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22nd Symposium of AER on VVER Reactor Physics and Reactor Safety
Pruhonice, Czech Republic, October 1-5, 2012
BENCHMARKING OF COBAYA3 PIN-BY-PIN FOR VVER
N. Zheleva, J.J.Herrero*, G.Todorova, P.Ivanov, N.Kolev
Institute for Nuclear Research and Nuclear Energy, 1784 Sofia,
Bulgaria
[email protected]
*Universidad Politecnica de Madrid [email protected]
ABSTRACT
This paper presents results of the benchmarking of COBAYA3
pin-by-pin for VVER-1000 obtained in the frame of the EU NURISP
project. The 3D lattice solver in COBAYA3 uses transport corrected
multi-group diffusion approximation with side-dependent interface
discontinuity factors of GET or Selengut Black Box type. The
objective of this study is to test the few-group calculation scheme
when using structured and unstructured spatial meshes. Unstructured
mesh is necessary to model the water gaps between the hexagonal
assemblies. The benchmark problems include pin-by-pin calculations
of 2D subsets of the core and comparison with APOLLO2 and TRIPOLI4
transport reference solutions. COBAYA3 solutions in 2, 4 and 8
energy groups have been tested. The results show excellent
agreement with the reference ones when using side-dependent
interface discontinuity factors.
1. INTRODUCTION COBAYA3 [1]-[7] is a 3D core simulator code for
Cartesian and hexagonal geometry, developed by UPM. It includes a
nodal solver based on the ACMFD method [1], [5] and a pin-by-pin
solver using the fine-mesh finite-difference (FMFD) method. [2],
[3], [7]. The current pin-by-pin version [2], [7] solves the
time-dependent multi-group diffusion equation corrected by
interface discontinuity factors. A nodal acceleration can be used
to speed up the full core pin-by-pin solution process.
In the frame of the EU NURESIM [8] and NURISP [9] projects, it
has evolved to include capabilities of using multi-parameter
cross-section (XS) libraries and interface discontinuity factors
(IDF) in table-interpolation and functional-fitting format. The
code has been coupled with core thermal-hydraulics [3], [4], [5],
[6] for reactor safety analysis. Neighborhood-dependent IDF [10] of
GET [11] and Selengut Black Box homogenization (BBH) [12] type can
be applied. Parallelized coupled pin-by-pin calculations [3], [4],
[6] using alternate dissections have been implemented in Cartesian
geometry.
The numerical validation base at the pin level includes a series
of computational benchmarks for PWR [13], [14], [15], VVER [16] and
BWR [17]. This work presents COBAYA3 calculations of the NURISP
VVER lattice benchmark [16] performed by INRNE and UPM. The aim is
to test the pin-by-pin solver for homogenized cells in structured
and unstructured meshes. A specific objective is to test the
APOLLO2.8 [18] generated pin-by-pin XS and IDF, and to assess the
impact of the number of broad energy groups.
1
mailto:[email protected]:[email protected]
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In this paper, the benchmark problems are described in Section
2. The utilized pin-by-pin XS calculation schemes [16] are based on
the Method of Characteristics (MOC) in APOLLO2 and are summarized
in Section 3. Results and conclusions are given in Sections 4 and 5
respectively.
2. TEST PROBLEMS
The considered geometries are 2D subsets of a VVER-1000 core
(19-pin clusters, fuel assembly and assembly cluster), as
illustrated in Figures 1 and 2.
Figure 1: UOX-GT 19-pin cluster
Figure 2:
a) UOX assembly of 4.23 w/o av. enrichment (246 pins of 4.4w/o
and 66 pins of 3.6w/o) b) 7-assembly UOX-CR /UOX-GT cluster of
4.23w/o with UOX-CR in the center
2
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The NURISP VVER lattice benchmark [16] includes test problems
for core simulators in structured and unstructured meshes. The
structured mesh cases are 19-pin clusters as used for branch
calculations with APOLLO2 to generate multi-parameter pin-by-pin
libraries of neighborhood-dependent XS and IDF. The unstructured
mesh problems consist of fuel assemblies and assembly clusters with
inter-assembly water gaps.
In this study, results for the following test cases are
considered:
19-pin clusters - UOX-GT: guide tube surrounded by two rings of
UOX pins (Figure 1)
- UOX-CT: central tube surrounded by UOX pins
- UOX-CR: control rod surrounded by UOX pins
Fuel assemblies - UOX-GT: uncontrolled assembly
- UOX-CR: controlled assembly
7-assembly cluster of a central UOX-CR assembly and 6 peripheral
UOX-GT assemblies (forming a color set as shown in Figure 2).
The 19-pin clusters are to be calculated for fixed state
parameters: 39.8MWd/kgHM, HZP at 574.15K, Dm=740kg/m3, Cb
=53ppm.
The UOX-CR assembly is to be calculated for five states listed
in Table 1, as usually done for calculation of the reactivity
effects.
Table 1: Assembly thermal-hydraulic states to be calculated
Moderator Fuel Cladding Conditions Temp,K Density g/cm3 Temp,
K
Densityg/cm3
Temp, K
Density g/cm3
CB ppm
S1: HZP state (ref) 552 0.76665 552 Ref 552 ref 600 S2: Fuel
Doppler react 552 0.76665 924 Ref 552 ref 600 S3: Coolant
reactivity 574 0.72527 552 Ref 552 ref 600 S4: 100% void 624
0.09610 552 Ref 552 ref 600 S5: Boron reactivity 552 0.76665 552
Ref 552 ref 0
The 7-assembly cluster is of fresh fuel and is to be calculated
for fixed state parameters: HZP at 574.15K, Dm=740 kg/m3 and Cb
=53ppm.
The task is to calculate the multiplication factor and the
pin-by-pin fission reaction rates in comparison with transport
reference solutions:
- APOLLO2 MOC 281g /JEFF3.1.1 solutions [16] validated against
TRIPOLI4 results - Well converged TRIPOLI4 /JEFF3.1.1 solutions
[16] with σ (k) = ± 10-14 pcm
TRIPOLI4 [19] is a 3D Monte Carlo code, trademark of CEA.
3
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The results presented here have been obtained with reflection
boundary conditions on the external boundaries and zero buckling.
Benchmarking of COBAYA3 pin-by-pin with XS and IDF from
multi-parameter libraries obtained through pin-cluster branch
calculations with critical buckling is subject of a separate
analysis.
3. CROSS-SECTIONS AND INTERFACE DF Accurate MOC based
calculation schemes [16] with APOLLO2, validated against Monte
Carlo solutions have been used to generate the pin-by-pin XS and
IDF in 2, 4 and 8 energy groups for COBAYA3. Table 2 shows the
adopted energy group structure.
Table 2: Broad energy group structure
2 group structure 4 group structure 8 group structure Lower
energy cut off (eV) 1 2.2313E+06 2 8.2085E+05 1 3 9.1188E+03 4
1.3007E+02
2 5 3.9279E+00
1
3 6 6.2506E-01 7 1.4572E-01
2 4 8 0.0000E+00
The pin-by-pin XS and IDF for the considered states are
cell-position dependent and have been obtained with the
CEA2005V4.1.2 library based on JEFF3.1.1, making use of the
following modeling assumptions in APOLLO2:
19-pin clusters - Reference two-step 281g Pij-MOC calculation
scheme in APOLLO2 with SHEM
[20] energy mesh - Step MOC (UOX-GT, UOX-CT) or higher-order
Linear Surface (LS) MOC [21]
(UOX-CR) - Fine MOC spatial mesh with 4 rings in the fuel,
smeared gap-cladding, 3 radial
meshes in the moderator, 12 azimuth sectors [16] - Simplified LS
MOC spatial mesh with 4 rings in the fuel, smeared gap-cladding,
one
‘ring’ in the moderator and no azimuth sectors - MOC parameters:
tracking step dr=0.008cm, number of azimuth angles Nφ=48,
number of polar angles Nψ=3, Bickley quadrature, P3 scattering
anisotropy; LS MOC surface subdivision factor Ndiv=6, threshold
size 0.74 cm
Fuel assembly - Reference two-step 281g Pij-MOC calculation
scheme in APOLLO2 with SHEM
energy mesh - Step MOC solver - MOC spatial mesh with 2 rings in
the fuel, smeared gap-cladding, 6 azimuth sectors
only in CR and peripheral cells, 2566 regions in a whole
assembly - MOC parameters: dr=0.001 cm, Nφ =36, Nψ =3, Bickley,
P0*
4
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Assembly cluster
- Reference two-step 281g Pij-MOC calculation scheme in APOLLO2
with SHEM energy mesh
- LS MOC solver - LS MOC spatial mesh with 2 rings in the fuel,
smeared gap-cladding, one ‘ring’ and
no azimuth sectors in the moderator except for CR cells where 6
azimuth sectors are used; 1070 regions in 1/6 color set
- LS MOC parameters: dr = 0.008, Nφ = 36, Nψ = 2, P1; Ndiv= 6,
threshold 0.74 cm
The same nuclear data and calculation parameters have been used
to obtain the APOLLO2 deterministic reference solutions [16] for
the considered cases.
4. RESULTS
4.1 19-pin clusters
This configuration allows the use of structured spatial mesh in
COBAYA3. Table 3 summarizes the comparison of COBAYA3 vs. APOLLO2
computed multiplication factors and normalized pin-by-pin fission
reaction rates (FRR). The results show that the impact of the
number of broad energy groups is small compared to that of the
transport correction of homogenization errors. Table 4 shows a
comparison with TRIPOLI4 reference solutions.
Table 3: Biases of COBAYA3 vs. APOLLO2 reference results
UOX-GT UOX-CR Code
k-inf Δk(C3-A2) pcm maxΔFRR (C3-A2)*100 k-inf
Δk(C3-A2) pcm
maxΔFRR (C3-A2)*100
APOLLO2 ref 0.96217 0.61971 C3 2g, no IDF 0.96302 +85 0.22
0.61367 -604 0.11 C3 4g, no IDF 0.96230 +14 0.19 0.60688 -1283 0.06
C3 8g, no IDF 0.96199 -17 0.22 0.60745 -1227 0.11 C3 2g, GET
0.96214 -2 0.02 0.61972 +0.3 0.02 C3 4g, GET 0.96214 -2 0.02
0.61971 -0.2 0.02 C3 8g, GET 0.96214 -2 0.02 0.61971 -0.2 0.02
Table 4: Multiplication factors and biases to TRIPOLI4 reference
solution
UOX-GT UOX-CR Code k-inf Δk, pcm k-inf Δk, pcm
TRIPOLI4 ref 0.96253 ± 11E-5 - 0.61981± 11E-5 - APOLLO2 LS MOC
281g 0.96216 -37 0.61971 -10 COBAYA3 8g, GET IDF 0.96214 -39
0.61971 -10
Table 5 presents the computed pin fission rates for 1/6 19-pin
clusters at 39.8 MWd/kgH. The COBAYA3 results show a perfect
reproduction of the APOLLO2 reference solutions when using side-
and cell position dependent GET IDF. The solutions with IDF are
nearly the same in 2, 4 and 8 energy groups.
5
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Table 5: COBAYA3 2g vs. APOLLO2 ref solutions for 1/6 pin
clusters at 39.8MWd/kgH
UOX-CT UOX-GT UOX-CR Cell N C3 FRR ΔFRR, % C3 FRR ΔFRR, % C3 FRR
ΔFRR, %
1 0.991 0.00 0.993 -0.01 1.018 0.02 2 0.992 -0.01 0.994 0.01
1.014 -0.01 3 1.013 0.00 1.010 0.00 0.976 -0.01 4 0.991 0.00 0.993
-0.01 1.018 0.00 5 1.013 0.00 1.010 0.00 0.975 0.00
Figures 3 - 5 illustrate the biases of COBAYA3 to APOLLO2 and
TRIPOLI4 computed pin- by-pin fission rate distributions.
Comparison C3 versus A2-04
0 0,015 2
GT 0 -0,016 3 1
Dev Kinf (A2), pcm 1Max dev FRR, % 0,0108Average dev FRR, %
0,01Kinf A2 Kinf C3
0,962670,96268
Comparison C3 versus T4-0,1
40,1 05 2
GT 0,1 -0,16 3 1
Dev Kinf (T4), pcm 15Max dev FRR, % 0,08Average dev FRR, %
0,05Kinf T4Kinf C3
0,962530,96268
Figure 3: Biases of COBAYA 8g GET to APOLLO2 MOC and TRIPOLI4
ref results
for 19-pin UOX-GT cluster
Comparison C3 versus A20,00
40,00 -0,01
5 2CT 0,00 0,00
6 3 1
Dev Kinf (A2), pcm 1Max dev FRR, % 0,0075Average dev FRR, %
0,00Kinf A2 Kinf C3
0,986680,98668
Comparison C3 versus T4-0,01
40,01 0,02
5 2CT 0,03 -0,05
6 3 1
Dev Kinf (T4), pcm 20Max dev FRR, % 0,0461Average dev FRR, %
0,0234Kinf T4Kinf C3
0,986480,98668
Figure 4: Biases of COBAYA 8g GET to APOLLO2 MOC and TRIPOLI4
ref results
for 19-pin UOX-CT cluster
6
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Comparison C3 versus A2 Comparison C3 versus T40,00 -0,04
4 40,00 -0,01 0,25 -0,43
5 2 5 2CR -0,01 0,02 CR 0,30 -0,08
6 3 1 6 3
Dev Kinf (A2), pcm 0,3 Dev Kinf (T4), pcm -9Max dev FRR, % 0,02
Max dev FRR, % 0,43Average dev FRR, % 0,01 Average dev FRR, %
0,22Kinf A2 Kinf T40,61971 0,61981
1
Figure 5: Biases of COBAYA 8g GET to APOLLO2 LS MOC and TRIPOLI4
ref results
for 19-pin UOX-CR cluster
4.2 Fuel assembly A profiled VVER-1000 assembly of 4.23w/o
average initial enrichment is considered: a) UOX-CR assembly at
39.8 MWd/kgHM b) UOX-GT assembly at zero burn-up In order to model
the peripheral water gap, unstructured spatial mesh must be used.
Table 6 summarizes the comparison of COBAYA3 vs. APOLLO2 solutions
for UOX-CR assembly when using GET discontinuity factors for the
interior cells and the irregular peripheral cells.
Table 6: COBAYA3 vs. APOLLO2 results for UOX-CR assembly at
39.8MWd/kgHM
State Code k-inf Δk (C3-A2), pcm max ΔFRR*100
S1 A2 MOC 281g P0* 0,73812 - - COBAYA3 2g GET 0,73827 15 0,27
COBAYA3 4g GET 0,73820 7 0,37 COBAYA3 8g GET 0,73820 8 0,34 S2 A2
MOC 281g P0* 0,73010 - - COBAYA3 2g GET 0,73024 14 0,27 COBAYA3 4g
GET 0,73017 7 0,32 COBAYA3 8g GET 0,73017 7 0,35 S3 A2 MOC 281g P0*
0,73062 - - COBAYA3 2g GET 0,73075 13 0,26 COBAYA3 4g GET 0,73067 5
0,33 COBAYA3 8g GET 0,73067 5 0,33 S4 A2 MOC 281g P0* 0,42612 - -
COBAYA3 2g GET 0,42612 0 0,03 COBAYA3 4g GET 0,42611 -1 0,03
COBAYA3 8g GET 0,42611 -1 0,04 S5 A2 MOC 281g P0* 0,77432 - -
COBAYA3 2g GET 0,77441 9 0,31 COBAYA3 4g GET 0,77433 1 0,36 COBAYA3
8g GET 0,77433 1 0,38
7
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Good performance of the COBAYA3 pin-by-pin solver across the
mesh irregularities is displayed. The results show that:
- the biases of the inside assembly pins are very low, similar
to those for structured mesh - the average absolute bias is below
0.05 % - a single corner pin #1 shows bias of app. 0.3%
Figure 6 illustrates the COBAYA3 2g computed pin-by-pin fission
rate distribution for irradiated UOX-CR assembly in State 1 and the
biases to APOLLO2 ref solution, if no discontinuity factors are
used. The bias in k-infinity is - 973 pcm. The maximum bias in pin
fission rates is -1.70 (expressed as ΔFRR*100) for pin #40 near a
CR, or -1.82 % for pin #15 (with relative FRR of 0.928) next to a
CR.
Figure 7 shows the COBAYA3 2g GET computed pin-by-pin fission
rate distribution for the same UOX-CR assembly in State 1 and the
biases to APOLLO2 ref solution.
Figure 8 shows the COBAYA3 8g BBH computed pin-by-pin fission
rate distribution for a fresh UOX-GT assembly in State 1 and the
biases to APOLLO2 ref solution.
2 energy groups, no DF
1,1931,1860,69
46
1,220 1,1641,212 1,1550,81 0,82
47 37
Max FRR deviation 1,70 1,120 1,188 1,143Average FRR deviation
0,83 1,123 1,182 1,134Delta K inf, pcm -973 -0,34 0,66 0,86
48 38 29
1,022 1,086 1,166 1,1311,037 1,091 1,160 1,122-1,55 -0,51 0,60
0,89
49 39 30 22
0,862 0,982 1,058 1,153 1,1260,874 0,999 1,067 1,148 1,117-1,29
-1,70 -0,89 0,51 0,87
50 40 31 23 16
0,772 0,829 0,917 1,046 1,154 1,1310,771 0,837 0,933 1,058 1,148
1,1220,13 -0,84 -1,59 -1,21 0,52 0,88
51 41 32 24 17 11
0,735 0,758 0,000 0,917 1,059 1,166 1,1430,729 0,753 0,000 0,934
1,068 1,160 1,1340,59 0,50 0,00 -1,61 -0,90 0,60 0,86
52 42 33 25 18 12 7
0,000 0,737 0,764 0,832 0,983 1,086 1,188 1,1640,000 0,732 0,759
0,840 1,000 1,092 1,182 1,1550,00 0,53 0,52 -0,85 -1,69 -0,51 0,67
0,84
53 43 34 26 19 13 8 4
0,755 0,733 0,778 0,780 0,864 1,023 1,120 1,221 1,1930,745 0,726
0,775 0,779 0,877 1,038 1,124 1,212 1,1870,97 0,70 0,24 0,12 -1,33
-1,57 -0,35 0,81 0,69
54 44 35 27 20 14 9 5 2
0,833 0,744 0,732 0,750 0,000 0,911 1,075 1,161 1,135 1,1970,820
0,735 0,726 0,744 0,000 0,928 1,086 1,159 1,127 1,195
0,00 1,27 0,84 0,68 0,61 0,00 -1,69 -1,16 0,14 0,88 0,2656 55 45
36 28 21 15 10 6 3 1
FRR devN
C3 FRRA2 FRR
Figure 6: Pin-by-pin fission rates and biases (C3 2g no DF -
A2ref)*100 for UOX-CR assembly at 39.8 MWd/kgHM, in State 1: HZP at
552K
8
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2 energy groups, GET DF
C3 FRR 1.186A2 FRR 1.186FRR dev -0.05
N 461.212 1.1561.212 1.155-0.01 0.03
47 37Max FRR deviation 0.27 1.123 1.182 1.135Average FRR
deviation 0.03 1.123 1.182 1.134Delta K inf, pcm 15 -0.02 0.02
0.07
48 38 291.038 1.091 1.160 1.1231.037 1.091 1.160 1.1220.00 0.01
0.03 0.09
49 39 30 220.874 0.999 1.067 1.149 1.1190.874 0.999 1.067 1.148
1.1170.00 0.00 0.03 0.04 0.11
50 40 31 23 16
0.771 0.837 0.933 1.058 1.149 1.1230.771 0.837 0.933 1.058 1.148
1.122-0.02 0.00 -0.02 0.03 0.04 0.11
51 41 32 24 17 110.729 0.753 0.000 0.934 1.068 1.161 1.1350.729
0.753 0.000 0.934 1.068 1.160 1.134-0.03 -0.02 0.00 0.00 0.01 0.05
0.10
52 42 33 25 18 12 70.000 0.731 0.759 0.840 1.000 1.092 1.182
1.1560.000 0.732 0.759 0.840 1.000 1.092 1.182 1.1550.00 -0.01
-0.02 -0.01 -0.01 0.00 0.02 0.05
53 43 34 26 19 13 8 4
0.745 0.726 0.775 0.778 0.877 1.038 1.123 1.212 1.1860.745 0.726
0.775 0.779 0.877 1.038 1.124 1.212 1.187-0.02 -0.02 -0.01 -0.03
-0.02 -0.02 -0.01 -0.01 -0.03
54 44 35 27 20 14 9 5 20.820 0.735 0.726 0.744 0.000 0.928 1.086
1.159 1.126 1.1920.820 0.735 0.726 0.744 0.000 0.928 1.086 1.159
1.127 1.195-0.01 -0.02 -0.02 -0.01 0.00 -0.01 -0.03 -0.03 -0.06
-0.27
55 45 36 28 21 15 10 6 3 1
Figure 7: Pin-by-pin fission rates and biases (C3 2g GET -
A2ref)*100 for UOX-CR assembly at 39.8 MWd/kgHM, in State 1: HZP at
552K
9
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8 energy groups, BBH DF
0,969
0,969-0,03
46
1,026 0,9561,026 0,956-0,02 0,04
47 37
Max FRR deviation, % 0,28 0,995 1,018 0,950Average FRR
deviation, % 0,02 0,994 1,018 0,950Delta K inf, pcm 2 0,01 0,02
0,02
48 38 29
1,001 0,993 1,015 0,9481,001 0,992 1,015 0,9480,03 0,02 0,03
0,03
49 39 30 22
1,005 1,007 0,996 1,014 0,9471,005 1,006 0,996 1,014 0,9470,01
0,02 0,01 0,04 0,02
50 40 31 23 16
1,017 1,009 1,002 0,997 1,014 0,9481,018 1,009 1,002 0,997 1,013
0,9470,00 0,00 0,00 0,03 0,04 0,02
51 41 32 24 17 11
1,025 1,019 0,000 1,001 0,996 1,015 0,9511,025 1,019 0,000 1,001
0,996 1,015 0,950-0,01 0,00 0,00 0,00 0,02 0,02 0,04
52 42 33 25 18 12 7
0,000 1,023 1,018 1,009 1,006 0,992 1,018 0,9560,000 1,024 1,019
1,009 1,006 0,992 1,018 0,9560,00 -0,03 -0,02 -0,01 0,01 0,03 0,03
0,02
53 43 34 26 19 13 8 4
1,038 1,029 1,031 1,014 1,004 1,000 0,995 1,026 0,9691,038 1,029
1,031 1,014 1,004 1,000 0,994 1,026 0,9690,00 -0,03 -0,01 0,00 0,01
0,00 0,01 0,00 -0,04
54 44 35 27 20 14 9 5 2
1,048 1,037 1,029 1,019 0,000 0,998 1,000 1,004 0,939 0,9631,048
1,037 1,030 1,020 0,000 0,998 1,000 1,004 0,939 0,965-0,02 0,00
-0,04 -0,02 0,00 0,00 0,02 0,01 -0,05 -0,28
55 45 36 28 21 15 10 6 3 1
C3 FRRA2 FRRFRR dev
N
Figure 8: Pin-by-pin fission rates and biases (C3 8g BBH -
A2ref)*100 for a fresh UOX-GT assembly in State 1: HZP at 552K
10
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4.3 Color set results
The hexagonal color set consists of a central UOX-CR assembly
and 6 halves of peripheral UOX-GT assemblies with 4.23 w/o average
enrichment. This is a challenging test problem characterized by
radial variation of the enrichment and steep thermal flux gradients
near the CR as well as in the water holes (GT, CT) and the
inter-assembly water gaps. The modeling of inter-assembly water
gaps requires the use of unstructured spatial mesh. Table 7 shows
the biases of COBAYA pin-by-pin to APOLLO2 LS MOC 281g results when
using GET discontinuity factors for the interior cells and the
irregular inter-assembly cells. Good agreement with the reference
results is displayed. Figure 9 illustrates the deviations of
COBAYA3 2g to the reference pin fission rates in 1/6 of the central
UOX-CR assembly normalized over the whole color set.
Table 7: Summary of COBAYA3 vs. APOLLO2 LS MOC results with 60o
rot. symmetry
APOLLO2 COBAYA3 2g GET Δk(C3-A2), pcm max ΔFRR*100 max
ΔFRR*100
Central UOX-CR FA
Peripheral UOX-GT 1.30908 1.30892 -16 1.02 1.24
0,8846
1,02 0,9547 37
0,95 0,99 0,9448 38 29
0,86 0,87 0,92 0,9249 39 30 22
0,69 0,72 0,76 0,85 0,8650 40 31 23 16
0,56 0,54 0,55 0,63 0,74 0,7751 41 32 24 17 11
0,53 0,39 0,00 0,45 0,53 0,63 0,6652 42 33 25 18 12 7
0,00 0,15 0,25 0,32 0,33 0,39 0,50 0,5453 43 34 26 19 13 8 4
0,53 -0,34 -0,12 0,52 0,24 0,18 0,27 0,36 0,4454 44 35 27 20 14
9 5 2
0,00 0,45 -0,28 -0,48 0,14 0,00 0,27 0,53 0,78 0,68 0,3056 55 45
36 28 21 15 10 6 3 1
Figure 9: Central UOX-CR assembly of the color set: Biases
(COBAYA3-APOLLO2)*100 in normalized pin fission reaction rates
11
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5. SUMMARY AND CONCLUSIONS
The results show that:
COBAYA3 pin-by-pin successfully performs unstructured mesh
calculations with Interface DF
The transport-corrected diffusion theory solutions for 2D
sub-sets of the core with neighborhood-dependent XS and DF are very
close to the reference results
The impact of the number of broad energy groups is small
compared to that of the transport correction of homogenization
errors
COBAYA3 pin-by-pin is an accurate and computationally efficient
core simulator for hexagonal geometry
The analyzed benchmark solutions prove that the use of
side-dependent interface discontinuity factors allows achieving the
target pin-by-pin fidelity for safety analysis.
ACKNOWLEDGEMENTS
This work is partially funded by the NURISP project (Contract n°
232124) in the 7th Euratom Framework Program of the European
Union.
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