High Fidelity Neutronics Model for Lead-cooled Fast Reactor (LFR)
Contact: Hansol Park, [email protected]
Model link: LFR Single Assembly Griffin Model
This VTB model provides a high fidelity neutronics model for a representative example of a lead-cooled fast reactor with an annular MOX (UPuO) fuel. Its design is based on an early iteration of an LFR-prototype assembly provided by Westinghouse Electric Company, LLC (Grasso et al., 2019). The original purpose of this model is to characterize the impact of various sources of uncertainties, such as theoretical and experimental uncertainties, instrumentation uncertainties, manufacturing tolerances, correlation uncertainties, and the method and simulation uncertainties, on peak cladding, fuel and coolant temperatures in the system. For this purpose, high fidelity neutronics (fine mesh heterogeneous transport - Griffin) and thermalhydraulics (computational fluid dynamics - NekRS) calculations were performed to compute hot channel factors (HCFs) (Shemon et al., 2021). A 3D heterogeneous single assembly steady-state problem was used since a full core model is seldom used for the HCF evaluation. In this VTB model, only the neutronics standlone model is explained.
First, the LFR model is described, followed by the cross section generation procedure using MC2-3 (Lee et al., 2018). Then, the Griffin standalone calculation setting with the discontinuous finite element method (DFEM) discrete ordinate (SN) scheme with the Coarse Mesh Finite Difference (CMFD) acceleration is explained and the results are discussed.
Description of LFR design
The key parameters of the LFR design are listed in Table 1. The power output is 950 MWth (~450 MWe) for the whole core and the nominal power of an inner core fuel assembly is 3.7 MWth. The fuel assembly pitch is 16.3 cm with a 4 mm lead-filled gap between assemblies and 3.5 cm thick duct wall as shown on the right in Figure 1. Each assembly contains 127 cladded fuel pins arranged in a triangular lattice with pitch 1.33 cm within a hexagonal wrapper (duct). Each fuel pin has a cold fuel inner/outer diameter of 4.00/8.55 mm respectively, a fuel-cladding gap of 0.175 mm and a cladding outer diameter of 10.7 mm with a cladding thickness of 0.90 mm, depicted in Figure 2. The center hole and gap are filled with helium. To minimize the flow speed and consequently mitigate corrosion issues, a relatively wide lattice (P/D=1.24) design is adopted. Grid spacers are planned to maintain pin spacing, rather than the wire wrap used in conventional SFR designs.
The active fuel region in the middle is located between upper and lower thermal insulators, gas plenum, bundle grid and pins plug, and inlet and outlet wrappers. Bundle grid and pins plug, inlet and outlet wrappers, and lower core plate are radially homogenized while radially heterogeneous fine-meshes were used in the other five axial regions. The annular fuel shape in Figure 2 is explicitly modeled for the active fuel region and materials inside the cladding are radially homogenized for the four axial regions of thermal insulators and gas plenum.
Table 1: Key parameters of Lead-Cooled Fast Reactor (LFR) model
| Parameter | Value | Unit |
|---|---|---|
| Thermal power | ||
| Active core height | ||
| Number of fuel pins per assembly | ||
| Gap thickness | ||
| Duct thickness | ||
| Fuel pin diameter | ||
| Fuel pin pitch | ||
| P/D | ||
| Cladding thickness | ||
| Fuel pellet outer diameter | ||
| Fuel pellet inner diameter | ||
| Reynolds number | ||
| Prandtl number | ||
| Peclet number |
Figure 1: Axial and radial geometry of the LFR single assembly model
Figure 2: LFR annular fuel pin geometry
Cross Section Generation using MC2-3
It is worth explaining the procedure to generate cross sections using MC2-3 for this model. MC2-3 is the cross section generation module in Griffin. The axial leakage effect needs to be considered using the MC2-3/TWODANT two-step procedure for the generation of both homogeneous cross sections for non-fuel axial regions and heterogeneous region-wise cross sections for the fuel axial region. At this point of time, the MC2-3/TWODANT procedure is not fully available in Griffin due to a licensing issue with TWODANT. Thus, MC2-3 was used externally, not via Griffin, in this work. Once the feature is available in Griffin, the description below will be updated.
First step
The first step is to generate a 1041-group rzmflx, which is the flux solution file of a TWODANT (Alcouffe et al., 1984) SN calculation. It contains zone-wise Legendre moments of the angular flux solution up to a specified order. In this problem, a pseudo one-dimensional (1D) slab problem is solved using TWODANT by assigning the reflective boundary condition on the left and right boundaries in the x-y geometry. TWODANT is called inside MC2-3 when its executable path is specified by the c_twodantexe input parameter in the library block of an MC2-3 input with l_twodant=T. If TWODANT is not available, PARTISN (Alcouffe et al., 2009) can be used alternatively since it creates a rzmflx file. c_twodant_group=BG means that the TWODANT transport calculation is performed using a group structure specified in c_group_structure. c_geometry_type=mixture means that homogeneous materials cooresponding to axial regions are used to generate macroscopic cross sections (in the 1041-group structure in this example) to be used in the TWODANT transport calculation.
&library
c_mcclibdir ="$lib/lib.mcc.new"
c_pwlibdir ="$lib/lib.pw.200.new","."
c_twodantexe ="/software/MCC3/twodant.x"
/
&control
c_group_structure =ANL1041
i_number_region =10
c_geometry_type =mixture
i_scattering_order =3
l_twodant =T
c_twodant_group =BG
/
&output
l_edit_flux = T
/
Volume-homogenized compositions representing different axial regions are specified in the material block. In each composition, a list of isotopes needs to be specified. Each line for an isotope should have four entries: an MC2-ID such as FE54_7, a user-defined name to be included in the ISOTXS file, for example, FE54_IG, an atomic number density (#/cm barn), and a temperature in Kelvin. (In this step, temperature does not need to be very accurate.) The full list of MC2-IDs is available in (Lee et al., 2018). For the user-defined name, _IG is, for example, a suffix to indicate the name of the axial zone for the upper thermal insulator and differentiate the same isotope in different regions. In this first step, since the resulting ISOTXS file is only used for the TWODANT calculation, any suffix is allowed as long as the same isotope in different compositions can be differentiated by its name. This is needed because cross sections of all isotopes are contained in a single ISOTXS file where composition IDs are not present. This suffix needs to be set carefully in the second step as explained later.
&material
t_composition(:, 1)=
! IA=Lower Core Plate (AISI 316, DS4-Wrapper, Pb)
FE54_7 FE54_IA 2.3571E-03 600.0
FE56_7 FE56_IA 3.7002E-02 600.0
FE57_7 FE57_IA 8.5453E-04 600.0
FE58_7 FE58_IA 1.1372E-04 600.0
NI58_7 NI58_IA 4.9645E-03 600.0
NI60_7 NI60_IA 1.9123E-03 600.0
NI61_7 NI61_IA 8.3135E-05 600.0
NI62_7 NI62_IA 2.6501E-04 600.0
NI64_7 NI64_IA 6.7529E-05 600.0
CR50_7 CR50_IA 4.6700E-04 600.0
CR52_7 CR52_IA 9.0056E-03 600.0
CR53_7 CR53_IA 1.0212E-03 600.0
CR54_7 CR54_IA 2.5419E-04 600.0
MN55_7 MN55_IA 6.8040E-04 600.0
MO92_7 MO92_IA 1.2088E-04 600.0
MO94_7 MO94_IA 7.5345E-05 600.0
MO95_7 MO95_IA 1.2968E-04 600.0
MO96_7 MO96_IA 1.3587E-04 600.0
MO97_7 MO97_IA 7.7789E-05 600.0
MO98_7 MO98_IA 1.9655E-04 600.0
MO1007 MO100IA 7.8441E-05 600.0
SI28_7 SI28_IA 6.3469E-04 600.0
SI29_7 SI29_IA 3.2228E-05 600.0
SI30_7 SI30_IA 2.1245E-05 600.0
C____7 C____IA 1.4140E-04 600.0
P31__7 P31__IA 2.9631E-05 600.0
S32__7 S32__IA 1.5017E-05 600.0
S33__7 S33__IA 1.2022E-07 600.0
S34__7 S34__IA 6.7864E-07 600.0
S36__7 S36__IA 3.1638E-09 600.0
TI46_7 TI46_IA 4.3921E-06 600.0
TI47_7 TI47_IA 3.9608E-06 600.0
TI48_7 TI48_IA 3.9246E-05 600.0
TI49_7 TI49_IA 2.8801E-06 600.0
TI50_7 TI50_IA 2.7577E-06 600.0
V____7 V____IA 3.7518E-06 600.0
ZR90_7 ZR90_IA 1.0779E-06 600.0
ZR91_7 ZR91_IA 2.3507E-07 600.0
ZR92_7 ZR92_IA 3.5931E-07 600.0
ZR94_7 ZR94_IA 3.6413E-07 600.0
ZR96_7 ZR96_IA 5.8663E-08 600.0
W182_7 W182_IA 2.7550E-07 600.0
W183_7 W183_IA 1.4877E-07 600.0
W184_7 W184_IA 3.1979E-07 600.0
W186_7 W186_IA 2.9556E-07 600.0
CU63_7 CU63_IA 2.0804E-06 600.0
CU65_7 CU65_IA 9.2725E-07 600.0
CO59_7 CO59_IA 3.2430E-06 600.0
CA40_7 CA40_IA 4.6229E-06 600.0
CA42_7 CA42_IA 3.0854E-08 600.0
CA43_7 CA43_IA 6.4378E-09 600.0
CA44_7 CA44_IA 9.9476E-08 600.0
CA46_7 CA46_IA 1.9075E-10 600.0
CA48_7 CA48_IA 8.9176E-09 600.0
NB93_7 NB93_IA 1.0286E-06 600.0
N14__7 N14__IA 6.7973E-06 600.0
N15__7 N15__IA 2.5106E-08 600.0
AL27_7 AL27_IA 3.5417E-06 600.0
TA1817 TA181IA 5.2812E-07 600.0
B10__7 B10__IA 7.0367E-07 600.0
B11__7 B11__IA 2.8324E-06 600.0
PB2047 PB204IA 1.1702E-04 600.0
PB2067 PB206IA 2.0144E-03 600.0
PB2077 PB207IA 1.8472E-03 600.0
PB2087 PB208IA 4.3799E-03 600.0
t_composition(:, 2)=
! IB=Inlet Wrapper (DS4-Wrapper, Pb)
FE54_7 FE54_IB 2.6147E-04 600.0
FE56_7 FE56_IB 4.1044E-03 600.0
FE57_7 FE57_IB 9.4790E-05 600.0
FE58_7 FE58_IB 1.2615E-05 600.0
NI58_7 NI58_IB 6.8720E-04 600.0
NI60_7 NI60_IB 2.6471E-04 600.0
NI61_7 NI61_IB 1.1508E-05 600.0
NI62_7 NI62_IB 3.6683E-05 600.0
NI64_7 NI64_IB 9.3475E-06 600.0
CR50_7 CR50_IB 4.6316E-05 600.0
CR52_7 CR52_IB 8.9315E-04 600.0
CR53_7 CR53_IB 1.0128E-04 600.0
CR54_7 CR54_IB 2.5210E-05 600.0
MN55_7 MN55_IB 1.0437E-04 600.0
MO92_7 MO92_IB 8.8679E-06 600.0
MO94_7 MO94_IB 5.5275E-06 600.0
MO95_7 MO95_IB 9.5133E-06 600.0
MO96_7 MO96_IB 9.9675E-06 600.0
MO97_7 MO97_IB 5.7068E-06 600.0
MO98_7 MO98_IB 1.4419E-05 600.0
MO1007 MO100IB 5.7546E-06 600.0
SI28_7 SI28_IB 1.0670E-04 600.0
SI29_7 SI29_IB 5.4179E-06 600.0
SI30_7 SI30_IB 3.5715E-06 600.0
C____7 C____IB 2.8642E-05 600.0
P31__7 P31__IB 5.5534E-06 600.0
S32__7 S32__IB 1.6977E-06 600.0
S33__7 S33__IB 1.3592E-08 600.0
S34__7 S34__IB 7.6723E-08 600.0
S36__7 S36__IB 3.5768E-10 600.0
TI46_7 TI46_IB 2.6352E-06 600.0
TI47_7 TI47_IB 2.3765E-06 600.0
TI48_7 TI48_IB 2.3548E-05 600.0
TI49_7 TI49_IB 1.7281E-06 600.0
TI50_7 TI50_IB 1.6546E-06 600.0
V____7 V____IB 2.2511E-06 600.0
ZR90_7 ZR90_IB 6.4675E-07 600.0
ZR91_7 ZR91_IB 1.4104E-07 600.0
ZR92_7 ZR92_IB 2.1558E-07 600.0
ZR94_7 ZR94_IB 2.1848E-07 600.0
ZR96_7 ZR96_IB 3.5198E-08 600.0
W182_7 W182_IB 1.6530E-07 600.0
W183_7 W183_IB 8.9261E-08 600.0
W184_7 W184_IB 1.9187E-07 600.0
W186_7 W186_IB 1.7734E-07 600.0
CU63_7 CU63_IB 1.2482E-06 600.0
CU65_7 CU65_IB 5.5635E-07 600.0
CO59_7 CO59_IB 1.9458E-06 600.0
CA40_7 CA40_IB 2.7737E-06 600.0
CA42_7 CA42_IB 1.8512E-08 600.0
CA43_7 CA43_IB 3.8627E-09 600.0
CA44_7 CA44_IB 5.9686E-08 600.0
CA46_7 CA46_IB 1.1445E-10 600.0
CA48_7 CA48_IB 5.3506E-09 600.0
NB93_7 NB93_IB 6.1715E-07 600.0
N14__7 N14__IB 4.0784E-06 600.0
N15__7 N15__IB 1.5064E-08 600.0
AL27_7 AL27_IB 2.1250E-06 600.0
TA1817 TA181IB 3.1687E-07 600.0
B10__7 B10__IB 4.2220E-07 600.0
B11__7 B11__IB 1.6994E-06 600.0
PB2047 PB204IB 3.8856E-04 600.0
PB2067 PB206IB 6.6887E-03 600.0
PB2077 PB207IB 6.1336E-03 600.0
PB2087 PB208IB 1.4543E-02 600.0
t_composition(:, 3)=
! IC=Lower Bundle Grid and Pins Plug (DS4-Wrapper, DS4-Clad, Pb)
FE54_7 FE54_IC 1.2517E-03 600.0
FE56_7 FE56_IC 1.9649E-02 600.0
FE57_7 FE57_IC 4.5378E-04 600.0
FE58_7 FE58_IC 6.0390E-05 600.0
NI58_7 NI58_IC 3.2898E-03 600.0
NI60_7 NI60_IC 1.2672E-03 600.0
NI61_7 NI61_IC 5.5090E-05 600.0
NI62_7 NI62_IC 1.7561E-04 600.0
NI64_7 NI64_IC 4.4748E-05 600.0
CR50_7 CR50_IC 2.2172E-04 600.0
CR52_7 CR52_IC 4.2757E-03 600.0
CR53_7 CR53_IC 4.8483E-04 600.0
CR54_7 CR54_IC 1.2068E-04 600.0
MN55_7 MN55_IC 4.9962E-04 600.0
MO92_7 MO92_IC 4.2453E-05 600.0
MO94_7 MO94_IC 2.6461E-05 600.0
MO95_7 MO95_IC 4.5542E-05 600.0
MO96_7 MO96_IC 4.7716E-05 600.0
MO97_7 MO97_IC 2.7320E-05 600.0
MO98_7 MO98_IC 6.9028E-05 600.0
MO1007 MO100IC 2.7548E-05 600.0
SI28_7 SI28_IC 5.1079E-04 600.0
SI29_7 SI29_IC 2.5937E-05 600.0
SI30_7 SI30_IC 1.7098E-05 600.0
C____7 C____IC 1.3712E-04 600.0
P31__7 P31__IC 2.6585E-05 600.0
S32__7 S32__IC 8.1275E-06 600.0
S33__7 S33__IC 6.5068E-08 600.0
S34__7 S34__IC 3.6729E-07 600.0
S36__7 S36__IC 1.7123E-09 600.0
TI46_7 TI46_IC 1.2615E-05 600.0
TI47_7 TI47_IC 1.1377E-05 600.0
TI48_7 TI48_IC 1.1273E-04 600.0
TI49_7 TI49_IC 8.2727E-06 600.0
TI50_7 TI50_IC 7.9210E-06 600.0
V____7 V____IC 1.0776E-05 600.0
ZR90_7 ZR90_IC 3.0962E-06 600.0
ZR91_7 ZR91_IC 6.7520E-07 600.0
ZR92_7 ZR92_IC 1.0321E-06 600.0
ZR94_7 ZR94_IC 1.0459E-06 600.0
ZR96_7 ZR96_IC 1.6850E-07 600.0
W182_7 W182_IC 7.9132E-07 600.0
W183_7 W183_IC 4.2731E-07 600.0
W184_7 W184_IC 9.1853E-07 600.0
W186_7 W186_IC 8.4895E-07 600.0
CU63_7 CU63_IC 5.9755E-06 600.0
CU65_7 CU65_IC 2.6634E-06 600.0
CO59_7 CO59_IC 9.3151E-06 600.0
CA40_7 CA40_IC 1.3278E-05 600.0
CA42_7 CA42_IC 8.8623E-08 600.0
CA43_7 CA43_IC 1.8492E-08 600.0
CA44_7 CA44_IC 2.8573E-07 600.0
CA46_7 CA46_IC 5.4790E-10 600.0
CA48_7 CA48_IC 2.5614E-08 600.0
NB93_7 NB93_IC 2.9544E-06 600.0
N14__7 N14__IC 1.9524E-05 600.0
N15__7 N15__IC 7.2114E-08 600.0
AL27_7 AL27_IC 1.0173E-05 600.0
TA1817 TA181IC 1.5169E-06 600.0
B10__7 B10__IC 2.0212E-06 600.0
B11__7 B11__IC 8.1355E-06 600.0
PB2047 PB204IC 2.5702E-04 600.0
PB2067 PB206IC 4.4244E-03 600.0
PB2077 PB207IC 4.0572E-03 600.0
PB2087 PB208IC 9.6199E-03 600.0
t_composition(:, 4)=
! ID=Lower Gas Plenum (tube) (DS4-Wrapper, DS4-Clad, Helium, Pb)
FE54_7 FE54_ID 9.7769E-04 600.0
FE56_7 FE56_ID 1.5348E-02 600.0
FE57_7 FE57_ID 3.5445E-04 600.0
FE58_7 FE58_ID 4.7170E-05 600.0
NI58_7 NI58_ID 2.5696E-03 600.0
NI60_7 NI60_ID 9.8982E-04 600.0
NI61_7 NI61_ID 4.3031E-05 600.0
NI62_7 NI62_ID 1.3717E-04 600.0
NI64_7 NI64_ID 3.4953E-05 600.0
CR50_7 CR50_ID 1.7319E-04 600.0
CR52_7 CR52_ID 3.3398E-03 600.0
CR53_7 CR53_ID 3.7870E-04 600.0
CR54_7 CR54_ID 9.4267E-05 600.0
MN55_7 MN55_ID 3.9025E-04 600.0
MO92_7 MO92_ID 3.3160E-05 600.0
MO94_7 MO94_ID 2.0669E-05 600.0
MO95_7 MO95_ID 3.5573E-05 600.0
MO96_7 MO96_ID 3.7271E-05 600.0
MO97_7 MO97_ID 2.1339E-05 600.0
MO98_7 MO98_ID 5.3918E-05 600.0
MO1007 MO100ID 2.1518E-05 600.0
SI28_7 SI28_ID 3.9897E-04 600.0
SI29_7 SI29_ID 2.0259E-05 600.0
SI30_7 SI30_ID 1.3355E-05 600.0
C____7 C____ID 1.0710E-04 600.0
P31__7 P31__ID 2.0766E-05 600.0
S32__7 S32__ID 6.3484E-06 600.0
S33__7 S33__ID 5.0824E-08 600.0
S34__7 S34__ID 2.8689E-07 600.0
S36__7 S36__ID 1.3375E-09 600.0
TI46_7 TI46_ID 9.8539E-06 600.0
TI47_7 TI47_ID 8.8864E-06 600.0
TI48_7 TI48_ID 8.8052E-05 600.0
TI49_7 TI49_ID 6.4618E-06 600.0
TI50_7 TI50_ID 6.1870E-06 600.0
V____7 V____ID 8.4174E-06 600.0
ZR90_7 ZR90_ID 2.4184E-06 600.0
ZR91_7 ZR91_ID 5.2739E-07 600.0
ZR92_7 ZR92_ID 8.0613E-07 600.0
ZR94_7 ZR94_ID 8.1694E-07 600.0
ZR96_7 ZR96_ID 1.3161E-07 600.0
W182_7 W182_ID 6.1810E-07 600.0
W183_7 W183_ID 3.3377E-07 600.0
W184_7 W184_ID 7.1746E-07 600.0
W186_7 W186_ID 6.6311E-07 600.0
CU63_7 CU63_ID 4.6675E-06 600.0
CU65_7 CU65_ID 2.0804E-06 600.0
CO59_7 CO59_ID 7.2760E-06 600.0
CA40_7 CA40_ID 1.0372E-05 600.0
CA42_7 CA42_ID 6.9223E-08 600.0
CA43_7 CA43_ID 1.4444E-08 600.0
CA44_7 CA44_ID 2.2318E-07 600.0
CA46_7 CA46_ID 4.2796E-10 600.0
CA48_7 CA48_ID 2.0007E-08 600.0
NB93_7 NB93_ID 2.3077E-06 600.0
N14__7 N14__ID 1.5250E-05 600.0
N15__7 N15__ID 5.6328E-08 600.0
AL27_7 AL27_ID 7.9461E-06 600.0
TA1817 TA181ID 1.1849E-06 600.0
B10__7 B10__ID 1.5787E-06 600.0
B11__7 B11__ID 6.3546E-06 600.0
HE4__7 HE4__ID 6.8773E-06 600.0
PB2047 PB204ID 1.7712E-04 600.0
PB2067 PB206ID 3.0489E-03 600.0
PB2077 PB207ID 2.7959E-03 600.0
PB2087 PB208ID 6.6292E-03 600.0
t_composition(:, 5)=
! IE=Lower thermal insulator (DS4-Wrapper, DS4-Clad, Helium, Pb, YSZ)
FE54_7 FE54_IE 7.5276E-04 600.0
FE56_7 FE56_IE 1.1817E-02 600.0
FE57_7 FE57_IE 2.7290E-04 600.0
FE58_7 FE58_IE 3.6318E-05 600.0
NI58_7 NI58_IE 1.9785E-03 600.0
NI60_7 NI60_IE 7.6209E-04 600.0
NI61_7 NI61_IE 3.3131E-05 600.0
NI62_7 NI62_IE 1.0561E-04 600.0
NI64_7 NI64_IE 2.6911E-05 600.0
CR50_7 CR50_IE 1.3334E-04 600.0
CR52_7 CR52_IE 2.5714E-03 600.0
CR53_7 CR53_IE 2.9157E-04 600.0
CR54_7 CR54_IE 7.2579E-05 600.0
MN55_7 MN55_IE 3.0047E-04 600.0
MO92_7 MO92_IE 2.5531E-05 600.0
MO94_7 MO94_IE 1.5914E-05 600.0
MO95_7 MO95_IE 2.7389E-05 600.0
MO96_7 MO96_IE 2.8696E-05 600.0
MO97_7 MO97_IE 1.6430E-05 600.0
MO98_7 MO98_IE 4.1513E-05 600.0
MO1007 MO100IE 1.6567E-05 600.0
SI28_7 SI28_IE 3.0718E-04 600.0
SI29_7 SI29_IE 1.5598E-05 600.0
SI30_7 SI30_IE 1.0282E-05 600.0
C____7 C____IE 8.2461E-05 600.0
P31__7 P31__IE 1.5988E-05 600.0
S32__7 S32__IE 4.8878E-06 600.0
S33__7 S33__IE 3.9131E-08 600.0
S34__7 S34__IE 2.2089E-07 600.0
S36__7 S36__IE 1.0298E-09 600.0
TI46_7 TI46_IE 7.5868E-06 600.0
TI47_7 TI47_IE 6.8419E-06 600.0
TI48_7 TI48_IE 6.7794E-05 600.0
TI49_7 TI49_IE 4.9751E-06 600.0
TI50_7 TI50_IE 4.7636E-06 600.0
V____7 V____IE 6.4809E-06 600.0
ZR90_7 ZR90_IE 3.8368E-03 600.0
ZR91_7 ZR91_IE 8.3671E-04 600.0
ZR92_7 ZR92_IE 1.2789E-03 600.0
ZR94_7 ZR94_IE 1.2961E-03 600.0
ZR96_7 ZR96_IE 2.0880E-04 600.0
W182_7 W182_IE 4.7589E-07 600.0
W183_7 W183_IE 2.5698E-07 600.0
W184_7 W184_IE 5.5240E-07 600.0
W186_7 W186_IE 5.1055E-07 600.0
CU63_7 CU63_IE 3.5936E-06 600.0
CU65_7 CU65_IE 1.6017E-06 600.0
CO59_7 CO59_IE 5.6020E-06 600.0
CA40_7 CA40_IE 7.9856E-06 600.0
CA42_7 CA42_IE 5.3297E-08 600.0
CA43_7 CA43_IE 1.1121E-08 600.0
CA44_7 CA44_IE 1.7184E-07 600.0
CA46_7 CA46_IE 3.2950E-10 600.0
CA48_7 CA48_IE 1.5404E-08 600.0
NB93_7 NB93_IE 1.7768E-06 600.0
N14__7 N14__IE 1.1742E-05 600.0
N15__7 N15__IE 4.3369E-08 600.0
AL27_7 AL27_IE 6.1180E-06 600.0
TA1817 TA181IE 9.1226E-07 600.0
B10__7 B10__IE 1.2155E-06 600.0
B11__7 B11__IE 4.8926E-06 600.0
HE4__7 HE4__IE 8.2368E-07 600.0
PB2047 PB204IE 1.7712E-04 600.0
PB2067 PB206IE 3.0489E-03 600.0
PB2077 PB207IE 2.7959E-03 600.0
PB2087 PB208IE 6.6292E-03 600.0
Y89__7 Y89__IE 1.2963E-03 600.0
O16__7 O16__IE 1.6852E-02 600.0
t_composition(:, 6)=
! IF=Active Fuel (DS4-Wrapper, DS4-Clad, Helium, Pb, UPuO)
FE54_7 FE54_FWR 2.6274E-04 900.0
FE56_7 FE56_FWR 4.1245E-03 900.0
FE57_7 FE57_FWR 9.5253E-05 900.0
FE58_7 FE58_FWR 1.2676E-05 900.0
NI58_7 NI58_FWR 6.9056E-04 900.0
NI60_7 NI60_FWR 2.6600E-04 900.0
NI61_7 NI61_FWR 1.1564E-05 900.0
NI62_7 NI62_FWR 3.6863E-05 900.0
NI64_7 NI64_FWR 9.3932E-06 900.0
CR50_7 CR50_FWR 4.6542E-05 900.0
CR52_7 CR52_FWR 8.9752E-04 900.0
CR53_7 CR53_FWR 1.0177E-04 900.0
CR54_7 CR54_FWR 2.5333E-05 900.0
MN55_7 MN55_FWR 1.0488E-04 900.0
MO92_7 MO92_FWR 8.9112E-06 900.0
MO94_7 MO94_FWR 5.5545E-06 900.0
MO95_7 MO95_FWR 9.5598E-06 900.0
MO96_7 MO96_FWR 1.0016E-05 900.0
MO97_7 MO97_FWR 5.7347E-06 900.0
MO98_7 MO98_FWR 1.4490E-05 900.0
MO1007 MO100FWR 5.7827E-06 900.0
SI28_7 SI28_FWR 1.0722E-04 900.0
SI29_7 SI29_FWR 5.4443E-06 900.0
SI30_7 SI30_FWR 3.5889E-06 900.0
C____7 C____FWR 2.8782E-05 900.0
P31__7 P31__FWR 5.5805E-06 900.0
S32__7 S32__FWR 1.7060E-06 900.0
S33__7 S33__FWR 1.3658E-08 900.0
S34__7 S34__FWR 7.7098E-08 900.0
S36__7 S36__FWR 3.5943E-10 900.0
TI46_7 TI46_FWR 2.6481E-06 900.0
TI47_7 TI47_FWR 2.3881E-06 900.0
TI48_7 TI48_FWR 2.3663E-05 900.0
TI49_7 TI49_FWR 1.7365E-06 900.0
TI50_7 TI50_FWR 1.6627E-06 900.0
V____7 V____FWR 2.2621E-06 900.0
ZR90_7 ZR90_FWR 6.4991E-07 900.0
ZR91_7 ZR91_FWR 1.4173E-07 900.0
ZR92_7 ZR92_FWR 2.1664E-07 900.0
ZR94_7 ZR94_FWR 2.1954E-07 900.0
ZR96_7 ZR96_FWR 3.5369E-08 900.0
W182_7 W182_FWR 1.6611E-07 900.0
W183_7 W183_FWR 8.9697E-08 900.0
W184_7 W184_FWR 1.9281E-07 900.0
W186_7 W186_FWR 1.7820E-07 900.0
CU63_7 CU63_FWR 1.2543E-06 900.0
CU65_7 CU65_FWR 5.5907E-07 900.0
CO59_7 CO59_FWR 1.9553E-06 900.0
CA40_7 CA40_FWR 2.7873E-06 900.0
CA42_7 CA42_FWR 1.8603E-08 900.0
CA43_7 CA43_FWR 3.8816E-09 900.0
CA44_7 CA44_FWR 5.9977E-08 900.0
CA46_7 CA46_FWR 1.1501E-10 900.0
CA48_7 CA48_FWR 5.3767E-09 900.0
NB93_7 NB93_FWR 6.2016E-07 900.0
N14__7 N14__FWR 4.0983E-06 900.0
N15__7 N15__FWR 1.5137E-08 900.0
AL27_7 AL27_FWR 2.1354E-06 900.0
TA1817 TA181FWR 3.1842E-07 900.0
B10__7 B10__FWR 4.2426E-07 900.0
B11__7 B11__FWR 1.7077E-06 900.0
FE54_7 FE54_FCD 4.9002E-04 900.0
FE56_7 FE56_FCD 7.6922E-03 900.0
FE57_7 FE57_FCD 1.7765E-04 900.0
FE58_7 FE58_FCD 2.3641E-05 900.0
NI58_7 NI58_FCD 1.2879E-03 900.0
NI60_7 NI60_FCD 4.9609E-04 900.0
NI61_7 NI61_FCD 2.1567E-05 900.0
NI62_7 NI62_FCD 6.8749E-05 900.0
NI64_7 NI64_FCD 1.7518E-05 900.0
CR50_7 CR50_FCD 8.6801E-05 900.0
CR52_7 CR52_FCD 1.6739E-03 900.0
CR53_7 CR53_FCD 1.8980E-04 900.0
CR54_7 CR54_FCD 4.7246E-05 900.0
MN55_7 MN55_FCD 1.9559E-04 900.0
MO92_7 MO92_FCD 1.6619E-05 900.0
MO94_7 MO94_FCD 1.0359E-05 900.0
MO95_7 MO95_FCD 1.7829E-05 900.0
MO96_7 MO96_FCD 1.8680E-05 900.0
MO97_7 MO97_FCD 1.0695E-05 900.0
MO98_7 MO98_FCD 2.7023E-05 900.0
MO1007 MO100FCD 1.0785E-05 900.0
SI28_7 SI28_FCD 1.9996E-04 900.0
SI29_7 SI29_FCD 1.0154E-05 900.0
SI30_7 SI30_FCD 6.6934E-06 900.0
C____7 C____FCD 5.3678E-05 900.0
P31__7 P31__FCD 1.0408E-05 900.0
S32__7 S32__FCD 3.1818E-06 900.0
S33__7 S33__FCD 2.5473E-08 900.0
S34__7 S34__FCD 1.4379E-07 900.0
S36__7 S36__FCD 6.7034E-10 900.0
TI46_7 TI46_FCD 4.9387E-06 900.0
TI47_7 TI47_FCD 4.4538E-06 900.0
TI48_7 TI48_FCD 4.4131E-05 900.0
TI49_7 TI49_FCD 3.2386E-06 900.0
TI50_7 TI50_FCD 3.1009E-06 900.0
V____7 V____FCD 4.2188E-06 900.0
ZR90_7 ZR90_FCD 1.2121E-06 900.0
ZR91_7 ZR91_FCD 2.6433E-07 900.0
ZR92_7 ZR92_FCD 4.0403E-07 900.0
ZR94_7 ZR94_FCD 4.0945E-07 900.0
ZR96_7 ZR96_FCD 6.5964E-08 900.0
W182_7 W182_FCD 3.0979E-07 900.0
W183_7 W183_FCD 1.6729E-07 900.0
W184_7 W184_FCD 3.5959E-07 900.0
W186_7 W186_FCD 3.3235E-07 900.0
CU63_7 CU63_FCD 2.3393E-06 900.0
CU65_7 CU65_FCD 1.0427E-06 900.0
CO59_7 CO59_FCD 3.6467E-06 900.0
CA40_7 CA40_FCD 5.1983E-06 900.0
CA42_7 CA42_FCD 3.4694E-08 900.0
CA43_7 CA43_FCD 7.2391E-09 900.0
CA44_7 CA44_FCD 1.1186E-07 900.0
CA46_7 CA46_FCD 2.1449E-10 900.0
CA48_7 CA48_FCD 1.0028E-08 900.0
NB93_7 NB93_FCD 1.1566E-06 900.0
N14__7 N14__FCD 7.6433E-06 900.0
N15__7 N15__FCD 2.8231E-08 900.0
AL27_7 AL27_FCD 3.9826E-06 900.0
TA1817 TA181FCD 5.9385E-07 900.0
B10__7 B10__FCD 7.9125E-07 900.0
B11__7 B11__FCD 3.1849E-06 900.0
PB2047 PB204FGP 1.8749E-05 900.0
PB2067 PB206FGP 3.2274E-04 900.0
PB2077 PB207FGP 2.9596E-04 900.0
PB2087 PB208FGP 7.0173E-04 900.0
PB2047 PB204FCO 1.5837E-04 900.0
PB2067 PB206FCO 2.7262E-03 900.0
PB2077 PB207FCO 2.4999E-03 900.0
PB2087 PB208FCO 5.9275E-03 900.0
HE4__7 HE4__FHE 2.4109E-06 1200.0
U234_7 U234_FFL 4.4048E-08 1200.0
U235_7 U235_FFL 1.0966E-05 1200.0
U238_7 U238_FFL 4.3201E-03 1200.0
PU2387 PU238FFL 3.0997E-06 1200.0
PU2397 PU239FFL 8.4988E-04 1200.0
PU2407 PU240FFL 3.2865E-04 1200.0
PU2417 PU241FFL 2.1555E-05 1200.0
PU2427 PU242FFL 3.0738E-05 1200.0
AM2417 AM241FFL 5.1971E-05 1200.0
O16__7 O16__FFL 1.1066E-02 1200.0
t_composition(:, 7)=
! IG=Upper thermal insulator (DS4-Wrapper, DS4-Clad, Helium, Pb, YSZ)
FE54_7 FE54_IG 7.5276E-04 900.0
FE56_7 FE56_IG 1.1817E-02 900.0
FE57_7 FE57_IG 2.7290E-04 900.0
FE58_7 FE58_IG 3.6318E-05 900.0
NI58_7 NI58_IG 1.9785E-03 900.0
NI60_7 NI60_IG 7.6209E-04 900.0
NI61_7 NI61_IG 3.3131E-05 900.0
NI62_7 NI62_IG 1.0561E-04 900.0
NI64_7 NI64_IG 2.6911E-05 900.0
CR50_7 CR50_IG 1.3334E-04 900.0
CR52_7 CR52_IG 2.5714E-03 900.0
CR53_7 CR53_IG 2.9157E-04 900.0
CR54_7 CR54_IG 7.2579E-05 900.0
MN55_7 MN55_IG 3.0047E-04 900.0
MO92_7 MO92_IG 2.5531E-05 900.0
MO94_7 MO94_IG 1.5914E-05 900.0
MO95_7 MO95_IG 2.7389E-05 900.0
MO96_7 MO96_IG 2.8696E-05 900.0
MO97_7 MO97_IG 1.6430E-05 900.0
MO98_7 MO98_IG 4.1513E-05 900.0
MO1007 MO100IG 1.6567E-05 900.0
SI28_7 SI28_IG 3.0718E-04 900.0
SI29_7 SI29_IG 1.5598E-05 900.0
SI30_7 SI30_IG 1.0282E-05 900.0
C____7 C____IG 8.2461E-05 900.0
P31__7 P31__IG 1.5988E-05 900.0
S32__7 S32__IG 4.8878E-06 900.0
S33__7 S33__IG 3.9131E-08 900.0
S34__7 S34__IG 2.2089E-07 900.0
S36__7 S36__IG 1.0298E-09 900.0
TI46_7 TI46_IG 7.5868E-06 900.0
TI47_7 TI47_IG 6.8419E-06 900.0
TI48_7 TI48_IG 6.7794E-05 900.0
TI49_7 TI49_IG 4.9751E-06 900.0
TI50_7 TI50_IG 4.7636E-06 900.0
V____7 V____IG 6.4809E-06 900.0
ZR90_7 ZR90_IG 3.8368E-03 900.0
ZR91_7 ZR91_IG 8.3671E-04 900.0
ZR92_7 ZR92_IG 1.2789E-03 900.0
ZR94_7 ZR94_IG 1.2961E-03 900.0
ZR96_7 ZR96_IG 2.0880E-04 900.0
W182_7 W182_IG 4.7589E-07 900.0
W183_7 W183_IG 2.5698E-07 900.0
W184_7 W184_IG 5.5240E-07 900.0
W186_7 W186_IG 5.1055E-07 900.0
CU63_7 CU63_IG 3.5936E-06 900.0
CU65_7 CU65_IG 1.6017E-06 900.0
CO59_7 CO59_IG 5.6020E-06 900.0
CA40_7 CA40_IG 7.9856E-06 900.0
CA42_7 CA42_IG 5.3297E-08 900.0
CA43_7 CA43_IG 1.1121E-08 900.0
CA44_7 CA44_IG 1.7184E-07 900.0
CA46_7 CA46_IG 3.2950E-10 900.0
CA48_7 CA48_IG 1.5404E-08 900.0
NB93_7 NB93_IG 1.7768E-06 900.0
N14__7 N14__IG 1.1742E-05 900.0
N15__7 N15__IG 4.3369E-08 900.0
AL27_7 AL27_IG 6.1180E-06 900.0
TA1817 TA181IG 9.1226E-07 900.0
B10__7 B10__IG 1.2155E-06 900.0
B11__7 B11__IG 4.8926E-06 900.0
HE4__7 HE4__IG 8.2368E-07 900.0
PB2047 PB204IG 1.7712E-04 900.0
PB2067 PB206IG 3.0489E-03 900.0
PB2077 PB207IG 2.7959E-03 900.0
PB2087 PB208IG 6.6292E-03 900.0
Y89__7 Y89__IG 1.2963E-03 900.0
O16__7 O16__IG 1.6852E-02 900.0
t_composition(:, 8)=
! IH=Upper gas plenum (spring) (DS4-Wrapper, DS4-Clad, Helium, Pb)
FE54_7 FE54_IH 8.7383E-04 900.0
FE56_7 FE56_IH 1.3717E-02 900.0
FE57_7 FE57_IH 3.1679E-04 900.0
FE58_7 FE58_IH 4.2159E-05 900.0
NI58_7 NI58_IH 2.2967E-03 900.0
NI60_7 NI60_IH 8.8466E-04 900.0
NI61_7 NI61_IH 3.8459E-05 900.0
NI62_7 NI62_IH 1.2260E-04 900.0
NI64_7 NI64_IH 3.1240E-05 900.0
CR50_7 CR50_IH 1.5479E-04 900.0
CR52_7 CR52_IH 2.9850E-03 900.0
CR53_7 CR53_IH 3.3847E-04 900.0
CR54_7 CR54_IH 8.4252E-05 900.0
MN55_7 MN55_IH 3.4880E-04 900.0
MO92_7 MO92_IH 2.9637E-05 900.0
MO94_7 MO94_IH 1.8473E-05 900.0
MO95_7 MO95_IH 3.1794E-05 900.0
MO96_7 MO96_IH 3.3312E-05 900.0
MO97_7 MO97_IH 1.9072E-05 900.0
MO98_7 MO98_IH 4.8190E-05 900.0
MO1007 MO100IH 1.9232E-05 900.0
SI28_7 SI28_IH 3.5659E-04 900.0
SI29_7 SI29_IH 1.8107E-05 900.0
SI30_7 SI30_IH 1.1936E-05 900.0
C____7 C____IH 9.5723E-05 900.0
P31__7 P31__IH 1.8560E-05 900.0
S32__7 S32__IH 5.6739E-06 900.0
S33__7 S33__IH 4.5425E-08 900.0
S34__7 S34__IH 2.5641E-07 900.0
S36__7 S36__IH 1.1954E-09 900.0
TI46_7 TI46_IH 8.8071E-06 900.0
TI47_7 TI47_IH 7.9424E-06 900.0
TI48_7 TI48_IH 7.8698E-05 900.0
TI49_7 TI49_IH 5.7753E-06 900.0
TI50_7 TI50_IH 5.5298E-06 900.0
V____7 V____IH 7.5232E-06 900.0
ZR90_7 ZR90_IH 2.1615E-06 900.0
ZR91_7 ZR91_IH 4.7137E-07 900.0
ZR92_7 ZR92_IH 7.2049E-07 900.0
ZR94_7 ZR94_IH 7.3016E-07 900.0
ZR96_7 ZR96_IH 1.1763E-07 900.0
W182_7 W182_IH 5.5243E-07 900.0
W183_7 W183_IH 2.9831E-07 900.0
W184_7 W184_IH 6.4124E-07 900.0
W186_7 W186_IH 5.9267E-07 900.0
CU63_7 CU63_IH 4.1716E-06 900.0
CU65_7 CU65_IH 1.8593E-06 900.0
CO59_7 CO59_IH 6.5030E-06 900.0
CA40_7 CA40_IH 9.2699E-06 900.0
CA42_7 CA42_IH 6.1869E-08 900.0
CA43_7 CA43_IH 1.2909E-08 900.0
CA44_7 CA44_IH 1.9947E-07 900.0
CA46_7 CA46_IH 3.8250E-10 900.0
CA48_7 CA48_IH 1.7882E-08 900.0
NB93_7 NB93_IH 2.0625E-06 900.0
N14__7 N14__IH 1.3630E-05 900.0
N15__7 N15__IH 5.0344E-08 900.0
AL27_7 AL27_IH 7.1020E-06 900.0
TA1817 TA181IH 1.0590E-06 900.0
B10__7 B10__IH 1.4110E-06 900.0
B11__7 B11__IH 5.6795E-06 900.0
HE4__7 HE4__IH 7.6960E-06 900.0
PB2047 PB204IH 1.7712E-04 900.0
PB2067 PB206IH 3.0489E-03 900.0
PB2077 PB207IH 2.7959E-03 900.0
PB2087 PB208IH 6.6292E-03 900.0
t_composition(:, 9)=
! II=Upper Bundle Grid and Pins Plug (DS4-Wrapper, DS4-Clad, Pb)
FE54_7 FE54_II 1.2517E-03 900.0
FE56_7 FE56_II 1.9649E-02 900.0
FE57_7 FE57_II 4.5378E-04 900.0
FE58_7 FE58_II 6.0390E-05 900.0
NI58_7 NI58_II 3.2898E-03 900.0
NI60_7 NI60_II 1.2672E-03 900.0
NI61_7 NI61_II 5.5090E-05 900.0
NI62_7 NI62_II 1.7561E-04 900.0
NI64_7 NI64_II 4.4748E-05 900.0
CR50_7 CR50_II 2.2172E-04 900.0
CR52_7 CR52_II 4.2757E-03 900.0
CR53_7 CR53_II 4.8483E-04 900.0
CR54_7 CR54_II 1.2068E-04 900.0
MN55_7 MN55_II 4.9962E-04 900.0
MO92_7 MO92_II 4.2453E-05 900.0
MO94_7 MO94_II 2.6461E-05 900.0
MO95_7 MO95_II 4.5542E-05 900.0
MO96_7 MO96_II 4.7716E-05 900.0
MO97_7 MO97_II 2.7320E-05 900.0
MO98_7 MO98_II 6.9028E-05 900.0
MO1007 MO100II 2.7548E-05 900.0
SI28_7 SI28_II 5.1079E-04 900.0
SI29_7 SI29_II 2.5937E-05 900.0
SI30_7 SI30_II 1.7098E-05 900.0
C____7 C____II 1.3712E-04 900.0
P31__7 P31__II 2.6585E-05 900.0
S32__7 S32__II 8.1275E-06 900.0
S33__7 S33__II 6.5068E-08 900.0
S34__7 S34__II 3.6729E-07 900.0
S36__7 S36__II 1.7123E-09 900.0
TI46_7 TI46_II 1.2615E-05 900.0
TI47_7 TI47_II 1.1377E-05 900.0
TI48_7 TI48_II 1.1273E-04 900.0
TI49_7 TI49_II 8.2727E-06 900.0
TI50_7 TI50_II 7.9210E-06 900.0
V____7 V____II 1.0776E-05 900.0
ZR90_7 ZR90_II 3.0962E-06 900.0
ZR91_7 ZR91_II 6.7520E-07 900.0
ZR92_7 ZR92_II 1.0321E-06 900.0
ZR94_7 ZR94_II 1.0459E-06 900.0
ZR96_7 ZR96_II 1.6850E-07 900.0
W182_7 W182_II 7.9132E-07 900.0
W183_7 W183_II 4.2731E-07 900.0
W184_7 W184_II 9.1853E-07 900.0
W186_7 W186_II 8.4895E-07 900.0
CU63_7 CU63_II 5.9755E-06 900.0
CU65_7 CU65_II 2.6634E-06 900.0
CO59_7 CO59_II 9.3151E-06 900.0
CA40_7 CA40_II 1.3278E-05 900.0
CA42_7 CA42_II 8.8623E-08 900.0
CA43_7 CA43_II 1.8492E-08 900.0
CA44_7 CA44_II 2.8573E-07 900.0
CA46_7 CA46_II 5.4790E-10 900.0
CA48_7 CA48_II 2.5614E-08 900.0
NB93_7 NB93_II 2.9544E-06 900.0
N14__7 N14__II 1.9524E-05 900.0
N15__7 N15__II 7.2114E-08 900.0
AL27_7 AL27_II 1.0173E-05 900.0
TA1817 TA181II 1.5169E-06 900.0
B10__7 B10__II 2.0212E-06 900.0
B11__7 B11__II 8.1355E-06 900.0
PB2047 PB204II 2.5702E-04 900.0
PB2067 PB206II 4.4244E-03 900.0
PB2077 PB207II 4.0572E-03 900.0
PB2087 PB208II 9.6199E-03 900.0
t_composition(:, 10)=
! IJ=Outlet Wrapper (DS4-Wrapper, Pb)
FE54_7 FE54_IJ 7.6045E-04 900.0
FE56_7 FE56_IJ 1.1937E-02 900.0
FE57_7 FE57_IJ 2.7569E-04 900.0
FE58_7 FE58_IJ 3.6689E-05 900.0
NI58_7 NI58_IJ 1.9987E-03 900.0
NI60_7 NI60_IJ 7.6988E-04 900.0
NI61_7 NI61_IJ 3.3469E-05 900.0
NI62_7 NI62_IJ 1.0669E-04 900.0
NI64_7 NI64_IJ 2.7186E-05 900.0
CR50_7 CR50_IJ 1.3471E-04 900.0
CR52_7 CR52_IJ 2.5977E-03 900.0
CR53_7 CR53_IJ 2.9456E-04 900.0
CR54_7 CR54_IJ 7.3321E-05 900.0
MN55_7 MN55_IJ 3.0354E-04 900.0
MO92_7 MO92_IJ 2.5792E-05 900.0
MO94_7 MO94_IJ 1.6076E-05 900.0
MO95_7 MO95_IJ 2.7669E-05 900.0
MO96_7 MO96_IJ 2.8990E-05 900.0
MO97_7 MO97_IJ 1.6598E-05 900.0
MO98_7 MO98_IJ 4.1938E-05 900.0
MO1007 MO100IJ 1.6737E-05 900.0
SI28_7 SI28_IJ 3.1032E-04 900.0
SI29_7 SI29_IJ 1.5757E-05 900.0
SI30_7 SI30_IJ 1.0387E-05 900.0
C____7 C____IJ 8.3303E-05 900.0
P31__7 P31__IJ 1.6152E-05 900.0
S32__7 S32__IJ 4.9378E-06 900.0
S33__7 S33__IJ 3.9531E-08 900.0
S34__7 S34__IJ 2.2314E-07 900.0
S36__7 S36__IJ 1.0403E-09 900.0
TI46_7 TI46_IJ 7.6644E-06 900.0
TI47_7 TI47_IJ 6.9119E-06 900.0
TI48_7 TI48_IJ 6.8487E-05 900.0
TI49_7 TI49_IJ 5.0260E-06 900.0
TI50_7 TI50_IJ 4.8123E-06 900.0
V____7 V____IJ 6.5471E-06 900.0
ZR90_7 ZR90_IJ 1.8810E-06 900.0
ZR91_7 ZR91_IJ 4.1021E-07 900.0
ZR92_7 ZR92_IJ 6.2701E-07 900.0
ZR94_7 ZR94_IJ 6.3542E-07 900.0
ZR96_7 ZR96_IJ 1.0237E-07 900.0
W182_7 W182_IJ 4.8076E-07 900.0
W183_7 W183_IJ 2.5961E-07 900.0
W184_7 W184_IJ 5.5804E-07 900.0
W186_7 W186_IJ 5.1577E-07 900.0
CU63_7 CU63_IJ 3.6304E-06 900.0
CU65_7 CU65_IJ 1.6181E-06 900.0
CO59_7 CO59_IJ 5.6593E-06 900.0
CA40_7 CA40_IJ 8.0672E-06 900.0
CA42_7 CA42_IJ 5.3842E-08 900.0
CA43_7 CA43_IJ 1.1234E-08 900.0
CA44_7 CA44_IJ 1.7359E-07 900.0
CA46_7 CA46_IJ 3.3287E-10 900.0
CA48_7 CA48_IJ 1.5562E-08 900.0
NB93_7 NB93_IJ 1.7949E-06 900.0
N14__7 N14__IJ 1.1862E-05 900.0
N15__7 N15__IJ 4.3812E-08 900.0
AL27_7 AL27_IJ 6.1805E-06 900.0
TA1817 TA181IJ 9.2159E-07 900.0
B10__7 B10__IJ 1.2279E-06 900.0
B11__7 B11__IJ 4.9426E-06 900.0
PB2047 PB204IJ 3.2241E-04 900.0
PB2067 PB206IJ 5.5500E-03 900.0
PB2077 PB207IJ 5.0894E-03 900.0
PB2087 PB208IJ 1.2067E-02 900.0
/
The twodant block is to generate a TWODANT input internally for calling TWODANT. niso and ngroup are filled by MC2-3, mt and nzone are the number of materials and coarse meshes, im and jm are the number of coarse meshes in the x and y directions, it and jt are the total number of fine meshes in the x and y directions, igeom=6 means x-y geometry, isn is the Sn order, and maxlcm and maxscm are the maximum memory size (in a unit of word = 2 bytes) of central small core memory and peripheral large core memory. xmesh and ymesh are x and y coordinates of coarse meshes, xints and yints are the number of fine meshes in each coarse x and y meshes, and zones are composition numbers in the material block assigned to each x and y coarse mesh.
Input parameters from isct to rmflux are solver options. Important ones are isct: Legendre order of scattering, ievt=1: calculation type=k-eff, ibl, ibr, ibt, ibb: boundary conditions for left, right, top and bottom (0/1/2/3=vacuum/reflective/periodic(only for top and bottom)/white), epsi: inner iteration convergence precision (default=0.0001), epso: outer iteration convergence precision (default=epsi), oitm: maximum number of outer iterations, iitm, iitl: maximum number of inner iterations per group at the first outer iteration and near fission source convergence.
The cross section set for the TWODANT calculation is the ISOTXS output file of the MC2-3 calculation in this first step. MC2-3 fills the matls option in the twodant block for the native TWODANT input with isotope names and atomic number densities taken from the material block. Thus, users do not need to take care of this part.
&twodant
1
niso=,
ngroup=,
mt=10,nzone=10,
im=1, it=4,
jm=10, jt=71,
igeom=6,isn=12,maxlcm=195000000,maxscm=19000000,
t
xmesh=0.0 2.0,
ymesh=0.0 10.07 40.86 47.42 133.27 134.79 240.86 242.37 254.50 259.55 353.42,
xints=4,
yints= 2 6 1 17 1 21 1 2 1 19 ,
zones= 1 ;
2 ;
3 ;
4 ;
5 ;
6 ;
7 ;
8 ;
9 ;
10 ;
t
lib=isotxs,balxs=0,
t
matls=
assign=
t
isct=3,ievt=1,ibl=1,ibr=1,ibt=0,ibb=0,iquad=-2,
ith=0,fluxp=0,xsectp=0,fissrp=0,sourcp=0,angp=0,geomp=0,
influx=0,norm=1.000e+00,epsi=0.0010,epso=.000001,
oitm=20,iitm=35,iitl=30,insors=0,raflux=0,rmflux=1,
chi=,
t
rzmflx=1,
t
/
Figure 3 compares the TWODANT spectra of different axial regions. The spectrum is hardest at the fuel region and gets softer at lower or upper regions due to moderations. Figure 4 compares the TWODANT spectra with the infinite homogeneous medium ultrafine group (UFG: 2082-group) spectrum for each axial region. The infinite homogeneous medium spectrum is very similar to the TWODANT spectrum for the active fuel region. On the other hand, those two spectra are very different for thin lower and upper thermal insulator regions where neutrons quickly leak to their lower and upper regions without having a chance to be moderated enough, resulting in spectra similar to that of their adjacent source region which is the active fuel region. For information, just a fixed source slowing down problem is solved using the fission spectrum of U-238 as a fixed source to obtain an infinite homogeneous medium UFG spectrum of a composition which does not have any fissionable isotopes. For axial regions close to top and bottom boundaries, the TWODANT spectrum is softer than the infinite homogeneous medium spectrum since neutrons have been already moderated on the way to get their regions from the center fuel region and the amount of the moderation is stronger than that in the infinite homogeneous medium of the composition of the axial region of interest. This result indicates the need for considering the axial leakage effect via the TWODANT calculation for obtaining a weighting spectrum for condensation.
Figure 3: Comparison of TWODANT spectra of different axial regions
Figure 4: Comparison of zero-dimensional (0D) UFG and TWODANT spectra of different axial regions
Second step
The second step is to condense the UFG (2082-group) cross section to the broad group (BG) cross section using the TWODANT spectrum. For clarification, the TWODANT calculation in the first step is the 1041 group calculation. In this secton step, the 0D UFG calculation is performed for each mixture of non-fuel axial regions and the 1D UFG calculation is performed for the fuel axial region using MC2-3. Then, resulting UFG spectra are superimposed to 1041-group TWODANT spectra for condensation of UFG cross sections to the broad group structure specified in the c_group_structure of the &control block. Broad group cross sections for the activel fuel region and the other regions are prepared separately and merged at the last step.
For the fuel region, fine mesh-based region-wise cross sections need to be generated as the Griffin transport calculation is fine-mesh based. This can be achieved by setting up an MC2-3 input that employs a 1D heterogeneous tranport calculation using the collision probability method (CPM) whose model is shown in Figure 5. Hexagonal ring-wise cross sections are generated for fuel (7 sets) and one set of cross sections is generated for each of clad, duct, and lead for inner and outer regions of duct. The annular fuel and helium hole and gap are smeared and its homogenized material is used to build the model as microscopic cross sections of isotopes comprising them are not affected by such volume homogenization.
Figure 5: 1D R-geometry model for hexagonal ring-wise cross section generation (red: fuel + helium, blue: lead, gray: clad, cyan: duct)
Below shows the control block. c_group_structure is the broad group structure (target group structure). Specifying c_geometry_type=cylinder automatically sets the problem type as a 1D CPM transport problem. i_number_region means the number of different cross section regions. The self-shielding condition is calculated per cross section region and thus UFG cross sections are unique per cross section region. c_externalspectrum_ufg=rzmflx means to use the TWODANT spectrum in the condensation step after transport calculation. For this, the rzmflx file needs to be placed in the same folder where the MC2-3 input exists with the filename of rzmflx without extension.
&control
c_group_structure =ANL9
i_number_region =29
c_geometry_type =cylinder
i_scattering_order =3
c_externalspectrum_ufg =rzmflx
/
The most important part is l_spatial_homogenization=F in the control1d block. This is for region-wise cross section generation, not for assembly-homogenized one. To be more concrete, for each user-defined isotope name, its UFG microscopic cross sections are flux-volume averaged over regions where the isotope is present, not over the entire region, and condensed into a BG structure.
&control1d
l_spatial_homogenization = F
/
For 1D geometry, there should be 29 cross section regions as indicated by i_number_region=29, which means that the number of elements of i_mesh (the number of fine-mesh in each cross section region), r_location (coordinates of each cross section region from center to periphery in a unit of determined to preserve each material volume), and i_composition (index of composition assigned to each cross section region) must be 29. Composition indices from 2 to 8 are fuel corresponding to hexagonal rings 1 to 7, 1 is lead inside the duct, 9 is clad, 10 is duct, and 11 is lead outside the duct, as shown in the material block. For 1D cylindrical and slab geometries, only the white boundary condition is used.
&geometry
i_mesh = 4 4 4 4 4
4 4 4 4 4
4 4 4 4 4
4 4 4 4 4
4 4 4 4 4
4 4 4 4
r_location = 0.4495 0.5404 1.0541 1.1752 1.6104
1.6921 2.1694 2.2905 2.7696 2.8654
3.3589 3.4774 3.9659 4.0668 4.5650
4.6818 5.1737 5.2771 5.7773 5.8929
6.3865 6.4913 6.9925 7.1074 7.6018
7.7076 8.0553 8.4263 8.6193
i_composition = 2 9 1 9
3 9 1 9
4 9 1 9
5 9 1 9
6 9 1 9
7 9 1 9
8 9 1 10 11
/
In the material block, 7 different materials are defined for the fuel regions of 7 hexagonal rings. Even though the composition is the same, different isotope names are assigned to the same isotope to generate cross sections separately. On the other hand, only a single material is defined for each of lead, clad and duct regions, which means that only the average values over multiple cross section regions are generated per material. i_externalspectrum(1)=6 means that the TWODANT spectrum of Zone 6 is superimposed to cross section region-wise spectrum for condensation. The index of i_externalspectrum, which is 1 here, is a special rule for a heterogeneous MC2-3 calculation that the superposition is applied to all cross section regions.
Suffices in all compositions need special attention since it is directly related to how the ISOTXS file will be converted to the ISOXML file. When the resulting ISOTXS file that contains all isotopes in all compositions without composition IDs is converted to the ISOXML file, the last single character in the user-defined name is used to differentiate compositions and store cross sections of different compositions in different library IDs. Library IDs are increasing in the alphabetical order of the last single character, from the starting value of . In this MC2-3 input, eleven compositions are differentiated by the characters from A to K and the library IDs of them in the ISOXML file to be converted in a later stage are from to . If a isotope name excluding the last single character is not the standard isotope name defined in ISOXML, the pre-fix pseudo_ is attached. Otherwise, the isotope name is used as is.
&material
i_externalspectrum(1) = 6 ! Active Fuel, use region 6 flux from MC2-3/TWODANT Calculation
!************************************
!Description Composition #
!Coolant 1
!Fuel Ring 1 2
!Fuel Ring 2 3
!Fuel Ring 3 4
!Fuel Ring 4 5
!Fuel Ring 5 6
!Fuel Ring 6 7
!Fuel Ring 7 8
!Clad 9
!Duct 10
!Gap Coolant 11
!************************************
t_composition(:,1)= ! Pb Coolant in active fuel zone; density= 10.402 g/cc
PB2047 PB204A 4.2322E-04 808.0
PB2067 PB206A 7.2854E-03 808.0
PB2077 PB207A 6.6808E-03 808.0
PB2087 PB208A 1.5840E-02 808.0
t_composition(:,2)= ! UPuO-He smeared mixture in active fuel zone ring 1; density= 7.289 g/cc
U234_7 U234B 1.2754E-07 1300.0
U235_7 U235B 3.1753E-05 1300.0
U238_7 U238B 1.2509E-02 1300.0
PU2387 PU238B 8.9755E-06 1300.0
PU2397 PU239B 2.4609E-03 1300.0
PU2407 PU240B 9.5162E-04 1300.0
PU2417 PU241B 6.2414E-05 1300.0
PU2427 PU242B 8.9004E-05 1300.0
AM2417 AM241B 1.5049E-04 1300.0
O16__7 O16B 3.2041E-02 1300.0
HE4__7 HE4B 6.9850E-06 1300.0
t_composition(:,3)= ! UPuO-He smeared mixture in active fuel zone ring 2; density= 7.289 g/cc
U234_7 U234C 1.2754E-07 1300.0
U235_7 U235C 3.1753E-05 1300.0
U238_7 U238C 1.2509E-02 1300.0
PU2387 PU238C 8.9755E-06 1300.0
PU2397 PU239C 2.4609E-03 1300.0
PU2407 PU240C 9.5162E-04 1300.0
PU2417 PU241C 6.2414E-05 1300.0
PU2427 PU242C 8.9004E-05 1300.0
AM2417 AM241C 1.5049E-04 1300.0
O16__7 O16C 3.2041E-02 1300.0
HE4__7 HE4C 6.9850E-06 1300.0
t_composition(:,4)= ! UPuO-He smeared mixture in active fuel zone ring 3; density= 7.289 g/cc
U234_7 U234D 1.2754E-07 1300.0
U235_7 U235D 3.1753E-05 1300.0
U238_7 U238D 1.2509E-02 1300.0
PU2387 PU238D 8.9755E-06 1300.0
PU2397 PU239D 2.4609E-03 1300.0
PU2407 PU240D 9.5162E-04 1300.0
PU2417 PU241D 6.2414E-05 1300.0
PU2427 PU242D 8.9004E-05 1300.0
AM2417 AM241D 1.5049E-04 1300.0
O16__7 O16D 3.2041E-02 1300.0
HE4__7 HE4D 6.9850E-06 1300.0
t_composition(:,5)= ! UPuO-He smeared mixture in active fuel zone ring 4; density= 7.289 g/cc
U234_7 U234E 1.2754E-07 1300.0
U235_7 U235E 3.1753E-05 1300.0
U238_7 U238E 1.2509E-02 1300.0
PU2387 PU238E 8.9755E-06 1300.0
PU2397 PU239E 2.4609E-03 1300.0
PU2407 PU240E 9.5162E-04 1300.0
PU2417 PU241E 6.2414E-05 1300.0
PU2427 PU242E 8.9004E-05 1300.0
AM2417 AM241E 1.5049E-04 1300.0
O16__7 O16E 3.2041E-02 1300.0
HE4__7 HE4E 6.9850E-06 1300.0
t_composition(:,6)= ! UPuO-He smeared mixture in active fuel zone ring 5; density= 7.289 g/cc
U234_7 U234F 1.2754E-07 1300.0
U235_7 U235F 3.1753E-05 1300.0
U238_7 U238F 1.2509E-02 1300.0
PU2387 PU238F 8.9755E-06 1300.0
PU2397 PU239F 2.4609E-03 1300.0
PU2407 PU240F 9.5162E-04 1300.0
PU2417 PU241F 6.2414E-05 1300.0
PU2427 PU242F 8.9004E-05 1300.0
AM2417 AM241F 1.5049E-04 1300.0
O16__7 O16F 3.2041E-02 1300.0
HE4__7 HE4F 6.9850E-06 1300.0
t_composition(:,7)= ! UPuO-He smeared mixture in active fuel zone ring 6; density= 7.289 g/cc
U234_7 U234G 1.2754E-07 1300.0
U235_7 U235G 3.1753E-05 1300.0
U238_7 U238G 1.2509E-02 1300.0
PU2387 PU238G 8.9755E-06 1300.0
PU2397 PU239G 2.4609E-03 1300.0
PU2407 PU240G 9.5162E-04 1300.0
PU2417 PU241G 6.2414E-05 1300.0
PU2427 PU242G 8.9004E-05 1300.0
AM2417 AM241G 1.5049E-04 1300.0
O16__7 O16G 3.2041E-02 1300.0
HE4__7 HE4G 6.9850E-06 1300.0
t_composition(:,8)= ! UPuO-He smeared mixture in active fuel zone ring 7; density= 7.289 g/cc
U234_7 U234H 1.2754E-07 1300.0
U235_7 U235H 3.1753E-05 1300.0
U238_7 U238H 1.2509E-02 1300.0
PU2387 PU238H 8.9755E-06 1300.0
PU2397 PU239H 2.4609E-03 1300.0
PU2407 PU240H 9.5162E-04 1300.0
PU2417 PU241H 6.2414E-05 1300.0
PU2427 PU242H 8.9004E-05 1300.0
AM2417 AM241H 1.5049E-04 1300.0
O16__7 O16H 3.2041E-02 1300.0
HE4__7 HE4H 6.9850E-06 1300.0
t_composition(:,9)= ! DS4 Clad in active fuel zone; density= 7.734 g/cc
FE54_7 FE54I 3.1861E-03 843.0
FE56_7 FE56I 5.0014E-02 843.0
FE57_7 FE57I 1.1550E-03 843.0
FE58_7 FE58I 1.5372E-04 843.0
NI58_7 NI58I 8.3738E-03 843.0
NI60_7 NI60I 3.2256E-03 843.0
NI61_7 NI61I 1.4023E-04 843.0
NI62_7 NI62I 4.4700E-04 843.0
NI64_7 NI64I 1.1390E-04 843.0
CR50_7 CR50I 5.6437E-04 843.0
CR52_7 CR52I 1.0883E-02 843.0
CR53_7 CR53I 1.2341E-03 843.0
CR54_7 CR54I 3.0719E-04 843.0
MN55_7 MN55I 1.2717E-03 843.0
MO92_7 MO92I 1.0806E-04 843.0
MO94_7 MO94I 6.7355E-05 843.0
MO95_7 MO95I 1.1592E-04 843.0
MO96_7 MO96I 1.2146E-04 843.0
MO97_7 MO97I 6.9539E-05 843.0
MO98_7 MO98I 1.7571E-04 843.0
MO1007 MO100I 7.0122E-05 843.0
SI28_7 SI28I 1.3002E-03 843.0
SI29_7 SI29I 6.6019E-05 843.0
SI30_7 SI30I 4.3520E-05 843.0
C____7 CI 3.4901E-04 843.0
P31__7 P31I 6.7670E-05 843.0
S32__7 S32I 2.0688E-05 843.0
S33__7 S33I 1.6562E-07 843.0
S34__7 S34I 9.3490E-07 843.0
S36__7 S36I 4.3585E-09 843.0
TI46_7 TI46I 3.2111E-05 843.0
TI47_7 TI47I 2.8959E-05 843.0
TI48_7 TI48I 2.8694E-04 843.0
TI49_7 TI49I 2.1057E-05 843.0
TI50_7 TI50I 2.0162E-05 843.0
V____7 VI 2.7430E-05 843.0
ZR90_7 ZR90I 7.8809E-06 843.0
ZR91_7 ZR91I 1.7186E-06 843.0
ZR92_7 ZR92I 2.6270E-06 843.0
ZR94_7 ZR94I 2.6622E-06 843.0
ZR96_7 ZR96I 4.2889E-07 843.0
W182_7 W182I 2.0142E-06 843.0
W183_7 W183I 1.0877E-06 843.0
W184_7 W184I 2.3380E-06 843.0
W186_7 W186I 2.1609E-06 843.0
CU63_7 CU63I 1.5210E-05 843.0
CU65_7 CU65I 6.7793E-06 843.0
CO59_7 CO59I 2.3711E-05 843.0
CA40_7 CA40I 3.3799E-05 843.0
CA42_7 CA42I 2.2558E-07 843.0
CA43_7 CA43I 4.7068E-08 843.0
CA44_7 CA44I 7.2729E-07 843.0
CA46_7 CA46I 1.3946E-09 843.0
CA48_7 CA48I 6.5198E-08 843.0
NB93_7 NB93I 7.5201E-06 843.0
N14__7 N14I 4.9696E-05 843.0
N15__7 N15I 1.8356E-07 843.0
AL27_7 AL27I 2.5894E-05 843.0
TA1817 TA181I 3.8612E-06 843.0
B10__7 B10I 5.1447E-06 843.0
B11__7 B11I 2.0708E-05 843.0
t_composition(:,10)= ! DS4 Duct (Wrapper) in active fuel zone; density= 7.750 g/cc
FE54_7 FE54J 3.1925E-03 808.0
FE56_7 FE56J 5.0115E-02 808.0
FE57_7 FE57J 1.1574E-03 808.0
FE58_7 FE58J 1.5403E-04 808.0
NI58_7 NI58J 8.3908E-03 808.0
NI60_7 NI60J 3.2321E-03 808.0
NI61_7 NI61J 1.4051E-04 808.0
NI62_7 NI62J 4.4790E-04 808.0
NI64_7 NI64J 1.1413E-04 808.0
CR50_7 CR50J 5.6552E-04 808.0
CR52_7 CR52J 1.0905E-02 808.0
CR53_7 CR53J 1.2366E-03 808.0
CR54_7 CR54J 3.0781E-04 808.0
MN55_7 MN55J 1.2743E-03 808.0
MO92_7 MO92J 1.0828E-04 808.0
MO94_7 MO94J 6.7491E-05 808.0
MO95_7 MO95J 1.1616E-04 808.0
MO96_7 MO96J 1.2170E-04 808.0
MO97_7 MO97J 6.9680E-05 808.0
MO98_7 MO98J 1.7606E-04 808.0
MO1007 MO100J 7.0264E-05 808.0
SI28_7 SI28J 1.3028E-03 808.0
SI29_7 SI29J 6.6152E-05 808.0
SI30_7 SI30J 4.3608E-05 808.0
C____7 CJ 3.4972E-04 808.0
P31__7 P31J 6.7807E-05 808.0
S32__7 S32J 2.0730E-05 808.0
S33__7 S33J 1.6596E-07 808.0
S34__7 S34J 9.3679E-07 808.0
S36__7 S36J 4.3673E-09 808.0
TI46_7 TI46J 3.2176E-05 808.0
TI47_7 TI47J 2.9017E-05 808.0
TI48_7 TI48J 2.8752E-04 808.0
TI49_7 TI49J 2.1100E-05 808.0
TI50_7 TI50J 2.0203E-05 808.0
V____7 VJ 2.7486E-05 808.0
ZR90_7 ZR90J 7.8969E-06 808.0
ZR91_7 ZR91J 1.7221E-06 808.0
ZR92_7 ZR92J 2.6323E-06 808.0
ZR94_7 ZR94J 2.6676E-06 808.0
ZR96_7 ZR96J 4.2976E-07 808.0
W182_7 W182J 2.0183E-06 808.0
W183_7 W183J 1.0899E-06 808.0
W184_7 W184J 2.3427E-06 808.0
W186_7 W186J 2.1653E-06 808.0
CU63_7 CU63J 1.5241E-05 808.0
CU65_7 CU65J 6.7930E-06 808.0
CO59_7 CO59J 2.3759E-05 808.0
CA40_7 CA40J 3.3867E-05 808.0
CA42_7 CA42J 2.2604E-07 808.0
CA43_7 CA43J 4.7164E-08 808.0
CA44_7 CA44J 7.2877E-07 808.0
CA46_7 CA46J 1.3974E-09 808.0
CA48_7 CA48J 6.5330E-08 808.0
NB93_7 NB93J 7.5354E-06 808.0
N14__7 N14J 4.9797E-05 808.0
N15__7 N15J 1.8393E-07 808.0
AL27_7 AL27J 2.5947E-05 808.0
TA1817 TA181J 3.8690E-06 808.0
B10__7 B10J 5.1551E-06 808.0
B11__7 B11J 2.0750E-05 808.0
t_composition(:,11)= ! Pb Coolant in interassembly gap; density= 10.402 g/cc
PB2047 PB204K 4.2322E-04 808.0
PB2067 PB206K 7.2854E-03 808.0
PB2077 PB207K 6.6808E-03 808.0
PB2087 PB208K 1.5840E-02 808.0
/
The superposition rule is depicted in Figure 6. The first two boxes represent First step to generate a TWODANT spectrum and the third up and low two boxes represent Second step for non-fuel and fuel regions, respectively. If c_geometry_type=mixture, the 0D UFG solution of mixture is adjusted by the ratio of the TWODANT spectrum to the 0D solution condensed to the TWODANT group structure. If the TWODANT group structure is UFG, just the TWODANT spectrum is used as a weighting function for condensation. If c_geometry_type is not mixture, each region-wise UFG solution is adjusted by the ratio of the TWODANT spectrum to the whole domain-averaged solution condensed to the TWODANT group structure. To simply state, the adjusted region-wise UFG solution is obtained by multiplying the spatial self-shielding factor obtained by the MC2-3 1D calculation to the TWODANT spectrum.
Figure 6: MC2-3 cross section generation procedure with the axial leakage effect considered using TWODANT
Without l_spatial_homogenization=F in an input, which is an easy mistake to make, one will end up using the assembly average cross section for each region in heterogeneous fine-mesh transport calculation. Figure 7 shows the relative difference of assembly average cross section to hexagonal ring-wise fuel cross section for U-238 capture. These differences are basically the same as the spatial self-shielding factor of each ring: the ratio of hexagonal ring-wise flux to assembly average flux. Since spectrum is softer for peripheral regions than for central regions, central region flux is lower than the assembly average flux at low energy and higher at high energy. Thus, a test showed that the use of assembly average cross section instead of region-wise cross section resulted in about +400 pcm error in k-effective due to underestimation of low energy capture and overestimation of high energy fission.
Figure 7: Relative difference of assembly average cross section to hexagonal ring-wise fuel cross section for U-238 capture
For the non-fuel region, the setting is almost similar to the first step input except c_externalspectrum_ufg=rzmflx instead of l_twodant=T in the control block and i_externalspectrum(composition #)=TWODANT zone # in the material block. For reminder, TWODANT zone #s are found in the zones= section in the &twodant block of the MC2-3 input in First step. In this input, nine compositions are differentiated by the character from A to J omitting F, resulting in library IDs from to in the ISOXML file to be converted.
#!/bin/bash
# ***************************************************************************************
# LFR 127-pin fuel assembly
# Strategy:
# 1) Homogenize each axial region of fuel assembly radially -> 1041g MCC3 infinite medium
# 2) Represent axial regions in TWODANT -> 1041g RZMFLX
# 3) [Non-fuel regions] Collapse 1041g MCC3 infinite medium mixture with RZMFLX
# ** 4) [Fuel/Control] Collapse 1D MCC3 cylinder geometry with RZMFLX
# ***************************************************************************************
lib=/software/MCC3
cp ../../Step1/LFR_InnerFuel_HOM_1041g_TWODANT.mcc3.sh.rzmflx rzmflx
cat > input << EOF
&library
c_mcclibdir ="$lib/lib.mcc.new"
c_pwlibdir ="$lib/lib.pw.200.new","."
/
&control
c_group_structure =ANL9
i_number_region =9
c_geometry_type =mixture
i_scattering_order =3
c_externalspectrum_ufg =rzmflx
/
&material
i_externalspectrum(1)=1
t_composition(:, 1)=
! A=Lower Core Plate (AISI 316, DS4-Wrapper, Pb)
FE54_7 FE54A 2.3571E-03 693.0
FE56_7 FE56A 3.7002E-02 693.0
FE57_7 FE57A 8.5453E-04 693.0
FE58_7 FE58A 1.1372E-04 693.0
NI58_7 NI58A 4.9645E-03 693.0
NI60_7 NI60A 1.9123E-03 693.0
NI61_7 NI61A 8.3135E-05 693.0
NI62_7 NI62A 2.6501E-04 693.0
NI64_7 NI64A 6.7529E-05 693.0
CR50_7 CR50A 4.6700E-04 693.0
CR52_7 CR52A 9.0056E-03 693.0
CR53_7 CR53A 1.0212E-03 693.0
CR54_7 CR54A 2.5419E-04 693.0
MN55_7 MN55A 6.8040E-04 693.0
MO92_7 MO92A 1.2088E-04 693.0
MO94_7 MO94A 7.5345E-05 693.0
MO95_7 MO95A 1.2968E-04 693.0
MO96_7 MO96A 1.3587E-04 693.0
MO97_7 MO97A 7.7789E-05 693.0
MO98_7 MO98A 1.9655E-04 693.0
MO1007 MO100A 7.8441E-05 693.0
SI28_7 SI28A 6.3469E-04 693.0
SI29_7 SI29A 3.2228E-05 693.0
SI30_7 SI30A 2.1245E-05 693.0
C____7 CA 1.4140E-04 693.0
P31__7 P31A 2.9631E-05 693.0
S32__7 S32A 1.5017E-05 693.0
S33__7 S33A 1.2022E-07 693.0
S34__7 S34A 6.7864E-07 693.0
S36__7 S36A 3.1638E-09 693.0
TI46_7 TI46A 4.3921E-06 693.0
TI47_7 TI47A 3.9608E-06 693.0
TI48_7 TI48A 3.9246E-05 693.0
TI49_7 TI49A 2.8801E-06 693.0
TI50_7 TI50A 2.7577E-06 693.0
V____7 VA 3.7518E-06 693.0
ZR90_7 ZR90A 1.0779E-06 693.0
ZR91_7 ZR91A 2.3507E-07 693.0
ZR92_7 ZR92A 3.5931E-07 693.0
ZR94_7 ZR94A 3.6413E-07 693.0
ZR96_7 ZR96A 5.8663E-08 693.0
W182_7 W182A 2.7550E-07 693.0
W183_7 W183A 1.4877E-07 693.0
W184_7 W184A 3.1979E-07 693.0
W186_7 W186A 2.9556E-07 693.0
CU63_7 CU63A 2.0804E-06 693.0
CU65_7 CU65A 9.2725E-07 693.0
CO59_7 CO59A 3.2430E-06 693.0
CA40_7 CA40A 4.6229E-06 693.0
CA42_7 CA42A 3.0854E-08 693.0
CA43_7 CA43A 6.4378E-09 693.0
CA44_7 CA44A 9.9476E-08 693.0
CA46_7 CA46A 1.9075E-10 693.0
CA48_7 CA48A 8.9176E-09 693.0
NB93_7 NB93A 1.0286E-06 693.0
N14__7 N14A 6.7973E-06 693.0
N15__7 N15A 2.5106E-08 693.0
AL27_7 AL27A 3.5417E-06 693.0
TA1817 TA181A 5.2812E-07 693.0
B10__7 B10A 7.0367E-07 693.0
B11__7 B11A 2.8324E-06 693.0
PB2047 PB204A 1.1702E-04 693.0
PB2067 PB206A 2.0144E-03 693.0
PB2077 PB207A 1.8472E-03 693.0
PB2087 PB208A 4.3799E-03 693.0
i_externalspectrum(2)=2
t_composition(:, 2)=
! B=Inlet Wrapper (DS4-Wrapper, Pb)
FE54_7 FE54B 2.6147E-04 693.0
FE56_7 FE56B 4.1044E-03 693.0
FE57_7 FE57B 9.4790E-05 693.0
FE58_7 FE58B 1.2615E-05 693.0
NI58_7 NI58B 6.8720E-04 693.0
NI60_7 NI60B 2.6471E-04 693.0
NI61_7 NI61B 1.1508E-05 693.0
NI62_7 NI62B 3.6683E-05 693.0
NI64_7 NI64B 9.3475E-06 693.0
CR50_7 CR50B 4.6316E-05 693.0
CR52_7 CR52B 8.9315E-04 693.0
CR53_7 CR53B 1.0128E-04 693.0
CR54_7 CR54B 2.5210E-05 693.0
MN55_7 MN55B 1.0437E-04 693.0
MO92_7 MO92B 8.8679E-06 693.0
MO94_7 MO94B 5.5275E-06 693.0
MO95_7 MO95B 9.5133E-06 693.0
MO96_7 MO96B 9.9675E-06 693.0
MO97_7 MO97B 5.7068E-06 693.0
MO98_7 MO98B 1.4419E-05 693.0
MO1007 MO100B 5.7546E-06 693.0
SI28_7 SI28B 1.0670E-04 693.0
SI29_7 SI29B 5.4179E-06 693.0
SI30_7 SI30B 3.5715E-06 693.0
C____7 CB 2.8642E-05 693.0
P31__7 P31B 5.5534E-06 693.0
S32__7 S32B 1.6977E-06 693.0
S33__7 S33B 1.3592E-08 693.0
S34__7 S34B 7.6723E-08 693.0
S36__7 S36B 3.5768E-10 693.0
TI46_7 TI46B 2.6352E-06 693.0
TI47_7 TI47B 2.3765E-06 693.0
TI48_7 TI48B 2.3548E-05 693.0
TI49_7 TI49B 1.7281E-06 693.0
TI50_7 TI50B 1.6546E-06 693.0
V____7 VB 2.2511E-06 693.0
ZR90_7 ZR90B 6.4675E-07 693.0
ZR91_7 ZR91B 1.4104E-07 693.0
ZR92_7 ZR92B 2.1558E-07 693.0
ZR94_7 ZR94B 2.1848E-07 693.0
ZR96_7 ZR96B 3.5198E-08 693.0
W182_7 W182B 1.6530E-07 693.0
W183_7 W183B 8.9261E-08 693.0
W184_7 W184B 1.9187E-07 693.0
W186_7 W186B 1.7734E-07 693.0
CU63_7 CU63B 1.2482E-06 693.0
CU65_7 CU65B 5.5635E-07 693.0
CO59_7 CO59B 1.9458E-06 693.0
CA40_7 CA40B 2.7737E-06 693.0
CA42_7 CA42B 1.8512E-08 693.0
CA43_7 CA43B 3.8627E-09 693.0
CA44_7 CA44B 5.9686E-08 693.0
CA46_7 CA46B 1.1445E-10 693.0
CA48_7 CA48B 5.3506E-09 693.0
NB93_7 NB93B 6.1715E-07 693.0
N14__7 N14B 4.0784E-06 693.0
N15__7 N15B 1.5064E-08 693.0
AL27_7 AL27B 2.1250E-06 693.0
TA1817 TA181B 3.1687E-07 693.0
B10__7 B10B 4.2220E-07 693.0
B11__7 B11B 1.6994E-06 693.0
PB2047 PB204B 3.8856E-04 693.0
PB2067 PB206B 6.6887E-03 693.0
PB2077 PB207B 6.1336E-03 693.0
PB2087 PB208B 1.4543E-02 693.0
i_externalspectrum(3)=3
t_composition(:, 3)=
! C=Lower Bundle Grid and Pins Plug (DS4-Wrapper, DS4-Clad, Pb)
FE54_7 FE54C 1.2517E-03 693.0
FE56_7 FE56C 1.9649E-02 693.0
FE57_7 FE57C 4.5378E-04 693.0
FE58_7 FE58C 6.0390E-05 693.0
NI58_7 NI58C 3.2898E-03 693.0
NI60_7 NI60C 1.2672E-03 693.0
NI61_7 NI61C 5.5090E-05 693.0
NI62_7 NI62C 1.7561E-04 693.0
NI64_7 NI64C 4.4748E-05 693.0
CR50_7 CR50C 2.2172E-04 693.0
CR52_7 CR52C 4.2757E-03 693.0
CR53_7 CR53C 4.8483E-04 693.0
CR54_7 CR54C 1.2068E-04 693.0
MN55_7 MN55C 4.9962E-04 693.0
MO92_7 MO92C 4.2453E-05 693.0
MO94_7 MO94C 2.6461E-05 693.0
MO95_7 MO95C 4.5542E-05 693.0
MO96_7 MO96C 4.7716E-05 693.0
MO97_7 MO97C 2.7320E-05 693.0
MO98_7 MO98C 6.9028E-05 693.0
MO1007 MO100C 2.7548E-05 693.0
SI28_7 SI28C 5.1079E-04 693.0
SI29_7 SI29C 2.5937E-05 693.0
SI30_7 SI30C 1.7098E-05 693.0
C____7 CC 1.3712E-04 693.0
P31__7 P31C 2.6585E-05 693.0
S32__7 S32C 8.1275E-06 693.0
S33__7 S33C 6.5068E-08 693.0
S34__7 S34C 3.6729E-07 693.0
S36__7 S36C 1.7123E-09 693.0
TI46_7 TI46C 1.2615E-05 693.0
TI47_7 TI47C 1.1377E-05 693.0
TI48_7 TI48C 1.1273E-04 693.0
TI49_7 TI49C 8.2727E-06 693.0
TI50_7 TI50C 7.9210E-06 693.0
V____7 VC 1.0776E-05 693.0
ZR90_7 ZR90C 3.0962E-06 693.0
ZR91_7 ZR91C 6.7520E-07 693.0
ZR92_7 ZR92C 1.0321E-06 693.0
ZR94_7 ZR94C 1.0459E-06 693.0
ZR96_7 ZR96C 1.6850E-07 693.0
W182_7 W182C 7.9132E-07 693.0
W183_7 W183C 4.2731E-07 693.0
W184_7 W184C 9.1853E-07 693.0
W186_7 W186C 8.4895E-07 693.0
CU63_7 CU63C 5.9755E-06 693.0
CU65_7 CU65C 2.6634E-06 693.0
CO59_7 CO59C 9.3151E-06 693.0
CA40_7 CA40C 1.3278E-05 693.0
CA42_7 CA42C 8.8623E-08 693.0
CA43_7 CA43C 1.8492E-08 693.0
CA44_7 CA44C 2.8573E-07 693.0
CA46_7 CA46C 5.4790E-10 693.0
CA48_7 CA48C 2.5614E-08 693.0
NB93_7 NB93C 2.9544E-06 693.0
N14__7 N14C 1.9524E-05 693.0
N15__7 N15C 7.2114E-08 693.0
AL27_7 AL27C 1.0173E-05 693.0
TA1817 TA181C 1.5169E-06 693.0
B10__7 B10C 2.0212E-06 693.0
B11__7 B11C 8.1355E-06 693.0
PB2047 PB204C 2.5702E-04 693.0
PB2067 PB206C 4.4244E-03 693.0
PB2077 PB207C 4.0572E-03 693.0
PB2087 PB208C 9.6199E-03 693.0
i_externalspectrum(4)=4
t_composition(:, 4)=
! D=Lower Gas Plenum (tube) (DS4-Wrapper, DS4-Clad, Helium, Pb)
FE54_7 FE54D 9.7769E-04 693.0
FE56_7 FE56D 1.5348E-02 693.0
FE57_7 FE57D 3.5445E-04 693.0
FE58_7 FE58D 4.7170E-05 693.0
NI58_7 NI58D 2.5696E-03 693.0
NI60_7 NI60D 9.8982E-04 693.0
NI61_7 NI61D 4.3031E-05 693.0
NI62_7 NI62D 1.3717E-04 693.0
NI64_7 NI64D 3.4953E-05 693.0
CR50_7 CR50D 1.7319E-04 693.0
CR52_7 CR52D 3.3398E-03 693.0
CR53_7 CR53D 3.7870E-04 693.0
CR54_7 CR54D 9.4267E-05 693.0
MN55_7 MN55D 3.9025E-04 693.0
MO92_7 MO92D 3.3160E-05 693.0
MO94_7 MO94D 2.0669E-05 693.0
MO95_7 MO95D 3.5573E-05 693.0
MO96_7 MO96D 3.7271E-05 693.0
MO97_7 MO97D 2.1339E-05 693.0
MO98_7 MO98D 5.3918E-05 693.0
MO1007 MO100D 2.1518E-05 693.0
SI28_7 SI28D 3.9897E-04 693.0
SI29_7 SI29D 2.0259E-05 693.0
SI30_7 SI30D 1.3355E-05 693.0
C____7 CD 1.0710E-04 693.0
P31__7 P31D 2.0766E-05 693.0
S32__7 S32D 6.3484E-06 693.0
S33__7 S33D 5.0824E-08 693.0
S34__7 S34D 2.8689E-07 693.0
S36__7 S36D 1.3375E-09 693.0
TI46_7 TI46D 9.8539E-06 693.0
TI47_7 TI47D 8.8864E-06 693.0
TI48_7 TI48D 8.8052E-05 693.0
TI49_7 TI49D 6.4618E-06 693.0
TI50_7 TI50D 6.1870E-06 693.0
V____7 VD 8.4174E-06 693.0
ZR90_7 ZR90D 2.4184E-06 693.0
ZR91_7 ZR91D 5.2739E-07 693.0
ZR92_7 ZR92D 8.0613E-07 693.0
ZR94_7 ZR94D 8.1694E-07 693.0
ZR96_7 ZR96D 1.3161E-07 693.0
W182_7 W182D 6.1810E-07 693.0
W183_7 W183D 3.3377E-07 693.0
W184_7 W184D 7.1746E-07 693.0
W186_7 W186D 6.6311E-07 693.0
CU63_7 CU63D 4.6675E-06 693.0
CU65_7 CU65D 2.0804E-06 693.0
CO59_7 CO59D 7.2760E-06 693.0
CA40_7 CA40D 1.0372E-05 693.0
CA42_7 CA42D 6.9223E-08 693.0
CA43_7 CA43D 1.4444E-08 693.0
CA44_7 CA44D 2.2318E-07 693.0
CA46_7 CA46D 4.2796E-10 693.0
CA48_7 CA48D 2.0007E-08 693.0
NB93_7 NB93D 2.3077E-06 693.0
N14__7 N14D 1.5250E-05 693.0
N15__7 N15D 5.6328E-08 693.0
AL27_7 AL27D 7.9461E-06 693.0
TA1817 TA181D 1.1849E-06 693.0
B10__7 B10D 1.5787E-06 693.0
B11__7 B11D 6.3546E-06 693.0
HE4__7 HE4D 6.8773E-06 693.0
PB2047 PB204D 1.7712E-04 693.0
PB2067 PB206D 3.0489E-03 693.0
PB2077 PB207D 2.7959E-03 693.0
PB2087 PB208D 6.6292E-03 693.0
i_externalspectrum(5)=5
t_composition(:, 5)=
! E=Lower thermal insulator (DS4-Wrapper, DS4-Clad, Helium, Pb, YSZ)
FE54_7 FE54E 7.5276E-04 693.0
FE56_7 FE56E 1.1817E-02 693.0
FE57_7 FE57E 2.7290E-04 693.0
FE58_7 FE58E 3.6318E-05 693.0
NI58_7 NI58E 1.9785E-03 693.0
NI60_7 NI60E 7.6209E-04 693.0
NI61_7 NI61E 3.3131E-05 693.0
NI62_7 NI62E 1.0561E-04 693.0
NI64_7 NI64E 2.6911E-05 693.0
CR50_7 CR50E 1.3334E-04 693.0
CR52_7 CR52E 2.5714E-03 693.0
CR53_7 CR53E 2.9157E-04 693.0
CR54_7 CR54E 7.2579E-05 693.0
MN55_7 MN55E 3.0047E-04 693.0
MO92_7 MO92E 2.5531E-05 693.0
MO94_7 MO94E 1.5914E-05 693.0
MO95_7 MO95E 2.7389E-05 693.0
MO96_7 MO96E 2.8696E-05 693.0
MO97_7 MO97E 1.6430E-05 693.0
MO98_7 MO98E 4.1513E-05 693.0
MO1007 MO100E 1.6567E-05 693.0
SI28_7 SI28E 3.0718E-04 693.0
SI29_7 SI29E 1.5598E-05 693.0
SI30_7 SI30E 1.0282E-05 693.0
C____7 CE 8.2461E-05 693.0
P31__7 P31E 1.5988E-05 693.0
S32__7 S32E 4.8878E-06 693.0
S33__7 S33E 3.9131E-08 693.0
S34__7 S34E 2.2089E-07 693.0
S36__7 S36E 1.0298E-09 693.0
TI46_7 TI46E 7.5868E-06 693.0
TI47_7 TI47E 6.8419E-06 693.0
TI48_7 TI48E 6.7794E-05 693.0
TI49_7 TI49E 4.9751E-06 693.0
TI50_7 TI50E 4.7636E-06 693.0
V____7 VE 6.4809E-06 693.0
ZR90_7 ZR90E 3.8368E-03 693.0
ZR91_7 ZR91E 8.3671E-04 693.0
ZR92_7 ZR92E 1.2789E-03 693.0
ZR94_7 ZR94E 1.2961E-03 693.0
ZR96_7 ZR96E 2.0880E-04 693.0
W182_7 W182E 4.7589E-07 693.0
W183_7 W183E 2.5698E-07 693.0
W184_7 W184E 5.5240E-07 693.0
W186_7 W186E 5.1055E-07 693.0
CU63_7 CU63E 3.5936E-06 693.0
CU65_7 CU65E 1.6017E-06 693.0
CO59_7 CO59E 5.6020E-06 693.0
CA40_7 CA40E 7.9856E-06 693.0
CA42_7 CA42E 5.3297E-08 693.0
CA43_7 CA43E 1.1121E-08 693.0
CA44_7 CA44E 1.7184E-07 693.0
CA46_7 CA46E 3.2950E-10 693.0
CA48_7 CA48E 1.5404E-08 693.0
NB93_7 NB93E 1.7768E-06 693.0
N14__7 N14E 1.1742E-05 693.0
N15__7 N15E 4.3369E-08 693.0
AL27_7 AL27E 6.1180E-06 693.0
TA1817 TA181E 9.1226E-07 693.0
B10__7 B10E 1.2155E-06 693.0
B11__7 B11E 4.8926E-06 693.0
HE4__7 HE4E 8.2368E-07 693.0
PB2047 PB204E 1.7712E-04 693.0
PB2067 PB206E 3.0489E-03 693.0
PB2077 PB207E 2.7959E-03 693.0
PB2087 PB208E 6.6292E-03 693.0
Y89__7 Y89E 1.2963E-03 693.0
O16__7 O16E 1.6852E-02 693.0
! Removed fuel since the 1D cross sections are collapsed with RZMFLX rather than the homogeneous ones
i_externalspectrum(6)=7 ! numbering is offset due to removal of composition 6
t_composition(:, 6)=
! G=Upper thermal insulator (DS4-Wrapper, DS4-Clad, Helium, Pb, YSZ)
FE54_7 FE54G 7.5276E-04 923.0
FE56_7 FE56G 1.1817E-02 923.0
FE57_7 FE57G 2.7290E-04 923.0
FE58_7 FE58G 3.6318E-05 923.0
NI58_7 NI58G 1.9785E-03 923.0
NI60_7 NI60G 7.6209E-04 923.0
NI61_7 NI61G 3.3131E-05 923.0
NI62_7 NI62G 1.0561E-04 923.0
NI64_7 NI64G 2.6911E-05 923.0
CR50_7 CR50G 1.3334E-04 923.0
CR52_7 CR52G 2.5714E-03 923.0
CR53_7 CR53G 2.9157E-04 923.0
CR54_7 CR54G 7.2579E-05 923.0
MN55_7 MN55G 3.0047E-04 923.0
MO92_7 MO92G 2.5531E-05 923.0
MO94_7 MO94G 1.5914E-05 923.0
MO95_7 MO95G 2.7389E-05 923.0
MO96_7 MO96G 2.8696E-05 923.0
MO97_7 MO97G 1.6430E-05 923.0
MO98_7 MO98G 4.1513E-05 923.0
MO1007 MO100G 1.6567E-05 923.0
SI28_7 SI28G 3.0718E-04 923.0
SI29_7 SI29G 1.5598E-05 923.0
SI30_7 SI30G 1.0282E-05 923.0
C____7 CG 8.2461E-05 923.0
P31__7 P31G 1.5988E-05 923.0
S32__7 S32G 4.8878E-06 923.0
S33__7 S33G 3.9131E-08 923.0
S34__7 S34G 2.2089E-07 923.0
S36__7 S36G 1.0298E-09 923.0
TI46_7 TI46G 7.5868E-06 923.0
TI47_7 TI47G 6.8419E-06 923.0
TI48_7 TI48G 6.7794E-05 923.0
TI49_7 TI49G 4.9751E-06 923.0
TI50_7 TI50G 4.7636E-06 923.0
V____7 VG 6.4809E-06 923.0
ZR90_7 ZR90G 3.8368E-03 923.0
ZR91_7 ZR91G 8.3671E-04 923.0
ZR92_7 ZR92G 1.2789E-03 923.0
ZR94_7 ZR94G 1.2961E-03 923.0
ZR96_7 ZR96G 2.0880E-04 923.0
W182_7 W182G 4.7589E-07 923.0
W183_7 W183G 2.5698E-07 923.0
W184_7 W184G 5.5240E-07 923.0
W186_7 W186G 5.1055E-07 923.0
CU63_7 CU63G 3.5936E-06 923.0
CU65_7 CU65G 1.6017E-06 923.0
CO59_7 CO59G 5.6020E-06 923.0
CA40_7 CA40G 7.9856E-06 923.0
CA42_7 CA42G 5.3297E-08 923.0
CA43_7 CA43G 1.1121E-08 923.0
CA44_7 CA44G 1.7184E-07 923.0
CA46_7 CA46G 3.2950E-10 923.0
CA48_7 CA48G 1.5404E-08 923.0
NB93_7 NB93G 1.7768E-06 923.0
N14__7 N14G 1.1742E-05 923.0
N15__7 N15G 4.3369E-08 923.0
AL27_7 AL27G 6.1180E-06 923.0
TA1817 TA181G 9.1226E-07 923.0
B10__7 B10G 1.2155E-06 923.0
B11__7 B11G 4.8926E-06 923.0
HE4__7 HE4G 8.2368E-07 923.0
PB2047 PB204G 1.7712E-04 923.0
PB2067 PB206G 3.0489E-03 923.0
PB2077 PB207G 2.7959E-03 923.0
PB2087 PB208G 6.6292E-03 923.0
Y89__7 Y89G 1.2963E-03 923.0
O16__7 O16G 1.6852E-02 923.0
i_externalspectrum(7)=8
t_composition(:, 7)=
! H=Upper gas plenum (spring) (DS4-Wrapper, DS4-Clad, Helium, Pb)
FE54_7 FE54H 8.7383E-04 923.0
FE56_7 FE56H 1.3717E-02 923.0
FE57_7 FE57H 3.1679E-04 923.0
FE58_7 FE58H 4.2159E-05 923.0
NI58_7 NI58H 2.2967E-03 923.0
NI60_7 NI60H 8.8466E-04 923.0
NI61_7 NI61H 3.8459E-05 923.0
NI62_7 NI62H 1.2260E-04 923.0
NI64_7 NI64H 3.1240E-05 923.0
CR50_7 CR50H 1.5479E-04 923.0
CR52_7 CR52H 2.9850E-03 923.0
CR53_7 CR53H 3.3847E-04 923.0
CR54_7 CR54H 8.4252E-05 923.0
MN55_7 MN55H 3.4880E-04 923.0
MO92_7 MO92H 2.9637E-05 923.0
MO94_7 MO94H 1.8473E-05 923.0
MO95_7 MO95H 3.1794E-05 923.0
MO96_7 MO96H 3.3312E-05 923.0
MO97_7 MO97H 1.9072E-05 923.0
MO98_7 MO98H 4.8190E-05 923.0
MO1007 MO100H 1.9232E-05 923.0
SI28_7 SI28H 3.5659E-04 923.0
SI29_7 SI29H 1.8107E-05 923.0
SI30_7 SI30H 1.1936E-05 923.0
C____7 CH 9.5723E-05 923.0
P31__7 P31H 1.8560E-05 923.0
S32__7 S32H 5.6739E-06 923.0
S33__7 S33H 4.5425E-08 923.0
S34__7 S34H 2.5641E-07 923.0
S36__7 S36H 1.1954E-09 923.0
TI46_7 TI46H 8.8071E-06 923.0
TI47_7 TI47H 7.9424E-06 923.0
TI48_7 TI48H 7.8698E-05 923.0
TI49_7 TI49H 5.7753E-06 923.0
TI50_7 TI50H 5.5298E-06 923.0
V____7 VH 7.5232E-06 923.0
ZR90_7 ZR90H 2.1615E-06 923.0
ZR91_7 ZR91H 4.7137E-07 923.0
ZR92_7 ZR92H 7.2049E-07 923.0
ZR94_7 ZR94H 7.3016E-07 923.0
ZR96_7 ZR96H 1.1763E-07 923.0
W182_7 W182H 5.5243E-07 923.0
W183_7 W183H 2.9831E-07 923.0
W184_7 W184H 6.4124E-07 923.0
W186_7 W186H 5.9267E-07 923.0
CU63_7 CU63H 4.1716E-06 923.0
CU65_7 CU65H 1.8593E-06 923.0
CO59_7 CO59H 6.5030E-06 923.0
CA40_7 CA40H 9.2699E-06 923.0
CA42_7 CA42H 6.1869E-08 923.0
CA43_7 CA43H 1.2909E-08 923.0
CA44_7 CA44H 1.9947E-07 923.0
CA46_7 CA46H 3.8250E-10 923.0
CA48_7 CA48H 1.7882E-08 923.0
NB93_7 NB93H 2.0625E-06 923.0
N14__7 N14H 1.3630E-05 923.0
N15__7 N15H 5.0344E-08 923.0
AL27_7 AL27H 7.1020E-06 923.0
TA1817 TA181H 1.0590E-06 923.0
B10__7 B10H 1.4110E-06 923.0
B11__7 B11H 5.6795E-06 923.0
HE4__7 HE4H 7.6960E-06 923.0
PB2047 PB204H 1.7712E-04 923.0
PB2067 PB206H 3.0489E-03 923.0
PB2077 PB207H 2.7959E-03 923.0
PB2087 PB208H 6.6292E-03 923.0
i_externalspectrum(8)=9
t_composition(:,8)=
! I=Upper Bundle Grid and Pins Plug (DS4-Wrapper, DS4-Clad, Pb)
FE54_7 FE54I 1.2517E-03 923.0
FE56_7 FE56I 1.9649E-02 923.0
FE57_7 FE57I 4.5378E-04 923.0
FE58_7 FE58I 6.0390E-05 923.0
NI58_7 NI58I 3.2898E-03 923.0
NI60_7 NI60I 1.2672E-03 923.0
NI61_7 NI61I 5.5090E-05 923.0
NI62_7 NI62I 1.7561E-04 923.0
NI64_7 NI64I 4.4748E-05 923.0
CR50_7 CR50I 2.2172E-04 923.0
CR52_7 CR52I 4.2757E-03 923.0
CR53_7 CR53I 4.8483E-04 923.0
CR54_7 CR54I 1.2068E-04 923.0
MN55_7 MN55I 4.9962E-04 923.0
MO92_7 MO92I 4.2453E-05 923.0
MO94_7 MO94I 2.6461E-05 923.0
MO95_7 MO95I 4.5542E-05 923.0
MO96_7 MO96I 4.7716E-05 923.0
MO97_7 MO97I 2.7320E-05 923.0
MO98_7 MO98I 6.9028E-05 923.0
MO1007 MO100I 2.7548E-05 923.0
SI28_7 SI28I 5.1079E-04 923.0
SI29_7 SI29I 2.5937E-05 923.0
SI30_7 SI30I 1.7098E-05 923.0
C____7 CI 1.3712E-04 923.0
P31__7 P31I 2.6585E-05 923.0
S32__7 S32I 8.1275E-06 923.0
S33__7 S33I 6.5068E-08 923.0
S34__7 S34I 3.6729E-07 923.0
S36__7 S36I 1.7123E-09 923.0
TI46_7 TI46I 1.2615E-05 923.0
TI47_7 TI47I 1.1377E-05 923.0
TI48_7 TI48I 1.1273E-04 923.0
TI49_7 TI49I 8.2727E-06 923.0
TI50_7 TI50I 7.9210E-06 923.0
V____7 VI 1.0776E-05 923.0
ZR90_7 ZR90I 3.0962E-06 923.0
ZR91_7 ZR91I 6.7520E-07 923.0
ZR92_7 ZR92I 1.0321E-06 923.0
ZR94_7 ZR94I 1.0459E-06 923.0
ZR96_7 ZR96I 1.6850E-07 923.0
W182_7 W182I 7.9132E-07 923.0
W183_7 W183I 4.2731E-07 923.0
W184_7 W184I 9.1853E-07 923.0
W186_7 W186I 8.4895E-07 923.0
CU63_7 CU63I 5.9755E-06 923.0
CU65_7 CU65I 2.6634E-06 923.0
CO59_7 CO59I 9.3151E-06 923.0
CA40_7 CA40I 1.3278E-05 923.0
CA42_7 CA42I 8.8623E-08 923.0
CA43_7 CA43I 1.8492E-08 923.0
CA44_7 CA44I 2.8573E-07 923.0
CA46_7 CA46I 5.4790E-10 923.0
CA48_7 CA48I 2.5614E-08 923.0
NB93_7 NB93I 2.9544E-06 923.0
N14__7 N14I 1.9524E-05 923.0
N15__7 N15I 7.2114E-08 923.0
AL27_7 AL27I 1.0173E-05 923.0
TA1817 TA181I 1.5169E-06 923.0
B10__7 B10I 2.0212E-06 923.0
B11__7 B11I 8.1355E-06 923.0
PB2047 PB204I 2.5702E-04 923.0
PB2067 PB206I 4.4244E-03 923.0
PB2077 PB207I 4.0572E-03 923.0
PB2087 PB208I 9.6199E-03 923.0
i_externalspectrum(9)=10
t_composition(:, 9)=
! J=Outlet Wrapper (DS4-Wrapper, Pb)
FE54_7 FE54J 7.6045E-04 923.0
FE56_7 FE56J 1.1937E-02 923.0
FE57_7 FE57J 2.7569E-04 923.0
FE58_7 FE58J 3.6689E-05 923.0
NI58_7 NI58J 1.9987E-03 923.0
NI60_7 NI60J 7.6988E-04 923.0
NI61_7 NI61J 3.3469E-05 923.0
NI62_7 NI62J 1.0669E-04 923.0
NI64_7 NI64J 2.7186E-05 923.0
CR50_7 CR50J 1.3471E-04 923.0
CR52_7 CR52J 2.5977E-03 923.0
CR53_7 CR53J 2.9456E-04 923.0
CR54_7 CR54J 7.3321E-05 923.0
MN55_7 MN55J 3.0354E-04 923.0
MO92_7 MO92J 2.5792E-05 923.0
MO94_7 MO94J 1.6076E-05 923.0
MO95_7 MO95J 2.7669E-05 923.0
MO96_7 MO96J 2.8990E-05 923.0
MO97_7 MO97J 1.6598E-05 923.0
MO98_7 MO98J 4.1938E-05 923.0
MO1007 MO100J 1.6737E-05 923.0
SI28_7 SI28J 3.1032E-04 923.0
SI29_7 SI29J 1.5757E-05 923.0
SI30_7 SI30J 1.0387E-05 923.0
C____7 CJ 8.3303E-05 923.0
P31__7 P31J 1.6152E-05 923.0
S32__7 S32J 4.9378E-06 923.0
S33__7 S33J 3.9531E-08 923.0
S34__7 S34J 2.2314E-07 923.0
S36__7 S36J 1.0403E-09 923.0
TI46_7 TI46J 7.6644E-06 923.0
TI47_7 TI47J 6.9119E-06 923.0
TI48_7 TI48J 6.8487E-05 923.0
TI49_7 TI49J 5.0260E-06 923.0
TI50_7 TI50J 4.8123E-06 923.0
V____7 VJ 6.5471E-06 923.0
ZR90_7 ZR90J 1.8810E-06 923.0
ZR91_7 ZR91J 4.1021E-07 923.0
ZR92_7 ZR92J 6.2701E-07 923.0
ZR94_7 ZR94J 6.3542E-07 923.0
ZR96_7 ZR96J 1.0237E-07 923.0
W182_7 W182J 4.8076E-07 923.0
W183_7 W183J 2.5961E-07 923.0
W184_7 W184J 5.5804E-07 923.0
W186_7 W186J 5.1577E-07 923.0
CU63_7 CU63J 3.6304E-06 923.0
CU65_7 CU65J 1.6181E-06 923.0
CO59_7 CO59J 5.6593E-06 923.0
CA40_7 CA40J 8.0672E-06 923.0
CA42_7 CA42J 5.3842E-08 923.0
CA43_7 CA43J 1.1234E-08 923.0
CA44_7 CA44J 1.7359E-07 923.0
CA46_7 CA46J 3.3287E-10 923.0
CA48_7 CA48J 1.5562E-08 923.0
NB93_7 NB93J 1.7949E-06 923.0
N14__7 N14J 1.1862E-05 923.0
N15__7 N15J 4.3812E-08 923.0
AL27_7 AL27J 6.1805E-06 923.0
TA1817 TA181J 9.2159E-07 923.0
B10__7 B10J 1.2279E-06 923.0
B11__7 B11J 4.9426E-06 923.0
PB2047 PB204J 3.2241E-04 923.0
PB2067 PB206J 5.5500E-03 923.0
PB2077 PB207J 5.0894E-03 923.0
PB2087 PB208J 1.2067E-02 923.0
/
EOF
################################################
# End of the MCC3 input file
################################################
# $lib/mcc3.x
~/codes/mcc3/src/mcc3.x
mv ISOTXS.merged $0.ISOTXS
Run scripts and merging ISOTXS files
The process to prepare the final isoxml file is described here. First, the TWODANT running script is run as
cd Step1
./LFR_InnerFuel_HOM_1041g_TWODANT.mcc3.sh
Once the LFR_InnerFuel_HOM_1041g_TWODANT.mcc3.sh.rzmflx file is created, two scripts need to be run as
cd ../Step2/Fuel
./LFR_127Pin_Fuel_1D_9g.mcc3.sh
cd ../NonFuel
./LFR_127Pin_NonFuel_9g.mcc3.sh
cd ../../
The order to run two scripts doesn't matter. Once the above two scripts are run, LFR_127Pin_Fuel_1D_9g.mcc3.sh.ISOTXS and LFR_127Pin_NonFuel_9g.mcc3.sh.ISOTXS files are created. The next step is to convert those two ISOTXS files to isoxml files by running
griffin-opt --isoxml-nisotxs ./Step2/Fuel/LFR_127Pin_Fuel_1D_9g.mcc3.sh.ISOTXS
griffin-opt --isoxml-nisotxs ./Step2/NonFuel/LFR_127Pin_NonFuel_9g.mcc3.sh.ISOTXS
, which creates LFR_127Pin_Fuel_1D_9g.mcc3.sh.xml and LFR_127Pin_NonFuel_9g.mcc3.sh.xml files in respective folders. Before merging these two files, library IDs in LFR_127Pin_Fuel_1D_9g.mcc3.sh.xml need to be manually shifted by the number of library IDs in LFR_127Pin_NonFuel_9g.mcc3.sh.xml. Without this manual change of the library ID, two xml files cannot be merged. Finally, two xml files are merged to produce the final xml file as
griffin-opt --isoxml-merge ./Step2/Fuel/LFR_127Pin_Fuel_1D_9g.mcc3.sh.xml ./Step2/NonFuel/LFR_127Pin_NonFuel_9g.mcc3.sh.xml > LFR_127Pin_9g.xml
In the final xml file, one will note that all the cross sections are tabulated at a single grid value of in the grid name of Tfuel. This is the default setting in the conversion of ISOTXS to ISOXML. This is obviously wrong, but not of a concern though, because this work does not account for multiphysics coupling and temperature interpolation is not involved. For a Multiphysics coupled calculation, this part needs to be treated correctly.
Griffin Model
This section decribes the input file for Griffin using the DFEM-SN solver with the CMFD acceleration.
Input parameters
Defining input parameters in advance is beneficial to make the input tractable because the same value can be used in multiple places. Radial and axial specifications of pin and assembly, block IDs and material IDs to be assigned to block IDs and the total power are defined as input parameters to be used in the main input later. It should be noted that Library IDs need to be consistent with those in the final xml file.
# Geometry Info.
# ==============================================================================
half_pinpitch = 0.0067123105 # m
fuel_r_o = 0.004318648 # m
fuel_r_i = 0.00202042 # m
clad_r_i = 0.004495 # m
clad_r_o = 0.0054037675 # m
duct_thickness = 0.003533 # m
asmgap_thickness = 0.0018375 # m
flat_to_flat = 0.153424 # m
half_asmpitch = ${fparse flat_to_flat / 2 + duct_thickness + asmgap_thickness}
# Below are axial coordinates in meter.
hA = 0.1007 # Lower Core Plate
hB = 0.4086 # Inlet Wrapper
hC = 0.4742 # Lower Bundle Grid and Lower Pins Plug
hD = 1.3327 # Lower Gas Plenum
hE = 1.3479 # Lower Thermal Insulator
hF = 2.4086 # Active Fuel Region
hG = 2.4237 # Upper Thermal Insulator
hH = 2.5450 # Upper Gas Plenum
hI = 2.5955 # Upper Bundle Grid and Upper Pins Plug
hJ = 3.5342 # Outlet Wrapper
# Below are heights of each axial zone in meter.
dhA = ${fparse hA - 0.0}
dhB = ${fparse hB - hA}
dhC = ${fparse hC - hB}
dhD = ${fparse hD - hC}
dhE = ${fparse hE - hD}
dhF = ${fparse hF - hE}
dhG = ${fparse hG - hF}
dhH = ${fparse hH - hG}
dhI = ${fparse hI - hH}
dhJ = ${fparse hJ - hI}
# Below are the numbers of axial meshes per axial zone.
num_axmeshA = 1
num_axmeshB = 3
num_axmeshC = 1
num_axmeshD = 9
num_axmeshE = 1
num_axmeshF = 20
num_axmeshG = 1
num_axmeshH = 2
num_axmeshI = 1
num_axmeshJ = 9
# ==============================================================================
# Library IDs
# ==============================================================================
lid_A = 1
lid_B = 2
lid_C = 3
lid_D = 4
lid_E = 5
lid_G = 6
lid_H = 7
lid_I = 8
lid_J = 9
lid_F_lead = 11
lid_F_fuel_R1 = 12
lid_F_fuel_R2 = 13
lid_F_fuel_R3 = 14
lid_F_fuel_R4 = 15
lid_F_fuel_R5 = 16
lid_F_fuel_R6 = 17
lid_F_fuel_R7 = 18
lid_F_clad = 19
lid_F_duct = 20
lid_F_leadgap = 21
# ==============================================================================
# Material IDs
# ==============================================================================
mid_A = 100 # lid_A
mid_B = 200 # lid_B
mid_C = 300 # lid_C
# lid_D
mid_D_lead = 410
mid_D_clad = 420
mid_D_duct = 430
mid_D_tubemix = 440 # Plenum tube + Helium mixture
# lid_E
mid_E_lead = 510
mid_E_clad = 520
mid_E_duct = 530
mid_E_yszmix = 540 # YSZ + Helium mixture
mid_F_lead = 620 # lid_F_lead
mid_F_helium = 610 # lid_fuel_R1
mid_F_fuel_R1 = 601 # lid_fuel_R1
mid_F_fuel_R2 = 602 # lid_fuel_R2
mid_F_fuel_R3 = 603 # lid_fuel_R3
mid_F_fuel_R4 = 604 # lid_fuel_R4
mid_F_fuel_R5 = 605 # lid_fuel_R5
mid_F_fuel_R6 = 606 # lid_fuel_R6
mid_F_fuel_R7 = 607 # lid_fuel_R7
mid_F_clad = 640 # lid_F_clad
mid_F_duct = 650 # lid_F_duct
mid_F_leadgap = 630 # lid_F_leadgap
# lid_G
mid_G_lead = 710
mid_G_clad = 720
mid_G_duct = 730
mid_G_yszmix = 740 # YSZ + Helium mixture
# lid_H
mid_H_lead = 810
mid_H_clad = 820
mid_H_duct = 830
mid_H_springmix = 840 # Spring + Helium mixture
mid_I = 900 # lid_I
mid_J = 1000 # lid_J
# ==============================================================================
# Block IDs
# ==============================================================================
bid_A = 100
bid_B = 200
bid_C = 300
bid_I = 900
bid_J = 1000
bid_Ac = 101
bid_Bc = 201
bid_Cc = 301
bid_Ic = 901
bid_Jc = 1001
bid_D_lead = 410
bid_D_clad = 420
bid_D_duct = 430
bid_D_tubemix = 440 # Plenum tube + Helium mixture
bid_D_tubemixc = 441 # Plenum tube + Helium mixture
bid_E_lead = 510
bid_E_clad = 520
bid_E_duct = 530
bid_E_yszmix = 540 # YSZ + Helium mixture
bid_E_yszmixc = 541 # YSZ + Helium mixture
bid_F_fuel_R1 = 601
bid_F_fuel_R2 = 602
bid_F_fuel_R3 = 603
bid_F_fuel_R4 = 604
bid_F_fuel_R5 = 605
bid_F_fuel_R6 = 606
bid_F_fuel_R7 = 607
bid_F_helium = 610
bid_F_heliumc = 611
bid_F_lead = 620
bid_F_leadgap = 630
bid_F_clad = 640
bid_F_duct = 650
bid_G_lead = 710
bid_G_clad = 720
bid_G_duct = 730
bid_G_yszmix = 740 # YSZ + Helium mixture
bid_G_yszmixc = 741 # YSZ + Helium mixture
bid_H_lead = 810
bid_H_clad = 820
bid_H_duct = 830
bid_H_springmix = 840 # Spring + Helium mixture
bid_H_springmixc = 841 # Spring + Helium mixture
# ==============================================================================
# Power
# ==============================================================================
totalpower = 3700000.0 # WMesh
The mesh system is built on-the-fly using the MOOSE reactor module (Shemon et al., 2022).
First, pins for each hexagonal ring are defined using PolygonConcentricCircleMeshGenerator. Since there are 7 rings, 7 pins are defined. They have different block IDs (bid_F_fuel_R1 to bid_F_fuel_R7) for fuel region so that different material IDs can be assigned later. Since generally different element types should have different block IDs, the innermost helium hole of a triangular element and the helium gap between fuel and cladding of a quadrilateral element need to have different block IDs (bid_F_heliumc and bid_F_helium). Through sensitivity study, carrying just one radial mesh for the annular fuel region was turned out to be enough.
[Mesh]
[Pin1]
type = PolygonConcentricCircleMeshGenerator
num_sides = 6 # must be six to use hex pattern
num_sectors_per_side = '2 2 2 2 2 2'
polygon_size = ${half_pinpitch}
ring_radii = '${fuel_r_i} ${fuel_r_o} ${clad_r_i} ${clad_r_o}'
ring_intervals = '1 1 1 1'
ring_block_ids = '${bid_F_heliumc} ${bid_F_fuel_R1} ${bid_F_helium} ${bid_F_clad}'
background_intervals = 1
background_block_ids = ${bid_F_lead}
preserve_volumes = on
quad_center_elements = false
[]
[Pin2]
type = PolygonConcentricCircleMeshGenerator
num_sides = 6 # must be six to use hex pattern
num_sectors_per_side = '2 2 2 2 2 2'
polygon_size = ${half_pinpitch}
ring_radii = '${fuel_r_i} ${fuel_r_o} ${clad_r_i} ${clad_r_o}'
ring_intervals = '1 1 1 1'
ring_block_ids = '${bid_F_heliumc} ${bid_F_fuel_R2} ${bid_F_helium} ${bid_F_clad}'
background_intervals = 1
background_block_ids = ${bid_F_lead}
preserve_volumes = on
quad_center_elements = false
[]
[Pin3]
type = PolygonConcentricCircleMeshGenerator
num_sides = 6 # must be six to use hex pattern
num_sectors_per_side = '2 2 2 2 2 2'
polygon_size = ${half_pinpitch}
ring_radii = '${fuel_r_i} ${fuel_r_o} ${clad_r_i} ${clad_r_o}'
ring_intervals = '1 1 1 1'
ring_block_ids = '${bid_F_heliumc} ${bid_F_fuel_R3} ${bid_F_helium} ${bid_F_clad}'
background_intervals = 1
background_block_ids = ${bid_F_lead}
preserve_volumes = on
quad_center_elements = false
[]
[Pin4]
type = PolygonConcentricCircleMeshGenerator
num_sides = 6 # must be six to use hex pattern
num_sectors_per_side = '2 2 2 2 2 2'
polygon_size = ${half_pinpitch}
ring_radii = '${fuel_r_i} ${fuel_r_o} ${clad_r_i} ${clad_r_o}'
ring_intervals = '1 1 1 1'
ring_block_ids = '${bid_F_heliumc} ${bid_F_fuel_R4} ${bid_F_helium} ${bid_F_clad}'
background_intervals = 1
background_block_ids = ${bid_F_lead}
preserve_volumes = on
quad_center_elements = false
[]
[Pin5]
type = PolygonConcentricCircleMeshGenerator
num_sides = 6 # must be six to use hex pattern
num_sectors_per_side = '2 2 2 2 2 2'
polygon_size = ${half_pinpitch}
ring_radii = '${fuel_r_i} ${fuel_r_o} ${clad_r_i} ${clad_r_o}'
ring_intervals = '1 1 1 1'
ring_block_ids = '${bid_F_heliumc} ${bid_F_fuel_R5} ${bid_F_helium} ${bid_F_clad}'
background_intervals = 1
background_block_ids = ${bid_F_lead}
preserve_volumes = on
quad_center_elements = false
[]
[Pin6]
type = PolygonConcentricCircleMeshGenerator
num_sides = 6 # must be six to use hex pattern
num_sectors_per_side = '2 2 2 2 2 2'
polygon_size = ${half_pinpitch}
ring_radii = '${fuel_r_i} ${fuel_r_o} ${clad_r_i} ${clad_r_o}'
ring_intervals = '1 1 1 1'
ring_block_ids = '${bid_F_heliumc} ${bid_F_fuel_R6} ${bid_F_helium} ${bid_F_clad}'
background_intervals = 1
background_block_ids = ${bid_F_lead}
preserve_volumes = on
quad_center_elements = false
[]
[Pin7]
type = PolygonConcentricCircleMeshGenerator
num_sides = 6 # must be six to use hex pattern
num_sectors_per_side = '2 2 2 2 2 2'
polygon_size = ${half_pinpitch}
ring_radii = '${fuel_r_i} ${fuel_r_o} ${clad_r_i} ${clad_r_o}'
ring_intervals = '1 1 1 1'
ring_block_ids = '${bid_F_heliumc} ${bid_F_fuel_R7} ${bid_F_helium} ${bid_F_clad}'
background_intervals = 1
background_block_ids = ${bid_F_lead}
preserve_volumes = on
quad_center_elements = false
[]
These pin types are used to build the assembly with duct using HexIDPatternedMeshGenerator. Each pin type represents fuel pins for each hexagonal ring. HexIDPatternedMeshGenerator is meant to assign some extra element integer ID, here pin_id, for differentiating pins. It should be noted that background_block_id needs to be different from background_block_ids for a pin in PolygonConcentricCircleMeshGenerator in order to properly generate pin_id, which is why bid_F_lead + 1 is used instead of bid_F_lead in background_block_id. Note that duct and assembly lead gap regions are built using duct_block_ids, duct_sizes and duct_intervals.
# This assembles the 7 pins into an assembly with a duct
[ASM]
type = HexIDPatternedMeshGenerator
inputs = 'Pin1 Pin2 Pin3 Pin4 Pin5 Pin6 Pin7'
pattern_boundary = hexagon
hexagon_size = ${half_asmpitch}
background_intervals = 1
background_block_id = '${fparse bid_F_lead + 1}' # To generate pin_ids correctly
duct_sizes = '${fparse flat_to_flat/2} ${fparse flat_to_flat/2 + duct_thickness}'
duct_intervals = '1 1'
duct_block_ids = '${bid_F_duct} ${bid_F_leadgap}'
duct_sizes_style = apothem
external_boundary_id = 997
assign_type = 'cell' # different pin_id for different pins
pattern = '6 6 6 6 6 6 6;
6 5 5 5 5 5 5 6;
6 5 4 4 4 4 4 5 6;
6 5 4 3 3 3 3 4 5 6;
6 5 4 3 2 2 2 3 4 5 6;
6 5 4 3 2 1 1 2 3 4 5 6;
6 5 4 3 2 1 0 1 2 3 4 5 6;
6 5 4 3 2 1 1 2 3 4 5 6;
6 5 4 3 2 2 2 3 4 5 6;
6 5 4 3 3 3 3 4 5 6;
6 5 4 4 4 4 4 5 6;
6 5 5 5 5 5 5 6;
6 6 6 6 6 6 6'
id_name = 'pin_id'
[]Before extruding the 2D assembly geometry built above, an interface between the duct and the lead region is added.
[interface_define]
input = ASM
type = SideSetsBetweenSubdomainsGenerator
new_boundary = DuctLeadInterface
paired_block = ${fparse bid_F_lead + 1}
primary_block = ${bid_F_duct}
[]The 2D assembly is now extruded to the z-direction and new block IDs are assigned.
# This extrudes the 7-pin assembly axially and renames block IDs appropriately
[extrude]
type = AdvancedExtruderGenerator
input = interface_define
direction = '0 0 1'
top_boundary = 998
bottom_boundary = 999
heights = '${dhA} ${dhB} ${dhC} ${dhD} ${dhE} ${dhF} ${dhG} ${dhH} ${dhI} ${dhJ}'
num_layers = '${num_axmeshA} ${num_axmeshB} ${num_axmeshC} ${num_axmeshD} ${num_axmeshE} ${num_axmeshF} ${num_axmeshG} ${num_axmeshH} ${num_axmeshI} ${num_axmeshJ}'
subdomain_swaps = '${bid_F_fuel_R1} ${bid_A} ${bid_F_fuel_R2} ${bid_A} ${bid_F_fuel_R3} ${bid_A} ${bid_F_fuel_R4} ${bid_A} ${bid_F_fuel_R5} ${bid_A} ${bid_F_fuel_R6} ${bid_A} ${bid_F_fuel_R7} ${bid_A} ${bid_F_heliumc} ${bid_Ac} ${bid_F_helium} ${bid_A} ${bid_F_lead} ${bid_A} ${fparse bid_F_lead + 1} ${bid_A} ${bid_F_leadgap} ${bid_A} ${bid_F_clad} ${bid_A} ${bid_F_duct} ${bid_A};
${bid_F_fuel_R1} ${bid_B} ${bid_F_fuel_R2} ${bid_B} ${bid_F_fuel_R3} ${bid_B} ${bid_F_fuel_R4} ${bid_B} ${bid_F_fuel_R5} ${bid_B} ${bid_F_fuel_R6} ${bid_B} ${bid_F_fuel_R7} ${bid_B} ${bid_F_heliumc} ${bid_Bc} ${bid_F_helium} ${bid_B} ${bid_F_lead} ${bid_B} ${fparse bid_F_lead + 1} ${bid_B} ${bid_F_leadgap} ${bid_B} ${bid_F_clad} ${bid_B} ${bid_F_duct} ${bid_B};
${bid_F_fuel_R1} ${bid_C} ${bid_F_fuel_R2} ${bid_C} ${bid_F_fuel_R3} ${bid_C} ${bid_F_fuel_R4} ${bid_C} ${bid_F_fuel_R5} ${bid_C} ${bid_F_fuel_R6} ${bid_C} ${bid_F_fuel_R7} ${bid_C} ${bid_F_heliumc} ${bid_Cc} ${bid_F_helium} ${bid_C} ${bid_F_lead} ${bid_C} ${fparse bid_F_lead + 1} ${bid_C} ${bid_F_leadgap} ${bid_C} ${bid_F_clad} ${bid_C} ${bid_F_duct} ${bid_C};
${bid_F_fuel_R1} ${bid_D_tubemix} ${bid_F_fuel_R2} ${bid_D_tubemix} ${bid_F_fuel_R3} ${bid_D_tubemix} ${bid_F_fuel_R4} ${bid_D_tubemix} ${bid_F_fuel_R5} ${bid_D_tubemix} ${bid_F_fuel_R6} ${bid_D_tubemix} ${bid_F_fuel_R7} ${bid_D_tubemix} ${bid_F_heliumc} ${bid_D_tubemixc} ${bid_F_helium} ${bid_D_tubemix} ${bid_F_lead} ${bid_D_lead} ${fparse bid_F_lead + 1} ${bid_D_lead} ${bid_F_leadgap} ${bid_D_lead} ${bid_F_clad} ${bid_D_clad} ${bid_F_duct} ${bid_D_duct};
${bid_F_fuel_R1} ${bid_E_yszmix} ${bid_F_fuel_R2} ${bid_E_yszmix} ${bid_F_fuel_R3} ${bid_E_yszmix} ${bid_F_fuel_R4} ${bid_E_yszmix} ${bid_F_fuel_R5} ${bid_E_yszmix} ${bid_F_fuel_R6} ${bid_E_yszmix} ${bid_F_fuel_R7} ${bid_E_yszmix} ${bid_F_heliumc} ${bid_E_yszmixc} ${bid_F_helium} ${bid_E_yszmix} ${bid_F_lead} ${bid_E_lead} ${fparse bid_F_lead + 1} ${bid_E_lead} ${bid_F_leadgap} ${bid_E_lead} ${bid_F_clad} ${bid_E_clad} ${bid_F_duct} ${bid_E_duct};
${bid_F_fuel_R1} ${bid_F_fuel_R1} ${bid_F_fuel_R2} ${bid_F_fuel_R2} ${bid_F_fuel_R3} ${bid_F_fuel_R3} ${bid_F_fuel_R4} ${bid_F_fuel_R4} ${bid_F_fuel_R5} ${bid_F_fuel_R5} ${bid_F_fuel_R6} ${bid_F_fuel_R6} ${bid_F_fuel_R7} ${bid_F_fuel_R7} ${bid_F_heliumc} ${bid_F_heliumc} ${bid_F_helium} ${bid_F_helium} ${bid_F_lead} ${bid_F_lead} ${fparse bid_F_lead + 1} ${bid_F_lead} ${bid_F_leadgap} ${bid_F_leadgap} ${bid_F_clad} ${bid_F_clad} ${bid_F_duct} ${bid_F_duct};
${bid_F_fuel_R1} ${bid_G_yszmix} ${bid_F_fuel_R2} ${bid_G_yszmix} ${bid_F_fuel_R3} ${bid_G_yszmix} ${bid_F_fuel_R4} ${bid_G_yszmix} ${bid_F_fuel_R5} ${bid_G_yszmix} ${bid_F_fuel_R6} ${bid_G_yszmix} ${bid_F_fuel_R7} ${bid_G_yszmix} ${bid_F_heliumc} ${bid_G_yszmixc} ${bid_F_helium} ${bid_G_yszmix} ${bid_F_lead} ${bid_G_lead} ${fparse bid_F_lead + 1} ${bid_G_lead} ${bid_F_leadgap} ${bid_G_lead} ${bid_F_clad} ${bid_G_clad} ${bid_F_duct} ${bid_G_duct};
${bid_F_fuel_R1} ${bid_H_springmix} ${bid_F_fuel_R2} ${bid_H_springmix} ${bid_F_fuel_R3} ${bid_H_springmix} ${bid_F_fuel_R4} ${bid_H_springmix} ${bid_F_fuel_R5} ${bid_H_springmix} ${bid_F_fuel_R6} ${bid_H_springmix} ${bid_F_fuel_R7} ${bid_H_springmix} ${bid_F_heliumc} ${bid_H_springmixc} ${bid_F_helium} ${bid_H_springmix} ${bid_F_lead} ${bid_H_lead} ${fparse bid_F_lead + 1} ${bid_H_lead} ${bid_F_leadgap} ${bid_H_lead} ${bid_F_clad} ${bid_H_clad} ${bid_F_duct} ${bid_H_duct};
${bid_F_fuel_R1} ${bid_I} ${bid_F_fuel_R2} ${bid_I} ${bid_F_fuel_R3} ${bid_I} ${bid_F_fuel_R4} ${bid_I} ${bid_F_fuel_R5} ${bid_I} ${bid_F_fuel_R6} ${bid_I} ${bid_F_fuel_R7} ${bid_I} ${bid_F_heliumc} ${bid_Ic} ${bid_F_helium} ${bid_I} ${bid_F_lead} ${bid_I} ${fparse bid_F_lead + 1} ${bid_I} ${bid_F_leadgap} ${bid_I} ${bid_F_clad} ${bid_I} ${bid_F_duct} ${bid_I};
${bid_F_fuel_R1} ${bid_J} ${bid_F_fuel_R2} ${bid_J} ${bid_F_fuel_R3} ${bid_J} ${bid_F_fuel_R4} ${bid_J} ${bid_F_fuel_R5} ${bid_J} ${bid_F_fuel_R6} ${bid_J} ${bid_F_fuel_R7} ${bid_J} ${bid_F_heliumc} ${bid_Jc} ${bid_F_helium} ${bid_J} ${bid_F_lead} ${bid_J} ${fparse bid_F_lead + 1} ${bid_J} ${bid_F_leadgap} ${bid_J} ${bid_F_clad} ${bid_J} ${bid_F_duct} ${bid_J}'
[]Plane-wise ids are assigned to the extruded 3D mesh for the purpose of axial pin power tally. Since non-fuel regions have zero power while PlaneIDMeshGenerator needs to cover the whole domain, each of lower and upper non-fuel axial planes is assigned with a single plane_id and active fuel regions are assigned with different plane_ids in 20 axial meshes.
# This assigns plane_id for the purpose of axial pin power tally
[assign_planeid]
type = PlaneIDMeshGenerator
input = extrude
plane_coordinates = '0.0 ${hE} ${hF} ${hJ}'
num_ids_per_plane = '1 ${num_axmeshF} 1'
plane_axis = 'z'
id_name = 'plane_id'
[]Sidesets are renamed with common sensical names.
# This renames sidesets to common sensical names
[rename_sidesets]
type = RenameBoundaryGenerator
input = assign_planeid
old_boundary = ' DuctLeadInterface 998 999 997'
new_boundary = 'DUCT_INNERSIDE ASSEMBLY_TOP ASSEMBLY_BOTTOM ASSEMBLY_SIDE'
[]Material IDs are assigned to block IDs. This part needs to be consistent with the specification in Materials.
[assign]
type = SubdomainExtraElementIDGenerator
input = rename_sidesets
extra_element_id_names = 'material_id'
subdomains = '${bid_A} ${bid_Ac} ${bid_B} ${bid_Bc} ${bid_C} ${bid_Cc} ${bid_D_lead} ${bid_D_clad} ${bid_D_duct} ${bid_D_tubemix} ${bid_D_tubemixc} ${bid_E_lead} ${bid_E_clad} ${bid_E_duct} ${bid_E_yszmix} ${bid_E_yszmixc} ${bid_F_fuel_R1} ${bid_F_fuel_R2} ${bid_F_fuel_R3} ${bid_F_fuel_R4} ${bid_F_fuel_R5} ${bid_F_fuel_R6} ${bid_F_fuel_R7} ${bid_F_heliumc} ${bid_F_helium} ${bid_F_lead} ${bid_F_leadgap} ${bid_F_clad} ${bid_F_duct} ${bid_G_lead} ${bid_G_clad} ${bid_G_duct} ${bid_G_yszmix} ${bid_G_yszmixc} ${bid_H_lead} ${bid_H_clad} ${bid_H_duct} ${bid_H_springmix} ${bid_H_springmixc} ${bid_I} ${bid_Ic} ${bid_J} ${bid_Jc}'
extra_element_ids = '${mid_A} ${mid_A} ${mid_B} ${mid_B} ${mid_C} ${mid_C} ${mid_D_lead} ${mid_D_clad} ${mid_D_duct} ${mid_D_tubemix} ${mid_D_tubemix} ${mid_E_lead} ${mid_E_clad} ${mid_E_duct} ${mid_E_yszmix} ${mid_E_yszmix} ${mid_F_fuel_R1} ${mid_F_fuel_R2} ${mid_F_fuel_R3} ${mid_F_fuel_R4} ${mid_F_fuel_R5} ${mid_F_fuel_R6} ${mid_F_fuel_R7} ${mid_F_helium} ${mid_F_helium} ${mid_F_lead} ${mid_F_leadgap} ${mid_F_clad} ${mid_F_duct} ${mid_G_lead} ${mid_G_clad} ${mid_G_duct} ${mid_G_yszmix} ${mid_G_yszmix} ${mid_H_lead} ${mid_H_clad} ${mid_H_duct} ${mid_H_springmix} ${mid_H_springmix} ${mid_I} ${mid_I} ${mid_J} ${mid_J}'
[]A coarse mesh is generated for the CMFD acceleration. For better alignment of peripheral pin meshes near duct, only the peripheral pins have two radial meshes divided by the cladding outer radius while inner pins have one radial mesh. Azimuthal divisions are the same as the fine mesh. The duct mesh is also the same as the fine mesh, otherwise the CMFD solve didn't converge. The axial mesh is also the same as the fine mesh because the use of a coarser axial mesh increased the number of transport sweeps significantly.
[PinIn_CM]
type = PolygonConcentricCircleMeshGenerator
num_sides = 6 # must be six to use hex pattern
num_sectors_per_side = '2 2 2 2 2 2'
polygon_size = ${half_pinpitch}
background_intervals = '1'
background_block_ids = '1'
preserve_volumes = on
quad_center_elements = false
[]
[PinOut_CM]
type = PolygonConcentricCircleMeshGenerator
num_sides = 6 # must be six to use hex pattern
num_sectors_per_side = '2 2 2 2 2 2'
polygon_size = ${half_pinpitch}
ring_radii = '${clad_r_o}'
ring_intervals = '1'
ring_block_ids = '2'
background_intervals = '1'
background_block_ids = '3'
preserve_volumes = on
quad_center_elements = false
[]
# This assembles the 7 pins into an assembly with a duct
[ASM_CM]
type = PatternedHexMeshGenerator
inputs = 'PinIn_CM PinOut_CM'
pattern_boundary = hexagon
background_intervals = '1'
hexagon_size = ${half_asmpitch}
duct_sizes = '${fparse flat_to_flat/2} ${fparse flat_to_flat/2 + duct_thickness}'
duct_sizes_style = apothem
duct_intervals = '1 1'
background_block_id = '4'
duct_block_ids = '5 6'
external_boundary_id = 997
pattern = '1 1 1 1 1 1 1;
1 0 0 0 0 0 0 1;
1 0 0 0 0 0 0 0 1;
1 0 0 0 0 0 0 0 0 1;
1 0 0 0 0 0 0 0 0 0 1;
1 0 0 0 0 0 0 0 0 0 0 1;
1 0 0 0 0 0 0 0 0 0 0 0 1;
1 0 0 0 0 0 0 0 0 0 0 1;
1 0 0 0 0 0 0 0 0 0 1;
1 0 0 0 0 0 0 0 0 1;
1 0 0 0 0 0 0 0 1;
1 0 0 0 0 0 0 1;
1 1 1 1 1 1 1'
[]
[coarse_mesh]
type = AdvancedExtruderGenerator
input = ASM_CM
heights = '${dhA} ${dhB} ${dhC} ${dhD} ${dhE} ${dhF} ${dhG} ${dhH} ${dhI} ${dhJ}'
num_layers = '${num_axmeshA} ${num_axmeshB} ${num_axmeshC} ${num_axmeshD} ${num_axmeshE} ${num_axmeshF} ${num_axmeshG} ${num_axmeshH} ${num_axmeshI} ${num_axmeshJ}'
direction = '0 0 1'
top_boundary = 998
bottom_boundary = 999
[]
[cmesh]
type = CoarseMeshExtraElementIDGenerator
input = assign
coarse_mesh = coarse_mesh
extra_element_id_name = coarse_element_id
[]Figure 8 shows the radial cross section view of the fine and coarse meshes. Note that the coarse mesh on the right is not a separate mesh that Griffin holds, but just a visual representation of coarse element IDs assigned to the fine mesh on the left.
Figure 8: Radial cross section view of (Left) fine mesh and (Right) coarse mesh
Transport systems
For the transport system, particle is neutron and equation_type is eigenvalue. The number of energy groups is 9 given by G and VacuumBoundary and ReflectingBoundary are sideset names renamed in [rename_sidesets]. Top and bottom surfaces are vacuum and lateral surfaces are reflective. In the sub-block of [sn], the DFEM-SN scheme is specified. Between monomial and L2-Lagrange families of basis functions supported for discontinuous elements, the L2Lagrange type is selected with the first order since it gives more accurate solution than monomial in general. The angular quadrature type (AQtype) is set to Gauss-Chebyshev for having a freedom to choose a different number of angles in the azimuthal direction and in the polar direction in 3D. The number of azimuthal angles (NAzmthl) and that of polar angles (NPolar) per octant are set to and , respectively, from a sensitivity study. The anisotropic scattering order (NA) is set to 1. using_array_variable=true and collapse_scattering=true are recommended options for performance reason in general.
[TransportSystems]
particle = neutron
equation_type = eigenvalue
G = 9
VacuumBoundary = 'ASSEMBLY_TOP ASSEMBLY_BOTTOM'
ReflectingBoundary = 'ASSEMBLY_SIDE'
[sn]
scheme = DFEM-SN
family = L2_LAGRANGE
order = FIRST
AQtype = Gauss-Chebyshev
NPolar = 2
NAzmthl = 3
NA = 1
using_array_variable = true
collapse_scattering = true
[]
[]Executioner
The SweepUpdate executioner is used for the CMFD acceleration. SweepUpdate is a special Richardson executioner for performing source iteration with a transport sweeper. This source iteration can be accelerated by turning on cmfd_acceleration which invokes the CMFD solve where the low order diffusion equation is solved with a convection closure term to make the diffusion system and the transport system consistent. coarse_element_id is a name of the extra element integer ID assigned by CoarseMeshExtraElementIDGenerator in [Mesh]. If the CMFD solve does not converge, one can use different options for diffusion_eigen_solver_type which is the eigenvalue solver for CMFD. There are four options: power, arnoldi, krylovshur and newton. newton is the default which is recommended to stick with. If newton does not converge a solution, either krylovshur is the second option to go with, or cmfd_prec_type can be changed to lu from its default value of boomeramg for a small problem. Also one can try cmfd_closure_type=syw or cmfd_closure_type=pcmfd as different ways, but it is recommended to stick with its default value of traditional_cmfd.
richardson_rel_tol or richardson_abs_tol is the tolerance used to check the convergence of the Richardson iteration. If richardson_postprocessor is specified, its PostProcessor value is used as the convergence metric. Otherwise Griffin uses the L2 norm difference of the angular flux solution between successive Richardson iterations, which is added to richardson_postprocessor with the name of flux_error internally. richardson_rel_tol is the tolerance for the ratio of the richardson_postprocessor value of the current iteration to that of the first iteration. richardson_value is for the console output purpose to show the history of PostProcessor values over Richardson iterations. inner_solve_type is about the way to perform the inner solve of the Richardson iteration. There are three options: none, SI and GMRes. none is just a direct transport operator inversion per residual evaluation, while scattering source is updated together for SI and GMRes per residual evaluation. The latter two options involve more number of transport sweeps per residual evaluation than none, leading to the reduction of the number of residual evaluations and possibly the total run time. For GMRes, the scattering source effect is accounted for at once by performing the GMRes iterations and max_inner_its is the maximum number of GMRes iterations. For SI, the scattering source effect is accounted for by performing source iterations and max_inner_its is the maximum number of source iterations. The whole energy group is solved at once for enable_group_sweep=false (default) and a within-group linear system is solved group-by-group for enable_group_sweep=true with the scattering source being updated during the group sweep using the latest flux solution. max_thermal_its (the number of thermal iterations) is not relevant to this problem since there is no up-scattering for the fast reactor application.
[Executioner]
type = SweepUpdate
verbose = true
richardson_rel_tol = 1e-4
richardson_max_its = 500
richardson_value = 'eigenvalue'
inner_solve_type = SI
max_inner_its = 7
cmfd_acceleration = true
coarse_element_id = coarse_element_id
[]Flux normalization for producing the total power
The flux solution can be normalized for producing the total power using the [PowerDensity] block. power is the user-specified total power and power_density_variable is a required AuxVariable name for power density. Power is calculated using the kappaFission cross section in the cross section library which is the total recoverable energy per fission multiplied by the fission cross section and does not account for non-fission heating.
[PowerDensity]
power = ${totalpower}
power_density_variable = power_density
[]Non-fission heating will be added in the [PowerDensity] block in the future.
Power output
To output pin-wise and axial mesh-wise power, ExtraIDIntegralVectorPostprocessor VectorPostprocessors is used using pin_id and plane_id generated by the mesh generators. ExtraIDIntegralVectorPostprocessor performs integration of variables given in variable over the unique combinations of extra element integer IDs given in id_name. In variable, volume, x_coord and y_coord are for locating a center of each cell of the hexagonal lattice. x_coord/volume and y_coord/volume are the (x, y) coordinate of a cell. It should be noted that there are 129 pin_ids while there are 127 fuel pins. Two extra pin_ids are assigned for the duct (pin_id=127) and the assembly gap (pin_id=128) regions which have zero power.
[AuxVariables]
[volume]
family = MONOMIAL
order = CONSTANT
initial_condition = 1
[]
[x_coord]
family = LAGRANGE
order = FIRST
[InitialCondition]
type = FunctionIC
function = x
[]
[]
[y_coord]
family = LAGRANGE
order = FIRST
[InitialCondition]
type = FunctionIC
function = y
[]
[]
[]
[VectorPostprocessors]
[pin_powers]
type = ExtraIDIntegralVectorPostprocessor
variable = 'volume x_coord y_coord power_density'
id_name = 'pin_id plane_id'
[]
[]
[Outputs]
[console]
type = Console
outlier_variable_norms = false
[]
[pgraph]
type = PerfGraphOutput
level = 2
[]
csv = true
execute_on = 'timestep_end'
[]Materials
The [Materials] block is constructed using MicroNeutronicsMaterial. The main reason for using this material instead of MixedNeutronicsMaterial is that each library (library ID) in the library file is not generated for each material (material ID) in the Griffin transport calculation. Using MicroNeutronicsMaterial, different material IDs can be freely generated in the same library ID. For example, for Fuel_Ring1_Hole, two materials are defined with two different IDs of mid_F_helium and mid_F_fuel_R1 using isotopes in the same library ID of lid_F_fuel_R1. These two materials are present in three block IDs of bid_F_fuel_R1, bid_F_heliumc, and bid_F_helium. This specification needs to be consistent with the material assignment in Mesh. Note that materials must be assigned in Mesh to use MicroNeutronicsMaterial. Materials are separated by semicolons and a material name given before a material ID is not used in the code but for user information.
[GlobalParams]
library_file = '../cross_section/LFR_127Pin_9g.xml'
library_name = ISOTXS-neutron
is_meter = true
plus = true
dbgmat = false
grid_names = 'Tfuel'
grid = '1'
maximum_diffusion_coefficient = 1000
[]
[Compositions]
[Fuel_Hole]
type = IsotopeComposition
isotope_densities = 'HE4 2.512611E-05'
density_type = atomic
composition_ids = ${mid_F_helium}
[]
[Fuel_Ring]
type = IsotopeComposition
isotope_densities = 'U234 1.769055E-07
U235 4.404137E-05
U238 1.735054E-02
PU238 1.244939E-05
PU239 3.413306E-03
PU240 1.319941E-03
PU241 8.656869E-05
PU242 1.234538E-04
AM241 2.087265E-04
O16 4.444138E-02'
density_type = atomic
composition_ids = '${mid_F_fuel_R1} ${mid_F_fuel_R2} ${mid_F_fuel_R3} ${mid_F_fuel_R4} ${mid_F_fuel_R5} ${mid_F_fuel_R6} ${mid_F_fuel_R7}'
[]
[Fuel_Clad]
type = IsotopeComposition
isotope_densities = 'FE54 3.185952E-03
FE56 5.001168E-02
FE57 1.154947E-03
FE58 1.537129E-04
NI58 8.373412E-03
NI60 3.225451E-03
NI61 1.402235E-04
NI62 4.469793E-04
NI64 1.138947E-04
CR50 5.643439E-04
CR52 1.088250E-02
CR53 1.234043E-03
CR54 3.071758E-04
MN55 1.271641E-03
MO92 1.080550E-04
MO94 6.735188E-05
MO95 1.159146E-04
MO96 1.214544E-04
MO97 6.953578E-05
MO98 1.757019E-04
MO100 7.011875E-05
SI28 1.300140E-03
SI29 6.601594E-05
SI30 4.351798E-05
C12 3.489938E-04
P31 6.766687E-05
S32 2.068704E-05
S33 1.656123E-07
S34 9.348567E-07
S36 4.358298E-09
TI46 3.210951E-05
TI47 2.895766E-05
TI48 2.869267E-04
TI49 2.105602E-05
TI50 2.016107E-05
V50 2.742873E-05
ZR90 7.880535E-06
ZR91 1.718520E-06
ZR92 2.626878E-06
ZR94 2.662077E-06
ZR96 4.288701E-07
W182 2.014107E-06
W183 1.087650E-06
W184 2.337892E-06
W186 2.160800E-06
CU63 1.520930E-05
CU65 6.778986E-06
CO59 2.370990E-05
CA40 3.379743E-05
CA42 2.255696E-07
CA43 4.706582E-08
CA44 7.272563E-07
CA46 1.394535E-09
CA48 6.519498E-08
NB93 7.519752E-06
N14 4.969370E-05
N15 1.835515E-07
AL27 2.589280E-05
TA181 3.861021E-06
B10 5.144462E-06
B11 2.070704E-05'
density_type = atomic
composition_ids = '${mid_F_clad} ${mid_D_clad} ${mid_E_clad} ${mid_G_clad} ${mid_H_clad}'
[]
[Lead]
type = IsotopeComposition
isotope_densities = 'PB204 4.232323E-04
PB206 7.285612E-03
PB207 6.680995E-03
PB208 1.584046E-02'
density_type = atomic
composition_ids = '${mid_F_lead} ${mid_F_leadgap} ${mid_D_lead} ${mid_E_lead} ${mid_G_lead} ${mid_H_lead}'
[]
[Duct]
type = IsotopeComposition
isotope_densities = 'FE54 3.192503E-03
FE56 5.011505E-02
FE57 1.157401E-03
FE58 1.540302E-04
NI58 8.390808E-03
NI60 3.232103E-03
NI61 1.405101E-04
NI62 4.479004E-04
NI64 1.141301E-04
CR50 5.655206E-04
CR52 1.090501E-02
CR53 1.236601E-03
CR54 3.078103E-04
MN55 1.274301E-03
MO92 1.082801E-04
MO94 6.749107E-05
MO95 1.161601E-04
MO96 1.217001E-04
MO97 6.968007E-05
MO98 1.760602E-04
MO100 7.026407E-05
SI28 1.302801E-03
SI29 6.615206E-05
SI30 4.360804E-05
C12 3.497203E-04
P31 6.780707E-05
S32 2.073002E-05
S33 1.659602E-07
S34 9.367909E-07
S36 4.367304E-09
TI46 3.217603E-05
TI47 2.901703E-05
TI48 2.875203E-04
TI49 2.110002E-05
TI50 2.020302E-05
V50 2.748603E-05
ZR90 7.896908E-06
ZR91 1.722102E-06
ZR92 2.632303E-06
ZR94 2.667603E-06
ZR96 4.297604E-07
W182 2.018302E-06
W183 1.089901E-06
W184 2.342702E-06
W186 2.165302E-06
CU63 1.524101E-05
CU65 6.793007E-06
CO59 2.375902E-05
CA40 3.386703E-05
CA42 2.260402E-07
CA43 4.716405E-08
CA44 7.287707E-07
CA46 1.397401E-09
CA48 6.533006E-08
NB93 7.535407E-06
N14 4.979705E-05
N15 1.839302E-07
AL27 2.594703E-05
TA181 3.869004E-06
B10 5.155105E-06
B11 2.075002E-05'
density_type = atomic
composition_ids = '${mid_F_duct} ${mid_D_duct} ${mid_E_duct} ${mid_G_duct} ${mid_H_duct}'
[]
[LowerCorePlate]
type = IsotopeComposition
isotope_densities = 'FE54 2.357119E-03
FE56 3.700230E-02
FE57 8.545370E-04
FE58 1.137209E-04
NI58 4.964541E-03
NI60 1.912316E-03
NI61 8.313568E-05
NI62 2.650122E-04
NI64 6.752956E-05
CR50 4.670038E-04
CR52 9.005674E-03
CR53 1.021208E-03
CR54 2.541921E-04
MN55 6.804056E-04
MO92 1.208810E-04
MO94 7.534562E-05
MO95 1.296811E-04
MO96 1.358711E-04
MO97 7.778964E-05
MO98 1.965516E-04
MO100 7.844165E-05
SI28 6.346952E-04
SI29 3.222827E-05
SI30 2.124518E-05
C12 1.414012E-04
P31 2.963124E-05
S32 1.501712E-05
S33 1.202210E-07
S34 6.786456E-07
S36 3.163826E-09
TI46 4.392136E-06
TI47 3.960833E-06
TI48 3.924632E-05
TI49 2.880124E-06
TI50 2.757723E-06
V50 3.751831E-06
ZR90 1.077909E-06
ZR91 2.350719E-07
ZR92 3.593130E-07
ZR94 3.641330E-07
ZR96 5.866348E-08
W182 2.755023E-07
W183 1.487712E-07
W184 3.197926E-07
W186 2.955624E-07
CU63 2.080417E-06
CU65 9.272576E-07
CO59 3.243027E-06
CA40 4.622938E-06
CA42 3.085425E-08
CA43 6.437853E-09
CA44 9.947682E-08
CA46 1.907516E-10
CA48 8.917673E-09
NB93 1.028608E-06
N14 6.797356E-06
N15 2.510621E-08
AL27 3.541729E-06
TA181 5.281244E-07
B10 7.036758E-07
B11 2.832423E-06
PB204 1.170210E-04
PB206 2.014417E-03
PB207 1.847215E-03
PB208 4.379936E-03'
density_type = atomic
composition_ids = '${mid_A}'
[]
[InletWrapper]
type = IsotopeComposition
isotope_densities = 'FE54 2.614802E-04
FE56 4.104560E-03
FE57 9.479369E-05
FE58 1.261549E-05
NI58 6.872268E-04
NI60 2.647203E-04
NI61 1.150845E-05
NI62 3.668443E-05
NI64 9.347864E-06
CR50 4.631781E-05
CR52 8.931848E-04
CR53 1.012839E-04
CR54 2.521098E-05
MN55 1.043741E-04
MO92 8.868246E-06
MO94 5.527715E-06
MO95 9.513671E-06
MO96 9.967888E-06
MO97 5.707022E-06
MO98 1.441956E-05
MO100 5.754824E-06
SI28 1.067042E-04
SI29 5.418111E-06
SI30 3.571639E-06
C12 2.864312E-05
P31 5.553616E-06
S32 1.697766E-06
S33 1.359253E-08
S34 7.672599E-08
S36 3.576939E-10
TI46 2.635303E-06
TI47 2.376593E-06
TI48 2.354892E-05
TI49 1.728167E-06
TI50 1.654664E-06
V50 2.251188E-06
ZR90 6.467752E-07
ZR91 1.410455E-07
ZR92 2.155884E-07
ZR94 2.184885E-07
ZR96 3.519937E-08
W182 1.653064E-07
W183 8.926448E-08
W184 1.918775E-07
W186 1.773469E-07
CU63 1.248249E-06
CU65 5.563717E-07
CO59 1.945876E-06
CA40 2.773808E-06
CA42 1.851272E-08
CA43 3.862851E-09
CA44 5.968833E-08
CA46 1.144545E-10
CA48 5.350809E-09
NB93 6.171741E-07
N14 4.078559E-06
N15 1.506459E-08
AL27 2.125083E-06
TA181 3.168823E-07
B10 4.222165E-07
B11 1.699466E-06
PB204 3.885751E-04
PB206 6.688961E-03
PB207 6.133839E-03
PB208 1.454357E-02'
density_type = atomic
composition_ids = '${mid_B}'
[]
[LowerBundle]
type = IsotopeComposition
isotope_densities = 'FE54 1.251752E-03
FE56 1.964981E-02
FE57 4.537988E-04
FE58 6.039250E-05
NI58 3.289936E-03
NI60 1.267252E-03
NI61 5.509228E-05
NI62 1.756173E-04
NI64 4.474985E-05
CR50 2.217292E-04
CR52 4.275877E-03
CR53 4.848501E-04
CR54 1.206850E-04
MN55 4.996407E-04
MO92 4.245476E-05
MO94 2.646209E-05
MO95 4.554388E-05
MO96 4.771797E-05
MO97 2.732113E-05
MO98 6.903086E-05
MO100 2.754914E-05
SI28 5.108111E-04
SI29 2.593807E-05
SI30 1.709871E-05
C12 1.371257E-04
P31 2.658610E-05
S32 8.127836E-06
S33 6.507069E-08
S34 3.673052E-07
S36 1.712371E-09
TI46 1.261552E-05
TI47 1.137747E-05
TI48 1.127347E-04
TI49 8.273042E-06
TI50 7.921328E-06
V50 1.077645E-05
ZR90 3.096328E-06
ZR91 6.752279E-07
ZR92 1.032143E-06
ZR94 1.045943E-06
ZR96 1.685070E-07
W182 7.913527E-07
W183 4.273277E-07
W184 9.185680E-07
W186 8.489851E-07
CU63 5.975747E-06
CU65 2.663510E-06
CO59 9.315485E-06
CA40 1.327855E-05
CA42 8.862667E-08
CA43 1.849277E-08
CA44 2.857418E-07
CA46 5.479227E-10
CA48 2.561506E-08
NB93 2.954522E-06
N14 1.952481E-05
N15 7.211698E-08
AL27 1.017342E-05
TA181 1.516963E-06
B10 2.021284E-06
B11 8.135837E-06
PB204 2.570306E-04
PB206 4.424583E-03
PB207 4.057368E-03
PB208 9.620298E-03'
density_type = atomic
composition_ids = '${mid_C} ${mid_I}'
[]
[TUBEMIX]
type = IsotopeComposition
isotope_densities = 'FE54 6.532669E-04
FE56 1.025499E-02
FE57 2.368260E-04
FE58 3.151812E-05
NI58 1.716934E-03
NI60 6.613685E-04
NI61 2.875159E-05
NI62 9.165281E-05
NI64 2.335454E-05
CR50 1.157225E-04
CR52 2.231534E-03
CR53 2.530392E-04
CR54 6.298624E-05
MN55 2.607607E-04
MO92 2.215631E-05
MO94 1.381068E-05
MO95 2.376862E-05
MO96 2.490384E-05
MO97 1.425877E-05
MO98 3.602700E-05
MO100 1.437779E-05
SI28 2.665818E-04
SI29 1.353663E-05
SI30 8.923334E-06
C12 7.156191E-05
P31 1.387470E-05
S32 4.241824E-06
S33 3.395960E-08
S34 1.916872E-07
S36 8.936736E-10
TI46 6.584079E-06
TI47 5.937654E-06
TI48 5.883443E-05
TI49 4.317539E-06
TI50 4.134003E-06
V50 5.624293E-06
ZR90 1.615914E-06
ZR91 3.523885E-07
ZR92 5.386347E-07
ZR94 5.458561E-07
ZR96 8.794009E-08
W182 4.130003E-07
W183 2.230133E-07
W184 4.793831E-07
W186 4.430761E-07
CU63 3.118706E-06
CU65 1.390070E-06
CO59 4.861645E-06
CA40 6.930147E-06
CA42 4.625299E-08
CA43 9.650875E-09
CA44 1.491290E-07
CA46 2.859556E-10
CA48 1.336860E-08
NB93 1.541900E-06
N14 1.018998E-05
N15 3.763731E-08
AL27 5.309332E-06
TA181 7.916938E-07
B10 1.054905E-06
B11 4.245925E-06
HE4 1.990687E-05'
density_type = atomic
composition_ids = '${mid_D_tubemix}'
[]
[YSZMIX]
type = IsotopeComposition
isotope_densities = 'ZR90 1.110556E-02
ZR91 2.421721E-03
ZR92 3.701685E-03
ZR94 3.751388E-03
ZR96 6.043603E-04
Y89 3.753788E-03
O16 4.880044E-02
HE4 2.388520E-06'
density_type = atomic
composition_ids = '${mid_E_yszmix} ${mid_G_yszmix}'
[]
[SPRINGMIX]
type = IsotopeComposition
isotope_densities = 'FE54 3.504949E-04
FE56 5.501991E-03
FE57 1.270690E-04
FE58 1.691020E-05
NI58 9.211855E-04
NI60 3.548352E-04
NI61 1.542610E-05
NI62 4.917349E-05
NI64 1.252989E-05
CR50 6.208541E-05
CR52 1.197285E-03
CR53 1.357596E-04
CR54 3.379340E-05
MN55 1.398999E-04
MO92 1.188684E-05
MO94 7.409526E-06
MO95 1.275291E-05
MO96 1.336095E-05
MO97 7.649844E-06
MO98 1.932937E-05
MO100 7.713948E-06
SI28 1.430302E-04
SI29 7.262616E-06
SI30 4.787540E-06
C12 3.839473E-05
P31 7.444329E-06
S32 2.275762E-06
S33 1.822029E-08
S34 1.028473E-07
S36 4.794741E-10
TI46 3.532451E-06
TI47 3.185626E-06
TI48 3.156524E-05
TI49 2.316465E-06
TI50 2.217958E-06
V50 3.017514E-06
ZR90 8.669616E-07
ZR91 1.890634E-07
ZR92 2.889905E-07
ZR94 2.928608E-07
ZR96 4.718135E-08
W182 2.215757E-07
W183 1.196485E-07
W184 2.571983E-07
W186 2.377169E-07
CU63 1.673219E-06
CU65 7.457830E-07
CO59 2.608385E-06
CA40 3.718164E-06
CA42 2.481576E-08
CA43 5.177868E-09
CA44 8.000768E-08
CA46 1.534209E-10
CA48 7.172310E-09
NB93 8.272788E-07
N14 5.466988E-06
N15 2.019243E-08
AL27 2.848602E-06
TA181 4.247602E-07
B10 5.659602E-07
B11 2.278062E-06
HE4 2.228358E-05'
density_type = atomic
composition_ids = '${mid_H_springmix}'
[]
[OutletWrapper]
type = IsotopeComposition
isotope_densities = 'FE54 7.604462E-04
FE56 1.193694E-02
FE57 2.756886E-04
FE58 3.668882E-05
NI58 1.998690E-03
NI60 7.698761E-04
NI61 3.346883E-05
NI62 1.066895E-04
NI64 2.718586E-05
CR50 1.347093E-04
CR52 2.597687E-03
CR53 2.945585E-04
CR54 7.332063E-05
MN55 3.035385E-04
MO92 2.579187E-05
MO94 1.607592E-05
MO95 2.766886E-05
MO96 2.898985E-05
MO97 1.659792E-05
MO98 4.193779E-05
MO100 1.673692E-05
SI28 3.103184E-04
SI29 1.575692E-05
SI30 1.038695E-05
C12 8.330258E-05
P31 1.615192E-05
S32 4.937775E-06
S33 3.953080E-08
S34 2.231389E-07
S36 1.040295E-09
TI46 7.664362E-06
TI47 6.911865E-06
TI48 6.848666E-05
TI49 5.025975E-06
TI50 4.812276E-06
V50 6.547067E-06
ZR90 1.880991E-06
ZR91 4.102079E-07
ZR92 6.270069E-07
ZR94 6.354168E-07
ZR96 1.023695E-07
W182 4.807576E-07
W183 2.596087E-07
W184 5.580372E-07
W186 5.157674E-07
CU63 3.630382E-06
CU65 1.618092E-06
CO59 5.659272E-06
CA40 8.067160E-06
CA42 5.384173E-08
CA43 1.123394E-08
CA44 1.735891E-07
CA46 3.328683E-10
CA48 1.556192E-08
NB93 1.794891E-06
N14 1.186194E-05
N15 4.381178E-08
AL27 6.180469E-06
TA181 9.215854E-07
B10 1.227894E-06
B11 4.942575E-06
PB204 3.224084E-04
PB206 5.549972E-03
PB207 5.089375E-03
PB208 1.206694E-02'
density_type = atomic
composition_ids = '${mid_J}'
[]
[]
[Materials]
[Fuel_Ring1_Hole]
type = MicroNeutronicsMaterial
block = '${bid_F_fuel_R1} ${bid_F_heliumc} ${bid_F_helium}'
library_id = '${lid_F_fuel_R1}'
[]
[Fuel_Ring2]
type = MicroNeutronicsMaterial
block = '${bid_F_fuel_R2}'
library_id = '${lid_F_fuel_R2}'
[]
[Fuel_Ring3]
type = MicroNeutronicsMaterial
block = '${bid_F_fuel_R3}'
library_id = '${lid_F_fuel_R3}'
[]
[Fuel_Ring4]
type = MicroNeutronicsMaterial
block = '${bid_F_fuel_R4}'
library_id = '${lid_F_fuel_R4}'
[]
[Fuel_Ring5]
type = MicroNeutronicsMaterial
block = '${bid_F_fuel_R5}'
library_id = '${lid_F_fuel_R5}'
[]
[Fuel_Ring6]
type = MicroNeutronicsMaterial
block = '${bid_F_fuel_R6}'
library_id = '${lid_F_fuel_R6}'
[]
[Fuel_Ring7]
type = MicroNeutronicsMaterial
block = '${bid_F_fuel_R7}'
library_id = '${lid_F_fuel_R7}'
[]
[Fuel_Clad]
type = MicroNeutronicsMaterial
block = '${bid_F_clad}'
library_id = '${lid_F_clad}'
[]
[Fuel_Lead]
type = MicroNeutronicsMaterial
block = '${bid_F_lead}'
library_id = '${lid_F_lead}'
[]
[Fuel_LeadGap]
type = MicroNeutronicsMaterial
block = '${bid_F_leadgap}'
library_id = '${lid_F_leadgap}'
[]
[Fuel_Duct]
type = MicroNeutronicsMaterial
block = '${bid_F_duct}'
library_id = '${lid_F_duct}'
[]
[LowerCorePlate]
type = MicroNeutronicsMaterial
block = '${bid_A} ${bid_Ac}'
library_id = '${lid_A}'
[]
[InletWrapper]
type = MicroNeutronicsMaterial
block = '${bid_B} ${bid_Bc}'
library_id = '${lid_B}'
[]
[LowerBundle]
type = MicroNeutronicsMaterial
block = '${bid_C} ${bid_Cc}'
library_id = '${lid_C}'
[]
[LowerGasPlenum]
type = MicroNeutronicsMaterial
block = '${bid_D_lead} ${bid_D_clad} ${bid_D_duct} ${bid_D_tubemix} ${bid_D_tubemixc}'
library_id = '${lid_D}'
[]
[LowerInsulator]
type = MicroNeutronicsMaterial
block = '${bid_E_lead} ${bid_E_clad} ${bid_E_duct} ${bid_E_yszmix} ${bid_E_yszmixc}'
library_id = '${lid_E}'
[]
[UpperInsulator]
type = MicroNeutronicsMaterial
block = '${bid_G_lead} ${bid_G_clad} ${bid_G_duct} ${bid_G_yszmix} ${bid_G_yszmixc}'
library_id = '${lid_G}'
[]
[UpperGasPlenum]
type = MicroNeutronicsMaterial
block = '${bid_H_lead} ${bid_H_clad} ${bid_H_duct} ${bid_H_springmix} ${bid_H_springmixc}'
library_id = '${lid_H}'
[]
[UpperBundle]
type = MicroNeutronicsMaterial
block = '${bid_I} ${bid_Ic}'
library_id = '${lid_I}'
[]
[OutletWrapper]
type = MicroNeutronicsMaterial
block = '${bid_J} ${bid_Jc}'
library_id = '${lid_J}'
[]
[]In [GlobalParams], is_meter=true is to indicate that the mesh is in a unit of meter and plus=true to indicate that absorption, fission, and kappa fission cross sections are to be evaluated. grid_names is the grid name in <Tabulation> of a library and grid is its associated grid index of the target cross section table in the library. Since the grid name is the same and there is only one grid point of in all the libraries, they are specified in [GlobalParams]. Again, the value means nothing but is just a dummay value in this work.
Results
The k-effective result of MCNP is and that of Griffin is which is pcm off. Pin power results are also in a good agreement with a root-mean-square error of and a maximum error of . Figure 9 shows the axial power distribution of each of 127 pins normalized to have the unity average value for the whole axial and radial meshes. They are very similar to each other since fuel pins are identical and the mean free path of neutron is much larger than the pin pitch. The axial power distribution is slightly top skewed because of slighly harder spectrum at the upper part of the fuel region caused by stronger leakage to the top than to the bottom. Harder spectrum causes more fission in a fast spectrum. Figure 10 compares the axial power distribution of MCNP at the center pin with that of Griffin and shows the relative error of the Griffin result. The Griffin result matches well in error. Errors are similar for other pins.
Figure 9: MCNP axial power distribution for each of 127 pins
Figure 10: Comparison of MCNP and Griffin axial power distributions of the center pin and the relative error (%) of the Griffin result
Figure 11, Figure 12, and Figure 13 show radial power density profiles of Griffin at the middle, lowest and highest axial meshes of the fuel region. At the lowest and highest axial meshes, inner pins have lower power, peripheral pins have higher power, and the corner pins have the highest power, with difference between the highest and smallest power. At the middle axial mesh, center pins have relatively higher power than they do at lower and upper axial meshes and peripheral pins have relatively lower power than they do at lower and upper axial meshes, resulting in flatter radial profile with difference between the highest and smallest power.
Figure 11: Radial power density profile at the middle axial mesh of the fuel region
Figure 12: Radial power density profile at the lowest axial mesh of the fuel region
Figure 13: Radial power density profile at the highest axial mesh of the fuel region
Figure 14 compares performance of calculations with and without CMFD using different input options using 144 processors in the Sawtooth HPC cluster of Idaho National Laboratory. The top left plot shows the total number of Richardson iterations until convergence with the relative tolerance of . The legend applies to the other three plots, too. The top right plot shows the total computing wall time (minutes). The bottom left plot shows the average computing time (seconds) of transport sweeps per Richardson iteration. The bottom right plot shows the average computing time (seconds) of CMFD solves per Richardson iteration. inner_solve_types of GMRes and SI with enable_group_sweep=true and false, and inner_solve_type=none were tested and a pure transport sweeps without the CMFD acceleration was also tested.
First of all, from the top left plot, the GMRes inner solve type is very effective, immediately dropping the number of Richardson iterations from to . Then, the number of Richardson iterations does not decrease much over increasing maximum number of inner iterations, which means the small number of inner iterations is sufficient for GMRes. Meanwhile, SI is not immediately effective, but needs larger number of inner iterations to drop the number of Richardson iterations to the similar level with GMRes. The number of Richardson iterations of SI becomes smaller than that of GMRes at the maximum number of inner iterations of to . Meanwhile, the total computing time of SI becomes smaller than that of GMRes at the maximum number of inner iterations of to mainly because of the smaller computing time of transport sweeps per Richardson iteration for SI. Turning enable_group_sweep on always degrades the performance because of larger transport sweeping time with almost no effect of decreasing the number of Richardson iterations. The best performance is observed with SI without group sweeping at the maximum number of inner iterations of (almost similar between to ). It should be noted that the CMFD acceleration shows an excellent performance of 10 times speed-up in total time (6.5 minutes with CMFD vs. 65 minutes without CMFD). inner_solve_type=none with the CMFD acceleration shows almost the same performance as SI with the maximum number of inner iterations of . It should be noted that this performance characteristics is specific to this problem and calculation settings (fine and coarse meshes, etc.) and would be different for different problems.
Figure 14: Performance comparison of calculations with and without CMFD using different input options
Future works
Future works include the following.
The cross section data will be generated in a single Griffin input. The MC2-3/TWODANT procedure will be replaced by a native Griffin procedure and the development is under progress.
A multiphysics coupled calculation with the computational fluid dynamics code NekRS (Fischer et al., 2022) through the Cardinal (Novak et al., 2022) interface and the MOOSE heat conduction module will be performed .
Run command
Griffin can be run using the following command. The additional command line argument -pc_hypre_boomeramg_agg_nl is for the speed-up of the calculation. Detailed information can be found in HYPRE/BoomerAMG.
mpirun -np 144 griffin-opt -i neutronics.i -pc_hypre_boomeramg_agg_nl 4
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