FastNeutronFluxFromPower

Computes fast neutron flux and fluence for fuels composed of U, Pu, and other minor non-heavy metal elements that don't contribute to the total fission rate.

Description

The fast neutron flux, $var element = document.getElementById("moose-equation-939a60ad-dfc1-42cc-a0a4-94893f0d8d05");katex.render("{\\phi}_{fast}(t,z)", element, {displayMode:false,throwOnError:false});$ , can be estimated by back-calculating the total flux, $var element = document.getElementById("moose-equation-ce04450d-b81b-4c12-a990-28d1bdc5a311");katex.render("{\\phi}_{tot}(t,z)", element, {displayMode:false,throwOnError:false});$ , from the axial fission rate density, $var element = document.getElementById("moose-equation-d2b7ad12-ea30-49b9-8898-3a21108a5f6b");katex.render("\\dot{F}(t,z)", element, {displayMode:false,throwOnError:false});$ , dividing by the macroscopic cross-section estimated from the initial isotopics of the fuel, $var element = document.getElementById("moose-equation-dc5beebf-1bb3-4950-b7f8-af3e952db5d3");katex.render("\\Sigma_{tot}", element, {displayMode:false,throwOnError:false});$ , and estimating the ratio of fast to total neutron flux, $var element = document.getElementById("moose-equation-325966d9-1081-46ea-b567-5a51cc676494");katex.render("\\gamma_{fast}", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-de5eb21a-ecbf-4da5-9825-f50f10cf880c");katex.render(" {\\phi}_{fast}(t,z) = \\frac{\\dot{F}(t,z)}{\\Sigma_{tot}} \\gamma_{fast}.", element, {displayMode:true,throwOnError:false});$

The axial fission rate density can be calculated using the average rod power and axial profile, similar to the treatment in UPuZrFissionRate, in cylindrical 2DRz geometry only (i.e., radial direction $var element = document.getElementById("moose-equation-cac10fdd-8a0d-4504-addb-6f5b6af9f915");katex.render("r", element, {displayMode:false,throwOnError:false});$ and axial direction $var element = document.getElementById("moose-equation-b3ae14f7-4ccf-423a-ac62-0f8f153e56be");katex.render("z", element, {displayMode:false,throwOnError:false});$ ). $var element = document.getElementById("moose-equation-29d49db5-6549-4e0c-b9d5-a5892d2c298d");katex.render("\\dot{F}(t, z)", element, {displayMode:false,throwOnError:false});$ is calculated based on the rod linear power $var element = document.getElementById("moose-equation-337a1b5a-0f87-4540-ac7b-c3f5589eb10c");katex.render("P_l(t)", element, {displayMode:false,throwOnError:false});$ and axial power profile $var element = document.getElementById("moose-equation-8c6c76c0-4426-4f44-a662-7b1c20e09fd8");katex.render("P_a(t, z)", element, {displayMode:false,throwOnError:false});$ as, $var element = document.getElementById("moose-equation-8bc1db15-247f-41d8-bb8a-e1f26a63fa56");katex.render(" \\dot{F}(t, z) = P_l(t) \\cdot P_a(t, z) \\cdot epf,", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-82963473-5dc1-4dd8-a22e-dec6243fdb68");katex.render("epf = 3.28\\times10^{-11}", element, {displayMode:false,throwOnError:false});$ (J/fsn) is the energy released per fission event.

$var element = document.getElementById("moose-equation-a01b577b-2ddd-4afb-9376-5b81283fd95c");katex.render("P_l(t)", element, {displayMode:false,throwOnError:false});$ is passed as a Function given only as a function of time. This function corresponds to the power produced by the entire fuel pin.

$var element = document.getElementById("moose-equation-b83f006b-12f9-4d6e-9258-587b5492fb91");katex.render("P_a(t, z)", element, {displayMode:false,throwOnError:false});$ is also passed as a Function, only as a function of time and axial position. This can be completed in any Function, but is typically provided via PowerPeakingFunction. $var element = document.getElementById("moose-equation-99650089-654e-405a-9269-ecf3c8206629");katex.render("P_a", element, {displayMode:false,throwOnError:false});$ represents the ratio between the power at any axial slice of the fuel and the total rod power $var element = document.getElementById("moose-equation-161be455-31c9-496f-ab3a-c87ea1e109af");katex.render("P_l", element, {displayMode:false,throwOnError:false});$ , and must be normalized to return an average value of 1 over the entire length of the rod, $var element = document.getElementById("moose-equation-417da917-5231-40c7-aa6f-d8ccadf2f94b");katex.render(" \\frac{\\int_0^L P_a(t,z)dz}{L} = 1,", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-cb2c9ffd-c50a-4edf-a9f6-f7e71076a1e3");katex.render("L", element, {displayMode:false,throwOnError:false});$ is the length of the rod.

The macroscopic cross-section can be estimated from the weighted sum of number density of the individual fuel constituents, $var element = document.getElementById("moose-equation-03703f70-156a-4b3d-b867-a156eafb2a18");katex.render("N", element, {displayMode:false,throwOnError:false});$ , by their microscopic fission cross-sections $var element = document.getElementById("moose-equation-0a53a380-205e-4a35-a1f8-561835c5fcb2");katex.render("\\sigma", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-b145251f-b4ec-4f21-b864-b39f155cea32");katex.render(" \\Sigma_{tot} = \\sum_i^I N_i \\sigma_i,", element, {displayMode:true,throwOnError:false});$ where the set of all constituents, $var element = document.getElementById("moose-equation-571ab8dc-6f9f-4522-b089-9c3deb348448");katex.render("I", element, {displayMode:false,throwOnError:false});$ , is taken as {U-235, U-238, Pu-239, Pu-240}. The individual number densities are calculated from the atom weights of the constituents, $var element = document.getElementById("moose-equation-099475be-e83d-441e-9166-35ae52e03b63");katex.render("A_i", element, {displayMode:false,throwOnError:false});$ , the atom fractions of each constituent $var element = document.getElementById("moose-equation-5812c56f-4b6b-4fce-a1f0-2564a737289b");katex.render("X_i", element, {displayMode:false,throwOnError:false});$ , and the total fuel density, $var element = document.getElementById("moose-equation-a98dc8bf-8795-4cf2-9cee-d474427be3a5");katex.render("\\rho", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-c7d3560a-95d8-461d-bf6f-362c88f05178");katex.render(" N_i = \\frac{X_i N_A \\rho}{\\sum_i^I \\left(X_i A_i\\right)}.", element, {displayMode:true,throwOnError:false});$ The atomic weights of the non-heavy metal atoms can be selected from a "non_heavy_metal_atom" (e.g., Zr, N, C for UZr, UC, UN fuels). If a non-metal atom is not in "non_heavy_metal_atom", the atomic weight of the custom non-heavy metal atom can be supplied via "A_custom_non_heavy_metal_atom". If more than one non-heavy metal atom is present (e.g., U(N,C)), "A_custom_non_heavy_metal_atom" should be the weighted average of the atomic weights, for example, with U(C,N), $var element = document.getElementById("moose-equation-74b8a5b9-d674-4bec-a390-8928dadba766");katex.render(" A_{C,N} = \\frac{A_C X_C + A_N X_N}{X_{C,N}}.", element, {displayMode:true,throwOnError:false});$

The microscopic fission cross-sections implemented as defaults in FastNeutronFluxFromPower are collapsed from the eight-group cross-sections provided in Waltar et al. (2011), weighted by the EBR-II flux spectrum from Withop et al. (1969)

The ratio of the fast to total neutron flux, $var element = document.getElementById("moose-equation-9dc381fb-a04a-448b-955b-3376522471d6");katex.render("\\gamma_{fast}=0.9", element, {displayMode:false,throwOnError:false});$ , is estimated from Withop et al. (1969), and corresponds to the neutron flux with energies above 0.1 MeV.

Given the flux at each timestep, the fast neutron fluence can be optionally calculated via an average over the current and previous time step, $var element = document.getElementById("moose-equation-f21a3392-4510-43a8-a773-65d766ca73be");katex.render("\\Phi = \\Phi_{old} + 0.5 \\Delta t ({\\phi} + {\\phi}_{old}).", element, {displayMode:true,throwOnError:false});$

Similarly, the displacements per atom (dpa) can be calculated assuming a conversion factor of $var element = document.getElementById("moose-equation-78115f86-4d16-46aa-8382-688db07e28cb");katex.render("f = 2\\times 10^{25}", element, {displayMode:false,throwOnError:false});$ n/m $var element = document.getElementById("moose-equation-752ae7ac-9a68-4f24-ab0d-221622074abc");katex.render("^2", element, {displayMode:false,throwOnError:false});$ per dpa from Waltar et al. (2011), $var element = document.getElementById("moose-equation-837a6bdd-65ed-4078-b641-ad5496d7c72e");katex.render("\\text{dpa} = \\text{dpa}_{old} + 0.5 \\Delta t f^{-1} (\\phi + \\phi_{old}).", element, {displayMode:true,throwOnError:false});$

Example Input Syntax

[Materials<<<{"href": "../../syntax/Materials/index.html"}>>>]
  [flux]
    type = FastNeutronFluxFromPower<<<{"description": "Computes fast neutron flux and fluence for fuels composed of U, Pu, and other minor non-heavy metal elements that don't contribute to the total fission rate.", "href": "FastNeutronFluxFromPower.html"}>>>
    axial_power_profile<<<{"description": "Function that describes the axial power profile as a function of axial position and time."}>>> = power_history
    rod_linear_power<<<{"description": "Function that describes the linear power as a function of time."}>>> = axial_peaking_factors
    initial_X_Pu<<<{"description": "Initial atom fraction of plutonium"}>>> = 0.2
    initial_X_non_heavy_metal_atoms<<<{"description": "Relative atomic weight of non-metal contributions to the fuel. In the case for more than one non-metal atoms, this should be the sum of all non-metal atoms."}>>> = 0.1
    non_heavy_metal_atom<<<{"description": "Non-metal atom in fuel (non-actinides). Choices are: CUSTOM ZR N C. If custom is picked, 'A_nhm_custom' must be provided"}>>> = Zr
    initial_density<<<{"description": "Initial density of the fuel"}>>> = 15800
    pellet_radius<<<{"description": "Fuel pellet radius"}>>> = 0.003
    enrichment_Pu240<<<{"description": "Initial ratio of Pu-240 to total plutonium"}>>> = 0.3
    enrichment_U235<<<{"description": "Initial ratio of U-235 to total uranium"}>>> = 0.2
    outputs<<<{"description": "Vector of output names where you would like to restrict the output of variables(s) associated with this object"}>>> = all
    calculate_fluence<<<{"description": "Flag to calculate total neutron fluence from the fast flux."}>>> = true
  []
[]

Input Parameters

axial_power_profileFunction that describes the axial power profile as a function of axial position and time.
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:Function that describes the axial power profile as a function of axial position and time.
initial_X_PuInitial atom fraction of plutonium
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Initial atom fraction of plutonium
initial_X_non_heavy_metal_atomsRelative atomic weight of non-metal contributions to the fuel. In the case for more than one non-metal atoms, this should be the sum of all non-metal atoms.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Relative atomic weight of non-metal contributions to the fuel. In the case for more than one non-metal atoms, this should be the sum of all non-metal atoms.
initial_densityInitial density of the fuel
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Initial density of the fuel
non_heavy_metal_atomNon-metal atom in fuel (non-actinides). Choices are: CUSTOM ZR N C. If custom is picked, 'A_nhm_custom' must be provided
C++ Type:MooseEnum
Options:CUSTOM, ZR, N, C
Controllable:No
Description:Non-metal atom in fuel (non-actinides). Choices are: CUSTOM ZR N C. If custom is picked, 'A_nhm_custom' must be provided
pellet_radiusFuel pellet radius
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Fuel pellet radius
rod_linear_powerFunction that describes the linear power as a function of time.
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:Function that describes the linear power as a function of time.

Required Parameters

A_custom_non_heavy_metal_atomAtomic weight of non-metal contributions to the fuel. In the case for more than one non-metal atoms, each individual atom weight should be multiplied by the relative concentration to the total non-metal atom ratio. (kg/mol).
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Atomic weight of non-metal contributions to the fuel. In the case for more than one non-metal atoms, each individual atom weight should be multiplied by the relative concentration to the total non-metal atom ratio. (kg/mol).
blockThe list of blocks (ids or names) that this object will be applied
C++ Type:std::vector<SubdomainName>
Controllable:No
Description:The list of blocks (ids or names) that this object will be applied
boundaryThe list of boundaries (ids or names) from the mesh where this object applies
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:The list of boundaries (ids or names) from the mesh where this object applies
calculate_dpaFalseFlag to calculate dpa.
Default:False
C++ Type:bool
Controllable:No
Description:Flag to calculate dpa.
calculate_dpa_rateFalseFlag to calculate dpa rate.
Default:False
C++ Type:bool
Controllable:No
Description:Flag to calculate dpa rate.
calculate_fluenceFalseFlag to calculate total neutron fluence from the fast flux.
Default:False
C++ Type:bool
Controllable:No
Description:Flag to calculate total neutron fluence from the fast flux.
computeTrueWhen false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
Default:True
C++ Type:bool
Controllable:No
Description:When false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
constant_onNONEWhen ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
Default:NONE
C++ Type:MooseEnum
Options:NONE, ELEMENT, SUBDOMAIN
Controllable:No
Description:When ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
declare_suffixAn optional suffix parameter that can be appended to any declared properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:An optional suffix parameter that can be appended to any declared properties. The suffix will be prepended with a '_' character.
dpa_conversion_factor2e+25Conversion factor from fast neutron fluence to dpa, in (n/m^2 per dpa).
Default:2e+25
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Conversion factor from fast neutron fluence to dpa, in (n/m^2 per dpa).
dpa_namedpaName of the dpa material property this object creates
Default:dpa
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:Name of the dpa material property this object creates
energy_per_fission3.28451e-11energy per fission
Default:3.28451e-11
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:energy per fission
enrichment_Pu2400.1Initial ratio of Pu-240 to total plutonium
Default:0.1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Initial ratio of Pu-240 to total plutonium
enrichment_U2350.67Initial ratio of U-235 to total uranium
Default:0.67
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Initial ratio of U-235 to total uranium
fast_neutron_fluence_namefast_neutron_fluenceName of the fast neutrom flux material property this object creates
Default:fast_neutron_fluence
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:Name of the fast neutrom flux material property this object creates
fast_neutron_flux_namefast_neutron_fluxName of the fast neutrom flux material property this object creates
Default:fast_neutron_flux
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:Name of the fast neutrom flux material property this object creates
fast_spectrum_ratio0.9Ratio of fast flux (greater than 0.1 MeV) to total flux.
Default:0.9
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Ratio of fast flux (greater than 0.1 MeV) to total flux.
flux_scale_factor1Scalar multiplied against the flux for calibration or sensitivity studies
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Scalar multiplied against the flux for calibration or sensitivity studies
pellet_inner_radius0Pellet inner radius
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Pellet inner radius
sigma_Pu2391.658Collapsed one-group fission cross-section for plutonium-239 (b)
Default:1.658
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Collapsed one-group fission cross-section for plutonium-239 (b)
sigma_Pu2400.703Collapsed one-group fission cross-section for plutonium-240 (b)
Default:0.703
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Collapsed one-group fission cross-section for plutonium-240 (b)
sigma_U2351.327Collapsed one-group fission cross-section for uranium-235 (b)
Default:1.327
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Collapsed one-group fission cross-section for uranium-235 (b)
sigma_U2380.095Collapsed one-group fission cross-section for uranium-238 (b)
Default:0.095
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Collapsed one-group fission cross-section for uranium-238 (b)

Optional Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:Yes
Description:Set the enabled status of the MooseObject.
implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Controllable:No
Description:Determines whether this object is calculated using an implicit or explicit form
seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Controllable:No
Description:The seed for the master random number generator
use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Default:False
C++ Type:bool
Controllable:No
Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

Advanced Parameters

output_propertiesList of material properties, from this material, to output (outputs must also be defined to an output type)
C++ Type:std::vector<std::string>
Controllable:No
Description:List of material properties, from this material, to output (outputs must also be defined to an output type)
outputsnone Vector of output names where you would like to restrict the output of variables(s) associated with this object
Default:none
C++ Type:std::vector<OutputName>
Controllable:No
Description:Vector of output names where you would like to restrict the output of variables(s) associated with this object

Outputs Parameters

prop_getter_suffixAn optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:An optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
use_interpolated_stateFalseFor the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.
Default:False
C++ Type:bool
Controllable:No
Description:For the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.

Material Property Retrieval Parameters

Input Files

(test/tests/fast_neutron_flux_from_power/rods.i)
(test/tests/fast_neutron_flux_from_power/nonad.i)
(test/tests/fast_neutron_flux_from_power/exact.i)
(test/tests/fast_neutron_flux_from_power/ad.i)

References

A.E. Waltar, D.R. Todd, and P.V. Tsvetkov. Fast Spectrum Reactors. Springer US, 2011. ISBN 9781441995728. URL: https://books.google.com/books?id=z8z\_RNUZSbEC.

@book{waltar2011fast,
    author = "Waltar, A.E. and Todd, D.R. and Tsvetkov, P.V.",
    title = "Fast Spectrum Reactors",
    isbn = "9781441995728",
    lccn = "2011935931",
    url = "https://books.google.com/books?id=z8z\\_RNUZSbEC",
    year = "2011",
    publisher = "Springer US"
}

A Withop, B A Hutchins, and G C Martin. Analytical Procedures and Applications of Fluence Determinations from EBR-II Flux Wires. Technical Report, General Electric Company, January 1969.

@techreport{Withop:1969ct,
    author = "Withop, A and Hutchins, B A and Martin, G C",
    title = "{Analytical Procedures and Applications of Fluence Determinations from EBR-II Flux Wires}",
    institution = "General Electric Company",
    year = "1969",
    month = "January"
}

(test/tests/fast_neutron_flux_from_power/nonad.i)

# This test checks the fast neutron flux calculated FastNeutronFluxFromPower
# coupled to material properties using nonAD methods

[Mesh]
  coord_type = RZ
  [mesh]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 4
    ny = 10
    ymax = 0.343
    xmax = 0.002
  []
[]

[Variables]
  [damage]
  []
[]

[Kernels]
  [damage_dt]
    type = TimeDerivative
    variable = damage
  []
  [damage_generation]
    type = FissionRateHeatSource
    fission_rate = fast_neutron_flux
    variable = damage
  []
[]

[Functions]
  [power_history]
    type = PiecewiseLinear
    x = '0 1'
    y = '0 30000'
  []
  [axial_peaking_factors]
    type = PowerPeakingFunction
    fit = EBRII_ROW_3
    pellet_length = 343.0e-3
    pellet_y_start = 2.55e-3
  []
[]

[Materials]
  [flux]
    type = FastNeutronFluxFromPower
    axial_power_profile = power_history
    rod_linear_power = axial_peaking_factors
    initial_X_Pu = 0.2
    initial_X_non_heavy_metal_atoms = 0.1
    non_heavy_metal_atom = Zr
    initial_density = 15800
    pellet_radius = 0.003
    enrichment_Pu240 = 0.3
    enrichment_U235 = 0.2
    outputs = all
    calculate_fluence = true
  []
[]

[Executioner]
  type = Transient

  dt = 0.1
  num_steps = 5
[]

[Postprocessors]
  [flux_avg]
    type = ElementAverageValue
    variable = fast_neutron_flux
  []
  [fluence_avg]
    type = ElementAverageValue
    variable = fast_neutron_fluence
  []
  [damage_avg]
    type = ElementAverageValue
    variable = damage
  []
[]

[Outputs]
  exodus = true
[]

(test/tests/fast_neutron_flux_from_power/rods.i)

# This test checks the fast neutron flux calculated FastNeutronFluxFromPower for a series of rods, and
# ensures the correct values are calculated depending on a mix of flux, fluence, and dpa calculation
# options.

[Problem]
  solve = false
[]

[Mesh]
  coord_type = RZ
  # rod specific parameters
  [smeared_pellet_mesh]
    type = FuelPinMeshGenerator
    clad_thickness = 0.381e-03
    pellet_outer_radius = 2.197e-03
    pellet_height = 344.3e-3
    clad_top_gap_height = 2.979e-1
    clad_gap_width = 0.348e-03
    bottom_clad_height = 2.24e-3 # arbitrary
    top_clad_height = 2.24e-3 # arbitrary
    clad_bot_gap_height = 0.31e-3 # arbitrary
    # meshing parameters
    clad_mesh_density = customize
    pellet_mesh_density = customize
    nx_p = 3
    ny_p = 10
    nx_c = 4
    ny_c = 30
    ny_cu = 3
    ny_cl = 3
    pellet_quantity = 1
  []
  # mesh options
  partitioner = centroid
  centroid_partitioner_direction = y
[]

[DefaultElementQuality]
  failure_type = Warning
[]

[Functions]
  [dp11]
    type = PiecewiseLinear
    x = '0 10 20'
    y = '0 23000 32000'
  []
  [dp16]
    type = PiecewiseLinear
    x = '0 10 20'
    y = '0 44000 48000'
  []
  [dp81]
    type = PiecewiseLinear
    x = '0 10 20'
    y = '0 29000 32000'
  []
  [t179]
    type = PiecewiseLinear
    x = '0 10 20'
    y = '0 40000 42000'
  []
  [row_3]
    type = PowerPeakingFunction
    fit = EBRII_ROW_3
    pellet_length = 343.0e-3
    pellet_y_start = 2.55e-3
    zero_beyond_top_and_bottom = false
  []
  [row_4]
    type = PowerPeakingFunction
    fit = EBRII_ROW_4
    pellet_length = 343.0e-3
    pellet_y_start = 2.55e-3
    zero_beyond_top_and_bottom = false
  []
[]

[Materials]
  [dp11]
    type = FastNeutronFluxFromPower
    axial_power_profile = row_3
    rod_linear_power = dp11
    initial_X_Pu = 0
    initial_X_non_heavy_metal_atoms = 0.225
    non_heavy_metal_atom = Zr
    initial_density = 15800
    pellet_radius = 2.192e-03
    enrichment_U235 = 0.675
    outputs = all
    fast_neutron_flux_name = dp11_flux
  []
  [dp16]
    type = FastNeutronFluxFromPower
    axial_power_profile = dp16
    rod_linear_power = row_4
    initial_X_Pu = 0.163
    initial_X_non_heavy_metal_atoms = 0.225
    non_heavy_metal_atom = Zr
    initial_density = 15800
    pellet_radius = 2.192e-03
    enrichment_Pu240 = 0.109
    enrichment_U235 = 0.697
    outputs = all
    fast_neutron_flux_name = dp16_flux
    dpa_name = dp16_dpa
    calculate_dpa = true
  []
  [dp81]
    type = FastNeutronFluxFromPower
    axial_power_profile = dp81
    rod_linear_power = row_3
    initial_X_Pu = 0
    initial_X_non_heavy_metal_atoms = 0.225
    non_heavy_metal_atom = Zr
    initial_density = 15800
    pellet_radius = 2.192e-03
    enrichment_U235 = 0.675310345
    outputs = all
    fast_neutron_flux_name = dp81_flux
    fast_neutron_fluence_name = dp81_fluence
    calculate_fluence = true
  []
  [t179]
    type = FastNeutronFluxFromPower
    axial_power_profile = t179
    rod_linear_power = row_4
    initial_X_Pu = 0.163
    initial_X_non_heavy_metal_atoms = 0.225
    non_heavy_metal_atom = Zr
    initial_density = 15800
    pellet_radius = 2.192e-03
    enrichment_Pu240 = 0.057
    enrichment_U235 = 0.573
    outputs = all
    fast_neutron_flux_name = t179_flux
    fast_neutron_fluence_name = t179_fluence
    dpa_name = t179_dpa
    calculate_dpa = true
    calculate_fluence = true
  []
[]

[Executioner]
  type = Transient
  num_steps = 2
  dt = 10
[]

[Postprocessors]
  [dp11_flux_avg]
    type = ElementAverageValue
    variable = dp11_flux
  []
  [dp16_flux_avg]
    type = ElementAverageValue
    variable = dp16_flux
  []
  [dp81_flux_avg]
    type = ElementAverageValue
    variable = dp81_flux
  []
  [t179_flux_avg]
    type = ElementAverageValue
    variable = t179_flux
  []
  [dp16_dpa_avg]
    type = ElementAverageValue
    variable = dp16_dpa
  []
  [dp81_fluence_avg]
    type = ElementAverageValue
    variable = dp81_fluence
  []
  [t179_fluence_avg]
    type = ElementAverageValue
    variable = t179_fluence
  []
  [t179_dpa_avg]
    type = ElementAverageValue
    variable = t179_dpa
  []
[]

[VectorPostprocessors]
  [cladding_flux]
    type = LineMaterialRealSampler
    property = 'dp11_flux dp16_flux dp81_flux t179_flux'
    start = '0.0027 0 0'
    end = '0.0027 0.6469 0'
    sort_by = y
  []
[]

[Outputs]
  csv = true
[]

(test/tests/fast_neutron_flux_from_power/nonad.i)

# This test checks the fast neutron flux calculated FastNeutronFluxFromPower
# coupled to material properties using nonAD methods

[Mesh]
  coord_type = RZ
  [mesh]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 4
    ny = 10
    ymax = 0.343
    xmax = 0.002
  []
[]

[Variables]
  [damage]
  []
[]

[Kernels]
  [damage_dt]
    type = TimeDerivative
    variable = damage
  []
  [damage_generation]
    type = FissionRateHeatSource
    fission_rate = fast_neutron_flux
    variable = damage
  []
[]

[Functions]
  [power_history]
    type = PiecewiseLinear
    x = '0 1'
    y = '0 30000'
  []
  [axial_peaking_factors]
    type = PowerPeakingFunction
    fit = EBRII_ROW_3
    pellet_length = 343.0e-3
    pellet_y_start = 2.55e-3
  []
[]

[Materials]
  [flux]
    type = FastNeutronFluxFromPower
    axial_power_profile = power_history
    rod_linear_power = axial_peaking_factors
    initial_X_Pu = 0.2
    initial_X_non_heavy_metal_atoms = 0.1
    non_heavy_metal_atom = Zr
    initial_density = 15800
    pellet_radius = 0.003
    enrichment_Pu240 = 0.3
    enrichment_U235 = 0.2
    outputs = all
    calculate_fluence = true
  []
[]

[Executioner]
  type = Transient

  dt = 0.1
  num_steps = 5
[]

[Postprocessors]
  [flux_avg]
    type = ElementAverageValue
    variable = fast_neutron_flux
  []
  [fluence_avg]
    type = ElementAverageValue
    variable = fast_neutron_fluence
  []
  [damage_avg]
    type = ElementAverageValue
    variable = damage
  []
[]

[Outputs]
  exodus = true
[]

(test/tests/fast_neutron_flux_from_power/exact.i)

# This test checks FastNeutronFluxFromPower against a hand calculation while varying all possible input
# parameters.
#
# dpa should compute to 1 at the final timestep to ensure fluence and dpa are being calculated correctly

[Problem]
  solve = false
[]

[Mesh]
  coord_type = RZ
  [mesh]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 1
    ny = 8
    ymax = 8
  []
[]

[Functions]
  [linear_power]
    type = ParsedFunction
    expression = 't'
  []
  [axial_profile]
    type = ParsedFunction
    expression = 'y'
  []
  [flux_exact_fcn]
    type = ParsedFunction
    symbol_names = 'linear_power axial_profile'
    symbol_values = 'linear_power axial_profile'
    expression = 'epf := 1 / pi / 10.0;
             rad_outer := 2;
             rad_inner := 1;
             ratio := 0.3;
             fsnrateden := ratio * linear_power * axial_profile / (rad_outer^2 - rad_inner^2) / pi / epf;
             U_ratio := 0.2;
             Pu_ratio := 0.3;
             X_Pu := 0.2;
             X_Zr := 0.1;
             X_U := 1.0 - X_Pu - X_Zr;
             X_U235 := X_U * U_ratio;
             X_U238 := X_U - X_U235;
             X_Pu240 := X_Pu * Pu_ratio;
             X_Pu239 := X_Pu - X_Pu240;
             A_U235 := 0.2350439231;
             A_U238 := 0.2380507826;
             A_Pu239 := 0.2390521565;
             A_Pu240 := 0.2400538075;
             A_Zr := 0.091224;
             Atot := X_U235 * A_U235 + X_U238 * A_U238 + X_Pu239 * A_Pu239 + X_Pu240 * A_Pu240 + X_Zr * A_Zr;
             sigma_U235 := 1.0e4;
             sigma_U238 := 1.0e3;
             sigma_Pu239 := 1.0e4;
             sigma_Pu240 := 8199.0380426;
             density := 4;
             Ntot := density * 6.02214076e23 * 1.0e-28 / Atot;
             sigma_tot := Ntot * (X_U235 * sigma_U235 + X_U238 * sigma_U238 + X_Pu239 * sigma_Pu239 + X_Pu240 * sigma_Pu240);
             fsnrateden / sigma_tot'
  []
[]

[Materials]
  [flux]
    type = FastNeutronFluxFromPower
    axial_power_profile = axial_profile
    rod_linear_power = linear_power
    fast_spectrum_ratio = 0.3
    initial_X_Pu = 0.2
    initial_X_non_heavy_metal_atoms = 0.1
    non_heavy_metal_atom = Zr
    initial_density = 4
    pellet_inner_radius = 1.0
    pellet_radius = 2.0
    enrichment_Pu240 = 0.3
    enrichment_U235 = 0.2
    sigma_U235 = 1.0e4
    sigma_U238 = 1.0e3
    sigma_Pu239 = 1.0e4
    sigma_Pu240 = 8199.0380426
    energy_per_fission = 0.031830989
    dpa_conversion_factor = 1.9245015
    outputs = all
    calculate_fluence = true
    calculate_dpa = true
    calculate_dpa_rate = true
    fast_neutron_flux_name = 'asdf_fast_neutron_flux'
    fast_neutron_fluence_name = 'asdf_fast_neutron_fluence'
    dpa_name = 'asdf_dpa'
  []
  [flux_exact]
    type = GenericFunctionMaterial
    prop_names = 'flux_exact'
    prop_values = 'flux_exact_fcn'
    outputs = all
  []
[]

[Executioner]
  type = Transient
  num_steps = 2
[]

[Postprocessors]
  [flux_old]
    type = ElementAverageValue
    variable = asdf_fast_neutron_flux
    execute_on = 'TIMESTEP_BEGIN'
  []
  [flux_avg]
    type = ElementAverageValue
    variable = 'asdf_fast_neutron_flux'
  []
  [flux_exact_avg]
    type = ElementAverageValue
    variable = 'flux_exact'
  []
  [flux_error]
    type = ElementL2Error
    variable = asdf_fast_neutron_flux
    function = flux_exact_fcn
  []

  [dt]
    type = TimestepSize
  []
  [fluence_avg]
    type = ElementAverageValue
    variable = 'asdf_fast_neutron_fluence'
  []
  [dfluence_exact]
    type = ParsedPostprocessor
    pp_names = 'flux_avg flux_old dt'
    expression = 'dt * (flux_avg + flux_old) / 2'
  []
  [fluence_exact]
    type = CumulativeValuePostprocessor
    postprocessor = dfluence_exact
  []
  [fluence_diff]
    type = ParsedPostprocessor
    pp_names = 'fluence_avg fluence_exact'
    expression = '(fluence_avg - fluence_exact) / fluence_exact'
    outputs = console
  []
  [fluence_max_diff]
    type = TimeExtremeValue
    postprocessor = fluence_diff
    value_type = abs_max
  []

  [dpa_rate_avg]
    type = ElementAverageValue
    variable = 'asdf_dpa_rate'
  []
  [dpa_rate_exact]
    type = ParsedPostprocessor
    pp_names = 'flux_avg flux_old dt'
    expression = '(flux_avg + flux_old) / 2 / 1.9245015'
  []
  [dpa_rate_diff]
    type = ParsedPostprocessor
    pp_names = 'dpa_rate_avg dpa_rate_exact'
    expression = '(dpa_rate_avg - dpa_rate_exact) / dpa_rate_exact'
    outputs = console
  []
  [dpa_rate_max_diff]
    type = TimeExtremeValue
    postprocessor = dpa_rate_diff
    value_type = abs_max
  []

  [dpa_avg]
    type = ElementAverageValue
    variable = 'asdf_dpa'
  []
  [dpa_exact]
    type = CumulativeValuePostprocessor
    postprocessor = 'dpa_rate_exact'
  []
  [dpa_diff]
    type = ParsedPostprocessor
    pp_names = 'dpa_avg dpa_exact'
    expression = '(dpa_avg - dpa_exact) / dpa_exact'
    outputs = console
  []
  [dpa_max_diff]
    type = TimeExtremeValue
    postprocessor = dpa_diff
    value_type = abs_max
  []
[]

[Outputs]
  csv = true
[]

(test/tests/fast_neutron_flux_from_power/ad.i)

# This test checks the fast neutron flux calculated FastNeutronFluxFromPower
#  coupled to other material properties using AD

[Mesh]
  coord_type = RZ
  [mesh]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 4
    ny = 10
    ymax = 0.343
    xmax = 0.002
  []
[]

[Variables]
  [damage]
  []
[]

[Kernels]
  [damage_dt]
    type = ADTimeDerivative
    variable = damage
  []
  [damage_generation]
    type = ADFissionRateHeatSource
    fission_rate = fast_neutron_flux
    variable = damage
  []
[]

[Functions]
  [power_history]
    type = PiecewiseLinear
    x = '0 1'
    y = '0 30000'
  []
  [axial_peaking_factors]
    type = PowerPeakingFunction
    fit = EBRII_ROW_3
    pellet_length = 343.0e-3
    pellet_y_start = 2.55e-3
  []
[]

[Materials]
  [flux]
    type = ADFastNeutronFluxFromPower
    axial_power_profile = power_history
    rod_linear_power = axial_peaking_factors
    initial_X_Pu = 0.2
    initial_X_non_heavy_metal_atoms = 0.1
    non_heavy_metal_atom = Zr
    initial_density = 15800
    pellet_radius = 0.003
    enrichment_Pu240 = 0.3
    enrichment_U235 = 0.2
    outputs = all
    calculate_fluence = true
  []
[]

[Executioner]
  type = Transient

  dt = 0.1
  num_steps = 5
[]

[Postprocessors]
  [flux_avg]
    type = ElementAverageValue
    variable = fast_neutron_flux
  []
  [fluence_avg]
    type = ElementAverageValue
    variable = fast_neutron_fluence
  []
  [damage_avg]
    type = ElementAverageValue
    variable = damage
  []
[]

[Outputs]
  exodus = true
[]

Description
Example Input Syntax
Input Parameters
Input Files
References