NUREG/IA-0160

International

Agreement Report

Analysis of the Critical Flow Model

in TRAC-BF1

Prepared by

M. G6mez, E. Valero, I. E. Parra

Department of Applied Mathematics and Statistics

Universidad Polit6cnica de Madrid

Spain

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555-0001

May 1999

Prepared as part of

The Agreement on Research Participation and Technical Exchange

under the International Code Application and Maintenance Program (CAMP)

Published by

U.S. Nuclear Regulatory Commission
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NUREG/IA-0160

International

Agreement Report

Analysis of the Critical Flow Model

in TRAC-BF1

Prepared by

M. G6mez, E. Valero, I. E. Parra

Department of Applied Mathematics and Statistics

Universidad Polit6cnica de Madrid

Spain

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555-0001

May 1999

Prepared as part of

The Agreement on Research Participation and Technical Exchange

under the International Code Application and Maintenance Program (CAMP)

Published by

U.S. Nuclear Regulatory Commission

ABSTRACT

Five Marviken Tests are modelled using TRAC-BF1. The code simulations are

compared to Marviken data so as to analyse the capacity of TRAC-BF1 to reproduce

subcooled and saturated blowdowns under critical conditions. Consequently, the

critical flow model included in TRAC-BFI will be validated.

Owing to the quasi-steady flow arising through the waste pipe, conserved

quantities are useful to check the results accuracy. The influence of mesh refinement is

also analysed.

Conclusions indicate that critical conditions must be imposed at the adequate

sections to assure the calculations admissibility. However, the critical flow model

introduces intrinsic errors that cannot be eliminated by means of mesh refinement.

iii

TABLE OF CONTENTS

Page

A bstract .......................................................... iii

Executive Summary ...................................... xi

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

1.1 Calculation of critical conditions .... 2

1.2 TRAC-BF1 critical flow model ...... 4

2. EXPERIMENTS DESCRIPTION ............... 9

3. CODE INPUT MODEL DESCRIPTION ..... 11

3.1 Components and boundary

conditions ................................ 11

3.2 Nodalization .................................. 11

3.3 Initial conditions ............................ 12

4. RESULTS .................................................. 17

5. RUN STATISTICS ...................................... 23

6. CONCLUDING REMARKS ........................ . 24

7. REFERENCES ........................................... 26

FIG URES ......................................................... 27

V
LIST OF FIGURES Pa&.

FIGURE 1: Analytical pressure profiles at convergent nozzles ........ 28

FIGURE 2:Comparison between analytical and numerical pressure profiles 28

FIGURE 3: Weight factor used in the transition zone ................... 29

FIGURE 4: Basic computational cell upstream of the critical section ..... 29

FIGURE 5: Initial temperature profiles at the vessel ................................. 29

FIGURE 6: Vessel and pipe nodalizations ................................................ 30

FIGURE 7: Steam dome pressure evolution (Test 15) ............................. 31

FIGURE 8: Idem. (Test 21) ..................................................................... 31

FIGURE 9: Idem. (Test 24) ..................................................................... 32

FIGURE 10: Idem. (Test 10) ................................................................... 32

FIGURE 11: Idem. (Test 23) ................................................................... 33

FIGURE 12: Mass flow rate evolution (Test 15) ...................................... 34

FIGURE 13: Idem. (Test 21) ................................................................... 34

FIGURE 14: Idem. (Test 24) ................................................................... 35

FIGURE 15: Idem . (Test 10) ..................................... , ................................. 35

FIGURE 16: Idem. (Test 23) ................................................................... 36

FIGURE 17: Void fraction evolution at last cell (Test 15) ........................ 37

FIGURE 18: Idem (Test 21) .................................................................. 37

FIGURE 19: Idem (Test 24) .................................................................. 38

FIGURE 20: Idem (Test 10) .................................................................. 38

FIGURE 21: Idem (Test 23) .................................................................. 39

FIGURE 22: Discharge pipe pressure profiles (4 cells, Test 15) ............... 40

FIGURE 23: Discharge pipe pressure profiles (8 cells, Test 15) ............... 40

FIGURE 24: Steam dome pressure evolution (Test 15, ICHOKE=O) ..... 41

FIGURE 25: Mass flow rate evolution (Test 15, ICHOKE=O) ................ 41

FIGURE 26: Discharge pipe pressure profiles (2 cells, Test 21) ............... 42

FIGURE 27: Discharge pipe pressure profiles (4 cells, Test 21) ............... 42

vi
FIGURE 28: Steam dome pressure evolution (Test 21, ICHOKE=O) ..... 43

FIGURE 29: Mass flow rate evolution (Test 21, ICHOKE=O) ................ 43.3

FIGUJRE 30: Discharge pipe pressure profiles (2 cells, Test 24) ............... 44

FIGURE 31: Discharge pipe pressure profiles (4 cells, Test 24) ............... 44

FIGURE 32: Steam dome pressure evolution (Test 24, ICHOKE=0) ........... 45

FIGURE 33: Mass flow rate evolution (Test 24, ICHOKE=0) ..................... 0

FIGURE 34: Discharge pipe pressure profiles (4 cells, Test 10) ............... 46

FIGURE 35: Discharge pipe pressure profiles (8 cells, Test 10) ............... 46

FIGURE 36: Steam dome pressure evolution (Test 10, ICHOKE=0) ..... 47

FIGURE 37: Mass flow rate evolution (Test 10, ICHOKE=0) ................ 47

FIGURE 38: Discharge pipe pressure profiles (2 cells, Test 23) ................... 41;

FIGURE 39: Discharge pipe pressure profiles (4 cells, Test 23) ................... 43

FIGURE 40: Steam dome pressure evolution (Test 23, ICHOKE=O) ..... 4!)

FIGURE 41: Mass flow rate evolution (Test 23, ICHOKE=O) ................ 4!)

FIGURE 42: Initial dome pressure evolution (Test 15, diverse nodalizations) 50

FIGURE 43: Initial mass flux evolution (Test 15, diverse nodalizations) ........ 50

FIGURE 44: Liquid total pressure along the pipe (Test 15, ICHOKE=I) ...... 51

FIGURE 45: Idem. (Test 15, ICHOKE=0) ............................................. 51

FIGURE 46: Stagnation enthalpy along the pipe (Test 15, ICHOKE=1) ....... 52

FIGURE 47: Idem. (Test 15, ICHOKE=0) ............................................. 52

FIGURE 48: Entropy along the pipe (Test 15, ICHOKE-1) .................... 53

FIGURE 49: Idem (Test 15, ICHOKE=0) ................................................ 53

FIGURE 50: Liquid total pressure along the pipe (Test 21, ICHOKE=I) ...... 54

FIGURE 51: Idem. (Test 21, ICHOKE=0) ............................................... 54

FIGURE 52: Stagnation enthalpy along the pipe (Test 21, ICHOKE=1) ....... 55

FIGURE 53: Idem. (Test 21)ICHOKE=0) ................................................ 55

FIGURE 54: Entropy along the pipe (Test 21, ICHOKE=I) ..................... 56

FIGURE 55: Idem (Test 21, ICHOKE=0) ................................................ 56

FIGURE 56: Liquid total pressure along the pipe (Test 24, ICHOKE=I) ...... 5 7

vii
FIGURE 57: Idem. (Test 24, ICHOKE=0) ............................................. 57

FIGURE 58: Stagnation enthalpy along the pipe (Test 24, ICHOKE=I) ....... 58

FIGURE 59: Idem. (Test 24, ICHOKE=0) ................................................... 58

FIGURE 60: Entropy along the pipe (Test 24, ICHOKE=-I) ..................... 59

FIGURE 61: Idem (Test 24, ICHOKE=0) ................................................ 59

FIGURE 62: Liquid total pressure along the pipe (Test 10, ICHOKE=1) ...... 60

FIGURE 63: Idem. (Test 10, ICHOKE=0) ................................................... 60

FIGURE 64: Stagnation enthalpy along the pipe (Test 10, ICHOKE=1) ....... 61

FIGURE 65: Idem. (Test 10, ICHOKE=0) ............................................. 61

FIGURE 66: Entropy along the pipe (Test 10, ICHOKE=I) ..................... 62

FIGURE 67: Idem (Test 10, ICHOKE=0) ................................................ 62

FIGURE 68: Liquid total pressure along the pipe (Test 23, ICHOKE=I) ...... 63

FIGURE 69: Idem. (Test 23, ICHOKE=0) ............................................. 63

FIGURE 70: Stagnation enthalpy along the pipe (Test 23, ICHOKE=I) ....... 64

FIGURE 71: Idem. (Test 23, ICHOKE=0) ............................................. 64

FIGURE 72: Entropy along the pipe (Test 23, ICHOKE=1) ..................... 65

FIGURE 73: Idem (Test 24, ICHOKE=0) ................................................ 65

FIGURE 74: TRAC execution time vs. real time (Test 15) ....................... 66

FIGURE 75: Time step vs. real time (Test 15) .......................................... 66

viii
LIST OF TABLES Pag.

TABLE 1: TRAC-BF1 critical flow model ................................................ 8

TABLE 2: Characteristic parameters in Marviken Tests ........................... 10

TABLE 3: Typical input data ................................................................... 13

TABLE 4: Marviken 15, run statistics .................................................... 23

ix

EXECUTIVE SUMMARY

With the aim of v-erificating the critical flow model in TRAC-BFI, five

blowdown experiments of the Marviken Test Series are modelled with such a

thermalhydraulic code. The obtained results are compared with Marviken data and the

HEM analytical correlation.

In order to study the maximum range of conditions, aside from two purely

saturated blowdowns (Tests 10 and 23), three experiments presenting initial

subcooled blowdown (Tests 15, 21 and 24) are chosen.

In a convergent nozzle (as those used in Marviken Tests) the critical condition

appears as a turning point of the pressure profile arising at the outlet. However, the

discretization used in the TRAC-BF1 numerical scheme fails to simu[ate this

behaviour and the discretized pressure profiles can reach exterior pressures lower than

the critical one. Consequently, critical conditions must be imposed on the numerical

scheme externally.

In TRAC-BF1 this task is done by the subroutine CHOKE, which ch~ecks the

fulfilment of critical conditions at externally determined sections. In this work the

modelled tests are reproduced both with and without critical conditions imposed at

the exit. The obtained results show the expected behaviour. On the one hand, when

Xi
CHOKE is inactive, the pressure profiles reach improperly the ambient pressure at the

outlet and large errors arise in cells nearest to the pipe end. On the other hand, if

critical pressure is imposed at the exit, the results are more exact. However, intrinsic

errors, induced by CHOKE calculations, are unavoidable.

Experiments with different length to diameter ratios at the exit nozzle (from

0'3 in tests 23 and 24 to 3'6 in test 15), are chosen to study thermal disequilibrium

effects. As a result, it is observed that those effects are not well modelled in TRACBF1 and, in general, critical flow is underestimated for subcooled blowdowns through

short nozzles.

Diverse nozzle nodalizations are tried to study the influence of mesh

refinement in TRAC-BF1 calculations. The cases analysed in this work indicate that

increasing the number of cells improves the result. However, when subroutine

CHOKE is active, the accuracy of global results is limited by inherent CHOKE errors

in spite of mesh refinement.

In Marviken Tests, after a few seconds from the start, steady flow through the

pipe can be considered. Therefore, some integral quantities must be conserved along

pipe cells (mass flow rate, total enthalpy, entropy and liquid total pressure). In all

cases studied here those quantities are checked to determine the results accuracy. As

it has been mentioned above, errors accumulate at the pipe end, if CHOKE is inactive.

xii
The general concluding remark of this work points out the need of activating

the subroutine CHOKE at the adequate sections so as to obtain admissible results.

Moreover, excessive mesh refinements do not improve code calculations beyond the

limit imposed by CHOKE errors.

xiii

1. INTRODUCTION

The idea of critical velocity appears when the fluid motion is described by an

hyperbolic system of conservation laws. Such a critical condition holds when the

sound speed of the fluid coincides with the velocity of fluid particles and, a&; a result,

the perturbations of motion variables (velocity and pressure) cannot go upstream.

The discharge of a vessel filled with liquid at high pressure and temperature is

a practical situation where critical conditions can arise (LOCA phenomenon, fuel

injection, ...). Usually, the flow through the nozzle is directly related with the

difference between interior and exterior pressures. However, when the oute:, pressure

falls below the critical value, either the fluid velocity equals the sound speel at some

section or exceeds it. After that, as the information about the exterior pressure cannot

travel upwards to the pipe inlet, the mass flux in the nozzle remains invariable and

does not increase. So, the concept of critical flow can be defined practicdly as the

maximum discharging flow attained for fixed vessel pressure and temperature.

In order to assess the capability of TRAC-BFI code for modellhg critical

flows, five blowdown experiments of the Marviken Test Series have been chosen.

Most of the time the blowdowns are saturated, but three of them also pres;ent initial

stages of subcooled blowdown (tests 15, 21 and 24) and cover a wide range of inlet

conditions. Furthermore, experiments with nozzles of different length to diameter

I
ratio (from 0.3 in tests 23 and 24 to 3.6 in tests 10 and 15), are chosen to analyse the

code efficiency in simulating thermal disequilibrium effects.

The following section gives a brief introduction to critical solutions of

analytical models. After that, the first chapter ends describing the discretized solutions

introduced by the TRAC-BF1 numerical scheme, whose behaviour justifies a critical

module were introduced in the code. The rest of the work is organised as follows:

Chapters 2 and 3 contain respectively the description of the selected experiments and

the corresponding code models. Chapter 4 is dedicated to expose the key results of

the calculations. Some results about the run statistics of the calculations are included

in Chapter 5. Finally, the principal concluding remarks are summed up in Chapter 6.

1.1 Calculation of critical conditions

For the motion through a pipe, the critical condition is set up mathematically

cancelling out the first eigenvalue of the corresponding one-dimensional hyperbolic

system, see, e.g., [1] and [2]. An equivalent condition is obtained when a steady

solution passes through a singular point of the respective system of ordinary

differential equations, [3] and [4]. For instance, if the flow in a convergent nozzle,

through which a pressurised vessel is discharged, is modelled with the Homogeneous

Equilibrium Model (HEM), the pressure profiles along the nozzle adopt the shape

sketched in figure 1. All of these solutions possess a turning point. When such a

2
critical point arises at the outlet section, the corresponding solution i:; critical.

Observe that, either the turning point is smooth with vertical tangent or it is a comer

point. In the first case, the critical point arises in the mixture zone and the

corresponding critical condition is similar to the classical criterion of gas dynamics:

the fluid velocity coincides with the sound speed, (6T / i9p) " 2. In the second case, the

bending point is discontinuous because of the existing discontinuity in the state

equations along the saturation line, so the critical condition reduces to considering

saturated liquid at the exit.

Similar conclusions are obtained for more complex and complete mcodels, see,

e.g., [31 where a general analysis of the problem is developed. However, to take into

account thermal disequilibrium properly, a non-linear integral equation introducing

delays in the generation of vapor must be added to the system of motion equations.

As a consequence of that, the hyperbolic character of the fluid motion equations and

the classical concept of critical condition are lost. In particular, supersaturated liquid

can arise inside of the nozzle because of the delay in vapor generation. When a certain

supersaturation degree is reached, the new phase appears and the mixture evolves

quickly to attain either the saturation state or a metastable state compatible, with the

ambient conditions. In the first case, after the saturated conditions are approached, the

mixture behaves near to equilibrium until critical conditions are reached. Then, if the

exterior pressure is lower than the critical one, the ambient pressure is rapidly attained

under metastable conditions.

3
In order to stress the differences between models, pressure profiles obtained

with the disequilibrium model E.V.U.T. (Equal Velocity Unequal Temperature) are

also sketched and compared to H.E.M. profiles in figure 1. Observe that, the

disequilibrium solutions have not turning points as those arising at equilibrium curves.

In those profiles, critical points are substituted by thin layers where ambient pressures

are reached under metastable conditions. The position of these layers, which

determines the "critical" mass flux in the disequilibrium model, are either the end of

the metastable liquid region or the critical point of an equilibrium curve reached after

the metastable layer inside of the pipe. Such an equilibrium curve is in general over

the one corresponding to the equilibrium model and only appears for pipes with high

length to diameter ratio. As a consequence of that, the "critical" non-equilibrium mass

fluxes are greater than those calculated in the equilibrium model for either high inlet

subcoolings or short nozzles.

1.2 TRAC-BF1 critical flow model

In TRAC-BF1 the six conservation equations of the two-fluid onedimensional model are integrated numerically. The steady solutions of the

corresponding numerical scheme present qualitative behaviour different from that

explained in Section 1.1. To be exact, the numerical scheme does not have critical

solutions as those described above for the equilibrium analytical model. Consequently,

the critical condition must be imposed on the model externally.

4
In order to illustrate this assertion, the discharge through a convergent nozzle,

modelled using the HEM approximation, is discretized following the T7RAC-BF1

numerical scheme (see [5] and [6]). The steady solutions are obtained supposing

constant magnitudes at successive time steps:

p 1AJ,112V,_112 =- pjAj+,,, 2VJ,+, = 9,j 1,...,NV, = (1)

~ =i'",,+( --1 AX+/ 12 ,, _, , l..,s.(2)

APJ+1/2 j- Pj+1 - Ax, /2 j+1/2(v,+1/2 -V-/) ,,N 2

The notation is taken from references [5] and [6]. The parameter 0z is the mass

flow rate, which is a conserved quantity under steady conditions. In this model, p is

the mean density of the mixture, ap, + (1- a)p,, and V is the common v.-locity of

both phases. The discharging duct is divided into N computational cells, where the

inlet and outlet cells are indexed under j=I and j = N, respectively. The fractional

indexes correspond to sections between cells.

Boundary conditions at the entrance and the exit must be included in the

system:

1-

PO = P, +2P 12,V, 2 , (3)

P•N, = P. (4)

where the input data, Po and P°,, are respectively stagnation and exterior pre!;sures.

5
Finally, a relation between the mean density of the mixture and pressure,

which closes the system, is obtained from the equations of state and the hypothesis of

isentropy:

p, = p(P.so). (5)

The following non-linear system can be obtained from equations (1), (2), (3)

and (5):

API/2 = Po +P1 (6)

4A'1/2 AO

AIxJ+1 2 ¢ 2 (AX + bAx,+,)(P +P+,)( 1 1 =4A,.,,. AXp, pA-•.,,2 I p,_,A,_,,2)' j= ,...,N, (7)

where

i=O

The above system is implicit because of the presence of p,+1 at the right members of

Eqs. (6) and (7), which otherwise depend only on magnitudes calculated in lower

order cells. Therefore, the system (6,7) possesses a lower triangular Jacobian matrix,

whose diagonal elements are

J,,2.1/2 I + 42 (PJ,so), (8)

4AI1PO P

'j+1/2.J+1I2 = 1 + 02 (A+ AXj,+I) 1 .l9sp), j=1,...,N. (9)

4AJ+,1,2Ax6pj PjA1 +,2 Pj-IAj-u-21

As the modelized nozzle is convergent and the density is an increasing function of the

pressure, the quantities (8) and (9) are strictly positive. Note that, if the nozzle

6
presents divergent zones, the above elements are also positive for fine nodalizations.

Consequently, the system (6,7) possesses unique solution for every set of parameters,

Po,So and q, including the case of fine nodalizations in divergent channels. The

components of such a solution are the pressure increments between consecutive cells,

being all of them positive for convergent nozzles.

To sum up, if stagnation conditions, Po and so, and mass flux, 0, are given,

pressure profiles as those sketched in figure 2 are obtained from equations (1), (2), (3)

and (5). Two typical H.E.M. pressure profiles are also included in Fig. 2, a;o that the

different behaviour of the two types of solutions is emphasized. Observe that, unlike

the H.E.M. solutions, the numerical ones cannot present critical behaviour, i.e., they

neither possess bending points nor present maximum existence intervals. Furthermore,

the parameter 0 and the pressure at the exit cell, PN+I, are directly related and, as a

result, the mass flow rate is determined by the exterior pressure through thc boundary

condition (4).

The numerically -calculated mass flow rate, like that obtained analytically,

grows as the exit pressure decreases. However, there are not critical limitations to

pressures at the outlet in the numerical scheme, because the pressure pro:51les fit for

reaching the ambient pressure whatever it is. Therefore, if the exterior pressure is

under the critical value, the mass fluxes are overestimated by the numerical scheme of

TRAC-BF1.

7
.Consequently, in order to improve the TRAC-BFI calculations, a subroutine

of critical flow (CHOKE) is included in the code. At each time step, this subroutine

checks whether the fluid velocity goes beyond the critical value. The sections of

checking are selected externally activating the corresponding logical variable

ICHOKE at the input data deck. The critical models used in TRAC-BF1 and their

range of applicability are described in Table 1. The auxiliary figures 3 and 4 contain,

respectively, the functional dependence on void fraction of a weight factor used in the

range 0.01 < a < 0.1 and the computational cell upstream the critical section.

Table I

TRAC-BFI critical flow model

Void fraction at the critical section Critical Velocity

05a<0.0l

0.01: < 0r<.1

0.1:< a < 0.999999

0.999999 < I<1

-asK=2(P,- Ps(T) + AP(as)) + /V•2J) 2 ,

112

-aH(a) =4 I

-a,. =i)

&,,it = mar(a,,aH (0))

acnt = wa, (0. 1) + (l - w)U,,

(W plotted in Fig. 3)

a,, =a.(a)

a,,,, = av

see Fig. 4, AP given by the ALl correlation,

1

7Jy 18].

VF4 V,.,I(I+F4 )

(mimture. depending on a)

(pure steam. a=])

8
2. EXPERIMENTS DESCRIPTION

The experiments modelled in this work are extracted from the Series of

Marviken Full Scale Critical Flow Tests. Those experiments were peribrmed at

Marviken Power Station (Sweden) and sponsored by a multinational consottium. The

United States Nuclear Regulatory Commission (USNRC) participated in such a

consortium and includes part of the data output in the validation matrix of its code

assessment programs (ICAP, CAMP).

The principal characteristics of the experimental device used in these tests are

summed up in Volumes 1 to 8 of [9]. Here, only the relevant parameters for the

performed calculations are enumerated. Essentially, the experimental facility, which is

reactor-sized, consists of: a pressurised vessel containing steam and water at high

temperature, an exhaust pipe placed at the vessel bottom and a convergent nozzle

ending the pipe. Each experiment initiates when the nozzle is suddenly opc:ned, after

that the pressures, temperatures and densities at various sections are measured during

the subsequent blowdown.

In Marviken two type of experiments are done: totally saturated blowdowns

and initially subcooled blowdowns. In the first case, before the experiments were

initiated, the water was heated until the saturation temperature was uniformiy reached

in all the sections of the vessel. In the second case, initially the vessel presented

9
subcooled temperatures at the bottom whereas the conditions at the dome are

saturated. Furthermore, various exit nozzles with length to diameter ratios under 4 are

proven.

For this work five representative experiments of the Marviken programme are

chosen: three sucooled tests (experiments 15, 21 and 24) and two saturated ones

(tests 10 and 23). These experiments are performed with nozzles which cover widely

the range of length to diameter ratios used in Marviken tests (from 0'3 in tests 23 and

24 to 3'6 in test 15). The other relevant parameters corresponding to the chosen

experiments are summed up in table 2 and figure 5.

Table 2

Characteristic parameters in Marviken Tests

Test No. Test 15 Test 21 Test 24

Mass of water (Mg.) 327 330 330

Mass of steam (Mg.) 0.6 0.6 0.63

Mass of saturated water (Mg.) 73.1 48.9 39.4

Vessel initial level (m.) 19.93 19.95 19.88

Initial steam dome pressure (MPa.) 5.04 4.94 4.96

Nozzle length to diameter ratio 3.6 1.5 0.3

Test 10

279

1.8

208

17.66

4.97

3.1

Test 23

314

-0.65

310.7

19.85

4.96

0.3

10
3. CODE INPUT MODEL DESCRIPTON

A typical input data deck used for the Marviken simulations is shown in Table

3.

3.1 Components and boundary conditions

The vessel is modelled with a PIPE component as well as the discharge pipe

together with the nozzle, which are included in a second PIPE component. In order to

simulate the boundary conditions, two components are used: a FILL comp:nent with

zero velocities modelling the closed end of the vessel, and a constant pressure

BREAK component for modelling the break.

3.2 Nodalization

Firstly, the basic configuration defined in all the tests is being described. The

PIPE component modelling the vessel is the same one in all the cases and it is shown

in figure 6. This component is divided into 27 cells of different length (fi'om .37 to

1.42m). The lengths of cells 5 and 6 differ in each test in order to locate the initial

liquid level in the vessel on the common face to both cells (see figure 6).

The discharge pipe is always modelled with the first 17 cells of the second

PIPE component with a minimum length of .025m and a maximum of 0.57m. (see

11
figure 6). The number of cells modelling the nozzle differs depending on the test (2

for short nozzles and 4 for the longest ones). Moreover, in order to analyse the code

sensitivity to such a parameter, nozzle nodalizations both finer and coarser than the

basic one are considered (see Fig. 6 for details).

3.3 Initial conditions

The initial pressure imposed in each cell of the PIPE components corresponds

to the hydrostatic pressure calculated from the pressure at the steam dome. The liquid

temperature profile is the experimental one (see figure 5) and the vapor temperature is

the saturation one corresponding to the pressure at the steam dome. The void fraction

is either 1 or 0 for the cells located respectively above or below the initial liquid level.

The initial velocities are lx10 5 m/s.

The blowdown is simulated at time zero by setting the BREAK pressure to the

value 0.1 MPa. The time step is free with an initial value of 1xIO 5s.

12
Table 3

Typical input data

= MARVIKEN BLOWDOWN TEST 15 ON

** IEOS NTRACE IST NEXTR MASPR ICONT

OPTIONS 0 5 0 0 3 0

CHECKOUT 20000 0 0 0 00 0

** DSTEP, START TIMET

MAINOI -1 1.50

** STDYST TRANSI NCOMP NIUN WATERPAK

MAIN02 1 0 4 3 0

** CONVER EPSO

MAIN03 1.OE-04

** ITER oITMAX

MAIN04 8

* CONTROL SYS

MAIN05 0

** COMPONENTS

EPSI EPSS IMPCON

1.OE-05 1.OE-02 0

IITMAX COURANT NTRX NLEAKP NAXN NDMPTR

0 100. 0 0 0 0

BORON IAIR NROT NUMMP LEVI

0 0 0 0 0

LIST ORDER CARDS

COMPLISTO0 1 2 4 3

* TIME STEP DATA

* DTMIN DTMAX

* EDINT GRFINT

TIMESTEPO01 1.E-4 .01

TIMESTEP012 1.7 .5

TEND

DMPINT

10.

10.

RTWFP

SEDINT

10.0

200.

TIMESTEP021 1.E-4

TIMESTEP022 2.5

TIMESTEP031 1.E-4

TIMESTEP032 2. $

$

.01 50.

.5 10.

10.

1000.

.01 110. 10.

.1 45. 1000.

$$$$$$ PIPE HEADER CARD

PIPE01000 1 " VESSEL PIPE

$$$$$$ PIPE PARAMETER CARD

* NCELLS NODES JUNI JUN2 MAT

PIPE01010 27 0 1 2 6

* ICHF IPVHT RADIN TH

PIPE01011 -1 0 2.5265E+00 1.62560000E-03

* HOUTL HOUTV TOUTL TOUTV

PIPED0112 .OOOOOOOOE+00 .00000000E+00 .OOOOOOOOE+02

* mHTS IWT

PIPE01050 0 0

***** DX

PIPE01DX0 1.42000E+00 .78500E+00 .83000E+00 .97200E

PIPEOIDXI .36900E+00 .96900E+00 .95100E+00 R02.975

PIPEO1DX2 .97700E+00 .96800E+00 R03.97000E+00 .974

PIPEOIDX3 1.94000E+00 .97000E+00 .97400E+00 .96800E

PIPEOIDX4 .96400E+00 .45500E+00 .51500E+00 .37000E4

.OOOOOOOOE+02

+00 .61300E+00

00E+00

00E+00 .98200E+00

+00 .98400E+00

00 .74000E+00 E

13
Table 3 (Continued)

***** VOL

PIPEO0VOLO 2.5090E+00 1.3870E+00 1.467E+00 9.499E

PIPEOVOL1 .78970E+01 2.0737E+01 2.0352E+01 R02

PIPEOIVOL2 2.0909E+01 2.0716E+01 R03 2.0759E+01 2

PIPE01VOL3 4.1518E+01 2.0759E+01 2.0844E+01 2.0716E

PIPEO1VOL4 2.0630E+01 9.737E+00 9.960E+00 2.895E+O(

***** FA

PIPEO1FAO R04 1.767E+00 R21 2.14008E+01 1.7349E+01

PIPEO0FAl 1.327E+00 .444146E+00 E

***** FKLOS

PIPEO1FKLOSO R28 .OOOOOOOE+OO E

***** RKLOS

PIPEO1RKLOSO R28 .OOOOOOOOE+OO E

***** GRAV

PIPEO1GRAVO R28 -1.00000000E+OO E

***** H

PIPEO1HDO R28 0. E

***** EPSD

PIPEO1EPSDO R28 .OOOODOOOE+OO E

***** ICHOKE

PIPEO1ICHOKEO R28 0 E

***** ICCFL

PIPE01ICCFLO R28 0 E

***** ALP

PIPEO1ALPO R05 1.OE+00 R22 0.OOOOE+00 E

***** VL

PIPEO1VLO R06 1.OOOE-05 R03 .6500E+00 .6400E+0(

PIPEO1VLI R03 .6500E+00 .6400E+00 R08 .6200E+4

PIPEO1VL2 R03 .6100E+00 .7600E+00 9.8900E+00 2.

***** VV

.+00 1.3119E+01

.0866E+01

.0844E+01 2.1016E+01

.401 2.1058E+01

.626E+00 E

)0

~55E+01 E

PIPEO1VV0 P28 1.OOE-05 E

***** TL

PIPEO0TLO ROS 5.34250E+02

PIPEO1TL1 5.33150E+02 5.

PIPEO1TL2 5.28650E+02 5,

PIPE01TL3 5.08450E+02 5,

PIPEO1TLA 5.08850E+02 5,

PIPEOITL5 5.06250E+02 5,

***** TV

PIPEO1TVO R27 5.3516E+02 E

***** p

PIPEOIPO R05 4.85000E+06 4

PIPEO0PI 4.86230E+06 4.8

PIPEO1P2 4.87710E+06 4.8

PIPEO1P3 4.89510E+06 4.9

PIPEO1P4 4.91450E+06 4.9

PIPEO1P5 4.92600E+06 4.8

****** ILEV1

*PIPE01640 R06 0 1 R23 0 E

5.33850E+02 5.3425E+02 5.34850E+02

.33650E+02 5.3365E+02 5.34150E+02

.13850E+02 5.0815E+02 5.08750E+02

.07450E+02 5.0835E+02 5.08550E+02

.06450E+02 5.0695E+02 5.06650E+02

.05950E+02 5.0565E+02 E

.85130E+06 4.8550E+06 4.8586E+06

6600E+06 4.8697E+06 4.8734E+06

8100E+06 4.8849E+06 4.8888E+06

0290E+06 4.9067E+06 4.9106E+06

1850E+06 4.9224E+06 4.9242E+06

8750E+06 4.57 1OE+06 E

14
Table 3 (Continued)

****** ALPA

*P1PE01650 R06

****** ALPB

*PIPE01660 R06

****** DZLVI

*PIPE0 1670 R06

******VLEVI

*PIPE01680 R06

$

I.E+00 I.E+00 R23 0.E+00 E

I.E+00 0.E+00 R23 0.E+00 E

0.E+00 0.810E+00 R23 O.E+O0 E

0.E+00 0.OE+00 R23 0.E+00 E

5

$5$$55 PIPE HEADER CARD

PIPE02000 2" DISCHARGE PIPE

5$$$$$ PIPE PARAMETER CARD

* NCELLS NODES JUNI JUN2 MAT

PIPE02010 22 0 2 3 6

* IC-F IPVHT RADIN TH

PIPE02011 -1 0 .3760E+00 1.62560000E-03

* HOUrL HOUTV TOUTL TOUTV

PIPE02012 .00000000E+00 .OOOOOOOOE+00 2.98000000E+02 2.98000000E+02

* HITS IWT

PIPE02050 0 0

***** DX

PIPE02DXO .5700E+00 R02.0600E+00 R04.4950E+00 R02 .0600E+00

PIPE02DXI R04.44450E+00.2750E+OO R02.350E+00.0250E+00.156E+00

PIPE02DX2 R04.450E+00 E

***** VOL

PIPE02VOLO .25320E+00 R02 2.66500E-02 R04.21990E+00 2.6650E-02

PIPE02VOL1 2.7653E-02 R04 .21240E+00 .12670E+00 R02 .1555E+00

PIPE02VOL2 1.5168E-02 6.6139E-02 .1323E+00 R03.08884E+OO E

***** FA

PIPE02FAO R09 .444146E+00 R05.4780E+00 R04.444146E+00 .4041E+00

PIPE02FA1 R04.19635E+00 E

***** FKLOS

PIPE02FKLOSO R23 .OOOOOOOOE+00 E

***** RKLOS

PIPE02RKLOSO R23 .OOOOOOOOE+O0 E

***** GRAV

PIPE02GRAVO R23 -1.00000000E+O0 E

***** HD

PIPE02HDO R23 0. E

***** EPSD

PIPE02EPSDO R23 .OOOOOOOOE+00 E

***** ICHOKE

PIPE02ICHOKEO 1 0 R15 0 R05 0 1 E

***** ICCFL

PIPE021CCFLO R23 0 E

***** ALP

PIPE02ALPO R22 0.0000E+00 E

15
Table 3 (Continued)

***** VL

PIPE02VLO

PIPE02VLI

PlPE02VL2

PIPE02VL3

***VV

2.955E+01 2.963E+01 2.972E+01 2

2.970E+01 2.968E+01 2.967E+0-1 2

R02 2.754E+01 2.752E+01 2.75113+01

.973E+01 2.972E-I01

.966E+01

R05 2.9 60E+01

3.252E+01 R04 66.93E+00 E

PIPE02WO R23 1.OOOE-05 E

***** TL

PIPE02TLO 5.0728E+02 5.

PIPE02TLI 5.0868E+02 5.(

PIPE02TL2 5.0773E+02 5.(

PIPE02TL3 5.0660E+02 5.(

PIPE02TL4 R07 5.0663E+02

***** TV

PIPE02TVO R22 5.3516E+02 E

***** p

PIPE02PO 4.5713E+06 4.5w

PIPE02P1 4.5741E+06 4.5

PIPE02P2 4.6293E+06 4.6:

PIPE02P3 4.5880E+06 4.5:

PIPE02P4 4.5920E+06 4.5

PIPE02P5 3.1158E+06 3.1 $

)908E+02

)833E+02

)755E+02

)35E+02

E

5.0923E+02

5.0797E+02

5.0724E+02

5.0638E+02

4.5694E+06

4.5788E+06

4.6333E+06

4.5905E+06

3.1 122E+06

5.0903E-f02

5.0778E+02

5.0692E+02

4.5716E+06

4.5793E+06

4.6353E+06

4.59 19E+06

3.1 140E4-06

694E+06

766E+06

31 IE+06

891E+06

180E+06

176E+06 E

$

$$$$$$ BREAK HEADER CARD

BREAK03000 3 " BLOWDOWN BREAK

* JUN1 IBROP NBTB ISAT ICOMT

BREAK03010 3 0 0 0 0

* DXIN VOLIN ALPIN TIN

BREAK03011 .45000000E+00 .0884E+00 1.00O00000E+00 3.730000E+02

* PIN,

BREAK03012 . 10000000E+06 $

$$$$$$ FILL HEADER CARD

FILLO4000 4 "INLET FILL

* JUNI IFTY IFTR NFrX ICOMT

FILLJO4010 1 1 0 0 0

* DXIN VOLIN ALPIN VIN

FILL04011 1.4200000E+00 2.50900E+00 1.0000000OE+00 .0000000+00

* TIN PIN BORCIN

CHECKOUT 20000 0 0 00 0 7

FILL04012 5.3516000E+02 4.85000000E+06

16
4. RESULTS

The results obtained in the performed calculations are summarized in figures 7

to 71. In a first group (Figs. 7 to 11), the evolution of vessel pressure is represented

for the five analysed experiments. The figures from 12 to 16 contain the

corresponding evolutions of mass flow rate. In these graphs, experimental data are

compared with TRAC-BF1 results obtained using the basic nodalizations (see section

3) and with the subroutine CHOKE both active and inactive at the exit. Moreover,

theoretical critical mass fluxes, calculated using the HEM model for experimental

stagnation conditions, are included in the second group of figures.

When critical conditions are imposed at the exit (ICHOKE=I), the obtained

results are acceptable. However, the calculated mass flow rates are under the

experimental values. Such an underestimate is specially noticeable in tests 23 and 24

and during the subcooled stages of tests 15 and 21, where the HEM correlation gives

the maximum underestimate too. The main reason for this behaviour is that thermal

disequilibrium, that is of great importance in subcooled blowdowns and discharges

through short nozzles, is poorly evaluated by TRAC-BF1 and neglected by the HEM

correlation.

In order to confirm the previous observations, the evolutions of the calculated

void fractions at the exit cell are plotted in figures 17 to 21. The initial subcooled

17
stages of tests 15, 21 and 24 are characterized by void fractions less than 0.1 in the

curves corresponding to ICHOKE=I. In those regions, subroutine CHOKE corrects

the HEM critical model, used in the remaining regimes, with the Alamgir, Lienhard

and Jones (ALJ) correlation, see [7] and [8]. To be exact, a weighted average

between the result corrected with the above correlation and the HEM critical velocity

corresponding to ca=0.1 is taken in the transition zone (0.01< a<0.1, table 1). The ALJ

correlation could introduce essential errors in the calculations, because it was

developed using data corresponding to very rapid depressurizations (greater than 400

MPa/s). However, for subcooled blowdowns, the steady flow through the discharging

pipe usually implies pressure undershoots reached at the pipe end after a slow

depressurization (less than 300 MPa/s. in the tests modelled here).

On the other hand, note that the void fraction at the critical node is greater

than 0.1 during all the test 23 and the latter stages of the test 24. It means that the

HEM correlation is being used by CHOKE. As the nozzles employed in these tests are

very short, there are foreseeable thermal disequilibria which have not been taken into

account.

In order to compare the results obtained when subroutine CHOKE is either

active (ICHOKE=I) or inactive (ICHOKE=0), calculations performed with

ICHOKE=0 are also included in the figures from 7 to 21. As a general rule, the mass

flow rates are overestimated if critical conditions are not imposed externally.

18
Explanation of this behaviour has been given in section 1.2: the pressur,,- profiles

obtained with the TRAC-BF1 numerical scheme adapt to reach the exterior pressure,

even if it is subcritical. Note, for instance, the excessive values attained by the exit

void fraction when CHOKE is inactive. Consequently, calculated pressure gradients

-and mass fluxes are greater than the adequate critical values.

It has been mentioned (section 1.2) that TRAC-13F1 models cannot attain a

critical behaviour in a natural way, so the subroutine CHOKE is needed. :However,

refining the mesh near the critical section may apparently improve the results, even if

CHOKE is not active. To verify this assertion in the cases analysed here, some

calculations have been performed with different nozzle refinements and ICHOKE=0.

The results are summarized in the figures from 22 to 41, that are grouped in series of

four corresponding to the five modelled tests. Pressure profiles along the discharging

nozzles, calculated with CHOKE both active and inactive, are plotted for various time

steps and using two different nodalizations in the two leading figures of each group.

The two last figures of each set contain respectively the evolutions of the steam dome

pressure and the mass flow rate calculated with ICHOKE=0 for the different pipe

nodalizations described in figure 6. Calculations performed with ICHOKE=1 have

also been done, but in such a case the magnitude evolutions hardly vary with

nodalization and the corresponding curves have not been included. However, in order

to check the influence of subroutine CHOKE, results corresponding to CHOKE both

19
active and inactive are compared in figures 42 and 43 for the finest nodalizations of

Test 15.

As it is expected, the pressure profiles along the nozzle reach the exterior

pressure (0.1 Mpa) when they are calculated with ICHOKE=O. While restricting the

exit velocities with the subroutine CHOKE implies that pressure cannot fall under the

corresponding limit pressure. Moreover, as it has been anticipated in section 1.2, the

mass fluxes calculated without critical limitations are generally greater than the

experimental ones.

It is also observed that, when CHOKE is inactive, the finer is the nozzle

nodalization the smaller is the calculated mass flux through the pipe. To explain this

behaviour, first observe that the second member of Eq. (7) is very small when the

corresponding cells are filled with subcooled liquid. Consequently, the pressure jump

arises basically at the cells nearest to the exit and after the saturated conditions are

reached. Thus refining the mesh implies bringing near the outlet the point where the

saturation pressure is reached the first time. As a consequence of that, the subcooled

mass flow rate drops, approaching from above the result obtained with the HEM

correlation (saturated liquid at the exit, see section 1.1). Remember that HEM

neglects thermal disequilibrium and, as a result, underestimates the critical mass flow

rates under subcooled conditions. So, when the mesh is fine enough, calculated mass

20
fluxes can be occasionally under the experimental data (see subcooled stages of the

tests 15, 21 and 24, Figs. 25, 29 and 33).

On the other hand, for saturated blowdowns, if CHOKE is inactive, errors are

distributed along the discharging nozzle and the mass flux is always overestimated

independently of mesh refinement. However, if the nozzle nodalization is refined, the

erroneous pressure gradients are accumulated at the exit, lowering the mass flow rates

and improving the results.

In any case, there is a "natural" mass flux limitation when CHOKE :is inactive.

Such a restraint is weaker than the H.E.M. critical condition, but approaches it from

above when the mesh is refined. Therefore, for fine nodalizations, this meshdependent limit must be taken into account when critical conditions differernt from the

H.E.M. correlation are employed. Observe, for instance, in figures 42 and 43, the

earliest stages of Marviken Test 15 calculated with fine nodalizations at the exit. Note

that, activating CHOKE has no influence in the results,, because the numerical

restraint to the mass flux is stronger than that imposed by the subroutine CHOKE

(which in this case corresponds to the A.L.J. correlation, [71 and [81).

Finally, in order to check the results accuracy, the evolution of some

conserved quantities are calculated at given nodes along the pipe. The underlying idea

is that pipe flow can be considered frictionless and stationary and, as a result, there is

21
some quantities that must be uniformly conserved along the pipe: Mass flow rate,

entropy and stagnation enthalpy of the mixture and total pressure in the liquid phase.

Actually entropy grows when both slip and mass transfer between phases exist,

however the slip between phases is very small in the cases analysed here.

The results relative to each experiment are presented in six consecutive figures

(see Figs. from 44 to 73). In each graph, the evolution of a conserved quantity at four

different nodes is plotted (mass flow rate is excluded, because it hardly varies in any

of the performed calculations). Three figures of each group show calculations done

with ICHOKE=I, the remaining three are obtained with ICHOKE=O. In all cases,

apart from two intermediate cells, the inlet and outlet cells are taken as checking

nodes.

The results indicate the acceptable accuracy of the code when CHOKE is

active. The small drop of stagnation enthalpy and entropy at the exit cells could be

produced by the errors originated in the subroutine CHOKE and the TRAC-BF1

inability to simulate a critical behaviour.

However, if CHOKE is inactive, a considerable increase in the liquid total

pressure and appreciable decreases in stagnation enthalpy and entropy are observed at

the outermost cells. Such variations in quantities which must be conserved denote the

22
inaccuracy of the corresponding results, which actually violate the condition of

nondecreasing entropy.

5. RUN STATISTICS

The runs are performed on a SUN station 4, model 100 computer with TRACBFI/MOD1 version NRC 0.4. The run statistics for test 15 are given on table 4, and

figures 74 and 75 show typical plots of the Courant limited time step and CPU time

versus real time. It is shown that either activating CHOKE or not hardly has influenee

in the computational cost. However, it is observed that the mean time step

corresponding to CHOKE=1 is appreciably longer than the one obtained for

CHOKE=0. Statistics corresponding to the rest of the tests are very similar and are

not included for the sake of brevity.

Table 4

Marviken 15, run statistics

ICHOKE 0 1

Real time (s) 62 82

Time step number 6392 8364

Mean time step .082 .144

CPU time (s) 2.912 3.162

CPU time/real time .047 .039

23
6. CONCLUDING REMARKS

Five blowdown experiments of the Marviken Test Series have been modelled

with the TRAC-BF1 thermalhydraulic code. Three of them present an initial stage of

subcooled blowdown, the remaining two cases are totally saturated blowdowns.

The general conclusions obtained from the comparative study between the

code results, the experimental data and the HEM correlation are summarized below:

First, provided that the TRAC-BF1 numerical scheme is unable to reproduce

critical solutions in a natural way, an externally imposed critical condition is needed.

In TRAC-BFI, such a condition is supplied by the subroutine CHOKE, developed on

the basis of HEM correlation and other semiempirical models. These models can

introduce essential errors in TRAC-BF1 calculations, which are, however, acceptable

enough when CHOKE is active.

Second, both the analytical model discretized in TRAC-BF1 and the CHOKE

critical correlation fail to reproduce the thermal disequilibrium arising in the transition

from monophasic liquid to boiling mixture. Therefore, the critical mass flow rates are

underestimated in subcooled blowdowns and discharges through very short nozzles.

24
Third, when the subroutine CHOKE is not active, the pressure profiles can fall

under subcritical pressures at the exit. Therefore, if the exterior pressure is subcritical,

TRAC-BFI generally overestimates the pressure gradients and the mass fluxes at the

nozzle. The previous effect can be balanced by the code inability to model thermal

disequilibrium and, as a result, the calculated mass fluxes are occasionally under the

experimental data specially for subcooled blowdowns.

Four, provided that critical conditions are not imposed, refining the mesh near

the critical section could apparently improve the results. However, owing* to the

improper pressure drop at the exit, such an improvement is very limited for saturated

blowdowns. On the other hand, there is a natural TRAC restriction to the calculated

mass flux, even if CHOKE is inactive. Such a limitation is mesh dependent and must

be taken into account when critical conditions weaker than H.E.M. conrelation are

used.

Five, the verification along the pipe of some conserved quantities shows

clearly the erroneous behaviour of the code when the ambient pressure i, subcritical

and CHOKE is inactive. The computational results actually violate the condition of

nondecreasing entropy. Errors are concentrated at the cells nearest to the critical

section, this suggests that in more complex installations errors could propagate after

the critical section if CHOKE is not adequately activated.

25
7. REFERENCES

1. Trapp J. A., Ransom V.H., 1982. A choked-flow calculation criterion for

nonhomogeneous, nonequilibrium, two-phase flows. Int. J. Multiphase flow 8,

No.6, 669-681.

2. Sani S.M., Duong T., 1989 A transient model for predicting nonhomogeneous

critical two-phase flows. Nuclear Technology 85, 98-108.

3. Bilicki Z., Dafermos C., Kestin J., Majda G., Zeng D.L., 1987. Trajectories and

singular points in steady-state models of two-phase flows. Int. J. Multiphase flow

13, No,4,511-533.

4. Bilicki Z., Kestin J.,1990. Physical aspects of the relaxation model in two-phase

flow. Proc. R. Soc. Lond. A 428, 379-397.

5. TRAC-BF1/MODI: An Advanced Best-Estimate Computer Program for BWR

Accident Analysis. NUREG/CR-4356, EGG-2626, 1992.

6. TRAC-BF1I/MODI: Models and Correlations. NUREG/CR-4391, EGG-2680,

1992.

7. Alamgir Md., Lienhard J.H., 1981. Correlation of Pressure Undershoot During

Hot-Water Despressurization. ASME J. Heat Transfer 103, 52-55.

8. Jones, O.C., 1980. Flashing Inception in Flowing Liquids, ASME J. Heat Transfer

102, 439-444.

9. EPRI Final Report NP-2370, 1982. The Marviken Full Scale Critical Flow Tests.

Volumes 1 to 35.

26
FIGURES

27
Pd

P sd 

.........

Psn 5.A, P1,

I 

I

o 

x

Figure 1. Analytical pressure profiles at convergent nozzles

Pd

-." 2 2 2 H. .M. C oeL ion

N tn er: le " K" " Ak

I I

I I,

% t, I

%

% Pa

Xn

Figure 2. Comparison between analytical and numerical pressure profiles

28
Basic computational cell upstream

.Weight factor used in the transition zone of the critical section

~10

w A Vu -A~Vt

0 . . . . . . .. ... . . .

001 002 003 004 005 006 007 008 009 010

---- Figure3 _-Figure-4.

Initial temperature profiles at the vessel-

... +. i . fl~ . -

tA.U~

-- - - - 9.0

(Di~o

0.0

I I I + : - I., I I I I

Test 21 ,24: ,'

Tt 1

L--i .-- - -- - ----. 

.-. Test 10,23 - I

L - I1 I I 

-I -

-I~ --- -I

-I--

-I- ---

1.

-. I

5

1

.1 2

----I I

I I

I - -- I

*1 _ _ '- I

i I * 245 I 255

235- "+245 255

Temperature (Celsius)

Figure 5

265

29
Vessel and pipe nodalizations

5.22m. , 0.780 a

1.5. 0.752.

a 1.A2 0.57

VES.E85 2 0.06

3 0.83 3 0.06

0.972 PIPE 4 0.495 s ee table below "itkia level s 0.495

.9see table below cT--o is to 24) 0.495

70.99 s 0.495

1 0.951 2initiallevel a 0.06 , 0.-975 (T"-d t0) 0.06

10 0.975 10 0.4445

t t 0.977 11t 0.4445

12 0.96 12 0.4445

13 0.97 13I 0.4445

14 0.97 4 0.275

Is 0.97 is 0.35

i6 0.974 16 0.35

7 0o.982 17 0.02

is 1.94 ,

19 0.97 NOZZLE0 20 0.974 1.

21 0.968

a2 0.984 * u.N

23 0.964 ' 0.5 ..

24 0.55 0.752 m

20.37

Nozzle Nodalizations

Lengths of vessel cells 5 and 6

Test L5(m) L6(m)

10 .613 .369

15 .613 .369

21 .593 .389

23 .693 .289

24 .643 .339

Test N L18(m) L18+I1(I:1...N) (m)

15 2 .156 .90

*4 .156 .45

8 .156 .275

21 2 .225 .365

*4 .225 .1825

8 .225 .09125

23,24 *1 .225 .166

3 .1125 L19=.1125

I__ L20,L21=.083

10 2 .156 .7946

*4 .156 .3973

8 .156 .19865

N--nurnber of constant section cells in the nozzle

* Basic configuration

Figure 6

30
Marviken 15

Steam dome pressure evolution

5

4

3

P (MPa)

2

1

0 0 10 20 30 40 50 60 70

t (s)

Figure 7

Marviken 21

Steam dome pressure evolution

P (MPa)

5

4

3

2

1

0

0 15 30 45 60 75

t (s)

90

Figure 8

31
Marviken 24

Steam dome pressure evolution

5

4

P(MPa)

3

2

0 20 40 60

t (s)

Figure 9

Marviken 10

Steam dome pressure evolution

80

5

4

3

P(MPa)

2

1

0

0 20 40 60

t (s)

80

Figure 10

32
Marviken 23

Steam dome presssure evolution

5

4

P (MPa) 3

2

1

0 10 20 30 "40 50 60 70 80

t (s)

Figure 11

33
Marviken 15

Mass flow rate evolution

10

12000

10000

8000

6000

4000

2000

0

0

t (sec)

Figure 12

Marviken 21

Mass flow rate evolution

10

12000

10000

8000

6000

4000

2000

0

0 15 30 45 60 75

t (s)

90

Figure 13

34
Marviken 24

Mass flow rate evolution

14000

11200

8400

5600

.-- I

CDI

2800

0

0 20 40 60

t (s)

80

Figure 14

Marviken 10

Mass flow rate evolution

10000

8000

6000

4000

U)

5-

a

2000

0

0 20 40 60

t (s)

Figure 15

80

35
Marviken 23

Mass flow rate evolution

12000

*.Experimental

Trac-bfl (ICH

'--Trac-bfl (ICH - - - Theoretical (I8000

0\

1• 000000

4000 V • . . -. . T ' .

0 0 10 20 30 40 50 60 7

t (s)

Figure 16

36
Marviken 15

'Void fraction evolution at last cell

a

1.0

0.8

0.6

0.4

0.2

0.0

0 10 20 30 40 50 60

t (s)

70

Figure 17

Marviken 21

Void fraction evolution at last cell

1.0

0.8

0.6

Oa

0.4

0.2

0.0

0 15 30 45 60 75

t (s)

Figure 18

90

37
-Marviken 24

fraction -evolution at last cell

--1.0

0.8

0.6

. . . . . . . . . . . T. ac. b 1 (.. .... =1 --- Trac-bfl (ICHOKE=I)

Trac-bl ICOKE=O.,

/

/

/

/

/

/

/

/

//

(X

0.4

0.2

0.0

0 20 40 60

t (s)

Figure 19

Marviken 10

Void fraction evolution at last cell

80

1.0

0.8

0.6

a

0.4

0.2

0.0

0 20 40 60

t(s)

Figure 20

80

38
Marviken 23

Void fraction evolution at last cell

1.0 .......... ,..... .... ... ' ....... ....

I

0.'8 ,\ I

/

0.6

a

0.4

0.2 - Trac-bfl (ICHOKE = "1":

- Trac-bfl (ICHOKE = 6

0.0

0 10 20 30 40 50 60 70 80

t (s)

Figure 21

39
Marviken 15

Discharge pipe pressure profiles (4 cells)

5

4

3

P (MPa)

2

0-

0.2 0.6 1.0 1.4 1.8 2.2 2.6

h (m)

Figure 22

Marviken 15

Discharge pipe pressure profiles (8 cells)

5

4

3

P (MPa)

2/

0

0.2 0.6 1.0 1.4 1.8 2.2 2.6

h (m)

Figure 23

40
Marviken 15

Steam dome pressure evolution (ICHOKE = 0)

6

4

P (MPa)

2

0

0 10 20 30 40 50 60 70

t (s)

Figure 24

Marviken Test 15

Mass flow rate evolution (ICHOKE = 0)

13000

10400

tm

7800

5200

2600

0

0 10 20 30 40 50 60 70

t (s)

Figure 25

41
Marviken 21

Discharge pipe pressure profiles (2 cells)

5

4

3

t-2 S

2

10

10

20

30

40

5o

60 P (MPa)

2

0

0.2 0.6 1.0 1.4 1.8

h (m)

Figure 26

Marviken 21

Discharge pipe pressure profiles (4 cells)

5.0

4.0

3.0

-1

P (MPa)

2.0

1.0

0.0 1-

0.2 0.6 1.0 1.4 1.8

h (m)

Figure 27

42
Marviken 21

Steam dome pressure -evolution (ICHOKE = 0) 5

* Experimental

2 cells 4 4 cells

8 cells

P (MPa)

2 

\ 0

0 15 30 45 60 75 90

t (s)

Figure 28

Marviken 21

Mass flow rate evolution (ICHOKE = 0)

12000

* Experimental

10000 2 cells

4 cells

8000 8 cells 8000

~ 6000

4000

2000

0

0 15 30 45 60 75 90

t (s)

Figure 29

43
Marviken 24

Discharge pipe pressure profiles (2 cells)

5

4

3

-1 10

P (MPa)

2

1

0 L0.2

h (m)

Figure 30

Marviken 24

Discharge pipe pressure profiles (4 cells)

5

4

3 20

30

40

50

P (MPa)

2

1

0

0.2 0.6

h (m)

Figure 31

1.0

44
Marviken 24

Steam dome pressure evolution (ICHOKE = 0)

5

4

P(MPa)

3

2

0 10 20 30 40 50 60 70

t (s)

Figure 32

Marviken 24

Mass flow rate evolution (ICHOKE = 0)

14000

11200

8400

5600

a,

2800

0

0 10 20 30 40 50 60

t (s)

Figure 33

70

45
Marviken 10

Discharge pipe pressure profiles (4 cells)

5

4

3

2

10

20

30

40

50

P (MPa)

2

0

0.2 0.6 1.0 1.4 1.8

h(m)

*Figure 34

Marviken 10

Discharge pipe pressure profiles (8 cells)

5

4

3

P (MPa)

2

1

0

0.2 0.6 1.0 1.4 1.8

h (m)

Figure 35

46
Marviken 10

Steam dome pressure evolution (ICHOKE=O)

-5

4

3

P(MPa)

2

1

0

0 0 20 40 60

t (s)

Figure 36

Marviken 10

Mass flow rate evolution (ICHOKE = 0)

80

10000

8000

6000

4000

(J~

C)

2000

0

0 20 40 60

t (s)

Figure 37

80

47
Marviken 23

Discharge pipe pressure profiles (2 cells)

5

4

3

- - - - - - - - - - - - - - - - - - - - 2

10 --. 20

30 - - - - 40 10

so

------------------------- ý2O

30

P (MPa)

40

I

2

1

ICHOKE -1

ICHOKE-0

so

00.-2 0.6

h (m)

1.0

Figure 38

Marviken 23

Discharge pipe pressure profiles (4 cells)

5

- - - -- -- --- -o-_.

4 -30

2

10

20

30

40

so

3

P (MPa)

2

looo

0 L

0.2 0.6

h (m)

Figure 39

1.0

48
Marviken 23

Steam dome pressure evolution (ICHOKE = 0)

5

4

P (MPa) 3

2

1

12000

8000

0 10 20 30 40 50 60 70

t (s)

Figure 40

Marviken 23

Mass flow rate evolution (ICHOKE = 0)

80

0-1

4000

0

40

t (s)

Figure 41

49
Marviken 15

Initial dome pressure evolution (diverse nodalizations)

5.0

4.5

-P(MPa)

4.0

3.5

0 5 10 15

t (s)

20

Figure 42

Marviken 15

Initial mass flux evolution (diverse nodalizations)

13000

10400

0) 7800

• Experimental

-- - 4 cells (ICHOKE=0)

,---- 8 cells (ICHOKE=0)

4 cells (ICHOKE=1)

8 cells (ICHOKE=1) .......... 

10-...

5200

2600

0 5 10

t (s)

Figure 43

15 20

50
Marviken 15

Liquid total pressure along the pipe (ICHOKE = 1)

8

6

.-

2

0L

0 10. 20 30 40 50 60

t (s)

*70

Figure 44

Marviken 15

Liquid total pressure along the pipe (ICHOKE = (1)

8

6

0-

a7

2

0

0 10 20 30 40 50

t (s)

60

Figure 45

51
Marviken 15

Stagnation enthalpy along the pipe (ICHOKE 1)

1100

1050

1000

950

I900

850

1100

1050

1000

950

0 10 20 30 40 50 60 70

t (s)

Figure 46

Marviken 15

Stagnation enthalpy -along the pipe (ICHOKE = 0)

I

900

850

0 10 20 30 40 50

t (s)

60

Figure 47

52
Marviken 15

3.0

2.8

" 2.6

U) 2.4

2.2

2.0

0 10 20 30 40 50 60 70

t (S)

Figure 48

Marviken 15

Entropy along the pipe (ICHOKE = 0)

3.0

2.8

-" 2.6

• 2.4

2.2

2.0

0 10 20 30 40 50

t (s)

60

Figure 49

53
Marviken 21

Liquid total pressure along the pipe (ICHOKE = 1)

8

6

a:-

2

0

0 15 30 45 60 75

t (s)

90

Figure 50

Marviken 21

Liquid total pressure along the pipe (ICHOKE = 0)

8

6

a- 24

a.-

2

0

0 _- 10 20 30 40 50 60

t (s)

70

Figure 51

54
MarViken 21

Stagnation 'enthalpy talong the pipe (ICHOKE 1)

1100

1000 1S

900

800 L

0 15 30 45 60 75

t(s)

90

Figure 52

Marviken 21

Stagnation enthalpy along the pipe (ICHOKE = 0)

1100

1000

C)

5-

I

900

.800

0 10 20 30 40 50 60

t (s)

70

Figure 53

55
Marviken 21

Entropy along the pipe (ICHOKE = 1)

3.0

2.8

" 2.6

CO 2.4

2.2

2.0

0 15 30 45 60

t (s)

75 90

Figure 54

Marviken 21

Entropy along the pipe (ICHOKE = 0)

3.0

2.8

2.6

•"2.4

2.2

2.0

0 10 20 30 40 50 60 70

t (s)

Figure 55

56
Marviken 24

Liquid total pressure along the pipe (ICHOKE = 1)

6

5

CL

a3

3

2

2 0 20 40 60

t (s)

E0

Figure 56

Marviken 24

Liquid total pressure along the pipe (ICHOKE = 0)

6

5

a?-

3

2

0 10 20 30 40

t (s)

Figure 57

57
Marviken 24

Stagnation enthalpy along the pipe (ICHOKE = 1)

1050

1000

0)

CD 950

*900 H

850

0 20 40 60 80

t (s)

Figure 58

Marviken 24

Stagnation enthalpy along the pipe (ICHOKE = 0)

1050

1000

-r" 950

850 °°F L

0 10 20 30 40

t (s)

50

Figure 59

58
Marviken 24

Entropy along the pipe (ICHOKE = 1)

2.9

2.8

2.7

- 2.6

U,

2.5

2.4

2.3

0 20 40 60

t (s)

Figure 60

Marviken 24

Entropy along the pipe (ICHOKE = 0)

80

2.9

2.8

2.7

2.6

CD,

2.5

2.4

2.3

0 10 20 30 40

t (s)

Figure 61

50

59
Marviken 10

Liquid total pressure -along the pipe .(ICHOKE = 1)

12

10

8

0~

a?

6

4

2

0

0 20 40 60

t (s)

80

Figure 62

Marviken 10

Liquid total pressure along the pipe (ICHOKE = 0)

12

10

8

ca 6

4

2

0

0 10 20 30 40 50

t (s)

60

Figure 63

60
Marviken 10

Stagnation enthalpy along the pipe (ICHOKE = 1)

1200

1100

1000

900

800

0 20 40 60

t (s)

Figure 64

Marviken 10

80

Stagnation enthalpy along the pipe (ICHOKE = 0)

1200

1100

0)

I

1000

900

800

800 0 10 20 30 40 50

t (s)

Figure 65

61
Marviken 10

3.0

2.8

, 2.6

U) Z

co2.4

2.2

2.0.

.Entropy along the pipe (ICHOKE = 1)

-' . .. . .. .. . .. .

0 20 40 60

t (s)

Figure 66

Marviken 10

Entropy along the pipe (ICHOKE = 0)

80

3.0

2.8

" 2.6

o•2.4

2.2

2.0

0 10 20 30 40 50

t (s)

60

Figure 67

62
Marviken 23

Liquid total pressure along the pipe (ICHOKE = 1)

10

8

0~

oF

6

4

2

13 * 0 10 20 30 40 50 60 70 13

t (s)

Figure 68

Marviken 23

Liquid total pressure along the pipe (ICHOKE = 0)

0

10

8

Ca7

6

4

2

0

0 10 20 30 40

t (s)

50

Figure 69

63
Marviken 23

Stagnation enthalpy along the pipe (ICHOKE = 1) 1200 . . . . , . . . . , . . . . , . . , .

cell 1

1100 -- cell 19

1000

900

800 0 .... 10 ' . . 20 . 30 ., . . . ., . . . ., . . 40 50 60 70 80

t (s)

Figure 70

Marviken 23

Stagnation enthalpy along the pipe (ICHOKE 0)

1200 .

cell 1

cell 18 I

1100 .............. 119 cell 19 j I ' " ...~~~~..................•< - •I- .............

,, 1000"...... "-•

900

0 10 20 30 40 50

t (s)

Figure 71

64
Marviken 23

Entropy along the pipe (ICHOKE = 1)

3.0 .

cell 1

2.9 cell 9 - -- cell 18

cell 18

" 2.8

CD .7

2.6

2.5

0 10 20 30 40 50 60 70 80

t (s)

Figure 72

Marviken 24

Entropy along the pipe (ICHOKE = 0)

2.9 . . . . .

cell 1 I1

2.8 ". .cell9 9 "

2.7 ............ ce1l19

2.6

2.4 ..................

2 .3 r . . . .i . . . . . . . . . . . . . .I . . . . . .

0 10 20 30 40 50

t (s)

Figure 73

65
Marviken 15

TRAC execution time vs. real time

Cn

a)

E

4-_

0o

3.0

2.5

2.0

1.5

1.0

0.5

0.0

0 10 20 30 40 50 60 70

t (s)

Figure 74

Marviken 15

Time step vs. real time

C,,

CD

E

4-P

0.30

0.25

0.20

0.15

0.10

0.05

0.00

0 10 20 30 40 50 60 70

t (s)

Figure 75

66
NRC FORM 335 U.S. NUCLEAR REGULATORY COMMISSION 1. REPORT NUMIBER

W RI•M -8 1102, (Assigned and Addendun" by N RC. Numbere, Add Vol, Supp., Rev, If anly.)

321.3202 BIBLIOGRAPHIC DATA SHEET

(See instructions on the reverse)

2. TITLE AND SUBTITLE NUREGJIA-0160

ANALYSIS OF THE CRITICAL FLOW MODEL IN TRAC-BF1

3. DATE REPORT PUBLISHED

MONTH YEAR

May 1999

4. FIN OR GRAI"" NUMBER

5. AUTHOR(S) 6. TYPE OF REPORT

M. Gomez, E. Valero, and I. E. Parra Technical

7. PERIOD COVERED (thdusive Dates)

8. PERFORMING ORGANIZATION -NAME AND ADDRESS (If NRC, provide Division, Office or Region, U.S. NutearRegulatory Comnisssion, and maling ,ddress; ffcontractr,

prowvde name and maiing address.)

UNIVERSIDAD POLITECNICA DE MADRID, Department of Applied Mathematics and Statistics

CONSEJO DE SEGURIDAD NUCLEAR, SPAIN

9. SPONSORING ORGANIZATION - NAME AND ADDRESS [IfNRC. 6Wp 'Samne as above*, #fcontractor, provide NRC Division. Office or Region, U.S. Nucher Regulatory Comirission, end mailing address.)

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555-0001

10. SUPPLEMENTARY NOTES

T. Lee, NRC Project Manager

11. ABSTRACT (200 words or less)

The critical flow model in TRAC-BF1 is assessed against five Marviken tests that include saturated and subcooled blowdowns

under critical conditions with length-to-diameter ratio at the exit nozzle ranging from 0.3 to 3.6.

Results of this study indicate that the numerical scheme of TRAC-BF1 does not have critical solutions such aIs those described

by the equilibrium analytical model; the critical condition must be imposed externally in the code using the semi-empirical model, CHOKE. When CHOKE is activated, the code calculates acceptable results although CHOKE still introduces certain

intrinsic errors.

Both the CHOKE model and the analytical model fail to reproduce non-equilibrium effects arrising from transition from

monophasic liquid to boiling mixture. Critical mass flow rates are generally underpredicted in subcooled blo#downs and

discharges through very short nozzles.

When CHOKE is not activated, the code calculates erroneous results. A subcritical pressure is calculated al the nozzle exit.

Pressure pradients and mass fluxes at the nozzle are generally overestimated. Erroneous behaviors are obh;erved regarding conservation of quantities. Specifically, code calculations indicated that the second law of thermodynamics. with regard to

entropy could be violated.

12. KEY WORDSIDESCRIPTORS (List words or phrases that will assist researchers in locating the report.)

Assessment of the Critical Flow model, TRAC-BF1, Marviken tests

I13. A% AILABILITY STATEMENT

unlimited

14. SE CURITY CLASSIFICATION

(This Page)

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(This Report)

unclassified

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