VALIDATION OF BATAN'S STANDARD DIFFUSION CODES ON IAEA BENCHMARK STATIC CALCULATIONS

Transcription

1 VALIDATION OF BATAN'S STANDARD DIFFUSION CODES ON IAEA BENCHMARK STATIC CALCULATIONS Sembiring, T.M. and Liem P.H." ABSTRACT VALIDATION OF BATAN'S STANDARD CODES ON laea BENCHMARK STATIC CALCULATIONS. Extensive benchmark calculations using the combination of Batan's standard diffusion code and WIMSID4 have been conducted to check the validity and accuracy of the codes, and to obtain proper cell modeling for MTR type fuel and control elements which will be used in designing the next high loading silicide fuel of RSG-GAS. The benchmark object and parameters to be calculated are defined by the IAEA in the IAEA TECDOC-233 and IAEA-TECDOC-643. In general, the combination of Batan's standard diffusion code, Batan-2DIFF, and WIMSID4 gave very satisfactory results which proved the validity of the proposed WIMSID4 cell model and the accuracy of the Batan's diffusion code used in the benchmark calculations. Four-energy-group, multiplate options of WIMSID4 were sufficient to give accurate results in term of infinite multiplication factors, fuel depletion results and diffusion constants for whole core calculations. Two-dimensional, four-group diffusion model supplied with a correct axial buckling value can be considered accurate enough for the MTR whole core calculations. INTRODUCTION Research activities with high priority in the Center for Multipurpose Reactor (PRSG), National Atomic Energy Agency (Batan), include RSG G.A. Siwabessy core conversion program from oxide to silicide fuel (both utilize low enriched uranium - LEU, i.e w/o). This activity has been coordinated with research and development programs in Nuclear Fuel Element Center (PEBN-Batan) and presently four experimental silicide fuel elements, with 250 gram 235Uloading per fuel element, have been irradiated in the oxide core of RSG-GAS. Among other advantages of silicide fuel, its high loading of fissile material is expected to increase the operation cycle of RSG-GAS, hence, higher capacity factor and utilization of RSG-GAS can be achieved. Historically, the RSG-GAS was designed and commissioned by Interatom/Siemens as the vendors, while the first batch of RSG-GAS fuel elements were supplied by NUKEM. However, the next RSG-GAS core conversion program, which consists of: Center for Multipurpose Reactor - BATAN 73

2 (a) Preliminary parametric survey on the neutronic and thermal-hydraulic aspects of silicide core, followed by (b) Final neutronic and thermal-hydraulic designs of RSG-GAS silicide core, (c) Safety design and accident analyses, and supported by (d) Silicide fuel element development program ofpebn, is expected to be conducted mainly throught Batan's own efforts. In order to support those efforts, from the neutronic design aspects of the RSG-GAS silicide core, several Batan's standard codes have been and are being developed: (a) Multidimensional multigroup neutron diffusion codes for solving criticality and fixed source problems, calculations of integral kinetic parameters and application of perturbation theory for rapid calculation of reactivity change (Batan-2DIFF & -3DIFF codes (1,2)) (b) Computer codes for operational in-core fuel management and for obtaining an equilibrium core condition (Batan-FUEL and -EQUIL-2D codes (3,4)) Batan-2DIFF and -3DIFF codes have several features which are not always available in other generic diffusion codes. These are: (1) special treatment of the (n,2n) neutron scattering which is significant for beryllium reflected RSG-GAS core, (2) option for directional diffusion constants, (3) up-scattering, and (4) power peaking factor calculation based on flux on the mesh edge which is more conservative than the one based on mesh center. The codes supports safety and transient analyses by providing integral kinetic parameters, i.e. the effective delayed neutron fractions, prompt neutron life time and neutron generation time. They can also be used to compute, in a fast and efficient way, small reactivity changes and various feedback reactivity coefficients using the perturbation theory. The validation and accuracy of these codes have been checked and verified by using 2DBUM (5) and 3DBUM (6) codes, generic diffusion codes developed by Battelle North West Laboratory and later modified by University of Michigan. Batan-EQUIL-2D code has been developed to obtain directly the equilibrium condition of the RSG-GAS silicide core which will serve as the typical working core (TWC) for further thermal and safety analysis. In addition to the validity and accuracy of the above-mentioned Batan's standard codes, another important factor influencing the accuracy of the 74

3 neutronic design results is proper modeling of the fuel and control elements in the cell calculations for generation of the diffusion cross section set. As widely known, WIMS/D4 cell calculation code (7) has been verified and used by neutronic communities in various institutions/organizations. This code has also been independently verified in Batan and it is expected to be one potential code for generation of the diffusion cross section set of the RSG-GAS silicide fuel elements. WIMS/D4 and the above stated Batan's standard codes were installed and executable on VAX 8550 and VAX 2100 mainframe computers in the Informatics Development Center of Batan (PPI-Batan). However, our codes were designed as machine independent as possible so that those codes in principle are also executable even on a personal computer with relatively slower computation speed and for some cases with smaller dimension of problem. In order to properly conduct the neutronic design of the new RSG-GAS silicide core using the combination ofwims/d4 and Batan's standard codes, a series of benchmark calculation must be done first. In this paper, the results of the static part of the safety-related benchmark calculation proposed by IAEA are reported and discussed. A typical 10 MWth Material Testing Reactor (MTR) with LEU core defined by the International Atomic Energy Agency (IAEA) in the Appendix F of IAEA- TECDOC-233 (8) is taken as the benchmark core. This core is suitable for our benchmarking problem since it is an MTR core and its fuel element configuration is considerably close to the one of the RSG-GAS. The benchmark calculations cover almost all aspects of neutronic design such as: criticality, various types of power peaking factor, isothermal feedback reactivity coefficients, fuel element and control rod worths, etc. Seven countries with their own code systems have participated in this benchmark calculation project, hence, they provided results which can be directly compared to calculation results of the Batan's code system. Therefore, the present work reported here has twofold goals: (a) Obtaining a proper neutronic modeling of the LEU silicide fuel and control elements of RSG-GAS in both cross sections generation and diffusion calculation phases. (b) A means of evaluating the performance and accuracies of Batan's standard codes for neutronic design and to find ways to improve those codes systematically. The organization of this paper is as follows. First, the IAEA benchmark problem definition is briefly reviewed. This is followed by discussions of neutronic modeling proposed in the WIMS/D4 cell calculations for the 75

4 benchmark core. Then, the diffusion calculation results by Batan's codes are presented and compared to the ones of other countries. Conclusion and suggestion concerning the proper neutronic modeling. for the RSG GAS silicide fuel elements and core will be given in the last part of this paper. BENCHMARK PROBLEM DEFINITION The present work consists of two phases, i.e. benchmark calculations based on IAEA TECDOC-233 (8) followed by safety-related benchmark calculations based on [AEA- TECDOC-643 (9). IAEA-TECDOC-233 Benchmark Calculations (7 participants) The aim of these benchmark calculations defined in IAEA TECDOC-233 is comparison of the different calculation methods and cross section data sets used in different laboratories, limited conclusion for real core conversion problem. The reactor used for these benchmark calculations described in the Appendix F of IAEA- TECDOC-233 is a 10 MWth reactor with MTR type fuel. The reactor primary data and configuration are shown in Table I and Fig.l, respectively. As depicted in Fig.l, the reactor consists of core and reflectors made of graphite or water. In the core, besides standard fuel elements, there are four control fuel elements (fuel element with absorber plates). The participants are obliged to provide the multiplication factor; flux and flux ratios along the two symmetry-axes of the core in three groups and for begin of life (BOL) and end of life (EOL), respectively. IAEA- TECDOC-643 (5 participants) Safety-Related Benchmark Calculations For the safety-related benchmark problem, the reactor description is the same one utilized for the benchmark problem solved in the previously discussed IAEA-TECDOC-233, except for a change in the description of the central flux trap (See Fig.l). The water in the central flux trap in the original core is replaced with a 7.7 cm x 8.1 cm block of aluminum containing a square hole 5 cm on each side in order to compute more realistic radial and local power peaking factors for the limiting standard fuel element. The safety-related benchmark calculations are divided into two main groups, i.e., static and transients calculations. However, this paper merely discusses the static calculations since only neutronics modeling and codes are involved (for transient calculations, neutron dynamics, time-dependent thermal-hydraulics modeling and codes are involved which are out of the 76

5 scope of our discussion). Furthermore, the participants are obliged to conduct the following static calculations: 1. Isothermal Reactivity Feedback Coefficients a). Change of Water Temperature Only - 38, 50, 75, 100 0c. b). Change of Water Density Only , 0.988, 0.975, g/cc. c). Change of238u Temperature Only - 38, 50, 75, 100,200 0c. d). Core Void Coefficient - Change Water Density Only - 10, 20 % Void. e). Local Void Coefficient - Change Water Density Only - 5, 10 % Void separately in SFE-2, SFE-3 and SFE-4 (this is optional). 2. Radial and Local Power Peaking Factors a). Replace burned CFE-I with fresh CFE. b). Replace burned SFE-l with fresh SFE. c). Note reactivity changes for all cases. Note that (a) SFE and CFE stand for standard fuel element and control fuel element, respectively; (b) The beginning of life (BOL) core, shown in Fig.I, contains fission products; and (c) fresh SFE and CFE contain no fission products. PROPOSED NEUTRONICS MODELING The neutronics modeling proposed for the present static calculations consists of two main parts, i.e., cross sections generation using WIMS/D4 cell calculation code and neutron diffusion theory calculations using Batan's standard neutron diffusion code, Batan-2D1FF. Cross Sections Generation with WIMSill4 Cross sections in four energy groups (Table 2) for core materials as a function of 235U burnup were generated using 1-D lattice cell calculation code, WIMS/D4. No detailed explanations on WIMS/D4 code is given here and readers can find them in relevant references. It should be emphasized here that cell calculations in WIMS/D4 consist of two main parts. The first part is eigenvalue transport calculation in a simplified geometry, i.e. fuelcladding-moderator-extra region, to determine the neutron spectra for those four regions. In this.case, the transport calculation is conducted in 69 energy group but without considering the detailed mesh division in each region. 77

6 All regions of fuel are collected in the fuel region and similarly for cladding, moderator and extra regions. The four kinds of neutron spectra obtained are then used to collapse the cross sections into few group (for our benchmark calculation is a four-energy group). Then the second part of the WIMS/D4 cell calculation is conducted. [n the second part, another transport calculation is conducted in few group by considering the real unit cell geometry and the fine mesh division prescribed by user. Finally, the space dependent group neutron fluxes accross the unit cell are used for generating the effective cross sections of the unit cell by volume weighting. The proposed model for standard fuel element, SFE, is depicted in Fig. 2. The 2-D SFE geometry is approximated by 1-0 cell calculation model (WIMS/D4 cell calculation code can only treat 1-0 cell model). For SFE, the multiplate model is chosen. The unit cell consists of eleven and a half identical fuel regions and one extra region where each fuel region is divided further into fuel meat, aluminum cladding, water moderator regions. The extra region in WIMS/D4 is used to include regions which are not covered by meat-cladding-moderator fuel plate configurations. Those regions are side plates, small parts of aluminum cladding adjacent to side plates. and water gaps between fuel elements. After cell calculation completion W[MS/04 homogenizes the effective cross sections for the whole equivalent unit cell of the SFE by spectrum and volume weighting. For a control fuel element, CFE, (see Fig. 3) careful modeling for the CFE unit cell is needed. The following method is proposed for CFE. The CFE is divided into two parts, i.e., regions for fuel and absorber, respectively, where the cross sections for each part are generated separately. The cross sections for fuel region part are generated with multiplate option in the same way as for SFE (Fig. 3). Since the present benchmark calculation does not include the control worth and kinetic calculation, we only consider the case where in the absorber region the absorber blade is not inserted (fully withdrawn). Therefore, the cross sections for absorber region are generated in the same way as for other structural or reflector materials. For non-fuel (reflector) regions (i.e., graphite, water and aluminum) and absorber region of CFE, cross section sets are generated with the model shown in Fig. 4. Three and a half fuel plate regions are included to simulate the core spectra which are expected to influence the extra region where the structural parts exist. To some extent this modeling can be justified for structural parts which are located inside the core or in the core periphery. However, the authors doubt that the model can be used for reflector regions which are far (in term of neutron mean free path length) from the core periphery. For those regions, a higher order method such as 1-0 or 2-D transport codes must be used to obtain more accurate results. Fortunately, the effective multiplication factor and the neutron flux and power distributions 78

7 across the core are not strongly affected by the accuracy of the reflector's cross sections which is not located adjacent to the core. For our benchmark calculations, the cross sections of the graphite and water reflectors which are located directly adjacent to the core region are generated consideraing that the core neutron spectra will interact with the graphite and water reflectors. The best way one can do with WIMSID4 cell calculation code is by the modeling shown in Fig. 4. For the cross sections of the outest water reflectors the same set of cross section for the inner water reflector are used. Even with this modeling the calculation results suprisingly show good agreement with other institution's results. Diffusion Calculations with Batan-2DIFF Similar to other institutions/organizations, the neutron transport problems are treated with few group 2-D diffusion theory. For calculations of reactor criticality, flux and power peaking factor distributions, and reactivity changes, Batan-2DIFF code is used. Batan-2DIFF code adopts the placing of flux on the mesh center rather than in the mesh boundary (edge). However, conservative power peaking factor has to be evaluated at the mesh edge, therefore, based on the continuity condition of neutron flux at the medium interface, a relationship between fluxes calculated at the centers of mesh intervals and the corresponding values at the mesh boundary or edge has been built into the code. It should be emphasized here that not all diffusion codes (for e.g. CITATION code) have the capability to calculate power peaking factor based on the edge mesh flux. Contrast to the more homogeneous core of power reactors, the research and test reactors usually have cores with strong heterogenity, not only in term of different fuel element bum up levels but also in the existence of various irradiation positions. Furthermore, to minimize the core critical mass excellent reflector materials are used. In the interface boundaries between a fuel element and reflector then a large gradient of (especially thermal) neutron flux and consequently a high power peaking factor will appear. Estimation of local power peaking factor by center mesh flux will give an under-estimated value. This is the reason that the IAEA benchmark problem required the participants to produce the power peaking factor calculated by mesh edge flux. Another advantage of using mesh edge flux for calculating power peaking factor is that the calculated power peaking factor is relatively insensitive to the mesh widths used in the calculation. For most calculations, in general, one block SFE, CFE or reflector with dimension of 8.] x 7.7 cm2, is divided uniformly into 4 x 4 meshes. It has 79

8 been checked that these mesh widths produced enough accuracy in the calculation of criticality and power peaking factors. BENCHMARK CALCULATION RESULTS & DISCUSSIONS IAEA- TECDOC-233 Benchmark Calculation Results The criticality calculation results (multiplication factor, keff) for the fresh, BOL and EOL cores are tabulated in Table 3. Hereinafter, figures in the parentheses show the relative difference (%) from the values calculated by ANL. The ANL results were chosen since they provided also some values calculated by the continuous energy Monte Carlo method. It should be emphasized here that those figures are not relative error since IAEA did not determine which one is the best estimate. For the fresh core, ANL deliberately provided keff value calculated with the continuous energy Monte Carlo method, which in our opinion can be considered to be the most accurate result. It can be observed that the combination of WIMS/D4 and Batan-2DIFF codes can give the multiplication factors with high accuracy since they were inside the range of the values calculated with the Monte Carlo method. The accuracy of the criticality calculations for the BOL and EOL cores depend strongly also on the accuracy of the WIMSID4 bum up calculations during the cross section set generation. Even for these cases, very accurate estimation for keffof both BOL and EOL cores can be produced. As required by the IAEA, the group neutron flux distributions at the midplane of the reactor calculated with Batan-2DIFF code are shown in Fig. 5, while the flux ratio distribution (against thermal neutron flux) are shown in Fig. 6. In the interface boundaries between flux trap (Al+water) and fuel element regions the thermal neutron flux distribution shows a very steep gradient and the neutron spectra (in term of flux ratio shown in Fig. 6) also change significantly. In the fuel region, the neutron spectra are determined by the moderator to heavy metal atomic ratio and fission process while in the flux trap region the neutron spectra are attributed by slowing down process of fast neutrons leaking from fuel region. Hence, the neutron spectra in the fuel region are much harder than the flux trap region. It can be understood that the power peaking factors for the adjacent fuel elements have to be calculated by mesh edge flux. Table 4 shows the thermal neutron flux in the flux trap region. It can be observed that Batan-2DIFF code produced thermal neutron flux close to other institutions' results. It should be noted that the relative differences among the participants' results are expected to occur in the vicinity of flux trap region where the neutron flux peak appears. 80

9 Table 5 summarized the calculated results for various isothermal temperature and void reactivity coefficients defined previously. Three temperature ranges in which MTRs are commonly operated were investigated. In addition, reactivity coefficients arised from water density changes which simulates the moderator void or boiling phenomena were also investigated. In general, the combination of WIMSID4 and Batan's code provided very close calculated values to other institutions' results. The largest relative difference compared to ANL results appeared in the reactivity coefficient o of water moderator in the temperature range of C. - Table 6 gives the calculated results for the local void coefficients in some prescribed standard fuel elements. The benchmark calculation results for this case were only provided by ANL. It can be observed from the table that not only for whole core void reactivity coefficients shown in the previous table but our calculation results for local void reactivity coefficients were very close to the ANL results. The calculated power peaking factors for some prescribed fuel and control elements when they are substituted with their fresh compositions are shown in Table 7. These values are very important parameter in the thermal and safety design of an MTR for e.g. in simulating operator' error in refueling operation. As already discussed earlier, the power peaking factors are conservative, that is, the values at the edge of the mesh interval with highest power, and not the value at the center of the mesh interval with highest power. Normally, there is a sharp rise in the power density at the edge of a fuel element facing moderator or reflector region. It can be observed from the table that even for those severe flux gradients our calculation results either for local, radial power peaking factors and their product values were very close the ANL results. This results also proved that the edge-mesh power peaking factor calculations in Batan-2DIFF are valid. CONCLUDING REMARKS AND FUTURE WORKS Extensive benchmark calculations using combination of WIMSID4 and Batan's standard diffusion code have been conducted to check the validity, accuracy of the codes, and to obtain proper cell modeling for MTR type fuel and control elements which will be used in designing the next high loading silicide fuel ofrsg-gas. The object and parameters of the benchmark calculations are defined by the IAEA in the IAEA-TECDOC-233 and IAEA-TECDOC-643. In general, the combination of WIMS/D4 and Batan's standard diffusion codes gave very satisfied results which proved the validity of the WIMSID4 cell model proposed and the accuracy of the Batan's diffusion code used in the 8]

10 benchmark calculations. Four energy group, multiplate options of WIMSID4 are sufficient to give accurate results in term of infinite multiplication factors, fuel depletion results and diffusion constants for whole core calculations. Two-dimensional, four group diffusion model supplied with a correct axial buckling value can be considered accurate enough for the MTR whole core calculations. Of course, 3-D few group diffusion model will be necessary for further refined analyses which can be done by our Batan-3DIFF diffusion code. The capability of Batan-2DIFF code to calculate power peaking factors in a conservative way, that is, based on the mesh edge flux, widens the code applicability for safety analyses especially on heterogenous cores such as research or test reactors' cores. As future works, the second part of the benchmark calculations will be elaborated in which the reactor kinetic parameters, control rod worths, axial power distributions used in those calculations have to be calculated first. These works will require other Batan's standard codes such as Batan ADJOINT-2D and Batan-3DIFF codes. ACKNOWLEDGMENTS The authors express their gratitude to Ir. Bakrie Arbi, Ir. Alfahari Mardi M.Sc., Ir. Iman Kuntoro, and all staff member of Reactor Physics Division, Center for Multipurpose Reactor, for their keen interest and encouragement given for the present work. REFERENCES 1. LIEM, P.H., "Development and Verification of Batan's Standard, Two Dimensional Multigroup Neutron Diffusion Code (Batan-2DIFF)", Atom Indonesia, 20 ( 1), Jakarta (1994) 2. LIEM, P.H., "Pengembangan Program Komputer Standar Batan Diffusi Neutron Banyak Kelompok 3-D (Batan-3DIFF)", Risalah Komputasi dalam Sains dan Teknologi Nuklir V, PPI-Batan, Jakarta (1995) 3. LIEM, P.H., "Batan-FUEL: A General In-Core Fuel Management Code", accepted to be published in Atom Indonesia 4. LIEM P.H., et al., "Development of algorithm for searching equilibrium core condition of a nuclear reactor", Proceeding of Workshop on Computation in Nuclear Science and Technology IV, Batan, Jakarta (1994) 5. LITTLE, Jr., W.W. and HARDIE, R.W., "2DB User's Manual Revision I", BNWL-831 REV 1. See also 2DBUM (2DB University of Michigan) documentation on tape 82

11 6. LITTLE, Jr., W.W. and HARDIE, R.W., "3DB User's Manual", documentation on tape 7. ASKEW, lr., FAYERS, FJ. and KEMSHELL, P.B., "A General Description of the Code WIMS", Jour. of Brit. Nuc. Energy Soc. 5 (1966) 8. IAEA, "Research Reactor Core Conversion from the Use of Highly Enriched Uranium to the Use of Low Enriched Uranium Fuels Guide Book", IAEA-TECDOC-233, Vienna (1980) 9. IAEA, "Research Reactor Conversion Guide Book - Volume 3: Analytical Verification ", IAEA-TECDOC-643, Vienna (1992) 10. FOWLER, T.B. and VONDY, D.R., "Nuclear Reactor Core Analysis Code: CITATION", ORNL-TM-2496, Rev. 2 (1971) 83

12 Tabel 1. Data and specification agreed for benchmark problem (8). Active core height 600 mm Extrapolation length 80 mm (in 80 mm distance from the core, the cosine-shaped flux goes to zero) X- Y calculation only Space at the grid plate per fuel element 77 mm x 81 mm Fuel element cross-section 76 mm x 80.5 mm including support plate 76 mm x 80.0 mm without support plate Meat dimensions 63 mm x 0.51 mm x 600 mm Aluminum-canning with p A12.7 g/cc Thickness of support plate 4.75 mm; p AI 2.7 glee Number of fuel plates per fuel element: 23 identical plates, each 1.27 mm thick Number of fuel plates per control element: 17 identical plates, each 1.27 mm thick Identification of the remaining plate positions of the control element: 4 plates of pure aluminium pal 2.7 g/cc, each 1.27 mm thick in the position of the first, the third, the twenty-first, and the twenty-third standard plate position; water gaps between the two sets of aluminum plates. Specifications of the (UAlx-AI Fuel) for LEU corresponding to the previous definitions: Enrichment 20 w/o U gram U-235 per fuel element (23 plates) 72 w/o of uranium in the UAlx-AI only U-235 and U-238 in the fresh fuel Total power: 10 MWth (power buildup by 3.1 x 1010 fission/joule) Thermal hydraulic data: o Water temperature 20o C Fuel temperature 20 C Pressure at core height 1.7 bar 84

13 Table 2. Four group structure for cross section generation by WIMS/D4 cell calculation code. Energy - Region 6 Upper Lower 3 (ev) Energy xenergy Bound 10 Bound Table 3. Calculation results of the effective multiplication factor (laea TECDOC-233). - (+0.029) (+3.974) (+0.050) (+1.]58) (-) EOL BOL (-) Core1.168±0.003 Fresh - (+0.026)a 1.] INSTITUTION(+0.769)b (-0.140) (-1.059) (+3.574) (+1.772) (+1.165) (+0.636)b (-0.343) ) 1.048) (+1.113) (+1.60]) (-0.762) (0.0) 1.292) 1.130) ANL a) Relative difference from MC (%) b) Relative difference from ANL (%) 85

14 j.... Flux Tabel 4. Calculated thermal neutron flux in the flux trap region (IAEA- TECDOC-233). 10 fern s ) (-7.9) at 14 the Center I. (-8.4) (-2.9) (10 (-) (-8.0) (-3.6) (-) - Flux ) fern (+6.5)a (-) at s) the Cent~rMi~fl.~~. a) Relative difference from ANL (%) 86

15 Table 5. Isothermal reactivity coefficients (IAEA-TECDOC-643). -t.ppc x 105) 105) /] t.pw ) React. INTER laeri ANL len Batan (_3.7)a (-4.8) (-24) (+2.4) (+17) (+3.7) (-1.8) (-4.2) 2.] (-3.6) (+3.0) (+2]) (+64) (-13) (-4.9) (+14) (-10) (+20) (-3.7) (+3.8) (-7.4) (-8.9) (-16) (-26) (-2.5) (+59) 3.08 (+29) (-8.1) (-3.8) ] 24.6 (+5.1) (-23) (-2.7) (-16) (-21) (-8.2) (-8])(-33) (-6.8) (-] (-25) (-22) 1.89 (-15) (-2.0) 2.19 (-1.9) (-13) (+17) (+19) (+36) (+61) (+49) (+60) (0) (-77) (+1.2) (+3.9) (-6.4) (-5.2) (-5.9) 2.55 (-4.9) ( (-3.6) (0.0) ).. EIR>I.... ATOM... Notes at'!; a Dw a 7j = Reactivity coeff. of water temperature = Reaclivity coeff. of water density = Reactivity coeff. of fuel temperature a" = Reactivity coeff. of void in terms of water density a) Relative difference from ANL (%) 87

16 Table 6. Calculated local void coefficients (~P x 1000) (IAEA TECDOC-643). (-) ElementNoided Ii (+0.84)a (+0.36) (0.0) ANt(USA) Batan(Indonesia) a) Relative difference from ANL (%) Table 7. Power peaking factor (IAEA-TECDOC-643). Radial Element INTER (0.0) (0.0) (+18.6) (+24.6) (+19.4) (+24.7) 2.13 (-15.8) (-16.0) (-29.7) (+4.55) (+3.92) JEN (-1.53) 1.24 (-6.77) 1.51 (-8.57) (+3.64) (-2.94) 1.14 EIR ANt1.02 Batan (-2.58) (+0.76) (+2.26) (+2.86) (+0.58) (+0.91) (0.0)1.31 \.27) \.28) 1.28) I ATOM a) Relative difference from ANL (%) b) Calculated by mesh edge flux 88

17 W - W 45%45%25% HP AI SFE-3 SFE-2 GGW FECE G5% CFE-l GWFE SFE-l W I FE I W : Water G : Graphite FE,SFE CE,CFE : Standard Fuel Element : Control Element Figure]. IAEA 10 MW benchmark reactor configuration (BOL) as defined in IAEA-TECDOC ~~ _ O.O~I Modera.or Moderator 1/2 Reflective Fuel Clad Meat Meal (AI) (H2O) BC On. Fuel Plate Dimension ( ) EQUIV ALENT UNIT CELL OF SFE lox lox One Fuel Plate Extra Region (AI & H20) Reflective BC (em) Figure 2. WIMS/D4 equivalent unit cell model for FE with multiplate option. 89

18 Reflective BC j ,0255 i 1/2 Fuel Meat 0,038 ' ~ 0,223 i Moderator Clad (AI) (H20) I 0,038 0,051 0.Q Clad (AI) I ---~, i i Fuel Meat i I One Fuot Plate DimenSion, (0,33885) Clad (AI~,_._. Moderator (H20) J\il EQUIVALENT UNIT CELL OF CFE 7x 7x 0,33885 One Fuel Plat. 0,4611 Extra Region (AI & H20), 1. Rcflective BC (em) Figure 3. WIMS/D4 equivalent unit cell model for CE with multiplate option (absorber region is treated separately). ~- Structural Dimensionand ~ Moderalor Reflective 1/2 Clad Fuel Meat (H2O) (AI) i Reflector One 2x Fuel Plate ,038 BC ,038, /!\ Materials 0,223 One Fuel Plate ( ) Homogenized 8.0 (C. AI or H2O) t Macroscopic Cross Sections 11\ \" Clad.- Reflective(em) BC (AI) Extra - ---K! Moderator Region(H2O) \11 2x - i ----fj Figure 4. WIMSID4 cell model for structural and reflector materials cross section generation. 90

19 [xl -, 3 '" ~ 014] ~!;:c8 c.:j... d) ::3 :: C E 2 >< I I I I I H20 :FE:FE:~AI+:~FE:FE: H20,-... g=4 a X-direction (cm) 100 Figure 5. X-direction group neutron flux distributions at the reactor center (2-D geometry). 6 H20!FE i FEi~A,+i~ FE! FE! H20 H20 o 50 X-direction (cm) 100 Figure 6. X-direction fast to thermal neutron flux ratio at the reactor center (2-D geometry). 91