- Email: [email protected]
Moderator temperature effects on reactivity of HEU core of MNSR
Annals of Nuclear Energy 49 (2012) 207–211
Contents lists available at SciVerse ScienceDirect
Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene
Technical note
Moderator temperature effects on reactivity of HEU core of MNSR Siraj-ul-Islam Ahmad ⇑, Tasveer Muhammad Sahibzada Pakistan Institute of Engineering and Applied Sciences, Islamabad 45650, Pakistan
a r t i c l e
i n f o
Article history: Received 28 May 2012 Received in revised form 30 June 2012 Accepted 4 July 2012 Available online 2 August 2012 This article is dedicated to our late Professor Nasir Ahmad. The work presented had been carried out in his guidance.
a b s t r a c t In this article we report on analyses that were performed to investigate the influence of cross section differences among libraries released by various centers on reactivity of Miniature Neutron Source Reactors. The 3D model of the core was developed with WIMS-D and PRIDE codes and six cross section libraries were used including JENDL-3.2, JEF-2.2, JEFF-3.3, ENDF/B-VI and ENDF/B-VII, and IAEA library. It was observed that all the libraries predict the reactivity within 10%, with IAEA library giving minimum reactivity worth, and JEF-2.2 data library resulted in highest worth. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: MNSR Moderator temperature coefficient WIMS-D PRIDE Cross section libraries
1. Introduction Reactivity is affected by many factors, including temperature of coolant, moderator, fuel and structural materials and the density of these materials. Change in reactivity per unit increase in temperature is known as temperature coefficient of reactivity and is measured in units of mk/°C. As temperature of the moderator is changed, its number density changes and hence moderator to fuel ratio (Nm/Nf) is changed. The Nm/Nf affects the thermal utilization factor and the resonance escape probability. The thermal utilization factor decreases with increase in Nm/Nf. This is due to the fact that with increase in moderator concentration, the absorption in it also increases, which causes thermal utilization factor to decrease. On the other hand the resonance escape probability increases with increase in Nm/Nf, because as moderation increases more neutrons will cross the resonance region without absorption. For low values of Nm/Nf the increase in resonance escape probability is dominant as compared to decrease in thermal utilization factor so effective multiplication factor will increase with increase in Nm/Nf. For values above an optimum value of Nm/Nf the change in thermal utilization factor becomes dominant as compared to change in resonance escape probability which causes the multiplication factor to decrease with increase in Nm/Nf. The nuclear cross section data plays a vital role in reactor physics calculations. For accurate analysis this data is continuously up⇑ Corresponding author. Tel.: +92 51 9258517. E-mail address: [email protected] (S.I. Ahmad). 0306-4549/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.anucene.2012.07.004
graded by various data centers. Due to different models and experiments used by laboratories, there always exists some difference in various evaluations of this data. For suitability of a specific data library, it needs to compute reactor physics parameters with various data sets and to identify the differences in parameter values. Recently released evaluated nuclear data files: ENDF/B-VI (Lemmel et al., 2001), JENDL-3.2 (Nakagawa et al., 1995), CENDL2.1 (INDC, 1991), FOND (Koscheev et al., 2001), BROND-2 (Manokhin, 1989) and JEFF-3.1 (JEFF, 2005; IAEA, 2005) were processed by International Atomic Energy Agency during a coordinated research project, and the resultant WIMS-D (Halsall, 1980) libraries were freely distributed through web to interested users. These data libraries have been used to perform analysis of MTR type research reactors (Ahmad et al., 2004, 2006, 2009a; Ahmad and Ahmad, 2005, 2006a,b). In this work we intend to investigate the effect of various data libraries on Miniature Neutron Source Reactor (MNSR) moderator temperature coefficient of reactivity. The studies were carried out using ENDF/B-VI, ENDF/B-VII, JENDL-3.2, JEF-2.2, IAEA and JEFF-3.1 cross-section libraries. 2. Reactor description Pakistan Research Reactor-2 is a 30 kW tank in pool type MNSR, cooled, moderated, reflected and shielded by demineralized light water and Beryllium (Wyne and Meghji, 1990). PARR-2 is fueled with 90% enriched Uranium and the fuel meat is Uranium–Aluminum alloy of U-Al4. The core of PARR-2 consists of 344 fuel pins arranged in concentric arrays and forms a square cylinder with
208
S.I. Ahmad, T.M. Sahibzada / Annals of Nuclear Energy 49 (2012) 207–211
(a) cm 380
Table 2 Problem mesh details.
Jin=0 10
30
50
70
90
130
150
170
360
280
Case no.
Mesh size (cm)
No. of meshes
Radial
Axial
Radial
Axial
1 2 3 4 5
20.00 10.00 5.00 2.50 1.667
40.00 20.00 10.00 5.00 3.333
9 17 34 68 102
10 19 38 76 114
900 5.814 45,220 356,592 1,197,684
Table 3 Comparison of multiplication factors and power peaks. Case no.
J=0
1 2 3 4 5
Jin=0
280
0
Jin=0 X
0 10 0 10
30
50
70
90
Multiplication factor
Peak to average power density
Reported
PRIDE
Reported
PRIDE
1.03176 1.02913 1.02864 1.02887 1.02896
1.03177 1.02913 1.02864 1.02887 1.02896
2.3765 2.5672 2.5035 2.4081 2.3780
2.3818 2.5676 2.5033 2.4078 2.3809
B C D E F G H I 0.6574 0.9101 0.9707 0.5802 1.3178 1.5651 1.4485 0.7356 2 0.6574 0.9101 0.9707 0.5802 1.3177 1.5650 1.4484 0.7355 0.0000 0.0000 0.0000 0.0000 -0.0001 -0.0001 -0.0001 -0.0001 0.6366 0.9537 1.0619 1.1406 1.4045 1.5742 1.5604 3 0.6367 0.9212 1.0619 1.1406 1.4045 1.5741 1.5602 0.0001 -0.0325 0.0000 0.0000 0.0000 -0.0001 -0.0002 0.5459 0.9420 1.0755 1.2226 1.4030 1.4797 4 0.5459 0.9421 1.0755 1.2226 1.4030 1.4796 0.0000 0.0001 0.0000 0.0000 0.0000 -0.0001 0.7383 0.8970 1.0083 1.2480 5 0.7383 0.8970 1.0083 1.2480 0.0000 0.0000 0.0000 0.0000 0.4725 0.6720 0.4244 Reported 6 0.4726 0.6720 0.4244 Calculated 0.0001 0.0000 0.0000 Difference 0.4717 7 0.4717 0.0000
20
(b)
Unknowns
110 130 150 170 cm
Fig. 2. Comparison of relative power densities for Case 2.
30 50 70 Y
90
Fuel 1
110 =0 J in
Fuel 2
130
Fuel 2 + Rod
150
Reflector
170 cm
Reflector + Rod
Fig. 1. IAEA 3D PWR benchmark problem (a) axial and (b) radial core configurations.
Table 1 Two-group constants for IAEA 3D PWR problem. S.no.
Material
1 2 3 4 5
Fuel 1 Fuel 1 + rod Fuel 2 Reflector Reflector + rod
D (cm)
Ra (cm 1)
mRf (cm 1)
Rs (cm 1)
1
2
1
2
1
2
1?2
1.5 1.5 1.5 2.0 2.0
0.4 0.4 0.4 0.3 0.3
0.01 0.01 0.01 0.00 0.00
0.085 0.130 0.080 0.010 0.055
0.0 0.0 0.0 0.0 0.0
0.135 0.135 0.135 0.000 0.000
0.02 0.02 0.02 0.04 0.04
Control Rod
Fuel
Control Rod Guide Tube
Reflector
Water
Irradiation Site
Fig. 3. Cross-sectional view of fuel region of MNSR.
S.I. Ahmad, T.M. Sahibzada / Annals of Nuclear Energy 49 (2012) 207–211
230 mm diameter. The total fuel loading in the fresh core is about 994.8 g of 235U. Upper and lower grid plates secure the fuel pins to form a fuel cage. The fuel pins are fixed in the bottom grid plate by slightly conical self-locking fittings and are free to expand through the upper grid plate. Four out of the 354 holes, provided in the grid plates are used for fixing stainless steel tie bolts to keep the fuel cage intact, rest of the six holes are occupied by Aluminum dummy pins. The core is provided with a guide tube in the center, which facilitates the movement of 4.9 mm diameter Cadmium control rod.
3. Applied codes The analyses were carried out using reactor analysis codes WIMS-D and PRIDE (Halsall, 1980; Ahmad et al., 2009b). WIMS-D is well known in reactor analysis community and has been exten-
sively used lattice cell code. It was used to determine lattice parameters. The PRIDE code (Program for Reactor In-Core Analysis using Diffusion Equation), is a finite difference multi-group diffusion code developed for analysis of rectangular, cylindrical and spherical cores.
4. Validation of PRIDE PRIDE is a newly developed multi group and multi dimensional neutron diffusion theory code. It can be used for solution of steady state eigenvalue problems. One, two and three dimensional problems can be tackled by this code. In this code the diffusion equation is solved by finite difference approximation (Ahmad et al., 2009a). The code is validated for the IAEA 3D benchmark problem, designed to serve as test for coarse mesh methods and flux synthesis approximation. Initially it was defined by Micheelsen (RISØ) and
(b)
Reactivity Worth (mk)
Reactivity Worth (mk)
(a)
Temperature (o C)
Temperature (o C)
(c)
Reactivity Worth (mk)
Reactivity Worth (mk)
(d)
Temperature (o C)
(e)
Temperature (o C)
Reactivity Worth (mk)
Reactivity Worth (mk)
(d)
Temperature (o C)
209
Temperature (o C)
Fig. 4. Reactivity worth (mk) for temperature change above 20 °C (a) JEFF-3.1, (b) JENDL-3.2, (c) IAEA, (d) JEF-2.2, (e) ENDF/B-VII and (f) ENDF/B-VI.
210
S.I. Ahmad, T.M. Sahibzada / Annals of Nuclear Energy 49 (2012) 207–211
Table 4 Change in reactivity with change of water temperature above 20 °C. T (°C)
JENDL-3.2
20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0
WIMSD–IAEA
0.00000 1.45052 3.11656 5.00311 7.10327 9.43479 12.03460 14.91392
JEFF-3.1
0.00000 1.36483 3.02315 4.89167 6.97015 9.27689 11.83279 14.67440
JEF-2.2
0.00000 1.46805 3.12479 4.99110 7.13917 9.51062 12.10516 14.94272
Table 5 Ratios of worth from different libraries to worth from JENDL-3.2. T (°C)
WIMS-D–IAEA
JEFF-3.1
JEF-2.2
ENDF/B-VI
ENDF/B-VII
30.00 40.00 50.00 60.00 70.00 80.00 90.00
0.94 0.97 0.98 0.98 0.98 0.98 0.98
1.01 1.00 1.00 1.01 1.01 1.01 1.00
1.05 1.05 1.04 1.05 1.05 1.05 1.04
1.03 1.03 1.02 1.02 1.02 1.02 1.01
1.02 1.02 1.02 1.02 1.02 1.01 1.01
has been used for validation of various codes results worldwide by researches and code developers (Misfeldt, 1975; Trkov and Najzer, 1990; Hébert, 1993; Joo and Downar, 1996). Two group diffusion equation has been solved taking various mesh intervals. The core pattern is shown in Fig. 1 and the corresponding group constants for various regions are given in Table 1. There are 177 fuel assemblies in the core with 15 fuel assemblies across the core major axis. The dimension of each assembly is 20.0 20.0 cm. One layer of reflector surrounds the fuel assemblies. The active core height is 340 cm. Core is reflected from top and bottom by 20.0 cm thick reflector layer. In our calculations 1/8th symmetry was used with extrapolated (no-incoming current) boundaries at outer boundaries. The convergence criterion was set 10 5 in the maximum relative change in mesh fluxes. The calculations were carried out for different mesh intervals as defined in Table 2. The comparison for multiplication factor, power peaks, assembly power densities were carried out with reported results from VENTURE code (Vondy et al., 1977). The multiplication factors and the power peaking factors are tabulated in Table 3. It can be seen that the differences in multiplication factors with the reference results are within 10 5. The power densities of various cases were also compared with the reported results. Fig. 2 gives the results for Case 2. It can be seen that the results are same for all assemblies as reported, except value at position C3. The reported value 0.9537 is in error due to typo mistake. Using power densities reported by Lee et al. (1977) in the same reference the value becomes 0.9212, which is same as calculated from PRIDE.
0.00000 1.51945 3.26328 5.20863 7.45024 9.91548 12.61346 15.58095
ENDF/B-VI
ENDF/B-VII
0.00000 1.49369 3.20385 5.12533 7.25604 9.61783 12.22300 15.13175
0.00000 1.48143 3.18251 5.10434 7.23560 9.59658 12.20423 15.11107
into 46 regions each in x and y-directions and 10 regions in z-direction. The regions in z-direction from the top are water (20.0 cm), shim tray (0.3 cm), water (0.75 cm), upper non fuel region-1 (0.5 cm), upper non fuel region-2 (0.4 cm), fuel region (23.0 cm), lower non fuel region-1 (5.0 cm), lower non fuel region-2 (3.0 cm), lower Beryllium reflector (5.0 cm) and water (20.0 cm). First the analysis was carried out by taking the moderator temperature of 20 °C. The PRIDE code was used for calculation of reactivity of the core. The moderator temperature was increased and the corresponding number density was used to calculate the change in reactivity. The reactivity worth for given temperature change was calculated by subtracting reactivity at 20 °C from the reactivity obtained at that temperature. In order to study the effect of various newly evaluated crosssection libraries the lattice parameters were calculated with WIMS-D using JENDL-3.2, ENDF/B-VI, ENDF/B-VII, JEF-2.2, JEFF3.1 and IAEA cross-section libraries. These library dependent group constants were fed to diffusion theory code PRIDE for corresponding reactivity worth calculations. Analyses were carried out to observe the effects of increase in moderator temperature on reactivity worth. Results obtained are shown in Figs. 4a–f and Table 4. Decrease in moderator worth with increase in temperature is observed in all cases. Increase in the moderator temperature results a decrease in density, which causes the moderator to fuel ratio to decrease. As PARR-2 is under moderated, its reactivity decreases with decrease in moderator to fuel ratio. The ratios of the reactivity based on different libraries to that using JENDL for different temperatures are listed in Table 5. The Tables 4 and 5 show that the nearest match to JENDL-3.2 is for JEFF-3.1 i.e., within 1.2%. The maximum difference between results from JENDL-3.2 and IAEA is 6% at 20–30 °C. JEF-2.2 resulted in almost maximum deviation of 5%, whereas, ENDF/B-VI and ENDF/ B-VII gave maximum deviation of 3% and 2% respectively. 6. Conclusion Based on the analysis carries out to study effects in temperature variation of moderator on reactivity change in PARR-2 using crosssections released by various agencies, the following conclusions can be drawn:
5. Analysis of PARR-2 For analysis, the core of PARR-2 was modeled using WIMS-D and PRIDE code in three dimensions. WIMS-D was used to obtain lattice parameters such as diffusion coefficient (D), absorption cross-section (Ra), production cross-section (tRf) and scattering cross-sections (Rs). The lattice parameters were generated with WIMS-D/4 for various fuel and non-fuel regions using six energy groups with upper energy boundaries 10.0 MeV, 3.679 MeV, 0.821 MeV, 5.53 keV, 0.625 eV and 0.140 eV. These lattice parameters were used as input to PRIDE. The cylindrical core of PARR-2 was modeled in rectangular (XYZ) geometry. One fourth of the core was modeled using right and bottom reflections as shown in Fig. 3. The core was divided
The value of worth for all libraries is within 10%. There is very close agreement between the results obtained using JENDL-3.2 and JEFF-3.1. The maximum worth is obtained for JEF-2.2, whereas IAEA library gives least worth among all libraries. References Ahmad, S.I., Ahmad, N., 2005. Effect of updated WIMS-D libraries on neutron energy spectrum at irradiation site of Pakistan research reactor-1 using 3D modeling. Ann. Nucl. Energy 32, 521–548. Ahmad, S.I., Ahmad, N., 2006a. Plutonium build-up credits for a material test research reactor and influence of cross-section differences on actinide production. Nucl. Eng. Des. 236, 2537–2546.
S.I. Ahmad, T.M. Sahibzada / Annals of Nuclear Energy 49 (2012) 207–211 Ahmad, S.I., Ahmad, N., 2006b. Burnup dependent core neutronics analysis and calculation of actinide and fission product inventories in discharged fuel of a material test research reactor. Prog. Nucl. Energy 48, 599–616. Ahmad, S.I., Ahmad, N., Aslam, 2004. Effect of new cross-section evaluations on criticality and neutron energy spectrum of a typical material test research reactor. Ann. Nucl. Energy 31, 1867–1881. Ahmad, S.I., Ahmad, N., Aslam, 2006. Effect of different cross-section data sets on reflectors of a typical material test research reactor. Prog. Nucl. Energy 48, 155– 164. Ahmad, A., Ahmad, S.I., Ahmad, N., Chaudri, K.S., Sahibzada, T.M., Ahmad, M., 2009a. Influence of evaluated data of fission product poisons on criticality. Prog. Nucl. Energy 51, 334–338. Ahmad, S.I., Gul, R., Ahmad, N., 2009b. PRIDE User Manual. Reactor Analysis Group, PAEC, Islamabad. Halsall, M.J., 1980. A Summary of WIMS-D4 Input Options AEEW-M 1327, Winfrith, UK. Hébert, A., 1993. Application of a dual variational formulation to finite element reactor calculations. Ann. Nucl. Energy 20, 823–845. IAEA, 2005.. INDC, 1991. CENDL (versions 2.2 and 3). Chinese Nuclear Data Centre. A Brief Description of the Second Version of the Chinese Evaluated Nuclear Data Library CENDL-2. Communication of Nuclear Data Progress No. 6 [INDC(CPR)-25]. Beijing, China. JEFF, 2005. JEFF-3.1 Nuclear Data Library is released through NEA data bank.
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Koscheev, V.N., Nikolaev, M.N., Korchagina, Zh.A., Savoskina, G.V., 2001. The FOND2.2, Evaluated Neutron Data Library (Russian Library of Evaluated Neutron Data Files for Generating Sets of Constants in the ABBN Constants System). INDC(CCP)-429, pp. 57–93 (English translation). Lee, R.R. et al., 1977. Multi-Dimensional (x–y–z) LWR Model. Benchmark Problem Book, ANL 7416 (Suppl. 2). Argonne Code Center, Argonne National Laboratory, Argonne, Illinois 6043. Lemmel, H.D., McLaughlin, P.K., Pronyaev, V.G., 2001. Summary of Contents, ENDF/ B-VI, Release 8. The US Evaluated Nuclear Data Library for Neutron Reaction Data by the US National Nuclear Data Center 1990. Manokhin, V.N., 1989. BROND USSR Evaluated Nuclear Data Library. IAEA NDS-90, Rev.-2. Misfeldt, 1975. Solution of the Multigroup Neutron Diffusion Equations by the Finite Element Method. Department of Reactor Technology, Danish Atomic Energy Commission, Rise, Roskilde, Denmark. Nakagawa, T., Shibata, K., Chiba, S., 1995. Japanese evaluated nuclear data library version 3 Rev.-2, JENDL-3.2. J. Nucl. Sci. Technol. 32, 1259. Trkov, A., Najzer, M., 1990. Variant of Green’s function nodal method for neutron diffusion. J. Nucl. Sci. Technol. 27, 8. Vondy, D.R., Fowler, T.B., Cunninghum, G.W., 1977. VENTURE: A Code Block for Solving Multigroup Neutronics Problems Applying the Finite Difference Diffusion Theory Approximation to Neutron Transport. Oak Ridge National Laboratory. Wyne, M.F., Meghji, J.H., 1990. Reactor Description and Experiments. Centre for Nuclear Studies, Islamabad.
Contents lists available at SciVerse ScienceDirect
Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene
Technical note
Moderator temperature effects on reactivity of HEU core of MNSR Siraj-ul-Islam Ahmad ⇑, Tasveer Muhammad Sahibzada Pakistan Institute of Engineering and Applied Sciences, Islamabad 45650, Pakistan
a r t i c l e
i n f o
Article history: Received 28 May 2012 Received in revised form 30 June 2012 Accepted 4 July 2012 Available online 2 August 2012 This article is dedicated to our late Professor Nasir Ahmad. The work presented had been carried out in his guidance.
a b s t r a c t In this article we report on analyses that were performed to investigate the influence of cross section differences among libraries released by various centers on reactivity of Miniature Neutron Source Reactors. The 3D model of the core was developed with WIMS-D and PRIDE codes and six cross section libraries were used including JENDL-3.2, JEF-2.2, JEFF-3.3, ENDF/B-VI and ENDF/B-VII, and IAEA library. It was observed that all the libraries predict the reactivity within 10%, with IAEA library giving minimum reactivity worth, and JEF-2.2 data library resulted in highest worth. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: MNSR Moderator temperature coefficient WIMS-D PRIDE Cross section libraries
1. Introduction Reactivity is affected by many factors, including temperature of coolant, moderator, fuel and structural materials and the density of these materials. Change in reactivity per unit increase in temperature is known as temperature coefficient of reactivity and is measured in units of mk/°C. As temperature of the moderator is changed, its number density changes and hence moderator to fuel ratio (Nm/Nf) is changed. The Nm/Nf affects the thermal utilization factor and the resonance escape probability. The thermal utilization factor decreases with increase in Nm/Nf. This is due to the fact that with increase in moderator concentration, the absorption in it also increases, which causes thermal utilization factor to decrease. On the other hand the resonance escape probability increases with increase in Nm/Nf, because as moderation increases more neutrons will cross the resonance region without absorption. For low values of Nm/Nf the increase in resonance escape probability is dominant as compared to decrease in thermal utilization factor so effective multiplication factor will increase with increase in Nm/Nf. For values above an optimum value of Nm/Nf the change in thermal utilization factor becomes dominant as compared to change in resonance escape probability which causes the multiplication factor to decrease with increase in Nm/Nf. The nuclear cross section data plays a vital role in reactor physics calculations. For accurate analysis this data is continuously up⇑ Corresponding author. Tel.: +92 51 9258517. E-mail address: [email protected] (S.I. Ahmad). 0306-4549/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.anucene.2012.07.004
graded by various data centers. Due to different models and experiments used by laboratories, there always exists some difference in various evaluations of this data. For suitability of a specific data library, it needs to compute reactor physics parameters with various data sets and to identify the differences in parameter values. Recently released evaluated nuclear data files: ENDF/B-VI (Lemmel et al., 2001), JENDL-3.2 (Nakagawa et al., 1995), CENDL2.1 (INDC, 1991), FOND (Koscheev et al., 2001), BROND-2 (Manokhin, 1989) and JEFF-3.1 (JEFF, 2005; IAEA, 2005) were processed by International Atomic Energy Agency during a coordinated research project, and the resultant WIMS-D (Halsall, 1980) libraries were freely distributed through web to interested users. These data libraries have been used to perform analysis of MTR type research reactors (Ahmad et al., 2004, 2006, 2009a; Ahmad and Ahmad, 2005, 2006a,b). In this work we intend to investigate the effect of various data libraries on Miniature Neutron Source Reactor (MNSR) moderator temperature coefficient of reactivity. The studies were carried out using ENDF/B-VI, ENDF/B-VII, JENDL-3.2, JEF-2.2, IAEA and JEFF-3.1 cross-section libraries. 2. Reactor description Pakistan Research Reactor-2 is a 30 kW tank in pool type MNSR, cooled, moderated, reflected and shielded by demineralized light water and Beryllium (Wyne and Meghji, 1990). PARR-2 is fueled with 90% enriched Uranium and the fuel meat is Uranium–Aluminum alloy of U-Al4. The core of PARR-2 consists of 344 fuel pins arranged in concentric arrays and forms a square cylinder with
208
S.I. Ahmad, T.M. Sahibzada / Annals of Nuclear Energy 49 (2012) 207–211
(a) cm 380
Table 2 Problem mesh details.
Jin=0 10
30
50
70
90
130
150
170
360
280
Case no.
Mesh size (cm)
No. of meshes
Radial
Axial
Radial
Axial
1 2 3 4 5
20.00 10.00 5.00 2.50 1.667
40.00 20.00 10.00 5.00 3.333
9 17 34 68 102
10 19 38 76 114
900 5.814 45,220 356,592 1,197,684
Table 3 Comparison of multiplication factors and power peaks. Case no.
J=0
1 2 3 4 5
Jin=0
280
0
Jin=0 X
0 10 0 10
30
50
70
90
Multiplication factor
Peak to average power density
Reported
PRIDE
Reported
PRIDE
1.03176 1.02913 1.02864 1.02887 1.02896
1.03177 1.02913 1.02864 1.02887 1.02896
2.3765 2.5672 2.5035 2.4081 2.3780
2.3818 2.5676 2.5033 2.4078 2.3809
B C D E F G H I 0.6574 0.9101 0.9707 0.5802 1.3178 1.5651 1.4485 0.7356 2 0.6574 0.9101 0.9707 0.5802 1.3177 1.5650 1.4484 0.7355 0.0000 0.0000 0.0000 0.0000 -0.0001 -0.0001 -0.0001 -0.0001 0.6366 0.9537 1.0619 1.1406 1.4045 1.5742 1.5604 3 0.6367 0.9212 1.0619 1.1406 1.4045 1.5741 1.5602 0.0001 -0.0325 0.0000 0.0000 0.0000 -0.0001 -0.0002 0.5459 0.9420 1.0755 1.2226 1.4030 1.4797 4 0.5459 0.9421 1.0755 1.2226 1.4030 1.4796 0.0000 0.0001 0.0000 0.0000 0.0000 -0.0001 0.7383 0.8970 1.0083 1.2480 5 0.7383 0.8970 1.0083 1.2480 0.0000 0.0000 0.0000 0.0000 0.4725 0.6720 0.4244 Reported 6 0.4726 0.6720 0.4244 Calculated 0.0001 0.0000 0.0000 Difference 0.4717 7 0.4717 0.0000
20
(b)
Unknowns
110 130 150 170 cm
Fig. 2. Comparison of relative power densities for Case 2.
30 50 70 Y
90
Fuel 1
110 =0 J in
Fuel 2
130
Fuel 2 + Rod
150
Reflector
170 cm
Reflector + Rod
Fig. 1. IAEA 3D PWR benchmark problem (a) axial and (b) radial core configurations.
Table 1 Two-group constants for IAEA 3D PWR problem. S.no.
Material
1 2 3 4 5
Fuel 1 Fuel 1 + rod Fuel 2 Reflector Reflector + rod
D (cm)
Ra (cm 1)
mRf (cm 1)
Rs (cm 1)
1
2
1
2
1
2
1?2
1.5 1.5 1.5 2.0 2.0
0.4 0.4 0.4 0.3 0.3
0.01 0.01 0.01 0.00 0.00
0.085 0.130 0.080 0.010 0.055
0.0 0.0 0.0 0.0 0.0
0.135 0.135 0.135 0.000 0.000
0.02 0.02 0.02 0.04 0.04
Control Rod
Fuel
Control Rod Guide Tube
Reflector
Water
Irradiation Site
Fig. 3. Cross-sectional view of fuel region of MNSR.
S.I. Ahmad, T.M. Sahibzada / Annals of Nuclear Energy 49 (2012) 207–211
230 mm diameter. The total fuel loading in the fresh core is about 994.8 g of 235U. Upper and lower grid plates secure the fuel pins to form a fuel cage. The fuel pins are fixed in the bottom grid plate by slightly conical self-locking fittings and are free to expand through the upper grid plate. Four out of the 354 holes, provided in the grid plates are used for fixing stainless steel tie bolts to keep the fuel cage intact, rest of the six holes are occupied by Aluminum dummy pins. The core is provided with a guide tube in the center, which facilitates the movement of 4.9 mm diameter Cadmium control rod.
3. Applied codes The analyses were carried out using reactor analysis codes WIMS-D and PRIDE (Halsall, 1980; Ahmad et al., 2009b). WIMS-D is well known in reactor analysis community and has been exten-
sively used lattice cell code. It was used to determine lattice parameters. The PRIDE code (Program for Reactor In-Core Analysis using Diffusion Equation), is a finite difference multi-group diffusion code developed for analysis of rectangular, cylindrical and spherical cores.
4. Validation of PRIDE PRIDE is a newly developed multi group and multi dimensional neutron diffusion theory code. It can be used for solution of steady state eigenvalue problems. One, two and three dimensional problems can be tackled by this code. In this code the diffusion equation is solved by finite difference approximation (Ahmad et al., 2009a). The code is validated for the IAEA 3D benchmark problem, designed to serve as test for coarse mesh methods and flux synthesis approximation. Initially it was defined by Micheelsen (RISØ) and
(b)
Reactivity Worth (mk)
Reactivity Worth (mk)
(a)
Temperature (o C)
Temperature (o C)
(c)
Reactivity Worth (mk)
Reactivity Worth (mk)
(d)
Temperature (o C)
(e)
Temperature (o C)
Reactivity Worth (mk)
Reactivity Worth (mk)
(d)
Temperature (o C)
209
Temperature (o C)
Fig. 4. Reactivity worth (mk) for temperature change above 20 °C (a) JEFF-3.1, (b) JENDL-3.2, (c) IAEA, (d) JEF-2.2, (e) ENDF/B-VII and (f) ENDF/B-VI.
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Table 4 Change in reactivity with change of water temperature above 20 °C. T (°C)
JENDL-3.2
20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0
WIMSD–IAEA
0.00000 1.45052 3.11656 5.00311 7.10327 9.43479 12.03460 14.91392
JEFF-3.1
0.00000 1.36483 3.02315 4.89167 6.97015 9.27689 11.83279 14.67440
JEF-2.2
0.00000 1.46805 3.12479 4.99110 7.13917 9.51062 12.10516 14.94272
Table 5 Ratios of worth from different libraries to worth from JENDL-3.2. T (°C)
WIMS-D–IAEA
JEFF-3.1
JEF-2.2
ENDF/B-VI
ENDF/B-VII
30.00 40.00 50.00 60.00 70.00 80.00 90.00
0.94 0.97 0.98 0.98 0.98 0.98 0.98
1.01 1.00 1.00 1.01 1.01 1.01 1.00
1.05 1.05 1.04 1.05 1.05 1.05 1.04
1.03 1.03 1.02 1.02 1.02 1.02 1.01
1.02 1.02 1.02 1.02 1.02 1.01 1.01
has been used for validation of various codes results worldwide by researches and code developers (Misfeldt, 1975; Trkov and Najzer, 1990; Hébert, 1993; Joo and Downar, 1996). Two group diffusion equation has been solved taking various mesh intervals. The core pattern is shown in Fig. 1 and the corresponding group constants for various regions are given in Table 1. There are 177 fuel assemblies in the core with 15 fuel assemblies across the core major axis. The dimension of each assembly is 20.0 20.0 cm. One layer of reflector surrounds the fuel assemblies. The active core height is 340 cm. Core is reflected from top and bottom by 20.0 cm thick reflector layer. In our calculations 1/8th symmetry was used with extrapolated (no-incoming current) boundaries at outer boundaries. The convergence criterion was set 10 5 in the maximum relative change in mesh fluxes. The calculations were carried out for different mesh intervals as defined in Table 2. The comparison for multiplication factor, power peaks, assembly power densities were carried out with reported results from VENTURE code (Vondy et al., 1977). The multiplication factors and the power peaking factors are tabulated in Table 3. It can be seen that the differences in multiplication factors with the reference results are within 10 5. The power densities of various cases were also compared with the reported results. Fig. 2 gives the results for Case 2. It can be seen that the results are same for all assemblies as reported, except value at position C3. The reported value 0.9537 is in error due to typo mistake. Using power densities reported by Lee et al. (1977) in the same reference the value becomes 0.9212, which is same as calculated from PRIDE.
0.00000 1.51945 3.26328 5.20863 7.45024 9.91548 12.61346 15.58095
ENDF/B-VI
ENDF/B-VII
0.00000 1.49369 3.20385 5.12533 7.25604 9.61783 12.22300 15.13175
0.00000 1.48143 3.18251 5.10434 7.23560 9.59658 12.20423 15.11107
into 46 regions each in x and y-directions and 10 regions in z-direction. The regions in z-direction from the top are water (20.0 cm), shim tray (0.3 cm), water (0.75 cm), upper non fuel region-1 (0.5 cm), upper non fuel region-2 (0.4 cm), fuel region (23.0 cm), lower non fuel region-1 (5.0 cm), lower non fuel region-2 (3.0 cm), lower Beryllium reflector (5.0 cm) and water (20.0 cm). First the analysis was carried out by taking the moderator temperature of 20 °C. The PRIDE code was used for calculation of reactivity of the core. The moderator temperature was increased and the corresponding number density was used to calculate the change in reactivity. The reactivity worth for given temperature change was calculated by subtracting reactivity at 20 °C from the reactivity obtained at that temperature. In order to study the effect of various newly evaluated crosssection libraries the lattice parameters were calculated with WIMS-D using JENDL-3.2, ENDF/B-VI, ENDF/B-VII, JEF-2.2, JEFF3.1 and IAEA cross-section libraries. These library dependent group constants were fed to diffusion theory code PRIDE for corresponding reactivity worth calculations. Analyses were carried out to observe the effects of increase in moderator temperature on reactivity worth. Results obtained are shown in Figs. 4a–f and Table 4. Decrease in moderator worth with increase in temperature is observed in all cases. Increase in the moderator temperature results a decrease in density, which causes the moderator to fuel ratio to decrease. As PARR-2 is under moderated, its reactivity decreases with decrease in moderator to fuel ratio. The ratios of the reactivity based on different libraries to that using JENDL for different temperatures are listed in Table 5. The Tables 4 and 5 show that the nearest match to JENDL-3.2 is for JEFF-3.1 i.e., within 1.2%. The maximum difference between results from JENDL-3.2 and IAEA is 6% at 20–30 °C. JEF-2.2 resulted in almost maximum deviation of 5%, whereas, ENDF/B-VI and ENDF/ B-VII gave maximum deviation of 3% and 2% respectively. 6. Conclusion Based on the analysis carries out to study effects in temperature variation of moderator on reactivity change in PARR-2 using crosssections released by various agencies, the following conclusions can be drawn:
5. Analysis of PARR-2 For analysis, the core of PARR-2 was modeled using WIMS-D and PRIDE code in three dimensions. WIMS-D was used to obtain lattice parameters such as diffusion coefficient (D), absorption cross-section (Ra), production cross-section (tRf) and scattering cross-sections (Rs). The lattice parameters were generated with WIMS-D/4 for various fuel and non-fuel regions using six energy groups with upper energy boundaries 10.0 MeV, 3.679 MeV, 0.821 MeV, 5.53 keV, 0.625 eV and 0.140 eV. These lattice parameters were used as input to PRIDE. The cylindrical core of PARR-2 was modeled in rectangular (XYZ) geometry. One fourth of the core was modeled using right and bottom reflections as shown in Fig. 3. The core was divided
The value of worth for all libraries is within 10%. There is very close agreement between the results obtained using JENDL-3.2 and JEFF-3.1. The maximum worth is obtained for JEF-2.2, whereas IAEA library gives least worth among all libraries. References Ahmad, S.I., Ahmad, N., 2005. Effect of updated WIMS-D libraries on neutron energy spectrum at irradiation site of Pakistan research reactor-1 using 3D modeling. Ann. Nucl. Energy 32, 521–548. Ahmad, S.I., Ahmad, N., 2006a. Plutonium build-up credits for a material test research reactor and influence of cross-section differences on actinide production. Nucl. Eng. Des. 236, 2537–2546.
S.I. Ahmad, T.M. Sahibzada / Annals of Nuclear Energy 49 (2012) 207–211 Ahmad, S.I., Ahmad, N., 2006b. Burnup dependent core neutronics analysis and calculation of actinide and fission product inventories in discharged fuel of a material test research reactor. Prog. Nucl. Energy 48, 599–616. Ahmad, S.I., Ahmad, N., Aslam, 2004. Effect of new cross-section evaluations on criticality and neutron energy spectrum of a typical material test research reactor. Ann. Nucl. Energy 31, 1867–1881. Ahmad, S.I., Ahmad, N., Aslam, 2006. Effect of different cross-section data sets on reflectors of a typical material test research reactor. Prog. Nucl. Energy 48, 155– 164. Ahmad, A., Ahmad, S.I., Ahmad, N., Chaudri, K.S., Sahibzada, T.M., Ahmad, M., 2009a. Influence of evaluated data of fission product poisons on criticality. Prog. Nucl. Energy 51, 334–338. Ahmad, S.I., Gul, R., Ahmad, N., 2009b. PRIDE User Manual. Reactor Analysis Group, PAEC, Islamabad. Halsall, M.J., 1980. A Summary of WIMS-D4 Input Options AEEW-M 1327, Winfrith, UK. Hébert, A., 1993. Application of a dual variational formulation to finite element reactor calculations. Ann. Nucl. Energy 20, 823–845. IAEA, 2005.
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Koscheev, V.N., Nikolaev, M.N., Korchagina, Zh.A., Savoskina, G.V., 2001. The FOND2.2, Evaluated Neutron Data Library (Russian Library of Evaluated Neutron Data Files for Generating Sets of Constants in the ABBN Constants System). INDC(CCP)-429, pp. 57–93 (English translation). Lee, R.R. et al., 1977. Multi-Dimensional (x–y–z) LWR Model. Benchmark Problem Book, ANL 7416 (Suppl. 2). Argonne Code Center, Argonne National Laboratory, Argonne, Illinois 6043. Lemmel, H.D., McLaughlin, P.K., Pronyaev, V.G., 2001. Summary of Contents, ENDF/ B-VI, Release 8. The US Evaluated Nuclear Data Library for Neutron Reaction Data by the US National Nuclear Data Center 1990. Manokhin, V.N., 1989. BROND USSR Evaluated Nuclear Data Library. IAEA NDS-90, Rev.-2. Misfeldt, 1975. Solution of the Multigroup Neutron Diffusion Equations by the Finite Element Method. Department of Reactor Technology, Danish Atomic Energy Commission, Rise, Roskilde, Denmark. Nakagawa, T., Shibata, K., Chiba, S., 1995. Japanese evaluated nuclear data library version 3 Rev.-2, JENDL-3.2. J. Nucl. Sci. Technol. 32, 1259. Trkov, A., Najzer, M., 1990. Variant of Green’s function nodal method for neutron diffusion. J. Nucl. Sci. Technol. 27, 8. Vondy, D.R., Fowler, T.B., Cunninghum, G.W., 1977. VENTURE: A Code Block for Solving Multigroup Neutronics Problems Applying the Finite Difference Diffusion Theory Approximation to Neutron Transport. Oak Ridge National Laboratory. Wyne, M.F., Meghji, J.H., 1990. Reactor Description and Experiments. Centre for Nuclear Studies, Islamabad.