- Email: [email protected]
Investigation of thermal margin in an advanced PWR core loaded with hexagonal fuel assembly
Pergamon PII: SO306-4549(97)00009-I
INVESTIGATION
OF THERMAL
Ann. Nucl. Energy. Vol. 24, No. 9, pp. 735-142, 1997 0 1997 Elsevier Science Ltd. All rights reserved Printed in Great Britain. 0306-4549197 $17.00 + 0.00
MARGIN IN AN ADVANCED
PWR CORE LOADED WITH HEXAGONAL
FUEL ASSEMBLY
Dae-Hyun Hwang, Yeon-Jong Yoo, Young-Jin Kim, Hyung-Kook Joo Korea Atomic Energy Research Institute P.O.Box 105, Yusung, Taejon, Korea Fax : +82 42 868 8307 Email : [email protected] (Received 17 December 1996) Abstract - An evaluation study has been performed on currently available CHF prediction models, including empirical correlations and phenomenological models, and experimental data base to determine their applicability to the analysis of thermal-hydraulic performance for triangular lattice assembly. It turns out, as the result of study, that the KfK-3 CHF correlation with the limit CHFR of 1.24 is the best prediction model. The thermal margin of hexagonal fuel assembly, which have been optimized in the aspect of maximizing the thermal margin, in 600MWe class PWR core have been evaluated and compared with those of square lattice fuel assemblies such as VANTAGE-SH and KOFA. COBRA-VI with Kl 10 correlation and TORC with KRB-1 correlation have been used for VANTAGE-SH and KOFA respectively. The analysis result shows that hexagonal fuel assembly is generally superior to square fuel assemblies with normal grids(KOFA), and comparable to those with turbulence promoters(VANTAGE5H), in terms of steady-state overpower margin. 0 1997 Elsevier Science Ltd. All rights reserved.
I. INTRODUCTION Since the second half of 1994, the Korea Atomic Energy Research Institute (KAERI) has been developing various elemental technologies to be incorporated into an advanced integral PWR concept(Chang, 1995), SMART(System integrated Modular Advanced Reactor) with an output in the range of 100 to 600 MWe. The reactor is purposed to be utilized as an energy source for seawater desalination as well as small scale power generation. Advanced technologies such as intrinsic and passive safety features are incorporated in establishing the design concepts so as to achieve inherent safety, enhanced operational flexibility and good economy. In kwping with these goals, the design considerations of reactor core include the following main features; low power density, soluble boron free operation, extended fuel cycle and improved fuel utilization, etc.. The reactor core is currently being designed with the fuel design based on existing Korean Fuel Assembly(KOFA) which is in 17x 17 rectangular rod array. In parallel, we are evaluating the potential of hexagonal lattice reactor core design as an option in order to realize benefit from the use of hexagonal lattice fuel assembly due to its favorable characteristics. The thermal-hydraulic characteristics of triangular lattice bundles, such as critical heat flux(CHF), bundle pressure drop and interchannel mixing, are quite different from those of square lattice bundles. They are largely influenced by the fuel assembly geometries such as rod diameter, rod pitch, and spacer type, and so on. In view of the subchannel geometry, the velocity profile in triangular lattice is much more regular than that in the square lattice, which results in more efficient heat removal from the heated surfaces. The hydraulic diameter of triangular lattice channel, however, will be reduced compared to square lattice channel for the same rod diameter and rod pitch. This may deteriorate the CHF performance and increase the hydraulic resistance in the subchannel. Since the existing thermal-hydraulic analysis models for square lattice bundles are mostly not valid for triangular lattice bundles, an investigation of adequate thermal-hydraulic models for the analysis of non-square lattice. bundle is required in the first place. Therefore, we performed an evaluation study on the currently available CHF prediction models, including empirical correlations and phenomenological models, to determine their applicability to triangular lattice bundle analysis. Based on the most adequate model, the better performance of triangular lattice fuel assembly in terms of steady-state overpower margin has been demonstrated by comparing to square lattice fuel assembly. 735
D.-H. Hwang et al.
136
II. CHF IN TRIANGULAR-LATTICE FUEL BUNDLES 1I.A
CHF Data Base
CHF data for triangular lattice bundles were collected from open literature. The CHF data provided in EPRI report(Fighetty & Reddy, 1982) has been obtained from a 19-rod hexagonal test bundle. The test bundle consisted of triangular lattice subchannels and was supported by four spacer grids without mixing devices. The JAERI performed steady-state CHF experiments using 3 test sections arranged in a triangular lattice(Iwamura, 1990). The test bundles are made of 4 or 7 electrically heated rods placed in ceramic flow shrouds. The rod bundles were supported by grid-type spacers. The CHF experiments at Bettis Atomic Power Laboratory were conducted as part of the light water breeder reactor development program (LeToumeau, 1975). The test bundles consisted of 20 heated rods arranged in a 5-by-4 array on a equilateral triangular pitch. The bundle was enclosed in a rhombic shroud box. In the Bettis experiments, CHF data were obtained from 14 different test sections with various types of spacer grids and heat flux distributions. They included one test bundle with axially nonuniform heat flux distribution, which is not used in the present study. The geometry of the test bundles and ranges of experiments are given in table 1. The configuration of CHF test bundles are shown in figure 1 ar-lattice C HF test bundle geometry and operating dat;a Table 1. Triant Wl# I lParameters EPBI JAEBI WAPD TS-B 1 TS-C 1 TS-D IAssembly configuration hexagonal hexagonal hexagonal rhombic rhombic Lattice type triangular triangular triangular triangular triangular Number of heated rods 19 7 7 4 20 Spacer type grid grid grid grid grid Grid spacing, m 0.38 0.24 0.2 0.2 0.3 Rod diameter, mm 10.7 9.5 9.5 9.5 6.35 I7.11 Rod-rod gap, mm 4.4 1.2 1.9 1.9 2.3 I 1.5 Pitch-to-diameter ratio 1.41 1.13 1.20 1.20 1.36 I 1.21 Heated length, m 1.52 0.5 0.5 1.37 1.0 Hydraulic diameter, mm 12.9 3.8 5.6 6.6 14.5 5.6 1.09 1.18 Radial peaking factor 1.28 1.0 to 1.5 1.0 Axial power profile UllifOllll uniform uniform uniform UllifOllll 39 103.4 10 - 39 10 - 39 28 - 139 Pressure, bar 1348 - 4078 1012 - 2669 1023 - 3087 1162 - 4267 1294 - 5466 Mass velocity, kg/m% 96 - 568 89 - 307 171 - 352 51- 475 112- 1172 Inlet subcooling, kJ/kg 0.19 - 0.49 0.14 - 0.44 -0.21 - 1.0 Channel exit quality 0.02 - 0.30 0.23 - 0.63 496 38 12 96 84 Number of data
o 00
w 0o”o
EPRI 19-rod
WAPD 2Omd
Figure 1.
JAERI 7-rod
Configuration of triangular lattice CHF test bundles
0
JAERI 4-rod
Investigation
II.B
of thermal
margin
137
Assessment of CHF Prediction Models
11.8.1 CHF prediction models CHF is a condition in which a small increase in heat flux leads to abrupt wall overheating, especially for subcooled flow, caused by the transition from nucleate to film boiling. Thus CHF in subcooled flow boiling is associated with the departure from nucleate boiling to film boiling. A number of empirical correlations as well as a few phenomenological (or semi-empirical) CHF models have been proposed during the last few decades to Although many CHF correlations have been developed for square lattice rod predict CHF in various geometries. bundles representing conventional LWRs, most of them are not valid for triangular lattice rod bundles. The CHF correlations applicable to the triangular-lattice rod bundles were thoroughly investigated. The correlations based on the local parameter hypothesis were not evaluated in this study since they required relevant subchannel analysis codes which are not available to us at present. Some empirical correlations based on system parameter concept have been assessed for CHF data in triangular-lattice bundles in this study. In addition, several phenomenological CHF models have been applied since they are not restricted by the channel geometry in principle. The applicability of system parameter CHF correlations available for the triangular lattice bundles such as the KfK-3(Donne, 1991) PI-3(Pemica & Cizek, 1992) and Bowring(Bowring, 1977) correlations were investigated. The KfK-3 correlation was developed on the basis of WSC-2 correlation(Bowring, 1979). The geometry dependent parameters related to the spacers were again determined from the U-IF data including triangular array of rod bundles with very tight lattices( 1.02
D.-H. Hwang et al.
738
During the modeling of turbulent interchange between the bubbly layer and core regions, two empirically determined parameters have been adopted.
Table 2. Characteristics of theoretic
based DNB models
CBF expression / \
ILee & Mudawar(l988) Lin, Lee & Pei(1989)
6
: from lateral force balance (empirical)
u,
: axial force balance (greater than UL)
Same with Lee & M&war model except the use of
two-phasemixture properties
I
Weisman & Pei(1983)
Gs: empirically determined lateral turbulent velocity F : fraction of heat generate vapor that enters core
11.8.2 Assessment of triangular-lattice bundle CHF data In the single channel approach, which was adopted in this study for the calculation of CHF in test bundles, the mass velocity of hot channel (a central coolant channel) is directly related to the distribution of subchannel hydraulic diameters. Assuming uniform water density, constant friction factors, and equal pressure drop in the various coolant channels, the velocity distribution factor, FG, is given by (d
& +
+%4
+G%)fi
mg ~JD,+nJ,K+%4~’ where n, n,,, n, is the number of the central, wall and comer channels, and A, A,,, A, and Db DJ,,,,Dhcare the cross section areas and hydraulic diameters of the central, wall and comer channels respectively. This factor was assumed to be unchanged at different power levels during the application of phenomenological CHF models by the heat balance method. The assessment of various CHF prediction models described in 2.2.1 against triangular-lattice CHF test data results in their applicable ranges and prediction accuracy summarized in table 3. Table 3.
Results of the evaluation of P/M statistic for various CHF prediction models Applicable ranges for G>lOOO for all data Pressure Mass velocity Quality(x) or (h&/s)
(bar) 1 I 27tnlM -- -- --I 1tn1!27 ___.-, 6 to 155
Yt-u_?
mYa-*
Bowring Lee &
MudaT--
Wei_qma&pei
EPAU-l
1 t
I 20t0205 (4
1
____._-50 to4000
A9 tn 17h
,
Linet al.
68to5547 -~
I
2to196
K&t0
1 I
to 169
1) meanof P/M,
wito75nn
I
1
35tol5560
1
Nl. A
1.04’~/o.158z’/685”
1.01 IO.120 1437
0
9s /0.140/726 -.-~~ 1.07/0.216/659
0.9210.126/471
N/A
I 1
(rd.7
1
2.87 IO.993 / 106
2.88 / 0.9% / 105
N/A _ ._
1.10/0.229/404
1000 to 5000
ac0.5
1.54 IO.325 I _23
1.54 10.325 I23
1000 to 5000
ad.7
0.99 / 0.130 I97
0.9.9/0.170/97 _.___ _
I 35t01556(1 271 to 5560
I
void fraction( n ) I I
Qul.6 -0.25
1.1510.159/57 0.89 IO.065 / 314
1.15/0.159157 0.89 IO.068 I253
2) standard deviation of PM, 3) number of data points within applicable ranges
In this evaluation, the heat balance technique was adopted in the application of phenomenological CHF models and CHF correlations based on the local parameter concept. As shown in the table, system parameter
Investigation
of thermal
correlations predict the CHF data for triangular-lattice
margin
739
bundles with the mean error of 4 - 7%, and the standard
deviation of 14 - 22%. For JAERl4-rod bundle data, these correlations tend to underpredict CHF by about 10 It was revealed that phenomenological CHF - 20%, which may be attributed to the test section wall effects. models, especially for sublayer dryout models (Katto model and Lee-Mudawar model), tend to overpredict CHF values in general. The near-wall bubble crowding model (Weisman-Pei model) also overpredict by about 15%. On the other hand, the Lin model, which is an improved version of sublayer dryout model at high quality conditions, shows reasonable accuracy within its applicable ranges. Although some of phenomenological CHF models show comparatively good predictions at subcooled conditions, it is still far from successful application of these models to rod bundle analysis from the viewpoint of their applicable ranges and the convergence of solution. The EPRl-1 CHF correlation, which was developed on the basis of square-lattice bundle CHF dam at PWR and BWR conditions, underpredicts CHF in triangular-lattice bundle by about 10%. From this result, it can be deduced that the CHF performance of a triangular-lattice bundle, on the basis of the same equivalent diameters, may be better than that of a square-lattice bundle. For the data base considered in this study, KfK-3 CHF correlation shows the best prediction capability in various CHF prediction models, At low mass velocity conditions (approximately less than 1000 kg/m2/s), however, it tends to overpredict CHF values considerably as shown in figure 2
0
lcm
2000
0
JAERI 7-rod
0
JAERI 4-rod
+
WAPD 20-rod
mo0
4000
5000
30
Mass velocity (kg/m*/s) Figure 2.
Distribution of P/M with respect to the mass velocity for KfK-3 correlation
III. EVALUATION 1II.A
OF THERMAL
MARGINS IN 600 MWe CORE
Limit CHFRs
For higher mass velocity qonditions (greater than 1000 kg/m2/s), the mean error and the standard deviation of P/M(predicted-to-measured CHF ratio) by KfK-3 CHF correlation were calculated to be 1% and 12%, respectively. It should be noted that the value of P/M listed in table 3 represents the critical powei ratio(CPR), not the DNB ratio(DNBR). This means that the magnitude of PA4 uncertainty can be significantly increased when converting into the DNBR uncertainty. If the population of P/MS has a normal distribution, then the correlation limit CHFR(CHF-to-local heat flux ratio), which is the basis for the evaluation of thermal margin, can be determined by Owen’s one-sided tolerance limit factor(Owen, 1963). The normality of P/M distribution was checked by D’-test methodology(ANS, 1974). It is shown that the P/M distribution of KtK-3 CHF correlation can be treated as a normal distribution with 5% significance level as shown in figure 3. The tolerance limit of
D.-H.
140
Hwang et al.
P/M was calculated by CHF&n,r =(~~~)+kx,,,~~P/M and the limit value was calculated to be 1.24.
)
Normalitv of P/M Distribution bv KfK-3 correlation
0
05
06
07
08
09
1.0
Predicted-to-Measured
Figure 3.
1II.B
11
12 CHF
13
14
Ratio
Comparison of P/M frequency with normal distribution
Evaluation of Thermal Margins
The steady-state thermal margins of 600 MWe class PWR core by replacing the existing square lattice fuel assemblies with the hexagonal fuel assemblies were evaluated, Two types of hexagonal fuel assemblies were conceptually designed through optimization study(Hwang, 1996); one is a 33 l-rods with 9.5 mm rod diameter and 12.6 mm rod pitch and the other is a 397-rods with 9.5 mm diameter and 11.5 mm rod pitch. The overpower margins for various core inlet temperature conditions were determined by considering the CHF design criterion only. Although the fuel centerline temperature limit can be violated prior to the CHF design limit at low inlet temperature conditions, these cases were not taken into consideration in this comparative study. The square lattice fuel assemblies considered in this study are 17-by-17 square lattice fuel assembly with turbulence promoters(VANTAGE-5H: V5H) and those with normal spacers(Korean fuel assembly: KOFA). COBRA/K1 lO(Hwang, 1993) and TORUKRB-l(Hwang, 1995) analysis systems were applied in the evaluation of thermal margins for V5H and KOFA loaded cores respectively. Since the Kl 10 and KRB-1 CHF correlations were developed on the basis of local condition hypothesis, the overpower margin should be calculated through the power iterations, The limit DNBR of the two correlation systems have been determined to be 1.18 and 1.23, respectively. The main thermal-hydraulic design parameters used in the thermal margin evaluations are given in table 4. As shown in figure 4, the thermal power margin of the V5H loaded core was about 17% higher than the KOFA loaded core. This increase can be readily explained by the effect of augmented turbulence mixing between subchannels due to the mixing vanes on the spacers and turbulence promoters( intermediate Flow Mixer: IFM). It was also found that the overpower margin decreases almost linearly with the increase of core inlet temperature. For the two types of hexagonal fuel assemblies which were chosen from the optimization study, the overpower margins were calculated using the KtK-3 U-IF correlation with the limit CHFR of 1.24. The channel imbalance parameter, Y’, and the velocity distribution factor, FG, was not applied (that is, equal to unity) since the effect of bundle boundary is negligible due to the large bundle size. For the case of 33 l-rod hexagonal fuel assembly, which has the same rod diameter and pitch with the square lattice fuel assembly, the amount of fuel rods loaded in the core increases by about 14% compared to the square lattice fuel loaded core. The reduction of hydraulic diameter of the hot subchannel may result in the decrease of CHF, while the increase of the mass velocity exert a
Investigation
of thermal
margin
741
beneficial influence upon U-IF. In addition, the absence of IFM grids will reduce the thermal mixing and affect the CHF adversely. The integration of these various effects yields an overpower margin of hexagonal fuel core comparable to or better than that of the V5H loaded core as shown in figure 4. Due to the characteristics of the CHF correlations, the declination of the overpower margin versus core inlet temperature line appears steeper in the hexagonal fuel loaded core. The increase of thermal margin for the 397-rod hexagonal fuel assembly is attributed to the beneficial effects of the increased mass velocity and reduced average heat flux, which surpass the thermal margin degradation owing tc the reduction of hydraulic diameter
Table 4.
Thermal-hydraulic Parameters
rs used for the evaluation of thermal margins 17x17 square FA Hexagonal FA 331~rod 1 397~rod (V=D
parann
Core thermal power, MWth System pressure, bar Core inlet temperature, “C Core flow rate, kg/s Number of fuel assemblies Enthalpy rise hot channel factor Axial power profile Mass velocity, kg/m% Average linear heat rate, kW/m Average heat flux, kW/m’ Core pressure drop, bar Hydraulic diameter, mm Rod pitch, mm
1.55 2349.7 13.48 451.1 1.2 11.8 12.6 264 25 5
Number of fuel rods/assembly Number of guide tubes/assembly Number of IFM grids
1933 155.1 276.9 8404.1 145 1.65 lopped cosine 2543.2 12.15 407.1 0.74 8.9 12.6 300 31 0
3200.1 10.12 339.2 1.41 5.8 11.5 360 37 0
2.2
2.1
3
2.0
B !i -0
1.9
C 'p
1.8
5 $ zi p (u .6
1.7
1.6
1.5
I
I
I
I
260
270
280
2x!
lo
Core Inlet Temperature (“C)
Figure 4.
Comparison of thermal margins for 600 MWe core with various fuel assemblies
142
D.-H. Hwang et al.
IV. CONCLUSIONS The thermal-hydraulic characteristics of an advanced reactor core loaded with hexagonal fuel assemblies have been evaluated in this study. The important results obtained are as follows: 1) Currently available CHF prediction models, including empirical correlations and phenomenological CHF models, and CHF data base for triangular-lattice bundles have been investigated. As the result, the limit CHFR of KfK-3 CHF correlation, which turned out to be the best model for the triangular lattice bundles through the evaluation of CHF data base so far collected, was determined to be 1.24 on the basis of heat balance method with single channel approach. 2) The thermal margin of hexagonal fuel assembly, which have been optimized in the aspect of maximizing the thermal margin, in 600 MWe class PWR core have been evaluated and compared with those of square lattice fuel assemblies such as VANTAGE-5H and KOFA. It turns out, as the results of analysis, that the thermal performance of hexagonal fuel assembly is superior to square fuel assemblies with normal grids(KOFA), and comparable to those with turbulence promoters(VANTAGE-SH), in terms of steady-state overpower margin.
REFERENCES ANS (1974) ANSI N15.15. Bowring R.W. (1977) I. Mcch. E., 175. Bowring R.W. (1979) AEEW-R983. Chang M.H. (1995) KAERI/RR-1498/94, KAERI. Domte M.D. (1991) KfK-4826. Fighetti CF. and Reddy D.G. (1982) EPRI-NP-2609 Vo1.3. Hwang D.H. (1993) RNl-711-004-P, KAERI. HwangD.H.,YooY.J.,ParkJ.R.,andKimY.J. (1995) J. KNS, 27,518. HwangD.H.,YooY.J.,KimY.J.andChangM.H.(1996)Proc.KNSSpringMtg.,2,3F-10. Iwamura T., et al. (1990) JAERI-M-90-044. Katto Y. (1992) Int. J. Heat Mass Transfer, 35, 1115. Lee C.H. and Mudawar I. (1988) Int. 1. Multiphase Flow, 14, 711. LeToumeau B.W., et al. (1975) WAPD-TM-1013. Lin W.S., Lee C.H. and Pei B.S. (1989) Nuclear Technology, 88,294. Owen D.B.(1963) SCR-607. Pemica R. and Cizek J. (1992) NURETH-5, paper 2B2. Weisman J. and Pei B.S. (1983) Int. J. Heat Mass Transfer, 26, 1463.
INVESTIGATION
OF THERMAL
Ann. Nucl. Energy. Vol. 24, No. 9, pp. 735-142, 1997 0 1997 Elsevier Science Ltd. All rights reserved Printed in Great Britain. 0306-4549197 $17.00 + 0.00
MARGIN IN AN ADVANCED
PWR CORE LOADED WITH HEXAGONAL
FUEL ASSEMBLY
Dae-Hyun Hwang, Yeon-Jong Yoo, Young-Jin Kim, Hyung-Kook Joo Korea Atomic Energy Research Institute P.O.Box 105, Yusung, Taejon, Korea Fax : +82 42 868 8307 Email : [email protected] (Received 17 December 1996) Abstract - An evaluation study has been performed on currently available CHF prediction models, including empirical correlations and phenomenological models, and experimental data base to determine their applicability to the analysis of thermal-hydraulic performance for triangular lattice assembly. It turns out, as the result of study, that the KfK-3 CHF correlation with the limit CHFR of 1.24 is the best prediction model. The thermal margin of hexagonal fuel assembly, which have been optimized in the aspect of maximizing the thermal margin, in 600MWe class PWR core have been evaluated and compared with those of square lattice fuel assemblies such as VANTAGE-SH and KOFA. COBRA-VI with Kl 10 correlation and TORC with KRB-1 correlation have been used for VANTAGE-SH and KOFA respectively. The analysis result shows that hexagonal fuel assembly is generally superior to square fuel assemblies with normal grids(KOFA), and comparable to those with turbulence promoters(VANTAGE5H), in terms of steady-state overpower margin. 0 1997 Elsevier Science Ltd. All rights reserved.
I. INTRODUCTION Since the second half of 1994, the Korea Atomic Energy Research Institute (KAERI) has been developing various elemental technologies to be incorporated into an advanced integral PWR concept(Chang, 1995), SMART(System integrated Modular Advanced Reactor) with an output in the range of 100 to 600 MWe. The reactor is purposed to be utilized as an energy source for seawater desalination as well as small scale power generation. Advanced technologies such as intrinsic and passive safety features are incorporated in establishing the design concepts so as to achieve inherent safety, enhanced operational flexibility and good economy. In kwping with these goals, the design considerations of reactor core include the following main features; low power density, soluble boron free operation, extended fuel cycle and improved fuel utilization, etc.. The reactor core is currently being designed with the fuel design based on existing Korean Fuel Assembly(KOFA) which is in 17x 17 rectangular rod array. In parallel, we are evaluating the potential of hexagonal lattice reactor core design as an option in order to realize benefit from the use of hexagonal lattice fuel assembly due to its favorable characteristics. The thermal-hydraulic characteristics of triangular lattice bundles, such as critical heat flux(CHF), bundle pressure drop and interchannel mixing, are quite different from those of square lattice bundles. They are largely influenced by the fuel assembly geometries such as rod diameter, rod pitch, and spacer type, and so on. In view of the subchannel geometry, the velocity profile in triangular lattice is much more regular than that in the square lattice, which results in more efficient heat removal from the heated surfaces. The hydraulic diameter of triangular lattice channel, however, will be reduced compared to square lattice channel for the same rod diameter and rod pitch. This may deteriorate the CHF performance and increase the hydraulic resistance in the subchannel. Since the existing thermal-hydraulic analysis models for square lattice bundles are mostly not valid for triangular lattice bundles, an investigation of adequate thermal-hydraulic models for the analysis of non-square lattice. bundle is required in the first place. Therefore, we performed an evaluation study on the currently available CHF prediction models, including empirical correlations and phenomenological models, to determine their applicability to triangular lattice bundle analysis. Based on the most adequate model, the better performance of triangular lattice fuel assembly in terms of steady-state overpower margin has been demonstrated by comparing to square lattice fuel assembly. 735
D.-H. Hwang et al.
136
II. CHF IN TRIANGULAR-LATTICE FUEL BUNDLES 1I.A
CHF Data Base
CHF data for triangular lattice bundles were collected from open literature. The CHF data provided in EPRI report(Fighetty & Reddy, 1982) has been obtained from a 19-rod hexagonal test bundle. The test bundle consisted of triangular lattice subchannels and was supported by four spacer grids without mixing devices. The JAERI performed steady-state CHF experiments using 3 test sections arranged in a triangular lattice(Iwamura, 1990). The test bundles are made of 4 or 7 electrically heated rods placed in ceramic flow shrouds. The rod bundles were supported by grid-type spacers. The CHF experiments at Bettis Atomic Power Laboratory were conducted as part of the light water breeder reactor development program (LeToumeau, 1975). The test bundles consisted of 20 heated rods arranged in a 5-by-4 array on a equilateral triangular pitch. The bundle was enclosed in a rhombic shroud box. In the Bettis experiments, CHF data were obtained from 14 different test sections with various types of spacer grids and heat flux distributions. They included one test bundle with axially nonuniform heat flux distribution, which is not used in the present study. The geometry of the test bundles and ranges of experiments are given in table 1. The configuration of CHF test bundles are shown in figure 1 ar-lattice C HF test bundle geometry and operating dat;a Table 1. Triant Wl# I lParameters EPBI JAEBI WAPD TS-B 1 TS-C 1 TS-D IAssembly configuration hexagonal hexagonal hexagonal rhombic rhombic Lattice type triangular triangular triangular triangular triangular Number of heated rods 19 7 7 4 20 Spacer type grid grid grid grid grid Grid spacing, m 0.38 0.24 0.2 0.2 0.3 Rod diameter, mm 10.7 9.5 9.5 9.5 6.35 I7.11 Rod-rod gap, mm 4.4 1.2 1.9 1.9 2.3 I 1.5 Pitch-to-diameter ratio 1.41 1.13 1.20 1.20 1.36 I 1.21 Heated length, m 1.52 0.5 0.5 1.37 1.0 Hydraulic diameter, mm 12.9 3.8 5.6 6.6 14.5 5.6 1.09 1.18 Radial peaking factor 1.28 1.0 to 1.5 1.0 Axial power profile UllifOllll uniform uniform uniform UllifOllll 39 103.4 10 - 39 10 - 39 28 - 139 Pressure, bar 1348 - 4078 1012 - 2669 1023 - 3087 1162 - 4267 1294 - 5466 Mass velocity, kg/m% 96 - 568 89 - 307 171 - 352 51- 475 112- 1172 Inlet subcooling, kJ/kg 0.19 - 0.49 0.14 - 0.44 -0.21 - 1.0 Channel exit quality 0.02 - 0.30 0.23 - 0.63 496 38 12 96 84 Number of data
o 00
w 0o”o
EPRI 19-rod
WAPD 2Omd
Figure 1.
JAERI 7-rod
Configuration of triangular lattice CHF test bundles
0
JAERI 4-rod
Investigation
II.B
of thermal
margin
137
Assessment of CHF Prediction Models
11.8.1 CHF prediction models CHF is a condition in which a small increase in heat flux leads to abrupt wall overheating, especially for subcooled flow, caused by the transition from nucleate to film boiling. Thus CHF in subcooled flow boiling is associated with the departure from nucleate boiling to film boiling. A number of empirical correlations as well as a few phenomenological (or semi-empirical) CHF models have been proposed during the last few decades to Although many CHF correlations have been developed for square lattice rod predict CHF in various geometries. bundles representing conventional LWRs, most of them are not valid for triangular lattice rod bundles. The CHF correlations applicable to the triangular-lattice rod bundles were thoroughly investigated. The correlations based on the local parameter hypothesis were not evaluated in this study since they required relevant subchannel analysis codes which are not available to us at present. Some empirical correlations based on system parameter concept have been assessed for CHF data in triangular-lattice bundles in this study. In addition, several phenomenological CHF models have been applied since they are not restricted by the channel geometry in principle. The applicability of system parameter CHF correlations available for the triangular lattice bundles such as the KfK-3(Donne, 1991) PI-3(Pemica & Cizek, 1992) and Bowring(Bowring, 1977) correlations were investigated. The KfK-3 correlation was developed on the basis of WSC-2 correlation(Bowring, 1979). The geometry dependent parameters related to the spacers were again determined from the U-IF data including triangular array of rod bundles with very tight lattices( 1.02
D.-H. Hwang et al.
738
During the modeling of turbulent interchange between the bubbly layer and core regions, two empirically determined parameters have been adopted.
Table 2. Characteristics of theoretic
based DNB models
CBF expression / \
ILee & Mudawar(l988) Lin, Lee & Pei(1989)
6
: from lateral force balance (empirical)
u,
: axial force balance (greater than UL)
Same with Lee & M&war model except the use of
two-phasemixture properties
I
Weisman & Pei(1983)
Gs: empirically determined lateral turbulent velocity F : fraction of heat generate vapor that enters core
11.8.2 Assessment of triangular-lattice bundle CHF data In the single channel approach, which was adopted in this study for the calculation of CHF in test bundles, the mass velocity of hot channel (a central coolant channel) is directly related to the distribution of subchannel hydraulic diameters. Assuming uniform water density, constant friction factors, and equal pressure drop in the various coolant channels, the velocity distribution factor, FG, is given by (d
& +
+%4
+G%)fi
mg ~JD,+nJ,K+%4~’ where n, n,,, n, is the number of the central, wall and comer channels, and A, A,,, A, and Db DJ,,,,Dhcare the cross section areas and hydraulic diameters of the central, wall and comer channels respectively. This factor was assumed to be unchanged at different power levels during the application of phenomenological CHF models by the heat balance method. The assessment of various CHF prediction models described in 2.2.1 against triangular-lattice CHF test data results in their applicable ranges and prediction accuracy summarized in table 3. Table 3.
Results of the evaluation of P/M statistic for various CHF prediction models Applicable ranges for G>lOOO for all data Pressure Mass velocity Quality(x) or (h&/s)
(bar) 1 I 27tnlM -- -- --I 1tn1!27 ___.-, 6 to 155
Yt-u_?
mYa-*
Bowring Lee &
MudaT--
Wei_qma&pei
EPAU-l
1 t
I 20t0205 (4
1
____._-50 to4000
A9 tn 17h
,
Linet al.
68to5547 -~
I
2to196
K&t0
1 I
to 169
1) meanof P/M,
wito75nn
I
1
35tol5560
1
Nl. A
1.04’~/o.158z’/685”
1.01 IO.120 1437
0
9s /0.140/726 -.-~~ 1.07/0.216/659
0.9210.126/471
N/A
I 1
(rd.7
1
2.87 IO.993 / 106
2.88 / 0.9% / 105
N/A _ ._
1.10/0.229/404
1000 to 5000
ac0.5
1.54 IO.325 I _23
1.54 10.325 I23
1000 to 5000
ad.7
0.99 / 0.130 I97
0.9.9/0.170/97 _.___ _
I 35t01556(1 271 to 5560
I
void fraction( n ) I I
Qul.6 -0.25
1.1510.159/57 0.89 IO.065 / 314
1.15/0.159157 0.89 IO.068 I253
2) standard deviation of PM, 3) number of data points within applicable ranges
In this evaluation, the heat balance technique was adopted in the application of phenomenological CHF models and CHF correlations based on the local parameter concept. As shown in the table, system parameter
Investigation
of thermal
correlations predict the CHF data for triangular-lattice
margin
739
bundles with the mean error of 4 - 7%, and the standard
deviation of 14 - 22%. For JAERl4-rod bundle data, these correlations tend to underpredict CHF by about 10 It was revealed that phenomenological CHF - 20%, which may be attributed to the test section wall effects. models, especially for sublayer dryout models (Katto model and Lee-Mudawar model), tend to overpredict CHF values in general. The near-wall bubble crowding model (Weisman-Pei model) also overpredict by about 15%. On the other hand, the Lin model, which is an improved version of sublayer dryout model at high quality conditions, shows reasonable accuracy within its applicable ranges. Although some of phenomenological CHF models show comparatively good predictions at subcooled conditions, it is still far from successful application of these models to rod bundle analysis from the viewpoint of their applicable ranges and the convergence of solution. The EPRl-1 CHF correlation, which was developed on the basis of square-lattice bundle CHF dam at PWR and BWR conditions, underpredicts CHF in triangular-lattice bundle by about 10%. From this result, it can be deduced that the CHF performance of a triangular-lattice bundle, on the basis of the same equivalent diameters, may be better than that of a square-lattice bundle. For the data base considered in this study, KfK-3 CHF correlation shows the best prediction capability in various CHF prediction models, At low mass velocity conditions (approximately less than 1000 kg/m2/s), however, it tends to overpredict CHF values considerably as shown in figure 2
0
lcm
2000
0
JAERI 7-rod
0
JAERI 4-rod
+
WAPD 20-rod
mo0
4000
5000
30
Mass velocity (kg/m*/s) Figure 2.
Distribution of P/M with respect to the mass velocity for KfK-3 correlation
III. EVALUATION 1II.A
OF THERMAL
MARGINS IN 600 MWe CORE
Limit CHFRs
For higher mass velocity qonditions (greater than 1000 kg/m2/s), the mean error and the standard deviation of P/M(predicted-to-measured CHF ratio) by KfK-3 CHF correlation were calculated to be 1% and 12%, respectively. It should be noted that the value of P/M listed in table 3 represents the critical powei ratio(CPR), not the DNB ratio(DNBR). This means that the magnitude of PA4 uncertainty can be significantly increased when converting into the DNBR uncertainty. If the population of P/MS has a normal distribution, then the correlation limit CHFR(CHF-to-local heat flux ratio), which is the basis for the evaluation of thermal margin, can be determined by Owen’s one-sided tolerance limit factor(Owen, 1963). The normality of P/M distribution was checked by D’-test methodology(ANS, 1974). It is shown that the P/M distribution of KtK-3 CHF correlation can be treated as a normal distribution with 5% significance level as shown in figure 3. The tolerance limit of
D.-H.
140
Hwang et al.
P/M was calculated by CHF&n,r =(~~~)+kx,,,~~P/M and the limit value was calculated to be 1.24.
)
Normalitv of P/M Distribution bv KfK-3 correlation
0
05
06
07
08
09
1.0
Predicted-to-Measured
Figure 3.
1II.B
11
12 CHF
13
14
Ratio
Comparison of P/M frequency with normal distribution
Evaluation of Thermal Margins
The steady-state thermal margins of 600 MWe class PWR core by replacing the existing square lattice fuel assemblies with the hexagonal fuel assemblies were evaluated, Two types of hexagonal fuel assemblies were conceptually designed through optimization study(Hwang, 1996); one is a 33 l-rods with 9.5 mm rod diameter and 12.6 mm rod pitch and the other is a 397-rods with 9.5 mm diameter and 11.5 mm rod pitch. The overpower margins for various core inlet temperature conditions were determined by considering the CHF design criterion only. Although the fuel centerline temperature limit can be violated prior to the CHF design limit at low inlet temperature conditions, these cases were not taken into consideration in this comparative study. The square lattice fuel assemblies considered in this study are 17-by-17 square lattice fuel assembly with turbulence promoters(VANTAGE-5H: V5H) and those with normal spacers(Korean fuel assembly: KOFA). COBRA/K1 lO(Hwang, 1993) and TORUKRB-l(Hwang, 1995) analysis systems were applied in the evaluation of thermal margins for V5H and KOFA loaded cores respectively. Since the Kl 10 and KRB-1 CHF correlations were developed on the basis of local condition hypothesis, the overpower margin should be calculated through the power iterations, The limit DNBR of the two correlation systems have been determined to be 1.18 and 1.23, respectively. The main thermal-hydraulic design parameters used in the thermal margin evaluations are given in table 4. As shown in figure 4, the thermal power margin of the V5H loaded core was about 17% higher than the KOFA loaded core. This increase can be readily explained by the effect of augmented turbulence mixing between subchannels due to the mixing vanes on the spacers and turbulence promoters( intermediate Flow Mixer: IFM). It was also found that the overpower margin decreases almost linearly with the increase of core inlet temperature. For the two types of hexagonal fuel assemblies which were chosen from the optimization study, the overpower margins were calculated using the KtK-3 U-IF correlation with the limit CHFR of 1.24. The channel imbalance parameter, Y’, and the velocity distribution factor, FG, was not applied (that is, equal to unity) since the effect of bundle boundary is negligible due to the large bundle size. For the case of 33 l-rod hexagonal fuel assembly, which has the same rod diameter and pitch with the square lattice fuel assembly, the amount of fuel rods loaded in the core increases by about 14% compared to the square lattice fuel loaded core. The reduction of hydraulic diameter of the hot subchannel may result in the decrease of CHF, while the increase of the mass velocity exert a
Investigation
of thermal
margin
741
beneficial influence upon U-IF. In addition, the absence of IFM grids will reduce the thermal mixing and affect the CHF adversely. The integration of these various effects yields an overpower margin of hexagonal fuel core comparable to or better than that of the V5H loaded core as shown in figure 4. Due to the characteristics of the CHF correlations, the declination of the overpower margin versus core inlet temperature line appears steeper in the hexagonal fuel loaded core. The increase of thermal margin for the 397-rod hexagonal fuel assembly is attributed to the beneficial effects of the increased mass velocity and reduced average heat flux, which surpass the thermal margin degradation owing tc the reduction of hydraulic diameter
Table 4.
Thermal-hydraulic Parameters
rs used for the evaluation of thermal margins 17x17 square FA Hexagonal FA 331~rod 1 397~rod (V=D
parann
Core thermal power, MWth System pressure, bar Core inlet temperature, “C Core flow rate, kg/s Number of fuel assemblies Enthalpy rise hot channel factor Axial power profile Mass velocity, kg/m% Average linear heat rate, kW/m Average heat flux, kW/m’ Core pressure drop, bar Hydraulic diameter, mm Rod pitch, mm
1.55 2349.7 13.48 451.1 1.2 11.8 12.6 264 25 5
Number of fuel rods/assembly Number of guide tubes/assembly Number of IFM grids
1933 155.1 276.9 8404.1 145 1.65 lopped cosine 2543.2 12.15 407.1 0.74 8.9 12.6 300 31 0
3200.1 10.12 339.2 1.41 5.8 11.5 360 37 0
2.2
2.1
3
2.0
B !i -0
1.9
C 'p
1.8
5 $ zi p (u .6
1.7
1.6
1.5
I
I
I
I
260
270
280
2x!
lo
Core Inlet Temperature (“C)
Figure 4.
Comparison of thermal margins for 600 MWe core with various fuel assemblies
142
D.-H. Hwang et al.
IV. CONCLUSIONS The thermal-hydraulic characteristics of an advanced reactor core loaded with hexagonal fuel assemblies have been evaluated in this study. The important results obtained are as follows: 1) Currently available CHF prediction models, including empirical correlations and phenomenological CHF models, and CHF data base for triangular-lattice bundles have been investigated. As the result, the limit CHFR of KfK-3 CHF correlation, which turned out to be the best model for the triangular lattice bundles through the evaluation of CHF data base so far collected, was determined to be 1.24 on the basis of heat balance method with single channel approach. 2) The thermal margin of hexagonal fuel assembly, which have been optimized in the aspect of maximizing the thermal margin, in 600 MWe class PWR core have been evaluated and compared with those of square lattice fuel assemblies such as VANTAGE-5H and KOFA. It turns out, as the results of analysis, that the thermal performance of hexagonal fuel assembly is superior to square fuel assemblies with normal grids(KOFA), and comparable to those with turbulence promoters(VANTAGE-SH), in terms of steady-state overpower margin.
REFERENCES ANS (1974) ANSI N15.15. Bowring R.W. (1977) I. Mcch. E., 175. Bowring R.W. (1979) AEEW-R983. Chang M.H. (1995) KAERI/RR-1498/94, KAERI. Domte M.D. (1991) KfK-4826. Fighetti CF. and Reddy D.G. (1982) EPRI-NP-2609 Vo1.3. Hwang D.H. (1993) RNl-711-004-P, KAERI. HwangD.H.,YooY.J.,ParkJ.R.,andKimY.J. (1995) J. KNS, 27,518. HwangD.H.,YooY.J.,KimY.J.andChangM.H.(1996)Proc.KNSSpringMtg.,2,3F-10. Iwamura T., et al. (1990) JAERI-M-90-044. Katto Y. (1992) Int. J. Heat Mass Transfer, 35, 1115. Lee C.H. and Mudawar I. (1988) Int. 1. Multiphase Flow, 14, 711. LeToumeau B.W., et al. (1975) WAPD-TM-1013. Lin W.S., Lee C.H. and Pei B.S. (1989) Nuclear Technology, 88,294. Owen D.B.(1963) SCR-607. Pemica R. and Cizek J. (1992) NURETH-5, paper 2B2. Weisman J. and Pei B.S. (1983) Int. J. Heat Mass Transfer, 26, 1463.