Void-fraction distribution under high-pressure boil-off conditions in rod bundle geometry

Nuclear Engineenng ELSEVIER

Nuclear Engineering and Design 150 (1994) 95-105

andDesign

Void-fraction distribution under high-pressure boil-off conditions in rod bundle geometry H. K u m a m a r u ,

M. Kondo,

H. M u r a t a , Y. K u k i t a

Department of Reactor Safety Research, Japan Atomic Energy Research Institute, Tokai-Mura, Naka-Gun, Ibaraki-Ken 319-11, Japan

Received 18 May 1993

Abstract

Void fractions in a simulated pressurized water reactor (PWR) core rod bundle geometry were measured under boil-off conditions covering pressures from 3 to 12 MPa and mass fluxes from 5 to 100 kg m-2 s-i, with a particular interest in void fractions at higher pressures and relatively high mass fluxes. Test results showed that the Chexai-Leilouche model predicts best the present (volume-averaged) void-fraction data among correlations and models examined in this study. The volume-averaged void fractions obtained from differential pressure measurements are systematically smaller than the chordally averaged void fractions obtained from gamma densitometer measurements. Local void fractions were measured in the same bundle for non-heated steam-water two-phase flow of 3 MPa by using an optical void probe. It was found that the difference between the volume-averaged and chordally averaged void fractions mentioned above can be explained qualitatively by a local void-fraction distribution in the bundle measured in the latter tests.

I. Introduction

The prediction of two-phase mixture level in the nuclear core under boil-off conditions is of utmost imPortance for safety analyses of a small-break loss-of-coolant accident (LOCA) in a nuclear reactor. The mixture level is dependent on core liquid inventory and void-fraction distribution. Therefore, various correlations and models have been developed for the prediction of void fractions in a core fuel-rod bundle geometry. These include void-fraction correlations, drift-flux models and two-fluid models. Existing correlations and models are based on experimental data obtained mainly for pressures up to 8 MPa, i.e. void

fraction data for a rod bundle are scarcely available for pressures higher than 8 MPa (Anklam, 1982; Cunningham, 1973; Chexal, 1986). However, core boil-off at such high pressures is of recent concern in relation to certain classes of accidents and abnormal transients of a pressurized water reactor (PWR). For instance, core boil-off and dry-out may occur at the safety valve setpoint pressure (17 MPa) in a hypothetical event of a PWR station blackout (i.e. total loss of a.c. power) transient. Also, to date, boil-off experiments have been performed at mass fluxes les~ than about 40 kg m -2 s -I (Anklam, 1982; Anoda, 1990). However, co~e boil-off at higher mass fluxes is also of recent concern. For example, core

0029-5493/94/$07.00 © 1994 Elsevier Science S.A. All rights reserved SSD1 0029-5493(94) 00645-F

96

H. Kumamaru et aL / Nuclear Engineering and Design 150 (1994) 95-105

boil-off with high core power and corresponding high mass flux may occur during a hypothetical event of an anticipated transieat without scram (ATWS) in both a PWR and a boiling-water reactor (BWR). From these points of view, boil-off tests were conducted for pressures up to 12 MPa and mass fluxes up to 100 kg m -2 s -I in order to measure void fractions in a simulated core rod bundle geometry. Void-fraction data obtained from differential-pressure measurements are compared with several existing correlations and models in this paper. The volume-averaged void fractions obtained from differential pressure measurements showed systematically smaller values than chordally averaged void fractions obtained from gamma densitometer measurements. In order to explain this difference qualitatively, a local void-fraction distribution in the simulated core rod bundle was measured under high-pressure high-temperature conditions by using an optical void probe. To the authors' knowledge, this is the first attempt to measure the local void fractions under high-pressure high-temperature conditions by using a local void sensor. In this paper are also presented local void fractions measured in the tests and qualitative explanation of the difference between volumea',eraged and chordally averaged void fractions based on a local void-fraction distribution in a bundle measured in the tests.

2. Test facility Void fractions under boil-off conditions were measured in a heat-transfer test section of the Two-Phase Flow Test Facility (TPTF) (Nakamura, 1983) at the Japan Atomic Energy Research Institute (JAERI). Fig. 1 shows the schematic view of the heat transfer test section. (EL represents an elevation measured from the bottom of the heated length.) The test section contains 24 electrically-heated rods and 8 nonheated rods, simulating a full-length (3.7 m) PWR 17 x 17-type fuel bundle. The rods with an outer diameter of 9.5 mm are arranged at a 12.6 mm pitch and supported by spacers at seven eleva-

tions. The bundle has a radially and axially uniform power profile. The void fractions are measured with ten differential pressure transducers--nine segmental differential pressures distributed along the heated length (DP-I through DP-9) and one total differential pressure for the heated length (DP-10)-and with three gamma-ray densitometers (GD-I through GD-3). The gamma-ray beam of the gamma densitometer is 1.0 mm in horizontal width and 10.0 mm in vertical width. It is shot horizontally along the diameter of the pressure vessel, i.e. the direction from 270 ° to 90 ° (see cross-sectional view in Fig. 1). The gamma source is Cs-137 (10 Ci) and the detector is a NaI (TI) scintillation counter. In the tests, water alone (or steam and water separately) is (are) pumped from a boiler into the mixer, which is located beneath the test section inlet. The test section inlet flow rates are measured, for steam and water separately, with orifice flowmeters located upstream of the mixer. The steam and water temperatures are measured at the flowmeters and at the inlets of mixer.

3. Void fractions and comparison with correlations 3. I. Test conditions

The boil-off tests were performed under steadystate conditions. Nearly saturated (slightly subcooled) water was supplied to the test section inlet to compensate boiled-off (evaporated) water in the test section. The power input to the bundle was controlled so that the mixture level might be kept just above the top of the heated region. In total, 18 tests were conducted, covering test conditions of pressures from 3 to 12 MPa, mass fluxes from 5.7 to 101 kg m -2 s -~ and linear heating rates from 6.6 to 122 kW m -l. Table 1 (first five columns) presents the test conditions, including measuring errors for each variable. 3.2. Data reduction

Void fractions were derived from measurements of both differential pressure and gamma densito-

H. Kumamaru et al. I Nuclear Engineering and Design 150 (1994) 95-105 P : Pressure T : Temperolure DP : Differenliol Pressure

97

i-

,-, : Spacer

0

=, 2 e-~

o.

~ = -0 E "~r~ o

{,,

EL3500 EL3024

-[

EL2581 EL 209l

f

EL 1634

f 1.

EL118| ~

o"

'~(~(~

(~ (~ ~ ~ ~ ~

Unheo e oa ~Heoted Rod

©®®® 18¢ Rod Diameter = 9 . 5 mm Pitch = 12. 6 mm

Fig. 1. Schematic of heat transfer test section.

meter. The differential pressure under a boil-off (very low) flow condition arises mainly from the elevation pressure drop (loss). However, in calculating a void fraction from a differential pressure measurement, the frictional pressure drop for two-phase flow was estimated by using the Lockhart-Martinelli method (Lockhart, 1949). The form-loss pressure drop due to the spacer for two-phase flow was also calculated with the homogeneous model (Lahey, 1949). The form-loss coefficient of the spacer for single-phase flow was estimated from separate tests for the measurement of single-phase pressure drop in the test section.

However, both frictional and form-loss pressure drops were estimated to be negligible for the first four tests performed at each pressure (tests A1-A4, B1-B4 and C1-C4, refer to Table 1). It should be noted that the uses of the Lockhart-Martinelli method and the homogeneous model in calculating the two-ph~,se frictional and spacer form-loss pressure drops, respectively, are not assessed well for higher-pressure conditions. Table 1 (last four columns) also presents voidfraciion data including measuring errors obtained from DP-2, -4, -6 and -8, which do not include spacers.

H. Kumamaru et al. / Nuclear Engineering and Design 150 (1994) 95-105

98

Table i Test conditions and void-fraction data Test number

AI A2 A3 A4 A5 . -

B! B2 B3 B4 B5 B6 Ci C2 C3 C4 C5 C6

System pressure (MPa)

Linear power ( k W m -I)

Mass flux ( k g m - 2 s -t)

Inlet enthalpy ( kJ kg- i )

Void fraction ................................................. DP-2 DP-4 DP-6

DP-8

2.98 _+0.09 2.98 _+ 0.09 3.01 _+ 0.09 3.02 _+0.09 3.05 _+0.09 ,~. o IL 6.88 _+0.09 6.87_+0.09 6.91 _+0.09 6.91 _+0.09 6.92_+0.09 6.90_+0.09 ll.8+_0.1 ll.8_+ 0.1 li.8_+ 0.1 I 1.8 -+ 0. l 11,8_+ 0.1 il.8_+ 0.1

9.2 _+0.4 15.2 _+0.4 32.8 _+4.5 65.4 _+4.5 91.3 _+ 4.5 122.0+4,) 8.2 _+ 0.4 19.6 -+ 0.4 30.5 _+4.5 54.7 _+ 4.5 84.2_+4.5 109.6 -+ 4.5 6.6_+0.4 10.4_+ 0.4 25.6_+4.5 44.6 4- 4.5 75.9-+4.5 99.5_+4.5

5.9 _+0.3 10.6 _+0.3 20.7 _+0.3 40.5 _+0.3 70.4 _+0.1 100.1+0.1 5.7 _+0.3 ll.l _+0.3 20.8 _+0.3 40.8 _+0.3 71.3 -+0.1 100.7_+0.1 6.0-+0.3 11.5_+0.3 21.8_+0.3 42.3 -+ 0. l 71.8_+0.1 102.5 -+ 0.1

889__+ 11 907_+ li 940 _+ I l 969_+ II 988 + 11 992 -+ I ! Ill6_+ 12 1085 _+ 12 1189 -+ 12 1208_+ 12 1229 _+ 12 1234 _+ 12 1349_+ 16 1289 _+ 16 1351 _+ 16 1417 -+ 16 1440 _+ 16 1446 _+ 16

0.12_+0.01 0.19 -+ 0.01 0.32 ± 0.01 0.51 _+ 0.01 0,57 + 0 0 l 0.61 _+ 0.01 0.07_+0.02 0.12 _+ 0.02 0.22_+0.02 0.35_+0.02 0.46 _+ 0.02 0.50 _+ 0.02 0.06_+0.02 0.04 4- 0.02 0.18-+ 0.02 0.32_+0.02 0.42 4- 0.02 0.44 _+ 0.02

0.34_+0.02 0.48_+0.02 0.75 -+ 0.02 0.92_+0.02 0.92 _+0.02 0.92 _+0.02 0.24_+0.03 0.45 _+0.03 0.63_+0.03 0.82_+0.03 0.88 _+0.03 0.89 _+ 0.03 0.22_+0.04 0.28 -+ 0.04 0.53-+0.04 0.72_+0.04 0.85 -+ 0.04 0.86 _+0.04

V

.

U

7

- -

- -

3.3. Test results and comparison with correlations The volume-averaged void fractions obtained from the differential pressure measurements are compared with existing correlations and models which are considered to be applicable to rod bundle geometry. The correlations and models examined in this study are the Cunningham-Yeh (Cunningham, 1973), Anoda (Anoda, 1990) and Wilson (Meyer, 1964) correlations, the ChexalLellouche drift-flux model (Chexal, 1986), and the Bestion drift-flux model (Bestion, 1990) used in the CATHARE code (Rousseau, 1986). The Cunningham-Yeh correlation (Cunningham, 1973) was developed based on experiments conducted at pressures between 0.69 and 2.75 MPa in the Westinghouse Verification Test Facility (VTF). The VTF test section contained 480 electrically heated rods and 48 non-heated rods with a heated length of 3.66 m, simulating a 15 x 15-type fuel bundle. The radial power distribution was roughly uniform, but the axial distribution approximated a symmetric cosine with a peaking factor of 1.66.

0.23_____0.01 0.33 -+ 0.01 0.54 -+ 0.01 0.74 -+ 0.01 0.79 + 0.01 0.82 _+ 0.01 0.15 +0.02 0.29 _+ 0.02 0.44_+0.02 0.60_+0.02 0.70 _+ 0.02 0.74 _+0.02 0.13 -+ 0.03 0.16 4- 0.03 0.37_+0.03 0.52_+0.03 0.64 -+ 0.03 0.68 _+ 0.03

0.26__+0.01 0.37 -+ 0.01 0.61 -+ 0.01 0.82 -+ 0,01 0.86 _+0.01 0.89 _+ 0.01 0.17 -+ 0.02 0.35 _+ 0.02 0.51 _+0.02 0.69_+0.02 0.78 _+ 0.02 0.81 _+0.02 0.16_+ 0.03 0.20 -+ 0.03 0.42_+0.03 0.60-+0.03 0.74 _+ 0.03 0.77 _+0.03

The Anoda correlation (Anoda, 1990) is a modified version of the Cunningham-Yeh correlation. The modification was done by correlating test data obtained for pressures up to 17 MPa at the Large Scale Test Facility (LSTF) (JAERI, 1985) of JAERI. The LSTF is an integral test facility simulating a Westinghouse four-loop PWR. The LSTF core consists of about 1000 heated rods with a 3.66 m heated length simulating a PWR 17 x 17-type fuel bundle. The radial power profile was set to be uniform in the tests, while the axial profile had a peaking factor of 1.495. This test section is the largest among those which have been used for this kind of measurement at high pressures. The Wilson correlation (Meyer, 1964) is an empirical correlation based on experiments conducted at pressures from 4.2 to 14 MPa, using cylindrical vessels with diameters of 0.074, 0.3 and 0.45 m. The Chexal-Lellouche model (Chexal, 1986) is based on the drift-flux model, and is incorporated in the RELAPs/MOD3 code for the calculation of the interphase force between two phases (Carlson,

H. K u m a m a r u et ai. / Nuclear Engineering a n d Design 150 (1994) 9 5 - 1 0 5

• Test (DP) • Test (GD) o Cunningham-Yeh ---e - Anoda

!t

- e- -Wilson - - x - - ChexaI-Lellouche mz~- - Bestion

................

I ....

1 [

99

. . . . . . . . .

~ ~ / ' l

*d

................... ,....................... , ......................................

f 0.6 ................... !..................... i...~.:.!.~. .................................... i....................... i.................... i .'i el ~ i

0

,4_

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. . . . . . . . . . . . . . . . .

.," i

~ ......................

.........

o

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....................................................................

"

l& 3 ' ~ ~ 0.23'- ................. ~.-.--.F.I

j ....

1

j ....

1.5

j ....

2

I

IP

0

...................................................................

0.5

:

"....................................................

!

........

2.5

3

0.2

o

3MPa I 7MPa l-

!l 1.-, ,,

o-.,. ! ......

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

........

0

~

t. . . . . . . . . . . . . . . . . . . . . . . .

° t :

~r~ ,,o

i,,,!..,

0.4 0.6 0.8 Void Fraction (Measured)

Fig. 3. Comparison of void-fraction data using Cunningham3.5

Yeh correlation.

Elevation (m) Fig. 2. Example of void-fraction axial profile,

1

'

'

'

'

'

'

'

'

'

'

'

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I

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Z 0

1990). The model was developed by correlating several sets of steady-state test data covering wide ranges of conditions (0.1 to 7.6 MPa for bundle geometry) and geometries (PWR and BWR fuel assemblies as well as larger pipes up to 0.46 m in diameter). The Bestion model (Bestion, 1990) used in the CATHARE code (Rousseau, 1986) is also based on the drift-flux model. The Bestion drift-flux model was deduced from data for both core and steam generator tube bundle geometries. The core bundle data covered pressures ranging from 0.1 to 16 MPa. An e~_ample of the volume-averaged void-fraction axial profile, which was obtained from differential pressure measurements in Test B4, is shown in Fig. 2. Also in this figure are shown predictions by the correlations and models, and chordally-averaged void fractions obtained from gamma densitometer measurements. Figs. 3 - 5 show comparisons of all volume-averaged void fraction data from differential pressure measurements, except for DP-5 having the smallest measuring span, obtained in all the tests with the Cunningham-Yeh correlation, the

............................................................. i............................................................... " ...~............._"

0.8

•

0.4

i

i

I

i

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

o.0

-

i

i

~

' ' '

0.2

,,~

.................

i

''

'

i'

0.4 0.6 0.8 Void Fraction (Measured)

''

1

Fig. 4. Comparison of void-fraction data using Chexal-LelIouche correlation.

Chexal-Lellouche model and the Bestion model, respectively. Measuring errors for the void fraction data are presented in Table 1. (Measurement uncertainties for the void fractions obtained from DP-I, -3, -7 and -9 are nearly the same as for DP-2, -4, -6 and -8 presented in Table 1.) Table 2 summarizes statistical evaluations, mean error and standard deviation of each correlation for predicting the present data.

I00

H. Kumamaru et al. / Nuclear Engineering and Design 150 (1994) 95-105

1

. . . . . .

t

............

!. . . . . . . . . . . . .

e

o

.

.

.

0

.

O.e

!../

i

• 0.8

......

i. i

÷. . . . . . . . . .

;................

i

i

/~

: ...... o ~

o

i

•

..............

I

' ' ' ' I ' ' ' I ' ' ' , ,

0.4 0.6 0.8 Void Fraction (Measured)

Fig. 5. Comparison of void-fraction data using Bestion correlation.

The Cunningham-Yeh correlation overestimates the void fractions, particularly for higher void fractions. The degree of overestimation increases gradually with pressure. The reason for the overestimation may be that the correlation was developed based on bundle data covering pressures lower than about 3 MPa and obtained only for the total heated length. The Anoda correlation, a modification of the Cunningham-Yeh correlation, predicts the data somewhat better than the Cunningham-Yeh correlation. However, the Anoda correlation still overestimates the data, particularly in the region of higher void fractions, though the correlation was developed based on

bundle data covering pressures up to 17 MPa and obtained for segmental regions in the total heated length. The overestimation of the present data by the Cunningham-Yeh and Anoda correlations suggest that void fractions may depend on the bundle diameter or other factors. Generally, the Wilson correlation overestimates the data in the same degree as the CunninghamYeh correlation. However, the overestimation of the Wilson correlation decreases gradually with increasing pressure. The cause of overestimation is attributable to the fact that the correlation is based on cylindrical vessel data. Generally, the Chexal-LeUouche model predicts the void fraction data best among the correlations and models examined in this study. The model, however, overestimates the data for 3 MPa in the region of medium void fractions. The reason for its good prediction may be that the correlation is based on bundle data covering wide ranges of conditions. The Bestion model overestimates the data for all the pressures, except for the regions of very low void fractions and very high void fractions. However, the model prediction shows less scatter of the data than those calculated by the other correlations and models. The cause of overestimation is unclear to the authors at present. 3.4. Comparison between differential pressure data and gamma densitometer data

Fig. 6 compares the void fractions obtained from differential pressure measurements (which

Table 2 Mean errors and standard deviations 3

MPa

7

MPa

! 2 MPa

or

Cunningham-Yeh Anoda Wilson Chexal- Leliouche Bestion

0.065 0.028 0. ! 08 0.039 0.05 !

x X ( 0 t p r e d - - ~X. . . . ) or = X/(I/N) x X(%~d-- =.... _ e)2

e = (l/N)

0.051 0.040 0.064 0.042 0.059

0.080 0.052 0.065 - 0.002 0.062

0.059 0.048 0.055 0.029 0.058

Total

~;

or

£

0.077 0.059 0.026 - 0.040 0.046

0.08 ! 0.073 0:060 0.025 0.044

0.074 0.046 0.065 0.001 0.053

0.064 0.056 0.068 0.046 0.055

H. Kumamaru et al. / Nuclear Engineering and Design 150 (1994) 95-105

,.!..i..=.

distribution in the test section cross-section was measured by using an optical void probe.

t

i

[

i

'~ 0.8 g .g

, l

t '

),,

t

I

[]

4. Measurement

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

0.6

i

L Si

~,~ 0 . 4

................ I

,

'

i

...........i5.z~.-

0.2

>

I

0

0.2

,

i

oI'''i'''i'''i

,

0.4

distribution

Fig. 7 shows the schematic view of an optical probe which has been developed specially for use in high-pressure high-temperature conditions (Murata, 1992). The measuring principle of the probe is the same as that for an optical void probe used in low-pressure low-temperature conditions, i.e. projected light, passing down an optical fiber, is almost totally reflected (returned) or p a s ~ ~t the tip of probe when the probe is respectively in gas phase or liquid phase. However, the design of the probe has been modified for use in high-pressure high-temperature conditions. The materials - - sapphire, metallized/soldered layer, Kovar, etc. a n d the structure of these materials are seler,'ted specially for this purpose. The diameter of the tip is 1.8 mm. The light source for the projjected light is an infrared ray. The optical probe was set at the top position for the probe (EL 3500) out of three set positions (see Fig. 1, indicated with OP). The optical probe can be traversed along the bundle diameter, from the direction of 270 ° to 90 ° (see cross-sectional view in Fig. 1)0 by using a traversing equipment.

3MPa 7MPa .... 12MPa Figs. 8,9

&

i

of local void-fraction

4.1. Optical probe

1

"°

lOl

,

,

0.6

i i

,

,

,

0.8

Void Fraction (Differential Pressure) Fig. 6. Comparison of void-fraction data from differential pressure and g a m m a densitoraeter.

have been compared with correlations and models in the preceding section) with void fractions obtained from gamma densitometer measurements. The data plotted in Fig. 6 are obtained from combinations of DP-3 and GD-I, DP-6 and GD2, and DP-8 and GD-3. Measuring errors for the void fractions from the gamma densitometers are 0.03. This comparison shows that the gamma-densitometer-based void fractions, i.e. the chorda!ly averaged void fractions, are systematically greater than the differential-pressure-based void fractions, i.e. volume-averaged void fractions. It seems that the disagreement of these two void fractions comes from the non-uniform distribution of voids in the test section cross-section. In order to examine this point quantitatively, a local void-fraction

4.2. Test conditions Local void fractions were measured for steamwater two-phase flow without heat input from the for Light - Projecting

Fiber

Metolized/Soldered ! I ¢1 r n d

Layer /

Kava r

/

,

Light

/ Sapphire

Fig. 7. Optical void probe.

H. Kumamaru et al. I Nuclear Engineering and Design 150 (!994) 95-105

102

ooolooof

heated rods at 3 MPa, simulating boil-off conditions, i.e. steam-water two-phase mixture with the desired quality was provided to the test section. This is because the operating condition of the probe is limited to saturation temperature and pressure of 3 MPa at present. Four tests have been performed to date in slug flow region.

,0 0.8

ooo]o0=,,.0 o,

,:

.

6 = 20.8 ±0.4kg/mas x = 0.286_+0.015

I

,,.,..

4.3. Data reduction

0.6

A (volume-averaged) void fraction from differential pressure, 0tVA.[>p, is the average of data obtained from the top two differential pressure transducers, i.e. DP-8 and DP-9 (see Fig. 1). For these tests, the differential pressure arises only from the ,:levation pressure drop, and both frictional and form-loss pressure drops are negligible. A (chordally averaged) void fraction from the gamma densitometer, 0~CA.GD, is data obtained from the top gamma densitometer, i.e. GD-3. Figs. 8 and 9 show local void-fraction distributions along the bundle diameter measured with the optical probe under two different combinations of mass flux and quality. The optical probe was set at the top set position, i.e. EL 3500 (see Fig. l), as mentioned in the previous section. The local void fraction wa~ measured at each 2 mm

o oio o_oq_

0©0i0001

!.0

,

,

,

P = 2;9 : d . , Mi0 G = 10.5 *-0.4 kg/m'?s x = 0.467_+0.034

0.8 I

g 0.6 ,=-¢J h

0.4

0.2 B

o_

OCA,GO --

-40

'

= 0.39 +-0.03, OICA,OP= 0.36

f

-20 Radial

I

I

0 Position

I

k

i

2,, (ram)

Fig. 8. Local void-fraction distribution (!).

40

0.4 0

0.2 avA,op = 0.32 +-0.03, avA, oP = 0.33

o

= o,45._o.os. -40

= o.,44

-EO 0 20 Radial Position (ram)

40

Fig. 9. Local void-fraction distribution (2).

step along the bundle diameter, as shown in Figs. 8 and 9. Before steam-water two-phase flow tests, 100% and 0% output levels of the electrical signal (obtained from a light signal from the light-receiving fiber) were adjusted by output signals obtained in steam single-phase and water single-phase flow tests, respectively. Thereafter, output signals obtained in a steam-water two-phase flow test are treated basically as on-off signals by judging with use of a discriminating level of 15%, i.e. it is judged that the probe is in steam phase or in water phase when the output signal is respectively higher than or lower than 15%. The discriminating level of 15% was determined from a number of tests so that a chordally averaged void fraction obtained from local void fraction measured with the optical probe, as explained later, might agree with the chordally averaged void fraction measured with the gamma densitometer. The local void fraction was calculated from the on-off signals, i.e. the local void fraction is the ratio of the number of data points showing signals higher than 15% to the number of total data points. The output signal was taken at 500 Hz (500 measurements per second) for about 20 s at each point, i.e. at each 2 mm step. No significant difference in

H. Kumamaru et al. / Nuclear Eng#wering and Design 150 (1994) 95-105

the local void fraction was observed even if the data acquisition frequency was changed from 20 Hz to 500 Hz. The chordally-averaged void fraction from the optical probe, OtCA.OP,is calculated by simply averaging the local void fractions obtained along the bundle diameter with the optical probe. In the calculation, however, local void fractions in the peripheral region of the right side, where the local void fraction was not measured in order to protect the probe from damage at the wall of the right side, are estimated approximately by assuming a symmetric void fraction distribution but considering the measured asymmetry between the right side and left side. On the other hand, the volume-averaged (or area-averaged) void fraction based on the optical probe data, t~VA.OP, is calculated from the local void fractions obtained with the optical probe by assuming a pseudo-axial symmetry of void-fraction distribution as well as considering area distribution in each subchannel and in the entire bundle cross-se:tion. Fig. 10 shows weighting areas used in calculating ~VA.OP. Figs. 10(a) and 10(b) show the relation between measured points and weighting areas used to calculate an area-averaged void fraction in a subchannel for the cases of peripheral subchannel (dr, see Fig. 10(c)) and matrix subchannel (a, b~, b2, c~ and c2), respectively. The area-averaged void fraction in peripheral subchannel d2 is calculated from that for dj by considering the difference in void fraction between the right side and left side in the bundle. The area-averaged void fraction for subchannel b3 is an average of the void fractions for bx and b2. The area-averaged void fraction for subchannel e~ is estimated by interpolation between an average void fraction of c~ and c,, and an average void fraction of bl and b2, by considering the distances of subchannels from the bundle center. The area-averaged void fractions for the other matrix subchannels are estimated in the same manner. The area-averaged void fractions for peripheral subchanne!s d3 through d9 are assumed to be equal to an average void fraction of subchannels d~ and d2. The volume-averaged (or area-averaged) void fraction from the optical probe, ~VA.Op, is calculated from the area-averaged void

103

o Measured Point

.

_,

0.7

I_l_! 1_1~_

to ) Peripheral Subchonnel

..al_l I I ! I I ! I I 1_1

(b) Matrix Subcho nnel

(c) Bundle Fig. 10. Weighting areas used in obtaining area-averaged void fraction: (a) peripheral subchannel; (b) matrix subchannel; (c) bundle.

fractions for all the subchannels, obtained by the method mentioned above, by considering the subchannel areas which occupy in the bundle. The estimation of measuring errors for the void fractions obtained from the optical probe is difficult at present.

4.4. Test results and comparison with results obtained b), other methods As mentioned in the previous section, Figs. 8 and 9 show local void-fraction distributions along the bundle diameter measured with the optical probe under conditions of two different combinations of mass flux and quality. There is a non-uniform void distribution both in each subchannel and over the entire bundle. The local void fractions in the right side of the bundle have a ten-

104

H. Kumamaru et aL / Nuclear Engineering and Design 150 (1994) 95-105

dency to show somewhat higher values than the corresponding void fractions in the left side. Also in Figs. 8 and 9 are presented the void fraction ~VA.Or' (volume-averaged) and 0tCA.GD(chordally averaged) obtained from the differential pressure and gamma densitometer, respectively, and the void fraction ~VA.Op(volume-averaged) and ~CA.Op (chordally averaged) obtained from the optical probe by the methods mentioned in the preceding section. The relation between ~VA.DPand CtCA.GDis also plotted in Fig. 6 for these two tests. The void fractions ~VA.Dpand ~CA.GDagree nearly with the void fractions ~VA.Opand ~CA.OP, respectively, in both tests. This means that the difference between the volume-averaged void fraction from differential pressure and the chordally averaged void fraction from gamma densitometer can be explained quantitatively mainly by the local voidfraction distribution in the bundle. The difference between the volume-averaged and chordally averaged void fractions reflects mainly the difference in flow area between the central and peripheral regions, both in each subchannel and in the entire bundle, since the flow area of the peripheral region is relatively larger than that of the central region both in each subchannel and in the entire bundle. The present results suggest that bundle (volumeaveraged) void fractions may depend on the bundle diameter, radial power distribution, or other factors which affect the void distribution over the horizontal cross-section of bundle.

2. To investigate the difference mentioned above, local void fractions were measured in the same bundle for non-heated steam-water twophase flow of 3 MPa, simulating boil-off conditions, by using an optical void probe. It was found from test results that the difference between volume-averaged and chordally averaged void fractions mentioned above can be explained qualitatively by a local void fraction distribution in the bundle measured in the tests.

5. Conclusions

Subscripts

1. Void fractions in a simulated PWR core rod bundle geometry were measured under boil-off conditions covering pressures from 3 to 12 MPa and mass fluxes from 5 to 100 kg m -2 s -~. Test results showed that the Chexal-Lellouche model predicts best the present (volume-averaged) voidfraction data among correlations and models examined in this study. The test results also showed that the volume-averaged void fractions obtained from differential pressure measurements are systematically smaller than the chordally averaged void fractions obtained from gamma densitometer measurements.

CA DP GD meas OP pred VA

Acknowledgment The authors are indebted to Dr. Y. Anoda and other members of Thermo-Hydraulic Safety Engineering Laboratory of JAERI for their valuable suggestions and discussions during the course of this study.

Appendix A: Nomenclature G N P x

mass flux number of data pressure quality

Greek letters void fraction mean error standard deviation

chordalty averaged differential pressure gamma densitometer measured (experimental) optical probe predicted (calculated) volume-averaged

References T.M. Anklam and R.F. Miller, Void fraction under high pressure, low flow conditions in rod bundle geometry, Nucl. Eng. Des., 75 (1982) 99-108.

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Y. Anoda, Y. Kukita and K. Tasaka, Void fraction distribution in rod bundle under high pressure conditions, Proc. 1990 ASME Winter Annual Meeting, Dallas, Texas, November 1990, Advances in Gas-Liquid Flows, FED (99) 283-289. D. Bestion, Recent development on interfaciai fraction models, Proc. Eur. Two-Phase Flow Group Meeting, Geneva, 1990. K.E. Carlson et al., RELAP5/MOD3 Code Manual, Volume IV: Models and Correlations (Draft), NUREG/CR-5535, EGG-2596 (Draft) Vol. IV, 1990. B. Chexal and G. Lellouche, A full-range drift-flux correlation for vertical flows (Revision l), rep. EPRI NP-3989-SR, Revision l, 1986. J.P. Cunningham and H.C. Yeh, Experiments and void correlation for PWR small break LOCA conditions, Trans. Am. Nucl. Soc., 17 (1973) 367-370. R.T. Lahey and F.J. Moody, The Thermal-hydraulics of a Boiling Water Nuclear Reactor, American Nuclear Society, 1979, pp. 236-245.

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R.W. Lockhart and R.C. Martinelli, Proposed correlation of data for isothermal two-phase, two-component flow in pipes, Chem. Eng. Prog., 45 (1949) 39-48. C. Meyer and F. Wilson, Steam volume fractions in flowing and non-flowing two-phase mixtures, Trans. Am. Nucl. Soc., 7 (1964) 507-508. H. Murata, H. Kumamaru, K. Yamazaki and H. Yoshihama, Optical-method void meter for high-temperature high-pressure steam/water two-phase flow, Proc. 1992 Fall Meeting, Atomic Energy. Society of Japan, B56, Nagoya, Japan, 1992 (in Japanese). H. Nakamura et ai., System description for ROSA-IV two-phase flow test facility (TPTF), rep. JAERI-M 83-042, 1983. ROSA-IV Group, ROSA-IV large scale test facility (LSTF) system description, rep. JAERI-M 84-237, 1985. J.C. Rousseau et al., Assessment results of the French advanced safety code CATHARE, ENC Conf., Geneva, 1986.