ML20092A973

Independent Verification of Byron/Braidwood D4 SG Tube Support Plate Differential Pressures During Mslb

ML20092A973
Person / Time
Site:	Byron, Braidwood
Issue date:	09/01/1995
From:	COMMONWEALTH EDISON CO.
To:
Shared Package
ML20092A968	List: ML20092A965 ML20092A973
References
PSA-B-95-15, PSA-B-95-15-R, PSA-B-95-15-R00, NUDOCS 9509110261
Download: ML20092A973 (38)

Text

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An independent Verification of Byron /Braidwood D4 SG Tube Support Plate Differential Pressures during MSLB PSA-B-95-15 Revision 0 Commonwealth Edison

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Prepared by: ,

E ,d. _ _[- Date: > [ [9s' Reviewed by: ,

Date: 9!/ [ff Approved by: - - -

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~ Date: 9/ 75' (Udte is' sued) pSft9*kSocko$000454 p PDR

. PSA-B-95-15 Revision 0 Statement of Disclaimer This document was prepared by the Nuclear Fuel Services Department for use internal to the Commonwealth Edison Company. It is being made available to others upon the express understanding that neither Commonwealth Edison Company nor any of its officers, directors, agents, or employees makes any warranty or representation or assumes any obligation, responsibility or liability with respect to the contents of this i document or its accuracy or completeness.

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- . . . _ . - . - - . . . - . . - . ~ = . _ - . -

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• PSA-B-95-15 Revision 0 Release of Information Statement 1 This document is furnished in confidence solely for the purpose or purposes stated. No l

other use, direct or indirect, of the document or the information it contains is authorized.

The recipient shall not publish or otherwise disclose this document or information therein to others without prior written consent of the Commonwealth Edison Company, and shall return the document at the request of the Commonwealth Edison Company.

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PSA-B-95-15 Revision 0 Abstract The purpose of this calculation is to perform and document an independent assessment of the Westinghouse calculations generated to provide structuralloadings -

on the steam generator tube support plates during limiting transient conditions. The '

Main steam line break (MSLB) event from hot zero power was determined by the vendor to yield the highest differential pressures across the support plates. The vendor utilized the TRANFLO code for the initial work, and validated their results using the MULTIFLEX computer code. This assessment develops and utilizes methods based primarily on first principles physics to determine bounding differential pressures seen at the most highly loaded TSP. This provides a realistic assessment of the margin inherent in the vendor methods.

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PSA-B 95-15 S

Retrision 0 Table of Contents

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

1. Introduction.. ... . .. ........ . . .... . .. .... . ... ..

.2

2. Methodology /Model Description and Assumptions.. .. . .. . . . . . . . . . . . . . . . . .

.2 2.1 Description of the Problem. . . .. . . . .. . .... .. . . . . . .

2.2 Time Sequence. . . . . . . . . . . . . . .. . . . .. . . . . . . .. ... . . .......................2 2.3 Initial Conditions and Geometry ... . . .... .. ...... ...... . ... . ................4

. . . . . . . . . . . . . .......4 2.4 Discussion of Acoustic Phenomena ....... .. .. . . . .

2.5 Determination of Steam Space Pressure Response . .. . . . ... .. . . . ..... . . 5

. . . . . .....6 2.6 Determination of Bulk Fluid Motion... .. ... . .. .. . . .. ....

3. C alculation s . . . .. . .. . . . .. . . . . . . . . . . .. . . . .. . . . . ....... ... ......... . ..............11 3.1 Steam Region Depressurization Rate ... .. ....... ...... .. . . . . . .. 11  ;

3.2 Determination of Applied Pressure Gradient. ... ... . ..... . . ...... . . 11 i

. . . . . .. . .. 11 ,

3.3 Bulk Fluid Motion Calculations .. .. . . . . .. .. . . . . . . . . .

3.3.1 Single Phase Case -Small Control Volume.. .. ..... . .... . ..........11 3.3.2 Single Phase Case - Extended Control Volume .. .............12 3.3.3 Two Phase Case - Extended Control Volume. .. ................12

4. Results . ....... ... . . . . . . . . . . . . . . . . . . . . ......................................16

5. Conclusions / Discussion .. . ... ... .... .... ... . . ..... . . . .... .

.........................17

6. Refe rence s . . .. . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . ...................18 Appendix A - Mathcad Cases..... . . . . . - . . . . ~ . " " " ~ ~ " " - " "" " 19 I

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PSA-B-95-15 Revision 0 List of Tables Table 1 Key Geometric parameters of D4 Steam Generator.. . . . . .4 Table 2 Summary of Results. .

.. . . 16 vi

._ .. . _ _ _ _ . _ _ _ . . . . _ . _ _ . _ _ . _ . . _ . _ _ -.. _ ___. ~

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, I PSA-B-95-15 Revision 0 List of Figures Figure 1 Diagram of D4 Steam Generator.. ....... . ..... . ...............................8 Figure 2 Time Sequence for MSLB . . ....... .. ..... . . ... . ... .. . ..... .. ...............9

................... .10 Figure 3 Control Volume Diagram. .. . .. .... . . . . . . . . . . . . . . .

Figure 4 Velocity at P-TSP Single Phase Case .... .... . ... .. ...... ..................13

. . . . .. 13 ,

Figure 5 Pressure Drop at P TSP Single Phase Case. . ... . . . ... . ...... ... ....

... 14 Figure 6 Fluid velocity at P TSP - Extended CV case.. . . . . ........ . ...... .. ... .. '

.........14 Figure 7 Pressure Drop at P-TSP E < tended CV Case .. . .. ..... ........... . ........ . .

Figure 8 Velocity at P TSP -Extendeo CV two phase case ..... ........ ....... .... . . .......15 Figure 9 Pressure Drop at P TSP - Extended CV two phase case.. . ... ..... .. ........ ...15

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PSA-B-95-15 Revision 0

1. Introduction During a main steam line break event, the rapid blowdown of the faulted steam generator can lead to significant loads on the tube support plates. Westinghouse has performed transient thermal hydraulic calculations on the Byron 1/Braidwood 1 Model D4 steam generators in support of structural calculations regarding the extent of tube support plate deformation. Independent assessment with other computer codes has been performed, although some questions remain, particularly with respect to the margin of safety and the allowances for calculational uncertainties. Therefore, a method of characterizing the loads on the upper support plates based on first principles physics, independent of computer codes, was developed. This report documents the methods created for this purpose and details the results obtained.

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2. Methodology /Model Description and Assumptions 2.1 Description of the Problem The limiting case has been previously determined to be a break of the steam line directly outside the steam generator nozzle, with the generator at initial conditions of '

hot zero power and normal water level. The D4 steam generator is shown in Figure 1.

What is desired is the differential pressure vs. time that exists at the upper support plate during this event. To calculate this differential pressure, one must determine the dynamics of the fluid n otion in the tube region following the initiation of the break.

Calculation of the dynamic response of the tube region fluid requires that a number of related issues be addressed. These include characterization of the break flow and transient pressure response of the steam space, acoustic effects both prior to and following initiation of fluid motion, and determination of the differential pressure operating on the bulk fluid in the tube region.

2.2 Time Sequence An understanding of the time sequence of events following initiation of the break is important to understanding the relationships between the key physical phenomena. ('

Figure 2 provides a depiction of the key events and their relative temporal location for this event. As can be seen, this event can be thought of as consisting of three major regions, each dominated by different physical effects.

The initial phase is the acoustic region, characterized by the establishment of critical flow at the nozzle and initiation of depressurization of the steam regions of the generator, but prior to the initiation of bulk fluid motion. A key occurrence in this region is that a decompression wave traverses the generator, initially at high speed through the contiguous single phase regions. The effect of this decompression wave is to initiate voiding in the fluid, drastically reducing the acoustic velocity, which then determines the pressure response times in the subsequent phases.

The next phase is the bulk fluid motion phase. Given the reduced acoustic velocity of l' the two phase mixture and the continuing decompression of the steam regions, a differential pressure across the liquid region will occur, causing bulk motion of the fluid.

This motion is dominated by momentum effects and pressure losses at the grids and l other structures. The fluid will accelerate to maximum velocities early in this phase and then decelerate as viscous effects involve more of the upper structures of the steam generator. Additionally, the decompression rate decreases as time goes on, due to pressure reduction as well as increasing liquid content in the break effluent.

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PSA-B-95-15

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Revision 0 The last phase is the long term behavior. This phase can be thought of as a quasi- ,

i steady state condition dominated by mass balance effects. The fluid remaining in the tube regions will flow at a rate comparable to the break flow rate. The velocities at this l point are low and decrease with time as the blowdown progresses to completion.

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Revision 0 2.3 Initial Conditions and Geometry The vendor calculations indicate that the limiting case occurs at hot zero power conditions with water levels at normal values. The water level is at 487" , just below the swirl vanes in the separators. The temperature of the water and steam are uniform at 557 F, and saturation conditions are assumed. Key geometric parameters have been derived based on TRANFLO input descriptions and are presented in the table below:

Table 1 Key Geometric parameters of D4 Steam Generator Value Parameter Initial Steam Space Volume 2556.52 ft3 Steam space Path Length 27.745 ft 40.583 ft Liquid Region Path Length 56.45 ft2 Tube Bundle flow area 17 ft2 TSP flow area Entrance area of separators 22.01 ft2 1.08 TSP loss coefficient Separator Entrance loss coeff 13.9 Break Area (restricting Nozzle) 1.388 ft2 ,

2.4 Discussion of Acoustic Phenomena The break is assumed to occur over a time interval of 1 msec. Since this time interval is too short to assume equilibrium conditions (about 1/100 second or greater), a decompression wave will travel through the steam generator at high speeds. (about 3500 fps in the liquid and 1500 fps in the steam. This will require approximately 40 milliseconds. The result of the passage of this wave will be the generation of voids,

)

requiring about 10 milliseconds to occur. Therefore 50 milliseconds into the event, the initial decompression wave will have traversed the generator and initiated voiding in the l liquid regions. This is significant in that once the voiding occurs, the acoustic velocity j decreases dramatically Reference 1 provides a value of 157.5 fps for the speed of a i

decompression wave in equilibrium saturated water. This speed then dictates the rate at which pressure differentials can develop between the decompressing steam space l and the bottom of the fluid regions, since the pressure disturbance propagates at the acoustic speed. Therefore the maximum differential pressure operating on the fluid can be determined by estimating the rate of change of pressure in the steam space and employing the acoustic propagation length of the fluid to determine the time and therefore pressure lag at the bottom of the steam generator.

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PSA-B-95-15 Revision 0 2.5 Determination of Steam Space Pressure Response In the initial phases of the blowdown, the steam region pressure response can be readily characterized by treating the steam as a perfect gas and employing formulas for adiabatic blowdown (isentropic expansion) or isothermal blowdown of a pressure vessel (Reference 1). These in fact, give relatively good results in the period of time initially after the break initiates prior to the decompression wave reaching the fluid surface. Once, the fluid surface becomes involved however, the flashing rate leads to significantly lower pressure decay than would be predicted by the simple isentropic formulas. Therefore, alternate methods must be utilized to obtain the steam space pressure response.

A review of methods for determining the vessel dome pressure response indicates that this is generally accomplished via detailed numerical methods. Some textbooks provide plots of vessel pressure ratios, calculated using detailed methods, with dimensional time scales to provide an approximate method to assess the pressure response. Use of this type of approach for this problem yields depressurization rates of approximately 124 psi /sec. The figure with tangent lines drawn from Reference 3 used to establish this depressurization rate is enclosed in the Appendix. The generalized time axis value was based on the break area (1.388 ft2) divided by the initial liquid mass (145,256 lbm). The initial depressurization ratio estimated above,124 psi /sec, compares favorably to the value 132 psi /sec calculated by the TRANFLO code for the first .57 seconds of the event.

Therefore the maximum dynamic differential pressure that could exist in the steam generator prior to motion of the fluid is:

dP AP = g ( At, + At.)

where Ati, At, = acoustic transport times for the liquid and vapor regions dP/dt = rate of pressure decay in the steam region 5

~ ~ PSA.B-95-15 Ruision 0 _

l 2.6 Determination of Bulk Fluid Motion Once the pressure response of the steam space has been determined and a pressure differential across the fluid region defined, the bulk motion of the fluid can be characterized. For the purposes of this calculation, the pressure drop determined above will be applied across a control volume extending from the second highest support plate (N TSP) to the entrance to the separators. Figure 3 provides a diagram of the control volume. Using the one-dimensional Bernoulli integral approach (Reference 2), the following equation can be written:

' L' d\f M' l 1 K

< An dt

+ AP + pg(:

2 ~ 3 )2p+ - ( A,2A,- T+[ AT)= 0 i

where (UA)r = Total path inertia (length / area)

M= Mass flow rate AP= differential pressure z,,z2 = elevations at beginning and end of control volume p = fluid density ,

Ai,A 2= entrance and exit areas I(K/A )2 = friction factor / area representing viscous pressure loss terms at obstructions This equation can then be directly integrated to achieve a solution of the mass flow rate of fluid vs. time. The solution has the form: ,

c

'kbr_;

M(t) = -

_c r + 1, where K'

~

1 l I C,2 2 PAP _ A[

_ A,' # { _*A_

6

S

• PSA-B-95-15 Revision 0 This equation can then be solved for the bulk fluid motion. The pressure drop at the upper TSP can then be readily determined. It should be noted that this formulation ignores the effects of wall friction for conservatism.

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. - .. ._. . __.. .. --.- - . . - - _ . . . - - . . - . . _ - - - . . . - . . . - - - . - . - - - - ~ . _ . _ .

I PSA-B-95-15 Revision 0 Figure 1 Diagram of D4 Steam Generator O

,, e

.Mm o 3 ir i,.

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n "

=-

o *01 1 I l i

If a t I t l,49 Il h "I

,a

, , lu.II. . .

a e

g 9

e ,

o ?s 127.6 jp o IP e

y ,. 4, i

=>>.i >

<r e, t O 379.75 so.4 F

.ll =41 I taf'

[ 1.g J "

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• d i .. .

35.0 f u.o of I 4

,yu gJ 8

3 o

Stort of Blowdown c Initiot Acoustic Vove 3 N

~!

g Acoustic Vove Length  !

m

@ o

.o C

o

s o

-1 m Bulk Liquid Motion begins 3 8 $

(n Peak Velocity Reoched h c-5 8 U3 3

a C m, Velocity decreases os break quality drops LA o m 8 m

O 3

gg Pressure continues to decoy 8

o g Guosi-SS ochieved ~

8 m

s m $

8 End of Blowdown I.

o n.

• ' PSA-B-95-15 Revision 0 Figure 3 Control Volume Diagram Separator Inlet A=22.01 K=13.7 j u;

a.

w A= 56.45 m

$$$ N kkIb ' ControlVolume/ Path ,

PV

$ A=17 K=1.08 P TSP f -

DP applied eM V83 u

T..

A=56.45 s  ;

, N TSP A=17 K=1.08 I

f I

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PSA-B 95-15 Ravision 0

3. Calculations 3.1 Steam Region Depressurization Rate The steam region depressurization rate of 124 psi /sec was determined using the method presented in Section 2.5. By way of comparison, the TRANFLO code produces a depressurization rate of approximately 132 psi /sec during the first 500 milliseconds of the event.

3.2 Determination of Applied Pressure Gradient 1

Given the differential pressure rate calculated above, the maximum pressure that could be applied across the fluid region can then be determined. Using a value of 130 psi /sec, the pressure rate occurring just after the initial acoustic effects, the differential pressure acting on the fluid becomes:  !

DP = 124 psi / sec x(40.583ft /157.5ft / sec+ 27.75ft /1476.4ft / sec) l t

I DP = 34.28 psi 3.3 Bulk Fluid Motion Calculations 3.3.1 Single Phase Case -Small Control Volume {

Using the formulation discussed in section 2.6, the maximum velocity of the fluid at the tube support plate and then the pressure loss (load) on the support plate can be ,

calculated. The velocity at the P TSP is shown in Figure 4. The pressure drop that would result from this velocity of single phase fluid is shown in Figure 5. The pressure ,

drop is calculated using the relationship:

y,_ KpV' 2x144rg where ,

K= local loss coefficient p= density Ibm /sec V= velocity ft/sec 11 l

• ~ PSA-B-95-15 l Revision 0 3.3.2 Single Phase Case - Extended Control Volume This case was performed to provide a more realistic estimate of the maximum velocity of the fluid. This case extends the control volume to the bottom of the steam generator and accounts for the additional losses in the lower tube support plates. The areas were assumed to be continuous to the bottom, and the same loss coefficient was utilized for all support plates. This is conservative given that higher loss coefficients and slightly reduced areas exist in the preheater and boiler sections in the lower portions of the generator. The velocity at the P TSP is shown in Figure 6. The l

pressure drop that would result is shown in Figure 7.  ;

3.3.3 Two Phase Case - Extended Control Volume This case was performed to provide an indication of the effects of two phase fluid flow l l

in the tube regions. Since the initial decompression wave will cause void formation, some increase in fluid friction can be expected. The extended control volume model was modified to include a HEM multiplier on the local loss factors used. This approach is consistent with a " liquid only" based calculation per Reference 2, page 487. A two phase friction multiplier was selected assuming 1% mass quality, which bounds the amount of voids calculated by TRANFLO in the initial phase of the event. The velocity at the P TSP is shown in Figure 8. The pressure drop that would result is shown in Figure 9.

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-. . - . . - _ _ , - . - . . .. - . - . . . - . - . - . . - ~ . . . . - . . - . . . - . - .- . . .- . . - . . . . = .

~ ' PSA-B-95-15 t I

Revision 0 Velocity ft/sec  !

30

.r 20 ,

v(t) 10 0.8 1 1.2 0.2 0.4 0.6 0 '

t

- P TSP Velocity Time (seconds)

Figure 4 Velocity at P-TSP Single Phase Case 3 Pressure  :

Drop psi  !

T 4

I dP up(t)2 a

l l

l 0 08 12 g o2 o4 06 1 l t

Pressure Drop at P TSP Time (seconds)

Figure 5 Pressure Drop at P TSP Single Phase Case 13

• PSA-B-95-15 Revision 0 Velocity ft/sec 25

~

20 l

l 15 i 10 ,

S

/ ,

0 1.2 0 0.2 0.4 0.6 0.8 1 ,

t

- P TSP Velocity Time (seconds) i Figure 6 Fluid velocity at P TSP - Extended CV case Pressure Drop psi i

3 f t 2

i dp ,p(t) g 1

0 1.2 0 0.2 0.4 0.6 0.8 1 1

- Pressure Drop at P TSP Time (seconds)

Figure 7 Pressure Drop at P-TSP Extended CV Case 14

PSA-B-95-1f i Revision U i

Velocity

)

ft/sec 20 ._

15 1

i g) to 5

1 1.2 0.6 0.8 0- 04 o 0.2  ;

8

- P TSP Velocity Time (seconds)

Figure 8 Velocity at P TSP -Extended CV two phase case ,

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Pressure Drop psi 3

r -

2 dPtspU) i ,

1.2 06 08 1 02 0.4 0

1

- Pressure Drop at P TSP Time (seconds)  :

Figure 9 Pressure Drop at P TSP - Extended CV two phase case 15 ,

__ - . - . .. _ - - . . - . = _ - . - _ _ _ - - . . . . _ - . - . --

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4. Results The results obtained from these calculations are presented in Table 2. The base case HZP/NWL TRANFLO results are provided for comparison. As can be seen, the limiting CV case produces very conservative results. This is expected since the entire I pressure drop occurring in the steam generator is being applied to a small section of the upper tube bundle. This case is believed to be limiting, and demonstrates the conservatism inherent in the factor of two applied to the base TRANFLO results used to generate structuralloads. The extended CV cases provide a more physically realistic treatment of the total pressure drops in the generator, and support the results obtained with TRANFLO. The two phase case provides an estimate of the effects that would be seen if HEM multipliers are applied to the pressure drop determination. The increased pressure drop of the two phase flow is nearly compensated by a decrease in predic l velocity, with the net result being a minor variation in pressure drop.

Peak Velocity at Max. Pressure drop at P-Case Depressurization P-TSP TSP rate ft/sec psi psilsec 26.37 3.68 Base- small 124 CV 2.24  :

124 20.56 Extended CV 1G 18.81 2.23 Extended CV 124 2@

132 =17 1.6 (3.2 used in structural TRANFLO evaluation)

Table 2 Sumrnary of Results i

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5. Conclusions / Discussion A methodology to determine the peak loads on the upper tube support plate that would result from a design basis MSLB event has been developed and exercised. This methodology is based solely on first principles and has no reliance on computer codes.

The results obtained compare favorably with those obtained via computer simulation, and provide a basis to assess the margin of safety utilized in the analyses of TSP loads. It can be concluded that the factor of two used in the structural assessment results in a physically bounding pressure drop, even allowing for typical uncertainties in two phase pressure drop prediction I

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6. References

1) " Introduction to Unsteady Thermofluid Mechanics", F. J. Moody,1990.

2) " Nuclear Systems l", N. E. Todreas and M. S. Kazimi,1990.

3) "The Thermal Hydraulics of a Boiling Water Nuclear Reactor", R. T. Lahey Jr. and F. J. Moody,1977.

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. PSA-B-95-15 l Revision 0 Appendix A - Mathcad Cases l 4

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. J STEAM / WATER SMTEM. INITI ALLY A = OUTLET AREA tit 2, FILLED WITH S A s ORATED WATER AT 1000 pees 8 M =

SYSTEM INITI AL LIQUID MASS (1b,1 4

a = RE AL TIME (sec)

CRITICAL FLOW THROUGH "PERF ECT" NOZZLE 1000 l I -

g SATURATED LIOUID ESCAPE

% / I I  ! I

\g # '

SATURATED. HOMOGENEOUS MIXTURE ESCAPE g 800 *

'1 i i i l

,,e LIOulD " LEVEL" GONE AT t = (134.4110 g "6 UDMI a

\ s , ,

600 8 N \ \

? \ K 3 \ 1 d " 8(s h t I

n 1

SATURATED VAPOR ESCAPE

/

, \\ /

\

g '% -

\ N  %

% .%=  %  %,

0 0 I (200110-6 1400110-6 (600110-6 1800110-6 11000110-6 7(,.7 Yeun q e. M C ^ 6 Ag gg,2 gg ,g i GENERAllZED TIME -t

t. .. . b .d J , pre s t s' t1g aq M, sin,i

-4 Fig. 9-17a. Pressure transients-blowdowns from 1000-psia reference system.

- -.----a.. ~.-s . - . . . g m

', A Simplifind Approach to Assessing TSP Loads introduction A simple physical model to describe the fluid behavior at the upper TSP can be developed based on the Bernoulliintegral equation, as described in Kazimrs

• Nuclear Systems I" text. In the initial part of the transient, the fluid in the tube area adjacent to the upper support plate is single phase liquid. Following the break, this liquid is subjected to decompression and acceleration forces.

Blowdown calculations have been performed to estimate the driving pressure. By drawing a control volume around the upper support plate, one can solve the Bernoulliintegral equation for the flow rate of the fluid vs time, accounting for inertial and viscous effects. This is a reasonable approximation to the initial behavior of the fluid, since only minor void generation occurs initially.

Geometricalinput 2

A j :' 17 R Flow Area of N TSP, entrance to control volume 2

A o: 22.01. A Flow area of Separator inlet, exit of control volume 2

A tube : 56.45 R Flow area of tube region dp 3 .: 34.28 32.2144 ,

Differential Pressure (dynamic component)

Rsec' A tsp : 17 n Area of TSP K tsp : 108 2 Loss Coefficient of TSPs (P and N) 2 A yp = 22.01 n K yp 13 9 The inertia of the path can be determined by the path lengths divided by the respective areas

, _ 8.1666 R 3 5733 R 14.1567 A

^ tube Atube A sep p = 45.5 I 3 Fluid Density A

Neglect Gravity Effects, since applied load is only dynamic component P

g  : p 32.2 lb - , -((8 1666 4 3 5733) n) see lb dp edpi

G:ner:I S:luti:n Kazimi d: rives a solution with a constant Ca2 of the form indicated below-E l I f1 11

+

up + E W C := --

2 2 i

2 2 ,

2 p dp Ajj A gp Ag (A o i

l C :=h t .= 0 sec,.02 sec.1 sec The time dependent solution is of the form 2 C dp ,

1 e -I m(t) := - , c.,p g 3

e +1 The results are shown graphically below 4

2.5*10 i i i I i

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2*10

~

4 -

1.5*10 III.

4 -

1*10

~

5000 i l I I t

0 08 I l2 0 0.2 0.4 06 t

\

. =

4 Tha v focity et ths tube support plate is shown below m(t) 1 s(t) :=

pAtsp Velocity ft/sec 30 r 20

/

v(t) 10 1

o.4 0.6 0.8 1 1.2 ,

0 0.2 t

- P TSP Velocity  ;

Time (seconds) 1.08 ps(t)2 dp g,P(t) :=

2 144 32.2 Pressure Drop psi 1 4

f dp g,pf ) 2

/

o 0.2 c.4 o6 c.s  : 1.2 1

- Pressure Drop at P TSP Time (seconds) 1 i

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A Simplified Approach to Assessing TSP Loads-Full Tube Bundle Case j

\

Intrcductirn f

A simple physical model to describe the fluid behavior at the upper TSP can be developed based on the Bernottiiintegral equation, as described in Kazimi's " Nuclear Systems I" text. In the initial l l

part of the transient, the fluid in the tube area adjacent to the upper support plate is single phase '

liquid. Following the break, this liquid is subjected to decompression and acceleration forces.

The depressurization rate of the steam region can be estimated with textbook blowdown methods and a drMng pressure across the fluid region can be inferred. By drawing a controlvolume around i the fluid regions, one can solve the Bernoulliintegral equation for the flow rate of the fluid vs time, accounting for inertial and viscous effects, in this case the same basic approach is followed, but with the control volume extended to the bottom of the tube region.

Geometricallnput 2 Flow Area of N TSP, entrance to control volume A j = 17 fl 2

A g= 22.01 ft Flow area of Separator inlet, exit of control volume i

2 Flow area of tube region Atube = 56.45 ft dp 3 := 34.28 32.2144- Differential Pressure 2

flsec A 33p 't 17 A' Area of TSP The actual areas are smaller and the losses larger in the lower regions. For simplicity, it will l l

be conservatively assumed that the lower tube region can be modeled identically to the upper '

regions. This will underpredict the losses and inertias in the lower region.

K tsp = 1.08 8 Loss Coefficient of all TSPs (P to A) 2 A = 22.0111 K g.p := 13.9 9

The inertia of the path can be determined by the path lengths divided by the respective areas j ,8.1666 ft 3.5733 fi 14.1567 f1 3 . 0 11 2 + 2.5 ft 3.5733 2 ft Atube Atube Ap x ^ tube Atube Atube p = 45.5I Fluid Density ft' Gravity Effects are ignored since the elevation head is not added to the dyncmic load:

P = 0-pay 2 dp = dp g - P p,y

• ~ ' - - - - - -- -- - , _ _ _ \

GsnIr-l S:luti:n Kazimi deriv:s a solution with a constant C^2 of the form indicated below:

I

+

9 2

C o 2.pdp A o2 2

A ij Ag 2

Ag Ch t .: 0 sec,.02 sec.1.sec The time dependent solution is of the form 2 Cdp, m(t) 1. 21 4 ,

C I

e +1 The results are shown graphically below d , ,

2*no , , ,

4 l.$*l0 -

~

m(t) l'10 4 -

5000 I i l I i

p 1.2 O 02 0.4 06 08 1 8

l

Tha v21ocity ct the tube support plata is shown below

• ( ' }

v(t) =

pA4 Velocity ft/sec 25 20 -

/

15 9

10 0.4 06 0.8 I I.2 0 0.2 t

- P TSP Velocity Time (seconds) 1.08 p v(t)2 dPt (8) ^= 2 144 32.2 Pressure Drop psi 3

2 dp imptt) l 0.6 08 1 1.2 0 0.2 0.4 1

- Pressure Drop at P TSP Time (seconds)

A Simplified Approach to Assessing TSP Loads-Extended CV/2 phass Introductirn A simple physical model to describe the fluid behavior at the upper TSP can be developed based on the Bernoulliintegral equation, as described in Kazimrs

• Nuclear Systems l~ text. In the initial l

part of the transient, the fluid in the tube area adjacent to the upper support plate is single phase  !

liquid. Following the break, this liquid is subjected to decompression and acceleration forces.

The depressurization rate of the steam region can be estimated by textbook blowdown methods and a driving pressure across the fluid region can be inferred. By drawing a control volume around the fluid regions, one can solve the Bernoulliintegral equation for the flow rate of the fluid vs time, accounting for inertial and viscous effects.

In this case the same basic approach is foffowed, but with the control volume extended to the bottom of the tube region.

Geometricallnput l 2 Flow Area of N TSP, entrance to control volume A := 17 fl 2

Flow area of Separator intet, exit of control volume Ao := 22.01. A 2 Flow area of tube region A tube = 56.45 ft b i dp j 34.28-32.2144- Differential Pressure j 2

flsec  !

2 Area of TSP A 9.= 1711 i See attached table for HEM multiplier Isq.: 1.19 The actual areas are smaller and the losses larger in the lower regions. For simplicity,it will be conservatively assumed that the lower tube region can be modeled identically to the upper '

regions. This will underpredict the losses and inertias in the lower region.

Ktsp = 1.08 8 6 sq Loss Coefficient of all TSPs (P to A)

[

Ag 22.01 ff

K 3ep = 13.9 $ sq The inertia of the path can be determined by the path lengths divided by the respective areas 3.5733 A j ,8.1666 ft 3.5733 A 14.1567 ft 3.0- fi 2 + 2.5 A 2 Atube A sep ^ tube Atube Atube

^ tube p : 45.5 I Fluid Density it Gravity Effects will be ignored since only the dynamic load is applied P p,y = 0-2 flsec  !

dp = dp 3 - P pay

1 G:ner:1 S:lution Kazimi drriv:s a solution with a constant Ca2 of tha form indicated below:

E tsp K wp i  !! II C o ._ 2 2-Pdp A ,2 Agj A tsp A wp C=

t = 0 sec,.02 sec.1 sec The time dependent solution is of the form 2 c ap.,

• ~'

m(t) ':1. 2__c.g ,

C I

e +1 The results are shown graphically below d '

1.5'10 -

i i I  !

~

g.go d -

b 1

~

5000 i f f f i

p 0 0.2 0.4 06 08 1 1.2 8

5 k

Tha v:focity Lt th3 tube support plata is shown below "II) v(t)'=

pat 9 Velocity ft/sec 20 r

15 v( t) l0 0.4 0.6 0.8 1 1.2 0 0.2 1

- P TSP Veksity Time (. ,onds) 1.08 pv(t)2 4 q dp tT(t) .= 2 144 32.2 Pressure Drop psi 3

r-2 dP ts;d 8) 1 04 06 0.8 1 1.2 0 0.2 1

- Pressure Drop at P T$P Time (seconds) l l

, ei .,'

CONVECTIVE SOILING AND CONDENSATION Ta6h 2.1 Values of the two. phase frictional mukiplier de,3 for the hornogeneous model stess-water system

...:1.q)::i.q):- ,

. Pressure, har(pole)

Steam 141 6 89 M4 68 9 1 103 138 172 207 221 2 J'.uauty IT *t. (14 7) (100) (500) (loop) (!$00) (2000) (2500) , (3000) (3206)

I 14 21 J 40 1 44 1 19 l 10 14$ 144 lin 14 3 87 4 12 18 112 1 09 149 l 28 l 16 l ed 10 10 121 2 21 B $ 46 2 73 IM lM l 30 1 13 10 20 212 2 38 7 78 4 27 2 Il 2M 140 1 15 l0 30 2928 53 $ 11 74 $ 71 340 2 37 l's? lM 14 40 Ms 87 3 14 7 7 03 4M 3 04 2 14 1 48 14 30 43$ 302 17 43 8 30 348 3 48 241 140 14 80 300 92 4 30 14 9 50 5 76 3 91 247 1 71 10 70 3U 10&2 22 7 1070 4 44 4 33 2 89 l 82 14 80 623  !!$ 7 15 1 11 81 7 08 4 74 Fid 143 14 90 GRI 127 27 $ 12 90 7 73 5 21 3 27 244 14 100 738 137-4 278 1348 8 32 5 52 3 d0 2 14 14 Tehle L2 Values of the teio.phans fHetional muhiplier (s,8 for the Martinelli-Nelson model sisesMoeter sysism Steam 141 FIf 344 68 9 103 138 1 72 207 221 2 quakty

• /. by wi. (l&7) (100) ($00) (1000) (1500) (2000) (2$00) (2000) (3306) 1 H 33 1s 14 1 33 12 11 145 140 5 M 13 33 H 24 l 73 1 43 1 17 140 10 se 3 84 34 34 248 1 75 l 30 140 20 IN N 16 2 84 51 3 23 2 19 1 31 140 30 243 83 210 11 4 68 444 242 148 140 40 3M 115 292 144 84 4 82 Hl2 1 13 140 30 AM 143 M9 17 0 FD 3 59 1 38 147 140 60 MS 174 40 4 1t4 11 1 &M 3 7e 2 10 140 70 623 199 44 4 21 4 13 1 743 3M 2 23 140 le das lie 40 4 22 9 12 8 7 70 4 15 2 35 14D 90 720 210 48 4 22 3 13 0 7 95 4 20 2 38 140 100 $25 IM M4 15 4 56 5 90 1 70 2 15 140 l

I i

, . . .r a

CONVECTIVE BOi!.ING AND CONDENSATION Quality % by wt. '

,.,0 5 Pressum ,

go Bar'(pNa) l a to s f .* 7n rn 1

• g, 101',

047)l s j --

{./p j]jfjj 6 49 (N) .'.-.s

'% [ /,// //

06 '

' l A g u p s00> ' ~ g.g

(

/

/ / //// /

089(tdk)).s , j h

/ / (([ /

20s,'osh),'s f ///// /

138 (TuM);- ss, 172 '(25130) - s N M///

- < r ,

/ / 02 207 (2000) % ')4 dC/ 7 0 -

2214(3208)'

' ' ' M'.,'gVi - ' ~

0001 0 01 o 01 1 .

' Mass quality :

Fig. 2.6. Void fraction a as a function of quality and absolute pressure

.-. .. . _ . . - _ _ _ _ _ - - _ _ _ _ _