EutecticThicknessFCCI

Computes eutectic penetration thickness based on boundary temperature.

Description

The EutecticThicknessFCCI AuxKernel is used to calculate the eutectic penetration thickness when the temperature is above the eutectic melting point for Fuel-Clad Chemical Interaction of metal fuels with the cladding. The boundary temperature is required. The rate of penetration is added to the variable tracking the penetration thickness for each time step. The penetration thickness may only grow or remain the same.

For metal fuel, a Fuel-Clad Chemical Interaction eutectic may form and melt when the temperature is above the eutectic melting temperature. The formation and melt front then move through the cladding, which thins the clad weakening it. This usually occurs during shorter transients, such as TOP events. In BISON, the penetration thickness of this eutectic melt is tracked similar to the approach used in Karahan and Buongiorno (2010). However, instead of using a diffusion coefficient, which can already be accomplished in BISON, this module relates temperature to penetration rate taken from Bauer et al. (1987) as $(1)var element = document.getElementById("moose-equation-599313ea-e7d6-4bc5-a458-9b71851a89af");katex.render(" \\dot{r}\\left[\\mu\\text{m}/\\text{s}\\right]=e^{22.847-27624/T}", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-f5ece4d6-cd54-4836-9d55-a5ab3e5cb1c6");katex.render("\\dot{r}", element, {displayMode:false,throwOnError:false});$ is the eutectic penetration rate reported in micrometers per second and $var element = document.getElementById("moose-equation-91b611bc-d4e8-4a7d-a139-067f67149894");katex.render("T", element, {displayMode:false,throwOnError:false});$ is the temperature in Kelvin. Between 1353.15 K and 1506.15 K, the penetration rate becomes $(2)var element = document.getElementById("moose-equation-0a2959c9-3a53-4228-baf8-dfd982555531");katex.render(" \\dot{r}\\left[\\mu\\text{m}/\\text{s}\\right]=922+2.9265\\left(T-1388\\right)-0.21522\\left(T- 1388\\right)^{2}+0.0011338\\left(T-1388\\right)^{3}", element, {displayMode:true,throwOnError:false});$ which accounts for the melting of the protective UFe $var element = document.getElementById("moose-equation-8cfb4282-3298-4bb7-b08d-22e55f33d747");katex.render("_{2}", element, {displayMode:false,throwOnError:false});$ layer. The eutectic only penetrates if the temperature is above the melting point usually taken as 988.15 K. BISON converts the rate to meters per second and provides a unit factor which multiplies this rate. The units or scaling may be adjusted using this unit factor. The rate is multiplied by the time step size and added to the current penetration thickness.

Example Input Syntax

[AuxKernels<<<{"href": "../../syntax/AuxKernels/index.html"}>>>]
  [fcci_eutectic]
    boundary<<<{"description": "The list of boundaries (ids or names) from the mesh where this object applies"}>>> = right
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = timestep_end
    type = EutecticThicknessFCCI<<<{"description": "Computes eutectic penetration thickness based on boundary temperature.", "href": "EutecticThicknessFCCI.html"}>>>
    temperature<<<{"description": "Coupled temperature of the boundary."}>>> = temp
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = thickness
  []
[]

Input Parameters

temperatureCoupled temperature of the boundary.
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Coupled temperature of the boundary.
variableThe name of the variable that this object applies to
C++ Type:AuxVariableName
Unit:(no unit assumed)
Controllable:No
Description:The name of the variable that this object applies to

Required Parameters

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
check_boundary_restrictedTrueWhether to check for multiple element sides on the boundary in the case of a boundary restricted, element aux variable. Setting this to false will allow contribution to a single element's elemental value(s) from multiple boundary sides on the same element (example: when the restricted boundary exists on two or more sides of an element, such as at a corner of a mesh
Default:True
C++ Type:bool
Controllable:No
Description:Whether to check for multiple element sides on the boundary in the case of a boundary restricted, element aux variable. Setting this to false will allow contribution to a single element's elemental value(s) from multiple boundary sides on the same element (example: when the restricted boundary exists on two or more sides of an element, such as at a corner of a mesh
eutectic_melt988.15Temperature at which the eutectic will melt.
Default:988.15
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Temperature at which the eutectic will melt.
execute_onLINEAR TIMESTEP_ENDThe list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.
Default:LINEAR TIMESTEP_END
C++ Type:ExecFlagEnum
Options:XFEM_MARK, NONE, INITIAL, LINEAR, NONLINEAR_CONVERGENCE, NONLINEAR, POSTCHECK, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, FINAL, CUSTOM, PRE_DISPLACE
Controllable:No
Description:The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.
unit_factor1Multiply to convert correlation from meters/sec.
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Multiply to convert correlation from meters/sec.

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.
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

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/fcci_ht9/eutectic_thickness/fcci_eutectic.i)
(assessment/metallic_fuel/TREAT/M7/analysis/binary_t427.i)

References

T. H. Bauer, G. R. Fenske, and J. M. Kramer. Cladding failure margins for metallic fuel in the integral fast reactor. Technical Report CONF-870812–22, Argonne National Laboratory, July 1987.

@techreport{bauer1987_cladfailuremargins,
    author = "Bauer, T. H. and Fenske, G. R. and Kramer, J. M.",
    title = "Cladding Failure Margins for Metallic Fuel in the Integral Fast Reactor",
    month = "July",
    year = "1987",
    number = "CONF-870812--22",
    institution = "Argonne National Laboratory"
}

A. Karahan and J. Buongiorno. A new code for predicting the thermo-mechanical and irradiation behavior of metallic fuels in sodium fast reactors. Journal of Nuclear Materials, 396(2):283–293, 2010. doi:10.1016/j.jnucmat.2009.11.022.

@article{KARAHAN2010283,
    author = "Karahan, A. and Buongiorno, J.",
    title = "A new code for predicting the thermo-mechanical and irradiation behavior of metallic fuels in sodium fast reactors",
    journal = "Journal of Nuclear Materials",
    volume = "396",
    number = "2",
    pages = "283-293",
    year = "2010",
    issn = "0022-3115",
    doi = "10.1016/j.jnucmat.2009.11.022"
}

(test/tests/fcci_ht9/eutectic_thickness/fcci_eutectic.i)

# The test increases the temperature of the adiabatic boundary as the
# temperature of the left boundary Dirichlet rises. The test calculates
# the rate of thickness growth and outputs the thickness. The calculated
# rate from the temperature on the boundary is:
# Time(seconds) | Rate(mircometers)
#       0             0
#       1             0
#       2             0
#       3             0
#       4             0.03164
#       5             0.30975
#       6             2.11336
#       7            10.85797
#       8           546.33223
#       9           152.18007
#      10           448.17412
# The current thickness should be the rate multiplied by the time step size
# added to the previous thickness size.

[Mesh]
  [mesh]
    type = GeneratedMeshGenerator
    dim = 1
    nx = 3
  []
[]

[AuxVariables]
  [thickness]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Variables]
  [temp]
    order = FIRST
    family = LAGRANGE
    initial_condition = 700
  []
[]

[AuxKernels]
  [fcci_eutectic]
    boundary = right
    execute_on = timestep_end
    type = EutecticThicknessFCCI
    temperature = temp
    variable = thickness
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = temp
  []
  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temp
  []
[]

[Functions]
  [tempbound]
    type = PiecewiseLinear
    x = '0 10'
    y = '700 1700'
  []
[]

[BCs]
  [left]
    type = FunctionDirichletBC
    variable = temp
    boundary = left
    function = tempbound
  []
[]

[Materials]
  [density]
    type = ParsedMaterial
    property_name = density
    expression = 1
  []
  [heatcond]
    type = HeatConductionMaterial
    specific_heat = 1
    thermal_conductivity = 1
  []
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  start_time = 0.0
  end_time = 10.0
  [TimeStepper]
    type = ConstantDT
    dt = 1.0
  []
[]

[Postprocessors]
  [right_thickness]
    type = SideAverageValue
    variable = thickness
    boundary = right
  []
  [right_value]
    type = AverageNodalVariableValue
    boundary = right
    variable = temp
    execute_on = 'initial timestep_end'
  []
[]

[Outputs]
  exodus = false
  csv = true
[]

(test/tests/fcci_ht9/eutectic_thickness/fcci_eutectic.i)

# The test increases the temperature of the adiabatic boundary as the
# temperature of the left boundary Dirichlet rises. The test calculates
# the rate of thickness growth and outputs the thickness. The calculated
# rate from the temperature on the boundary is:
# Time(seconds) | Rate(mircometers)
#       0             0
#       1             0
#       2             0
#       3             0
#       4             0.03164
#       5             0.30975
#       6             2.11336
#       7            10.85797
#       8           546.33223
#       9           152.18007
#      10           448.17412
# The current thickness should be the rate multiplied by the time step size
# added to the previous thickness size.

[Mesh]
  [mesh]
    type = GeneratedMeshGenerator
    dim = 1
    nx = 3
  []
[]

[AuxVariables]
  [thickness]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Variables]
  [temp]
    order = FIRST
    family = LAGRANGE
    initial_condition = 700
  []
[]

[AuxKernels]
  [fcci_eutectic]
    boundary = right
    execute_on = timestep_end
    type = EutecticThicknessFCCI
    temperature = temp
    variable = thickness
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = temp
  []
  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temp
  []
[]

[Functions]
  [tempbound]
    type = PiecewiseLinear
    x = '0 10'
    y = '700 1700'
  []
[]

[BCs]
  [left]
    type = FunctionDirichletBC
    variable = temp
    boundary = left
    function = tempbound
  []
[]

[Materials]
  [density]
    type = ParsedMaterial
    property_name = density
    expression = 1
  []
  [heatcond]
    type = HeatConductionMaterial
    specific_heat = 1
    thermal_conductivity = 1
  []
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
  start_time = 0.0
  end_time = 10.0
  [TimeStepper]
    type = ConstantDT
    dt = 1.0
  []
[]

[Postprocessors]
  [right_thickness]
    type = SideAverageValue
    variable = thickness
    boundary = right
  []
  [right_value]
    type = AverageNodalVariableValue
    boundary = right
    variable = temp
    execute_on = 'initial timestep_end'
  []
[]

[Outputs]
  exodus = false
  csv = true
[]

(assessment/metallic_fuel/TREAT/M7/analysis/binary_t427.i)

# TREAT M7 U-10Zr pin clad in HT9 transient only simulation.
#   Not using transferred initial condition.
# ANL-IFR-124 Test M7 T-427
# Units: m, W, kg, Pa

[Debug]
  show_var_residual = 'disp_x disp_y temperature'
  show_var_residual_norms = true
[]

[GlobalParams]
  order = SECOND
  family = LAGRANGE
  energy_per_fission = 3.28451e-11
  displacements = 'disp_x disp_y'
  stress_free_temperature = 586.0
  temperature = temperature
  # Some calculated values, which are nice to know.
  # u_weight = 0.90126
  # pu_weight = 0.00115
  # zr_weight = 0.0976
  # X_U = 0.779
  X_Pu = 0.000969
  X_Zr = 0.22
[]

[Problem]
  type = ReferenceResidualProblem
  extra_tag_vectors = 'ref'
  reference_vector = 'ref'
  group_variables = 'disp_x disp_y'
[]

[Mesh]
  coord_type = RZ
  [smeared_pellet_mesh]
    type = FuelPinMeshGenerator
    clad_bot_gap_height = 0.38e-3
    clad_gap_width = 1e-6
    clad_thickness = 0.38e-3
    clad_top_gap_height = 252.35e-3
    pellet_height = 37.3e-2
    pellet_outer_radius = 2.54e-3
    pellet_quantity = 1
    bottom_clad_height = 1.9e-3
    top_clad_height = 1.9e-3

    elem_type = QUAD8
    clad_mesh_density = customize
    pellet_mesh_density = customize
    nx_c = 3
    nx_p = 5
    ny_c = 150
    ny_cl = 3
    ny_cu = 3
    ny_p = 175
  []
  patch_size = 25
  partitioner = centroid
  patch_update_strategy = auto
  centroid_partitioner_direction = y
[]

[Functions]
  [power_history] # Peak power density
    type = PiecewiseLinear
    data_file = 'm7fa_digitized.csv'
    format = columns
    scale_factor = 78.8 # g; grams of fuel in pellet for W/g to W
  []
  [axial_peaking_factors] # Peak factor (1 max)
    type = PiecewiseBilinear
    data_file = 'm7_axial_tranAlone.csv'
    axis = 1
  []
  [q_heat]
    type = CompositeFunction
    functions = 'power_history axial_peaking_factors'
    scale_factor = 132273.8097 # m^-3; volume of fuel slug, 1/V, to make power density
  []
  [dt_fun]
    type = PiecewiseLinear
    x = '0   6   7    9    15   20    25'
    y = '0.5 0.5 0.01 0.01 0.01 0.001 0.1'
  []
[]

[Variables]
  [temperature]
    initial_condition = 586.0
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  add_variables = true
  strain = FINITE
  generate_output = 'stress_xx stress_yy stress_zz vonmises_stress hydrostatic_stress elastic_strain_xx elastic_strain_yy elastic_strain_zz strain_xx strain_yy strain_zz'
  [slug_mech]
    block = pellet
    additional_generate_output = 'creep_strain_xx creep_strain_yy creep_strain_zz'
    eigenstrain_names = 'slug_thermal_strain'
    extra_vector_tags = 'ref'
  []
  [clad_mech]
    block = clad
    additional_generate_output = 'creep_strain_xx creep_strain_yy creep_strain_zz'
    eigenstrain_names = 'clad_thermal_eigenstrain'
    extra_vector_tags = 'ref'
  []
[]

[Kernels]
  [gravity]
    type = Gravity
    variable = disp_y
    value = -9.81
    extra_vector_tags = 'ref'
  []
  [heat]
    type = ConstitutiveHeatConduction
    extra_vector_tags = 'ref'
    variable = temperature
    thermal_conductivity = 'thermal_conductivity'
    thermal_conductivity_args = 'temperature'
    thermal_conductivity_derivs = 'thermal_conductivity_dT'
  []
  [heat_ie]
    type = ConstitutiveHeatConductionTimeDerivative
    extra_vector_tags = 'ref'
    variable = temperature
    specific_heat = 'specific_heat'
    specific_heat_args = 'temperature'
    specific_heat_derivs = 'specific_heat_dT'
  []
  [vol_heat_source]
    type = HeatSource
    extra_vector_tags = 'ref'
    block = pellet
    function = q_heat
    variable = temperature
  []
[]

[AuxVariables]
  [power_density]
    block = pellet
  []
  [fission_rate]
    block = pellet
  []
  [fast_neutron_flux]
    block = clad
  []
  [fast_neutron_fluence]
    block = clad
  []
  [creep_rate_aux]
    order = CONSTANT
    family = MONOMIAL
  []

  # Aux variables for output
  [energy_density]
    block = pellet
    initial_condition = 0.0
  []
  [gap_cond]
    order = CONSTANT
    family = MONOMIAL
  []
  [coolant_htc]
    order = CONSTANT
    family = MONOMIAL
    block = clad
  []
  [coolant_temperature]
    order = CONSTANT
    family = MONOMIAL
    block = clad
  []
  [cumulative_damage_index]
    order = CONSTANT
    family = MONOMIAL
    block = clad
  []
  [element_failed]
    order = CONSTANT
    family = MONOMIAL
  []
  [eutectic_thickness_in]
    order = CONSTANT
    family = MONOMIAL
    block = clad
  []
  [eutectic_thickness_out]
    order = CONSTANT
    family = MONOMIAL
    block = clad
  []
[]

[AuxKernels]
  [calc_fission_rate]
    type = FissionRateGeneral
    fission_rate_formulation = POWER_DENSITY
    block = pellet
    power_density_function = q_heat
    variable = fission_rate
    execute_on = 'initial timestep_end'
  []
  [fast_neutron_flux]
    type = FastNeutronFluxAux
    variable = fast_neutron_flux
    block = clad
    factor = 0.6e19
    execute_on = 'initial timestep_end'
  []
  [fast_neutron_fluence]
    type = FastNeutronFluenceAux
    variable = fast_neutron_fluence
    block = clad
    fast_neutron_flux = fast_neutron_flux
    execute_on = 'initial timestep_end'
  []
  [calc_power_density]
    type = FunctionAux
    block = pellet
    function = q_heat
    variable = power_density
    execute_on = 'initial timestep_end'
  []
  [calc_energy_density]
    type = VariableTimeIntegrationAux
    block = pellet
    order = 2
    variable_to_integrate = power_density
    variable = energy_density
    execute_on = timestep_end
  []
  # Hoop stress_zz.
  [creep_rate_aux]
    type = MaterialRealAux
    property = creep_rate
    variable = creep_rate_aux
    execute_on = timestep_end
  []
  [conductance]
    type = MaterialRealAux
    property = gap_conductance
    variable = gap_cond
    boundary = 10
  []
  [coolant_temperature]
    type = MaterialRealAux
    property = coolant_temperature
    variable = coolant_temperature
    boundary = 2
  []
  [coolant_htc]
    type = MaterialRealAux
    property = coolant_channel_htc
    variable = coolant_htc
    boundary = 2
  []
  [cdf_amount]
    block = clad
    type = MaterialRealAux
    property = cdf_failure
    variable = cumulative_damage_index
  []
  [failed_element]
    type = MaterialRealAux
    property = failed
    variable = element_failed
  []
  [fcci_eutectic_in]
    execute_on = timestep_end
    type = EutecticThicknessFCCI
    boundary = 5
    variable = eutectic_thickness_in
  []
  [fcci_eutectic_out]
    execute_on = timestep_end
    type = EutecticThicknessFCCI
    boundary = 2
    variable = eutectic_thickness_out
  []
[]

[Postprocessors]
  [_dt]
    type = TimestepSize
    outputs = all
  []
  [fis_gas_released]
    type = ElementIntegralMaterialProperty
    mat_prop = fis_gas_rel
    block = pellet
    execute_on = 'initial timestep_end'
  []
  [ave_temp_interior]
    type = SideAverageValue
    boundary = 9
    variable = temperature
    execute_on = 'initial linear'
  []
  [avg_clad_temp]
    type = ElementAverageValue
    variable = temperature
    outputs = all
    block = clad
  []
  [avg_fuel_temp]
    type = ElementAverageValue
    variable = temperature
    outputs = all
    block = pellet
  []
  [max_outer_clad_temp]
    type = NodalExtremeValue
    variable = temperature
    value_type = max
    boundary = 2
  []
  [peak_clad_temp]
    type = ElementExtremeValue
    variable = temperature
    value_type = max
    block = clad
    outputs = all
  []
  [peak_fuel_temp]
    type = ElementExtremeValue
    variable = temperature
    value_type = max
    block = pellet
    outputs = all
  []
  [peak_outer_fuel_temp]
    type = NodalExtremeValue
    variable = temperature
    value_type = max
    boundary = 10
  []
  [peak_coolant_temperature]
    type = ElementExtremeValue
    variable = coolant_temperature
    value_type = max
    block = clad
    outputs = all
  []
  [max_power_density]
    type = ElementExtremeValue
    variable = power_density
    value_type = max
    block = pellet
  []
  [avg_power_density]
    type = ElementAverageValue
    variable = power_density
    block = pellet
    outputs = all
  []
  [total_deposit_pin_energy]
    type = ElementIntegralVariablePostprocessor
    variable = energy_density
    block = pellet
  []
  [clad_inner_vol]
    type = InternalVolume
    boundary = 7
  []
  [pellet_volume]
    type = InternalVolume
    boundary = 8
    execute_on = 'initial timestep_end'
  []
  [gas_volume]
    type = InternalVolume
    boundary = 9
    execute_on = 'initial linear'
    outputs = all
    addition = -2.0e-6 # m3; assuming all bond sodium displaced by closed gap
  []
  [clad_fuel_gap]
    type = NodalExtremeValue
    variable = penetration
    boundary = 10
    outputs = all
  []
  [max_eutectic_pen_in]
    type = ElementExtremeValue
    variable = eutectic_thickness_in
    block = clad
    value_type = max
    execute_on = timestep_end
    outputs = all
  []
  [max_eutectic_pen_out]
    type = ElementExtremeValue
    variable = eutectic_thickness_out
    block = clad
    value_type = max
    execute_on = timestep_end
    outputs = all
  []
[]

[Contact]
  [pellet_clad_mechanical]
    primary = 5
    secondary = 10
    penalty = 1e12
    model = frictionless
    normalize_penalty = true
    tangential_tolerance = 1e-3
    normal_smoothing_distance = 0.1
  []
[]

[ThermalContact]
  [thermal_contact]
    type = GapHeatTransfer
    variable = temperature
    primary = 5
    secondary = 10
    quadrature = true
    gap_conductivity = 73.70
    min_gap = 1e-3
  []
[]

[BCs]
  [no_x_all]
    type = DirichletBC
    variable = disp_x
    boundary = 12
    value = 0.0
  []
  [no_y_fuel]
    type = PenaltyDirichletBC
    penalty = 1e10
    variable = disp_y
    boundary = 20
    value = 0.0
  []
  [no_y_clad]
    type = DirichletBC
    variable = disp_y
    boundary = 1
    value = 0.0
  []
  [Pressure]
    [coolantPressure]
      boundary = '1 2 3'
      factor = 455054.0
    []
  []
  [PlenumPressure]
    [plenumPressure]
      boundary = 9
      initial_pressure = 1.41343e6
      initial_temperature = 309.0
      startup_time = 0.0
      R = 8.3143
      temperature = ave_temp_interior
      volume = gas_volume
      output = plenum_pressure
      material_input = fis_gas_released
      output_initial_moles = plenum_moles
    []
  []
[]

[CoolantChannel]
  [convective_clad_surface]
    boundary = '1 2 3'
    variable = temperature
    inlet_temperature = 586.0
    inlet_pressure = 455054.0
    inlet_massflux = 4520.72
    coolant_material = sodium
    flow_area = 2.22e-5
    hydraulic_diameter = 2.057e-3
    heated_perimeter = 1.835e-2
    heated_diameter = 4.84e-3
    number_axial_zone = 50
    htc_correlation_type = 3
    compute_enthalpy = true
  []
[]

[Materials]
  # Fuel Slug Properties
  [set_porosity]
    type = GenericConstantMaterial
    block = pellet
    prop_names = porosity
    prop_values = 0.31
  []
  [set_mat_fission_rate]
    type = ParsedMaterial
    block = pellet
    coupled_variables = 'fission_rate'
    expression = 'fission_rate * 1.0'
    property_name = 'fission_rate'
  []
  [melted]
    type = GenericMaterialFailure
    block = pellet
    compared = greater_than
    variable_check = temperature
    constant_criteria = 1600.0
  []
  [for_youngs]
    # Pulled equation from Bison manual and added temperature limit.
    type = ParsedMaterial
    block = pellet
    outputs = all
    output_properties = 'youngs_modulus'
    property_name = 'youngs_modulus'
    coupled_variables = 'temperature'
    material_property_names = 'porosity'
    constant_names = 'T_limit E_U T_meltU W_Zr W_Pu B_E Ta_start Ta_end'
    constant_expressions = '1550.0 1.6e11 1405.0 0.0976 0.00115 1.2 923.0 973.0'
    expression = 'E_p := 1.0 - B_E * porosity; E_W := (1.0 + 0.17 * W_Zr) / (1.0 + 1.34 * W_Zr) - W_Pu; T_act := if(temperature > T_limit, T_limit, temperature); x_smooth := (T_act - Ta_start) / (Ta_end - Ta_start); f_smooth := if(T_act < Ta_start, 0.0, if(T_act > Ta_end, 1.0, 6.0 * pow(x_smooth, 5) - 15.0 * pow(x_smooth, 4) + 10.0 * pow(x_smooth, 3))); E_T := 1.0 - 1.06 * (T_act - 588.0) / T_meltU - f_smooth * 0.3 * (1.0 - 1.06 * (Ta_end - 588.0) / T_meltU); E_U * E_T * E_p * E_W'
  []
  [for_poissons]
    # Pulled equation from Bison manual and added temperature limit.
    type = ParsedMaterial
    block = pellet
    outputs = all
    output_properties = 'poissons_ratio'
    property_name = 'poissons_ratio'
    coupled_variables = 'temperature'
    material_property_names = 'porosity'
    constant_names = 'T_limit nu_U T_meltU W_Zr B_nu'
    constant_expressions = '1550.0 0.24 1405.0 0.0976 0.8'
    expression = 'nu_p := 1.0 - B_nu * porosity; nu_W := (1.0 + 3.4 * W_Zr) / (1.0 + 1.9 * W_Zr); T_act := if(temperature > T_limit, T_limit, temperature); nu_T := 1.0 + 1.2 * (T_act - 588.0) / T_meltU; nu_U *nu_p * nu_W * nu_T'
  []
  [slug_elasticity_tensor]
    type = ComputeVariableIsotropicElasticityTensor
    block = pellet
    args = temperature
    youngs_modulus = youngs_modulus
    poissons_ratio = poissons_ratio
  []
  [slug_stress]
    type = ComputeMultipleInelasticStress
    tangent_operator = nonlinear
    inelastic_models = 'slug_creep'
    block = pellet
  []
  [slug_creep]
    type = UPuZrCreepUpdate
    block = pellet
    porosity = porosity
    max_inelastic_increment = 1e-3
  []
  [slug_thermal_expansion]
    type = ComputeThermalExpansionEigenstrain
    block = pellet
    thermal_expansion_coeff = 1.18e-5
    eigenstrain_name = slug_thermal_strain
  []
  [slug_thermal]
    type = UPuZrThermal
    block = pellet
    Na_depth = 0.0673
    fuel_outer_radius = 2.54e-3
    spheat_model = savage
    thcond_model = billone
    porosity_model = partially_logged
    initiating_porosity = 0.24
    outputs = all
    output_properties = thermal_conductivity
    porosity = porosity
  []
  [slug_density]
    type = StrainAdjustedDensity
    block = pellet
    strain_free_density = 15700.0
  []
  [slug_fission_gas_release]
    block = pellet
    type = UPuZrFissionGasRelease
    fission_rate = fission_rate
  []

  # Cladding Properties
  [clad_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 1.88e11
    poissons_ratio = 0.236
    block = clad
  []
  [clad_stress]
    type = ComputeMultipleInelasticStress
    block = clad
    tangent_operator = nonlinear
    inelastic_models = 'clad_creep'
  []
  [clad_fast_flux]
    type = FastNeutronFlux
    block = clad
    factor = 0.6e19
  []
  [clad_creep]
    type = HT9CreepUpdate
    block = clad
  []
  [clad_thermal_expansion]
    type = ComputeThermalExpansionEigenstrain
    block = clad
    thermal_expansion_coeff = 1.2e-5
    eigenstrain_name = clad_thermal_eigenstrain
  []
  [clad_thermal]
    type = HT9Thermal
    block = clad
  []
  [clad_density]
    type = StrainAdjustedDensity
    block = clad
    strain_free_density = 7874.0
  []
  [failclad]
    block = clad
    type = HT9FailureClad
    hoop_stress = stress_zz
    method = cdf_short
  []
[]

[Preconditioning]
  [SMP]
    type = SMP
    full = true
    solve_type = 'PJFNK'
    petsc_options = '-snes_ksp_ew -snes_converged_reason'
    petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -ksp_gmres_restart'
    petsc_options_value = 'lu       superlu_dist                  51'
  []
[]

[Executioner]
  type = Transient
  automatic_scaling = true
  compute_scaling_once = true
  line_search = 'none'
  l_max_its = 100
  l_tol = 1e-3
  nl_max_its = 200
  nl_rel_tol = 1e-6
  nl_abs_tol = 1e-9
  start_time = 0.0
  end_time = 25.0
  dtmin = 0.0001
  dtmax = 1.0
  [TimeStepper]
    type = FunctionDT
    function = dt_fun
  []
  [Quadrature]
    order = FIFTH
    side_order = SEVENTH
  []
[]

[PerformanceMetricOutputs]
[]

[Outputs]
  perf_graph = true
  time_step_interval =  1
  exodus = true
  csv = true # Figures comparing to experiment results are based off this csv output.
  [console]
    type = Console
    output_linear = true
    output_nonlinear = true
  []
  [check]
    # Numerical assessment test check at points near important features.
    #  Checking near the feature but not during it hopefully will not affect the feature computation.
    type = CSV
    execute_on = TIMESTEP_END
    sync_only = true
    sync_times = '10 16.5 20'
  []
[]

Description
Example Input Syntax
Input Parameters
Input Files
References