Application and development of tools for HTR neutronics and thermal hydraulics analysis at IKE W. Bernnat, M. Buck, N. BenSaid, K. Hossain, M. Mesina IKE, University of Stuttgart The PBMR-4 Core Design - 2nd Workshop - OECD/NEA, Issy les Moulineaux - 26-27 January 26
General Objectives: Development of an Integrated Tool for the Analysis of Stationary and Dynamic Behavior of HTRs thermal flux, 1.2 1.8.6.4.2 15 x 1-5 1 5 Height, cm -5 5 Neutronics reactor design (stationary and transient). 1 15 2 Radius, cm 25 3 In-Core Thermalhydraulics and fuel thermal behavior. Modeling of components and dynamics of Power Conversion Unit (PCU). The PBMR-4 Core Design - 2nd Workshop - OECD/NEA, Issy les Moulineaux - 26-27 January 26 2
HTR applications Neutronics stationary Neutronics transient Thermal hydraulics PCU simulation The PBMR-4 Core Design - 2nd Workshop - OECD/NEA, Issy les Moulineaux - 26-27 January 26 3
Codes available ZIRKUS, KIND THERMIX/KONVEK ANISN/DORT/TORT (1D-3D S N -transport) Monte Carlo : MCNP(X)/KENO NJOY (Cross section preparation) RSYST (IKE), general reactor physics applications MICROX-2 RESMOD (IKE), multicell spectralcode FLOWNEX (M-Tech), system code The PBMR-4 Core Design - 2nd Workshop - OECD/NEA, Issy les Moulineaux - 26-27 January 26 4
ZIRKUS Modular system with funcional modules and data base system Restricted to pebble bed HTR types Flexibility high, but rather complex Several adaptations to PBMR like systems (annular core) were made together with simplifications of input structure The PBMR-4 Core Design - 2nd Workshop - OECD/NEA, Issy les Moulineaux - 26-27 January 26 5
Main modular ZIRKUS sequence for stationary neutronics - thermal hydraulics calculations KUGEL WQRFL NIVERM NEWA MICROX MAGRU HBLOCK VORNEK Definition of spherical fuel element Cross-sections for reflectors (temperature, density, impurity) Number densities initialisation/shuffling Dancoff factors Cross section resonance treatment and spectral calculation (microscopic XS for spectral zones) Macroscopic cross sections for burnup zones 2D diffusion calculation, variable group numbers, Xe distribution Power density calculation The PBMR-4 Core Design - 2nd Workshop - OECD/NEA, Issy les Moulineaux - 26-27 January 26 6
Main modular ZIRKUS sequence for stationary neutronics - thermal hydraulics calculations ZBUCK S B U R N N Z W NZW AUS LDTHERMI T H E R M IX TZIRK DIFK Bucklings for spectral zones derived fro m d iffu sio n calcu latio n D ep letio n calcu latio n fo r all b u rn u p zones D ec a y h eat c alcu latio n Interface decay heat data Interface ZIRKUS-THERMIX T h erm al h yd rau lic c alcu latio n Interface THERMIX-ZIRKUS Diffusion constants for cavity region The PBMR-4 Core Design - 2nd Workshop - OECD/NEA, Issy les Moulineaux - 26-27 January 26 7
ZIRKUS-features first core transition core equilibrium core flow pattern of pebbles reload strategy fuel/moderator elements 2 D representation for burn up 3 D stationary calculations (burnup distribution 2D) with Monte-Carlo codes MCNP and/or KENO temperature coefficients water ingress xenon reactivity flexibility, connection to other codes possible The PBMR-4 Core Design - 2nd Workshop - OECD/NEA, Issy les Moulineaux - 26-27 January 26 8
Typical ZIRKUS/THERMIX applications Universität Stuttgart Crosssection Database MICROX/ MCNP FIRST-CORE TRANSITION CORE EQUILIBRIUM CORE ZIRKUS Database Calculation of Reactivity Coefficients. Database for Transients Monte Carlo, S N -Transport Thermal- LOFC hydraulic DLOCA analysis The PBMR-4 Core Design - 2nd Workshop - OECD/NEA, Issy les Moulineaux - 26-27 January 26 9
ZIRKUS options SINGLE MODULE INPUTS SEQUENCE OF MODULES EXECUTION OF SINGLE MODULES AND SEQUENCES ARCHIVING OF CALCULATIONAL RESULTS RESTART-OPTION INTERFACE TO THERMAL HYDRAULICS INTERFACE TO TRANSPORT PROGRAMS INTERFACE TO TRANSIENT CODES KIND; RZ KIND The PBMR-4 Core Design - 2nd Workshop - OECD/NEA, Issy les Moulineaux - 26-27 January 26 1
ZIRKUS modular chain Universität Stuttgart KUGEL, DIFK WQRFL ZBUCK NIVERM SBURN NEWA NZW MICROX NZWAUS MAGRU LDTHERMI HBLOCK THERMIX VORNEK TZIRK The PBMR-4 Core Design - 2nd Workshop - OECD/NEA, Issy les Moulineaux - 26-27 January 26 11
Simulation platform Universität Stuttgart The PBMR-4 Core Design - 2nd Workshop - OECD/NEA, Issy les Moulineaux - 26-27 January 26 12
Cross section data base and spectral code Data evaluations: JEFF 3.1 MICROX-2 spectral code RESMOD spectral code MCNP(X) Monte Carlo Thermal neutron scattering laws for graphite The PBMR-4 Core Design - 2nd Workshop - OECD/NEA, Issy les Moulineaux - 26-27 January 26 13
MICROX-2 for detailed calculation of spectra in fast, resonance and thermal range FDTAPE 92 groups fast range Geometry of cell, temperature Dancoff factor, buckling Zonewise Nuclide composition Z I GARTAPE Pointwise Resolved resonan-ce range MICROX-2 R K GGTAPE 11 groups thermal range Condensed microscopic cross sections U S The PBMR-4 Core Design - 2nd Workshop - OECD/NEA, Issy les Moulineaux - 26-27 January 26 14
Present MICROX-2 Library based on JEFF-3.1 158 Nuclides Temperatures: 3; 6; 8; 9; 11; 14; 18; 24 K 1-H-1 34-Se-79 47-Ag-19 58-Ce-141 63-Eu-151 9-Th-232 95-Am-241 5-B-1 36-Kr-83 47-Ag-11m 58-Ce-142 63-Eu-153 91-Pa-233 95-Am-242 5-B-11 37-Rb-87 48-Cd-11 58-Ce-143 63-Eu-154 93-Np-235 95-Am-242m 6-C- 38-Sr-9 48-Cd-111 58-Ce-144 63-Eu-155 93-Np-236 95-Am-243 7-N-14 4-Zr-93 48-Cd-113 59-Pr-141 63-Eu-156 93-Np-237 95-Am-244 8-O-16 4-Zr-95 5-Sn-126 59-Pr-143 63-Eu-157 93-Np-238 95-Am-244m 14-Si-28 41-Nb-94 52-Te-129m 6-Nd-142 64-Gd-152 93-Np-239 96-Cm-24 14-Si-29 41-Nb-95 52-Te-132 6-Nd-143 64-Gd-154 92-U-233 96-Cm-241 14-Si-3 42-Mo-1 53-I-129 6-Nd-144 64-Gd-155 92-U-234 96-Cm-242 24-Cr-5 42-Mo-95 53-I-131 6-Nd-145 64-Gd-156 92-U-235 96-Cm-243 24-Cr-52 42-Mo-99 53-I-135 6-Nd-146 64-Gd-157 92-U-236 96-Cm-244 24-Cr-53 43-Tc-99 54-Xe-131 6-Nd-147 64-Gd-158 92-U-237 96-Cm-245 24-Cr-54 44-Ru-11 54-Xe-132 6-Nd-148 64-Gd-16 92-U-238 96-Cm-246 25-Mn-55 44-Ru-12 54-Xe-133 6-Nd-15 65-Tb-159 94-Pu-238 96-Cm-247 26-Fe-54 44-Ru-13 54-Xe-134 61-Pm-147 65-Tb-16 94-Pu-239 96-Cm-248 26-Fe-56 44-Ru-14 54-Xe-135 61-Pm-148 66-Dy-16 94-Pu-24 96-Cm-249 26-Fe-57 44-Ru-16 55-Cs-133 61-Pm-148m 66-Dy-161 94-Pu-241 96-Cm-25 26-Fe-58 45-Rh-13 55-Cs-134 61-Pm-149 66-Dy-162 94-Pu-242 28-Ni-58 45-Rh-15 55-Cs-135 61-Pm-151 66-Dy-163 94-Pu-243 28-Ni-6 46-Pd-14 55-Cs-137 62-Sm-147 66-Dy-164 94-Pu-244 28-Ni-61 46-Pd-15 57-La-139 62-Sm-148 67-Ho-165 28-Ni-62 46-Pd-16 62-Sm-149 72-Hf-176 28-Ni-64 46-Pd-17 62-Sm-15 72-Hf-177 46-Pd-18 62-Sm-151 72-Hf-178 62-Sm-152 72-Hf-179 62-Sm-153 72-Hf-18 62-Sm-154 Universität Stuttgart The PBMR-4 Core Design - 2nd Workshop - OECD/NEA, Issy les Moulineaux - 26-27 January 26 15
Thermal neutron scattering on graphite Frequency distributions of graphite Universität Stuttgart 4 35 Rho(Omega) in 1/eV 3 25 2 15 1 GA ORNL NCSU 5..5.1.15.2.25 Omega in ev The PBMR-4 Core Design - 2nd Workshop - OECD/NEA, Issy les Moulineaux - 26-27 January 26 16
Comparison of measured and calculated spectra 5. 4. EPhi(E) (arbitrary units) 3. 2. 1. Experiment GAC-5A 274 K GAC-5a : GA model GAC-5a : ORNL model GAC-5a : NCSU model Experiment GAC-5F 6 K GAC-5f : GA model GAC-5F : ORNL model..1.1 1. Neutron Energy (ev) The PBMR-4 Core Design - 2nd Workshop - OECD/NEA, Issy les Moulineaux - 26-27 January 26 17
Transient calculations ZKIND and RZKIND codes Both are neutron kinetic/dynamic codes for the pebble bed core primarily developed for the HTR-MODUL reactor. The Tasks are: calculation of time dependent power distributions and reactivity effects temperature distributions The PBMR-4 Core Design - 2nd Workshop - OECD/NEA, Issy les Moulineaux - 26-27 January 26 18
Thermal-hydraulic Models Different models to simulate the heat production and temperature distribution in fuel Macro Model Macro and Micro Model enhanced Micro Model (2D RZKIND) (1D ZKIND) (1D PKIND) The PBMR-4 Core Design - 2nd Workshop - OECD/NEA, Issy les Moulineaux - 26-27 January 26 19
Macro Model: Macro and Micro model of Heat conduction In RZKIND at the time a homogeneous model is implemented. The Fuel spheres are subdivided into several shells but the fuel temperature is assumed to be identical to the graphite temperature in the corresponding shell. The fuel temperature calculated for reactivity feedback is averaged over all shells containing fuel (except outer shell). The moderator temperature is the average of graphite temperatures of all shells. The PBMR-4 Core Design - 2nd Workshop - OECD/NEA, Issy les Moulineaux - 26-27 January 26 2
Thermal-hydraulic Models used in KIND codes Macrosystem Microsystem <T> τ =T - <T> r K r C rm M r M r S Shell Matrix Kernel Share of Matrix Graphite Coating <T> : average Temperature over the fine structure τ : Temperature increase in the particle The PBMR-4 Core Design - 2nd Workshop - OECD/NEA, Issy les Moulineaux - 26-27 January 26 21
Data Flow to RZKIND ZIRKUS ZIRKUS Geometry Cross Section data Data Library RZKIND OUTPUT FILE User s Input File KONTR Condensation of cross sections ZIRKUS-Geometry RZKIND-Geometry ZKIND VPF Polynomial fit of cross sections RZKIND Data-Library The PBMR-4 Core Design - 2nd Workshop - OECD/NEA, Issy les Moulineaux - 26-27 January 26 22
Features of the KIND Codes Simulate Inlet temperature disturbances Mass flow disturbances Changes in power Reactivity disturbances Control rod movement or SAS insertion Xenon effects external reactivity effects The PBMR-4 Core Design - 2nd Workshop - OECD/NEA, Issy les Moulineaux - 26-27 January 26 23
Relative Power 2, 1,8 1,6 1,4 1,2 1,,8,6,4,2 Example: Control rod withdrawal (2D RZ-KIND calculation for HTR Modul) (a) (b) (c) control rod 1.Scram (a) 2.Scram (b) 2.Scram, control rods withdraw (c) (a) first scram works at 12% neutron flux (b) second scram works if average He coolant outlet Temperature exceeds limit (c) neither 1. Scram nor 2. scram works control rods withdraw to the maximum upper end position (-1cm), 1 2 3 4 5 Time (s) The PBMR-4 Core Design - 2nd Workshop - OECD/NEA, Issy les Moulineaux - 26-27 January 26 24
Influence of detailed fuel temperature model (control rod velocity: 1 cm/s) Relative Power [-] 8 7 6 5 4 3 2 Withdrawal of all rods with 1 cm/s RZKIND (bue) calculation Particle Modell of ZKIND (blue) 2D RZ-KIND calculation (red) 1D ZKIND particle model calculation Extreme differences between the two models 1 1 2 3 4 5 6 7 8 9 1 Time [s] The PBMR-4 Core Design - 2nd Workshop - OECD/NEA, Issy les Moulineaux - 26-27 January 26 25
Temperature [ C] 9 85 8 75 7 65 6 Fast transient calculation UO 2 Temperature Fuel Coat.1 Coat.2 Matrix-max Matrix-average FE_Shell average Matrix Temperature Fuel Element Shell ZKIND (Particle model) - 1 cm/s 55 5 2 4 6 8 1 Time [s] The PBMR-4 Core Design - 2nd Workshop - OECD/NEA, Issy les Moulineaux - 26-27 January 26 26
General Objectives : Thermal hydraulics Reliable and flexible integrated tool for analysis of static and dynamic behavior of HTRs: Emphasis on detailed description of in-vessel behavior, especially coupling of thermal-hydraulics and neutronics Existing tools as starting point for further development Present code THERMIX The PBMR-4 Core Design - 2nd Workshop - OECD/NEA, Issy les Moulineaux - 26-27 January 26 27
THERMIX discretisation Examples of analyses and applications HTR with annular core [PBMR] Design of PBMR with annular core and compact central column Thermal power: 4 MW System pressure: 85 bar Inlet temperature: 5 C Outlet temperature: 9 C Initial steady state temperature distribution central grahite column annular core The PBMR-4 Core Design - 2nd Workshop - OECD/NEA, Issy les Moulineaux - 26-27 January 26 28
Examples of analyses and applications Results for Annular Core Reactor LOFC with depressurization Solid temperature development LOFC without depressurization: Solid temperature development Gas temperature and velocity (annular core only) The PBMR-4 Core Design - 2nd Workshop - OECD/NEA, Issy les Moulineaux - 26-27 January 26 29
Further developments 3D calculations in ZIRKUS Improved treatment of streaming in cavities for diffusion calculations New 2D/3D thermal hydraulics module Extensions of the space time kinetics modules more energy groups more flexible mesh grid coupling to new thermal hydraulics code detailed heat transfer model for coated particles embedded into graphite matrix for 2D version The PBMR-4 Core Design - 2nd Workshop - OECD/NEA, Issy les Moulineaux - 26-27 January 26 3
Benchmark PBMR 4 Neutronics/Thermal hydraulics ZIRKUS and DORT model (exercise 1) THERMIX and KONVEK model (exercise 2) The PBMR-4 Core Design - 2nd Workshop - OECD/NEA, Issy les Moulineaux - 26-27 January 26 31
Mesh and media assignment : Steady State Exercise 1 73,6 8,55 92,5 1 117 134 151 168 185 192,5 24,5 211,4 225 243,6 26,6 275 287,5 292,5 Mesh subdivision 1 41 73,6 8,6 92,1 1 117 134 151 168 185 193 24 211 225 244 261 275 288 293 1 2 3 1 1 1 2 2 2 2 2 1 1 1 2 2 2 2 2 1-2 1 31 32,6 6,95 11,5 7,95 17 17 17 17 17 7,95 11,5 6,95 13,6 18,6 17 14,4 12,5 5-15 5 5 133 133 133 133 155 116 113 113 113 113 113 135 164 144 144 152 152 152 189 19-1 5 5 133 133 133 133 155 116 113 113 113 113 113 135 164 144 144 152 152 152 189 19-5 5 5 133 133 133 133 155 116 112 112 112 112 112 135 164 144 144 152 152 152 189 19 5 5 133 133 133 133 155 116 111 111 111 111 111 135 165 144 144 152 152 152 189 19 5 5 5 134 134 134 125 156 117 1 23 45 67 89 136 166 145 145 153 153 153 189 19 1 5 5 134 134 134 125 156 117 2 24 46 68 9 136 167 145 145 153 153 153 189 19 15 5 5 134 134 134 126 157 118 3 25 47 69 91 137 168 146 146 153 153 153 189 19 2 5 5 134 134 134 126 157 118 4 26 48 7 92 137 169 146 146 153 153 153 189 19 25 5 5 134 134 134 126 157 118 5 27 49 71 93 137 17 146 146 153 153 153 189 19 3 5 5 134 134 134 127 158 119 6 28 5 72 94 138 171 147 147 153 153 153 189 19 35 5 5 134 134 134 127 158 119 7 29 51 73 95 138 172 147 147 153 153 153 189 19 4 5 5 134 134 134 127 158 119 8 3 52 74 96 138 173 147 147 153 153 153 189 19 45 5 5 134 134 134 127 158 119 9 31 53 75 97 138 174 147 147 153 153 153 189 19 5 5 5 134 134 134 128 159 12 1 32 54 76 98 139 175 148 148 153 153 153 189 19 55 5 5 134 134 134 128 159 12 11 33 55 77 99 139 176 148 148 153 153 153 189 19 6 5 5 134 134 134 128 159 12 12 34 56 78 1 139 177 148 148 153 153 153 189 19 65 5 5 134 134 134 128 159 12 13 35 57 79 11 139 178 148 148 153 153 153 189 19 7 5 5 134 134 134 129 16 121 14 36 58 8 12 14 179 149 149 153 153 153 189 19 75 5 5 134 134 134 129 16 121 15 37 59 81 13 14 18 149 149 153 153 153 189 19 8 5 5 134 134 134 129 16 121 16 38 6 82 14 14 181 149 149 153 153 153 189 19 85 5 5 134 134 134 129 16 121 17 39 61 83 15 14 182 149 149 153 153 153 189 19 9 5 5 134 134 134 13 161 122 18 4 62 84 16 141 183 15 15 153 153 153 189 19 95 5 5 134 134 134 13 161 122 19 41 63 85 17 141 184 15 15 153 153 153 189 19 1 5 5 134 134 134 13 161 122 2 42 64 86 18 141 185 15 15 153 153 153 189 19 15 5 5 134 134 134 131 162 123 21 43 65 87 19 142 186 151 151 153 153 153 189 19 11 5 5 134 134 134 131 162 123 22 44 66 88 11 142 187 151 151 153 153 153 189 19 115 5 5 132 132 132 132 163 124 114 114 114 114 114 143 188 151 151 154 154 154 189 19 12 5 5 132 132 132 132 163 124 115 115 115 115 115 143 188 151 151 154 154 154 189 19 125 5 5 132 132 132 132 163 124 115 115 115 115 115 143 188 151 151 154 154 154 189 19 The PBMR-4 Core Design - 2nd Workshop - OECD/NEA, Issy les Moulineaux - 26-27 January 26 32
Compositions for Benchmark Model (THERMIX-Konvek) The PBMR-4 Core Design - 2nd Workshop - OECD/NEA, Issy les Moulineaux - 26-27 January 26 33
Results neutronics exercise 1 Calculations performed with the Diffusion code of ZIRKUS (2D) Cavities treated via direction dependent diffusion coefficients For comparisons: DORT 2D S N -calculations P - transport corrected Cavities treated as vacuum Value ZIRKUS/Diffusion DORT-S16 DORT-S12 DORT-S8 DORT-S6 DORT-S4 DORT-S2 k-eff 1.3488.992842.99194.99383.99745.99376.995983 Maximum Power density (W/cm3) 12.14 12.2994 12.325 12.3264 12.324 12.333 12.47 Maximum fast flux (n/cm2/s) 2.5E+14 2.41E+14 2.45E+14 2.45E+14 2.43E+14 2.46E+14 2.52E+14 Maximum thermal flux (n/cm2/s) 3.55E+14 3.141E+14 3.141E+14 3.153E+14 3.17E+14 3.153E+14 3.171E+14 Leakage from core (% per lost neutron) 15.4 15.24 15.28 15.2 15.6 15.2 15.12 Leakage from domain (% per lost neutron).29.28.21.211.213.167 The PBMR-4 Core Design - 2nd Workshop - OECD/NEA, Issy les Moulineaux - 26-27 January 26 34
Fast flux density PBMR-4 exercise 1 DORT S16 7 x 1-6 6 5 fast flux, 4 3 2 1 Bottom 15 1 5-5 5 Top Height, cm Radius, cm The PBMR-4 Core Design - 2nd Workshop - OECD/NEA, Issy les Moulineaux - 26-27 January 26 35 1 15 2 25 3
Thermal flux density PBMR-4 exercise 1 DORT- S16 1.2 x 1-5 1 thermal flux,.8.6.4.2 Bottom 15 1 5 5-5 Top Height, cm Radius, cm The PBMR-4 Core Design - 2nd Workshop - OECD/NEA, Issy les Moulineaux - 26-27 January 26 36 1 3 25 2 15
Relative difference DORT S8 to S16 reference solution (fast group) 2 1 diff fast flux s8-s16, -1-2 -3-4 -5 14 12 1 8 6 4 2-2 5 Height, cm Radius, cm The PBMR-4 Core Design - 2nd Workshop - OECD/NEA, Issy les Moulineaux - 26-27 January 26 37 1 15 2 25 3
Relative difference DORT S8 to S16 reference solution (thermal group) 2 diff thermal flux s8-s16, -2-4 -6-8 -1 14 12 1 8 6 4 2 3 25 2 15 1 5-2 Height, cm Radius, cm The PBMR-4 Core Design - 2nd Workshop - OECD/NEA, Issy les Moulineaux - 26-27 January 26 38
Relative difference DORT S2 to S16 reference solution (fast group) 2 15 diff fast flux s2-s16, 1 5-5 -1 15 1 5-5 5 Height, cm Radius, cm The PBMR-4 Core Design - 2nd Workshop - OECD/NEA, Issy les Moulineaux - 26-27 January 26 39 1 15 2 25 3
Relative difference DORT S2 to S16 reference solution (thermal group) 1 diff thermal flux s2-s16, -1-2 -3-4 15 1 5-5 Height, cm Radius, cm The PBMR-4 Core Design - 2nd Workshop - OECD/NEA, Issy les Moulineaux - 26-27 January 26 4 5 1 15 2 25 3
Fission neutron source distribution (DORT) S-16 calculation for exercise 1 3.5 x 1-8 3 fission source distribution, 2.5 2 1.5 1 TOP.5 1 2-2 2 4 6 8 1 12 14 3 Height, cm Radius, cm The PBMR-4 Core Design - 2nd Workshop - OECD/NEA, Issy les Moulineaux - 26-27 January 26 41
Relative difference in fission neutron source distribution between S-8 and S-16 calculation diff source distribution s8-s16,.3.2.1 -.1 -.2 -.3 TOP -.4-2 2 4 6 Height, cm 8 1 12 14 3 5 1 15 2 25 Radius, cm The PBMR-4 Core Design - 2nd Workshop - OECD/NEA, Issy les Moulineaux - 26-27 January 26 42
Relative difference in fission neutron source distribution between S-2 and S-16 calculation 4 3 diff source distribution s2-s16, 2 1-1 TOP -2-3 -2 2 4 6 8 1 12 5 1 15 2 25 3 14 Height, cm Radius, cm The PBMR-4 Core Design - 2nd Workshop - OECD/NEA, Issy les Moulineaux - 26-27 January 26 43
Exercise 2 Heat flow to surface cooling system 974,5 kw! Maximum fuel temperature 996,7 C! Inlet helium temperature ( C) 5 Outlet helium temperature ( C) 998.2 Inlet Pressure (MPa) 9.33944 Outlet Pressure (MPa) 9 Total pressure drop (kpa) - Inlet to outlet 339.44 Pebble bed pressure drop (kpa) - Top / bottom fuel 278 Average fuel temperature ( C) 815.28 Average moderator temperature ( C) 796.5 Average helium temperature in core ( C) 74.61 The PBMR-4 Core Design - 2nd Workshop - OECD/NEA, Issy les Moulineaux - 26-27 January 26 44
Pebble surface temperature distributiion exercise 2 1 9 8 15 1325 116 96 75 54 Radius [m] 33 12-1 -235 462,5 316 287,5 225 134 92,5 The PBMR-4 Core Design - 2nd Workshop - OECD/NEA, Issy les Moulineaux - 26-27 January 26 45 176,5 Height [m] 7 6 5 4 3 2 1 Surface Temperature [ C ] 9-1 8-9 7-8 6-7 5-6 4-5 3-4 2-3 1-2 -1
Flow field exercise 2 The PBMR-4 Core Design - 2nd Workshop - OECD/NEA, Issy les Moulineaux - 26-27 January 26 46
Remarks exercise 1 k eff strongly dependent from diffusion constants in cavity over pebble bed core for diffusion method k eff about 1% lower for S N (DORT) method, depending from SN order S N order from influence of fluxes at outer boundaries and cavities For S N calculations the absorber cross sections should be adopted transport correction for P calculation adequate? Treatment of cavities well defined for S N calculations The PBMR-4 Core Design - 2nd Workshop - OECD/NEA, Issy les Moulineaux - 26-27 January 26 47
Remarks exercise 2 Spatial discretisation could be refined fuel, moderator and reflector temperatures seem to be adequate for steady state cases The PBMR-4 Core Design - 2nd Workshop - OECD/NEA, Issy les Moulineaux - 26-27 January 26 48
Remarks exercise 3 A reproduction of the reference cross section data was not possible Coupled calculations with interpolated cross sections led to inconsistent results Some interpolated data should be compared The PBMR-4 Core Design - 2nd Workshop - OECD/NEA, Issy les Moulineaux - 26-27 January 26 49