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Effects of void uncertainties on the void reactivity coefficient and pin power distributions for a 10 × 10 BWR assembly
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NUCLEAR ENERGY Annals of Nuclear Energy 33 (2006) 119–125 www.elsevier.com/locate/anucene
Effects of void uncertainties on the void reactivity coefficient and pin power distributions for a 10 · 10 BWR assembly F. Jatuff a
a,*
, F. Giust b, J. Krouthe´n b, S. Helmersson c, R. Chawla
a,d
Laboratory for Reactor Physics and Systems Behaviour, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland Nordostschweizerische Kraftwerke AG Gescha¨ftseinheit Kernenergie, Parkstrasse 23, CH-5401 Baden, Switzerland c Westinghouse Electric Sweden, SE-721 63 Va¨stera˚s, Sweden d Swiss Polytechnic Institute of Technology, CH-1015 Laussane, Switzerland
b
Received 3 August 2005; accepted 19 September 2005 Available online 2 November 2005
Abstract An important source of uncertainty in boiling water reactor physics is associated with the precise characterisation of the moderation properties of the coolant and by-pass regions, with significant impact on reactor physics parameters such as the lattice neutron multiplication, the neutron migration area and the pin-by-pin power distribution. In this paper, the effects of certain relevant void-fraction uncertainties on reactor physics parameters have been studied for a BWR assembly of the type Westinghouse SVEA-96 using CASMO-4, HELIOS/PRESTO-2 and MCNP4C. The SVEA-96 geometry is characterised by the sub-division of the assembly into four different sub-bundles, by means of an inner by-pass with a cruciform shape. The study has covered: (a) the effects of different cross-section data libraries on the void coefficient of reactivity, for a wide range of void fractions; (b) the consideration of a water film inside the sub-bundle walls, and (c) the impact of partly inserted absorber blades producing very different void fractions in different sub-bundles. 2005 Elsevier Ltd. All rights reserved.
1. Introduction It is well known that BWR core physics are more complex than PWR physics because the coolant enters the core in single phase but rapidly develops different two-phase flow regimes with very strong axial dependence. Starting with sub-cooled boiling in the lower part, bubbly flow evolves in the middle part, finishing with annular flow and very high void fractions in the upper part of the core. The axially heterogeneous void distribution is also at the basis of the strong coupling between thermal-hydraulics and neutronics phenomena in the core. For instance, it is well known that instabilities can occur in BWRs because of this coupling. Another important factor is that the two-phase coolant flow in BWRs takes place essentially inside the channels that contain the fuel rod bundles, so that there is a physical *
Corresponding author. Tel.: +41 56 310 2894; fax: +41 56 310 4527. E-mail address: fabian.jatuff@psi.ch (F. Jatuff).
0306-4549/$ - see front matter 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.anucene.2005.09.007
separation between the inside-channel water flow (coolant) and the outside-channel water flow (by-pass). Whereas in the lower part of the core the coolant and by-pass flows represent quite similar neutron moderation conditions (single-phase or very low void fractions), in the middle and upper core regions the coolant is very different from the by-pass water imposing a strong degree of radial heterogeneity. BWR core physics has become even more complicated in recent years because modern fuel assemblies have new sophisticated features such as inner by-pass regions, designed to flatten the power distribution within the assembly, and part-length rods that increase locally the channel flow area, introducing larger uncertainties in relation to void distributions and their impact on integral reactor physics parameters. Some relatively recent efforts have been directed towards the evaluation of water density uncertainties at the level of a fuel pin cell (Goltsev et al., 2000). For an individual subchannel (see Fig. 1), the basic question addressed was as to
F. Jatuff et al. / Annals of Nuclear Energy 33 (2006) 119–125
Fuel pin cell
North-east sub-bundle
Bulk boiling
J I Water canal
H
Water wing
F
Outer gap
E
G
Fuel Pin
Sub-cooled boiling
Bubbles in continuous liquid Bubbly flow
Liquid droplets in vapour core Annular flow
120
Fig. 1. Axially dependent two-phase flow phenomena at the level of a single BWR fuel pin.
which extent the water density or void fraction distribution can be considered homogeneous around the fuel pin or if a detailed density field has to be determined. From a physics viewpoint, the main question is as to whether this moderator heterogeneity is important, i.e. if the typical characteristic size of this heterogeneity is significant in units of neutron mean free paths. The referred study showed that, for example, the explicit heterogeneity modelled results in an increase of the multiplication factor k-eff 0.1–0.4% higher than in the case with the normal homogeneous representation. The study referred above provides a very good illustration of the importance of void fraction heterogeneity at fuel pin level, for instance in the context of defining numerical benchmark tests of pin cell calculations for BWRs, but it does not exhaust the evaluation of uncertainties at this level. For example, the different fuel pin cells are not isolated and in principle cross-flow and void homogenisation in the sub-channels take place to a certain extent, particularly as an effect produced by the presence of spacers. This homogenisation is fairly short range, however. The purpose of this paper is to review other significant or even more important sources of uncertainty related to neutron moderation conditions in BWRs and the impact of these on reactor physics parameters such as the lattice neutron multiplication factor, the neutron migration area and the pin power distribution within the assemblies. The evaluation is made on the advanced Westinghouse SVEA-96 BWR assembly design, described in Section 2. This modern 10 · 10 lattice, depicted in Fig. 2, is highly heterogeneous and includes several burnable absorber fuel pins (average 235U enrichment >4%). The results of diverse void-effect reactor physics studies for this assembly are given in Section 3. First, the sensitivity of the void coefficient of reactivity to different neutron cross-section data libraries and energy group structures has been investigated,
D
Assembly wall
C B A 10 9
8
7
6
5
4
3
2
1
South-east quarter-channel Fig. 2. Westinghouse SVEA-96 BWR assembly.
assuming uniform voiding. Then, a number of non-uniform void distributions in the assembly have been simulated. In this context, the effect of cold channel walls and consequent heterogeneous void distributions inside the SVEA-96 quarter-channels (water film inside the channel wall) has been studied, analogously to previous work performed for simpler lattices (e.g., see Edenius, 1980, for an analogous study of an 8 · 8 assembly with 2.75% 235U enrichment). Then, the void fraction heterogeneity induced in the SVEA-96 by the presence of partly inserted absorber blades was modelled, with the purpose of identifying the situation with the largest void fraction heterogeneity in the assembly (Chiang and Chu, 1994). Finally, conclusions are given in Section 4. 2. SVEA-96 BWR assembly description The Westinghouse SVEA-96 BWR assembly is depicted in Fig. 2. This 10 · 10 fuel element comprises a bundle of 96 fuel pins contained inside an assembly channel that separates the coolant from the outer-assembly by-pass region or outer water gap (Helmersson et al., 1989). The most significant feature of this assembly type is that the bundle is in fact a set of four different sub-bundles or quarter-bundles, each of which is contained in a separate quarter-channel. Each quarter-channel is limited by the outer assembly wall and by an inner by-pass region consisting of a diamondshaped central water canal and water wings. In the inner by-pass region, the water flows like in the outer by-pass region, with the purpose of increasing the neutron moderation at the top of the assembly and to flatten the pin power distribution. Thus, two-phase flow of the coolant is restricted to the quarter-channel areas, which are largely thermal-hydraulically separated from one another. For the effects discussed here, the presence of
F. Jatuff et al. / Annals of Nuclear Energy 33 (2006) 119–125
the cross is in fact of less importance; similar heterogeneities are also found for open lattice designs.
160 ENDF/B-IV 70 groups
150
ENDF/B-IV 40 groups
140
3. Reactor physics studies of void effects
1.073 1.066 1.059
k-inf
1.052 1.045 1.038 1.031 ENDF/B-IV 70 groups ENDF/B-IV 40 groups JEF-2.2 70 groups 1.010 0
10
20
30
40
50
60
70
80
90
Void Fraction [%] Fig. 3. Multiplication factor k-inf vs. void fraction.
100
M2 [cm2]
120 110 100 90 80 70 60 50 0
10
20
30
40
50
60
70
80
90
100
Void Fraction [%] Fig. 4. Migration area M2 vs. void fraction.
1.4E-03 1.3E-03 1.2E-03 1.1E-03 9.7E-04
B2 [cm-2]
A SVEA-96 fresh fuel assembly model, as shown in Fig. 2, with a typical 235U enrichment distribution in the range 2–5 wt% has been developed and used with the CASMO-4 code (Edenius et al., 1995) version 2.05.04. The fuel temperature was fixed at 767 K and the coolant temperature at 560 K, corresponding to a pressure of 7.12 MPa. Reflected assembly calculations were performed parametrically with different values of the sub-channel void fraction, from 0 (pure liquid) to 100% void (pure steam). Whereas the geometrical and material definitions were kept fixed, calculations were performed using two different ENDF/B-IV-based cross-section libraries, viz., e4lbl70 (70 energy groups) and e4lbl40 (40 energy groups). The purpose was to evaluate the impact of energy-group structure on the multiplication factor (k-inf) and the migration area (M2) as function of the void fraction. The critical buckling B2, i.e. the neutron flux curvature necessary to achieve criticality in each case, was calculated from the relation k-inf = 1 + M2B2. Additionally, the parametric calculations were repeated using the JEF-2.2-base library j2lbb70.970702 provided with the code in 70 energy groups. The purpose here was to evaluate the impact due to different nuclear data sets, having fixed the group structure. The various results obtained are shown in Figs. 3–5. The results indicate that the ENDF/B-based 40- and 70group libraries give very similar results, but these differ significantly from the JEF-2.2 cross-section library results. The results corresponding to the neutron multiplication k-inf, i.e. the ratio of total neutron production to the total neutron absorption rate in the system, are very similar in the range 45–55% void, discrepancies being the largest at
1.017
JEF-2.2 70 groups
130
3.1. Effects of different cross-section libraries
1.024
121
8.7E-04 7.7E-04 6.7E-04 5.7E-04 4.7E-04 3.7E-04 ENDF/B-IV 70 groups
2.7E-04
ENDF/B-IV 40 groups
1.7E-04
JEF-2.2 70 groups
7.0E-05 0
10
20
30
40
50
60
70
80
90
100
Void Fraction [%] Fig. 5. Critical buckling B2 vs. void fraction.
0% or 100% void fraction (pure liquid or pure steam inside the quarter-channels). The migration area is about 1.3 cm2 larger with JEF-2.2. The combination of the variations of both the neutron multiplication k-inf and the migration area M2 results in the variation of the critical buckling B2, again showing higher discrepancies at no void or at high void fractions. Different predictions for the critical buckling should imply a different pin power peaking factor in the assembly. For the variations shown in Fig. 5, however, this effect is <1%. As important as the neutron multiplication factor itself is its variation as function of void. This variation corresponds to the void reactivity coefficient, of importance in the prediction of reactor transient behaviour. Formally, the void reactivity coefficient a was calculated from the results obtained as the difference of the k-inf in pcm (1 pcm = 10 5) divided by the difference of void fraction in %. The results obtained are given in Fig. 6. Except for very high void fractions, a calculated with JEF-2.2 is systematically larger in absolute magnitude than the ENDF-B-based libraries, i.e. by about 15% at low void and up to 40% at 60% void. Above 60%, the results given
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F. Jatuff et al. / Annals of Nuclear Energy 33 (2006) 119–125 -30
α = ∆ k-inf / ∆void [pcm/%]
-35 -40 -45 -50 -55 -60 ENDF/B-IV 70 groups
-65
ENDF/B-IV 40 groups
-70
JEF-2.2 70 groups -75 0
10
20
30
40
50
60
70
80
90
100
Void Fraction [%] Fig. 6. Void reactivity coefficient a vs. void fraction.
by the different libraries require further analysis, but suggest in any case the high sensitivity of the calculated coefficient in the case of lattices where the coolant is essentially steam and the neutron moderation occurs mainly in the by-pass regions. Such discrepancies are of course significant for an accurate calculation of reactor transients, and are associated with the effects of different nuclear data sets and/or different neutron energy group structures used for the calculations. 3.2. Void heterogeneity due to water film inside quarterchannel walls Typical LWR calculational lines rely on detailed 1D and 2D neutron transport calculations performed at fuel pin and fuel assembly levels, followed by 3D neutron diffusion calculations at whole-core level. The 3D whole-core calculations are performed for systems composed of homogenised fuel assemblies, each assembly being typically characterised by two-energy group cross-section properties. The transport codes predict the assembly cross sections parametrically for different burnup, temperature, moderator density and void fractions. The normal assumption is that the void fraction can have different values but distributed homogeneously in the coolant volume in each case, i.e. the corresponding cross-section dataset is parametric only in the average void fraction values and does not consider void fraction radial heterogeneity inside the fuel assembly channel. As indicated earlier, this assumption has been reasonable but modern assemblies, as illustrated by the SVEA-96 design, deserve further experimental and analytical studies. One new aspect of the SVEA-96 lattice is the variation in the local flow areas, effect even more pronounced in later designs employing part-length rods. This means that, especially in sub-cooled boiling regimes, the void fraction inside the quarter-channels could exhibit a significant heterogeneity.
Fig. 7. SVEA-96 quarter-channel void distribution (Windecker and Anglart, 2001). Top: computational fluid dynamic predictions. Bottom: calculated vs. measured void fractions.
Related investigations have been reported by Windecker and Anglart (2001) for a SVEA-96 quarter-channel geometry. Computational fluid dynamic predictions were compared with detailed void fraction measurements performed in the FRIGG loop at Westinghouse Electric Sweden. The measurement technique was based on c-ray computer tomography, employing an industrial robot and a 137Cs c-ray source. It was observed that the void fraction near the quarter-channel walls is significantly lower than at the centre of the sub-bundle. Fig. 7 illustrates the void fraction heterogeneity thus characterised. To evaluate the reactor physics effects of cold walls and quarter-channel void fraction heterogeneity, a SVEA-96 assembly has been modelled using MCNP4C (Briesmeister, 2000). In this model, the inner and outer by-pass regions were ascribed the same moderator density (0% void), and the sub-channels were modelled, in two separate cases, with: (a) homogeneous moderator density corresponding to a 25% void fraction, and (b) heterogeneous moderator density, consisting of a peripheral quarter-channel area in contact with the cold surfaces (4.8% void fraction) and an inner quarter-channel area with 35% void. The average
F. Jatuff et al. / Annals of Nuclear Energy 33 (2006) 119–125
south-east
1.693 0.584
1.690 0.583
1.705 0.585
1.690 0.583
1.693 0.584
1.705 0.585
1.702 0.585
south-west
north-west
north-west
1.677 0.602
1.694 0.606
1.711 0.604
1.693 0.600
south-west
south-east
1.693 0.600
1.711 0.604
north-east
1.677 0.602
north-east
Fig. 9. Axially averaged quantities in four SVEA-96 Optima assemblies, absorber blade fully withdrawn: sub-bundle, sub-bundle power [MW], void fraction.
0.9 north-west sub-bundle
0.8
north-east sub-bundle south-west sub-bundle
Void Fraction
0.7
sout-east sub-bundle
0.6 0.5 0.4 0.3 0.2 0.1 (absorber blades fully withdrawn)
0.0 0
The last situation studied corresponds to quarter-channel-wise void heterogeneity produced by very different sub-bundle powers in the same fuel assembly, as found in the case of the presence of an absorber blade. The presence of absorber blades is considered to introduce the largest void fraction heterogeneity inside the assembly; for the uncontrolled assembly, the heterogeneity of the void distribution as predicted by detailed subchannel analysis and void drift is less important (Chiang and Chu, 1994; Ama et al., 2002). The situation of the SVEA-96 with absorber blades has been investigated by using appropriate models and the HELIOS/ PRESTO-2 calculational line (Studsvik-Scandpower, 1998a,b) The results discussed here are typical of real power reactor calculations in core regions corresponding to hot assemblies. Two core regions cases were identified: (a) without the presence of a cruciform absorber blade, and (b) with an absorber blade partly inserted (75% from the bottom). The case without absorber
south-east
1.702 0.585
south-west
1.695 0.607
3.3. Void heterogeneity due to absorber blades
north-east
north-west
south-east
void fraction in the quarter-channels was the same for the two cases considered. Fig. 8 indicates, for case (b), the two different quarter-channel regions with low (peripheral) and high (central) void, respectively. Eigenvalue calculations were performed using 50 settling cycles followed by 450 cycles of 10,000 neutron histories per cycle. The homogenous and heterogeneous quarterchannel cases gave k-eff values of 1.00111 ± 0.00032 and 0.99867 ± 0.00031, respectively, i.e. a difference larger than 200 pcm. The power of pins surrounding the water canal was found to be 4% higher for the heterogeneous case, because the heterogeneity represents an ‘‘increased’’ bypass moderation region.
south-west
north-west
north-east
Fig. 8. MCNP4C model for the investigation of water-film void fraction heterogeneity inside quarter-channels.
123
34
68
102
136
170
204
238
272
306
340
374
Elevation [cm] Fig. 10. Axial void profile in the four sub-bundles of one of the SVEA-96 Optima assemblies (absorber blade fully withdrawn).
blade is depicted in Figs. 9 and 10. For the four assemblies (16 sub-bundles), the sub-bundle powers and void fractions are similar in all quarter-channels. The results for the analogous controlled region with absorber blade partly inserted are shown in Figs. 11 and 12. In Fig. 11, the axially averaged quarter-channel powers and void fractions indicate that there is an overall power tilt in each of the four assemblies towards the vertex of the absorber blade. (The assemblies are rotated such that north-west sub-bundles are close to the absorber blade vertex.) Thus, north-west sub-bundles develop 63% of the power of sub-bundles far away from the absorber blade (south-east sub-bundles). If the absorber blade is inserted a significant fraction of the assembly length, as considered in this example (75%), the void fractions developed in each
F. Jatuff et al. / Annals of Nuclear Energy 33 (2006) 119–125
south-east
south-west
north-east
south-east
1.566 0.559
1.287 0.432
1.284 0.415
1.562 0.544
north-west
north-west
south-west
1.287 0.432
0.975 0.229
0.974 0.215
1.284 0.415
south-west
north-west
north-west
1.247 0.430
0.956 0.235
0.964 0.219
1.267 0.417
south-west
south-east
1.267 0.417
1.537 0.544
north-east
north-east
south-east
1.247 0.430
1.526 0.560
north-east
Fig. 11. Axially averaged quantities in four SVEA-96 Optima assemblies, partly-inserted blade (75%): sub-bundle, sub-bundle power [MW], void fraction.
to an assembly average void fraction (dotted line in Fig. 12) in the four quarter-channels simultaneously (homogenous quarter-channel void). The second case was also an uncontrolled, reflected assembly, but now the void fraction varied differently for each quarter-channels as indicated in Fig. 12 (heterogeneous quarter-channel void). This second case represents the assembly situation above the partly inserted blades. The parameters studied were k-inf, M2 and the pin power distribution. The principal results are presented in Figs. 13–15. The effect of heterogeneous quarter-channel void is found to be 75 pcm on k-inf on the average, with a maximum value of 100 pcm. This value is perhaps small, but not completely insignificant. However, and as expected, the pin power distribution inside the assembly is very different when considering the more realistic heterogeneous void in the quarter-channels compared to the normal assumption in core simulation, i.e. the same void fraction in the different quarter-channels of the same assembly. The pin power peaking factor, instead of decreasing monotonically with increasing average void, increases upto 1.36 with the
0.9
1.075 north-west sub-bundle north-east sub-bundle south-west sub-bundle sout-east sub-bundle assembly average
0.8
1.070
Heterogeneous Sub-Bundle Void
1.065
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1.060
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1.055
k-inf
Void Fraction
0.7
115 Homogeneous Sub-Bundle Void
110 105 100 95 90 85
1.050
0.4
80
1.045
0.3
75 70
1.040
0.2
Migration Area [cm2]
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65 1.035
0.1 (75%-inserted absorber blades)
60
1.030
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55 0
0
34
68
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238
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5 10 15 20 25 30 35 40 45 50 55 60 65 70 75
374
Void Fraction [%]
Elevation [cm]
Fig. 13. k-inf and M2 vs. void fraction.
Fig. 12. Axial void profile in the four sub-bundles of one of the SVEA-96 Optima assemblies (absorber blade 75% inserted). 1.380 1.360 1.340
Power Peaking Factor
quarter-channel are very different and introduce another type of void heterogeneity in the fuel assembly. Fig. 12 describes how the void fraction develops with different slopes in the four quarter-channels. Both in the controlled and uncontrolled regions, the different quarter-channel powers and void fractions were calculated by PRESTO-2 using assembly cross-sections obtained with HELIOS, where the void fraction was assumed homogeneous for the four quarter-channels, i.e. the void fraction heterogeneity calculated at core level is not fed back to recalculate with HELIOS the basic assembly properties. To study the effect of this quarter-channelwise heterogeneity, CASMO-4 calculations were performed for two different cases, parametrically on the assembly average void fraction. The first case was an uncontrolled, reflected assembly with void fractions varying according
1.320 1.300 1.280 1.260 1.240 1.220 1.200 Sub-Bundle Homogeneous Void
1.180
Sub-Bundle Heterogeneous Void
1.160 0
5
10 15 20 25 30 35 40 45 50 55 60 65 70 75
Void Fraction [%] Fig. 14. Assembly pin power peaking factor vs. void fraction.
F. Jatuff et al. / Annals of Nuclear Energy 33 (2006) 119–125 8.0
18.0 rms
14.0
maximum minimum
6.0
10.0
5.0
6.0
4.0
2.0
3.0
-2.0
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0.0
Maxima and Minima [%]
Root-mean-square [%]
7.0
-14.0 0
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75
Void Fraction [%] Fig. 15. Quarter-channel heterogeneous (He) vs. homogeneous (Ho) pin power distributions: root-mean square and extrema of (He–Ho).
more realistic quarter-channel heterogeneous void. The rms of the pin power map differences is up to 4–7%. 4. Conclusion The effects of void fraction uncertainties on reactor physics parameters have been investigated for a Westinghouse SVEA-96 type of BWR fuel assembly. The codes CASMO-4, MCNP4C and HELIOS/PRESTO-2 were used to model homogenous and heterogeneous void fraction distributions at different levels. Emphasis was placed in the study of data library effects, void heterogeneity within quarter-channels (cold wall effect), and quarter-channelwise void heterogeneity as produced by the presence of absorber blades. The main conclusions and recommendations are: Even using the same code, calculational method, geometry and material descriptions, and convergence parameters, the use of different nuclear data libraries can result in significant differences in void coefficient predictions (40% or larger for very high, still physical voidages in BWRs with high power densities). This suggests prioritising validatory experiments as currently being considered in the framework of the LWR-PROTEUS Phase III research project at PSI (Jatuff, 2004) due to the importance of the void feedback on the core power generation. Cold wall and local flow area effects introduce a void-fraction heterogeneity, studied experimentally with c-ray attenuation techniques. This void fraction heterogeneity can impact the prediction of reactivity and pin power distributions by as much as 200 pcm and 4%, respectively. The void fraction distribution across the assembly is very heterogeneous when it is subject to the influence of inserted absorber blades. Approximating the actual heterogeneous situation by a homogeneous one can lead to underpredictions of pin-power peaking factors of
125
more than 10% at the cusping. This suggests that such void heterogeneities need to be considered explicitly at assembly level for the reliable prediction of safety margins, particularly when introducing/withdrawing absorber blades in the core if the movement is performed at full power, because the irradiation history effect (e.g., high plutonium buildup concentrated in pins near the blades) could even increase these discrepancies. These effects have of course been known in general and treated by the BWR core designers when setting requirements for thermal margins. Nevertheless, they contribute significantly to overall uncertainties and suggest further experimental studies and analytical improvements, as currently on-going in the framework of the LWR-PROTEUS Phase III project aimed at the experimental validation of production codes and models for the prediction of axial and radial pin-power distributions in modern part-length rod BWR assemblies, as well as void reactivity worths. Acknowledgements The LWR-PROTEUS experiments are being conducted jointly by PSI and the Swiss Nuclear Utilities. We are particularly grateful to H. D. Berger, R. Brogli, D. Furtado, U. Georg and G. Meier for their support of the programme. Also thanked is P. Grimm for having observed the sensitivity of the void reactivity coefficient to nuclear data libraries. References Ama, T., Hyoudou, H., Takeda, T., 2002. Effect of radial void distribution within fuel assembly on assembly neutronic characteristics. J. Nucl. Sci. Technol. 39, 90–100. Briesmeister, J.F., 2000. MCNPe – A General Monte Carlo N-Particle Transport code – Version 4C. LA-13709-M, Los Alamos National Laboratory. Chiang, R.T., Chu, K.H., 1994. Nonuniform void effect on BWR lattice reactivity. Trans. Am. Nucl. Soc. 70, 371–372. Edenius, M., 1980. Analysis of BWR bundles with nonuniform void within the channel. Trans. Am. Nucl. Soc. 35, 543–544. Edenius, M., Ekberg, K., Forssen, B.H., Knott, D., 1995. CASMO-4. A Fuel Assembly Burnup Program. UserÕs Manual. Studsvik/SOA-95/1, Studsvik of America. Goltsev, A.O., Martynov, D.N., Marin, S.V., Lekomtsev, A.A., 2000. The impact of the steam–water mixture heterogeneity on the results of boiling water reactor cell calculations. Nucl. Technol. 131, 153–158. Helmersson, S., Nerman, H., Paulsson, L., 1989. SVEA-96: BWR fuel for the 1990s. Nucl. Eur. 1–2, 37–38. Jatuff F., 2004. Experimental test matrix of the LWR-PROTEUS Phase III experiments. PSI Internal Report AN-41-04-02, Paul Scherrer Institute. Studsvik-Scandpower, 1998a. HELIOS Methods, Program Manual Rev. 3, Program HELIOS-1.5. Studsvik-Scandpower, 1998b. PRESTO-2 Models Manual, Rev. 1, Program PRESTO-2.1.3. Windecker, G., Anglart, H., 2001. Phase distribution in a BWR fuel assembly and evaluation of a multidimensional multifield model. Nucl. Technol. 134, 49–61.
NUCLEAR ENERGY Annals of Nuclear Energy 33 (2006) 119–125 www.elsevier.com/locate/anucene
Effects of void uncertainties on the void reactivity coefficient and pin power distributions for a 10 · 10 BWR assembly F. Jatuff a
a,*
, F. Giust b, J. Krouthe´n b, S. Helmersson c, R. Chawla
a,d
Laboratory for Reactor Physics and Systems Behaviour, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland Nordostschweizerische Kraftwerke AG Gescha¨ftseinheit Kernenergie, Parkstrasse 23, CH-5401 Baden, Switzerland c Westinghouse Electric Sweden, SE-721 63 Va¨stera˚s, Sweden d Swiss Polytechnic Institute of Technology, CH-1015 Laussane, Switzerland
b
Received 3 August 2005; accepted 19 September 2005 Available online 2 November 2005
Abstract An important source of uncertainty in boiling water reactor physics is associated with the precise characterisation of the moderation properties of the coolant and by-pass regions, with significant impact on reactor physics parameters such as the lattice neutron multiplication, the neutron migration area and the pin-by-pin power distribution. In this paper, the effects of certain relevant void-fraction uncertainties on reactor physics parameters have been studied for a BWR assembly of the type Westinghouse SVEA-96 using CASMO-4, HELIOS/PRESTO-2 and MCNP4C. The SVEA-96 geometry is characterised by the sub-division of the assembly into four different sub-bundles, by means of an inner by-pass with a cruciform shape. The study has covered: (a) the effects of different cross-section data libraries on the void coefficient of reactivity, for a wide range of void fractions; (b) the consideration of a water film inside the sub-bundle walls, and (c) the impact of partly inserted absorber blades producing very different void fractions in different sub-bundles. 2005 Elsevier Ltd. All rights reserved.
1. Introduction It is well known that BWR core physics are more complex than PWR physics because the coolant enters the core in single phase but rapidly develops different two-phase flow regimes with very strong axial dependence. Starting with sub-cooled boiling in the lower part, bubbly flow evolves in the middle part, finishing with annular flow and very high void fractions in the upper part of the core. The axially heterogeneous void distribution is also at the basis of the strong coupling between thermal-hydraulics and neutronics phenomena in the core. For instance, it is well known that instabilities can occur in BWRs because of this coupling. Another important factor is that the two-phase coolant flow in BWRs takes place essentially inside the channels that contain the fuel rod bundles, so that there is a physical *
Corresponding author. Tel.: +41 56 310 2894; fax: +41 56 310 4527. E-mail address: fabian.jatuff@psi.ch (F. Jatuff).
0306-4549/$ - see front matter 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.anucene.2005.09.007
separation between the inside-channel water flow (coolant) and the outside-channel water flow (by-pass). Whereas in the lower part of the core the coolant and by-pass flows represent quite similar neutron moderation conditions (single-phase or very low void fractions), in the middle and upper core regions the coolant is very different from the by-pass water imposing a strong degree of radial heterogeneity. BWR core physics has become even more complicated in recent years because modern fuel assemblies have new sophisticated features such as inner by-pass regions, designed to flatten the power distribution within the assembly, and part-length rods that increase locally the channel flow area, introducing larger uncertainties in relation to void distributions and their impact on integral reactor physics parameters. Some relatively recent efforts have been directed towards the evaluation of water density uncertainties at the level of a fuel pin cell (Goltsev et al., 2000). For an individual subchannel (see Fig. 1), the basic question addressed was as to
F. Jatuff et al. / Annals of Nuclear Energy 33 (2006) 119–125
Fuel pin cell
North-east sub-bundle
Bulk boiling
J I Water canal
H
Water wing
F
Outer gap
E
G
Fuel Pin
Sub-cooled boiling
Bubbles in continuous liquid Bubbly flow
Liquid droplets in vapour core Annular flow
120
Fig. 1. Axially dependent two-phase flow phenomena at the level of a single BWR fuel pin.
which extent the water density or void fraction distribution can be considered homogeneous around the fuel pin or if a detailed density field has to be determined. From a physics viewpoint, the main question is as to whether this moderator heterogeneity is important, i.e. if the typical characteristic size of this heterogeneity is significant in units of neutron mean free paths. The referred study showed that, for example, the explicit heterogeneity modelled results in an increase of the multiplication factor k-eff 0.1–0.4% higher than in the case with the normal homogeneous representation. The study referred above provides a very good illustration of the importance of void fraction heterogeneity at fuel pin level, for instance in the context of defining numerical benchmark tests of pin cell calculations for BWRs, but it does not exhaust the evaluation of uncertainties at this level. For example, the different fuel pin cells are not isolated and in principle cross-flow and void homogenisation in the sub-channels take place to a certain extent, particularly as an effect produced by the presence of spacers. This homogenisation is fairly short range, however. The purpose of this paper is to review other significant or even more important sources of uncertainty related to neutron moderation conditions in BWRs and the impact of these on reactor physics parameters such as the lattice neutron multiplication factor, the neutron migration area and the pin power distribution within the assemblies. The evaluation is made on the advanced Westinghouse SVEA-96 BWR assembly design, described in Section 2. This modern 10 · 10 lattice, depicted in Fig. 2, is highly heterogeneous and includes several burnable absorber fuel pins (average 235U enrichment >4%). The results of diverse void-effect reactor physics studies for this assembly are given in Section 3. First, the sensitivity of the void coefficient of reactivity to different neutron cross-section data libraries and energy group structures has been investigated,
D
Assembly wall
C B A 10 9
8
7
6
5
4
3
2
1
South-east quarter-channel Fig. 2. Westinghouse SVEA-96 BWR assembly.
assuming uniform voiding. Then, a number of non-uniform void distributions in the assembly have been simulated. In this context, the effect of cold channel walls and consequent heterogeneous void distributions inside the SVEA-96 quarter-channels (water film inside the channel wall) has been studied, analogously to previous work performed for simpler lattices (e.g., see Edenius, 1980, for an analogous study of an 8 · 8 assembly with 2.75% 235U enrichment). Then, the void fraction heterogeneity induced in the SVEA-96 by the presence of partly inserted absorber blades was modelled, with the purpose of identifying the situation with the largest void fraction heterogeneity in the assembly (Chiang and Chu, 1994). Finally, conclusions are given in Section 4. 2. SVEA-96 BWR assembly description The Westinghouse SVEA-96 BWR assembly is depicted in Fig. 2. This 10 · 10 fuel element comprises a bundle of 96 fuel pins contained inside an assembly channel that separates the coolant from the outer-assembly by-pass region or outer water gap (Helmersson et al., 1989). The most significant feature of this assembly type is that the bundle is in fact a set of four different sub-bundles or quarter-bundles, each of which is contained in a separate quarter-channel. Each quarter-channel is limited by the outer assembly wall and by an inner by-pass region consisting of a diamondshaped central water canal and water wings. In the inner by-pass region, the water flows like in the outer by-pass region, with the purpose of increasing the neutron moderation at the top of the assembly and to flatten the pin power distribution. Thus, two-phase flow of the coolant is restricted to the quarter-channel areas, which are largely thermal-hydraulically separated from one another. For the effects discussed here, the presence of
F. Jatuff et al. / Annals of Nuclear Energy 33 (2006) 119–125
the cross is in fact of less importance; similar heterogeneities are also found for open lattice designs.
160 ENDF/B-IV 70 groups
150
ENDF/B-IV 40 groups
140
3. Reactor physics studies of void effects
1.073 1.066 1.059
k-inf
1.052 1.045 1.038 1.031 ENDF/B-IV 70 groups ENDF/B-IV 40 groups JEF-2.2 70 groups 1.010 0
10
20
30
40
50
60
70
80
90
Void Fraction [%] Fig. 3. Multiplication factor k-inf vs. void fraction.
100
M2 [cm2]
120 110 100 90 80 70 60 50 0
10
20
30
40
50
60
70
80
90
100
Void Fraction [%] Fig. 4. Migration area M2 vs. void fraction.
1.4E-03 1.3E-03 1.2E-03 1.1E-03 9.7E-04
B2 [cm-2]
A SVEA-96 fresh fuel assembly model, as shown in Fig. 2, with a typical 235U enrichment distribution in the range 2–5 wt% has been developed and used with the CASMO-4 code (Edenius et al., 1995) version 2.05.04. The fuel temperature was fixed at 767 K and the coolant temperature at 560 K, corresponding to a pressure of 7.12 MPa. Reflected assembly calculations were performed parametrically with different values of the sub-channel void fraction, from 0 (pure liquid) to 100% void (pure steam). Whereas the geometrical and material definitions were kept fixed, calculations were performed using two different ENDF/B-IV-based cross-section libraries, viz., e4lbl70 (70 energy groups) and e4lbl40 (40 energy groups). The purpose was to evaluate the impact of energy-group structure on the multiplication factor (k-inf) and the migration area (M2) as function of the void fraction. The critical buckling B2, i.e. the neutron flux curvature necessary to achieve criticality in each case, was calculated from the relation k-inf = 1 + M2B2. Additionally, the parametric calculations were repeated using the JEF-2.2-base library j2lbb70.970702 provided with the code in 70 energy groups. The purpose here was to evaluate the impact due to different nuclear data sets, having fixed the group structure. The various results obtained are shown in Figs. 3–5. The results indicate that the ENDF/B-based 40- and 70group libraries give very similar results, but these differ significantly from the JEF-2.2 cross-section library results. The results corresponding to the neutron multiplication k-inf, i.e. the ratio of total neutron production to the total neutron absorption rate in the system, are very similar in the range 45–55% void, discrepancies being the largest at
1.017
JEF-2.2 70 groups
130
3.1. Effects of different cross-section libraries
1.024
121
8.7E-04 7.7E-04 6.7E-04 5.7E-04 4.7E-04 3.7E-04 ENDF/B-IV 70 groups
2.7E-04
ENDF/B-IV 40 groups
1.7E-04
JEF-2.2 70 groups
7.0E-05 0
10
20
30
40
50
60
70
80
90
100
Void Fraction [%] Fig. 5. Critical buckling B2 vs. void fraction.
0% or 100% void fraction (pure liquid or pure steam inside the quarter-channels). The migration area is about 1.3 cm2 larger with JEF-2.2. The combination of the variations of both the neutron multiplication k-inf and the migration area M2 results in the variation of the critical buckling B2, again showing higher discrepancies at no void or at high void fractions. Different predictions for the critical buckling should imply a different pin power peaking factor in the assembly. For the variations shown in Fig. 5, however, this effect is <1%. As important as the neutron multiplication factor itself is its variation as function of void. This variation corresponds to the void reactivity coefficient, of importance in the prediction of reactor transient behaviour. Formally, the void reactivity coefficient a was calculated from the results obtained as the difference of the k-inf in pcm (1 pcm = 10 5) divided by the difference of void fraction in %. The results obtained are given in Fig. 6. Except for very high void fractions, a calculated with JEF-2.2 is systematically larger in absolute magnitude than the ENDF-B-based libraries, i.e. by about 15% at low void and up to 40% at 60% void. Above 60%, the results given
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F. Jatuff et al. / Annals of Nuclear Energy 33 (2006) 119–125 -30
α = ∆ k-inf / ∆void [pcm/%]
-35 -40 -45 -50 -55 -60 ENDF/B-IV 70 groups
-65
ENDF/B-IV 40 groups
-70
JEF-2.2 70 groups -75 0
10
20
30
40
50
60
70
80
90
100
Void Fraction [%] Fig. 6. Void reactivity coefficient a vs. void fraction.
by the different libraries require further analysis, but suggest in any case the high sensitivity of the calculated coefficient in the case of lattices where the coolant is essentially steam and the neutron moderation occurs mainly in the by-pass regions. Such discrepancies are of course significant for an accurate calculation of reactor transients, and are associated with the effects of different nuclear data sets and/or different neutron energy group structures used for the calculations. 3.2. Void heterogeneity due to water film inside quarterchannel walls Typical LWR calculational lines rely on detailed 1D and 2D neutron transport calculations performed at fuel pin and fuel assembly levels, followed by 3D neutron diffusion calculations at whole-core level. The 3D whole-core calculations are performed for systems composed of homogenised fuel assemblies, each assembly being typically characterised by two-energy group cross-section properties. The transport codes predict the assembly cross sections parametrically for different burnup, temperature, moderator density and void fractions. The normal assumption is that the void fraction can have different values but distributed homogeneously in the coolant volume in each case, i.e. the corresponding cross-section dataset is parametric only in the average void fraction values and does not consider void fraction radial heterogeneity inside the fuel assembly channel. As indicated earlier, this assumption has been reasonable but modern assemblies, as illustrated by the SVEA-96 design, deserve further experimental and analytical studies. One new aspect of the SVEA-96 lattice is the variation in the local flow areas, effect even more pronounced in later designs employing part-length rods. This means that, especially in sub-cooled boiling regimes, the void fraction inside the quarter-channels could exhibit a significant heterogeneity.
Fig. 7. SVEA-96 quarter-channel void distribution (Windecker and Anglart, 2001). Top: computational fluid dynamic predictions. Bottom: calculated vs. measured void fractions.
Related investigations have been reported by Windecker and Anglart (2001) for a SVEA-96 quarter-channel geometry. Computational fluid dynamic predictions were compared with detailed void fraction measurements performed in the FRIGG loop at Westinghouse Electric Sweden. The measurement technique was based on c-ray computer tomography, employing an industrial robot and a 137Cs c-ray source. It was observed that the void fraction near the quarter-channel walls is significantly lower than at the centre of the sub-bundle. Fig. 7 illustrates the void fraction heterogeneity thus characterised. To evaluate the reactor physics effects of cold walls and quarter-channel void fraction heterogeneity, a SVEA-96 assembly has been modelled using MCNP4C (Briesmeister, 2000). In this model, the inner and outer by-pass regions were ascribed the same moderator density (0% void), and the sub-channels were modelled, in two separate cases, with: (a) homogeneous moderator density corresponding to a 25% void fraction, and (b) heterogeneous moderator density, consisting of a peripheral quarter-channel area in contact with the cold surfaces (4.8% void fraction) and an inner quarter-channel area with 35% void. The average
F. Jatuff et al. / Annals of Nuclear Energy 33 (2006) 119–125
south-east
1.693 0.584
1.690 0.583
1.705 0.585
1.690 0.583
1.693 0.584
1.705 0.585
1.702 0.585
south-west
north-west
north-west
1.677 0.602
1.694 0.606
1.711 0.604
1.693 0.600
south-west
south-east
1.693 0.600
1.711 0.604
north-east
1.677 0.602
north-east
Fig. 9. Axially averaged quantities in four SVEA-96 Optima assemblies, absorber blade fully withdrawn: sub-bundle, sub-bundle power [MW], void fraction.
0.9 north-west sub-bundle
0.8
north-east sub-bundle south-west sub-bundle
Void Fraction
0.7
sout-east sub-bundle
0.6 0.5 0.4 0.3 0.2 0.1 (absorber blades fully withdrawn)
0.0 0
The last situation studied corresponds to quarter-channel-wise void heterogeneity produced by very different sub-bundle powers in the same fuel assembly, as found in the case of the presence of an absorber blade. The presence of absorber blades is considered to introduce the largest void fraction heterogeneity inside the assembly; for the uncontrolled assembly, the heterogeneity of the void distribution as predicted by detailed subchannel analysis and void drift is less important (Chiang and Chu, 1994; Ama et al., 2002). The situation of the SVEA-96 with absorber blades has been investigated by using appropriate models and the HELIOS/ PRESTO-2 calculational line (Studsvik-Scandpower, 1998a,b) The results discussed here are typical of real power reactor calculations in core regions corresponding to hot assemblies. Two core regions cases were identified: (a) without the presence of a cruciform absorber blade, and (b) with an absorber blade partly inserted (75% from the bottom). The case without absorber
south-east
1.702 0.585
south-west
1.695 0.607
3.3. Void heterogeneity due to absorber blades
north-east
north-west
south-east
void fraction in the quarter-channels was the same for the two cases considered. Fig. 8 indicates, for case (b), the two different quarter-channel regions with low (peripheral) and high (central) void, respectively. Eigenvalue calculations were performed using 50 settling cycles followed by 450 cycles of 10,000 neutron histories per cycle. The homogenous and heterogeneous quarterchannel cases gave k-eff values of 1.00111 ± 0.00032 and 0.99867 ± 0.00031, respectively, i.e. a difference larger than 200 pcm. The power of pins surrounding the water canal was found to be 4% higher for the heterogeneous case, because the heterogeneity represents an ‘‘increased’’ bypass moderation region.
south-west
north-west
north-east
Fig. 8. MCNP4C model for the investigation of water-film void fraction heterogeneity inside quarter-channels.
123
34
68
102
136
170
204
238
272
306
340
374
Elevation [cm] Fig. 10. Axial void profile in the four sub-bundles of one of the SVEA-96 Optima assemblies (absorber blade fully withdrawn).
blade is depicted in Figs. 9 and 10. For the four assemblies (16 sub-bundles), the sub-bundle powers and void fractions are similar in all quarter-channels. The results for the analogous controlled region with absorber blade partly inserted are shown in Figs. 11 and 12. In Fig. 11, the axially averaged quarter-channel powers and void fractions indicate that there is an overall power tilt in each of the four assemblies towards the vertex of the absorber blade. (The assemblies are rotated such that north-west sub-bundles are close to the absorber blade vertex.) Thus, north-west sub-bundles develop 63% of the power of sub-bundles far away from the absorber blade (south-east sub-bundles). If the absorber blade is inserted a significant fraction of the assembly length, as considered in this example (75%), the void fractions developed in each
F. Jatuff et al. / Annals of Nuclear Energy 33 (2006) 119–125
south-east
south-west
north-east
south-east
1.566 0.559
1.287 0.432
1.284 0.415
1.562 0.544
north-west
north-west
south-west
1.287 0.432
0.975 0.229
0.974 0.215
1.284 0.415
south-west
north-west
north-west
1.247 0.430
0.956 0.235
0.964 0.219
1.267 0.417
south-west
south-east
1.267 0.417
1.537 0.544
north-east
north-east
south-east
1.247 0.430
1.526 0.560
north-east
Fig. 11. Axially averaged quantities in four SVEA-96 Optima assemblies, partly-inserted blade (75%): sub-bundle, sub-bundle power [MW], void fraction.
to an assembly average void fraction (dotted line in Fig. 12) in the four quarter-channels simultaneously (homogenous quarter-channel void). The second case was also an uncontrolled, reflected assembly, but now the void fraction varied differently for each quarter-channels as indicated in Fig. 12 (heterogeneous quarter-channel void). This second case represents the assembly situation above the partly inserted blades. The parameters studied were k-inf, M2 and the pin power distribution. The principal results are presented in Figs. 13–15. The effect of heterogeneous quarter-channel void is found to be 75 pcm on k-inf on the average, with a maximum value of 100 pcm. This value is perhaps small, but not completely insignificant. However, and as expected, the pin power distribution inside the assembly is very different when considering the more realistic heterogeneous void in the quarter-channels compared to the normal assumption in core simulation, i.e. the same void fraction in the different quarter-channels of the same assembly. The pin power peaking factor, instead of decreasing monotonically with increasing average void, increases upto 1.36 with the
0.9
1.075 north-west sub-bundle north-east sub-bundle south-west sub-bundle sout-east sub-bundle assembly average
0.8
1.070
Heterogeneous Sub-Bundle Void
1.065
0.6
1.060
0.5
1.055
k-inf
Void Fraction
0.7
115 Homogeneous Sub-Bundle Void
110 105 100 95 90 85
1.050
0.4
80
1.045
0.3
75 70
1.040
0.2
Migration Area [cm2]
124
65 1.035
0.1 (75%-inserted absorber blades)
60
1.030
0.0
55 0
0
34
68
102
136
170
204
238
272
306
340
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75
374
Void Fraction [%]
Elevation [cm]
Fig. 13. k-inf and M2 vs. void fraction.
Fig. 12. Axial void profile in the four sub-bundles of one of the SVEA-96 Optima assemblies (absorber blade 75% inserted). 1.380 1.360 1.340
Power Peaking Factor
quarter-channel are very different and introduce another type of void heterogeneity in the fuel assembly. Fig. 12 describes how the void fraction develops with different slopes in the four quarter-channels. Both in the controlled and uncontrolled regions, the different quarter-channel powers and void fractions were calculated by PRESTO-2 using assembly cross-sections obtained with HELIOS, where the void fraction was assumed homogeneous for the four quarter-channels, i.e. the void fraction heterogeneity calculated at core level is not fed back to recalculate with HELIOS the basic assembly properties. To study the effect of this quarter-channelwise heterogeneity, CASMO-4 calculations were performed for two different cases, parametrically on the assembly average void fraction. The first case was an uncontrolled, reflected assembly with void fractions varying according
1.320 1.300 1.280 1.260 1.240 1.220 1.200 Sub-Bundle Homogeneous Void
1.180
Sub-Bundle Heterogeneous Void
1.160 0
5
10 15 20 25 30 35 40 45 50 55 60 65 70 75
Void Fraction [%] Fig. 14. Assembly pin power peaking factor vs. void fraction.
F. Jatuff et al. / Annals of Nuclear Energy 33 (2006) 119–125 8.0
18.0 rms
14.0
maximum minimum
6.0
10.0
5.0
6.0
4.0
2.0
3.0
-2.0
2.0
-6.0
1.0
-10.0
0.0
Maxima and Minima [%]
Root-mean-square [%]
7.0
-14.0 0
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75
Void Fraction [%] Fig. 15. Quarter-channel heterogeneous (He) vs. homogeneous (Ho) pin power distributions: root-mean square and extrema of (He–Ho).
more realistic quarter-channel heterogeneous void. The rms of the pin power map differences is up to 4–7%. 4. Conclusion The effects of void fraction uncertainties on reactor physics parameters have been investigated for a Westinghouse SVEA-96 type of BWR fuel assembly. The codes CASMO-4, MCNP4C and HELIOS/PRESTO-2 were used to model homogenous and heterogeneous void fraction distributions at different levels. Emphasis was placed in the study of data library effects, void heterogeneity within quarter-channels (cold wall effect), and quarter-channelwise void heterogeneity as produced by the presence of absorber blades. The main conclusions and recommendations are: Even using the same code, calculational method, geometry and material descriptions, and convergence parameters, the use of different nuclear data libraries can result in significant differences in void coefficient predictions (40% or larger for very high, still physical voidages in BWRs with high power densities). This suggests prioritising validatory experiments as currently being considered in the framework of the LWR-PROTEUS Phase III research project at PSI (Jatuff, 2004) due to the importance of the void feedback on the core power generation. Cold wall and local flow area effects introduce a void-fraction heterogeneity, studied experimentally with c-ray attenuation techniques. This void fraction heterogeneity can impact the prediction of reactivity and pin power distributions by as much as 200 pcm and 4%, respectively. The void fraction distribution across the assembly is very heterogeneous when it is subject to the influence of inserted absorber blades. Approximating the actual heterogeneous situation by a homogeneous one can lead to underpredictions of pin-power peaking factors of
125
more than 10% at the cusping. This suggests that such void heterogeneities need to be considered explicitly at assembly level for the reliable prediction of safety margins, particularly when introducing/withdrawing absorber blades in the core if the movement is performed at full power, because the irradiation history effect (e.g., high plutonium buildup concentrated in pins near the blades) could even increase these discrepancies. These effects have of course been known in general and treated by the BWR core designers when setting requirements for thermal margins. Nevertheless, they contribute significantly to overall uncertainties and suggest further experimental studies and analytical improvements, as currently on-going in the framework of the LWR-PROTEUS Phase III project aimed at the experimental validation of production codes and models for the prediction of axial and radial pin-power distributions in modern part-length rod BWR assemblies, as well as void reactivity worths. Acknowledgements The LWR-PROTEUS experiments are being conducted jointly by PSI and the Swiss Nuclear Utilities. We are particularly grateful to H. D. Berger, R. Brogli, D. Furtado, U. Georg and G. Meier for their support of the programme. Also thanked is P. Grimm for having observed the sensitivity of the void reactivity coefficient to nuclear data libraries. References Ama, T., Hyoudou, H., Takeda, T., 2002. Effect of radial void distribution within fuel assembly on assembly neutronic characteristics. J. Nucl. Sci. Technol. 39, 90–100. Briesmeister, J.F., 2000. MCNPe – A General Monte Carlo N-Particle Transport code – Version 4C. LA-13709-M, Los Alamos National Laboratory. Chiang, R.T., Chu, K.H., 1994. Nonuniform void effect on BWR lattice reactivity. Trans. Am. Nucl. Soc. 70, 371–372. Edenius, M., 1980. Analysis of BWR bundles with nonuniform void within the channel. Trans. Am. Nucl. Soc. 35, 543–544. Edenius, M., Ekberg, K., Forssen, B.H., Knott, D., 1995. CASMO-4. A Fuel Assembly Burnup Program. UserÕs Manual. Studsvik/SOA-95/1, Studsvik of America. Goltsev, A.O., Martynov, D.N., Marin, S.V., Lekomtsev, A.A., 2000. The impact of the steam–water mixture heterogeneity on the results of boiling water reactor cell calculations. Nucl. Technol. 131, 153–158. Helmersson, S., Nerman, H., Paulsson, L., 1989. SVEA-96: BWR fuel for the 1990s. Nucl. Eur. 1–2, 37–38. Jatuff F., 2004. Experimental test matrix of the LWR-PROTEUS Phase III experiments. PSI Internal Report AN-41-04-02, Paul Scherrer Institute. Studsvik-Scandpower, 1998a. HELIOS Methods, Program Manual Rev. 3, Program HELIOS-1.5. Studsvik-Scandpower, 1998b. PRESTO-2 Models Manual, Rev. 1, Program PRESTO-2.1.3. Windecker, G., Anglart, H., 2001. Phase distribution in a BWR fuel assembly and evaluation of a multidimensional multifield model. Nucl. Technol. 134, 49–61.