ML20090H892

Revised Downcomer Annulus Thermal Shock Study for Beaver Valley Power Station

ML20090H892
Person / Time
Site:	Beaver Valley
Issue date:	06/30/1983
From:	Healzer J, Sorensen J S. LEVY, INC.
To:
References
SLI-8310-1, TAC-10386, NUDOCS 8407270257
Download: ML20090H892 (5)

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SLI-8310-1 DOWNCOMER ANNULUS THERMAL SH0CK STUDY FOR BEAVER VALLEY POWER STATION prepared by J. M. Healzer J. M. Sorensen S. Levy Incorporated Campbell, California I

for Bro,okhaven National Laboratory May 1983

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1 ABSTRACT This report presents downcomer annulus temperature predictions at dif-ferent operating conditions for the Beaver Valley Power Station, Unit 1, a three-l oop 852 MWe Westinghouse Pressurized Water Reactor.

In the cases analyzed, temperature nonuniformity results from activation of the high pressure injection system when -the reactor is operating with the isolation valve in one of its three loops closed.

The cases considered are natural circulation at decay power, natural circulation af ter a rapid cooldown at reduced system pressure and decay power, forced circulation, and zero flow at reduced system pressure, a condition postulated to occur following certain hot leg small break accidents.

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SUMMARY

The objective -of = this ~ study is to provide a scoping analysis -of, the m--

possible temperature maldistribution in the downcomer annulus of a Pressurized Water Reactor (PWR), which could result from activation of the high pressure injection (HPI) system while the reactor system has one of its recirculation loops isolated.

The study examined four-cases:-

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1.

Natural circulation at decay power.

For this case, the reactor system is assumed to be operating with two loops and pressurized at rated system pressure, a condition which might occur after a trip and during natural circulation cooldown.

HPI activation at two dif-ferent natural circulation flows are examined, corresponding to expected system conditions a few minutes after the reactor ~ trip and at an hour af ter the trip.

2.

Natural circulation at decay power after a rapid cooldown.

For this case, the system is assumed to be operating with two loops and reduced pressure (1000 psia) and at lower downcomer temperatures

(~300*F), a condition which might occur after a' reactor trip following a rapid system ccoldown.

The effects of HPI activation at the-same two flows used in Case 1 above are studied.

3. " Forced circulation.

For this case, the system is assumed to be in two-loop op,erating at 70% flow and 65% power at the time of HPI activation.

4.

Zero Flow.

This is the condition which has been postulated to occur during certain small break accidents.

The downcomer temperature remains at rated conditions (550*F), but the system pressure is reduced to 1000 psia and the primary system recirculation flow has stopped.

It is again assumed that one of the three loops is iso-lated at the time of HPI activation. T,he primary effect of the iso-2 c

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lation valve in this case is that the isolated cold leg has less inventory to mix _with the HPI flow beford it enters the# annulus; i

l thus, the f, low from the isolated leg is slightly colder than the flow from the cold legs with isolation valves open.

The results of the analysis indicate that the downcomer annulus flow pat-tern in the forced and natural circulation cases (1 through 3) is always

~i n downflow following HPI activation, and there is always sufficient mixing and cross flow around the annulus to prevent the development of large temperature gradients.

Temperature gradients from the top to the bottom of the thermal shield in the downcomer are typically on the order I

of 30*F.

This is also typical of the circumferential variations of tem-1 perature around the annulus.

Figure I shows temperature histories 'at various positions in the downcomer under the isolated cold leg.

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for a very few seconds after HPI activation, temperatures remain constant

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j in the downcomer below the active cold legs.

The downcomer. flow pattern following HPI activation ~ for the zero flow case is different.

Cold flow from both the isolated and active cold l

l legs induce natura-l-circulation-within the annulus itself, with downflow under the cold legs and upflow between the cold legs.

The downcomer tem-peratures which result from this circulation pattern are shown in Figure

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1.

Temperature histories below the. isolated and active cold legs are

-shown as well'as temperature histories at similar locations between the cold legs.

Note that the predicted temperature difference from the top-to the bottom of the downcomer under the cold legs is on the order of 20*F.

Temperatures under the cold leg with the. isolation _ valve ' closed I

are only a few degrees colder than temperatures under the legs;with the isolation valve open.

The temperature - difference. in the downcomer bet-I ween the cold legs, - from top to bottom, is on the order of 30*F.

The temperature variation around the annulus, between the downflow regions under the cold-legs, and the upflow regions between the cold legs, is on the order of 100*F.

The circulation pattern within the' annulus.is an

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important element in determining the downcomer temperatures for this zero flow case. since~ it provides the ' mixing required to prevent evTn larger

. temperature differences from developing.

The analysis models used 'to.make these downcomer annulus temperature pre-dictions are relatively simple compared to the complex flow conditions which are analyzed.

It is felt, however, that -the modeling used, albeit simple, does capt0re the ' phenomenon controlling the flow and temperature distributions in the annulus and should provide a reasonable estimate of temperature gradients.in the annulus for the cases which have been analyzed.

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=' Page ABSTRACT

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SUMMARY

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CONTENTS 6

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t DESCRIPTION OF CASES' ANALYZED 8

DOWNCOMER ANNULUS-TEMPERATURE PREDICTIONS 13 i

REFERENCES 27 f

APPENDIX -A

, Geometric Description of Beaver Valley 1 28-Downcomer Annulus and Cold Leg APPENDIX B -

Model Input Parmeters 34 I

i APPENDIX C -

Model Descriptions 38

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INTRODUCTION l-Pressurized water reactor -(PWR-). -downcomer annulus temperature..dtstribu-tions following the actuation of the high pressure injection (HPI) system have been the focus of sev'eral studies, both experimental and analytical (1-4).

Most of these studies have concentrated on conditions where the L..

.HPI system is activated during a condition of zero or very,small cold leg l

flow.

This results in a rapid cooldown of the cold leg and the sector of the downcomer annulus directly below the cold leg.

The present study extends the simple model for HPI injection presented in reference 4 to l.

cases where the HPI system is activated when there is flow in the reactor primary system, but one of the cold legs has been isolated.

Under these conditions, the downcomer annulus will received flow which is a com-bination of the recirculation flow plus the HPI flow from the active cold legs, and only HP1 flow mixed with the initial cold leg inventory from-l the isolated cold leg.

Thus, the downtomer annulus below the isolated cold leg will receive less ' flow and at a different temperature than other l

regions of the downcomer annulus.

The purpose of this study is to eva-luate the degree of flow diversion and mixing that will occur in-the downcomer annulus and the resulting maldistribution in temperature that results when operating in this mode.

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DESCRIPTION OF CASES ANALYZED The plant geometry analyzed in this study is for a 2650 MWt (852 MWe) three-loop Westinghouse PWR.

Specific dimensions used in the analysis are shown in Appendix A.

'This geometry is typical of the Beaver Valley 1 plant operated by Duquesne Light Company.

. ~ Downcome r ~ annul us temperature predictions are made for the following.-

modes of reactor operation: forced circulation, natural circulation, and for the zero flow condition which has been predicted to oc' cur following a small hot leg break.

For each of these operating modes, it is assumed that the isolation valve in the ~ cold leg of one of the three loops is -

closed and primary system recirculation flow, if any, is through the other two loops.

For each case, the downcomer temperatures following activation of the HPI system in all three cold legs are studied.

Initial l

conditions for each of these operating modes is described below; the'ini

• tial system conditions are also summarized on Table 1.

Natural Circulation at Decay Power (Cases la and ib)

For operation in this mode, it is assumed that the reactor has been tripped.

The primary coolant system is in natural circulation, the core is at decay power levels, and one of the three loops is isolated.

Two separate cases are considered:

the first where the HPI system is acti-vated at about 12 minutes after the trip and the second where HPI activa-tion occurs about an hour after the trip. -The major difference between these cases is the coolant flow and the temperature in the active cold legs and downtomer annulus at the time of HPI acti vation.

For both cases, it is assumed the isolated cold leg is initially filled with water at rated operating temperature, 550'F, and that the system pressure remains at rated pressure during natural circulatinn operation and during HPI injection.

It is further assumed that for the time over which the calculation occurs, the system natural circulation flow remains constant.

i HPI injection flow is taken from Figure 6.3-4 of the Beaver Valley FSAR (shown in Appendix A).

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l The system power at 12 minutes and one hour after the trip is estimated from the ANS decay heat tables (5_) to be 2-1/2% and 1-1/2Wof rated power, respectively.

The natural circulation flow at these power levels is taken from Table 14.1-3 of the Beaver Valley FSAR (shown in Appendix A) to be 4.4% and 3.7% of rated flow.

This is the system flow assuming all loops active.

To account for the effect of two-loop operation on the flow. -the following approximate analysis is used.

It is assumed that steam generator-to-core temperature difference is proportional to power and inversely proportional to the core flow.

l AT = Ocore/Wcore Further, that the natural circulation driving head is related to the loop flow squared:

2 Ap = W oop = (Wcore/n)2 l

where n is the number of loops and Ap the density difference between the core and steam generator.

If the density difference 'is taken propor-tional to the temperature difference, a simplified relationship between loop flow and core power at natural circulation conditions is obtained.

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This approximate formula is used to adjust the FSAR values of natural circulation flow for two-loop operation.

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l Natural Circulation after Cooldown at Decay Power and Reduced Pressure l.

(Cases 2a and 25)'

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l This mode of operation could occur in the case of a trip and rapid l

cooldown that might occur due to a steam generator tube rupture or simi-I lar secondary side depressurization that would reduce the steam generator steam side temperature.

The particular case studied assumes the primary coolant pressure is reduced to 1000 psia and cold leg temperature to 300*F.

Initiation of the HP! system is assumed to occur at the same two natural circulation flow rates which were used in Cases la and Ib.

While

.these flows probably will not correspond to the same two decay power levels, they are felt to be representative of the range of. primary system natural circulation flows under these conditions.

The isolated cold leg initial temperature is taken to be at operating temperature, 550*F at the time of HP! initiation.

Initially, the flow from the isolated cold leg is hotter than the downcomer annulus, but the HPl flow soon cools the isolated cold leg down to below the annulus temperature.

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Like Cases la and Ib, both the natural circulation flow and temperature are heldaconstant over the period during which the HPI injection takes place and for which the downcomer annulus temperatures are calculated.

Forced Circulation (Case 3)

For this operating mode, the reactor system power is assumed to be 65%

and flow assumed to be 70% of rated, but the flow is carried by two instead of three loops.

The initial temperature in both the isolated and active cold legs to be the rated temperature, 550*F, and the system

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pressure at 2200 psia.

This combination of flow, power and cold leg tem-i perature is approximately consistent with an average core temperature _of 577'F.

The system flow and temperature are assumed 'o remain constant for the period of the calculation after HP! activation.

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Zero Flow (Case 4)

This operating condition is predicted to occur following a small hot leg break.

The primary coolant recirculation flow in the annulus and cold legs drop nearly to zero and system pressure reduces to I.pproximately 1000 psia.

i.ike the other cases, it is assumed that one of the three loops is isolated at the time of HPI system activation, and the downconer annulus and all three cold legs are at rated system temperature, 550'F.

The system pressure and zero flow condition are assumed to remain unchanged during the calculation period following HP! activation.

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e TABLE 1 Surmary of Cases Downcocer A.vulus and System Cold leg w/ Isolation valve Open Cold Leg w/ Isolation HPI Pressure Flow / Loop Initial Temp.

Valve Llosed Flow / Loop Temp.

Case Systes Ccndition (osia)

(Iba/sec)

(*F)

Initial Terp. (*F)

(1bm/sec)

(*F) la natural Circulation 2200 505.1 525 550 18.7 60 at Decay Power Ib Natural Circulation 2200 424.7 475 550 18.7 60 at Decay Power 2a natural Circulation 1000 50s.1 300 550 42.0 60 i

After raaldown at Decay Power 5

Zb natural Circulation 1000 424.7 300 550 42.0 60 After Cooldown at Decay Power 3

Forced Circulation 2200 13529.2 550 550 18.7 60 at 70 Flow & 65%

Power 4

Zero Flow During 1000 0

550 ~

550 42.0 60 Seall Hot Leg Break

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-,_gn DOWNCOMER ANNULUS TEMPERATURE PREDICTIONS s

Description of Analysis Models Predictions of downcomer annulus temperatures are made with a combination o f mode _1 s.

For the forced flow and two natural circulation flow cases (Cases 1 through 3), the annulus temperature predictions are made using the single-node model described in Reference 4 to analyze the mixing and discharge temperatures from the cold legs.

Downcomer annulus flow and temperatures are analyzed as a series of quasi-steady-state cases with a subchannel model similar to the COBRA code (6_).

Cold leg flows and tem-peratures, as predicted at different times in the transient following HPI initiation by the single-nede cold leg model, provided boundary con-ditions for the downcomer analysis.

More detailed descriptions of the

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models are given in Appendix C.

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' Justification for using a series of steady-state analyses to determine the mixing and temperatures in' the downcomer is based on a comparison of s

the time scales over which the events are occuring.

The temperature of the\\downcomer inlet ficw is changing slowly (degrees per minute) compared t'o the sweep time of the flow through the downcomer (a few seconds) for

'the forced and natural circulation flow circulation cases.

i Th'e tfowncomer nodalization used by thz subchannel model is shown in n;;(Figure 2.

For the cases analyzed here, the downcomer is divided into two hxial channels, each with connecting subchannels.

Attempts to use more

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than two. axial channels in. the downcomer with the subchannel model were-not successful for all the cases analyzed, so only results-with twoLaxial channels have been shown.

The subchannel code had difficulty converging 1-subchannel flows with 'more than two ' axial channels since the channel pressure drop under these flow conditions is so insensitive to flow.

The downcomer annulus pressure drop is ~ dominated by elevation and is less a

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.a two axial channels, each divided into connecting subchannels, were, however, well behaved and results should be representative of the actual conditions.

Input used by the subchannel model for the analysis is given in-Appendix B.

The zero flow' case (Case 4) is analyzed with a multi-node model, similar

- - 4to the oneudescribed rin Reference -4.. This model includes the-coldilegs, downcomer annulus, and lower plenum and was specifically developed for analysis of the zero flow condition.

It does not permit' as detailed axial nodalization and cross flow as the subchannel code, but it does

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- couple the -cold degs,s downcomery and lower plenum in a single transient-calculation.

Input for the multi-node model used for analysis of the zero flow case is also described in Appendix B.

The nodalization scheme used by the multi-node model is shown in Figure 3.

Two axial channels in "the' downcomer are used,"which -represent the sector of the' downcomer under the cold leg and the sector of the downcomer between the cold legs. The two channels are divided axially into two nodes along the thermal shield.

They receive flow from a mixing node at the cold leg discharge at the top

'of tihe'downcomer and connect with a common lower plenum node at-therbot-tom of the downcomer.

The multi-node model is described in more detail in Appendix C.

Verification studies to compare predictions by the multi-node model to recently obtained scaled data of the zero flow condition Q) 'is underway and will be reported at a later date.

Temperature Predictions

-Temperature histories at three annulus locations for the -.different operating modes of the reactor 'have already been shown in the Summary.

A different presentation of 'the same data 'is shown in Figures 4 through 9.

In these figures,- the cold leg' discharge temperature histories are -

plotted on the left and,- at selected times after HPI activation, the

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downcomer. annulus temperature distributions are shown on the right.

Since the zero flow case (Case 4) is somewhat different 4han the other cases, it is useful to consider it separately, and these results will be discussed later.

The general behavior for the other cases (Cases 1 through 3), where there is flow through the active cold legs, is simi-lar.

These cases all indicate downflow in the annulus and strong cross-flow between the region of the downcomer below the active cold legs and the region of the downcomer below the isolated cold leg.

For example in Figure 4, the two curves on the left show the temperature histories,of flow into the annulus from the active and the isolated cold legs.

The.

flow in the active cold leg drops quickly from its initial temperature of 525 F to 508 F as the HPI flow is mixed in with the natural circulation flow in the active cold legs.

The isolated cold leg cool-down transient is much slower since the HPI flow must mix with the isolated cold leg inventory.

On the right side of Figure 4, annulus temperature distribu-tions under the cold legs are shown at 300 and 2500 seconds after HPI initiation.

Note that the isolated cold leg discharge temperature is relatively cold compared to the downcomer temperature.

There is suf-ficient cross-flow to mix with the flow leaving the isolated cold leg so that by the time the flow reaches the top of the thermal shield, its tem-perature has risen to nearly be in equilibrium with the remainder of the flow in the annulus.

For many of the cases, the temperature predictions in the downcomer at different times after HPI initiation are only a degree or two apart and, when plotted, are sufficiently close that they cannot be shown as different lines on the graphs with the scale used.

Temperature distributions in the region of the downcomer between the cold leg discharge and the top of the thermal shield are shown in dotted lines in the figures to indicate there is more uncertainty in these temperature predictions.

Representation of the complex flow in this region with only two parallel channels, although they include several axial subchannels, is-an oversimplification.

However, the flow and temperatures appear to be suf ficiently 'well developed by the top of the thermal -shield that 17

there should be less modeling uncertainty in these temperature predic-tions.

J The zero flow case is shown in Figure 9.

The annulus temperature distri-butions shown are obtained with the multi-node model.

Downcomer annulus temperatures are shown for three times after HPI initiation.

Note that in Figure 9 the temperatures under the cold legs as well as temperatures between the cold legs have been shown.

This is necessary since, for this particular operating mode, the cold HP1 injection induces upf]ow from the lower plenum in the downcomer sectors between the cold legs.

This upflow brings lower plenum water to mix with the cold leg discharge flows and prevents even larger temperature differences from developing in the down-comer.

Even with the upflow, there is about a 100 F temperature i

variation circumferentially around the annulus between the regions under the cold leg discharge and between the cold legs.

Again, in this figure, the temperatures in the mi xing region between the cold leg discharge and the top of the thermal shield are dotted.

The temperatures which were shown for this same mixing region in the other cases were those actually calculated by the subchannel model.

For the zero flow case, the curves have been drawn in to look similar to the other cases, but the multi-node model used for analysis of this case represents this mixing region as a single node, so a detailed temperature distribution is not available.

To provide additional conformation of the multi-node model, the zero flow case was also analyzed as a series of quasi-steady-state conditions, as was done in the forced and natural circulation flow cases.

When this was done, it was found that the subchannel model would converge-to a flow condition with downflow both under the cold legs and between the cold legs.

This is a different downcomer flow pattern than predicted by the multi-node model.

Next, the subchannel model, with the same nodaliza-tion, was used in a transient mode to predict the zero flow case When this was done, circulation of flow up from the lower plenum between the i

18

cold legs was predicted.

This circulation pattern is consistent with the multi-node model predictions.

This indicates that for the dro flow case, two flow patterns are possible in the downcomer, both which satisfy balanced pressure conditions.

To obtain the flow pattern with ci r-culation up from the lower. plenum between the cold legs, the starting conditions are important.

The initial flow of HPI water into the down-comer at the cold leg discharge cools this downcomer sector.

The resu,lting increase in local density results in increased downflow under the cold leg.

To balance the increased pressure drop, up-flow is induced in the downcomer between the cold legs.

Without this starting sequence of events, the subchannel model, when used in a quasi-steady-state mode is unable to find this countercurrent flow pattern in the annulus and alway converges to a downflow flow pattern.

When the subchannel model was used for the full transient analysis of the zero flow case, it predicted an even greater mixing and induced even greater up flows between the cold legs than was predicted by the multi,

node model.

This resulted since the subchannel model only considers friction irreversible losses in the flow between subchannels and neglects the turning losses.

Downcomer annulus flow path modeling in the multi-node model include both friction and irreversible losses.

Temperature differences between flow under the cold legs and between the cold legs, as predicted by' the subchannel model, were on the order of half the tem-perature differences _from the multi-node model, which are shown here.

This reduction in temperature difference was due to greater induced flow between the cold legs, which is then available to mix with the cold leg discharge flow.

It is felt that the multi-node model results shown in Figure 9 are still realistic but may be closer to 'an upper bound of the temperatures expected since " conservative" irreversible loss coefficients were chosen for the multi-node model analysis.

A - final note ' about all the temperatures shown is that"these~are fluid temperatures.

They all, however, are very close to the wall tem-19

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The heat transfer coefficients for all cases are large enough that, for the heat fluxes ' associated with the wall sensibW energy losses, the fluid-to-wall temperature differences, should be no more than a couple of degrees F at the most and, for many cases, less than one degree F.

This difference; is well within the uncertainty of the tem-perature predictions, and it would not be unreasonable to assume the fluid temperatures are the same as the wall temperatures.

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REFERENCES

.e 1.

Rothe, P.

H., and M. W. Fanning, Thermal Mixing in a Model Cold leg and Downcomer at Low Flow Rates, Electric Power Research Institute Report NP-2935, March 1983.

?.

Sun, Bill, K._-H.,

and J.

P.

Sursock, " Mixing of HPI Jet in a Stagnant Cold Leg and Downcomer Flow," letter to distribution w/ attachments, September 17, 1982.

2.

Levy, S.,

An Approximate Prediction of Heat Transfer During Pressurized Thermal Shock,"

S.

Levy Incorporated Report SL1-8213, June 1982.

4

Levy, S.,

and J.

M.

Healzer, An Approximate Prediction of Heat Transfer During Pressurized Thermal Shock with No Loop Flow and with Metal Heat Addition, 5. Levy Incorporated Report SL1-8220 (Rev. 1)

August 1982.

5.

Decay Heat Power in Light Water Reactors, American Nuclear Society Standard 5.1, June 1978.

6.

Rowe, D.

S.,

COBRA-IIIC:

A Digital Computer Program for Steady-State and Transient Thermal-Hydraulic Analysis of Rod Bundle Nuclear Fuel

Elements, Pacific Northwest Laboratory

Report, BHL-1695, March 1973.

7.

Fanning, M.

W.

and Rothe, P.

H.,.

Transient Cooldown in a Model.

Cold Leg and Downcomer, Draft Electric Power Research Institute Report NP-3118, May,1983.

e a

1 27 L_ ~

Z _-

.e--

g.

a e

em APPENDIX A GE0 METRIC DESCRIPTION OF BEAVER VALLEY 1 00WNCOMER ANNULUS AND COLD LEG

?8

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. TABLE.14.1-3

' NATURAL CIRCULATION-REACTOR COOLANT

- FLOW VERSUS REACTOR POWER-

.t

~

Reactor Power,-

Reactor Coolatft Flow,

% of Full Power

% Nominal Flow

3. 5'

d. 8

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3.7 Y

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.i -

O 33 h

e e

1 af e

J APPENDIX B t10 DEL INPUT,PARAtiETERS 34 3

G B.1 Input for single node cold leg model (for input to subchannel model)

Isolated Cold Leg (valve closed)

Active Cold Leg (valve open)

HPI Case Initial Flow Cold L Heat Slab Initial Flow ColdLgg vol ftgt Slab temp 0F lbm/sec volftgg He Flow Tem 2

vol ft3 area ft temp 0F l bm/sec vol ft 2

area ft 1bm/sec 0F la 550 0

94.8 40.8 165.7 525 505 79.3 34.1 138.6 18.7 60 lb 550 0

94.8 40.8 165.7 475 424 79.3 34.1 138.6 18.7 60 2a 550 0

94.8 40.8 165.7 300 505 79.3 34.1 138.6 42 60 0

2b 550 0

94.8 40.8 165.7 300 425 79.3 34.1 138.6 42 60 3

550 0

94.8 40.8 165.7 550 10529 79.3 34.1 138.6 18.7 6@

4 550 0

94.8 40.8 165.7 550 0

138.5 59.6 242.0 42 60 3

heat slab density = 4891bm/ft heat slab specific heat = 0.12 BTU /lbm F 0

0 heat slab conductivity = 24 BTU /hr ft F l

lup '/t mle.k4 (LM k hw B.2 Input for Subchannel Model (represents W.ectx).

s kcun,ul I Channel 1 Channel 2

., 60 '

2

^

-flow area (in )

677.7 1355.4 ig

^ ^U channel length (in) 233.8 233.8 hydraulic dia (in) 8.9 8.9 axial nodes

• 40 40

% hu node length (in) 5.85 4.85 yessei % u getc

• b\\so can 10 L 20 codes

SUMMARY

OF SUBCHANNEL INLET CONDITIONS Case time after HPI press W1 T1 W2 T2 initiation sec psia lbm/sec 0F lbm/sec 0F la 300 2200 9.3 181.4 524 508.5 la 2500 2200 9.3 68.8 542 508.5 lb 300 2200

-9.3 181.4 444 457.7 i

Ib 2500 2200 9.3 68.8 444 457.7 2a 25 1000 21.0 430 547 281.7 1

2a 500 1000 21.0 78.9 547 281.7 2a 2500 1000 21.0 62.0 547 281.7 2b 25 1000 21.0 430 467 278.5 2b 5.00 1000 21.0 78.9 467 278.5 2b 2500 1000 21.0 62.0

'467 278.51 3

300 2500 9.3 181.4 10548 54 9.1 3

2500 2500 9.3 68.8 10548 549.1 36

B.3 Input for Multinode Model (for Case 4-Zero flow case only)

Node 1 (valve closed) 1 (valve open) 2 3

4 5

6 3

vol (ft )

4 62 593 108 1 08 1 08 1 08 1029 flow area (ft )

1 12.3 12.3 14.1 14.1 14.1 14.1 36.8 2

18.9 18.4 14.1 14.1 14.1 14.1 NA hyd dia (ft) 1 2,28 2.29

.79

.79

.79

.79 1.93 2

1.93 1.93

.78

.79

.79

.79 NA 1

496.8 725.9 2 91.5 2 91. 5 2 91.5 2 91.5 434.7 hea)) slab area (ft 2

198.5 198.5 157.5 157.5 157.5 157.5 NA heat glab cpm 1

7175 10484 1924 1924 1924 1924 10484 (BTV/ F) 2 8153 8153 6468 6468 6468 6468 NA heat sigb cond 1

24 24 10 10 10 10 24 (BTV/ft F) 2 24 24 24 24 24 24 NA W

37

0 o

APPENDIX C MODEL DESCRIPTIONS 38

C.1 Description of the Single Node Cold Leg Model and Subchannel

='

Downcomer Model The forced and natural circulation flow cases have been anal.s 'ed with a combination of two different models; a single-node model to represent the cold legs and a subchannel model to represent the downcomer annulus.

The single-node cold leg model calculates temperature histories in both the j

' active and isolated cold legs.

The subchannel model uses the cold leg discharge temperatures calculated by the single-node model and calculates downcomer annulus temperatures.

The downcomer annulus temperatures are calculated as a series of quasi-steady-state conditions.

Single Node Cold Leg Model The single-node cold leg model treats the cold leg fluid as a single thermodynamic node.

For the isolated cold leg, the cold leg fluid mass includes all fluid from the isolation valve to the cold leg discharge.

When the HPI system is activated, HPI flow mixes with the cold leg fluid mass and the discharge temperature into the downcomer annulus is the mixed mean cold leg temperature.

For the active cold leg, the cold leg fluid mass includes only fluid from the HPI injection point to the cold leg discharge.

Besides the HPI flow entering the node, the active leg recirculation flow also enters the node.

Discharge temperature from the i

active cold leg is the mixed mean cold leg temperature including both hPI flow and the active leg recirculation flow.

The cold leg models also have a single node heat slab model to represent the cold leg piping which transfers heat to the cold leg fluid through an input specified conduc-tion length and heat transfer coefficient calculated from the Dittus-Boelter correlation.

Governing equations for the single-node heat slab model are given by:

Cold Leg:

MtL @c.t. (

= %r2 k (TWI -Ich + N ec Cp,g k g - Te d + g t

33

Cold Leg Heat Slab:

Mp3 cpg (d]>} _

{ (\\/y) t (O/L)h,i Aas(TessTcy ot where the heat transfer coefficient is given by the following approximate formula

/ W 0B ui.lPH \\ A H%

Symbols used in these equations are defined in section C.3 of this Appendix.

Subchannel Model The subchannel model-used for analysis of the downcomer annulus 'is simi-lar in formulation to COBRA-IllC.

Both use the subchannel analysis con-cept where the flow path is divided into a

number of quasi-one-dimensional channels that communicate in the lateral direction by diversion crossflow and turbulent mixing.

Fluid properties in thh subchannel model are a function of local enthalpy and a uniform system pressure.

The model is capable of' either steady-state or transient calculations.

Application of the subchannel model requires that the user first specify the subchannel arrangement to represent the flow path to be analyzed.

The subchannel scheme used for the downcomer annulus is shown in Figure C.1 (similar to Figure 2 shown earlier).

The user must also specify the boundary conditions for the flow paths, inlet flow and inlet flow ' temperature for the nodes or subchannel on the flow path boundary.

For the annulus case, the cold leg discharge flow and flow enthalpy as calculated by the single-node model are used.

The governing equations used by the subchannel model are given below:

Continuity:

A & ura +g (fv> A + E ew(fos = o 9

40 I

l! \\

g) p;g s

+

.4 i

\\_

%cpe nock radgA be /_$'p, g 4'a a

isola %\\ coM % -inclA%

q.

mvMwe to itsh Vdc

( %. cou %)

(

s3 e node mode (

/

t

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- e

'4 CbuM 2 p ChAuntiI

,1

~ '

V

/

~ '

/ -

Q.notide.

cnbet% u d i 4

dr. doge p++ _ _ _ _ _ _ _ _ _ _ _.. -

e p-c suudvusul 2 s

I fuloCNw,;td 3

?

s t

.-je a q

-~ - be thu=\\

. _ _ _ _ _ _ m

~

suwo.~,a 9

=

7

_ 7 gg subcAw.,a> -

nu dd o 4 a'

.no*awne &

1 am-A wecuw

{

p.<

r se c.Y#

.E n We,LA$ 4 1

1

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y

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+

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botttw tbrvua.(

r Su a,4wel n j--__

gg o

4

/

r

\\0 c httn n Lc C L i

\\1vect to lower P A

+

t Fi3 tare' C. t - Ginole _ dock ad Steckamu\\ Rodds a

(

M MI M

MN i

c 41

'jL

,k !

.s.

~,.;.

Energy:

c.fhn t h 4 fuh) A + [ er<pv hys _

A bt

[ %4 4 h & T CaQj'- [Ov/ ah "5

Axial Momentum:

A $ (<. f U)> + h4f 0') A + T. e w Q UV)4-o

- A A 4?> -l d+ M qv') A - A<f" Dyne-a Mu c

c Lateral Momentum:

5 EfD +

• f U~

ji 'k 6 IVO d

t Symbols 'used in these equations are defined in section C.3 of this Appendix.

These equations, in finite different form, are solved by the subchannel model for each flow path subchannel.

The subchannel moael also includes heat slabs for each subchannel but for the downcomer annulus analysis, these were not used.

Since the calcula-tions were a series of steady-state evaluations, there was no way.to include the effects of the heat slabs.

In addition to specifying the flow path geometry, the flow path hydraulic

~

parameters must also be specified.

These include the 15ss coefficients and friction factors for flow paths connecting the subchannels.

For the downcomer annulus case, the calculations were made with nominal values for these parameters; smooth - tube friction. factor and no irreversible

' losses in the axial direction.

The subchannel model also requires irre--

versible loss coefficients.for transverse flow between subchannels.

Since the key output of the analysis is the -transverse flow mixing in the annulus, it was important to determine the sensitivity of the analysis to 42

w this input.

The recommended value'for cross-flow mixing loss coefficient (K ) for the.subchannel nodel is 0.5.

The downcomer annulus c5ses were G

analyzed with this value and a transverse loss coefficient of 5.0, a fac-tor of 10 greater.

Results from these cases were virtually identical, indicating that the transysrse flow loss coefficient is not a critical parameter in the downcomer annulus analysis.

Typically the role of the cross-flow in the downcomer annulus analysis is to provide sufficient mixing to warm up the HPI discharge flow from the isolated cold leg so there was a better match to the elevation head pressure drop components.

Calculations performed where the isolated cold leg discharge temperature was held at the same _ temperature as the active cold legs showed very little cross-flow and mixing.

C.2 Description of the Multi-node Model The model used to analyze the zero flow cases has been referred to in this report as the. multi-node model.

This is a six node model which includes the cold leg, annulus and lower plenum.

The nodalization used by the multi-node nodel is shown in Figure C.2 (similar Figure 3 shown earlier).

Identific'ation of each model node is given below:

Node Represents Heat Slabs 1

Cold leg and section of downcomer annulus 2 - cold leg pipe above the thermal shield.

wall and vessel wall above thermal shield l

2 Downcomer annulus under cold. leg-from 2 - vessel wall and l

top to mid-point of thermal shield thermal shield 3

Downcomer annulus under. cold leg-from 2 - vessel wall and mid-point to bottom of thermal shield thermal shield 4

Downcomer annulus between cold leg-from 2 - vessel wall and I

Ltop of thermal shield to mid-point thermal shield p

f 43

est e

/

/

f fi/.*// /

• fl O&

{A &

at

if

% swa i

/

/

Ap, d'p _+1( '4,,,9,, 3 _

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1 5'

Downcomer annulus between cold leg from 2 - vessel wall and mid-point of thermal shield to bottom trarmalsiileid 6

Lower plenum 1 - vessel wall To represent an isolated cold leg, node 1 of the multi-node model inclu-des all cold leg liquid inventor */ from the cold leg discharge break to the isolation valve.

To represent an active cold leg (although the cold

' leg flow is still zero), node 1 includes all cold leg inventory from the cold leg discharge back to the lowest point in the recirculation pump suction-line.

The prirnary difference between these two cases being the amount of liquid inventory which is available to mix with the HPI flow before it enters the downcomer annulus.

Governing equations for each node of the multi-node model are similar to the. governing equations for the. cold leg single-node model.

Node n Fluid Temperature:

Wn cp (T,'n-TU + ps hn Qn i

n Node n Heat Slab:

NHsn kas n

The equation used for the heat transfer coefficient is the same as given earlier for the single-node model.

The flow entering the downcomer annulus from the cold leg discharge is the HPI flow plus any recirculation flow.

The recirculation flow is zero for the zero flow cases.

At the top of. the downcomer annulus, the flow is split between the flow ' path down nodes 2 and 3 and down nodes 4 and 5.

The flow split-is determined to balance the pressure drop across these two

flow paths.

Balanced pressure drop requires:

kb 4 Lf2,s

• l 1 * " h +p q[

5 9

45

For both flow paths at the same temperature (as is the case before HPI is activated) the flow split is given by the square' root of the ratio of the irreversible losses in the two flow paths:

Dh+,s)

W2,5

'hE W9,s a {1,g + E Lg, J

The irreversible losses in flow paths 2 and 3 includes a contraction as the flow passes around the thermal shield,. friction and an expansion into the lower plenum.

In flow path 4 and 5, an added turning loss must be included as. flow is diverted around the annulus to the sector between the cold legs:

( N E.t

• 7' 3L 2,1

(.1,E. 4 O )gs :

L 02 '2 N

As the flow below the cold leg in nodes 2 and 3 is cooled by the HPI flo'w o

the flow direction in nodes 4 and 5 can reverse itself if this is requir-ed to balance the pressure drop betseen these-two flow paths.

This is this flow pattern.which typically develops in the zero flow case after HPI provides sufficient cooling to the flow through nodes 2 and 3.

C.3 Nomenclature for Appendix C Symbols 2

A flow area (ft )

-Cq fraccion of total rod power that enters coolant directly in subchannel model Cr transverse mixing factor. in subchannel model

_ spe'cific heat (BTVs/lbm*F) 46 l'

i

v, Dg' hydraulic diameter (ft) s lett summation convention in subchannel model to sum subchannels con-r,t nected with subchannel i f

friction factor 2

3 acceleration of_ gravity (ft/sec )

h enthalpy (BTUs/lbm) bh enthalpy difference between adjacent subchannels (BTUs/lbm) g heat transfer coefficient (BTUs/sec ft2 op)

{

irreversible loss coefficient irreversible loss coefficient for cross flow in subchannel model t6

-(

thermal conductivity (BTUs/sec ft F) at~

heat slab conduction length in subchannel model ~ (ft) f, downcomer flow path length in multi-node model (ft)

- 3 p, adjacent subchannel centroid distance in subchannel model (ft) g node mass for single and mult'i-node model -(lbm) p wetted perimeter (ft) 9 pressure heat rate (BTUs/sec) h

~ linear heat rate IBTUs/sec ft) i 2

h heat flux (BTVs/sec ft )

~S gap width between subchannels (ft)

T

_ temperature (*F) t time (sec)

U-velocity in axial flow direction in.subchannel model (ft/sec) gg axial velocity difference.between adjacent subchannels (ft/sec)

'y velocity. in transverse flow direction in subchannel.mo' del (ft/sec) _

w' weight flow (lbm/sec) 47

F o

/

V/

transverse mixing flow in subchannel model (lbm/sec) 7 distance in axial flow direction (ft) by subchannel axial length in subchannel model (ft) 3

[>

density (lbm/ft )

4 fraction of rod or heat slab perimeter facing a subchannel in subchannel nodel 9

orientation angle from vertical in subchannel nodel (deg)

Subscripts HPI high pressure injection flow or temperature REC recirculation flow or temperature HS heat slab CL cold leg n

node index Other area averaged volume averaged O

48

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