NUREG/IA-0015

International

Agreement Report

Assessment of Interphase

Drag Correlations in the

RELAP5/MOD2 and

TRAC-PF1/MOD2 Codes

Prepared by

K.H. Ardron. A.J. Clare

Central Electricity Generating Board

Barnwood, Gloucester

GL4 7RS

United Kingdom

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555

July 1989

Prepared as part of

The Agreement on Research Participation and Technical Exchange

under the International Thermal-Hydraulic Code Assessment

and Application Program (ICAP)

Published by

U.S. Nuclear Regulatory Commission
NOTICE

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their employees, makes any warranty, expressed or implied, or

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by such third party would not infringe privately owned rights.

Available from

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P.O. Box 37082

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and

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NUREG/IA-001 5

Intematdonal

Agreement Report

Assessment of Interphase

Drag Correlations in the

RELAP5/MOD2 and

TRAC-PF1/MOD2 Codes

Prepared by

K.H. Ardron. A.J. Clare

Central Electricity Generating Board

Barnwood. Gloucester

GL4 7RS

United Kingdom

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555

July 1989

Prepared as part of

The Agreement on Research Participation and Technical Exchange

under the International Thermal-Hydrauffc Code Assessment

and Application Program (ICAP)

Published by

U.S. Nuclear Regulatory Commission
NOTICE

This report is based on work performed under the sponsorship of the

United Kingdom Atomic Energy Authority. The information in this

report has been provided to the USNRC under the terms of the

International Code Assessment and Application Program (ICAP)

between the United States and the United Kingdom (Administrative

Agreement - WH 36047 between the United States Nuclear Regulatory

Commission and the United Kingdom Atomic Energy Authority Relating

to Collaboration in the Field of Modelling of Loss of Coolant

Accidents, February 1985). The United Kingdom has consented to the

publication of this report as a USNRC document in order to allow

the widest possible circulation among the reactor safety community.

Neither the United States Government nor the United Kingdom or any

agency thereof, or any of their employees, makes any warranty,

expressed or implied, or assumes any legal liability of

responsibility for any third party's use, or the results of such

use, or any information, apparatus, product or process disclosed

in this report, or represents that its use by such third party

would not infringe privately owned rights.
Abs tract: An assessment is carried out of the interphase drag correlations

used in modelling vertical two-phase flows in the advanced

thermalhydraulic codes RELAN5/Mod2 and TRAC-MFI/Modl. The

assessment is performed by using code models to calculate

void fraction in fully developed steam-water flows, and

comparing results wi:h predictions of standard correlations

and test data. The study is restricted to the bubbly and

slug flow regimes (void fractions below 0.75).

For upflows, at pressures of interest in PWR small break LOCA

and transient analysis the performance of She code models is

generally satisfactory. E:ccepcions are (i) small hydraulic

diameter channels at low pressure (p 4 :4Pa) (ii) large pipe

diameters at void fractions exceeding 0.5; in these cases void

fraction errors are cuCsLde normal uncertainty ranges.

For downflows, the code models give good agreement with limited

available void fraction data.

The numerical results given in :his paper allow a rapid estimate

co be made of void fraction errors likely to arise in a

particular code application due to deficiencies in interphase

drag modelling.

iii

Executive Surmarv

In some small break loss-of-coolant accidents (LOCAs) and pressurised

transients in PWRs, system behaviour depends strongly on the void

fraction in vertical loop components. For example, when the reactor

core is partially uncovered, the boildown rate is influenced by the

void fraction which determines the continuous liquid level. Similarly,

the void fraction in the core and other vertical flow paths strongly

influences the duration of core dry-out when core uncovering is caused

by a balance of hydrostatic forces. To provide an accurate numerical

simulation of these situations it is necessary to model properly

the interphase relative motion (slip) in the vertical loop components.

RELAP5/Mod2 [1] and TRAC-PFI/Modl [2] are advanced thermalhydraulic

codes presently being used in the UK for PWR fault transient analysis.

Both codes employ a two-fluid model in which separate momentum

equations are solved for the gas and liquid phases. Flow-regime

dependent constitutive equations are specified to model interphase

momentum transfer.

In mixed flow regimes such as bubbly, slug, and churn flow, it is

generally accepted that interphase slip is made up of separate contributions

from the motion of gas bubbles relative to the surrounding liquid

('local' slip) and from the non-uniform profiles of void fraction

and gas veloci:y over the pipe area ('profile' slip). The

one-dimensional two-fluid models in RELA.P5/Mod2 and T.RAC-PFl/Modl

assume a uniform profile of void fraction and steam velocity over the

pipe area; therefore profile slip is not modelled explicitly. Instead

profile effects are modelled indirectly by using empirically based

interphase drag coefficients. However, since the processes producing

the interphase slip are not fully simulated, the accuracy of this

approach is questionable.

The present note describes an assessment of the performance of the

interphase drag relationships in RELAP5/Mod2 and T1XAC-?Fl/Modl, in

modelling vertical flows. The method used to assess the drag relationships

is to apply them to calculate the void fraction in steady, fully-developed

vertical steam-water flows under condizions of typical interest in

reactor transient analysis. Results are then compared with the void

fraction predicted by standard empirical correlations, or with test

daca.

V
Graphical results are presented which can be used for a rapid

estimation of the void fraction error which is likely to arise in a

particular application of RELAP5/ModZ or TRAC-OFI/Modl due to

deficiencies in the in=erphase drag modelling. The main findings

can be summarised as follows:

Qi) the interphase drag models in R.ELAP5/Mod2 and T\AC-PFI/Modl

perform comparably well in modelling vertical flows;

(ii) errors in the two-phase mixture density increase with

decreasing liquid flux, increasing steam flux, increasing

pipe size and decreasing pressure;

(iii) for upflow, at the pressure of interest in modelling small

break LOCAs and transients in PWRs (p > 4MPa), the errors in

two-phase mixture density are not grossly different from

errors normally expected in applying standard correlations

for void fraction. Excepcions are large pipe sizes at void

fractions exceeding 0.5, and small pipe sizes at low pressure

(p 4:1 MPa). where errors become large.

For downflow the ccde models perform very well in comparison

with the limited void fraction data available.

Finally, it is noted that the paper examines the modelling equations

themselves, rather than their numerical implemen:ation in the codes.

:a practice the numerical value of the interphase drag force is

calculated by combining information from upstream and downstream

volumes. Therefore, computed values are sensitive to cell size

and positioning of node boundaries. Additional comparisons with

actual code calculations are needed to assess the implementation

of the models within the codes.

vi
Notation

A Pipe area

Dh Hydraulic diameter

Fwk Force on phase k per unit flow volume due to wall shear

fgl Interphase drag coefficient

g Acceleration due to gravity

G Mass flux

j Volumetric flux

d Interfacial drag force on phase k per

kz unit flow volume

p Pressure

u Velocity

z Axial co-ordinate

a Volumetric concentration

bRelative velocity (- ug - uL)

r Mass generation rate per unit flow volume

a Surface Tension

p Density

AD Density difference = (PZ - P)

9 Inclination angle of pipe

Subscri±ts

g Property of gas phase

2. Property of liquid phase

i Property of gas-liquid interface

g2. Difference between gas and liquid phase value

vii

. rODUCT:ON

In some small break loss-of-coolant accidents (LOCAs) and pressurised

transients in PWRs, system behaviour depends strongly on the void

fraction in vertical loop components. Tor example, when the reactor

core is partially uncovered, the boildown rate is influenced by the

void fraction which determines the continuous liquid level. Similarly,

the void fraction in the core and other vertical flow paths strongly

influences the duration of core dry-out when core uncovering is caused

by a balance of hydrostatic forces. To provide an accurate numerical

simulation of these situations it is necessary to model properly the

interphase relative motion (slip) in the vertical loop components.

RELA25/Mod2 (1. and 71.TC-MFI/Modl (2] are advanced thermalhydraullc

codes presently being used in the LIK for FWR fault transient analysis.

3oth codes employ a tvo-fluid model in which separate momentum

equations are solved for the gas and liquid phases. Flow-regime

dependent constitutlve equations are specified to model interphase

momentum transfer.

In mixed flow regimes such as bubbly, slug, and churn flow, it is

generally accepted that Lnterphase slip is made up of separate

contributions from the motion of gas bubbles relative to the

surrounding liquid ('local' slip) and from the non-uniform profiles of

void fraction and gas velocity over the pipe area ('profile' slip)

(see e.g. ref. (2]). The one-dimensional two-fluid models in

RELAPR/Mod2 and TAC-PFM/Modl assume a unifor= profile of -- and u,

over the pipe area: therefore profile slip is not modelled 9Xpliiicl-y.

Instead profile effects are modelled Indirectly by using epirically

based Interphase drag coefficients. However, since te processes

rroducing the interphase slip are not fully simulated, the accuracy of

this approach 's questionable.

The present note describes an assessment of the performance of the

interphase drag rela:ionsnips in .ZELAP5/Mod2 and ITAC-PFI/Mod 1, in

modelling vertical flows. The =echod used to assess the drag

relationships is to apply them to calculate the void fraction in

steady, fully-developed vertical steam-water flows under conditions of

t7pical interest in reactor transient analysis. Results are then

compared with the void fraction predicted by standard empirical

correlations, or with test data. The adequacy of the interphase drag

models is reviewed in the light of these comparisons. -he assessment

is confined to bubbly and slug flow conditions (i 40.75).

SELECTICN OF VOID FRACTION CORRELATTONS FOR CODE ASSESSMET

Correlations vere selected from the literature to provide 'best

estimate' void fraction predictions for comparison with the void

fractions calculated with the code models. Selection of appropriate

models for upf low and downflow is described below:

2.1 Co-current Utoflcw

There are extensive void fraction data available for

co-current upflow of steam-water and air-water mixtures, and a

number of void fraction correlations have been proposed in the

literature. For the present application a 'best-estimate'

model was developed by combining the correlations of ViUson

er al r4] and Rooney ([1.
The Wilson correlation has the functional form

a= f(jgI jy, pg, p P D) (1)

where the function f is defined in Appendix A, section Al.0.

The Wilson correlation is based on steam-water data for

pressures in the range 2.0 - 13.8 MPa and pipe diameters

between 100 - 914 = [4, 6). However in ref [7] the

correlation was tested against steam-water level-swell data

obtained in the THETIS rod bundle facility (D, - 9.12=) at

pressures between 0.2 and 4.0 .•a. in that study it was found

to perform well if the dimension D in the correlation was

equated with the hydraulic diameter of the rod bundle. Thus

the correlation is considered reliable for PWR core

conditions, despite the fact that this geometry is outside the

range of its original data-base.

For higher flows (Ku, 10) the Wilson correlation falls

outside its range ofovalidity. Then the Rooney correlation (5]

which has the form,

aJ (2)

is used. The parameter CO in equation(2) is pressure and flow

dependent and is defined in Appendix A section A2.0.

Well established correlations of the same form as equation(2)

have been given by Bankoff (8] and by Armand and Treschev (91

with slightly different specifications for the parameter Co;

the Rooney correlation has been selected in preference to

these correlations on the basis of its marginally better

performance in comparison with an HTFS data base [10].

The 'best est.mate' correlation of void fraction for upward

flow used in this assessment combines the Wilson and Rooney

correlations according to:

a. min (Wilson, Rooney) (3)

Equation(3) is found to satisfy the limits of validity of the

Wilson correlation.

2
-cuation (3) was used as a basis for assessing the perfor-ance

of the interphase drag equations used in the codes in upflow.

However it must be recognised that there is considerable

uncertaint7 in void fraction predictions obtained from any

empirical correlation. Ref (101 compared several commonly used

void correlations with steam-water and air-water data from

various sources. Even the most successful correlations give

RMS errors in two-phase mixture density in the range

-d - 30%.

In order to give an indication of these uncertainties,

comparisons were made between predictions of eq(3) and

predictions of some alternative correlations in common use.

The following correlations were selected for this purpose:

(I.) EPRI correlation (Ill. This correlation has been

validated against an extensive database although the

bulk of comparisons presented by the developers is for

small pipe sizes;

(ii) Zuber - Findlay correlation (3]. This model has a

simple form and has been widely used for modelling

vertical flows in open pipes;

(Iii) Cunningham - Yeh correlation (13]. This model was

developed fro= voidage data in a large PWR-type pin

bundle under static boildown conditions.

The forms of these correlations are given An Appendix A.

2.2 Cocurrent Downflow

For co-current downflow very few void fraction data are

available and no well established correlations are known to

the present authors. Accordingly, the performance of the code

models was assessed against the data of Pecrlck (121.

Petrick's data are for steam/water mixtures in a 49mm pipe at

pressures of 4.1, 7.0 and 10.3 '-Ta, with gas and liquid

superficial velocities up to about 1.5 m/s. Comparison with

these data provides a lUmited test of the code models at small

diameters and low to moderate flows. 't appears that no data

are available for larger pipe sizes.

3. ASSESSI._NT OF :NT=_KPASE DRAG MODELS .N.

TLU.C-?F1/M0DL and RZLAP5/%MDZ

To assess the interphase drag models in the codes, the drag equations

are first used to develop relationships between the void fraction and

the phase flow-races, for the case of a steady fully developed

steam-water flow in a uniform area vertical pipe. The void fractions

obtained from these relationships are then compared (i) with

predictions of the best-estimate empirical correlation for upflow

described in section 2 and (ii) with limited available data for

downflow.

3
3.i DeveloDment of Ecuation for Void Fraction

The momentum equations in the RELAP5/Mod2 and TRAC-PFI/Modl

models can be expressed in the following general form

ku A Z A k9kUk

--Pg sine- me -- ' + 

.Uk "k (4)

where 9 - , /2 for upflow and -. "2 for downflow. In both codes,

the interfacial drag force per unit flow volume is represented

by an equation of the form:

dd . _a/¢

Mgz " -fg* I i I (5)

where fg . is a generalised interphase drag coefficient and

tu - ug - ux

For steady, fully developed flow the derivative terms in the

left hand side of (4) can be set to zero. Eliminating (dp/dz)

between the resultant equations for the gas and liquid phases,

neglecting momentum exchange between the phases due to mass

transfer (which is usually small), and using equ(5), we

arrive at the following algebraic equation for the relative

velocity.

"I mlu - (gs ine cg ao - 'w• + mt ±wg) /gf (6)

Since uniform flow is assumed Zu is related to the phase k

superficial velocities by the equation:

igl/g - Z/,,j. - t, (7)

If formulations for the interphase and wall friction terms

Sg .' Fwk are specified, equations (6) and (7) can be used to

calculate the void fraction in terms of the phase superficial

velocities jg and J.

3.2 Comparisons with Empirical Void Correlations and Measurements

The formulations for interphase drag and wall friction used in

RELAP5/!iod2 and TRAAC-PFl/Modl, are given in Appendix B and

Appendix C. Short computer programmes were written to solve

equations (5)-(7) using these interphase/wall friction

relationships.
3.2.. Cmomarisons for Vertical Uaflow

Results of the calculations for vertical upflow are shown in

Figs. 1 and 2. The dashed lines are the predictions obtained

in the REIAP5 and R'RAC-PFI models. The solid lines are the

corresponding predictions of the Wilson-Rooney best-estimate

void correlation described in section 2.1. Calculations are

given for Dh - 0.Olm and 1.Om (nominal values for the reactor

core and main loop pipework respectively) at pressures of

10.0, 4.0 and 1.0 -Ta. (Note that the pressure range 4.0 -

10.0 '.Ta is the range of chief interest for PWR small break

LOCA analysis. At lower pressures emergency cooling water is

injected from accumulators, leading to rapid system

refilling.)

Znspection of the Figures shows reasonably good correspondence

between the RELA?5 and TRAC results and the Wilson-Rooney

correlation for moderate and high liquid flow-rates and small

hydraulic diameters. Discrepancies are largest for low

pressures, large pipe diameters, low values of J) and high

values of jg"

Since two-phase density rather than void fraction is the

quantity of physical interesc in =odelling an uncovered core,

it is more meaningful to discuss density errors than errors in

void fraction. Figure 3 plots percentage error in the density

against the void fraction, for the limit of zero liquid

flow-rate (Jt " 0 ) where errors tend to be largest. The

percentage error in the two-phase density is defined as

02 -. P 100

- I (8)

Where P1 is the density calculated with the Wilson-Rooney

correlation and P" is the density calculated with RELAP5 or

IUC models. The abscissa is the void fraction predicted by

the Wilson-Rooney correlation.

Fig. 3 shows chat the 'density errors' obtained using the

RELAP5 and TIRAC models are of comparable magnitude.

Figs. 4 and 5 compare the 'density errors' obtained using the

code models with the 'errors' obtained using the ocher

correlations for ;, in vertical upflow, listed in section 2.1.

The calculations ate for j= 0, and pressures of 4.0 and

10.0 MPa, which span the pressure range of chief interest in

PWR small break LOCA analysis. The 'density errors' associated

-ith each correlation are obtained from equ(S) by making P

equal to mixture density calculated with the correlation, and

the mixture density calculated with the Wilson-Rooney

model.

3
Examination of Figs.3-5 leads to the following observations:

(M) for small hydraulic diameters (characteristic of the

reactor core) the code models perform well at a

pressure of 10YPa. At lower pressure the void fraction

is increasingly over-predicted. At 4.0 I2a, density

errors of 30-40% are apparent at void fractions of

about 0.5, which are significantly outside the

uncertainty range of +1.5% indicated by the

correlations.

(2) for large hydraulic diameters the code models perform

well at all pressures for a 4 0.5. However for higher

values of ag, the density errors become large.

3.2.2 Comnarisons for Downflow

As noted in section 2.2, there appear to be no reliable

correlations for void fraction in vertical downflow. Therefore

void predictions obtained with the RELAP5/Mod2 and TRAC-PFl

models were compared directly with the test data of Petrick

[12]. Comparisons are shown in Fig. 5 for tests at a pressure

of 7.0 ,2'a (1000 psia). Agreement is very good in both cases,

with the RELAP5 models performing somewhat better than the

TIEAC models overall, particularly at high void fractions.

Similar comparisons were made with data at pressures of 4.1

and 10.3 ',Ta and similar conclusions were reached.

4. DISCUSSION AND CONCLUSIONS

The numerical calculations in Figs 1-3 can be used for a rapid

estimation of the void fraction error which is likely to arise in a

particular application of RELAP5/Mod 2 or TRAC-PFI/Mod 1 due to

deficiencies in the interphase drag modelling. In assessing the

magnitude and significance of the errors, our main conclusions are as

follows.

Mi) the interphase drag models in RELAP5/Mod 2 and TRACPF1/

Mod 1 perform comparably well in modelling vertical flows;

(ii) errors in the two-phase mixture density increase with

decreasing J., increasing Jg, increasing pipe size and

decreasing pressure;

(Iii) for upflow, at the pressure of interest in modelling small

break LOCAs and transients in PWRs (p >4•1_a), the errors in

two-phase mixture density are not grossly different from

errors normally expected in applying standard correlations for

void fraction. Exceptions are large pipe sizes at void

fractions exceeding 0.5, and small pipe sizes at low pressure

(p 4 4 11pa), where errors become large).

For downflow the code models perform very well in comparison

with the limited void fraction data available.

6
The present paper has examined the =odel!ing equations

themselves, rather than their numerical implementation in the

codes. In practice the numerical value of the interphase drag

force is calculated by combining information from upstream and

downstream volumes. Therefore, computed values are sensitive

to cell size and positioning of node boundaries. Comparisons

with actual test data are needed to assess the implementation

of the models within the codes.

REFERENCES

(11 V.H. Ransom et al "RELAP5/Mod2 Code Manual Vol. I: Code Structure,

Systems Models and Solution Methods". NUREG/CR-4312, Aug. 1985.

(2] D.R. Liles et al "TRAC-PFI/Modi. An Advanced Best Estimate Computer

Program for ?WR Thermal-hydraulic Analysis. Draft LAL Report, :May

1984.

[3] Zuber, N and Findlay, J.A. "Average Volumetric Concentration in Two

Phase Systems". J. Ht. Transfer Vol 37, 1965, p4 53.

(4] Wilson J.F., Grenda, R.J. and Patterson J.F. "Steam Volume Fraction in

a Bubbling Two Phase Mixture". Trans ANS, Nov. 1961.

r5] Rooney, H.H. "Void Fraction Prediction under Saturated Conditions" NEL

Report No. 386, 1968.

(6] Wilson J.F. et al, Primary Separation of Steam and Water by Natural

Separation: Part I" Allis Chalmers Atomic Energy Division, Report A

C,?-65002 April 1965.

[7] Clare A.J., Ardron, K.H., Hall, J.A. and Shires, G.L. Assessment of

the Calculation of Core Uncovering with RELA24iMod6: Comparison with

out-of-pile cluster experiments" CZGB Report TPRD/B/0027/N82, April

1982.

(8] Bankoff, S.G. "A Variable Density Single Fluid Model for Two-Phase

Flow with Reference to Steam Water Flow". J. Ht Transfer, Nov. 1960,

pp 263-272.

(91 Armand, A.A. and Treschev G.G., "Investigation of Resistance During

the Movement of Steam-Water Mixtures in a Heated Boiler Tube at High

Pressures" AERE Lib. Trans. 816.

[10] Collier, J.G., Ward, J.A., Claxton, K.T. and Chisholm D. "Two Phase

Pressure Drop and Void Frac:ion in Tubes". AERE Report AERE-R6434,

August 1972.

[111 Chexal B and Lellouche G "A Full Range Drift-Flux Correlation for

Vertical Flows". EPRI Report NP-3989-SR, June 1985.

(121 Patrick M., "A Study of Vapour Carryunder and Associated Problems".

ANI. Report ANL-6581, July, 1982.

(13] Cunningham, S.P. and Yeh H-C, "Experlments and Void Correlations for

OWR Small Break LOCA Conditions", Trans ANS Vol.17, 1973, p369.

7

APPENDIX A

Description of Void Fraction Correlations used for Code Assessment

Ai.0 Wilson correlation (41

This correlation is based on steam-water data in pipes of 100 = and

480 = diameter at pressures between 2.0 and 5.5 MPa [6], and

additional data obtained in 460 = and 914 = diameter pipes a:

pressures between 4.1 and 13.8 MPa (4]. The tests were done with

either zero liquid flow-rate (stagnant pool type conditions) or at

small liquid flow-rates established by natural circulation. The

correlation has the following form.

fp \

C-Cj,

\P~Y

C,

Kug

C 3 .a gp C 4

D1.1)c C5 (A!)

where

C1 - 0.564, C2 - 0.12, C3 - 0.67, C4 - 0.1, C5 - 0.6 for Kug 9 1.5

C1 0.619, C, - 0.12, C3 - 0.47, C4 - 0.1, C5 - 0.6 for Ku. 1.5

A2.0 Rooney correlation (31

This correlation has the form

C--C 493

(.12)

The parameter C0 is a function of flow-rate defined in the following

table:

IURlj jCoI

0

0.0 1.00

0.006 1.050

0.013 i.100

0.021 1.150

0.031 1.200

0.047 1.250

0.060 1.275

0.010 1.300

0.140 1.300

where

up - ( ( / 2 ) 0.25

Al
in ref.[10] the Rooney correlation was compared against the HTFS

database for steam-water flow in vertical tubes, (tube diameters in

the range 9 - 170 = and pressures in the range 3.0 - 16.5 Ma). The

correlation was shown to perform satisfactorily.

A3.0 EPRI Drift Flux correlation (Ill.

The EPRI correlation has the form

g /g/(Coj + Vg4) (A3)

where Co and 7g. are functions of flow properties, including void

fraction.

The EPRI correlation was developed from a large database of

steam-jater data. The database covered the following conditions:

G%" 0 0.1 C D h c G.2m 0.1 4 p o 0.4 '.2a

G2 0 Dh - 0.01m 0.1 4 p 4 0.3 M.Xa

GI 0 Dh - 0. 4 56m 4.0 4 p ' 14.0 MPa

100 G'G 300 kg 2 S_ D0. - 0.168M 8.0 - p - 16.0 .Ma

500 • C ZG k;m-" •CO 2 S 0.01 . D - 0.O5m 3.0 4 p ' 8.5 P a

A4.0 tuber - Findlav Correlation r3l

The Zuber-FIndlay correlation for vertical churn-turbulent flow has

the form

- 0.15, - /([Coj + 1.33 rcg / .0Z5j (A4)

Values for the profile parameter C. were given in the range 1.1 - 1.6;

a value of 1.2 has been used in the prasent work.

The Zuber-Fiadlay model is simple to apply and is widely used in

tj'o-phase flow analysis. An equation approximating to eq(A4) was

tasted against the HTFS steam-water database in ref. 10] and was found

to perio-= reasonably well.

A3.0 Cunni±ham-Yeh correlation "I3

This equation was developed from voidage measurements in a large

electrically heatad ?r.,R - type pin bundle. The equation has the same

form as (AU) but with revised constants, (Cd).

C. - 0.696, C., = 0.4, C3 - 0.67, C- = 0, C5 0 for Ku <..53

C, = 0.757, C.7 = 0.24, C3 - 0.a7, C4 M 0, C5 - 0 for Ku, 2 1.53

.12
.PPE'fDlIX B

Description of the RELAP5/Mod2 constitutive models for wall and interohase

friction for vertical flow

B3 Internhase Drag Models

The RELAP5/Mod2 flow regime map for vertical flow is divided into

regions of bubbly flow, slug flow and annular mist flow as shown in

Fig. Al. Transitional zones are placed between these regimes to ensure

smoothly varying functions. Below we give the equations used for fa

in the bubbly and slug flow regimes. These equations have been tak n

from a source code listing of RELAP5iMod2 Cycle 36.00 and differ in

some respects from the equations described in the code manual [I]. in

some cases, parameters defined below are constrained to lie within

prescribed ranges in the actual RELAP5 coding. For the sake of

brevity, these ranges are not indicated in all cases below.

(a) Bubble Flow Recion

The bubble flow region is defined as the region bounded by the

void fraction limits:

0 (' ra 

Where

aBS " •. G C 2000 kg m-2 S-1

-s a. + io-3 (G-2000) (0.5-a.) 2000 - G - 3000 kg m-2S- 1

-" 0. G ) 3000 kg m-2 S-1

and

- 0.25 Min (1.0, (D*/22.2) )

The drag coefficient in bubbly flow is defined as follows:

f - 0.125 P, ag C

w•here

ag - 3.6 a /d

- 24 (1 + 0.1 Rep 0.75)/ Re

Re. &i do

do = 5a/p. tu

31
(b) Slu; Flow Regime

The slug flow regime is defined as the region within void

fraction limits

aSs C % I SA

Where

7SA- '!ax..{0.75, 1.4 (a g p o 2 U9 .25i

and a3s is defined as in (a) above.

The drag coefficient in slug flow is calculated from the

equation:.

fg!) (C - %) 'B + fs

Where

- (a - as)/( - %s)

= 3s e.• {-6 ( - %S)/%a - S)

0.125 pt ag. CB

3

fs a 5.51 Pz (I.- %) 7bIDh

agB - 3.6 asldo

2

do - d P1 (.zUi)

CDOB 40 (1 + 0.075 ReO3 '7)/RIe

Re. a do P1 nu/(l - %)P

cc) Annular Mist Flow Regi=e

The lower boundary of the annular =ist region is defined by

the void fraction li=it

cg = a ...

where asA is defined in (b) above. The drag coefficient in

annular mist flow is calculated from the equation

- I(I - -F) 

B2
Where

e-s (1 - 10-4 (a p.D/") 0 "

2 5 )

s M 7.5 x 10- (auglu C)

uc 2.5 (c Ap /pg) 0 "

2 5

fD M0- 125 Pg a'g %D

agfd - 3.6 M/doD

MM = (.Z. a2 •) - a)

,s~D MO (L, ,)2/(.5 c) l;/doD - (=g )(1a

.•,,, - . b, (cay- aý)I/a

CDD - 40 (1 + 0.074 ReD0"75)/ReD

ReD M doD tu,,, pI (1 - a )5/2119

UF 0.5 S A.p

OSA Pgfic

S. - 6.1192775 a.O0.125 GI- aZ/D)

ft 0.005 + A (6)B

logloA - -0.56 + 9.07/D*

B - 1.63 + 4.74/D*

D* - D (gAo/ a)-

6* - 0.5 D* (1 -a.

An interpolation zone is defined in the region

(OSA - 0.05) 9 ' %SA

In this zone fj is calculated by interpolating between the

values for slug flow and annular mist flow, to ensure a

smooth transition.

32 Wall Friction M1odels

RELAP5/Mod2 has a complex method for calculating the wall friction

source terms F and F The formulation described below has been

taken from the code manual and has not been verified against source

code listing. According to the code manual, in all flow regimes, the

source terms are given by the equation (see equations (C24) and (225)

of ref.[1]).

2

wk M- % ' Pk jk k % e . 22

2Dl {Cgw g Pg Ug +~ C'U %I P.ujI

B3
Vnere 'A, and %' are friction factors which depend on F~ynolds number

and cube wall roughness. t is calculated based on the "mixture"

Reynolds number

Rek Dh

2

4 is a two-phase multiplier calculated from the

which is expressed as:

HT'S correlation,

2 PZ - I + C+ + 2

2 2

~+

Here C is the Martinelli parameter defined as:

2 21 2 2

and

C - ax. tz.o, (-2.0 -r fI(G)T)}

where

fL (G) = 28 - 0.3G

- ex• [ -(logj 0 2. + Z.5)/(".! - G(IO-)) ]

G P-ig + 021

aC., represents the fraction of the pipe wall perimeter in contact with

phase k. in the bubbly flow regions it is assumed that

In" l re

lz the slu; flow regions it is assumed that:

- gs and a2, - 1-nZs

where is defined in section

it is assumed that:

AI(b). in the annular-mist flow regime

12w 'IF O 0.25 and % -. 0"25

where =x is defined in section Al(c).
A-PPENIDL C

Descriot!on of the TRAC-PFI/Modl constitutive models for wall and

interphase friction

C1.0 Intervhase Drag Models

(a) Bubbly and Slue Flow

Evaluation of the interphase friction coefficient fg9 is based

on the flow regime map shown in Fig.Al. Here the upper limit

of the bubbly flow regime is shown at a - 0.25 as coded in

subroutine FEMOM, not at a - 0.3 as stated in the manual. In

both bubbly and slug flows the vapour phase is assumed to be

in the form of non-interacting spherical bubbles, and the drag

force is expressed as the product of a cross-sectional area

and a drag coefficient. Thus for bubble diameter Db and drag

coefficient

fgl - 0.75 agp,.ZC/Db

The bubbly and slug regimes differ only in the evaluation of

bubble diameter. Two basic diameters are calculated; firstly

a Weber number controlled diameter

Db' - Webc

P.Vrb

where Web - 7.5 and Vrb - =ax (0.1, lu -u.21), and secondly a

diameter equal to the local hydraulic giameter, Dh. Within the

range 0 M < ( 0.5 a weighted average of these two values is

taken:-

Db -max [((l - X)Db' + XDh) 1O-m

where

- (3 - ZX') (X)2,

X - X'exp[-(G-2000)700]

and

X- max [0, min(., 4(a - 0.25))!

Thus for the region shown as bubbly flow in Fig. 1, Db - Db'

is taken, and within the 'slug flow' region, Db is

interpolated between Db' and Dh,which is reached at ag - 0.5.

The drag coefficient is of a commonly used form developed from

measurements of the terminal velocity of spherical particles

falling through a stagnant liquid. The equations are:

C l
Cb =, Z-0

b M (2 4 /Reb)(1 + O.,5Reb)687

Re. < .L.031

0.103L < Reb 4 989

0.*44 Reb > 989

W-here

Reb - VrbPZDb/l.

(b) Annular-Mist Flow

For void fractions x, 0.75 annular-misc flow is assumed, with

no contribution from bubbly/slug flow. inter-facial shear

contributions from droplets and film are evaluated separately.

Firstly the fraction of liquid entrained as droplets (E) is

calculated from the equation:

E - max [j-exp(V, - V )/V7, 7.75 x iO-7 Iee 1.25Ee 0.25 1

where

1-- 2.33 aa ,el 0.Z5

Land

with ';ed ,

" -(Z )

Here the critical velocity for entrainment, V-., is equal to

the vapour velocity needed to just levitate a drop whose size

is governed by 'Wed, given a drag coefficient (Cd - 0.44)

appropriate to high droplet Reynolds numbers. The droplet drag is calculated in the same way as --he bubble drag, viz.

Dd d L

I r

V.ihere Wed 4 and V r = a (041, Iu~ -u~) and

= 0.75 ca=zcd/Dd

C2
where Cd is given by the same drag coefficient relations as for

bubbles except that the droplet Reynolds number

(Red - DdVrPg/Ug) is used.

The film shear is calculated using the following equation for the

interfacial shear stress coefficient

Cf - o.005[1 + 75 (1--) (1-cg)]

and an approximation to the film area given by:

- 4 (1l-E) c a;,

ai Th g A.f

aif 4 1-a a1-))qc

Dh I CA

Where a; 1 I - 45

-Dh

and 6 2.55 x 10-4M Is a minimum allowed thickness. The total

film shear coefficient is then fgf Z aifcfpg,/2

and the total annulir-mist drag coefficient is calculated as

fg2 g.+ •f f 

In the interpolated region 0.5:agcO.75 the bubbly/slug and

annular-mist coefficients are combined using linear interpolation using a weighting factor:

F - (4ag-ý)2(7-8ag).

In the transition zone the interphase friction coefficient f,. is

calculated based on a bubble size equal to Dh, and a modified bubble

velocity is used which transitions

from Vrb - max (0.i, Jug-u 2.) at a - 0.5

to V. 2.33 a Web(% _)0 "2 5 o Vrbb 7`) /C7 for a)0.55

C3

-Fl

0

0

0

0

-11

:u

0

0

If.

-1O

(A) p =U 10tPO

Offj 0.6

0.6i

a90.1

0-6

0.4

019

ig20rn/M

0-8

0-6

0.4

jg= 2*Osnls

0.2

Jo =0 .Smis

J = 0 O- I I/s

0-2

0

0-2 ;=0 -5 ns~

0 1 In/s

g=0-5 II/S

o :z 0.11114

0 a

0 I 2 a I 2 a I

i(rnmill

2

l I(m/|) ii fIns)

KEY-

- ~WILS0N-e~0t14EY CORRELATIOtN

54ELAP 6 / MOD. 2

-- - ~ RACPF) I HOD. I
0

~0

z

0

11

JA)p1P 0 p = 10.0 Mma C cI| p= I0"0 MPa

('E 0S

0.6

0-4

0-2

Olg 0-8

0.6

a0g Os

0.6

Jg = 2.Orals 0.

0.2

J9 =0.5mls

N

N

ig = 2 -Omnit

VOSniIs

g=0.t

= 2.Orls 0.4

0.2

jg =0.1

0 0 0

0 I

j( I(Ms I

2 0 I

j(MI/S)

2 0 1 2

•Irnls!

KEY :

WILSON-ROONEY CORRELATION

RELAP 5 1 HOD. 2

TRACPFI /MOD.I
(41 O h =001m

so

60

&o P210MP•

i20 ,0 so 

,- 0 C(g (*I-)}

-80

+100 r

(b) Ch : 1.0 e

8.0

20 jI g

- oI\

-- 20

-50

r KEY

-0 -- ELAP R- 5 1MCO 2

---- t";RAC - PFI tlOO 1

hERRORS IN MEAN TWO-PFHASE MIXTURE DENSITY FOR i 0 FIG. 3
s0

s0

p = lmpc

Ch = a-DIM

.11-000

I - X50 - w

LU.

40

20

0

-70

a0

-60

-80

-4-100

80

50

p = 4.0 MPc

Oh= 0.07M

Gn

LU

20

20

-20

-.----- - - - - • . I

----- S

-I Q9 (0.

llý.

-- S -

-60

-80

-100

KEY:-

-RELAP S

-- RA C - PFI

---- CUNNINGHAM - YEf

-.- ZBEZZ-ýINCLAY

- -E p R 1

COMPARISON OF CORRELATIONS FOR jt = 0

,Dh = O.Olm 'I G. 4,
•h - .Om

60

60

p} = 0

so

,u

- 60 -

-80

-SO

-100 r"LA 3 =UE MAYF-.0 

,- 0

0 -

COMPSON OF C LON F . .. 'R \U

-- OO I• .--.----- -- - .UE -•OA

... TR . ¢- PF1 -,-

COMPARISON OF CORRELATIONS FOR E=. ODh = 1.urn FIG. 3
1.0

(A ) RELAP 5 / MOO. 2

0.9

0.6

00

0

0

4

C.' 0

0-4

0-2

0

1-0

0-8

0-6

0.2 01. 0-6 0-9

a

MEAS

I1-0

o0 e C) TRA^CPFI/MOD.1

U

4

0.4

c

/I

IO0

I I I I

0-2 0-6 0"$ 1-c

MEAS

FIG. 6 COMP-ARISON OF MEASURED AND PREDICTED VOID FRACTIONS

PETRICK DOWNFLOW DATA (p=7OMPc Dh= /.9mm)
I!

I

I

! ANNULAR

MIST

BUBBLY SLUG

3000

2000

x

U.

ul

x

U,

4

TRANSITION

I I

I i

I I .ANNULAR

BUBBLY S. 'jG I MIST

I I *i I i I

a -S S-A

TRANSITION

VERTICALLY STRATiFIED FLOW

0 I

v/o0 o(a )

FIG. Al VERTICAL FLOW REGiME MAP IN RELAP 5/ IMCO. 2
x

LL.

4n

2700

2000

0.0 1.0

VAPOUR FRACTION a

FLOW-REGIME MAP FOR ONE-DIMENSiONAL

HYDRODYNAMICS IN TRACPFI: MCD. 1

FIG. 21
MAC FORM 231 US. NUCLEAR RIEULATORY COMMeUISON I REPORT NUMEIR IAUD,# or rooc mo vw No. 'C,,

"CM ,o2. NUREG/IA- 0015 3201 3"2 BIBLIOGRAPHIC DATA SHEET GD/PE-N/557 SEif INSTRUCTIONS ON% rI AEVErISE

Z TITLE ANOD A,1 IILE J LEAVE BLANK

Assessment of Interphase Drag Correlations in the

RELAP5/MOD2 and TRAC-PF1/MOD1 Codes 4 OAT! REPORT COMPLETED

MONTI YEAR

S AUT.ORISI

K. H. Ardron, A. J. Clare ,DATE ,PORTSSUEDAo 40NT. ,A

July 1989

I PERFORMING ORGANIZATION NAME ANO MAILING AODRESS IIIV', 110 C.-,l I PROJECTITASK/WORK UNIT NUMSER

Central Electricity Generating Board

Barnwood, Gloucester 9 FINOR GRANTNUBER

GL4 7RS

United Kinqdom

100 IING OAUANI% A ME AN00AILING ADOjRISS c.* Ie l. Is TYPE OF R•PORT

ofCe of ear egua tory lzesearch Technical Report

U.S. Nuclear Regulatory Commission

Washington, DC 20555 , U.o ---.-

12 SUPPLEMENTARY NOTES

13 ARSTRACT IdZ?-0. W' 1

An assessment is carried out of the interphase drag correlations used in

modelling vertical two-phase flows in the advanced thermal hydraulic codes

RELAP5/MOD2 and TRAC-PF1/MOD1. The assessment is performed by using code

models to calculate void fraction in fully developed steam-water flows, and

comparing results with predictions of standard correlations and test data.

The study is restricted to the bubbly and slug flow regimes (void fractions

below 0.75).

The numerical results given in this paper allow a rapid estimate to be

made of void fraction errors likely to arise in a particular code application due to deficiencies in interphase drag modelling.

t4 DOCUMENT ANALvYSIS a KIE'OROIOE•ISCRIPTORS I AVAILABILITY

RELAP5/MOD2, TRAC-PF1/MODI, ICAP Program, Interphase drag "'"MN

Unlimited

I SICURITY CLASSIPICATION

b IoNTIIERS/OpE4 ENoE01 TERMS 'Irn'l•assifie(

IT-V. UWVI

Unclassifiec

I I NIUM9ER0 PAGIS

is RC


NUREG/IA-0015 ASSESSMENT OF INTERPHASE DRAG CORRELATIONS IN THE RELAP5/MOD2 AND

TRAC-PFI/MOD2 CODES

JULY 1989

ire

z

U0.

U)o

z

0

C',

0 -4

LuC.)

z

Fn<

-ia.