
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
improvement?
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
correlations?
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
equations.
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
applicability.
If you look at the Chexal-Lellouche
results compared to previous RETRAN correlations, it's
much better at predicting void fraction in BWR
channels.
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
chance.
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
SER.
CHAIRMAN WALLIS: Now is this SER a final
document?
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
SER.
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
internationally.
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
basis.
We've resolved some things in the form of
errors which have been identified, which have been
corrected.
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
those.
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
that?
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
no?
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
that.
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
application.
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
that.
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
industry.
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
foolish.
DR. ZUBER: Foolish things kill big
things.
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
responsible.
DR. ZUBER: I also think it's the
responsibility of NRR to accept or discard such an
approach.
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
change?
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
that.
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
engineers.
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
estimate.
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
action.
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
formulation.
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
necessary.
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
staff.
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
today.
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
later.
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
something.
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-
dimensional.
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
champagne.
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
problem.
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
equation.
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
story.
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
documentation.
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
code.
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
correlations.
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
helpful.
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
hear.
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
here?
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
equations?
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
Falls.
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
RETRAN.
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
relation.
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
bottom.
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
questions.
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
all.
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
generalized.
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-
dimensional.
CHAIRMAN WALLIS: What does it mean? What
do you mean by that? I want to see what he says it
means.
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
correct.
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
direction?
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
clear.
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
equation?
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
equation.
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
is.
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
documentation.
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
together.
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
angles.
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
sections.
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
correct.
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
first.
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
effect.
(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
juncture.
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
different.
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
out.
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
allowable?
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
there.
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
k+1?
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.
Okay.
DR. PAULSEN: But in actual practice,
these either will be the same angle or in general 90
degrees.
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
junction.
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
mean?
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
forces?
DR. PAULSEN: Okay.
DR. SCHROCK: And how does that become a
one-dimensional equation? They are in different
directions.
DR. PAULSEN: Okay. That we'll show on
the next slide. Maybe you've already looked at the
equation.
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
minute.
(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
pressure.
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
assumption?
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
case.
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
perpendicular.
CHAIRMAN WALLIS: Forces normal to the
area.
DR. PAULSEN: Right.
CHAIRMAN WALLIS: Because in some earlier
derivation of this, you had some a-primes and all
that.
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
yet.
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
term.
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,
Tom?
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
tensor.
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
interesting.
DR. ZUBER: It's interesting, wrong,
amusing or sad.
CHAIRMAN WALLIS: Maybe it's all of the
above.
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
term.
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
made.
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-
contradictory.
DR. PAULSEN: You want this equation
derived?
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
him.
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
direction?
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
wall.
DR. PAULSEN: And the Tg is resolved as
well?
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
angle.
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
interface?
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
discontinuity?
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
straight.
So the whole idea is contrary to physics.
DR. ZUBER: Look, Graham, you see that
middle point, middle dotted line. It has a pressure
difference.
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
flow.
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
difference.
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
there.
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
direction?
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
horizontal.
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
line.
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
representation.
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
one.
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
pipe.
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,
yes.
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
California?
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
irrelevant?
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
up.
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
integrals.
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
it.
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
tried.
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
cell.
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
right.
DR. ZUBER: But the same area.
DR. PAULSEN: Two pipes here with the same
area.
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
explanation.
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
whatsoever.
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
meetings.
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
momentum.
CHAIRMAN WALLIS: No, he hasn't.
DR. SHACK: You better stick to a straight
pipe.
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
something?
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
up.
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
degrees.
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
model.
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.
Yes.
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
pipe.
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
here.
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
anywhere.
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
there.
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
there.
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
modeling.
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
happy.
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
again.
MR. HAUGH: Yes. I think, you know, it's
been made quite clear today that there are
shortcomings.
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
today.
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
successful.
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
it.
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
committee.
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
geometries.
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
guess?
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
then.
CHAIRMAN WALLIS: You can get started on
this.
DR. PAULSEN: Is he going to make a Vu-
graph?
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
locations.
So at those points we need to know those
velocities.
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
think.
CHAIRMAN WALLIS: But it isn't steady
state. The whole thing is a transient analysis.
DR. PAULSEN: This was just a steady state
example.
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-
W1.
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
there.
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
means?
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
that.
CHAIRMAN WALLIS: No. He's using -- These
are the terms that go into the momentum equation, this
1/2W2.
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
anything.
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
something.
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
somewhere.
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
average.
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
interpolate.
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.
Right.
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
1/2W3.
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
A2.
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
complicated.
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
question.
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
recovering.
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
all.
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
true.
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
nodalization.
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
irrelevant.
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
here?
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
approach.
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
other.
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
now.
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
waving.
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
changes.
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
data.
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
geometries?
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
on.
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
surface.
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
shows.
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
cell.
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
downwards?
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
modeled.
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
all.
I wouldn't have a clue how to evaluate Ak,
Ak+1.
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
incomprehensible.
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
program.
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
question.
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
pressure.
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
out.
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
channel.
DR. SCHROCK: Well, it's not the
downcomer.
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
volume.
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
shading.
DR. PAULSEN: It's in the RAI and it's an
attachment.
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
challenging.
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
with.
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
point.
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
is.
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
difficulty.
DR. KRESS: That is exactly the
difficulty.
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
means.
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
plenum.
DR. PAULSEN: That's right.
DR. SCHROCK: By looking at this flow
pattern.
CHAIRMAN WALLIS: It's the length of that
pipe?
DR. ZUBER: Yes. That pipe can be
anything.
DR. PAULSEN: It's the length of this flow
path.
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
something.
DR. SCHROCK: But in some cases, you
would.
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
up.
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
address.
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
impression.
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
happen.
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
being.
He says it's best estimate.
CHAIRMAN WALLIS: It's the best they could
do.
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
those.
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
effectively.
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
now?
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,
yes.
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
dw/dt.
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,
etcetera.
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
critique.
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,
yes.
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
issued?
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
code.
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
schedule.
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
that.
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
time.
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
well.
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
equations.
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
done.
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
that.
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.)
Page Last Reviewed/Updated Tuesday, August 16, 2016
Page Last Reviewed/Updated Tuesday, August 16, 2016