ML20066F433

Draft Analysis of Flow Stratification in Surge Line of Comanche Peak Reactor

ML20066F433
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Site:	Comanche Peak
Issue date:	01/31/1991
From:	Sha W, Shen Y, Sun J ARGONNE NATIONAL LABORATORY
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ARGONNE NATIONAL LABORATORY 9700 South Cass Avenue Argonne. Illinois 60439 1

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Analysis of Flow Stratification in the Surge Line' of.

the COMANCHE PEAK-' Reactor J.G, Sun,Y.H. Shen,and W.T.Sha Materials and Components Technology Division, Analytical Thermal Hydraulics Research Program.

l -- January 1991 l

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3 .i Contents Contents.. . . . . . . . . . . . . .. .

1 Introduction. . . . . .

2 Objectives.. ... .. . .. .. .. . .

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3 Brief Description of the COMMIX Code. . . . . . . . . .,

3.1 Background.. . . . . . . . . .

3.2 Equations Solved., . . . . . . . . .. . . . .

3.3 Uaque Featuits.. .. . . . .. . . . . . . . . ... . . . . . . . . .

3.4 Other Features. . . . . . . . . . . . . . . . . . . . . ..

4 Flow Stratification in a Surge Line., . .... .... ....... ... ... ... . . . .

4.1 Surge Line Layout of COMANCHE PEAK Reactor. ..., .. . . . . . . .

4.4.1 Initial Conditions.. . . . . . . . . . . . . .. .. . . . .. .. .

l 4.4 2 Boundary Conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . , ..

l l 4.2 Experimental Measurements. ., . .. . . . . . . . . . . . . . . . . .. . . . . . . .

4.3 Numerical Simulation Model Used in the COMMIX Code.. . . . ..

4.4 initial and Boundary Conditions.. . . . . .. . . , .. . . . . . . . . . . . .

4.5 COMMIX Results.. . . . .. . ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..

4.6 Comparison of COMMIX Results with Measurements. - . .. . . .. .

5 Discussion and Conclusions. , . . . . . . , . . .. . .. .. . .

Acknowledgment. .... . . . .. .. .

Refere nce.. . . .. . ., .... . . . . . . . . . . . . . . . ... . . . . . . . ..

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Executive Summary Flow stratification is known to occur in various reactor components during normal and off-normal operating conditions of both PWR and BWR. Large temperature difference is normally associated with Ocw stratification. Thus, when now stratification occurs in a reactor comynent, it will be subject to an additional thermal stress resulting from the local temperature difference. A number of nuclear power plants have reported failure of reactor components due to flow stratification. Flow stratification not only can cause reactor shut down due to unisolable leak resulting from failure of reactor component, but also has significant implications to rea. tor safety and can alter both the sequence and consequence of a reactor accident. Therefore, it is imperative to understand the causes of Gow stratifica-tion and more importantly, we shoula Le able to predict when and where Dow stratification will occur and its magnitude of temperature difference associated with the now stratift-cation. The work presented here represents the first step in this direction and will contribute to the resolution of the issue of Gow stratification.

An analysis is performed using the COMMIX-IC computer program for the surge line of COMANCHE PEAK reactor. The COMMIX-1C computer code is developed and sponsored by the Office of Nuclear Regulatory Research, United States Nuclear Regulatory Commission and is a three-dimensional transient single-phase computer program for thermal hydraulic analysis of single- and multicomponent engineering systems, it solves conservation of mass, momentum, and energy equations as a boundary value problem in space and an initial value problem in time-domain and has been applied to Dow stratification and natural circulation during postulated reactor accidents. The major objective of this work is to demonstrate that the COMMIX code is apable of predicting Dow stratification. The numer-leal results obtained from the COMMIX code for the surge line of the COMANCHE PEAK reactor presented here have been compared with the measurements provided by the Westinghouse Electric Corporation and the agreement is good, 1 Introduction Flow stratification results from density difference of two streams of a fluid or different fluids flowing at relatively low velocities with very little mixing. The density difference is

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2 Uhn7 attributed either to temperature difference of two streams of a given Guld or different Guids with different intrinsic density. The scope of this study is limited to now stratification ,

resulting from temperature difference of two streams of a given fluid. These two streams are Dowing at Iow velocity with very little turbulent mtxing between them. The lighter. hot Guld stays above. and the heavier, cold Guld stays below in a now domain.

A number of nuclear power plants have reported failure of reactor components due to flow stratification.1 The most common occurrerns of Dow stratification in reactor components during normal (including transtents) and off-normal operating conditions are surge line, hot leg. RHR line, feed water line, steam generator feed water ring, etc. Flow stratification not only can cause reactor shut down due to unisolable leaks resulting from failure of reactor components, but also has serious implications of reactor safety. It has been shown2 that now stratification can occur in a hot leg and most likely in a surge line' during postulated TLMB' accident (station blackout). One of the possiblP. ties of failure of the pressure boundary due to now stratificattor, prior to breach of the reactor vessel by molten core and should this failure occur early enough, the reactor system may depressurize suf0clently to avoid direct containment heating when the core debris is ejected following vessel failure. Thus, Gow stratification can alter both sequence and consequence of a severe accident. Therefore, fundamental understanding of Dow stratification is essential to avoid possible reactor shut down or leading to an undesirable reactor accident. The present work represents first step in that direction and will provide a reliable predictive capability of Gow stratification in terms of wnen, where, and the magnitude of temperature difference. It is to be noted that now stratification was not accounted for in the original design of all light water reactors (LWR) and it certainly has significant impact on life extension of all existing LWRs.

2 Objectives The objectives of this study are:

• In this particular analysts, surge line was not explienly included.

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To demonstrate the capability of the COMMIX computer code capable of predicting now struttfication in various reactor components 2.

To present results obtained from the COMMIX code for the surge hne of i

COMANCHE PEAK reactor and to compare with the plant measured data.

3. A Brief Description of the COMMIX Code The COMMLX code 3 4 5 is a generalized computer code for heat transfer and Guld Dow analysis. Its capabilities include steady-state / transient, three-dimensional, and single-phase analysis of nuclear reactor systems under normal and off-normal operating conditions. Recently, the COMMLX code has been and continues to be extended and modified to multiphase applications of various engineering syr aems.

COMMLX is a well-refined and -tested code. Already, a large number of computations have been performed for complex situations, and many organizations, both here in the U.S.

and abroad, are ustng the code to simulate industrial problems. The structure of the code is modular. Its many unique features are described in the following.

'3,1. Background The development of COMMLX began in the summer of 1976. The tri'4al version.

COMMIX-1,3 was documented and made available to the public (through the. U.S. Nuclear Regulatory Commission) in January 1978. The advanced version, COMMIX-1A,4 with more capabilities and Dexibilities, was released in 1983. Developmental work continued to add improved models and to expand applications to non-nuclear systems. The extended version, COMMLX-l!3, was released in December 1985. The latest verstoa is COMMLN-lC 5 which was released very recently (September 1990). Many additional improvements have been incorporated %to COMMLX-lC over COMMLX-18.

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3,2 Equations Solved Three-dimensional, time-dependent conservation equations of mass, momentum, and energy and transport equations of turbulence parameters, along with the equation of state, are solved as a boundary value problem in space and an initial value problem in time.

The solution provides three-dimensional detailed descriptions of

• velocity,

• temperature, and

• pressure, along with ancillary information such as heat transfer and resistance correlations. For easy interpretation, the numerical results can be transformed into graphic fonns (e.g., vector plots, isothenn plots, and video or flim showing fluid motion).

3,3 Unique Features COMMIX Porous-Medium Formulation COMMIX employs a new porous-medium formulation 6 based on local volume-avera This formulation uses four parameters-volume porosity, directional surface porosity, distributed resistance, and distributed heat source (sink)-to model the offects of internal sohd structures, in the conventional porous-medium formulation, only three parameters-volume porosity, distributed resistance, and distributed heat source-are used. The addition of a fourth parameter, directional surface porosity, is a new concept that gre facilitates modeling of velocity and temperature fields in anisotropic media and, in gen improves resolution and accuracy.

Two Solution Alcorithms COMMIX has two solution algorithms for single phase systems that are provided as user's options:

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A semi-implicit algorithm derived from the Los Alamos ICE Technique.7 8 9 This algorithm is ideally suited for analyzing fast transients, where one is interested in 4

details at small time intervals (on the order of Courant time step). I

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A fully implicit algorithm names SihtPLEST-ANL4 This algorithm is a modification of the Patankar-Spalding numerical procedurcio known as S!htPLE/ SIMPLER. It is particularly suitable for the analysis of slow and normal transients.

These two solution procedures are combined into one formulation. But they are implemented so that a user can switch from one solution scheme to another at any time dunng a transient simulation of a problem.

The Geometry Pnckare I

The geometty package developed and implemented in COhthilX :s capable of approximating any irregular geometry. It uses basic computational cells as building blocks to model the geometry under consideration. Then both volume porosities and directional surface porosities are used to account for the differences betwern the approximated and actual configurations.

To save computer storage, a computational cell is defined by a number rather than by its conventional (t, j, k) location, wherc 1. j, and k are the computational cell indices in the three principal axes (e.g., x, y, and z in the Cartesian coordinate system). With this approach, the storage requirement depends only on the total number of computational cells and not on the dimensional values of (IMAX ' JhtAX ' KhtAX), where lhtAX, JhtAX, and KhtAX denote the maximum values of computational cell indices in the three corresponding principal axes.

A normal three-dimensional computational cell has six surfaces. But to facilitate true 1 and proper modeling of a complex trregular geomt:try (and most geometries in engineering systems are complex and irregular), we have provided flexibility so that a user can specify an additional seventh surface, called an irregular surface to a computational cell.

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s 1i 3.4 Other Features Other features of COMMIX are described below.

• For bingle-phase applications, the following two turbulence model options are provided:

-Constant turbulent diffusivity model.

-Two-equation (k-t) model where k is the turbulent kinetic energy and t is the dissipation rate of k..

• A flow modulated skew-upwind difference schemes has been developed and implemented to reduce numerical diffusion, specifically for the case of Dow inclined to grid lines.

• The final form of all of the sets of discretization equations is e

al ce -1., a' t , -6,' = 0, where e is a dependent variable and the subscript i stands for neighboring points.

This general form of the discretization equation lends itself to various solution schemes, e g., SOR, Preconditioned Corgugate Gradient Method. and direct matrtx inversion.

• The solution has a decoupled-transient-simulation option that permits solution of

-mass-momentum equations only, or

-energy equation only, or

-coupled mass-momentun. and energy equations, at any given time step.

• The code has an option that allows use of either Cartesian or cylindrical coordinates.

• COMM!X has built-in properties for liquid sodium and water, with an option l

( permitting use of simplified property correlations for any Duld.

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• The code also contains: -

i j -A generalized resistance model to permit specification of resistance due to internal structures (fuel rods, wire wrap, bafDes, grid spacers, etc.). ,

-A generalized thermal structure formulation to model thermal Interaction between 1

structures (fuel rods, wire wTaps, duct wall, bafDes, etc.) and surrounding Guld. i i  !

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• Heat source / sink and boundary conditions can be functions of time,

, i The COMMIX code is structured to permit solution of one . two , or three-

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4 Flow Stratification in a Surge Line I

A detailed three-dimensional and time-dependent analysis is performed using the

COMMIX-1C code for the surge line of the COMANCHE PEAK reactor. Temperature distributions of both Guld and surge line wall are calculated.' First, the surge line layout of i

the COMANCHE PEAK reactor will be described, the experimental measurements provided by Westinghousell is presented, the numerical model used in the COMMIX calculation is -

out!!ned, both initial and boundary conditions based'on the limited measurements used in  !

the COMMIX code are followed. Finally, the detailed velocity profiles and temperature distributions of the surge line obtained from the- COMMIX code are presented'and compared with the experimental measurements.

4.1 Surge Line Layout of COMANCHE PEAK Reactor Figure 1 presents the layout of the' surge line of the COMANCHE PEAK reactor. 'All pipe -

t

- dimensions and pipe outside and inside diameters are shown in Fig.1. - The temperature .

t, monitoring locutions, namely T1, T2,- T3 and T4 'are also shown. In Figi 1. These temperature monitors record the outside pipe wall temperature at various circumferential locations.

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, --,_-m.-s3,, , - . ,., , y, ,,,yy,..,,y.,,-,y , .,y,m e., f w ,, ...,m,r--p..rw=--r--vew-- ,m----,e - , ,-w

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4.2 Experimental Measurements Figures 2-5 are temperature measurements as a function of time of T1. T2. T3. and T4 respectively, at the various ctrcumferential locations. Temperatures as a function of time of the four hot legs are shown in Fig. 6, the hot leg marked 4 in Fig. 6 is the hot leg with the pressurtze* The water level of the pressurizer as a function of time is marked 7 in Fig. 7.

Figure 7a is the enlarged view of a portion of Fig. 7. The relationship between the water level height of the pressurtzer versus volume is presented in Table 1.

4.3 Numerical Simulation Model Used in the COMMIX Code The numerical model simulates the surge line of the COMANCHE PEAK reactor are shown in Figs. 8-10. The computational mesh set up along the pipe line is shown in F Figure 9 presents the typical cross section of the surge line and the typical elbow is modeled as shown in Fig.10. In order to avoid modeling complications, the pipe marked L1 in Fig.1 is modeled as a vertical run as shown in Fig. 8. This simplification will not

( affect the results and will be discussed in Sec. 5.

The hea' capacity effect of the surge line is explicitly accounted for in the numerical calculation.

The wall thickness is equally dMded into two computational grids in the numerical model and the thermal physical properties of pipe wall used in the COMMIX calculations are as follows:

p (density) = 7977 - 0.4167 T (kg/m3) k (thermal conductMty) = 14.16 + 0.0131 T (W/m 'C) l Cp (specific heat) = 508.67 (J/kg 'C), and T (temperature) in 'C.

4.4 Initial and Boundary Conditions A close examination of the experimental measurements as shown in Figs. 2-5 reveals that flow stratification with large temperature difference took place approximately from 1/2 hours to 21 1/2 hours in the transient. One of the objectives of this work is to

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

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2 demonstrate the capability of the COMMIX code to analyze flow stratification. Consideration is also given to save computer running time It is thus decided to start our calculation at 17 hr. 31 min, and 10 see in the transient. -Since we do not start our calculation at the very beginning of the transient, the initial condition corresponding to- the beginning 'of our calculation must be constructed. Also the boundary conditions as a function of time at thel inlet of the surge line (from the hot' leg to surge line) must be provided. Both' initial and boundary conditions used in the COMMIX calculation will be described below.

y 4.4.1 Initial Conditions

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1

• Velocity distribution based on isothermal steady-state solution with-inlet velocity of i

d 0.002 m/s at the inlet of the surge line (from hot leg to surge line).  ;

• The outside pipe wall temperature distribution of all horizontal pipes (L2 and L3).

based on T2 and T3 readings and linearly interpreted and extrapolated both axially (along C:a pipe length) and circumferentially. The outside pipe wall temperatures .

t in L1 and L4 arc assumed ~ to be_-uniformly distributed according to T1 and T4 readings respectively. All fluid temperature next to the pipe wall of L2 and L3 are i

assumed to be the same and they are stratified. Temperatures'in' L1 and L4.are-assumed to be untform at 152.6'F (see Fig. 6) and 440F (same as surge line wall temperature, Fig. 5), respectively, it is to be noted that the assumption of uniform l ,

l fluid temperature in L1 and L4 is reasonable since both T1 and T4 readings after we started the calculation appear to support the assumption.

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4.4.2 Boundary Conditions

• At the inlet of surge line (from hot leg to surge line)

L

-Inlet velocity based on the water level of pressurtzer (Fig.7) as shown in Fig. I1.

Figure 11 is obtained in the following manner.

4 Since water is an incompressible fluid, its level change in the pressurtzer is .

l directly related to the water flow rate from the surge line to the pressurizer, i I-l

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

i 10- l f t

i which in tum, related to the flow rate from the hot leg to the surge line.

Therefore, the instantaneous mean inlet water velocity vin is evaluated from QdH

, -v,=

I L where H ts the water level in the pressurtzer (in %) as shown in Fig. 7. Q is the volume of the water in gallons in each percent change of the pressurtzer level as; shown in Table 1. A is the cross sectional area of the surge line pipe, and t is the-time, it-!s seen from the above equation that the inlet velocity is proportional to -

the slope of the water level change in the pressurtzer as a function of time. When the experimental data of Fig. 7 for the water level (in %) was enlarged by many a times (see Fig. 7a), it can be seen that the slope becomes positive from about 17 hr -

31 min, and it increases to a maximum after about 17 hr 36 min.' Then the slope decreases and comes back to another maximum, after which it gradually declines and eventually the slope reaches to very small value. The inlet velocity follows the same pattem as shown in Fig. I1.

-Inlet temperature based on the outside pipe wall temperature reading of the hot l leg (nearby the surge line) with pressurizer (Fig. 6) as shown in Fig.:12.

• At the outlet of surge line (from surge line to pressurtzer):

- hv BT g - g = 0.

4.5 COMMIX Results A number of assumptions have been used in the calculation and these assumptions are i listed below: ._

L

! - 1. No heat loss through the pipe wall of the surge line.

2. No pitch (slope) for horizontal pipe.

3. Calculation started at 17 hr 31 min 10 see in the transientc

, w- e s.ww-..-w-+a-rc%-w.._--uw--r,-. +w-.es--,-si- *w he saw+e+

-w-y-.+y= v a. -e- n y e e= , -- , ysic-- gre- - c ,%+ w -ev - s s-yr r-p- e+r'g--6eis--. e-

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

DRAR 4.

Using *best estimatt* Initial and boundary conditions based on very limited  ;

i experimental measurementt

!! is to be noted that these measurements are in graphie  :

plot (see F!gs. 2-7), but not in dignal form. 1

5. Approximating L1 pipe as a vertical run, j 6.

Pipe wall conduction limited to one dimension (radial direellon only), '

3 The typical velocity profiles and temperature distributions at ten minutes after started calculation will be presented. Both velocity profiles and temperature distributions at the centerline of the surge line in the vertical planes of L2'and L3 are shown in Figs.13-20 and Figs. 21-28 respectively. The temperature profiles of the surge !!ne cross sections at the locations of T1, T2, T3 and T4 are presented in Figs, 29-32 respectively, and both inside and outside temperatures of the surge line wall corresponding to the measured locations are also shown in these figures, i

4,6 Comparison of COMMIX Results with Measurements t

A comparison of the outside surge line wall temperatures calculated by the COMMIX i code with the measured data provided by the Westinghouse Electric Corp,ll namely T1, T2c T3, and T4, are shown in Figs. 29-32 respectively. The agreement between the calculated ~

l results and the experimental measurements are in reasonable agreement, 5 Discussions and Conclusions In spite of large uncertainties in constructing the *best estimate

• Initial and boundary conditions based oc. Hmited available measurements, it is gratifying that the agreement between the calculated results obtained from the COMMIX code and the experimental data _

is reasonably good, in our opinion,= the agreement can further be improved if both = Initial _

and boundary conditions can be more accurately quantified. 4 The wall temperatures of surge line were calculated by one d'mensional-(radial i i

direction only) approximation. The calculated results can be improved if the additional conductions om both circumferential and axial directions are incorporated into the i

m- w. - r+ e m e. -v,, --1 ++ 3 v-+,--..mr-., e*,~, e,w.-- ve,m m ~en e , e m - r- + -+ , . . . ,+r -w- o ~ ~ - - ,-m. - r ,mn---, -+

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COMMtX code. We recommend that this additional capability should be implemented into the COMMIX code.

Based on T1 and T4 readings. It appears that there is no flow stratification in both inchned pipe L1 and venical run IA after a very short period of time started the calculation as shown in Figs. 2 and 5 respectively. Thus, it seems justifiable to mcd:! inclined pipe 1.1 as a vertical run.

As stated before, the major thrust of this work is to de.nonstrate the capability of the COMMIX code which can be used to predict when, where, and magnitude of local tempera-ture difTerence in a flow stratified pipe. Based on the comparison between the calculated results from COMMIX code and the experimental measurements as shown in Figs. 33-36. It seems reasonable to conclude that the COMMIX code hat, demonstrated its capability for predicting the flow stratification in the surge line. While the COMMIX code has demonstrated its capability to perform Dow stratification analysis, it is desirable to have more assessments and valldations. In particular, the validation must be carried out to compare the COMMIX results with the well instrumented experiments which are not limited to the temperature measurements, but also include the velocity data.

Based on the calculated velocity profiles and temperature distributions as shown in Figs.13-20 and Figs. 21-28 respectively ten minutes after start of the calculation, the following imponant observations may be summarized below.

1. The location of maximum flow strattfication or maximum local ternperature difference between the top and bottom of the surge line is located at L2 right after the flow passing through the elbow from Lt. This location is different from either T1. U, T3.

and T4 locations. From the instrumentation point of view, it is very desirable to have measurements located at or nearby the maximum now stratification.

2. The calculated velocity profiles after ten minutes during the trantient calculation are similar to those shown in Figs.13-20. The calculated velocity profile in the surge line is very complicated, in a large portion of horizontal pipes L2 and L3. the Duld in both top and bottom of these pipes is flowing in the same direction and in the middle portion the fluid flows in the opposite direction, it is our belief that the flow pattern is

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highly sensitive to geometrical arrangement of a surge line as well as operating I conditions. Thus, it is very difTieult to make a pre-generaltration of flow pattern as well as temperature distribution in a stratified pipe.

3 It is interesting to observe that the calculated temperature at the top of the surge line (zero degree) is slightly higher than the temperature at 60' as shown in Fig. 35 at approximately ten minutes in the transient. This is due to the local velocity at the zero degree is higher than the 60' location, thus the corresponding heat transfer coefficient is higher. As we have mentioned before, the pipe wall conduction model used in the COMMIX code is limited to one dimension (radial direction only in this case), the spread of the calculated temperatures between O' and 90* location of T3 could be larger if the circumferential conduction of the pipe wall is included. Furthermore, the validity of the assumption of no heat loss through the surge line wall needs to be examined for future calculations.

Ptnally, it is to be noted that the COMMIX code is a general purpose, multidimensional computer program which is not umited to the flow stratification in a surge line. In fact, the COMMIX code can be applied to flow stratLIlcation problems occurring in any reactor component such as high pressure injection system, steam generator feedwater ring, etc.,

under various reactor operating conditions. It has also been used extensively for natural circulation analysis under severe accident conditions. Recently. the NRR/USNRC expressed some concern regarding the thermal stripping problem, it is our belief that, with some modification of the COMMIX code, we will be in a position to tackle the thermal stripping problem as well.

Acknowledgments The authors gratefully acknowledge the encouragement and support of Drs. Barry Koufer, George Lanik, Jack Rosenthal, and Nelson Su of AEOD, U.S. Nuclear Regulatory

^ommission. Stimulating discussions with our coworkers Drs. M. Bottoni, T. H. Chien and H. M. Domanus and the excellent typing of S. Moll are also acknowledged,

References 1, Su, Nelson T. Special Study Report Review of Thermal Strat\fication Operating Expertence AEOD/S902 (March 1990).

2. Domanus. H. M. and W. T. Sha, Analysis of Natural Convection Phenomena in a 3-loop PWR During a TMLD' Transient using the CObthtLX Code, NUREGICR-5070. ANL-S7-54 (December 1987),

3. Sha. W. T., et al.. COhollX-1: A Computer Program for Three-Dimensional. Transient.

Single-Phase Thermal Hydraulle Analys(s. NUREC/CR-0483, ANL-77-96 (September 1978).

4. Sha, W. T., et al., COhfMIX-1B: A Three-Dimenstonal Transient Single-Phase Computer Program for Therinal Hydraulic Analysts of Single and Multicomponent Systems, NUREG/CR-4348, ANL-85-42 (September 1985).

5. Domanus, H. M. et al., Coho!!X-!C: A Three-Dimensional Transtent Single-Phase Computer Program for Thermal Hydraulic Analysis of Single- and Multicomponent Engineering Systems, NUREG/CR-5649, ANL-90/33 (September 1990).

6. Sha, W. T., B. T. Chao, and S. L. Soo Conservation Equations for F(ntle Control Volume Containing Single Phase Fluid with Fixed, Dispersed Heat 3cnerating (or Absorbing)

Solids, NUREG/CR-0945 ANieCT-79-42 (July 1979),

7. Harlow, F. H., and A. A. Amsden A Numerical Muid Dynamics Calculadon Methodfor All Flow Speeds,1 Comnutational Phys. 8, p.197 (1971).

8. Harlow F H., and A. A. Amsden, Numer(cal Calculation of Multtphase Fluid Flow,1 Comoutational Phys.,1,7_, pp.19-52 (1975).

9. F. H. Harlow and A. A. Amsden, Flow of interpenetrating Matertal Phases, L Comoutationni Phys., R pp. 440-464 (1975).

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10, Patankar, S. V., Numerical Heat Transfer and Fluid flow, in Numerient Heat Transfer.

Vol. 2, New York:McGraw-Hill (1979),

11. FAX frorn Bill Coslow of Westinghouse Power Systems Division to W, T. Sha of Argonne National Laboratory, dated September 25,1990.

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-STRATIFICRTION AND THERMRL CYCLING n n.e tssa k i t

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157.3119 DCGF nyerege - 157.!SG DCGT nyeregn -

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ELRPSED TIME CHOURS) [

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1 2 3 4 5 6 7 rig. 9. Typical Cross Section of Surge Line 1

1 1

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17 17.5 18 18.5 19 l Titne (hr)

Fig. 11. Inlet Velocity of the Surge Line 1

I

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. _ . . ._. . .. ... .__ .....___.i 17 17.5 18 18.5 19 t

Time (hr)

Fig. 12. Inlet Temperature of the Surge Line 1

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15'T7T"11{ 77. . 173 .

ans . . mar **I4T . : s56 .- : s37 . v33 . x34  : 15C is7  ;

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• IUT  :  :

v. i. is-- .s- .w . > u  : .5 ,,  :. ,, 4-es:  : .

" I= 4- . Pipe L2 (i.p 10,.22) 4 Fig. 22.. Tesaperature Distribestions' at 10' Min..in Transient'

. .i

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)

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k 1.3

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99 . .

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. Pipe L3 (j = 10, 21) & B2' I')

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Fig. 23. Temperature Distributions at 10 Min. in Transient t I

?

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k 4

i I

1 i

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3mm -l

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

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t l

l

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m ro ,

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us- T-- nc 3 m 1 ni m nr 1 nr-*

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n r--'

~ ~ ~ ^^ **"Y f s if2 112 i f. j Yrs Yfa los 10r~-~~ 5 Yts"~~~1 ifo Pipe L3 (j = 22, 31)

J = /$.

Fig. 24. Temperature Distributions at 10 Min. In Transient d

"Z:7

.~..

1. vn us 1:n zus Tir"*~-j -

un Tf2 j

un 185~~~~j

us 18 5'~~*'!

z.x, ~'

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133 j t er **~~i T6, ter i, 169

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ncr n9 ur--- . .-r -~~ i s-~-~ nr , n, r nr--~ - n t---~---

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i 3

Y28'~~~*i ygg nt yg 12t'*~~*i

),, 79, 127 g ,,

Pipe L3 (j = 32, 41)

I = /}.

Fig. 25. Temperature Distributions at 10 Min. in Transient b,,

o ae<;<.

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teace.tecate x 4 -

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• I n ** *

.........,p. . .........123 "*]''""**125 "*"i"""*"T1I"" j "" "* 1:5 "";"' -

.... '!!U i' ' * * * * " *12T " * '* i '* *"12T * * *"l '"' '"' m * * *' *; ' ' * * * * -

I=4 Fig. 26. Temperature Distributions at 10 Min.-in Tr'ansient

_ _ _ _ -----_--____ - - - _ - - _ _ -d

1

, i.

2 n ci:l r's ns 2 .42 c c.c;c n4 2p: c,cicje,c :

2 ,n.nir,rjr'r 3 i

.......,..:..i....

Pipe I.4 (k = 33, 41) 2,:.n:,:):,  : 2 I:

..J.........

i

i 2icluic ic,1clc .

.......g......

i 2 0 ',O',3'lO .O 'C 0 2v.v.;c;c; sit 9 ii 6 :

2icicgccc)c9 c :s l

i l

I=4 1

I Fig. 27. Temperature Distributions at 10 Min. in Transient l

l l

t l

i P

-=..: ,, ,

i s x x x x x x3  : 0

. .. e- .. .. .e ..

.i 2;:::;:;21:;::2 ii' '

...........g.. .....

j i

2;ntu;c;c;ctu :n- .;

.]'

l

. 3. 3..

1-Pipe L4~(k = 42, 50)  !-  !

2;ule;c;c;c;u.i-2;O;C;212**"O .0 -

0

c 1

.. , . 3 . 3. . , . . .. 3..

-l 8 g-

'i. .

g <{

2nnm e an t-

, j.

......i...... . . . . . . . .

.l.1 2 n clc a u u s:

..g .. .. .......

2 ;u 72 1 nlt'n)t

'.1; l

2.c c c;s e e 6-l I=4 Fig. 28. Temperature Distributions-at 10 Min. in Transient-

Surge Line Wall Temperature ( )

J 64.1 64.1 63,1 daj J es : 68.1 61.1 as.t at es.s 68 1 64.1 68.1 68.1 $1.1 64.1 63.1 i

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , ., ,, . ....I............. An AA s.4 e.d

o. . o Nm o cc. e.

e MMN 64.1 n.1 at 64.1 6 .2 6a i ss.i oe mm m

ee vv vv

, . . . , , . . . . . . . . . . . , , . .1..,,.......

63.1 64.1 68.1 68.1 63.1 68.1 68.1

...q,.... . . , . . . . ,,. ... ..i...,,...,,. , , . . . .

,,3., , , ,,

dId II.\ 6I.\ 6I.\ 64 \ M.) J T1 on P;ipe L1 (k = 5) 3 4 u u.t at 63.1 .5 i

i K=5 Fig. 29. Temperature Profile at Tl Location

-4 .; . . , ,

4

.S62 .  ;

r (209.6)- Surge Line Wall-(209.4)- :x;- - ature s - ( -)

r .

,6.1 1,6J~ ~193.1 ~ 194[6 ',4.2 .

.............. .................~.. ............... . , . . . . . . . . . . . . . . . .

S3

& .% a  :

ue nu. :nu- i,o i,a ,a

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

T h

IM4 167.2 161.4 IMI[ 163J . 163.0 .  : 143.7 .

i.

.................,...................... . . . -........................................= ... ,-

4 nn er

-h M M 133.8 1319 1513 133.9 - 134.4 133.1 IN 4 ' -f mee mm V % esp 131,1 136J ' U6.7 _ 133.2.-- '134J '. 13 4.0 ' 13tk' s t

-l:-- j! j

................ - ~

$6.6 $44 f- 9 8.0 ..

- 99.0 ', 99J s t_.2 -

fG.O#p &9l.4 '

1. s,c 0 d\' .... ...................M. 9.n.. Ripe,.R.31.i9 20.L: . .. ,

,4

1. -

f 41.6 81Jl 79.4 18J .2 ;

s (105.6)

I = 20 .(111.9);

S66'- , ,

Fig. 30. Temperature-Profile at-T2[ Location i

W

..~l 1

i

- - - - - - r-- ,m-- e- -w-.-g ,..,.-.n., ., ,-en, ,. n 4- ,-r p - , ,--ep,m,1-~,.e. . -n-.,m...

. . , . - .._ . . _ . . _ ,m _ . . . . . . . . . . . . _ . - - . _ .-- _ _. _ - .-

l

. .i f?Fe WIlOsh{ ,

i 1

S67J j

- Surge Line-Wall; (213.4) Temperatures-( - )

(212'.0y

! .- 1 o.2 o llC0.1 119.s 119.4 'It.1 l 1

f #f.

- P 'e : -

q

\

"....~.........aa. .oma.*~a...... **......aa......

gE Jj -

j/.n'+J .

. J -

5.0 istl . 184,2 tilJ - 144.1 - 114.4 '13. l : - -l

-3 aaan a "a a =*.a a" ~ * .am* a-a. a ." . .au m aa~a. aan.au .h

.. .......................u..a.a ,

- 111.9.- .- 11tJ - 171J '- ' 11LJ 170 8-111.0 - 172.1-

. . . .. .. .. .~. . ... a. . . " . " ..". a .. "

• a nn a m a n aa a I : : .. ua.p : =4 am a na aa*m -

^ ^

I43,1 143.9

- 144.4 - ~ 144.6 - 144.8 :" ' 143.2 h. o.

94.9 nhm mm@'

m - y) - -i vv l' . _l --

,,..m................. ..a.....a..a..~...a.........................~.....................a.....

! f i

i U3.2 '  : 0 11 U2.4 U2.7. - -111.9 . l ulo 133 3 -

.................. .. .......a.............n...........a ... .a......... ,

s.4 us.1 - . us.1 uu ' us.s nu .u

. Q: 1 T3 on P i g; e.1..L..m 3- .(. .- 4.. 2.5.. ... S' ' .i

...~....-..... ..a., .....

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

- L cp -

to.s llo.: . inu- - no.2 .o :

(131.7)

J -

(138.0)'. +

S71- ,

i

Fig.' 31.

Temperature-Profile at 'T3 Location 1 t

i t

i' 4

6 e,, , - , - , , <c,,,e -- 6 i -- s +mw- 4 *e=,- r- srne ov e v , e e= -e - W y s m e t--.- m - w n*=-dew m w w +v s v . *r<= +-v.'r --%-" *Mfrs

• *' e i S72 (226.5) Surge Line Wall (226.3) Temperatures ( )

J.0 D .0 23 0 23.0 73 J.0 23.0 D.0 230 23.0 23.0 'n0 230 223 0 C.0 20 0 23.0 23.0 2U.0 23.0 23.0 m.0 130 23 0 230 2n0 C0 230 2.0 2n0 230 223.0 2n0

'no 223.0 M.0 230 23.0 3.0 J.0 T4 on Pipe 1.4 ( k = 50)

" .0 23.0 223 0 23.0 ,0 1

1 (226,3)

K = 50 (226.3)

S73 Fig. 32. Temperature Profile at T4 Location l

l l

i

.i g e : - e

. O

! en

(

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

1 1

\

^ '

"' .4 e t _. -.

-_,= ...:. . - - .

4 . . .- 3 .__ --

- --+-

-- _ t 3. . ,

m ,

- =-c= _t - .- a

, . =u _, ,_ =_. ==::. .

_ .y 4

.m , _ _ _ . _ . __

_.__7__..._

%_...____.___ _-5

. __- L=._-.--_i r: _.

i

__i_ - _ _

.-- s

---

- = , .

-4

. .i

. . - . _ - _ . _ _ .. - _ . y

_ = _ _ , _

e=: ._ _ ;.- -- e

.__ :3 -

t. --

== - _ ,

-__. Experimental Data- --.

4 C._OM..ti1X . Result s

~

= e__

. _ _ _.t.._ _.._

1, 400 - + _ ,

1 i

..')

+

-' .;i

- , ~

1

^ -

u. 350 -

o -

w ._.

U +

-L__

w _ _ _ .

D +-

w -

m W - _: - ._ == .

e c 300 -- i.

g H . _ . _

,' p r-- .__

t

- -- a

(

)

250 --

+

- - - _. o

.{

=\ - -

l _

5- , r = - __._ _..

200 =-__Xw - -

- ==

_- _ =_._ -

_=_ o . - :

.a ..-!- t=_

..._.= i

_q \ .\--pu-

___ r=_____.__. ,-_.- - . = = _i-_ --

- , - -t ,_._ - - _ --r-._ ..=- =

l ---<- 1

_t s e=-- - .-:- .__ t=:=ja =- _ ._. _

= c- - . _ . .

m

__ __r. r = --.=

=F :=. __ = f_:__,. =t _=: __:.e - _--

=.= n. \:t._. . __ w -- r =. __ i _=. __. ,: .=i =_ __ r. . :t==-t

-2.~_ :-2 .21:q:

..: .. L= :F~ ten.r*rzi--1.

w .:m =i :L--=.1:-u - .t -.-w?!,:.g. il --_. =r= -p - ..u:o =

- ;.a=. ==i -- -

r-

= : =. r-t_. -:-r.-t. r:-': - *_=-

,=_}._-, -

-150 t __., __.; .= =rt_

-- 1.--- . ,_ ,

=. & . __

. -g. _ . _. -

t.

._;t= _.__ .

_-_=v, -

-r .._. >= _p=::=.: = t -M~:__ .y==t- -y=.. ._ ,

u ___ _, _.._.-.._

__. __ :=. _:= r =t=, :- r::: l=.== =.:w r- =... t .

=i  ;

r  :;:i :

m.:_.u.:.

. :==:f. i.= ,.. :-: l:4r--_=.

===::= u -e._cl.: [.-l - -

. =. :.:l t.:.i=._.l:=s7 .- .st u =:}::::m:.:. , t 4r :..},-.==t.-. =.l . . .. .} . -:: ... .. 17.5 18 18.5 19' '19.5

- Time (br) t Fig. 33. ' COMMIX Resulta vs Experimental ~ Data'of T1 -

?

w+ .' T-F- - - - - - *y .-%e-y e .- t1ev5 ,*w .

DRA7

_p--  : =

5__

r_.__..__ _ _

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

~-

.j l

--- Experimental Data ___;

-~'

COMMIX Resulta ---

450c_ _

-o- 0" ---J-r o

1~ - D - 60 esc ~^- v g 2% - 6 _ IO

- Q - 120" Era ti==\=k --

M5D\~m =k - * - 1,8 0" rs MiBEE.=\-

Em t

'N 350g m#f=Er=n~-\.-

gF=F--~

EE: G-~ \

~$

\

^

A E-1 Bri : \- g- -

t = ) =n= 5t = *\- \- A e Mi=b=a=i a ~

A '

300 h , -~\

~

moma \ .

t 0

-%t.._\-

d-0m 0_ag e =#'%=Ag==\

-- , ==A \ _m

$9. \. W

-. \

(.== '\

-\ ~ W 600 ~59 250 __\ j. 'y .

\ ' -- _ . _

}[-~~~.\

h

\ \-%,_ _ _ _

-- 9 0 - 5 200 t

'.h.k.

N g

12 0 'EE

_p

~__^

180 5 ,

150 Y -. ~ .__ s ~

- _=_j 17.5 l'8 18.5 19 19.5 Time (hr)

Fig. 34. COMMIX Resulta vs Experimental Data of T2

r---------- n 5.M:.fr=.Er"in! -i.E " ' 9 F:rs.:f * . "l!E .EM::- ~:h: =J = = . . . .= .: =. ..a

_ _ : =_ :. = -.s :: =.=;:_ -- -- = = = :- - - - -_ _ __ _ . . _ _ .~-----.=--m

--=_:._===--.---=2.------ ___ _

m__ --

4

__ I

. _ . _ _ _ = . _ . . - -=..-:------n.._...:_.

-. =.=_=_ E xpc rimen ta ata

_..__________..__2,4

<_ -an4M11--9,, wks O

__.___._.__=_....

450-- -

__ - -_ ._: = __. - --_--_. ,

_ a. - - -

-- ._._..:.=-.-..__.::---___- .===.==== o

=_ .o. o-- -4

- ;. . , - v._. -0 -

6 0 '>

0 0 .- . , . ;:. ,. 4;pbg:. - -

- g- 90 o=

= @:i *=p_

-\.. ' _ 0 . 120"

. j. E5'iEE _- .

a: -+

_._ = - --

_* - )80 a

..J=_ . R& 5. .E . _ - .- --i

^350-=-* . __2_ _.--.-

o" EEM.: GE ~-- =.==.t G - -

5t- . 4 "

0 w - _:

_:4 e--;~_., ._ .

@~Z .-:O x

g w

""C) =- '

- ~

N _: :.:-_. _ - .

,** :"1 7 *~t

';= , n . < - M

c. 1 = .\ t _ , - nM Ei300 o

=

. _ _ =-_ rr:L

_0 h __

n- n

?"_i~

g_

1

.r_...

g * *'-~

• =

y' ::9 .._ _s. ---- 6 0 .=#a

= g-

-g -

250 -

2-

.. Y":.. _=*.

' -- o-

___ 40 EE!

---

m,

)

_.- ... - _ . ~

o=

.=,

200 -- _ _ :_ . - --

-'-~_.

..~

i - - -

_ __._j

=. r.

l;f ". ' J: :*C;i F.J;.**.Jr::*.T.L*:'.'* _ -  %

_ . _ .. '

0 .;h' c*4:!*1;_* ='.". _ _ _ .

. =.~.2 2 :* - _

O _._ ::= = :'_***:-- -. -=' :.T.;

• g *. *."3.

g-

', c:.=. .........

=_.._. C w.

..:=.-.:....,.~r___.-x__.._....._...____=.=.

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

,, __ = ---- I 8 0 150 -

---a ==_..

-- -.= =: - -

_._H . . _ . . .

._____.-..-=_=:.-.==__._.;_==_t==---

- ~. _ . , _ _ .

.._......_...___._....a

.L .. . _~:. .:. .. i. ' ."? ' *: T.* T, :-* =. . . '~\ ?..?..... .*~.....

= i _ . :;'.;." _. ._. . .__ _. ._ *

._....._.L:.~...'L.'_.._...:--._.~..

- __.._=.___--

c. _ _ _

3...... _- .:.= = ;- z z.i. =. = _. p : = =. .::.....:= _.,.._..;_.__

;==::=; .

17.5 18 18.5 19 19.5 Time (hr)

Fig. 35. COMMIX Results vs Experimental Data of T3 l

. - _-- -- ]

a C . l 1.....

__ _ _ . . . . . . . . . . _ . , . _ ,_- 4 __- _,._

.-_-_1_ _

-__y.-

_..__g

___.___.__2 --__;

._: __ f _ 2 . r- = ! __ __ _. -.1 r r --_-- . _:L _. _J -

---5 .

. ; .3__ ___:==- . -: .= .

C.___.- _n. a r=_..-__.._.._=_--- --- 9= =4 = :=a = .-- = _:---- ___,___-~l

+._ ----

-_ - __.- - .-; :_ _. _- -.__'---:-._.a = u_

~

-_=r~~~~~

r- :=.:.r. _ ._._ ;=== - " . . . _ ~ . _ ~ -E II ~

t-- - .

- ----j 4 5 Cr - _ .

_. a

,W__,An.__=a r_ -_.=_ _. ., _ __ ==_i=:r= =9_. :. .---_-------=:=_ __

_. ~. -4

~-

. _ _ _ . . _.1 j

^m _-

^"~. _.___ r --~

[

- -- , - _ _ . _ .r_. _ . - __ -

_i 400-__ _ . _ . _ _

C 2350 _ _  :

v 0 -

W 6

N W

E.300. -

h

@ -.___. Experimental Data . . . . -

(MMMTY Ro mi t : +- '

t-

- t 250

_ . _ _ _ _ - . .._._ a--- - >

-e .__.=-

~-

+ )e 200 ---

_s_ _ _ . _ _ _ _ .":=___._s----

,___.__.._.;. a

_- =:r _ __.

_ _ . _ -- w _ _ _. . . _.. ._ i=_.. = r. .

. r_ : .. -

_q s

.-- ._.__._..._.__i.__.__4_

.._ . . ._. =.=_ [,._ ". "u:::;.=. : 3, _ _ ___.....,_r...._f_~,.

. _ . . _.. _._. _ , - -A .

_4__.

=_.T___. - ~

. _ _ _ . _ _ _ :_.1.-

_ . . . = _ . _ , . _ . . . _ _ . . . _ _ _ . . _. ._ .._ _:.

- - --- n- > o,

-:=: -_.

_.i-.. ,

. _ _ . - .____._._=.__.s_....<.=..r__._..=_.1,.w..._=_L_-m_,=_=_.=___-.=__:._.:_t._=_=.=.=._.

a-

. _:d:u_=_.; -.: ___. ::::n

.=:d

r . r nlr..- c.: - .:.A:=w=::i . = :: I:.= :::_.h:: -

u. $.:.v.:d"..::=.}

_-:= = =:- _ n2: --

1i

_ .__._.__=__=:=_.__....__=.in_:..L._,.._..,_.,_-.l..____.._c.,._..L...=....._

_._._=. . _ _ _ . .

.=

___- 1_..=. _. _ . _ .J .=. _::. =_. _=_. _: = =_ s. r - - = . . . = . . _

• .: 77=-_,,_..  ;-* ~

- . _ _ _ m =: ==-I' -l =. = .:'=l"- _e :rlc =:=nt=i ._ :L.~t t== _ l' e:ri =r--m - :=p=== l:.- - .:

= -

.::::I_=.i=__1H E. :.=.r .' : =. i =. I :.=i. =.. l -- - -}- P:i .-. n. l: - c ..t.. .l . . . . .I 2 +1::.:=.;' E. _ =_=h.@_ ~ ;i '&

17.5 18 18.5 19 19.5 Time (hr)

Fig. 36. COMMIX Resulta vs Experimental Data at T4 L

_ _ _ _ _ . _ _ _ _