Output parameters

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This page lists the output parameters in the main [input]_res.m output file.


Homogenized group constants

Notes:

  • Group constants are calculated by first homogenizing the geometry using a multi-group structure with H energy groups. The data is then collapsed into the final few-group structure with G groups using the infinite and B1 leakage-corrected flux spectra.
  • The methodology used in Serpent for spatial homogenization is described in a paper published in Annals of Nuclear Energy in 2016.[1]
  • The B1 calculation is off by default, and invoked by the set fum option.
  • The intermediate multi-group structure is defined using option set micro.
  • The few-group structure is defined using option set nfg.
  • The universes in which the group constants are calculated are listed in option set gcu. The calculation is performed for root universe 0 by default, and can be switched off with "set gcu -1".
  • If data is produced in multiple universes within a single run, the data is assigned with different run indexes (idx)
  • The parameter names can be listed in the set coefpara option, and they will be included in the group constant output file when the automated burnup sequence is invoked.
  • The order in which two-dimensional data (scattering matrices, ADF and pin-power parameters) is printed in the .coef output is different from what is listed below in update 2.1.24 and earlier versions.

Common parameters

Parameter Size Description
GC_UNIVERSE_NAME (string) Name of the universe where spatial homogenization was performed
MICRO_NG 1 Number of energy groups in the intermediate multi-group structure (referred to as H below)
MICRO_E H + 1 Group boundaries in the intermediate multi-group structure (in ascending order)
MACRO_NG 1 Number of energy groups in the final few-group structure (referred to as G below)
MACRO_E G + 1 Group boundaries in the final few-group structure (in descending order)

Group constants homogenized in infinite spectrum

Parameter Size Description
INF_MICRO_FLX 2H Multi-group flux spectrum (integral, un-normalized)
INF_FLX 2G Few-group flux (integral, normalized)
INF_KINF 2 Infinite multiplication factor

Reaction cross sections

Parameter Size Description
INF_TOT 2G Total cross section
INF_CAPT 2G Capture cross section
INF_FISS 2G Fission cross section
INF_NSF 2G Fission neutron production cross section
INF_KAPPA 2G Average deposited fission energy (MeV)
INF_INVV 2G Inverse neutron speed (s/cm)
INF_NUBAR 2G Average neutron yield
INF_ABS 2G Absorption cross section (capture + fission)
INF_REMXS 2G Removal cross section (group-removal + absorption)
INF_RABSXS 2G Reduced absorption cross section (total - scattering production)

Fission spectra

Parameter Size Description
INF_CHIT 2G Fission spectrum (total)
INF_CHIP 2G Fission spectrum (prompt neutrons)
INF_CHID 2G Fission spectrum (delayed neutrons)

Scattering cross sections

Notes:

  • Scattering production includes multiplying (n,2n), (n,3n), etc. reactions.
Parameter Size Description
INF_SCATT0 2G Total P0 scattering cross section
INF_SCATT1 2G Total P1 scattering cross section
INF_SCATT2 2G Total P2 scattering cross section
INF_SCATT3 2G Total P3 scattering cross section
INF_SCATT4 2G Total P4 scattering cross section
INF_SCATT5 2G Total P5 scattering cross section
INF_SCATT6 2G Total P6 scattering cross section
INF_SCATT7 2G Total P7 scattering cross section
INF_SCATTP0 2G Total P0 scattering production cross section
INF_SCATTP1 2G Total P1 scattering production cross section
INF_SCATTP2 2G Total P2 scattering production cross section
INF_SCATTP3 2G Total P3 scattering production cross section
INF_SCATTP4 2G Total P4 scattering production cross section
INF_SCATTP5 2G Total P5 scattering production cross section
INF_SCATTP6 2G Total P6 scattering production cross section
INF_SCATTP7 2G Total P7 scattering production cross section

Scattering matrices

Notes:

  • Scattering production includes multiplying (n,2n), (n,3n), etc. reactions.
  • The order of values (.coe) or value pairs (_res.m) is: \Sigma_{1,1} \, \Sigma_{1,2} \, ... \, \Sigma_{2,1} \, \Sigma_{2,2}  \, ... where \Sigma_{g,g'} refers to scattering from group g to g'.
  • The data in the _res.m file can be read into a G by G matrix with Matlab reshape-command, for example:
reshape(INF_S0(idx,1:2:end), G, G);
Parameter Size Description
INF_S0 4G2 P0 scattering matrix
INF_S1 4G2 P1 scattering matrix
INF_S2 4G2 P2 scattering matrix
INF_S3 4G2 P3 scattering matrix
INF_S4 4G2 P4 scattering matrix
INF_S5 4G2 P5 scattering matrix
INF_S6 4G2 P6 scattering matrix
INF_S7 4G2 P7 scattering matrix
INF_SP0 4G2 P0 scattering production matrix
INF_SP1 4G2 P1 scattering production matrix
INF_SP2 4G2 P2 scattering production matrix
INF_SP3 4G2 P3 scattering production matrix
INF_SP4 4G2 P4 scattering production matrix
INF_SP5 4G2 P5 scattering production matrix
INF_SP6 4G2 P6 scattering production matrix
INF_SP7 4G2 P7 scattering production matrix

Diffusion parameters

Notes:

  • The cumulative migration method [2] was first developed for the OpenMC code. Currently the method works only when the homogenized region covers the entire geometry, and is surrounded by periodic or reflective boundary conditions.
  • Calculation of TRC_TRANSPXS and TRC_DIFFCOEF requires defining energy-dependent correction factors using the set trc option.
Parameter Size Description
INF_TRANSPXS 2G Transport cross section (calculated using the out-scattering approximation)
INF_DIFFCOEF 2G Diffusion coefficient (calculated using the out-scattering approximation)
CMM_TRANSPXS 2G Transport cross section calculated using the cumulative migration method (equivalent with the in-scattering approximation)
CMM_TRANSPXS_X 2G X-component of the directional transport cross section calculated using the cumulative migration method (equivalent with the in-scattering approximation)
CMM_TRANSPXS_Y 2G Y-component of the directional transport cross section calculated using the cumulative migration method (equivalent with the in-scattering approximation)
CMM_TRANSPXS_Z 2G Z-component of the directional transport cross section calculated using the cumulative migration method (equivalent with the in-scattering approximation)
CMM_DIFFCOEF 2G Diffusion coefficient calculated using the cumulative migration method (equivalent with the in-scattering approximation)
CMM_DIFFCOEF_X 2G X-component of the directional diffusion coefficient calculated using the cumulative migration method (equivalent with the in-scattering approximation)
CMM_DIFFCOEF_Y 2G Y-component of the directional diffusion coefficient calculated using the cumulative migration method (equivalent with the in-scattering approximation)
CMM_DIFFCOEF_Z 2G Z-component of the directional diffusion coefficient calculated using the cumulative migration method (equivalent with the in-scattering approximation)
TRC_TRANSPXS 2G Transport cross section calculated by applying user-defined transport correction factors to total cross section
TRC_DIFFCOEF 2G Diffusion coefficient calculated by applying user-defined transport correction factors to total cross section

Poison cross sections

Notes:

  • Printed only if poison cross section option is on (see set poi).
Parameter Size Description
INF_I135_YIELD 2G Fission yield of I-135 (cumulative, includes all precursors)
INF_XE135_YIELD 2G Fission yield of Xe-135
INF_PM149_YIELD 2G Fission yield of Pm-149 (cumulative, includes all precursors)
INF_SM149_YIELD 2G Fission yield of Sm-149
INF_I135_MICRO_ABS 2G Microscopic absorption cross section of I-135
INF_XE135_MICRO_ABS 2G Microscopic absorption cross section of Xe-135
INF_PM149_MICRO_ABS 2G Microscopic absorption cross section of Pm-149
INF_SM149_MICRO_ABS 2G Microscopic absorption cross section of Sm-149
INF_XE135_MACRO_ABS 2G Macroscopic absorption cross section of Xe-135
INF_SM149_MACRO_ABS 2G Macroscopic absorption cross section of Sm-149

Group constants homogenized in B1 leakage-corrected spectrum

Parameter Size Description
B1_MICRO_FLX 2H Multi-group flux spectrum (integral, un-normalized)
B1_FLX 2G Few-group flux (integral, normalized)
B1_KINF 2 Infinite multiplication factor
B1_KEFF 2 Effective multiplication factor
B1_B2 2 Critical buckling
B1_ERR 2 Absolute deviation of keff from unity

Reaction cross sections

Parameter Size Description
B1_TOT 2G Total cross section
B1_CAPT 2G Capture cross section
B1_FISS 2G Fission cross section
B1_NSF 2G Fission neutron production cross section
B1_KAPPA 2G Average deposited fission energy (MeV)
B1_INVV 2G Inverse neutron speed (s/cm)
B1_NUBAR 2G Average neutron yield
B1_ABS 2G Absorption cross section (capture + fission)
B1_REMXS 2G Removal cross section (group-removal + absorption)
B1_RABSXS 2G Reduced absorption cross section (total - scattering production)

Fission spectra

Parameter Size Description
B1_CHIT 2G Fission spectrum (total)
B1_CHIP 2G Fission spectrum (prompt neutrons)
B1_CHID 2G Fission spectrum (delayed neutrons)

Scattering cross sections

Notes:

  • Scattering production includes multiplying (n,2n), (n,3n), etc. reactions.
Parameter Size Description
B1_SCATT0 2G Total P0 scattering cross section
B1_SCATT1 2G Total P1 scattering cross section
B1_SCATT2 2G Total P2 scattering cross section
B1_SCATT3 2G Total P3 scattering cross section
B1_SCATT4 2G Total P4 scattering cross section
B1_SCATT5 2G Total P5 scattering cross section
B1_SCATT6 2G Total P6 scattering cross section
B1_SCATT7 2G Total P7 scattering cross section
B1_SCATTP0 2G Total P0 scattering production cross section
B1_SCATTP1 2G Total P1 scattering production cross section
B1_SCATTP2 2G Total P2 scattering production cross section
B1_SCATTP3 2G Total P3 scattering production cross section
B1_SCATTP4 2G Total P4 scattering production cross section
B1_SCATTP5 2G Total P5 scattering production cross section
B1_SCATTP6 2G Total P6 scattering production cross section
B1_SCATTP7 2G Total P7 scattering production cross section

Scattering matrices

Notes:

  • Scattering production includes multiplying (n,2n), (n,3n), etc. reactions.
  • The order of values (.coe) or value pairs (_res.m) is: \Sigma_{1,1} \, \Sigma_{1,2} \, ... \, \Sigma_{2,1} \, \Sigma_{2,2}  \, ... where \Sigma_{g,g'} refers to scattering from group g to g'.
  • The data in the _res.m file can be read into a G by G matrix with Matlab reshape-command, for example:
reshape(B1_S0(idx,1:2:end), G, G).
Parameter Size Description
B1_S0 4G2 P0 scattering matrix
B1_S1 4G2 P1 scattering matrix
B1_S2 4G2 P2 scattering matrix
B1_S3 4G2 P3 scattering matrix
B1_S4 4G2 P4 scattering matrix
B1_S5 4G2 P5 scattering matrix
B1_S6 4G2 P6 scattering matrix
B1_S7 4G2 P7 scattering matrix
B1_SP0 4G2 P0 scattering production matrix
B1_SP1 4G2 P1 scattering production matrix
B1_SP2 4G2 P2 scattering production matrix
B1_SP3 4G2 P3 scattering production matrix
B1_SP4 4G2 P4 scattering production matrix
B1_SP5 4G2 P5 scattering production matrix
B1_SP6 4G2 P6 scattering production matrix
B1_SP7 4G2 P7 scattering production matrix

Diffusion parameters

Parameter Size Description
B1_TRANSPXS 2G Transport cross section (calculated from diffusion coefficient)
B1_DIFFCOEF 2G Diffusion coefficient

Poison cross sections

Notes:

  • Printed only if poison cross section option is on (see set poi).
Parameter Size Description
B1_I135_YIELD 2G Fission yield of I-135 (cumulative, includes all precursors)
B1_XE135_YIELD 2G Fission yield of Xe-135
B1_PM149_YIELD 2G Fission yield of Pm-149 (cumulative, includes all precursors)
B1_SM149_YIELD 2G Fission yield of Sm-149
B1_I135_MICRO_ABS 2G Microscopic absorption cross section of I-135
B1_XE135_MICRO_ABS 2G Microscopic absorption cross section of Xe-135
B1_PM149_MICRO_ABS 2G Microscopic absorption cross section of Pm-149
B1_SM149_MICRO_ABS 2G Microscopic absorption cross section of Sm-149
B1_XE135_MACRO_ABS 2G Macroscopic absorption cross section of Xe-135
B1_SM149_MACRO_ABS 2G Macroscopic absorption cross section of Sm-149

Delayed neutron data

Notes:

  • The output always consists of 9 values: total, followed by precursor group-wise values. If the number of groups is 6, the last two values are zero.
  • The actual number of groups depends on the cross section library used in the calculations. JEFF-3.1, JEFF.3.2 and later evaluations use 8 precursor groups, while earlier evaluations, as well as all ENDF/B and JENDL data is based on 6 groups.
Parameter Size Description
BETA_EFF 9 Effective delayed neutron fraction (currently calculated using the Meulekamp method)
LAMBDA 9 Decay constants

Assembly discontinuity factors

Notes:

  • Calculation of assembly discontinuity factors requires the set adf option.
  • Surface flux and current tallies are used to calculate the boundary currents and fluxes. Mid-point and corner values are approximated by integrating over a small surface segment.
  • Fluxes and currents are normalized average values.
  • When the homogenized region is surrounded by reflective boundary conditions (zero net-current) the homogeneous flux becomes flat and equal to the volume-averaged heterogeneous flux. When the net currents are non-zero, the homogeneous flux is obtained using the Built-in diffusion flux solver.
  • The calculation currently supports only a limited number of surface types: infinite planes and square and hexagonal prisms.
  • The order of surface and mid-point values for square prisms is: X_{\mathrm{W},1} \, X_{\mathrm{W},2} \, ... \, X_{\mathrm{S},1} \, X_{\mathrm{S},2} \, ... \, X_{\mathrm{E},1} \, X_{\mathrm{E},2} \, ... \, X_{\mathrm{N},1} \, X_{\mathrm{N},2} \, ... and the order of corner values: X_{\mathrm{NW},1} \, X_{\mathrm{NW},2} \, ... \, X_{\mathrm{NE},1} \, X_{\mathrm{NE},2} \, ... \, X_{\mathrm{SE},1} \, X_{\mathrm{SE},2} \, ... \, X_{\mathrm{SW},1} \, X_{\mathrm{SW},2} \, ... where X_{k,g} refers to parameter X on surface/corner k and energy group g.
  • The order of surface and mid-point values for hexagonal prims runs clockwise starting from the north (Y-type) or east (X-type) face. The corner values start from the next corner in clockwise direction.
  • Note to developers: the description may be wrong for for X-type hexagonal prism.
Parameter Size Description
DF_SURFACE (string) Name of the surface used for the calculation
DF_SYM 1 Symmetry option defined in the input
DF_N_SURF 1 Number of surface values (denoted as NS below)
DF_N_CORN 1 Number of corner values (denoted as NC below)
DF_VOLUME 1 Volume (3D) or cross sectional area (2D) of the homogenized cell
DF_SURF_AREA NS Area (3D) or perimeter length (2D) of the surface region
DF_MID_AREA NS Area (3D) or perimeter length (2D) of the mid-point region
DF_CORN_AREA NS Area (3D) or perimeter length (2D) of the corner region
DF_SURF_IN_CURR 2G \times NS Inward surface currents
DF_SURF_OUT_CURR 2G \times NS Outward surface currents
DF_SURF_NET_CURR 2G \times NS Net surface currents
DF_MID_IN_CURR 2G \times NS Inward mid-point currents
DF_MID_OUT_CURR 2G \times NS Outward mid-point currents
DF_MID_NET_CURR 2G \times NS Net mid-point currents
DF_CORN_IN_CURR 2G \times NC Inward corner currents
DF_CORN_OUT_CURR 2G \times NC Outward corner currents
DF_CORN_NET_CURR 2G \times NC Net corner currents
DF_HET_VOL_FLUX 2G Heterogeneous flux over homogenized cell
DF_HET_SURF_FLUX 2G \times NS Heterogeneous surface flux
DF_HET_CORN_FLUX 2G \times NC Heterogeneous corner flux
DF_HOM_VOL_FLUX 2G Homogeneous flux over homogenized cell
DF_HOM_SURF_FLUX 2G \times NC Homogeneous surface flux
DF_HOM_CORN_FLUX 2G \times NC Homogeneous corner flux
DF_SURF_DF 2G \times NC Surface discontinuity factors
DF_CORN_DF 2G \times NC Corner discontinuity factors

Pin-power form factors

Notes:

  • Calculation of pin-power form factors requires the set ppw option.
  • The power distribution is calculated by tallying the few-group fission energy deposition in each lattice position and dividing the values with the total energy produced in the universe (sum over all values of PPW_POW equals 1).
  • The calculation of form factors depends on the boundary conditions:
    1. If the homogenized region is surrounded by reflective boundary conditions (zero net-current), the homogeneous flux becomes flat and equal to the volume-averaged heterogeneous flux. Variables PPW_HOM_FLUX and PPW_FF are then omitted.
    2. When the net currents are non-zero, the homogeneous flux is obtained using the built-in diffusion flux solver. The form-factors (PPW_FF) are obtained by dividing the pin- and group-wise powers with the corresponding homogeneous diffusion flux (PPW_HOM_FLUX).
  • Running the diffusion flux solver currently requires ADF calculation.
  • The order of values is: X_{1,1} \, X_{1,2} \, ... \, X_{2,1} \, X_{2,2} \, ... where X_{n,g} refers to parameter X of pin n and energy group g. For example, two-group power distributions in a 17\times17 lattice can be converted into matrix form using the reshape-command in Matlab:
P1 = reshape(PPW_POW(1,1:4:end), 17, 17);
P2 = reshape(PPW_POW(1,3:4:end), 17, 17);
Parameter Size Description
PPW_LATTICE (string) Name of the lattice used for the calculation
PPW_LATTICE_TYPE 1 Lattice type (corresponds to the lat-card)
PPW_PINS 1 Number of pin positions in the lattice (denoted as NP below)
PPW_POW 2G \times NP Pin-wise power distribution
PPW_HOM_FLUX 2G \times NP Pin-wise homogeneous flux distribution
PPW_FF 2G \times NP Pin-wise form factors

Albedos

References

  1. ^ Leppänen, J., Pusa, M. and Fridman, E. "Overview of methodology for spatial homogenization in the Serpent 2 Monte Carlo code." Ann. Nucl. Energy, 96 (2016) 126-136.
  2. ^ Liu, Z., Smith, K. and Forget, B. "A Cumulative Migration Method for Computing Rigorous Transport Cross Sections and Diffusion Coefficients for LWR Lattices with Monte Carlo." In proc. PHYSOR 2016, Sun Valley, Idaho, May 1-5, 2016.