NUREG/CR-1444

Investigation of Distorted-Geometry

Simulation of Pool Dynamics in

Horizontal-Vent BWR Containments

Prepared by N.G. Ruggieri, A.A. Sonin

Department of Mechanical Engineering

Massachusetts Institute of Technology

Prepared for

U.S. Nuclear Regulatory

Commission
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NUREG/CR-1444

R4

Investigation of Distorted-Geometry

Simulation of Pool Dynamics in

Horizontal-Vent BWR Containments

Manuscript Completed: May 1979

Date Published: April 1980

Prepared by

N.G. Ruggieri, A.A. Sonin

Department of Mechanical Engineering

Massachusetts Institute of Technology

Cambridge, MA 02139

Prepared for

Division of Reactor Safety Research

Office of Nuclear Regulatory Research

U. S. Nuclear Regulatory Commission

Washington, D.C. 20555

NRC FIN No. B6167

ABSTRACT

Experiments were conducted to investigate the accuracy of distortedgeometry testing of pool dynamics in horizontal-vent BWR containments.

Distorted-geometry testing implies testing in systems where the flow-wise

dimensions are full scale, but all dimensions transverse to the flow are

reduced in the same proportion. The assumption is that flow velocities,

pressures and other thermodynamic properties can be interpreted as being

the same in the distorted-geometry system as in its correctly proportioned

counterpart. Our experiments, which were done at small scale using the

established scaling laws, showed that the geometric distortions can have

a significant effect on the pool swell under conditions which are roughly

representative of horizontal-vent BWR containment systems during a LOCA.

Breakthrough occurred later, the water ligament was thicker, and pool

velocity lower in a system where the cross-sectional areas were reduced

by a factor of three. Some reasons for the differences are discussed.

iii

TABLE OF CONTENTS

Abstract ............................

List of Figures .....................

Symbols .............................

1. INTRODUCTION ....................

2. EXPERIMENTS .....................

3. RESULTS .........................

3.1 Pressure Histories .........

3.2 Vent Clearing Times ........

3.3 Pool Swell ........... .....

4. DISCUSSION AND CONCLUSIONS ......

References ...........................

Tables ..............................

Page

............................... iii

............................... vii

. ..... .ixl... ...........

..... ..... . ..... ... .1...... 

.2

.6

.7

................9

..10

............................... 13

............................... 19

............ .................. 21

Figures .......................................................... .25

Appendix A:

Appendix B:

RELATIONSHIP BETWEEN POOL PRESSURE OSCILLATIONS

AND WALL ACCELERATIONS ................................ 59

QUANTITATIVE ANALYSIS OF VENT CLEARING PROCESS ........ 63

v

LIST OF FIGURES

Figure Page

1. Systems A, B and C, side view .................................. 25

2. Proportions of systems A, B and C .............................. 26

3. Case 1, P2 vs time for systems A, B and C ....... I ............... 27

4. Case 1, P2 vs time for sytems A a d B, including long-time

behavior..... ........................................ 28

5. P2 and, window acceleration versus time in Case 1, system B

Also, window acceleration versus time resulting from tapping

window with hammer ............................................. 29

6. Case 1 at t-to = 20 ms ................................. 30

7. Case 1 at t-tO = 36 ms .............................. 3

8. Case 1 at t-to = 60 ms ......................................... 32

9. Case 1 at t-to = 90 ms ......................................... 33

10. Case 1 at t-t 0 = 120 ms ................................ 34

11. Case 2 at t-t 0 = 20 ms ................................. 35

12. Case 2 at t-t= 40 ms ................................. 36

13. Case 2 at t-to = 60 is ................................. 37

14. Case 2 at t-to = 90 ms .......................................... 38

15. Case 2 at t-to = 120 ms ......................................... 39

16. Case 3 at t-to = 5 ins, t-to = 10 ins.......................... 40

17. Case. 3 at t-to = 20 ms.. . . ................................................. 41

18. Case 3 at t-to = 40 ms ................................. 42

19. Case 3 at t-t 0 = 60 s...... . ........................... 43

20. Case 3 at t-to = 80 ms 42........................................44

21. Case 4 at t-to = 20 ms ................................ . ...... 45

vii
LIST OF FIGURES (cont')

Figure Page

22. Case 4 at t-t 0 = 30 ms ........................................... 46

23. Case 4 at t-t = 40 ms. ..............................

24. Case 4 at t-t° = 50 ms ........................................... 48

25. Case 1, water elevations vs time...... ........................... 49

26. Case 2, water elevations vs time ................................. 50

27. Case 3, water elevations vs time ................................. 51

28. Case 4, water elevations vs time................................. 52

29. Comparison of three different tests of Case 3 in system B,

at t-to = 40 ms ............................................... 53

30. Comparison of three different tests of Case 3 in system B,

at t-to = 90 ms .................................................. 54

31. Comparison of water elevations vs.. time in the three different

tests of Case 3, system B, referred to in Figs. 29 and 39 ........ 55

32. Comparison of two tests in system A, one with distilled water and

the other with water containing surfactant., Cm = 0.20, s/tv = 1.67,

cm(RTD/gzv)1⁄2 = 62, pD/Pw = 2.0 ................................... 56

33. Case 1, Horizontal displacements of starting vortex and burble

lEading edge vs time in system A ............................... 57

34. Case 2, Horizontal displacements of starting vortex and bubble

leading edge vs time in system A ................................. 58

viii
SYMBOLS

Ap cross-sectional area of vertical feed pipe

AV cross-sectional area of horizontal vent

b system breadth (long dimension)

Cm mass flux coefficient, Eq.(3) of Ref. 7.

d diameter of horizontal vent

g acceleration of gravity, 9.80 ms- 2

h system height

k vent system frictional loss coefficient for water clearing

Zv length of horizontal vent

p absolute pressure

Pw absolute pressure in wetwell airspace

PD absolute pressure in drywell

Ap amplitude of pool pressure oscillations due to wall

oscillations (App. A)

R specific gas constant for drywell gas

s submergence of horizontal vent (centerline,)

t time

to vent clearing time

t* time when air reaches upstream end of horizontal vent (App. B)

TD drywell gas temperature

V instantaneous upward velocity of pool (App. B)

Vo see Eq. (B.8), App. B

V instantaneous downward velocity of water in vertical feed pipe

v instantaneous water velocity in vent

w system width (short dimension),

ix
x in Figs. 32 and 33, horizontal displacement from vent exit;

in Appendix A, see Fig. A.l; in Appendix B, see Fig. B.1

x' in Appendix B, see Fig. B.l

Xo 0 in Appendix A, amplitude of wall displacement (see Fig. A.l)

y see Fig. A.l

z see Fig. A.l

za value of z at point where acceleration is measured (Appendix A).

Zw value of z at free water surface in pool (Appendix A).

y specific heat ratio c /CP v

ni to 7r4 see Eqs. (1) - (4)

p water density

T window oscillation period in Appendix A; vent flow characteristic

time, given by Eq. (B.9), in Appendix B.

x
1. INTRODUCTION

Two approaches have been used to develop design loads for BWR pressure

suppression containments under postulated accident conditions from out-ofscale experiments. One approach relies on small scale modeling of the

processes, and is based on a knowledge of the scaling laws which ensure

dynamic similarity between the model and the full scale system. This

method has been used to predict the air clearing loads for the General

Electric Corporation's Mark I and Mark II BWR containments [1-5]. The

scaling laws have been verified experimentally [6-9].

The other approach relies on tests in distorted-geometry systems

where the flow-wise (usually vertical) dimensions of the test system

are full scale, but all dimensions. transverse to the flow are reduced in

the same proportion. Full scale driving pressures and flow rates-per

unit area are imposed, and measured pressures and velocities are assumed

to be equal to those in the full scale prototype system. In other words,

the method assumes that the flow is essentially independent of its extent

transverse to the flow direction. The GE Mark III containment design has

relied heavily on this kind of simulation [10].

Distorted-geometry tests are used where completely full-scale tests

would require prohibitively high flow rates, even for a representative

single "cell" of a large system. In principle, they have the advantage

over small scale simulations that no a priori knowledge is needed of the
-2-

scaling laws: quantities are simply assumed to be equal to the full scale

values. The shortcoming of distorted-geometry tests lies in the fact that

little information is available on when they can be expected to yield

accurate results.

This paper describes a study of the accuracy of distorted-geometry

testing in a situation which is characteristic of the pool swell process

in a horizontal-vent BWR pressure-suppression containment. Our premise

is that the scaling laws for this process have already been established

[6-9], and that a check of the distorted-geometry testing concept can

therefore be carried out at a small scale.

Our study was conducted in small-scale systems which were roughly

similar to the GE Mark III containment and its distorted-geometry counterpart. Test conditions were chosen to simulate Mark III dynamic conditions

approximately. No attempt was made, however, to simul~ate any particular

system or event exactly. The purpose of our investigation was to check

the accuracy of distorted-geometry testing under conditions which were

typical of applications.

2. EXPERIMENTS

Comparison tests wereperformed in three small-scale systems shown

in Figs. I and 2. Tables 1 and 2 summarize the geometrical and dynamical

conditions, respectively, in the tests. The systems simulated a simple

wet pressure suppression containment system wi'th a single horizontal
-3-

vent. The pool had a rectangular cross-section, and the vent and its

vertical feed pipe were of circular cross-section. All three systems

had the same flow-wise dimension* (vent length, distance from floor to

vent, and submergence, the latter being adjustable). The dimensions

transverse to the flow (system width, system breadth, vent diameter,

vertical pipe diameter) were in constant proportion to each other in

each system, but the absolute values differed in the three systems.

System A had proportions roughly similar to the GE Mark III system,

except that it had a single vent rather than three. System B had crosssectional areas 1/3 of those in system A and was therefore a "1/3-scale"

distorted-geometry representation of system A. System C had crosssectional areas 1/9 of those in system A.

A vertical feed pipe linked the horizontal vent to a "drywell"

via a calibrated flow-adjustment orifice and fast-opening, pneumatically

operated valve similar to the one in [7]. In any particular set of

comparison tests, the "wetwell" pressure above the pool was set at a value

p and the drywell pressure was set at a higher value PD (Table 2). The

initial pressure of the gas trapped below the valve was the same as the

wetwell pressure in all runs. A transient was initiated by opening the

valve. The valve opening time was short and did not affect the ensuing

*Actually the distante from the vent centerline down to the bottom of

the vertical pipe differed in the three systems, being 14, 10 and 9 cm

in systems A, B and C respectively. Since this part of the pipe remains

filled with stagnant water, it should have no effect on the flow.
-4-

flow process significantly. During the entire recorded transient, both

PD and Pw remained essentially fixed at their initial values because the

drywell had a large volume and the wetwells of the three systems were

connected to an auxiliary tank which also had a large volume (Fig. 2).

The calibrated orifice was used to adjust the gas blowdown rate according

to the required scaling laws [1-9] and to ensure that the gas flow rate

per unit flow area was the same in all three systems in a given comparison

test.

The rectangular wetwells of systems B and C were constructed of

1 1/2 in (3.8 cm) thick plexiglas on all sides, while in system A the

large side walls were made of 3/4 in (1.9 cm) thick tempered glass, with

the remaining sides of 1 1/2 in plexiglas as in the smaller systems. The

vents and the vertical pipes were made of plexiglas tubing.

The test sections were fitted with pressure taps (for Kistler Model

205 low-pressure piezotron transducers) at five locations, numbers 1 to 5

on Fig. 2. Transducer responses were recorded on an oscilloscope.

High-speed films (1000 frames per second) were taken of the pool

swell from the broad side of the systems.

In all tests the working gas was air, and the liquid water, both

at room temperature. Except where indicated, the water was doped with

surfactant to minimize the presence of air bubbles on the walls [7, 9].

The dynamic conditions of the tests were chosen so that they would

be roughly representative of a loss-of coolant accident in a full--scale
-5-

system of comparable geometry. Dynamic conditions are modeled by four

dimensionless parameters [8i:

"I : Y (1)

I2 = Pw/Pg2v (2)

I3 = D/P (3)

T4 = cm (RTD/gZv) (4)

where Zv is the horizontal vent length, taken here as the characteristic

length of the systems, p is the water density,*g is the gravitational

acceleration, R is the specific gas constant for air, TD is the drywell

air temperature, and cm is a mass flux coefficient defined by Eq. (3) of

[7]. In all our tests, the specific heat ratio y of the gas was 1.4,

corresponding to air. The values of the other three modeling parameters

are listed in Table 2 for the cases discussed in this report. The

coefficient cm was adjusted to the desired value by using appropriate

orifices which were calibrated for cm by the method used in [7,9].

Actually, cm is generally somewhat dependent on the dimensionless pressure

difference (pD-p)/pD, where p is the pressure at the vent exit. The value

of cm given in table 2 is a reference value corresponding to a dimensionless

pressure difference of 1/3.

Table 1 shows that the proportions of System A are approximately similar

to those of a single "cell" of a GE Mark III containment except that our
-6-

model has one instead of three horizontal vents. From Table 2 we see,

furthermore, that comparisons number I. and 2 also simulate the vent flow

resistance, the submergence, and the dynamic blowdown conditions of the

Mark III system approximately, although it should be noted that our experiments are done with a constant drywell pressure and not with a linearly

increasing one as in the Mark III system. Comparisons 3 and 4 represent

a rather low simulated submergence as compared with Mark Ill, and comparison 4 furthermore has a very low scaled vent flow resistance, lower than

the minimum possible value of unity in a full-scale system.

3. RESULTS

Our main goal was to test whether the three different systems,

with identical flow-wise dimensions but different transverse dimensions,

would exhibit similar'pool swell transients under similar dynamic conditions.

Four sets of comparisons will be described here, labeled numbers 1 - 4.

Table 2 gives thedynamic similarity parameters for each 'set. The differences

in the four cases are in the dimensionless submergence (a geometric parameter),

and in the dimensionless parameters PD/Pw and cm (R TD/g Zv) which define

the dynamic driving conditions for the pool swell transient. The dimensionless

wetwell pressure Pw/Pg-2 v had the same value of 6.4 in all tests. The. reasons

for the choice of these particular values of the similarity parameters *is

apparent from the discussion in Section 4.
-7-

3.1 Pressure histories

The pressure histories in the pool turned out to be quite similar

in the three systems, except for a superposed oscillatory component which

apparently resulted from an induced pool. vibration and was different in the

three systems. This is shown in Figs. 3 and 4. The top trace injeach

oscillogram represents transducer no. 1 in Fig. 2, and indicates the

pressure in the vertical pipe, just downstream of the orifice; This pressure

rises rapidly to the drywell pressure as the vertical pipe pressurizes

after valve opening (the roughly 30 ms risetime in Fig. 3 is due to this.

effect, and does not reflect the valve opening time, which was short) and

stays there until the air enters the pool from the vent (vent clearing),

at which time the pressure begins to decrease. In case 4, which had a

large orifice, the pressure-rose to the drywell pressure in about 10 msec,

and thereafter showed a small s~inusoidal component which apparently resulted

from acoustic effects in the air-filled portions of the vertical pipe and

the vent.

The bottom trace in the oscillograms represents transducer no. 2, which

is located in the pool floor 1/4 of the system width from the wall with the

vent.

Transducer no. 2 shows no pressure rise, except for an oscillatory

component, until the vent clears. Shortly thereafter the pressure.rises

rapidly to a maximum value, and then drops as the bubble grows and the

pool swells. The pressure histories from the other transducers in the pool
-8-

(transducers no.. 3"and 4) were similar in structure to that shown by

transducer no. 2.

The oscillatory component of the pressure at thesubmerged points

appeared to be due to pool vibration which resulted from wall flexibility,

and possibly also from air bubbles which had not been completely cleared

from the pool. Fig. 5 indicates signals from an accelerometer mounted on

the outside of the side window in System B, the center of the pane,

together with P4 (t). The accelerometer shows a peak reading.which coincides with the peak in P4, and contains two dominant frequencies, one

which is about the same as the dominant frequency in p4 (of the order of

6 ms period in the case shown) and another which i~s higher (of the order

of 2 ms period). Fig. 5 (c) shows the response of transducer 2 when the side

wall was tapped with a hammer. The same two dominant frequencies appear

to be present. The,.higher frequency is of the order expected for the

natural frequency of this window, estimated [11) as being between 1 and 2 ms

in system B, depending on whether one assumed that the window was rigidly or

simply supported at its edges (the water mass associated with one window was

only about 1/4 that of the window, and hence the effective mass of the water

was not important for purposes of rough estimation).

The pressure histories are of secondary interest in the present study

because they appeared to be relatively insensitive to the details of the

pool swell process, and were therefore not useful as indicators of pool

.swell similarity in the three systems (see Figs. 3 - 5). For that reason,
-9-

we did not concentrate on taking pressure data, nor did we attempt to

systematically trace down the origin of the oscillations in the pressure

histories. In Appendix A we do provide an approximate analysis, however,

which suggests that the observed pressure oscillations are very roughly

consistent with the observed wall accelerations if one assumes that both

resulted from a common fluid-structure interaction.

3.2 Vent Clearing Times

The vent clearing time to is the period between the opening of the

valve, when the water in the feed tube begins to move, and the time when

air first enters the pool from the vent. This period was determined

directly from the high-speed films. Table 3 lists the values obtained

for the three systems in the various comparison tests. There is a

judgemental error of about ± 3 ms in these figures, associated with the

difficulty of determining the initiation time for the event from the

films. The possible error due to errors in film speed was negligible,

since the-clearing time was determined directly from time markers on the

film rather than by counting frames.

The vent clearing times generally tended to increase from system A

to B to C. We attribute the differences in to to differences in the'

hydraulic loss coefficients for the vents in the three systems. The

orifices at the tops of the vertical feed pipes of the systems were

calibrated so as to ensure the same loss coefficient in all three systems
-10-

for the air flow in the entire feed pipe/vent pipe system, from the

downcomer to the pool at the vent exit. No attempt was made, however,

to ensure the loss coefficients for the vent pipes, which control the

water outflow, were the same in all three systems. The vent flow Reynolds

numbers for the water were high, of the order of 105, and it is likely

that the differences were not due to Reynolds number effects, but resulted

simply from the geometrical differences between the three systems. The

geometrical differences are apparent from Fig. 1. If the vent system

head loss coefficient is determined by geometry and is Reynolds number

independent, then it should be the same in any given system, regardless of

the dynamic driving conditions (drywell pressure, etc.). The simple vent

clearing analysis in Appendix B shows that our results can be explained

reasonably well if one makes this assumption.

Geometrical differences would also exist between a full-scale system

and a distorted-geometry simulation of it. Hence, vent clearing time

differences similar to the ones observed here may also be found between

full scale systems and their distorted-geometry simulations.

3.3 Pool Swell

.Figs. 6 to 24 show comparisons of the pool profiles in the three systems

at various times after vent clearing. The figures are views of the broad side

of the systems, showing the apparent profiles of the top water surface and the

air-water interface of the bubble which emerges from the horizontal vent. They
-11-

were traced directly from projections of the high-speed films. The line

boundaries are visual approximations. The time to was determined to an J0

accuracy of ± 3 ms, and t- to, which was obtained by counting film frames,

is accurate to better than ± 5%.

Some of the figures also indicate the location of the starting vortex.

This is the ring vortex which forms when the vent flow begins, and then

moves into the pool. The vortex was often visible in the films, presumably

because it contained cavitation bubbles in its core.

Figs. 25 to 28 show the histories of maximum pool surface elevation and

maximum bubble elevation for the four comparison cases.

It is apparent from Figs. 6 to 24 that three-dimensional effects are

present and cause differences in the pool profiles between all three systems,

the differences being more profound between systems A and B than between

B and C. System A tends to have an earlier breakthrough than system B and

C, and the water ligament tends to be thinner at the top of the pool and the

ligament (or surface) velocity higher (see also Figs. 25 to 28).

The data shown in Figs. 6 to 28 should be viewed as containing some

uncertainty since the pool histories contained an element of randomness..

The degree of that randomness is illustrated in Figs. 29 to 31, which show

the results from three repeated runs in the same system at identical operating

conditions. Note that error the in to is better than ± 3 ms, and the error in

t - to is below ± 5%. The randomness appeared to be largest when the submergence

was small, as in the example, and pool breakthrough occurred early.
-12-

Surface tension effects did not appear to play a dominant role in the

pool swell process before pool breakthrough. Fig. 32 shows one of the test

cases which were run with and without detergent in the pool water. The

difference in the cases is insignificant, less than the scatter observed

in Fig. 31 (the smaller scatter is likely due to the-larger submergence,

and later breakthrough).

The dominant three-dimensional features of the pool, which are quite

apparent in all tests in system A, appear to be imprinted by the interaction

between the starting vortex and the bubble. The starting vortex is generated

at the vent exit when the vent clearing process begins. After the vortex

is formed, which takes a time about equivalent to the ejection of 2-3

vent diameters of water [12], it propels itself into the pool at a speed

less than 1/2 that of the water jet emerging from the vent (the vortex

speed is of the order of 1/2 the jet speed in an unconfined situation, but

in this case the side walls-have the effect of reducing the vortex convection

speed below that value). The leading edge of the bubble emerges at essentially

the water outflow speed at the instant of clearing (see Appendix B), and

begins to overtake the slower-moving vortex (see Fig. 6, for example, or

Fig. 11). If the pool is wide enough, the vortex will be overtaken before

it reaches the opposite wall. The circulatory flow field of the vortex first

speeds up the tip of the bubble as it closes in on the vortex, creating a

necking-down effect (Fig. 12, for example), and then the bubble is convected

outward as it reaches the other side of the vortex, and a mushroom-shaped
-13-

tip results (see Fig. 12, or Fig. 7, for.example). This characteristic

shape is retained through the rest of the pool swell (see Figs. 13-15,

for example). The rate of advance of the leading edge of the bubble tends

to slow somewhat after it penetrates the vortex (see Figs. 33 and 34). This

may be due more to the fact that the bubble is approaching the opposite wall

than to the effect of the vortex interaction, however.

When the system width is too small for the bubble to be able to overtake

the vortex before it approaches the other side, the bubble penetrates the pool

more uniformly and three-dimensional effects are less prominent in the pool.

This was the case in systems B and C in most of the present tests. A comparison

of cases 1 to 4 shows, however, that the degree of the differences between

systems A and B (and to a lesser extent, between B and C) appear to depend

not only on how fast the bubble catches up with the starting vortex,but also

on other dynamic factors such as the drywell pressure (pD/pw), the enthalpy

flux (C•mT•T/gtv), and the initial submergence (s/9vv).

4. DISCUSSION AND CONCLUSIONS

The comparisons-described here show that the reduction of flow crosssectional areas by a factor of 3 can cause significant differences in a

typical pool swell process in a simulated horizontal-vent containment system.

The degree of the difference depends on both system geometry (c.f. the

substantial differences between systems A and B, and the relatively small
-14-

differences between systems B and C), submergence (greater difference at

lower submergence), and the dynamic driving conditions (higher enthalpy

flux tends to cause more severe differences, for example, and lower

drywell pressure appeared to increase the differences, at least in the

cases examined here). The causes of the differences are too complex

and subtle to allow any general conclusions about the accuracy of distortedgeometry tests to be drawn from the datagenerated in this particular study.

We are not in a position to offer a general criterion for when a distortedgeometry tests will, or will not, be a reasonably accurate simulation.

The systems testedin this study were roughly similar, however, to a

single cell of the Mark III containment. Table 1 shows that the geometrical

features of system A were approximately similar to the full-scale Mark III

system, Systems B and C would then correspond to "1/3-scale" and "1/9-scale"

distorted-geometry representations (by area). There was, however, an

important difference between our systems and the Mark III: ours had a

single horizontal vent, while the Mark III has three vents arranged one

above the other.

The dynamic conditions (see Table 2) were also approximately similar

to those in the Mark III, although no attempt was made for an exact

simulation. The drywell pressure in our system was constant (or applied

as a step-function, as it were) after the initiation of the event, at a

value of either two or three times pw" In the Mark III, the drywell pressure

increases approximately linearly from about P w after the initiation of the
-15-

event to a value two or three times higher than pw" In our system the

V2

enthalpy flux simulation parameter cm(RTD/gzV) had a value of 22 in

Cases 1-3, and a value of 62 in Case 4. A full scale plant, with a

full scale Zv = 1.5m, would have a value cm (RTD/gzV) 22 if it's

vent flow resistance (1 + fk/d) were 4.6 (see Table 2). This resistance value of 4.6 is roughly representative of a Mark III system. The

enthalpy flux parameter of 62 in Case 4 would imply a full-scale vent

flow resistance (1 + ft/d) of 0.6, which is smaller than the lowest

possible value of 1. Thus, this case simulates an enthalpy flux which is,

as it were, an upper bound on physically possible values in any fullscale system.

The dimensionless submergences of s/kv = 1.67 in Cases 1 and 2 would

scale up to a submergence of 8.2 ft. in a full-scale plant with Zv = 1.5m

.(Table 2). This is a fairly representative value. The Case 3 and 4 submergences of s/Z. = 1.00 would imply a 5 ft. full scale submergence, which

is lower than suggested for Mark III use.

In summary, then, Cases 1 and 2 have dynamical conditions and submergences reasonably representative of those in Mark 3, while Case 3 has

a low submergence, and Case 4 has both a low submergence -and too high an

enthalpy flux. System A is roughly similar to a single cell of a Mark III,

and systems B and C are 1/3-scale and 1/9-scale (by area) distorted-geometry

representations, respectively. Note, however, that the similarities are

not exact. There are important differences: our systems have a single
-16-

horizontal vent, not three, and our drywell pressures are applied in a

step-function manner, and not as a linear rise from pw"

Insofar as our Cases l.and 2 are similar to the Mark III systems,

we can conclude the following:

(1) There are significant three dimensional differences in the pool

profiles between system A (representing the full-scale system)

and its "1/3-scale" counterpart, system B. See Figs. 6-15.

The "1/9-scale" system (system C) behavior is much closer to

that of the "1/3-scale" than the "1/3-scale" is to the "fullscale".

(2) Pool breakthrough occurs considerably earlier in the "full-scale"

system than in its "1/3-scale" or "1/9-scale" counterparts. This

is apparent in Figs. 25-28. In Case 2 (Fig. 26), the water

ligament thickness is reduced to about O.ls after a rise by

about 1.3s in system A. This water ligament thickness is not

attained until the surface has risen by more than 2s in systems

B and C (the precise level lies outside the data base). In Case

1 (Fig. 25), breakthrough occurs in System A near the point when

the water reaches the ceiling, a rise of 2s. At the same level,

systems B and C are still far from breakthrough. The differences

are even more pronounced in Cases 3 and 4 which are not, however,

as representative of Mark III as Cases 1 and 2.
(3) The relatively thinnerwater ligament in the "full-scale" system

causes a higher maximum pool rise velocity in that system than

in its "1/3-scale" and "1/9-scale" counterparts, at least at

times nearing breakthrough (See Figs. 25 and 26). We are not in

a position to make general statements about the amount of the

difference, as it appears to be rather sensitive to the dynamic

conditions as well as to the submergence.

One of the more interesting general conclusions that emerges from our

study is that the vent clearing process plays a significant rolein determining the shape of the bubble and the pool surface during thepool swell

process, at least if the pool is wide enough, as in system. A It does so

via the starting vortex which is generated in the early moments of vent

flow initiation. When the bubble emerges, it travels into the pool at a

speed higher than the vortex which preceded it (see Appendix B., and Figs. 33

and 34), and, if the pool is wide enough (as in our system.A), overtakes

the vortex. The interaction of the bubble with the vortex imprints a

mushroom shape on the leading side of the bubble, and this basic shape

is retained, with small modifications, throughout the pool swell process.

Clearly, any numer-ical code for computing the three dimensional

features of this kind of pool swell process is doomed to failure unless it

is capable of dealing accurately with the formation of the starting vortex

and its induced pool velocity field.

-19-

REFERENCES

1. J.E. Torbeck, D.L.Galyardt, J.P. Walker, "Mark I 1/12-Scale Pressure

Suppression Pool Swell Tests", GE Report NEDE-13456, 1976.

2. D.L. Galyardt, C.G. Hayes, S.L. Kushman, "Mark I Containment Program

1/4-Scale Pressure Suppression Pool Swell Test Program: Scaling Evaluation",

GE Report NEDO-21627, 1978.

3. E.W. McCauley, J.H. Pitts, et al., "Final Air Test Results for the 1/5-Scale

Mark I Boiling Water Reactor Pressure Suppression Experiment",.Lawrence

Livermore Laboratory Report UCRL-52371/NUREG/CR-0151, 1977.*

4. R.L. Kiang and B.J. Grossi, "Three Dimensional Pool Swell Modeling of a

Mark I Suppression System", EPRI Report EPRI NP-906, 1978.

5. R. L. Kiang and B.J. Grossi, "Dynamic Modeling of a Mark II Pressure

Suppression System", EPRI Report EPRI NP-441, 1977.

6. F.J. Moody, "A Systematic Procedure for Scale-Modeling of Problems in Unsteady

Fluid Mechanics", GE unpublished report, 1976. (Available from GE, 175 Curtner Ave.,

San Jose, Calif. 95114).

7. W.G. Anderson, P.W. Huber, A.A. Sonin, "Small Scale Modeling of Hydrodynamic

Forces in Pressure Suppression Systems", U.S. Nuclear Regulatory Commission

- Report NUREG/CR-0003, 1978.*

8. A.A. Sonin and P.W. Huber, "On the Scaling Laws for Air Clearing in Water-Type

Pressure Suppression Systems", J. Heat Transfer, 100, 601-604, 1978.

9. W.G. Anderson, P.W. Huber, A.A. Sonin, "Experimental Tests of the Scaling Laws

for Air Clearing in Water-Type Pressure Suppression Systems", J. Heat Transfer, 100,

605-612, 1978.

10. R.J. Ernst, T.R. Mclntyre,, L.L. Myers, J.E. Torbeck, "Mark III Confirmatory Test

Program One-Third Scale Three-Vent Tests", GE Report NEDM-13407, 1975.

11. C.M. Harris and C.E. Crede, editors, "Shock and Vibration Handbook", Vol. 1,

McGraw-Hill, New York, 1961, Chapter 7.

12. T. Maxworthy, J. Fluid Mechanics, 81, 465-495, 1977.

*Available for purchase from the NRC/GPO Sales Program, U.S. Nuclear Regulatory

Commission, Washington, D.C. 20555, and the National Technical Information Service,

Springfield, Virginia 22161.

-21-

TABLE 1: GEOMETRICAL PARAMETERS

Small-scale systems

Mark III

A B C

Vent length 9 cm 9 cm 9 cm 1.5 m

Pool width 39 cm 22.5 cm 13 cm 5.8 m

Pool width

Pool breadth 3.0 3.0 3.0 2.5

Vent diameter 0.10 0.lO O.lO 0.12

Pool width

Vertical ipe area 0.053 0.053 0.053 0.08

Pool Area

Pool width 4

Vent length 4.33 2.5 1.44 3.9
TABLE 2: OPERATING CONDITIONS

I 2 3 4 5 6 7 8

SMALL-SCALE TEST CONDITIONS

,__CORRESPONDING MARK III FULL

Test Conditions Scaling Parameters SCALE CONDITIONS

Comparison Cm Submergence Submergence Mark III Submergence Mark III vent resistance (2)

No. (cm) Vent Length m gL corresp. to Column 4 ft (2)

Wv w ________(l+ )corresp. to Column 5

1 0.07 15 1.67 22 3.0 2.5m (8.2.ft) 4.6

2 0.07 15 1.67 22 2.0 2.5m (8.2 ft) 4.6

3 0.07 9 1.00 22 3.0 1.5m (4.9 ft) 4.6

4 0.20 9 1.00 62 3.0 1.5m (4.9 ft) 0.6

(1) Lv vent length

(2) Based on relation (1 + =m C) ; To was computed on the assumption that the drywell air is compressed

isentropically by a pressure ratio of 2, starting from a temperature of 300 K.

For all small-scale tests, Pw/pglv = 6.4 (P =w 5.67 kPa)

For Mark III conditions, Pw/Pgtv = 6.8

I

DO

I
-23-

TABLE 3: EXPERIMENTAL VENT CLEARING

TIMES to

t ,ms. 0

Comparison System A System B System C

no.

1 112 115 145

2 154 179 182

3 70 82 96

4 74 85 89
I ,
I

NI

I3 CMI F- 22.5 CM-.] - -- 39CM

Fiqure 1: Systems A,..B and C, side view.
-26-

DRYWELL

ORIFICE'

-J

-JJ

w

>-

2:

0

-60 CM

C.,

o o.15b -. r

- p4

0.I.... 15CM

Figure 2: Proportions of systems A, B and C.
PD-P(o)

PD-P(o)

5

P(o)KPa

PD-P(o)

5.

P(o)KPa

-PD-P(o) 5

P(o)KPa

-5

.P(o) KPa

5

-P(o)KPa

0 (msec) 100.

SYSTEM A

CASE I

0(msec) 100

SYSTEM B

CASE I I%) I

I

PD.-P(o)

5

P(o) K Pa

O(msec) 100

SYSTEM C

CASE I

Figure 3: Case 1, P2 vs time for systems A, B and C.
-28-

A

5-

P(o)KPa-

- PD-P(o)

-5

- P(o) KPa

O(m sec) 250 500

SYSTEM B; CASE I

A B

PD(P(o)-

5-

P(o) KPa-

-PD-P(o)

-5

-P(o)KPa

O(msec) 250 500

SYSTEM A; CASE I

Figure 4: Case 1, P2 vs time for systems Aand B,

including long-time behavior.
PD-P(o)

5 2.5g{

-g

Ig_i - P(o) K Pa

ý----100 msec -- -'H

SYSTEM B; CASE I

FLOOR TRACE

ACCELEROMETER

SYST

ACCE

FLOO

PD P(o)

5

-P(o)KPa -

OO msec

EM B; CASE I

LEROME.TER

R TRACE

p2 and, window acceleration versus

time in Case 1, system B. Also,

window acceleration versus time

resulting from tapping window with

harner.

Figure 5: , ... IOrmsec

SYSTEM B

ACCELEROMETER TRACE

IMPULSE LOADING ON FRONT WALL
CASE -I, t-to 20ms

I|

STARTING

VORTEX .

C B A

Figure 6: Case 1 at t-t 0 = 20 ms.
CASE I, t-to = 36 ms

(I

A

Figure 7: Case 1 at t-t = 36 ms. 0
CASE I, t-to=6Oms

I

C B A

Figure 8: Case 1 at t-to = 60 ms.
CASE I., t-to= 9Oms

,n

C B A

Figure 9: Case 1 at t-to = 90 Ms.
CASE 1, -t,= 120ms

C B A

Figure 10: Case 1 at t-to = 120 ms.
CASE 2, t-to= 20ms

ci.

cQJ_:

S TARTING

VORTEX

B C A

Figure 11: Case 2 at t-to = 20 ms.
CASE 2, t-to= 40ms

!~

CC

C FB "

Figure 12: Case 2 at t-to = 40 mns.

A
CASE 2, t-to=60ms

C B ....- A

Figure 13: Case 2 at t-to = 60 ms.
CASE 2, t-to=9Oms

co

I

C B A

Figure 14: Case 2 at t-to = 90 Ms.
CASE 2, t-t o =12Oms

C B A

Figure 15: Case 2 at t-to = 120 ms.
.t-t.: 5ms

CASE 3

t-t0=lOms

A .A

Figure 16: Case 3 at t-t° = 5 ms, t-t 0 = 10 Ms.
CASE 3, t-to=20ms

!

,..,.i

!

C

cx

B A

Figure 17: Case 3 at t-to = 20 ms.
CASE 3, t-to=40ms

-\fý

•LI

C El A

Figure 18: Case 3 at t-to = 40 ms.
CASE 3, t-to=6Oms

(A

C B A

Figure 19: Case 3 at t-to =.60 ms.
CASE 3, t-t0=8Oms

POOL BREAKTHROUGH

HAS OCCURRED IN

SYSTEM A.

C B

Figure 20: Case 3 at t-t = 80 ms.
CASE 4, t-to.. 20ms

C B A

Figure 21: Case 4 at t-to = 20 ms.
C.ASE 4. t-to=3Oms

I.

C B A

Figure 22: Case 4 at t-t 30 ms.

0
CASE 4, t-to=4Oms

. B A

Figure 23: Case 4 at t-t = 40 ms. 0
CASE 4, t-to=5Oms

90

%r"*ýý

C B A

Figure 24: Case 4 at t-to = 50 ms.
-49-

z

h

140

t-to, ms

Figure 25: Case 1, water elevations vs time.
-50-

1.0

/1

.90 - i

.80 -

SYSTEMS B a C/ -8 /

z

.60 &

,//"A SYSTEM B C

MAXIMUM WATER ELEVATION 0 0 a

.30 -- MAXIMUM BUBBLE ELEVATION N * A

.25

0 30 60 .90 120 150' 180 210

t-to, ms

Figure 26: Case 2, water elevations vs time.
-51-

I.0

.90o

.80

0

SY7TE Ao

z " /Ul/

h

.60 //

.50- SYSTEMS BSC

.40-

SYSTEM

A B. C

..30 MAXIMUM WATER ELEVATION 0 0 a

•- - ,•••t MAXIMUM BUBBLE. ELEVATION 1 6

.25

0 20 40 60 80 100 120

t-to, ms

Figure 27: Case 3, water elevations vs time.
-52-

z I/

.60 /

SYSTEM A /". SYSTEMS B&C

.501/

.40 SYSTEM

A B C

/ / MAXIMUM WATER

ELEVATION

.30 MAXIMUM BUBBLE

ELEVATION

0 20 40 60 80 100 120

t-to, ms

Figure 28: Case 4, water elevations vs time.
tl-ot=40ms

TEST A TEST B TEST C

Figure 29: Comparison of three different tests

of Case 3 in system B, at t-t°= 40 ms.
t -to=90ms

TEST A TEST B TEST C

0,

Figure 30: Comparison of three different tests

of Case 3 in system B, at t-to = 90 Ms.
-55-

1.0

.90

.80

..70

z

h

.60

.50

.40

.30

.25

t-to, ms

Figure 31: .Comparison of water elevations

vs. time in the three different

tests of Case 3, system B, referred

to in Figs. 29 and 39.
-56-

I

.90

.80

.70

z

h

.60

.50

.40

.30-

.25 W

0 30 60 90 120 150

t- to, ms

Figure 32: Comparison of two tests in system A, one with distilled

water and the other with water containing surfactant.

Cm 0.20, s/zv = 1.67, cm(RTD/gkV)V2 = 62, pD/Pw = 2.0.
-57-

200-

t, ms

to

100-

50-

0

x, cm

Figure 33: Case 1, Horizontal displacements of

starting vortex and bubble leading

edge vs time in system A.
-58-

300

200

to 4

t, ms

100

00L

0 10 20 30

X, Cm

Figure 34: Case 2, Horizontal displacements of

starting vortex and bubble leading

edge vs time in system A.
-59-

APPENDIX A: RELATIONSHIP BETWEEN POOL PRESSURE OSCILLATIONS

AND WALL ACCELERATIONS.

What follows is an approximate model which links the pool pressure

oscillations with the side wall accelerations. The basic assumption

is that the side wall oscillation is the driving force for the pool

oscillation which in turn induces a pressure oscillation at other

points in the pool,. The purpose of this model is to show that the

observed pool pressure oscillations were roughly consistent with the

observed side wall'accelerations.

Let the outward displacement of the side wall at y, z (see Fig. A.l)'be

x(y,z,t), x0 sin T- sin b sin2T (M)

where T is the period of the wall oscillation, x is its amplitude at the

center of the side wall, t is time, and the other quantities are defined in

Fig. A.l..

The upward pool velocity v at z due to wall oscillation is obtained in

terms of x (y,z,t) from the mass conservation equation,

rz b

pvbw - pbwz + 2p f dy dz (A.2)

0 0

Here, p is the fluid.density. Using Eq.. (A..l) in Eq. (A.2), we obtain

Cos 28t (A.3)

"ý -- T
-60-

The vertical pressure gradient in the fluid is given by the equation

of motion (with the convective acceleration term neglected, for obvious

reasons):

az at (A.4)

Substituting.Eq. (A.3) into the right-hand side of Eq. (A.4) and

integrating from z to z we obtain the pressure in the fluid at

elevation z as

p 16px h (s n " wT rw A.5

p(zt)=Pw + 0 sin 2Lt zw z) - (si sin (A5 . WT2 WT2 T. T L w • h h. JT 

where pw is the pressure in the wetwell airspace, and zw is the elevation

of the top water surface in the pool. Now if an accelerometer is placed

on the side wall at y = and at an elevation z = za, then the acceleration

read by it is obtained from Eq. (A.1) as

a= x (z = za, y = b/2)

4 2x sin 2rt sin -a

T2T h

(A.6)

Eq. (A.6) can be substituted into Eq. (A.5) to eliminate xo. We then obtain

the following relation for the pressure at z:

p(z, t) = pw - Ap sin 2--t (A.7) T
-61-

where

A = 4 oha (zw- z) h h (A.8)

2

sin -

Consider now the data shown in Fig. 5a. Both the pressure trace and

the accelerometer trace show components at a common period of the order

of 6 ms (the accelerometer also shows a higher frequency component).

Just after the initiation of the blowdown, for example, the accelerometer

shows peak accelerations of about (•-)g at this frequency. Now for the case

under consideration (System B, case 1), h = 0.6 m, w = 0.075 m and zw w = 0.30 m.

The pressure gauge was mounted at z = 0 m and the accelerometer at za = 0.30 m.

Eq. (A.8) then predicts

Ap = 1.2 kPa

for a (-) g. This compares favorably with the observed pressure oscillation

amplitude, which is about 1.5 kPa.
-62-

,o i ooH -- -- b V;

F//

/ /

Figure A.1: Notation for Appendix A.
-63-

APPENDIX B: QUANTITATIVE ANALYSIS OF VENT

CLEARING PROCESS.

The vent clearing process consists of two parts. First, the

water is cleared from the vertical pipe, and then the water slug is

cleared from the horizontal vent itself. We shall develop a simple

model for these processes by assuming one-dimensional flow and that

the pressure on the upstream water interface is constant at the drywell pressure PD.

First, consider the clearing from the vertical pipe. Applying

the unsteady Bernoulli equation along a streamline from the upstream

water interface to the vent exit, (where the pressure is pw + pgs) and

accounting for the inertia of the water jet at the vent exit by adding

a length of one pipe diameter to the integration path, (Fig. B.l), we

get the equation

A dV A 2

P AXVP+ Z +d) v + + k Av2 2 P

• Ap2

: PD - Pw - pg (s-x) (B.l)

Here, V is the velocity in the vent pipe, x is the elevation of water in v

the vertical pipe (Fig. B.l), and we have assumed that the fricitional losses

are I kV and have used the mass conservation equation

A V =A Vp v v p p (B. 2)
-64-

where

- dx Vp- -t (B.3)

is the downward velocity in the vertical pipe.

Eqs. (B.l) - (B.3) can in principle be solved numerically, with

the initial conditions x = 0 and Vv = 0 at t = 0. A simple analytic

solution is available when one makes the assumptions, quite reasonable

in our case, that

xAv A--<< Z + d

p

(B.4)

(B.5) pg (s - x) << PD - Pw

Eq. (B.l) than takes the form

dV

p (Zv +d) d + 1+k

I t -

and has the straightforward solution

A v

A2 I

2 P~v = PD - Pw (B.6)

(B.7)

-t

V = V e T

v 0 -t

l+e T

where

v 11 k- v

o [p !+ k _Av_•"~/

(B.8)
-65-

T Z v + d (B.9)

Ap2

This solution is sketched in Fig. B.2. It is valid up to the time

t* where the air reaches the upstream end of the vent pipe. That time

is determined from the mass conservation relation.

Av f Vdt = A s (B.10)

0

After the air enters the horizontal vent, the governing equation

changes. Bernoulli's equation, applied from the upstream edge of the

water slug to the exit, allowing an extra diameter length for the

inertia of the jet, now yields

dVv

p (x'+ d) dt =PD - Pw - pgs (B.ll)

where x' is indicated in Fig. B.l. We have assumed no viscous losses

in the vent itself: The viscous losses are associated primarily with

the bend at the vent entrance. The variables Vv and x' are related by

V Vv dx' (B.12) - dt

Eqs. (B.11) and (B.12) can be combined into the form

px- + d) V v dV d v =PD - Pw - pgs (B.13) d(x' + d)
-66-

which can be integrated to yield

V 2 = V (t*) - 2n d (B.14) Vv = Vv Zv+

where V v(t*) is the solution of Eq. (B.7) at the time t* corresponding

to (B.lO), when the air first enters the vent. From Eqs. (B.14) and

(B.12), with the initial condition Vv = V, at t = t*, it is possible

in principle to obtain V v(t) for times between t* and the vent clearing

time to* The vent clearing time to is then obtained from the water

volume conservation requirement that

t

Av f Vv dt = ApS + Av (B.15)

0

For the purposes of this appendix, we take a much simplified,

approximate approach. In our tests, conditions were such that the

initial rise time of Vv , as given by Eqs. (B.9) and (B.8), is

fairly short compared with to, and the difference between to and t*

is also fairly short compared with to. We therefore make the approximation [see Eq. (B.7)] that

v -v° = (D (B.16)

P 1+k v

durinq the entire vent clearinq process (see Fiq. B.2), and hence the
-67-

vent clearing time to follows from Eq. (B.15) as

p 1 + k. - A2 A

z I _ s (B.17)

Table B.l lists values of to computed from Eq. (B.17), compared

with the experimentally measured values. The value of k for each of

the three systems (k = 0.50 for A, 1.0 for B, and 1.5 for C) was

chosen so as to make the comparison as good as possible. The facts

that the values of k-which fit the data are quite reasonable on

physical grounds, and the observed trends are reasonably well

predicted, gives some credence to this simple model for clearing.

Another vent clearing parameter which could be determined from

the experimental data was the final exit velocity V of the slug, e

equal to our Eq. (B.14) predicts this velocity as

Ve Vv(t*) V l+ 2.n + (B.18) Lvp Vv2 (t*) d

If we take V v(t*) V Vv, the latter given by Eq. (B.8), this becomes

P /P

_k -n _+1l - 2 i +p__ A 1 (ww ( + Ak )

)2
-68-

The final water exit velocity predicted by Eq. (B.19) is compared with

the observed bubble pool entry velocities in Figs. 33 and 34. The

value of k is taken as in Table B.l. The agreement is remarkably

good.
-69-

TABLE B.l: VENT CLEARING TIMES to PREDICTED

FROM EQ. (B.17).

Comparison System A, System B, System C,

No. with k=O.50 with kW.O0 with kW.50

1 103 ms 121 ms 136 ms

2 145 170 193

3 70 83 93

4 70 83 93
-70-

xl

d

Figure B. I : Notation for Appendix B.
-71-

VENT VELOCITY

Vv

V0

0

0 TIME, t

Figure B.2: Sketch of vent velocity, and value predicted

by Eq. B.16.

WU.S. GOVERNMENT PRINTING OFFICE: 1980 620-269/125 1-3

NRC FORM 335 1 REPORT NUMBER (Assigned by DDC)

(7.77) U.S. NUCLEAR REGULATORY COMMISSION

BIBLIOGRAPHIC DATA SHEET NUREG/CR-i444

4. TITLE AND SUBTITLE (Add Volume No., if appropriate) 2. (Leave blank)

Investigation of Distorted-Geometry Simulation of Pool

Dynamics in Horizontal-Vent BWR Containments 3. RECIPIENT'S ACCESSION NO. V

7. AUTHOR(S') 5. DATE REPORT COMPLETED

N. G. Ruggieri and A. A. Sonin MON Way llg

9. PERFORMING ORGANIZATION NAME AND MAILING ADDRESS (Include Zip Code) DATE REPORT ISSUED Massachusetts Institute of Technology MONTH YEAR Department of Mechanical Engineering April 1980

Cambridge, Mass 02139 6. (Leave blank)

8, (Leave blank)

12. SPONSORING ORGANIZATION NAME AND MAILING ADDRESS (Include Zip Code) 10. PROJECT/TASK/WORK UNIT NO.

Analysis Development Branch

Division of Reactor Safety Research 11. CONTRACT NO.

Office of Nuclear Regulatory Research

Washington, D. C. 20555 FIN No. B6167

13. TYPE OF REPORT PERIOD COVERED (inclusive dats)

Topical Report

15. SUPPLEMENTARY NOTES 14. (Leave blank)

16. ABSTRACT (200 words or less)

Experiments were conducted to investigate the accuracy of distorted-geometry

testing of pool dynamics in horizontal-vent BWR containments. Distortedgeometry testing implies testing in systems where the flow-wise dimensions

are full scale, but all dimensions transverse to the flow are reduced in the

same proportion. The assumption is that flow velocities, pressures and other

thermodynamic properties can be interpreted as being the same in the distortedgeometry system as in its correctly proportioned counterpart. Our experiments, which were done at small scale using the established scaling laws, showed that

the geometric distortions can have a significant effect on the pool swell under

conditions which are roughly representative of horizontal-vent BWR containment

systems during a LOCA. Breakthrough occurred later, the water ligament was

thicker, and pool velocity lower in a system where the cross-sectional areas

were reduced by a factor of three. Some reasons for the differences are discussed.

17. KEY WORDS AND DOCUMENT ANALYSIS 17a. DESCRIPTORS

17b. IDENTIFIERS/OPEN-ENDED TERMS

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