Protecting People and the EnvironmentUNITED STATES NUCLEAR REGULATORY COMMISSION
Official Transcript of Proceedings
NUCLEAR REGULATORY COMMISSION
Title: Advisory Committee on Reactor Safeguards
Thermal Hydraulic Phenomena Subcommittee
Docket Number: (not applicable)
Location: Corvallis, Oregon
Date: Wednesday, July 18, 2001
Work Order No.: NRC-325 Pages 323-556
NEAL R. GROSS AND CO., INC.
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NUCLEAR REGULATORY COMMISSION
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ADVISORY COMMITTEE ON REACTOR SAFEGUARDS
THERMAL HYDRAULIC PHENOMENA SUBCOMMITTEE MEETING
NRC-RES T/H RESEARCH PERTAINING TO
PTS RULE REEVALUATION
(ACRS)
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WEDNESDAY,
JULY 18, 2001
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CORVALLIS, OREGON
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The ACRS Thermal Hydraulic Phenomena
Subcommittee met at Oregon State University,
Richardson Hall, Room 313, Corvallis, Oregon, at 8:15
a.m., Dr. Graham B. Wallis, chairman presiding.
COMMITTEE MEMBERS PRESENT:
GRAHAM B. WALLIS, Chairman
THOMAS S. KRESS, Member
WILLIAM J. SHACK, Member
ACRS STAFF PRESENT:
PAUL A. BOEHNERT, ACRS Engineer
JACK ROSENTHAL, U.S. NRC, RES, SMSAB
DAVID BESSETTE, RES/SMSAB
STEPHEN BAJOREK, RES/SMSAB
VIRGIL SCHROCK, ACRS Consultant
ROY WOODS, NRC RES/DRAA/PRN3
NILESH C. CHOKSHI, NRC/RES/DET/MEB
JAMES T. HAN, RES/DSARE/SMSAB
A-G-E-N-D-A
Agenda Item Page
Loop Stagnation and Fluid Mixing in the
Reactor Vessel Downcomer Mechanics
for Primary Loop Stagnation. . . . . . . . 326
Cold Leg Thermal Stratification and
Plume Formation in APEX-CE . . . . . . . . 366
Downcomer Thermal Stratification in APEX-CE. . . 426
REMIX Calculations of APEX-CE Tests. . . . . . 436
3-D CFD Model of the APEX-CE Test Facility . . . 490
Summary and Reporting Schedule . . . . . . . . . 540
P-R-O-C-E-E-D-I-N-G-S
(8:15 a.m.)
CHAIRMAN WALLIS: This is the meeting of
the Thermal Hydraulic Subcommittee of the ACRS. We're
looking forward to hearing from Professor Jose Reyes
and his folks.
MR. REYES: Thank you.
LOOP STAGNATION AND FLUID MIXING IN THE REACTOR
VESSEL DOWNCOMER
MECHANICS FOR PRIMARY LOOP STAGNATION
MR. REYES: Yesterday we started by
discussing a little bit about the overall program and
we got into some of the integral test data.
Today we're going to focus more on the
separate effects or the local behavior in the
downcomer. So the presentations you'll see today all
deal with plume mixing and our predictions of plume
mixing or plume behavior in the downcomer.
And we'll also talk a little bit about the
-- this is kind of the bridge presentation here -- the
primary loop stagnation.
What we found was that some of the
behavior in the cold leg, as affected by HPI
injection, affects overall loop properties, in
particular, loop stagnation.
So we've identified the different
mechanisms for loop stagnation. So I will talk about
-- one of our tests is an inventory-reduction test.
And this is like being able to take snapshots of a
small break LOCA in progress. And it's similar to
some of the tests that performed the Semiscale. And
I actually compared some Semiscale data to our
facility just to give you a feel for where we lie in
comparison for that.
But that gives an idea of as we void the
plant and the steam generator tubes drain, at what
inventory would stagnation occur. And it coincides
with reflux condensation. So we'll look a little bit
more at tube voiding then.
Also in terms of one of our tests and what
we saw there, how tube draining would result in loop
stagnation for us.
And then steam generator reverse heat
transfer and then loop seal cooling. And I'll talk a
little bit about some of the downcomer behavior we
observed and how that affected the integral system.
The reason there's been so much focus on
stagnation in the past is that it was identified that
under stagnant loop conditions with HPSI injection,
that that would most likely be the most severe case
for producing cold plumes in a downcomer.
And I think today what you'll see is that
we've come to a slightly different opinion for this
particular plant, and we'll show you why.
So first the stepped inventory reduction
test. This test was performed basically by holding
the power constant. We had a constant steam generator
pressure, and we opened up a small break on the
reactor pressure vessel and we would drain some of the
inventory. We would stop the drain, and then we would
let the system go through natural circulation. And
we've measured the flow rates in each of the cold
legs. And we --
CHAIRMAN WALLIS: Do you have a break in
the vessel?
MR. REYES: Remarkable. It's just a small
little drain valve.
CHAIRMAN WALLIS: It doesn't sound like
one of those standard accidents, does it?
MR. REYES: No. It's not a -- this is not
a standard accident. This is a drain valve that we
use for setting up the plant.
So we would continue in step-wise fashion,
drain the plant. We stopped the drain. We let it
reach steady-state natural circulation conditions. We
go single phase and then we transition to two-phase
natural circulation. And then eventually we pass a
maximum and then to zero conditions.
And the same tests were performed in
Semiscale back in the 19- -- late '70s, early '80s
maybe -- a while ago.
MR. SCHROCK: So it's a series of
steady-state tests that reduced inventory; is that
basically it?
MR. REYES: That's correct.
So we start -- in this corner here, we're
starting with a system completely filled or including
a pressurizer, and we let it go to natural circulation
conditions. And so these are the flow rates, the
cold-leg flow rates that you'd see.
This is the sum of all the cold-leg flow
rates is the core flow rate. And you see for this
region here it's fairly flat. And what we're seeing
is just single-phase natural circulation.
We transition then. As we drain our
inventory on the bottom, on our x axis here, this is
a percent of overall reactor coolant, the primary-loop
inventory.
As we drain, we reach a knee here, an
inflection point, and now we're starting to go
two-phase. And we see an increase in our core flow
rates. And this is measured by the flow in the cold
legs.
And so what we found in this test is that
loop seals play a nice role of separating -- of
keeping the cold legs single-phase.
As we continued reducing our inventory, we
reach a maximum. And presumably the maximum coincides
with the point where you've essentially got two-phase
going up the tubes and essentially all-condensed
liquid coming down, or something very close to that.
So that would give you your maximum flow through the
core.
As we continue draining, then we start
seeing a decrease in the flow. These dark triangles
are steady-state points and the diamonds are actually
the transient data.
And we come down further and further as we
reduce -- somewhere around 60 percent of our overall
primary mass we reach a point where essentially we're
in reflux condensation.
And the measured flows then in the cold
leg are essentially zero. So injection during this
point would produce conditions similar to what's been
tested in the past: Cold injection with stagnant
conditions in the primary loop.
So our system was about 60 percent of the
overall inventory. We want to compare that to what
was done in the past with Semiscale. You can see that
the trends are very, very similar. We're just a
little bit offset to them. This has been normalized
to the same maximum there.
We -- somewhere they both around 65 to 70
percent -- my battery's charged -- somewhere around 60
to 65 percent of the mass -- of the total inventory --
now this excludes the pressurizer liquid mass. That's
why the number's different here.
Semiscale performed the test with the --
starting with their pressurizer essentially empty. So
they -- all their numbers were based on the percentage
of primary mass without the pressurizer inventory. So
that's what's been done here. So we have very similar
results for this design.
Okay. Well, that gives us an idea that if
our inventory during a small break LOCA drops to
about, in this case, 65 to 70 percent of the plant
inventory, of our initial inventory, we would expect
it to be in stagnant conditions.
MR. SCHROCK: There's an implicit
assumption that the inventory distribution is the same
in a steady-state reduced inventory situation as in a
transient. What transient, I guess, is the question
that comes to mind.
MR. REYES: That's right.
MR. SCHROCK: You have on the previous
graph a lot of data points designated as transient
data. What is the transient, just --
MR. REYES: Good. The --
Would you turn to the previous slide for
me, please? One more.
MR. SCHROCK: The one before that.
MR. REYES: Yeah, that's it. Thanks.
So what we're designating here is -- what
we were doing with these steady-state points, we were
holding at one position and just repeating the
measurement and coming up with an average condition.
And that's how the tests were performed at Semiscale.
When we looked at our actual measurements
throughout the test, as we were -- as we were
draining, we saw that our drain was slow enough to
where we actually could use the -- and I'm calling
this the transient data, because it includes the time
periods when we were actually draining the facility,
so the triangles represent the step changes.
We found that the transient data in
between the step changes, because the drain was slow
enough, seemed to match the steady-state data rather
well.
CHAIRMAN WALLIS: So this isn't some kind
of a standard transient. This is a transient that you
-- you -- you did --
MR. REYES: That's --
CHAIRMAN WALLIS: -- and you did it slow
enough so that it was quasi-steady state?
MR. REYES: That's right. So this is --
that's exactly right. So this is --
MR. SCHROCK: A small break line on the
vessel.
MR. REYES: Correct. So we're draining
from a low region in the plant.
And the idea was just to see what kind of
inventory behavior. So you're absolutely right.
Depending on the break location, we would see
different -- different behavior, different voiding of
the steam generator tubes. The void distribution is
important.
This is just a snapshot of a very
particular controlled test or controlled small break
LOCAs.
MR. SCHROCK: So your transient in this
case is -- appears to be always quasi-steady?
MR. REYES: That's right. That's right.
And originally we were just going to use
the steady-state data itself to compare with Semiscale
because that's how they performed their test. But as
we looked at the overall data we realized that --
actually the test was performed slow enough to where
we could use the transient data.
Okay. So that gave us -- at least that
gave us some idea of how the loop seals were
performing, and they were preventing bubbles from
getting into the cold leg, and at what conditions we
might expect to see some stagnation occurring.
So loop-stagnation phenomena. When we
talk about loop-stagnation phenomena what we're saying
is that the flow in the cold -- the flow through the
loop seals and up through the cold leg is essentially
zero. The flow rates are essentially zero.
You can have HPSI injection, which
produces some flow. And that will produce a cold
layer on the bottom of the pipe. And that concern, of
course, is that the cold layer spills into the
downcomer and it produces some plumes. And so you
might see it like this.
CHAIRMAN WALLIS: Now again in some of the
reactors the HPSI velocity is so great that the
momentum will carry it to the right.
MR. REYES: Correct. Yeah. So for
example for the side-injection B&W plant they have a
very high injection flow rate. It's a small injection
nozzle. And you'll actually jet across the pipe and
impinge the other side.
CHAIRMAN WALLIS: And it swells up on the
wall.
MR. REYES: That's right. So you get a
tremendous mixing.
This plant, for the Palisades plant, what
we found was that it was the opposite. They have a
very large pipe at fairly low injection flow rates.
So on a scale -- for their plant the maximum flow rate
was about 300 gallons per minute per cold leg of HPI
flow. So total injection flow was about 1200 gallons
per minute at the maximum.
CHAIRMAN WALLIS: So it makes a big
difference whether the stagnation is really zero flow,
or a little bit one way, or a little bit the other
way. I think that would make quite a difference since
your HPI flow is so low.
MR. REYES: That's right. Yeah, our HPI
flow is quite low. Yeah.
And there's a few things that we've
noticed that, again, we start to couple the separate
effects with the integral. And I'll show you what
happens with that.
CHAIRMAN WALLIS: I presume with this
Froude number criterion about whether any of it flows
back, and things like that.
MR. REYES: Right. Right. So the
criteria --
CHAIRMAN WALLIS: There must be some
condition where all the HPI goes into the vessel.
There must be enough. When there's enough flow rate
in the cold leg, then all the HPI flow will go to the
vessel itself. You've shown it sort of half and half,
or something like that.
MR. REYES: Right. This shows spilling
over this weird -- this little reactor coolant pipe
lip. And for certain conditions below a certain flow
rate all the flow will go towards the downcomer.
CHAIRMAN WALLIS: Does it then fill up the
loop seal and --
MR. REYES: About -- for higher flow
rates, you spill over and then you --
CHAIRMAN WALLIS: But then it eventually
fills up the loop seal with cold fluid, and then it
all comes back again, doesn't it?
MR. REYES: That's where -- that's where
I was surprised.
CHAIRMAN WALLIS: Hmm?
MR. REYES: This is where the data
produced a surprise for us, so I'll show you.
CHAIRMAN WALLIS: Okay. So we haven't
seen the -- this is just --
MR. REYES: Yeah, you haven't --
CHAIRMAN WALLIS: -- act 1, scene 1 so
far.
MR. REYES: That's right. The plot
thickens.
MR. SCHROCK: It looks like the plume
narrowed, though.
MR. REYES: The plume narrowed, but the
plot thickened.
These are the integral system tests that
we performed. And we wanted to understand a little
bit about the stagnation. One stagnation would occur
for these different types of integral system tests.
And so we had the -- numbers 7, 8, and 9,
these were essentially small break LOCAs -- well, they
are small break LOCAs. For 10 -- 11 and 12 are main
steam line breaks. And then number 10, which sits
right in the middle there, that was a combination,
stuck-open ADV, which would be like a main steam line
break, in combination with the stuck-open pressurizer
safety release valve. So it's a primary side break.
So it's a combination case. We wanted to see what
would happen with regard to stagnation.
What we observed in those tests is that
for the very small break LOCA, cold legs 1, 2, and 3
stagnated. And it stagnated because of the presence
of this cold loop plug in the loop seals, so it's kind
of interesting.
For Test Number 8 we saw a combination of
things happening as a larger break/small break. In
the previous test there was no tube voiding. In this
test there was tube draining.
So in the small break, the very small
break, what we found was that the HPI could keep up
with the break flow. As a result we saw the tubes in
the steam generator remaining full.
In the two-inch break we saw draining, so
we saw a combination of effects there. Cold leg 1 and
2 stagnated because of steam generator tube voiding.
And cold leg 3 and 4 stagnated a little
bit before each of the respective partners because of
this cold liquid plug forming in the loop seals.
For the main steam line breaks down below,
11 and 12, we saw 2 and 4 stagnating due to a loss of
steam generator heat sink, reverse heat transfer from
the steam generator. But we also saw some interesting
behavior here with regard to the downcomer.
The same thing with number 12 where we had
the break on the other side of the plant. Cold legs
1 and 3 stagnated due to the loss of the heat sink.
The combination, stuck-open ADV and
pressurizer safety relief valve, we saw 2 and 4
stagnate due to the -- because of reverse heat
transfer in steam generator 2.
So we observed different mechanisms for
stagnation for these different tests, which was very
nice because that allows us to characterize the
downcomer under different situations and plume
formation.
MR. ROSENTHAL: I'm sorry.
MR. REYES: Sure.
MR. ROSENTHAL: If you would just go back
one slide.
MR. REYES: Yes.
MR. ROSENTHAL: In all these cases the
steam generators are full?
MR. REYES: No.
MR. ROSENTHAL: Except for 10?
MR. REYES: In all -- so Test Number 8,
which was a two-inch break, in that case we did see --
MR. ROSENTHAL: I'm sorry.
MR. REYES: -- the steam generator tubes
drain. In the other test --
MR. ROSENTHAL: I meant the secondary side
of the steam generators.
MR. REYES: I'm sorry? The primary --
MR. ROSENTHAL: The secondary side.
MR. REYES: Oh, for the main steam line
breaks the secondary sides, of course, drain for the
-- for the broken steam generator. We let them drain
all the way out.
Now we --
MR. ROSENTHAL: Well, I mean the feed
water would keep up with the stuck-up in ADV, so these
are just postulated scenarios.
MR. REYES: Correct. Correct. That's
right. That's a very important point.
So some of the assumptions for the main
steam line breaks we assumed that the operator
continued to feed the broken steam generator for 10
minutes. And then we would adjust -- at which point
they would diagnose the situation and close the --
close the feed water to the broken steam generator.
And then they would work with the intact steam
generator to restore the heat transfer to the system.
For most of the cases, because we had such
a -- with such a -- in the main steam line break, for
most of those cases because we had such a rapid
cooldown, the feed-water flow and the steam flow on
the intact steam generator was essentially isolated,
because we just produced a very cold temperature in
the core.
CHAIRMAN WALLIS: Yeah. One steam
generator is quite enough to cool it down.
MR. REYES: That's -- that's right.
CHAIRMAN WALLIS: It's no problem at all.
MR. REYES: Absolutely.
Okay. So I wanted to just illustrate a
little bit of what we saw. I picked the two-inch
break because that had the draining of the steam
generator tubes, so I wanted to show that one.
It also had the -- the case of the loop
seal cooling, which resulted in stagnation. So I
picked this one. It's a little bit more complicated
to demonstrate, but I think it's reasonably clear,
but...
CHAIRMAN WALLIS: What you mean -- you
don't mean heat transfer from the loops. You mean the
cold fluid going into the loops?
MR. REYES: That's right. That's right up
where I mean.
CHAIRMAN WALLIS: Because I was really
puzzled when you had this had a loop seal coolant. It
means that it's got cold water in it.
MR. REYES: Right. It's -- right. It's
cold water mixing in the loop seal. Thanks.
So this is the behavior inside the steam
generator tubes for the two-inch break case. And what
we see is that this is -- we have a set of level
measurements, they're just DP cells in -- attached to
the long tubes, another set attached to the shorter
tubes. So we have the maximum and the minimum
basically for those and, as far as we can observe, the
draining in both of those, in both cases.
What we do see, and this is an area of
interest to us with regards to RELAP, is that the
tubes, first of all, they drain at different rates, at
different times. And that's what you'd expect.
What it does -- what it does mean, though,
is that if you're modeling in RELAP with a single
tube, the question comes up, well, which tube are you
modeling. Is it some average tube, or how does that
work.
So that's kind of interest to us because
as long as these short tubes are filled, you still see
flow in your primary loop. So there's a range here
from about 1500 seconds all the way out to, oh, maybe
about 3,000 seconds that you still see some flow --
CHAIRMAN WALLIS: Excuse me. Long tubes,
short tubes? There's some long tubes out here and
some short tubes in here, or something.
MR. REYES: That's correct. Yes. Long
tubes go all the way to the top of the steam generator
tube bundle and short tubes are the inner circle, the
inner tubes.
CHAIRMAN WALLIS: And you're scaling the
way a typical steam generator is in terms of the ratio
of the lengths, are you, or is it exaggerated in your
facility?
MR. REYES: So our facility, it's about --
the length ratio is constant. It's about 1 to 3.5.
So all of our lengths about 1 to 3.5 in the steam
generator.
So we're actually a little long compared
to -- compared to Palisades -- compared to our normal
one-fourth scale.
So that's what we see there. We see this
draining really begins somewhere around 1500 seconds
or a little bit earlier on the long tubes. But we
still see flow in the primary loop. And then we
continue to see flow until the shorter tubes start to
drain.
MR. BESSETTE: You see the same sort of
thing in ROSA at full height. Roughly, basically the
same.
CHAIRMAN WALLIS: It means that in RELAP
they might be useful to bundle the tubes.
MR. BESSETTE: In RELAP typically the
generators model a single tube.
CHAIRMAN WALLIS: Yeah, but that's --
MR. BESSETTE: We have done sensi- --
CHAIRMAN WALLIS: We miss that effect
altogether.
MR. REYES: Yeah. We have done
sensitivity studies where we model three tubes, or
whatever.
MR. BAJOREK: It depends on the sequence.
MR. REYES: So here's a look at the
cold-leg flow rates. And looking at cold leg number
2 and cold leg number 4 as a function of time for this
test.
And here I've identified when steam
generator tubes and the long tubes begin to drain, at
the very onset of draining the tubes. And then -- so
these are the two different flow rates. The one on
the bottom here, which comes along and -- they match
pretty well for this initial portion of the transient.
And then we see they kind of split off here. The cold
leg number 4, that goes to zero.
Cold leg number 2 experiences a small
increase and then continues to decrease down.
What's happening --
CHAIRMAN WALLIS: Where exactly are you
measuring this flow rate?
MR. REYES: These are being measured in
the cold legs.
CHAIRMAN WALLIS: Yeah, but where?
MR. REYES: Oh, so these are just after
the injection location.
Is that right, John?
MR. GROOME: Yeah. They're right after
the high-pressure injection --
CHAIRMAN WALLIS: You mean they're
upstream?
MR. GROOME: -- before the reactor vessel.
CHAIRMAN WALLIS: Oh, they're on the side
of the vessel.
MR. REYES: Right.
CHAIRMAN WALLIS: So --
MR. GROOME: They're on the downstream
side of the loop seal.
CHAIRMAN WALLIS: Yeah, but which side of
the injection point are they?
MR. REYES: So they sit --
MR. BESSETTE: The vessel side.
CHAIRMAN WALLIS: They're between the
injection and the vessel.
MR. REYES: Right.
CHAIRMAN WALLIS: So you could have zero
flow in the cold leg, and then you would just pick up
the injected flow --
MR. REYES: We would pick up some injected
flow.
CHAIRMAN WALLIS: -- which would be about
one gpm somewhere.
MR. REYES: Right. And then we have a
separate flow meter measuring our injection flow rate
also. So we know at all times how to --
CHAIRMAN WALLIS: When you say this goes
to zero, if you actually had injection --
MR. REYES: Injection flow.
CHAIRMAN WALLIS: -- it could be zero in
the cold -- in loop seal and then it would be the
injection flow where you're measuring it.
MR. REYES: That's right. That's right.
Yeah, we haven't subtracted those out.
CHAIRMAN WALLIS: Is that why it bottoms
out at one instead of zero?
MR. REYES: At one, yeah. That's right.
That's right.
So what we saw happening here, we were
interested in how this flow was splitting. We
expected that as the tubes drained, the flow in the
primary loop would just continue to drop.
Because we're draining 133 tubes, it just
kind of goes in a fairly well-behaved manner towards
zero. But we saw the split here, and we were curious
about how -- what was happening there.
And so what we observed was that this Weir
wall, there was spillover over the weir wall, this
reactor coolant pump lip. And the cold water would
create a plume basically and fall into the loop seal.
And now you're producing a very cold loop
seal. So the next figure here shows that, illustrates
that. So here both loop seals are warm, both for
number 4 and number 2.
When we get to this -- that point, that
transition point there, the 1500 seconds or so, and we
see that -- for the cold leg 4 we see some of the
plume spilling over into the loop seal and starting to
cool that off. And that corresponds exactly with the
time that we see that split.
So the loop seal forms -- it's basically
a cold-liquid plug which resists -- that gravity head
there resists the fairly low flow of the loop. And
the flow is diverted then to the other cold leg.
Through the common lower plenum of the
steam generator, the flow is diverted to cold leg
number 2. And so we see an increase in the flow rate
there and a zero flow in cold leg 4.
CHAIRMAN WALLIS: Did you get any kind of
loop seal blowout with these cold plugs being blown
out at some stage?
MR. REYES: We'll have to look at some of
the other tests to see.
CHAIRMAN WALLIS: That might not be too
good for the reactor vessel, blew out a plug of cold
water.
MR. REYES: If it put out some cold water.
MR. BESSETTE: You need larger breaks to
get a loop seal clearing basically in this.
CHAIRMAN WALLIS: You need a larger break
for that to happen?
MR. BESSETTE: Yeah, to create loop seals.
MR. ROSENTHAL: I'm not sure that the
vessel, given its mass, would even notice a slug.
MR. BESSETTE: Plus you've got to put the
break into the cold.
CHAIRMAN WALLIS: Well, it's a question of
local cooling, isn't it, and --
MR. BESSETTE: You've also got to put the
break in the cold leg. This was a hot leg break.
MR. REYES: Yeah, the thought was if --
CHAIRMAN WALLIS: It was just a thought,
I mean. While we're thinking about it, it's sort of
like the boron-dilution problem where you've got a
slug of something that comes in.
MR. SCHROCK: In the previous diagram you
have certain events highlighted, number 2, long tubes
begin to drain.
MR. REYES: Yeah.
MR. SCHROCK: Is that something that you
see from these traces, or that's just pointing out
that this is observed from other evidence at those
times?
MR. REYES: This was what was observed
from other evidence.
CHAIRMAN WALLIS: What's the big hiccup at
about 1100 seconds?
MR. REYES: We know that the initial steam
generator tube draining does result in an increase in
flow, so we're draining those tubes and they're
draining into the cold-leg side and to the hot-leg
side. And we expect to see some increase in flow
rate. I would suspect that's related to that.
CHAIRMAN WALLIS: Yeah. But how do you --
MR. REYES: And we don't see it in the
other one, so --
CHAIRMAN WALLIS: You need to blow-up the
scale to see for how long it stayed at zero at around
1100 seconds, if it did. You know you can't see it in
here. Eleven hundred seconds is a big hiccup.
MR. REYES: Oh, this -- this spike right
here you see. Yeah.
CHAIRMAN WALLIS: Yeah, it goes down to
zero, is the point.
MR. REYES: Right. Now the -- these
magnetic flow meters, they're very sensitive to
voiding. If you have a bubble through the line and it
goes past the instrument terminals, you might see a
spike like that.
However, I tend to think this might be a
real -- we'll look at that a little bit closer. This
might be a real...
So what we see is the creation of this
cold-liquid plug in the loop seals and the flow being
preferentially diverted to the -- through the steam
generator lower plenum to the other flowing leg with
the warm loop seal.
Later today we're going to show you how
this works. We'll take -- when we go to the lab we're
going to run this experiment for you. Here we have
the -- this Weir wall.
Imagine in the plant that this whole elbow
here would be the pump and this would be the outlet of
the pump. And you can see that it acts effectively as
a dam which keeps the cold water on the reactor vessel
side.
Eventually you will spill over, and you
will go into this loop seal, and you'll cool it off.
We'll show you that phenomena.
CHAIRMAN WALLIS: Now RELAP has great
trouble trying to predict that, doesn't it?
MR. REYES: Excuse me?
CHAIRMAN WALLIS: Doesn't RELAP have great
trouble trying to predict that, that sort of
phenomenon?
MR. REYES: I would say that there's no
way.
CHAIRMAN WALLIS: But you can still run
RELAP.
MR. REYES: That's right. And I think
what we saw in this test with the RELAP calculation is
that it did predict reasonably well the steam
generator tube voiding on some average basis.
And so it was in the ballpark. But as far
as the sequence of -- the timing and the exact
sequence, probably would miss. It can't --
CHAIRMAN WALLIS: It just mixes --
MR. REYES: -- it can't calculate this.
CHAIRMAN WALLIS: It just mixes
everything, doesn't it?
MR. REYES: Yeah.
We're looking at that, though, to see what
RELAP is predicting as a loop seal temperature during
the trading and comparing it to what we saw.
So you'll see that test a little bit
later. Chris Linrud and Ian Davis are here to do that
for us.
Okay. So we saw steam generator tube
voiding as a stagnation mechanism. We saw this cold
loop seal plug as another stagnation mechanism.
The third one that we observed was this
reverse heat transfer. And that's when the steam
generator and the main steam line break, we blow that
steam generator down on one side. The other intact
steam generator is bottled up and becomes a heat
source eventually.
And so you see in this schematic here,
this is for Test Number 12, a main steam line break at
full power. We have steam generator temperature and
the hot-leg temperature. We see initially the hot-leg
temperature is greater than the steam generator
temperature.
As we go through the blowdown, of course,
we drop that hot-leg temperature well below the steam
generator temperature. And we see stagnation of cold
legs 1 and 3 occurring within this band right here.
So it doesn't occur immediately. There's a band that
-- there's a delay time and then a band. And we were
curious about that.
Now later on what we see is the -- as the
primary plant reheats and repressurizes, our
temperature goes up above the steam generator
temperature. And we see a resumption in the cold leg
1 and 3 flow. So it works as expected. And again we
see that occurs relatively close to when we cross that
-- when we made that transition.
We were -- and that's to be expected.
What we were curious about was this little delay here
and what might be causing that. Here's looking at
the, again, cold-leg flow rates for 1 and 3. And you
can see that we start off with our pumps on, come way
down. We go to zero, essentially zero flow for the
flow meter.
Come -- and we resume our -- this steam
generator is a heat source. And here the steam
generator is a heat sink again. And we come back to
our flow intake.
CHAIRMAN WALLIS: What does negative flow
in the cold leg flow area mean?
MR. REYES: Negative flow, I don't think
we're seeing negative flow in this. It's just the --
CHAIRMAN WALLIS: Isn't that what it says?
MR. REYES: It certainly does, but I think
we're just zeroed. We're a little bit off in our
zero.
This flow meter is -- I'll ask John Groome
to tell me the range for that flow meter on the test.
Do you remember this one?
We've been struggling with memory lately,
myself.
MR. GROOME: Yeah, I'm sure my memory's
not any longer than yours though, Jose, so I don't
know if I'll be able to answer the question, but my
name's John Groome.
And these flow meters are ranged positive
to negative 100 gallons per minute. And, you know,
there's some interpretation that you have to do with
all data.
And I'm of the same opinion as Jose,
that's just a zero shift there on that second meter.
And that could be not just due to the meter. It could
be due to the actual estimate loop that carries the
signal back to the data acquisition, so...
CHAIRMAN WALLIS: You really need a more
sensitive flow meter because you're talking about low
flows in the order of one gallon per minute.
MR. GROOME: Yeah. And, you know, these
flow meters are actually quite phenomenal. When we
first worked with Westinghouse back in the early '90s
we couldn't measure flow in our cold legs. And so
part of the problem was our temperature and pressure.
And so we actually worked with them to
develop a new flow meter to -- that we put a flow
meter in to test, at about $4,000 a test we'd break a
flow meter. And so these flow meters have been in for
about going on three and a half years, and they've
worked for three and a half years successfully.
And, you know, this is a meter that's
capable of flow ranges up to about 700 to 800 gallons
a minute. So when you're down here looking at zero
and you're nitpicking about a gallon-per-minute flow,
I think you ought to be happy you have any data.
CHAIRMAN WALLIS: Well, how does a flow
meter work when you have, say, a stratified
countercurrent flow? Does it --
MR. GROOME: Well, it's a void average.
Unfortunately, it measures in gallons per minute. But
it's a void average flow, a volume-average flow.
CHAIRMAN WALLIS: So it has -- does a --
is it slices, or something, or --
MR. GROOME: No. It actually has just
two, and I can show you some flow meters today if
you'd like, but it just has two contact points in the
middle. So it assumes that the velocity profile
through the -- through this bore of the flow meter is
constant.
CHAIRMAN WALLIS: Well, that's very
difficult if you've got a countercurrent flow, with
cold water going one way and hot the other, --
MR. GROOME: Sure.
CHAIRMAN WALLIS: -- it must get very
confused.
MR. GROOME: Sure. And that could be
what's happening.
CHAIRMAN WALLIS: So it might well give
you a faulty reading.
MR. GROOME: Right. Right.
MR. REYES: Sure. Sure. Yeah.
Thanks, John.
CHAIRMAN WALLIS: So it just measures at
one point essentially?
MR. GROOME: Correct.
CHAIRMAN WALLIS: And then assumes a
velocity profile?
MR. GROOME: Correct.
CHAIRMAN WALLIS: Oh.
MR. REYES: So reduce the stagnation
occurring and then resumption.
CHAIRMAN WALLIS: So what it's measuring
is the velocity at the point where it measures what it
calls flow. That's what it's really doing.
John, it's --
MR. GROOME: Excuse me?
CHAIRMAN WALLIS: It's really just
measuring the velocity at the point where it measures.
MR. GROOME: Correct.
CHAIRMAN WALLIS: And then from that it
tries to predict the flow.
MR. GROOME: Right. In those -- in those
areas --
CHAIRMAN WALLIS: And if it has an S-shape
velocity profile, it's going to go --
MR. GROOME: It doesn't -- it doesn't know
how to calculate that, right.
CHAIRMAN WALLIS: But it still knows to
calculate the local velocity. That's what you --
MR. GROOME: Right. So it measures
essentially a velocity and it knows the area.
CHAIRMAN WALLIS: So you might actually
try looking at that velocity and recasting it in terms
of what's actually happening in the pipe and getting
a better sen- --
MR. REYES: And try to get the better,
yeah. Yeah.
MR. SCHROCK: Is it in the proximity of
the bend? Most everything is.
CHAIRMAN WALLIS: Everything is, yeah.
MR. REYES: How many -- how many l over
ds, John, from -- did we require for the --
MR. GROOME: It's -- l over ds, yeah, it's
right there on the bend. It's maybe like 2 d.
Actually I have a slide if you'd want to go back and
pull it up and we could actually look at a plan view
of it. But it's maybe like one and a half d from the
bend.
But that's fortunate for magnetic flow
meters to have the, you know, the least-required l
over d for flow measurement, or typically anywhere
from 1 to 5 d.
MR. REYES: Okay. So what we saw then was
loop stagnation due to the steam generator, one of the
steam generators becoming a heat source instead of
heat sink. But there was a delay, and we were curious
about that. So we investigated a little bit further.
And what we realized was that we're
injecting cold water to downcomer. And so we're
cooling off the downcomer. Of course, we have core
heat. And so we are creating a density difference in
the driving head. So the downcomer driving head,
because the system is completely liquid filled, is
still driving the flow.
And so what's happening is that the
reverse-heat transfer from the steam generator is
acting like a break. It's resisting the positive
flow, but it's not able to stop the flow. And so
that's why we see a continued natural circulation for
that period of time.
Eventually we get to a large enough delta
T on the steam generator where it is able to overcome
the driving head produced by the downcomer injection.
So you do have a downcomer recirculation.
That was -- that plays an important part
when you're working -- when you're looking at an
integral system injection. Because what that means is
even when you have "stagnant conditions," as soon as
you begin injecting, if you have any core heat, you
will create some natural circulation flow. And so you
-- by virtue of injecting you're producing a natural
circulation flow. So it's kind of --
CHAIRMAN WALLIS: As long as the injection
goes the right way.
MR. REYES: That's right, into the
downcomer. That's right.
Okay. So we observed those phenomena.
Steam generator tube voiding. That should
be the loop -- the cold-liquid plug --
CHAIRMAN WALLIS: If the steam generator
wins over the downcomer, then presumably the flow goes
the other way, if that's possible.
MR. REYES: The resistance is pretty large
in the other direction.
CHAIRMAN WALLIS: I was thinking of the
buoyancy. You're saying the buoyancy in the steam
generator counteracts the buoyancy in the downcomer.
MR. REYES: Right.
CHAIRMAN WALLIS: Presumably there's a
situation where the steam generator could win and the
flow could go the other way. Don't pull that cold
stuff into the loop seal, --
MR. REYES: Well, I think --
CHAIRMAN WALLIS: -- ready to come back
again.
MR. REYES: I think what -- of course, the
top of the plant will just get real hot and stay hot
and the cold water will stay on the bottom, so...
Okay. So we identified three modes of
loop stagnation, which we were interested in
understanding for integral tests.
One of them, the loop seal, the cold plug
in the loop seal actually is tied to a local
phenomenon, which I thought was one of the key
findings as far as relating our separate effects test
to the integral system test.
The other thing was the presence of this
RCP Weir wall. That really does delay the loop seal,
the formation of a cold-liquid plug in the loop seal.
And hence it delays stagnation in the loops.
So if we didn't have that Weir wall we
would have expected possibly to have stagnated a bit
earlier, because we would have formed cold plugs in
the loop seals. So that's kind of an interesting
result. So having them actually delays stagnation.
MR. SCHROCK: Isn't that Weir an attempt
at simulating the real plant?
MR. REYES: That's right, yeah.
MR. SCHROCK: And so how do you judge the
quality of that simulation?
MR. REYES: Right. Now at this point all
we can do is use our, in this case, CFD Codes to see
if we can, first of all, benchmark the CFD Code
against our test.
And then have a little bit of confidence
then that we can go forward and try to do a more
accurate model of the real plant.
Now in talking to the folks at Palisades,
they do indicate to us -- I mean they gave us the
dimension of this lip. And they have indicated to us
that, in fact, when they are draining, trying to drain
the cold legs they can't drain it completely because
of this lip. So we know it's an effect.
The other thing that it does cause -- that
we do observe is that the presence of that Weir wall
also, with side injection, we're going to see a lot of
stratification.
The plume doesn't come in from the top of
the pipe and then mix on the way down. So typically
the flow is going to be in the positive direction,
because it's not mixing on the way down, and you've
got this wall, this dam on the other side which, in
essence, is driving all the flow towards the downcomer
up to a certain point.
We said that reverse-heat transfer can
either -- it can reduce or stop the primary loop
natural circulation, depending on the available
downcomer fluid driving head.
Okay. So that's what we saw in the area
of loop stagnation.
CHAIRMAN WALLIS: What are your scaling
laws now? I would think that you have some scaling
laws for your loop.
MR. REYES: Correct.
CHAIRMAN WALLIS: And then I would think
that some sort of Froude numbers scale these, whether
it goes over the Weir and the stratification.
MR. REYES: That's right.
CHAIRMAN WALLIS: Is that consistent with
your scaling of other things like velocities and
dimensions?
MR. REYES: Yes.
CHAIRMAN WALLIS: It is?
MR. REYES: Yes. And so what we're doing
now is -- we have run a preliminary series. And we're
going to run several just to be sure. We're going to
identify the conditions for the onset of the loop seal
spillover, which is a very nice project for any
volunteering students.
It's a very straightforward effort. And
we know basically what the dimension of those groups
should be. And I think we can do a good job on that
one. So we're gathering that data right now.
MR. BAJOREK: Jose, your pump is down at
the bottom --
MR. REYES: Our pump is at the bottom of
the --
MR. BAJOREK: -- of the loop seal as
opposed to up at the top.
MR. REYES: Correct.
MR. BAJOREK: Are there any additional
restrictions in a regular PWR pump lower than the Weir
that a positive steam flow through the loop would
prevent some of that liquid coming back over the Weir
and delaying the cooling?
MR. REYES: Now we're talking steam flow?
MR. BAJOREK: Yes.
MR. REYES: There was a schematic that
John had showed us yesterday, and it's a fairly short
-- what it is it's kind of a relatively flat --
MR. BAJOREK: Impeller.
MR. REYES: -- impeller with -- in a
volute. Okay. I was looking for the right word, a
volute. So if that comes -- your cold leg comes out
at this angle, and then you've got this -- a short
drop and then to the loop seal.
So I don't think there's anything other
than the impeller itself that would hinder the steam
from getting up there and going out. Is that -- I'm
not sure if I understand.
So you're going to have -- you're going to
have -- the steam will come in, and if there's water
on the bottom of the cold leg, it's basically just a
stagnant pool almost, except for right at the surface.
Okay. Now we'll talk a little bit about
-- if there's no other questions on stagnation.
Again, the reason we looked at stagnation so heavily
was because in previous studies the thought was, well,
if the primary -- if the cold legs are stagnant, then
injection under those conditions would essentially be
the worst plume conditions. Okay. As we continued
with our study we saw that we came to a different
conclusion.
COLD LEG THERMAL STRATIFICATION AND
PLUME FORMATION IN APEX-CE
MR. REYES: So I'll talk a little bit
about cold leg thermal stratification first, and then
we'll talk about the plume behavior in the downcomer.
Okay. We did these flow visualization
tests, which were really very helpful. We started by
just doing a series of tests in APEX at pressure and
temperature. And we were measuring our -- we had our
thermocouple rake in there.
We were seeing constantly that we had cold
temperatures at the bottom for most of the flow rates
that we generated, the cold-leg flow rates. And we
were curious then what was going on. So we built this
very simple flow visualization test that allows us to
take a look at the similar Froude number conditions,
what might be going on in the pipe. And we --
CHAIRMAN WALLIS: This is green salty
water; is that what it is?
MR. REYES: That's green salty water. So
we're injecting -- we're using sodium fluorescein to
actually give us that green color. And if you hit it
with ultraviolet light you get a very bright image
with that.
So we've put sodium fluorescein in our
salty water. And we're using that to represent our
cold injection.
The pipe is initially filled with fresh
water. And that whole tank actually is filled with
fresh water initially.
So we begin our injection, and this is the
type of behavior that we see.
CHAIRMAN WALLIS: Where is the injection
here?
MR. REYES: I lost my mouse. Oh, here it
is. Thank you. So --
CHAIRMAN WALLIS: It's the pipe that we
can't see, which is there?
MR. REYES: Yeah, that's right. It's a
side injection. And so from a top view the injection
line would be behind the pipe.
CHAIRMAN WALLIS: That's why we can't see
it.
MR. REYES: That's right. That's right.
So... Thank you.
CHAIRMAN WALLIS: So is this fog flowing
down the Columbia Gorge.
MR. REYES: It's the fog coming down the
Columbia and out towards the ocean here, I guess.
Here's the Weir wall. So for this
injection flow rate and for this combination of
cold-leg flow rate, we're not getting it -- well,
maybe we are spilling over a little bit here. Here's
a side view. So we're not, okay. So for this --
CHAIRMAN WALLIS: It doesn't look like a
very flat layer, does it?
MR. REYES: Say again.
CHAIRMAN WALLIS: It doesn't look like a
very flat interface between the green and the blank.
MR. REYES: It's not very flat. For this
flow rate it's not very flat. That's right. So what
we're looking at then is a -- we're at about the 12-
gallons per minute in the cold leg. And we're
injecting probably somewhere around a gallon per
minute here through the -- so you see the side
injection.
The plume comes in. It travels both
directions, and back towards the vessel and towards
the loop seal. But this acts as an effective wall to
prevent the flow.
CHAIRMAN WALLIS: I guess the drag from
the other flow keeps the -- it's what causes it to
flow in this arrangement.
MR. REYES: So here's a closer look at it,
and I'll show you the Weir wall.
But here we're injecting again. This is
-- you can see this --
CHAIRMAN WALLIS: Well, that shows how
stratification inhibits the mixing.
MR. REYES: Right. Here's a close-up of
the -- of that --
CHAIRMAN WALLIS: You can't just use the
normal CFD in a stratified flow like that. K-epsilon
doesn't work in their stratified interface.
MR. REYES: That's one of the -- this is
where -- this is -- Ian's nodding his head yeah.
Working with CFD Codes, and we'll talk
about that a little bit later, but that's some of the
challenges that we face with using these types of
codes. And so we're going to be looking for some
advice from experts.
CHAIRMAN WALLIS: The turbulence is really
suppressed at the interface.
MR. REYES: Yeah. So this is at the Weir
wall, and we see that basically the cold fluid from
the cold leg -- I mean the cold-leg fluid is sweeping
all that fluid back.
Okay, another look here. We have a little
bit of spillover in this case. We've got the flow
rate. And then this is looking again at the spillover
into the loop seal. So we'll perform some of those
visualizations for you when we go over there after
lunch.
Okay. So let's talk a little bit about
what we saw with regards to the stratification in the
cold legs, some of the measurements from APEX-CE.
So we did --
CHAIRMAN WALLIS: Now are you going to
tell us about analysis of this in terms of some math
and some predictions?
MR. REYES: Yes.
CHAIRMAN WALLIS: Somebody -- somebody is.
MR. REYES: When we talk about the plumes.
CHAIRMAN WALLIS: Somebody is. Well, what
about the cold-leg behavior and the stratification and
all that?
MR. REYES: We have some predictions to
show you later on if you -- we can chart --
CHAIRMAN WALLIS: Any comparisons with
data?
MR. REYES: We have lots of data.
CHAIRMAN WALLIS: Do you have -- well,
come on.
MR. REYES: We'll give you some. You'd
like some theoretical...
Well, we have looked at the plumes in the
downcomer, and I'll present some equations there.
In the stratified region, we're still
looking at developing what's going on in that section.
We have a -- there was a -- I think I know
what you're referring to. Early on in the development
of this project we were real curious about the onset
of thermal stratification and came up with pretty good
criteria that was used -- that you could use to
predict when you have essentially well-mixed
conditions in the cold leg.
Now the presence of this Weir wall has
changed that somewhat. So we're looking -- that's why
we're changing the theory some, to examine that Weir
wall more closely and understand how that's affecting
the flow and what that really means in terms of a
stratification criteria.
CHAIRMAN WALLIS: It looks like a real
candidate for the Kelvin-Helmholtz instability type of
analysis.
MR. REYES: That's right. That's right.
So now you've got -- I mean that's exactly right. So
that's what we're looking at right now.
So what this tells me then is that the
stratification criteria that we use that P. F. Foss
had developed, and then the modified version which I
had developed, which was based on the Froude number of
the cold-leg stream squared plus the Froude number of
the hot leg squared equal to one.
With the presence of that Weir wall we
need to look at that and say, okay, now we've got a
slightly different situation.
CHAIRMAN WALLIS: What is 10 gpm in terms
of Froude number, using the density difference.
MR. REYES: Oh, 10, that -- with using
that combination, I think it's like .04. That's that
modified Froude number. That --
CHAIRMAN WALLIS: You're using the density
difference between the fluids?
MR. REYES: Density difference between the
fluids. And using --
CHAIRMAN WALLIS: That's the only Froude
number. It's not modified. That is the Froude
number.
MR. REYES: Well, this -- they're modified
in terms of -- it uses the HPI injection.
CHAIRMAN WALLIS: Density.
MR. REYES: Density --
CHAIRMAN WALLIS: Minus --
MR. REYES: -- with the cold leg --
CHAIRMAN WALLIS: Minus the density of the
--
MR. REYES: Oh, okay, I'm sorry. The
Froude for the cold leg. Yeah, I'll have to look that
one up. I was giving you the injection, injection
Froude. Yeah, I can look that up for you.
CHAIRMAN WALLIS: You can tell us after
the break.
MR. REYES: You bet. We've got lots of
calculators.
So what we found, though, is that the
presence of the Weir wall results in some
stratification for the full range of conditions that
we studied.
So this test 003, what we were doing was
we were putting -- we were parametrically varying the
cold-leg flow rate and the injection flow rate for 16
different cases. We wanted to see what we would
observe as far as stratification in the cold leg.
So what we saw was that at the presence of
the Weir wall there was always some stratification for
the flow conditions that we looked at. And we were
looking at essentially from one and a half percent to
K to four percent to K powers over a range of about
30- to 100-percent HPSI injection flow rates.
The spillover was not observed in any of
these tests, which meant that our -- above 30-percent
HPSI for us, what we saw was that we had enough flow.
It was greater than 10 gallons per minute in the --
excuse me -- for one-and-a-half percent to K power,
our flow in the cold legs was greater than 10 gallons
per minute.
So we always kept flowing in the direction
of the reactor vessel. And there was no spillover for
any of these tests. So this is the range of
conditions we cited.
We would vary the K power. That would
change our natural circulation of flow rate in the
loop. And in between each test we would turn our
pumps for a while and get everything back to uniform
temperature and then do another parametric study.
So here's that --
CHAIRMAN WALLIS: What's the basis of
these HPSI flow rates? What's the basis for choosing
these values?
MR. REYES: Oh, that's -- that basically
was the limits of what we could do. Yeah. So 30
percent, when you drop below 30 percent on our
injection, we have difficulty controlling our -- well,
for -- for the cases that we looked at, I guess we can
get down to --
CHAIRMAN WALLIS: Presumably it's a scaled
HPSI from reactor conditions.
MR. REYES: Right. Right. So point --
the lowest we did was .35 gallons per minute, which
corresponds to about 30 percent of one injection flow.
So that was what --
CHAIRMAN WALLIS: So this is a throttled
HPSI of --
MR. REYES: Right.
This shows the range of tests that we did.
And in between each test, again, we operated our
reactor coolant pumps.
Once we put in several hundred gallons per
minute through the loops. Of course, everything warms
up pretty uniformly. All our thermocouples matched
up.
This is looking at the top of the cold leg
number 3 and this is the bottom of cold leg number 3,
so we're going -- we're looking at the temperature
stratification in the cold legs.
And this shows that for the different
conditions we saw we always saw some stratification.
Even at our minimum being .35 gallons per minute, we
saw some stratification in cold leg number 3.
Again, this being the bottom of the cold
leg here and all the way up at the top would be the
top, so they actually went in order. So we saw that
stratification for our tests.
Here we are at -- for cold leg number 4,
the same test, we were running -- we ran two different
injection flow rates for that --
CHAIRMAN WALLIS: What is your temperature
of your HPSI?
MR. REYES: HPSI temperature is about 65
degrees Fahrenheit.
CHAIRMAN WALLIS: So this is a lot hotter
than the HPSI itself.
MR. REYES: Oh, much, much hotter, right.
Yeah. So what we're seeing is by the time we get to
this -- the typical rates, we are seeing some -- quite
a bit of mixing.
And the total -- well, I mean this is 150
degree delta T from the bottom of the pipe to the top
of the pipe, so it's a pretty big stratification.
This case and this case, we also used to
model with STAR-CD. So these two cases we modeled
with STAR-CD. And later on you'll see the results of
those comparisons.
CHAIRMAN WALLIS: So maybe if you had
bottom injection you might actually have those minima
going down to something like the HPSI temperature.
Because presumably it's bottom injection; it doesn't
mix with anything.
MR. REYES: That's right.
Now I'm not sure if there are any plants
that do bottom --
CHAIRMAN WALLIS: I don't think there are,
but just for comparison sake.
MR. REYES: -- with the big --
CHAIRMAN WALLIS: I mean you said with top
injection there's more mixing and side injection you
get more of this.
MR. REYES: Right. So the bottom might be
--
CHAIRMAN WALLIS: Presumably there's one
limit where you just ooze the cold water in and it
flows along without mixing with anything.
MR. WACHS: You get conducted heating from
the metal in the cold leg.
MR. REYES: Dan.
MR. WACHS: I said you'll still get
conducted heating from the metal in the cold leg, so
there will still be some warming. You won't -- you're
unlikely to --
CHAIRMAN WALLIS: Yes. Yes.
MR. WACHS: -- get that small.
CHAIRMAN WALLIS: Yeah, I guess you need
to estimate that, too.
MR. REYES: Okay. So the upshot of it for
us for these series of tests was that for all the
natural circulation cases that we examined, we always
saw some stratification.
And this case here being the maximum
stratification we observed, which was not the -- not
the lowest flow rate, but it was -- it was essentially
close to the highest flow rate, but not the -- not
necessarily the lowest. Well, like big yeah, the
trend is getting bigger as we go to lower -- lower
cold-leg flows.
Okay. So we always see some
stratification, which was different than what we've
seen in the past. If we kept the criteria, the
stratification criteria the way it was, it would
predict good mixing for some of these tests.
So we see that the Weir wall has no -- has
an effect. And we need to change that theoretical
model.
Okay. Now we'll talk a little bit what's
going on in the downcomer as far as plumes.
I'll start off with kind of a typical
analysis and what's been done in the past. The
classic analysis is you have a single planar plume
falling into a stagnant, uniform ambient fluid.
Okay. That would be the classic analysis.
And it's been done -- it's been done for a long time.
Bachelor did a study on it and Morton and Rouse and --
CHAIRMAN WALLIS: You say, "planar." You
mean it's 2 d?
MR. REYES: Correct. Yeah, they're 2 d.
CHAIRMAN WALLIS: They're also
cylindrically symmetrical. The simple ones are --
MR. REYES: Right. The --
CHAIRMAN WALLIS: -- planar or --
MR. REYES: Right, the axisymmetric --
CHAIRMAN WALLIS: -- axisymmetric.
MR. REYES: Right, axisymmetric case. You
just change the coordinates and unwrap it and get a
planar. Yeah, so the 2 d case.
And these involve some very classic
assumptions, some very -- which work very well for the
single planar plumes and also for the axisymmetric
plumes.
CHAIRMAN WALLIS: Oh, review that for me.
If I have, say, a faucet, the plume actually
accelerates instead of -- because the density
difference is so enormous.
MR. REYES: Right. Yeah.
CHAIRMAN WALLIS: And then if I have a
very low-density difference, presumably the buoyancy
is not so big and the plume spreads a lot. What sort
of range are you in in terms of the density
difference, in terms of, you know, whether the plume
spreads a lot or --
MR. REYES: Right.
CHAIRMAN WALLIS: -- doesn't because of
the gravity accelerating it?
MR. REYES: Right. For these tests, our
delta rho over rho was like .18. So I'd have to go
back and see what just a delta rho is. But -- so it's
comparable to what you would see in the plant, not --
not as large, but it's within 10 percent.
CHAIRMAN WALLIS: But it's something like
the plume from a cigarette, or something, in terms of
what you --
MR. REYES: Oh, no.
CHAIRMAN WALLIS: -- imagine in terms of
things you know about?
MR. REYES: Okay. So smoke and air, maybe
-- maybe like --
CHAIRMAN WALLIS: Smoke from a chimney,
from -- on a clear day. Something like that.
MR. REYES: Yeah. I'm thinking of my
backyard.
CHAIRMAN WALLIS: Yes, something like
that.
MR. REYES: I'm looking at the stack way
out there.
CHAIRMAN WALLIS: But, you see, if you
have a hot enough fire --
MR. REYES: I'm looking at the stack way
down there.
CHAIRMAN WALLIS: -- your plume actually
--
MR. REYES: Yeah, it would be similar --
CHAIRMAN WALLIS: -- can go up and
concentrate.
MR. REYES: Right. So --
CHAIRMAN WALLIS: Before it spreads.
MR. REYES: -- you'll see a lot of
examples of the reverse. You'll see a hot plume --
CHAIRMAN WALLIS: Right.
MR. REYES: -- going up in air.
CHAIRMAN WALLIS: Depends on how hot it
is.
MR. REYES: So it -- from the shape of it,
I'd say --
CHAIRMAN WALLIS: So I'm trying to get a
feel for which kind of a plume is it. I think it's a
spreading plume.
MR. REYES: It's a spreading plume.
CHAIRMAN WALLIS: Yeah. You have the
fire, the density difference is two to one or
something. So it's...
MR. SCHROCK: These theories pertain to,
as you've said, a large field. You've got the
downcomer walls that are confining the plume. Are you
going to address that?
MR. REYES: I'll cite the difficulties
with those things, right. Yeah.
We'll go on, and I'll show you some of the
problems we're facing --
CHAIRMAN WALLIS: There's a good --
there's a good book on this by some German whose name
I forget, who studied all kinds of plumes and all the
--
MR. REYES: I've got it in my bag.
CHAIRMAN WALLIS: Okay.
MR. REYES: It's Rodi and Chatney.
CHAIRMAN WALLIS: Rodi, that's right.
Rodi.
MR. REYES: They did a ton of work in --
you're welcome to look at the book. Yeah.
CHAIRMAN WALLIS: It's pretty
comprehensive.
MR. REYES: It is. It was a very nice --
one of the few that covered a wide range of
axisymmetric and -- but I'll show you another paper
today, which is fairly new, which is closer to our
situation.
CHAIRMAN WALLIS: It's got too many ns.
MR. REYES: So we're familiar with the
classic assumptions for the planar plumes. The idea
that there's a linear spread of plume radius with
axial position, because you have a constant
entrainment rate. And that assumption works
reasonably well for the planar plumes in stagnant
media.
You've used the similarity of velocity and
buoyancy profiles. And you can come up with some
universal curves that way. And in REMIX they kind of
use that technique of producing these universal
curves. And then at different locations it says,
okay, for this set of dimension groups you kind of
convert it back into what you should be reading there,
so that works well.
And, of course, they always -- you
typically assume the Gaussian-shaped profile for this
stagnant media. I'll show you a couple of pictures.
Back in 1934, we've got some data which
shows the same situation. Here you have the velocity
measurements inside the plume. The scale's missing
here. That should be centimeters per second on the y
axis.
The velocity measurements for the plumes
at different axial locations. And if you -- you can
actually scale it with a mean velocity of plume and
come up with a single shape, a single universal
Gaussian curve. So we know that that theory works
very well.
So the thought was, well, we can apply to
some of the similar concepts to our test --
CHAIRMAN WALLIS: Well, I'm trying to
think, though. When you pour -- pull this stuff over
the lip of a pipe, --
MR. REYES: Right.
CHAIRMAN WALLIS: -- you don't have the
sort of starting condition of a uniform velocity. It
has to sort of accelerate out of the pipe. So it's
accelerating for a little while before it does this
mixing.
MR. REYES: That's right.
CHAIRMAN WALLIS: Isn't it?
MR. REYES: So -- yeah, I was --
CHAIRMAN WALLIS: I don't quite know how
you modeled the starting condition for coming out of
the pipe and going over the lip and into the
downcomer. How do you start your plume for an
analysis like this?
MR. REYES: For an analysis like this what
we think is actually happening is that the plume is
jumping the gap. Eventually it's --
CHAIRMAN WALLIS: It hits the other wall.
MR. REYES: -- it hits the core barrel
wall. Now you've got another, another problem. So
that's what we believe happened.
CHAIRMAN WALLIS: This is like the
experiments that we did with the injection of water
into a steam down- -- filled downcomer. It jumps to
the wall and goes down the other side.
MR. REYES: Which test was that?
CHAIRMAN WALLIS: When was that done?
MR. REYES: Yeah.
CHAIRMAN WALLIS: 7-70, or something like
that. 1970 maybe.
MR. REYES: Yeah. For our test number 13
we're thinking of something similar, so I'll ask you
a little bit more about that.
The -- so that's right. There's some type
of flow establishment region. If you have a forced
flow, you have a momentum dominated, then some kind of
a transition. And then you eventually gets to this
buoyancy-dominated region for the plume.
So this region actually could be fairly
short. And where you'd like to be is kind of in this
region as far as analysis. So you've got this
spreading plume. But again that's for a stagnant
medium.
If you have -- if you have any
complications to it, you really have to -- I mean it
complicates the analysis quite a bit. If you're
impinging onto a core barrel wall, well, how do you
analyze that.
So we very quickly got -- as we started
looking at the different complications, that's where
we said, well, we need to use to some of the CFD and
see if we could understand that a little bit better.
CHAIRMAN WALLIS: Now let's look at Mr.
Foerthamnn's experiment.
MR. REYES: Sure. Can you go back?
CHAIRMAN WALLIS: Now it seems as if the
width of the plume is about four centimeters, or
something, but the velocity in the middle hasn't died
to half the initial one until it's gone 75
centimeters. So this is a plume that's very
persistent. It's gone an awful long way before its
velocity in the middle has gone down by a half.
MR. REYES: Right.
CHAIRMAN WALLIS: So your plumes aren't
anything like that. Yours --
MR. REYES: No.
CHAIRMAN WALLIS: -- spread much more
rapidly, don't they?
MR. REYES: Correct. Correct.
CHAIRMAN WALLIS: Why is that? There's
something different about some dimensionless number in
your experiment than in this one?
MR. REYES: Right. Now for this
experiment --
CHAIRMAN WALLIS: There must be something.
MR. REYES: I think -- yeah. There -- I'm
not exactly familiar with the delta rho over rho in
this test or the density difference in this test and
what was going on as far as the buoyancy.
CHAIRMAN WALLIS: I think this is actually
spreading less than the jet would in just -- the
shrifting-type jet with no buoyancy at all. This one
is actually buoyant, so it's spreading less than a
jet. And --
MR. REYES: Than the actual.
CHAIRMAN WALLIS: -- that's why it's so
surprising that your plumes spread so rapidly.
MR. REYES: Well, there's other -- so
there's other -- right. So there has to be other
mechanisms that are --
CHAIRMAN WALLIS: You think about the
plume from the stack from the incinerator next to your
-- do you have an incinerator next to your building?
MR. REYES: It's a -- well, I can see it
from --
CHAIRMAN WALLIS: That probably goes quite
a long way on a clear day before it spreads much.
MR. REYES: That's right.
So what we -- we started looking at our
plumes and realized that there's something -- it's
significantly more complicated, especially for the
conditions that we were looking at, because we had
multiple asymmetric plume interactions. We actually
had some cases where we had cold flow.
So now instead of a stagnant downcomer,
what you actually have is hot-leg flow. You're
putting hot water -- the way this was stratified,
you're -- basically the cold water is pouring --
pouring out the bottom of the pipe.
You still had positive hot-water flow on
the top of the cold leg going into the downcomer. And
you were forcing this flow through the downcomer co-
current with the plume. So now you've got a
could-current situation.
CHAIRMAN WALLIS: That could be worse.
MR. REYES: Yeah. So now I'm starting
thinking relevant velocity between the plume and your
medium. If you have a stagnant case, your plume comes
in and the relative velocity for that case is going to
be larger than if the media traveling with the plume
is at nearly the same velocity. So now the relative
velocity between the plume -- and that's a well
documented -- that's this plume behavior in cold flow.
And so we searched the literature for
that, and we found a paper that was fairly recent that
tried to address that, by Wood.
So potentially with some cold flow you can
actually have less -- you'll preserve the plume
further under certain conditions, okay.
There are other compounding conditions, of
course. We -- and our tests, of course, as opposed to
some of the studies done previously, we have a core
with a core barrel. And that's dumping heat into the
downcomer. So there are other things which are
heating up this plume and causing it to dissipate a
bit earlier.
So you have these -- all these different
factors, some trying to preserve the plume and some
trying to destroy the plume. Okay.
So we very quickly came to realize that if
we wanted to do a realistic or something realistic,
that maybe we can bound the problem asymptotically and
look at some of the ranges of the plume spreading.
But, in fact, the thought then came, we
need to do some type of CFD work. And that, of
course, brought with it its own set of problems, how
to understand CFD and who would volunteer to do the
work.
And so we'll present that later on. And
we're wide open to suggestions on that. But you'll
see some of the comparisons, and you can be the judge
of what the problems might be or what went right.
Okay. So, in essence, there is a test
facility in Finland, Imatran Voima Oy, which in the
good old days they did these flow visualizations. And
I guess they had an artist watching the stuff, because
this is an artist sketching. He must have been very
fast.
CHAIRMAN WALLIS: Well, Leonardo did it
all 500 and some odd years ago.
MR. REYES: That's right. I think this
may be a da Vinci.
CHAIRMAN WALLIS: But Creare did something
like this, too, didn't he?
MR. REYES: Yeah. So Creare had that --
well, they only had the single.
CHAIRMAN WALLIS: It was red or blue, that
stuff that they used, but it was -- they had pictures
like this, I think.
MR. REYES: They did? I don't think -- I
think they had a single injection, a single --
CHAIRMAN WALLIS: Unwrapped?
MR. REYES: -- cold leg.
CHAIRMAN WALLIS: I thought they had an
unwrapped --
MR. REYES: Well, maybe they did have two.
CHAIRMAN WALLIS: Maybe -- well, go back
and find out.
MR. REYES: I don't know if they ever --
I never saw they had for two. Yeah, I saw two tests
that they did.
But they had -- they were using that red
dye and they were injecting into each of the cold legs
and sometimes they flow, but they were getting some --
they were getting plume merging. And so, of course,
that -- you know, what's the strength of the plume
where they -- when they merge and how does that affect
heat-transfer coefficient, da-da-da. It goes on and
on.
So in terms of simple analyses, they very
quickly -- it became obvious that it was beyond what
you can do on the back of an envelope --
CHAIRMAN WALLIS: That plume seems to be
going a lot more than 4 ds. You were talking about
mixing by 5 ds. Or the beltline is at 5 ds from the
pipe, or something?
MR. REYES: Right. For Palisades it's
somewhere up there --
CHAIRMAN WALLIS: And this one seems to be
going down a lot more than that --
MR. REYES: This -- this -- yeah, this
looks like it's going down for -- now the flow rates
for the -- for what they were doing were very, very
high in these tests. So that's a big part of it.
And I think we have a picture later on
that we'll show you that kind of goes back to this
test. And, of course, we saw similar behavior as far
as merging, but we didn't see the plumes, you know,
getting --
MR. BESSETTE: You have to remember also
this is an artist's rendition.
MR. REYES: So da Vinci --
MR. BESSETTE: Done by -- Actually it was
done by Tuemisto himself.
MR. REYES: Tuemisto, okay.
MR. BESSETTE: Yeah.
MR. REYES: Tuemisto da Vinci.
CHAIRMAN WALLIS: They didn't have
photography in those days.
MR. REYES: We have some --
MR. BESSETTE: Not -- well, I don't know.
Like I say, he'd interpreted what he saw, and he did
it by drawing.
MR. REYES: So when we started looking at
the plumes we were having difficulty interpreting what
was going on in the downcomer. So Kent Abel, one of
our graduate students, came up with this idea of
putting together this, an unwrapped map.
And so each -- this shows all four of the
cold legs. On top of it, it gives you the flow rate
through the cold leg, and then the HPSI flow rate for
each of the cold legs. So those are listed up on top.
And then along side here he's got a color code for the
different temperatures.
And then here in the cold leg you can see
if the cold leg is stratified or not, so again by
temperature. So we can observe stratification. When
this light is green, it means that the HPSI is flowing
for that particular transit.
You can pull up any one of the tests that
we've performed into this format, and it'll just play
the downcomer for you, which I love it. I can -- I
sit there and watch the lights.
CHAIRMAN WALLIS: Do you have music?
MR. REYES: HPSI, HPSI. You get
hypnotized kind of by it.
But this is just an example. If we have
time I think we can run one of these or two to show
you a couple of different scenarios and what we see.
It's useful because we break it up into a
gradient, a delta T that your eye can actually catch
instead of a continuous type of a thing.
And what we see in this particular
snapshot, we see this plume, we see cold temperature
over here and cold temperature over here, so we're in
the dark, this dark blue region over here.
CHAIRMAN WALLIS: It's not very obvious.
MR. REYES: It's not real obvious, but it
does interact --
CHAIRMAN WALLIS: Can't you get more
contrast?
MR. REYES: Right. In some of the other
-- I think in some of the others we'll see more
contrast.
CHAIRMAN WALLIS: Yeah.
MR. REYES: But the thing is that the
temperature difference is not -- you're within --
they're typically within 10 degrees or so, 10 or 15
degrees. And so we could do some more contrast.
So what we see is a kind of interaction
here, and then we do see colder here and some cold
down here. So we kind of see a merging plume over
here. But then again the ambient is relatively cold
also.
So in terms of a delta rho, we're not
looking at a very large delta rho. However, we are
seeing this merging and then getting down blow here.
So you can imagine that if we had a couple thousand
more thermocouples, that would have been ideal.
So that's one example.
Now you can see it a little bit better as
we run -- is that the next -- yeah. We'll run this
for you, and then you can see a little bit better the
temperature changes. And this was for the -- this was
for the main steam line break case, so you'll see
eventually everything will turn blue because the --
CHAIRMAN WALLIS: Yeah. I think if it's
dynamic it will be easier to see.
MR. REYES: Right. And I think that's
what we'll do.
Okay. So it's running right now. We're
getting -- the time on the upper left-hand corner is
the time to start the test. And so it's jumping.
We're jumping about -- every step is about eight
seconds or so.
And this is the main steam line break. So
we've opened up the break, and so you see all the
temperatures are uniform. Now the break's open.
We're starting to see cooling, but that's not cooling
to the HPSI.
Now the green -- the HPSI's on now at this
point, and so you'll start seeing colder temperatures
underneath the cold legs. So there you go. So you
see some of the yellow and the green, so it's getting
colder underneath there.
CHAIRMAN WALLIS: Can you -- uh-huh, okay.
MR. REYES: And we can step through it if
you want to go slower. So you see --
CHAIRMAN WALLIS: So this is typically the
whole downcomer, so the beltline is sort of where in
this, in the middle --
MR. REYES: The beltline is between the 4
d and the 8 d.
CHAIRMAN WALLIS: Somewhere in the middle
of the page.
MR. REYES: Yeah. And we -- and that's
actually where our beltline is. We have a big flange
sitting there so we couldn't get thermocouples in it.
And so you can see at this point the cold
leg number 3 there is still so much stratified. Cold
leg number 4 is completely cold, but then that was
where the broken steam generator was. So you're
seeing some cold flows there.
So now that the whole downcomer is
overwhelmed basically by the transient itself, the
steam line break. Looking --
MR. BOEHNERT: So that was every eight
seconds, was it?
MR. REYES: Correct. Correct. Yeah, I
think we're -- were we jumping eight seconds there,
Ken? Yeah.
CHAIRMAN WALLIS: If you go back to about
one or two seconds after it began to turn yellow, --
MR. REYES: Okay.
CHAIRMAN WALLIS: -- you've got some --
some spludges pretty low down of the -- a really
different color from the surroundings. I got the
impression that there was some plume activity down to
maybe 10 d or something. Not insignificant.
MR. REYES: Right. Well, -- yeah. In
fact, we'll talk about what happens when you have that
cold-leg flow and you're trying to preserve the plume.
We see it -- the behavior is somewhat different. I
won't steal -- I won't steal their thunder.
But, yeah, we do see a different behavior
for cases where your cold legs are flowing and -- for
this plant.
(Discussion held away from the microphone and
simultaneous talking.)
MR. HAN: One of the things to keep in
mind --
MR. REYES: It was one of our
thermocouples --
MR. HAN: -- in terms of the vessel is
that transient --
(Discussion held away from the microphone.)
MR. HAN: -- behavior is not important
because of the time constant of the vessel wall --
MR. REYES: This is James Han.
MR. HAN: -- things that happened over the
time of, say, one minute, for example, don't matter
because you don't build up a stress. So you can have
these plumes. Let's say, if they're moving and
whatever, that the transient behavior doesn't matter.
It's the longer-term behavior that's important, things
that happen over the course of 15 minutes to 45
minutes.
CHAIRMAN WALLIS: It's a question of the
balance between the surface h and what you think of
sort of internal heat transfer distance of the wall.
MR. BESSETTE: And it's conduction -- it's
conduction --
CHAIRMAN WALLIS: It's certainly not an
infinite h on the surface.
MR. BESSETTE: No, but if it does -- the
h doesn't matter. It's because it's so conduction
controlled.
CHAIRMAN WALLIS: Yeah. So it's like an
infinite h?
MR. BESSETTE: It's like an infinite h.
If you had an infinite h or not an infinite h, it
doesn't really matter too much.
CHAIRMAN WALLIS: So you're immediately
chilling the surface to the temperature of the water?
MR. BESSETTE: Essentially your boundary
layer doesn't matter that much. It's the ambient --
CHAIRMAN WALLIS: But you had to know h
because if you assumed h is infinite it's not very
nice.
MR. BESSETTE: Well, --
CHAIRMAN WALLIS: You have to know h.
MR. BESSETTE: -- if H is infinite -- if
h is infinite, it means you have no boundary layer.
It means your ambient temperature is the temperature
of the surface of the wall.
CHAIRMAN WALLIS: I don't think you want
that.
MR. BESSETTE: It doesn't matter that
much.
CHAIRMAN WALLIS: It stresses the wall.
That temperature difference is what stresses the wall,
the difference from surface from the average, is it?
MR. REYES: There is a thermal penetration
of time that --
MR. BESSETTE: The difference between the
ambient fluid temperature and the wall surface
temperature is never large, no matter what h is.
CHAIRMAN WALLIS: Then you might as well
assume h is infinite for your -- and forget about
everything else as long as you know what the
temperature is.
MR. BESSETTE: That's right. You can do
that.
CHAIRMAN WALLIS: I don't think that's
very good for -- well, maybe we -- that's a different
discussion somewhere else.
I thought it was pretty critical what h
was.
MR. BESSETTE: No. In fact, we've done
those sensitivity studies already --
CHAIRMAN WALLIS: Okay. So we'll go back
to that some time.
MR. BESSETTE: -- to show that h is not
important.
MR. SHACK: I mean that's good news.
MR. BESSETTE: Yeah.
MR. HAN: That's good news, yeah.
CHAIRMAN WALLIS: So we just forget about
thermal hydraulics.
MR. SHACK: No, no. You had to set the
temperature.
MR. KRESS: No, you need the temperature.
CHAIRMAN WALLIS: Okay.
MR. BESSETTE: We've been trying to tell
you that.
(Laughter.)
MR. SHACK: But it's still your
penetration depth that you're interested in, isn't --
CHAIRMAN WALLIS: See, there's a white --
there's a light-colored one way down there, right?
Presumably that -- what's happening there? It looks
very strange to me. You've got colder stuff down
there than you've got --
MR. KRESS: At the middle it curled over.
CHAIRMAN WALLIS: Yeah. But it's just
going to warm again at the top, isn't it? Or, no,
maybe I've -- yeah, it's going to warm again at the
top. There's a plug, sort of a lump of cold fluid in
there not even connected to the pipe.
MR. REYES: Yeah. And sometimes what you
see is -- well, our thermocouples -- that's a good --
that's a good point.
Our thermocouples are closer to the vessel
wall because that's where we wanted to measure, what
was impacting the wall.
CHAIRMAN WALLIS: Oh, so if it jumps away
to the inside, --
MR. REYES: If it jumps --
CHAIRMAN WALLIS: -- you won't see it?
MR. REYES: Yeah. So quite often --
that's right. So quite often what we see is when
we're injecting -- it'll jump that first thermocouple.
And that one will read hot. And all the thermocouples
below will read cold. And so it's impacting the
barrel wall, mixing up, and then it's --
CHAIRMAN WALLIS: But here we have -- do
those yellow things -- are they those things -- they
look -- that doesn't look like a plume. It just looks
like a -- sort of a odd-shaped lump of fluid.
MR. REYES: It's not like the -- well,
again we don't have -- we don't have a lot of
thermocouples to get a good fine detail of this thing.
But you're right, the shapes are not going
to be nicely-spreading plumes. There are going to be
some meandering --
MR. SHACK: Will we see this in the CFD
calculation, something like this?
MR. REYES: Well, yeah, I think you'll see
that the CFD calculation does more of the meandering
and the curling-type behavior, so...
Okay. I'll let them get us back to the
presentation.
Okay. So one of the things that we've
observed is that at least as far as -- in terms of an
asymptotic solution or trying to imagine a little bit
of what's going on, there was a paper recently by
Wood. It was called, "Asymptotic Solutions and the
Behavior of Outfall Plumes."
And it was very nice -- nicely done
because you don't -- it was the only one I found that
was fairly recent that talked about the spreading of
the plume under some unusual conditions, either
crossflow or co-flow.
So what is done basically is the b
represents the half width of the plume. Okay, and z
is the axial position of the plume as it comes down.
And so this basically describes the
spreading of the plume. So for a stagnant case, u
subinfinite here, that's a stream velocity. Up is the
plume centerline velocity. And ks is the spread
constant.
And so for a stagnant media where you're
injecting these plumes, k is a constant. I mean this
goes to zero. The ups cancel in case. So he was able
to kind of unify that behavior.
Whenever you have a flow, this is the
angle between the trajectory of the plume versus your
flow. So if it's co-flow, that would be -- the
cosine's zero is one. So you'd have up over up plus
u infinite.
So what this is telling us then is it's a
factor that makes this constant smaller and as a
result you get a plume width which is smaller, tighter
as you go down in your axial position.
So this confirmed an idea that, well, for
co-flow you would expect to see tighter plumes. They
might be preserved a little bit longer than you'd
expect to see in a stagnant media.
So this suggests that for certain -- so
now a scenario comes to mind. You have stagnant
conditions in your -- in your downcomer. You inject
the plume.
You'll get very good mixing because the
relative velocity between the plume and the ambient is
go
