Post on 13-Jan-2022
OECD PBMR 400 BENCHMARK
P Mkhabela1, J Han1, B Tyobeka1, K Ivanov1, F Reitsma2
1The Pennsylvania State University2 PBMR(Pty)Ltd
Introduction
• The deterministic neutronics, thermal-hydraulics and transient analysis tools and methods available to design and analyse PBMRs have lagged behind the state of the art compared to other reactor technologies.
• This has motivated the testing of existing methods for HTGRs but also the development of more accurate and efficient tools to analyse the neutronics and thermal-hydraulic behaviour for the design and safety evaluations of the PBMR.
• In addition to the development of new methods, this includes defining appropriate benchmarks to verify and validate the new methods in computer codes.
Objectives• To Establish a standard benchmark for coupled codes
(neutronics/thermal-hydraulics) for PBMR design. • Code to code comparison using a common cross section
library – important for Verification and Validation.• Obtain a detailed understanding of the events and the
processes.• Benefit from different approaches, understanding
limitations and approximations.• Organize a special session at conference/special issue
of publication (good exposure)
EXERCISE 1Neutronics Solution with Fixed
Cross Sections
DESCRIPTION OF EXERCISE 1
• An equilibrium core: the reactor operational state achieved after a considerable time of operating at a specific set of conditions.
• Operating conditions are defined to be at full power and with the control rods inserted 2.0 m below the bottom of the top reflector (therefore 1.5 m alongside the pebble-bed).
• Once equilibrium is reached no significant changes can be observed in the properties of the core. For example the k-eff, power profile, temperatures and isotopic concentration distribution do no longer change.
DESCRIPTION OF EXERCISE 1
• Use the simplified cross section set with no state parameter dependence.
• No thermal-hydraulic solution required.• Report keff, power profile, 2-group flux
profile, core leakage.• calculational mesh to be determined by
each participant.
CROSS SECTIONS
• The benchmark definition provides the macroscopic cross sections required to perform the steady state.
• The cross-sections are generated making use of the isotopic distribution calculated in VSOP99.
• This approach will facilitate better and well-defined comparisons but also allow broader participation in the benchmark.
ZERO-DIMENSIONAL SET OF CROSS-SECTIONS
• There are 14 of two group (fast/thermal) parameters for each material, and
• Two single parameters for each material.• In total 30 parameters are provided for
each material set.
ZERO-DIMENSIONAL SET OF CROSS-SECTIONS
1. Diffusion Coefficient2. Macroscopic Absorption Cross-section 3. Macroscopic Nufission Cross-section 4. Macroscopic Fission Cross-section5. Macroscopic Scattering Cross-Section from group 1 to 26. Inverse velocity7. Fraction Beta(1) of delayed neutrons 8. Fraction Beta(2) of delayed neutrons9. Fraction Beta(3) of delayed neutrons 10.Fraction Beta(4) of delayed neutrons 11.Fraction Beta(5) of delayed neutrons 12.Fraction Beta(6) of delayed neutrons 13.Kappa, Energy release per fission14.Microscopic Absorption Xenon Cross-section
ZERO-DIMENSIONAL SET OF CROSS-SECTIONS
• Iodine yield• Xenon yield
CORE MODEL
• THERE ARE 190 DIFFERENT MATERIAL SETS FOR THE CORE AT EQUILIBRIUM
0 10 41 73.6 80.55 92.05 100 117 134 151 168 185 192.95 204.45 211.4 225 243.6 260.6 275 287.5 292.5-200 10 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
-150 50 133 133 133 133 155 116 113 113 113 113 113 135 164 144 144 152 152 152 189 190-100 50 133 133 133 133 155 116 113 113 113 113 113 135 164 144 144 152 152 152 189 190-50 50 133 133 133 133 155 116 112 112 112 112 112 135 164 144 144 152 152 152 189 1900 50 133 133 133 133 155 116 111 111 111 111 111 135 165 144 144 152 152 152 189 190
50 50 134 134 134 125 156 117 1 23 45 67 89 136 166 145 145 153 153 153 189 190100 50 134 134 134 125 156 117 2 24 46 68 90 136 167 145 145 153 153 153 189 190150 50 134 134 134 126 157 118 3 25 47 69 91 137 168 146 146 153 153 153 189 190200 50 134 134 134 126 157 118 4 26 48 70 92 137 169 146 146 153 153 153 189 190250 50 134 134 134 126 157 118 5 27 49 71 93 137 170 146 146 153 153 153 189 190300 50 134 134 134 127 158 119 6 28 50 72 94 138 171 147 147 153 153 153 189 190350 50 134 134 134 127 158 119 7 29 51 73 95 138 172 147 147 153 153 153 189 190400 50 134 134 134 127 158 119 8 30 52 74 96 138 173 147 147 153 153 153 189 190450 50 134 134 134 127 158 119 9 31 53 75 97 138 174 147 147 153 153 153 189 190500 50 134 134 134 128 159 120 10 32 54 76 98 139 175 148 148 153 153 153 189 190550 50 134 134 134 128 159 120 11 33 55 77 99 139 176 148 148 153 153 153 189 190600 50 134 134 134 128 159 120 12 34 56 78 100 139 177 148 148 153 153 153 189 190650 50 134 134 134 128 159 120 13 35 57 79 101 139 178 148 148 153 153 153 189 190700 50 134 134 134 129 160 121 14 36 58 80 102 140 179 149 149 153 153 153 189 190750 50 134 134 134 129 160 121 15 37 59 81 103 140 180 149 149 153 153 153 189 190800 50 134 134 134 129 160 121 16 38 60 82 104 140 181 149 149 153 153 153 189 190850 50 134 134 134 129 160 121 17 39 61 83 105 140 182 149 149 153 153 153 189 190900 50 134 134 134 130 161 122 18 40 62 84 106 141 183 150 150 153 153 153 189 190950 50 134 134 134 130 161 122 19 41 63 85 107 141 184 150 150 153 153 153 189 190
1000 50 134 134 134 130 161 122 20 42 64 86 108 141 185 150 150 153 153 153 189 1901050 50 134 134 134 131 162 123 21 43 65 87 109 142 186 151 151 153 153 153 189 1901100 50 134 134 134 131 162 123 22 44 66 88 110 142 187 151 151 153 153 153 189 1901150 50 132 132 132 132 163 124 114 114 114 114 114 143 188 151 151 154 154 154 189 1901200 50 132 132 132 132 163 124 115 115 115 115 115 143 188 151 151 154 154 154 189 1901250 50 132 132 132 132 163 124 115 115 115 115 115 143 188 151 151 154 154 154 189 190
PBMR400 CORE MODEL
REQUESTED NEUTRONICS OUTPUT
a) global parameters
• k-eff• leakage from the core / fuel region and out
of the system (neutronics domain)
b) profiles (in the given mesh)
• relative power profiles (reported for the 22 axial and 5 radial meshes)
• 2-group neutron flux distribution (reported for the neutronics domain; 20 radial and 29 axial meshes)
c) local / detailed results in material / calculational mesh
• k-inf for each material / spectrum region• atomic densities• macroscopic cross sections• The 11 x 22 mesh within the neutronics
model (see Figure 5) must be used to represent all the appropriate (2-D) results.
PARTICITPANTS
ZirkusGermanyU Stuttgart-IKE12VSOP99/3South AfricaPBMR-VSOP11MGRAC (OSCAR-4)South AfricaNECSA10
WIMSUKSerco Assurance9PARCSUSAPurdue University8NEMU.S.APSU-INL7TINTERSAPBMR-TINTE6TOPSRepublic of KoreaKAIST5
MASTERKOREAKAERI4rz 2D FDMKOREAKAERI3
EVENTNetherlands, USADelft-University, Georgia Tech
2
3D Diffusion (R-Z mode)NetherlandsDelft-University1
Codes usedCountryORGANIZATION'S NAME
#
K-EFFECTIVE
0.99
0.992
0.994
0.996
0.998
1
1.002
1.004
1.006
3D D
iffusio
n(R-Z m
ode)
EVENTrz
2D FD
MMASTER
TOPS
TINTE
NEMPARCS
WIMS
MGRAC (OSCAR-4)
VSOP99/3
(REF)
Zirkus
VSOP99/3 (REF)= AVERAGE =0.99999
K-EFFECTIVE
• The reference value was 0.9999.• The average k-effective value was
1.000097.• EVENT predicted the lowest (0.9952898) • 3-D Diffusion code predicted the highest
(1.0041758).
POWER DISTRIBUTION
• The power distribution reported by participants was in 2-D maps
• This data was reduced by radiallyaveraging for axial power distribution and axially averaging for radial distribution.
• The reduced results are presented below
MAXIMUM POWER DENSITY(W/CM3)
9
9.5
10
10.5
11
11.5
12
12.5
3D D
iffusio
n(R-Z
mod
e)EVENT
rz 2D
FDMMASTE
R
TOPS
TINTE
NEMPARCS
WIMS
MGRAC (OSCAR-4)
VSOP99/3
(REF)
Zirku
s
MA
XIM
UM
PO
WER
DEN
SIT
Y(W
/CM
3)
VSOP (REF)= 10.55W/CM3
AVERAGE= 10.78W/CM3
AXIAL POWER PROFILE
0
1
2
3
4
5
6
7
8
9
10
0 200 400 600 800 1000 1200
AXIAL POSITION(CM)
PO
WE
R D
ENS
ITY(
W/C
M3)
DELFT-DIFFUSION DELFT-EVENT KAERI-FD KAERI-MASTERKAIST PBMR-TINTE PSU-INL PURDUESERCOASSURANCE PBMR-VSOP IKE NECSA
RADIAL POWER PROFILE
0
1
2
3
4
5
6
100 110 120 130 140 150 160 170 180 190 200
RADIAL POSITION(CM)
PO
WE
R D
ENS
ITY(
W/C
M3)
DELFT-DIFFUSION DELFT-EVENT KAERI-FD KAERI-MASTERKAIST PBMR-TINTE PSU-INL PURDUESERCOASSURANCE PBMR-VSOP IKE NECSA
FLUX DISTRIBUTIONS
• The flux distribution reported by participants was in 2-D maps.
• This data was reduced by radial-averaging for axial flux distributions and axial-averaging for radial flux distributions.
• The reduced results are presented below
Max Fast Flux
1.85E+14
1.9E+14
1.95E+14
2E+14
2.05E+14
2.1E+14
2.15E+14
2.2E+14
2.25E+14
3D Diffu
sion(R
-Z mod
e)
EVENTrz
2D FD
MMASTE
R
TOPS
TINTE NEM
PARCS
WIMS
MGRAC (OSCAR-4)
VSOP99/3
(REF)
Zirku
s
AVERAGE = 2.08E14
AXIAL FAST FLUX PROFILE
0
1E+13
2E+13
3E+13
4E+13
5E+13
6E+13
7E+13
-200 0 200 400 600 800 1000 1200
AXIAL DISTANCE
FLU
X
DELFT-DIFFUSION DELFT-EVENT KAERI-FD KAERI_MASTERKAIST PBMR-TINTE PSU-INL PURDUESERCOASSURANCE PBMR-VSOP IKE NECSA
RADIAL FAST FLUX
0
1E+13
2E+13
3E+13
4E+13
5E+13
6E+13
7E+13
8E+13
9E+13
0 50 100 150 200 250 300
RADIAL DISTANCE
FLU
X
DELFT-DIFFUSION DELFT-EVENT KAERI-FD KAERI_MASTERKAIST PBMR-TINTE PSU-INL PURDUESERCOASSURANCE IKE PBMR-VSOP NECSA
Max Thermal Flux
0
5E+13
1E+14
1.5E+14
2E+14
2.5E+14
3E+14
3.5E+14
3D Diffu
sion(R
-Z mod
e)
EVENTrz
2D FD
MMASTE
R
TOPS
TINTE
NEM
PARCS
WIMS
MGRAC (OSCAR-4)
VSOP99/3
(REF)
Zirku
s
AVERAGE = 3.12E14
AXIAL THERMAL FLUX
0
2E+13
4E+13
6E+13
8E+13
1E+14
1.2E+14
1.4E+14
1.6E+14
1.8E+14
2E+14
-200 0 200 400 600 800 1000 1200
AXIAL DISTANCE
FLU
X
Delft-Diffusion DELFT-EVENT KAERI-FD KAERI-MASTERKAIST PBMR-TINTE PSU-INL PURDUESERCOASSURANCE PBMR-VSOP IKE NECSA
RADIAL THERMAL FLUX
0
2E+13
4E+13
6E+13
8E+13
1E+14
1.2E+14
1.4E+14
1.6E+14
0 50 100 150 200 250 300
RADIAL DISTANCE
FLU
X
DELFT-DIFFUSION DELFT-EVENT KAERI-FD KAERI-MASTERKAIST PBMR-TINTE PSU-INL PURDUESERCOASSURANCE PBMR-VSOP IKE NECSA
DISCUSSION
• The 1-Dimensional averaging smoothens the differences in the results obtained by different participants.
• Hence there was agreement in the axial and the radial power distributions.
• More differences were observed when in the 2-D power distribution comparisons of the results
DISCUSSION
• Although reasonable agreement is observed among the averaged flux distributions, EVENT tended to have higher flux than other participants.
• This could be demonstrated by the comparison of the maximum flux values in the 2-D maps
DISCUSSION
• There were some reported cases of difficulties in the modeling of the core barrel.
CONCLUSION
• It can be concluded that there was a fair agreement in the modeling of the PBMR by the participating codes in this exercise.
• The difference in the actual neutronicparameters could be attributed to the different methods used by the codes since the same set of cross sections was used.