ZryRIACladdingFailure

Models the failure of Zircaloy-2 or Zircaloy-4 cladding due to PCMI under RIA conditions.

Description

For modeling failure due to PCMI induced failure of Zircaloy-2 and Zircaloy-4 claddings during Reactivity Insertion Accidents. The failure criteria are functions of peak radial average fuel enthalpy rise and cladding excess hydrogen where excess hydrogen corresponds to the amount of hydrogen in hydrides (Clifford, 2020).

For lined Zircaloy-2 (RXA) cladding the critical value for increase in peak radial average enthalpy is given by: $var element = document.getElementById("moose-equation-ace12261-d704-4afd-a326-db677e0736a5");katex.render(" \\Delta H_{fail} = \\begin{cases} \\min \\left( 150, 4.5 \\times 10^5 C_{prec}^{-1.9} + 33\\right), & \\text{for } T \\leq 533.15~\\text{K}\\\\ \\min \\left( 150, 5.5 \\times 10^5 C_{prec}^{-1.9} + 50\\right), & \\text{for } T > 533.15~\\text{K} \\end{cases}", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-3ba0ecd3-58ca-4dcd-9eee-37aa94986722");katex.render("\\Delta H_{fail}", element, {displayMode:false,throwOnError:false});$ is the threshold increase in peak radial average enthalpy that is allowed before failure is assumed (cal/g), $var element = document.getElementById("moose-equation-cb280810-c791-47de-9fea-e82f9870bec3");katex.render("C_{prec}", element, {displayMode:false,throwOnError:false});$ is the hydrogen in hydrides, and $var element = document.getElementById("moose-equation-ae51b52a-6f00-4d32-a00d-69bbcf268cd1");katex.render("T", element, {displayMode:false,throwOnError:false});$ is the cladding temperature in K at the start of the transient. For unlined Zircaloy-2 (RXA) cladding: $var element = document.getElementById("moose-equation-c9f7082b-9237-4147-affa-89306b6cdba9");katex.render(" \\Delta H_{fail} = \\begin{cases} \\min \\left( 150, 4.5 \\times 10^5 C_{prec}^{-2.0} + 33\\right), & \\text{for } T \\leq 533.15~\\text{K}\\\\ \\min \\left( 150, 5.5 \\times 10^5 C_{prec}^{-2.0} + 50\\right), & \\text{for } T > 533.15~\\text{K} \\end{cases}", element, {displayMode:true,throwOnError:false});$ and for Zircaloy-4 (SRA) cladding: $var element = document.getElementById("moose-equation-54787bd0-860a-4956-b4be-134b3d97660c");katex.render(" \\Delta H_{fail} = \\begin{cases} \\min \\left( 150, 1.6 \\times 10^5 C_{prec}^{-1.5} + 45\\right), & \\text{for } T \\leq 533.15~\\text{K}\\\\ \\min \\left( 150, 1.8 \\times 10^5 C_{prec}^{-1.5} + 60\\right), & \\text{for } T > 533.15~\\text{K} \\end{cases}", element, {displayMode:true,throwOnError:false});$

Examples

[Materials<<<{"href": "../../syntax/Materials/index.html"}>>>]
  [failure_criterion]
    type = ZryRIACladdingFailure<<<{"description": "Models the failure of Zircaloy-2 or Zircaloy-4 cladding due to PCMI under RIA conditions.", "href": "ZryRIACladdingFailure.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = 0
    peak_radial_average_enthalpy<<<{"description": "The name of the postprocessor that holds the peak radial average enthalpy."}>>> = peak_radial_average_enthalpy
    total_hydrogen_in_hydride<<<{"description": "The name of the postprocessor that holds the total hydrogen content in the form of hydrides (wt. ppm)."}>>> = total_hydrogen_in_hydride
    temperature<<<{"description": "The coupled temperature variable."}>>> = temperature
  []
[]

Input Parameters

peak_radial_average_enthalpyThe name of the postprocessor that holds the peak radial average enthalpy.
C++ Type:PostprocessorName
Unit:(no unit assumed)
Controllable:No
Description:The name of the postprocessor that holds the peak radial average enthalpy.
temperatureThe coupled temperature variable.
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The coupled temperature variable.
total_hydrogen_in_hydrideThe name of the postprocessor that holds the total hydrogen content in the form of hydrides (wt. ppm).
C++ Type:PostprocessorName
Unit:(no unit assumed)
Controllable:No
Description:The name of the postprocessor that holds the total hydrogen content in the form of hydrides (wt. ppm).

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
cladding_typeZircaloy4The cladding type used in the simulation. Options are Zircaloy-2 and Zircaloy-4.
Default:Zircaloy4
C++ Type:MooseEnum
Options:Zircaloy2, Zircaloy4
Controllable:No
Description:The cladding type used in the simulation. Options are Zircaloy-2 and Zircaloy-4.
comparedless_equalOptions for variable _compared_ to criteria: greater_than greater_equal less_equal less_than
Default:less_equal
C++ Type:MooseEnum
Options:greater_than, greater_equal, less_equal, less_than
Controllable:No
Description:Options for variable _compared_ to criteria: greater_than greater_equal less_equal less_than
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_criteria0Numerical value providing criteria value.
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Numerical value providing criteria value.
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.
function_criteriaFunction name providing criteria value.
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:Function name providing criteria value.
include_linerFalseWhether a liner is present on the interior surface of the cladding.
Default:False
C++ Type:bool
Controllable:No
Description:Whether a liner is present on the interior surface of the cladding.
variable_checkVariable name which is compared to criteria. Example: Var < 0, true=failed
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Variable name which is compared to criteria. Example: Var < 0, true=failed

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/zry_ria_clad_failure/zry_ria_clad_failure.i)

References

Paul Clifford. Pressurized-water reactor control rod ejection and boiling-water reactor control rod drop accidents. Technical Report Regulatory Guide RG 1.236, United States Nuclear Regulatory Commission, 2020.

@techreport{nrc_reg_guide_1236,
    author = "Clifford, Paul",
    institution = "United States Nuclear Regulatory Commission",
    pages = "1-29",
    title = "Pressurized-water reactor control rod ejection and boiling-water reactor control rod drop accidents",
    number = "Regulatory Guide RG 1.236",
    year = "2020"
}

(test/tests/zry_ria_clad_failure/zry_ria_clad_failure.i)

#--------------------------------------------------------------------------------
#
# This test case is prepared to test the LOCA RIA criterion for Zirconium alloy
# using the ZryRIACladdingFailure materials for Zircaloy-4. Command line
# arguments are used in the tests file to additionally test both lined and
# unlined Zircaloy-2.
#
# The temperature is held constant at 500 K and the peak radial average enthalpy
# in the fuel is linearly increased in time from 0 to 100 J/kg over 100 seconds
# with a constant hydrogen excess of 600 wppm.
#
# Failure is assumed when the peak radial average enthalpy exceeds:
#
# H_{fail} = min (150, 1.6e5 C_{prec}^{-1.5} + 45)
# H_{fail} = 55.89 cal/g
#
# where  C_{prec} is the amount of hydrogen in hydrides wt. ppm with the linear
# increase in peak radial average enthalpy failure is analytically expected at a
# time of 56 seconds. This is confirmed by looking at the burst AuxVariable.
#
#--------------------------------------------------------------------------------

[Mesh]
  coord_type = RZ
  [generated_mesh]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 1
    ny = 1
    xmin = 0.005
    xmax = 0.0055
    ymin = 0.0
    ymax = 0.01
  []
[]

[Variables]
  [temperature]
    order = FIRST
    family = LAGRANGE
    initial_condition = 500.0
  []
[]

[AuxVariables]
  [burst]          # Did cladding burst occur?
    order  = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [hydride_function]
    type = ConstantFunction
    value = 600.0
  []
  [radial_average_enthalpy_function]
    type = PiecewiseLinear
    x = '0 100'
    y = '0 418400'
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = temperature
  []
[]

[AuxKernels]
  [hasburst]
    type = MaterialRealAux
    variable = burst
    property = failed
    block = 0
    execute_on = timestep_end
  []
[]

[BCs]
  [temp_bc_1]
    type = DirichletBC
    variable = temperature
    boundary = 'left right top bottom'
    value = 500
  []
[]

[Materials]
  [thermal]
    type = HeatConductionMaterial
    block = 0
    specific_heat = 1.0
    thermal_conductivity = 100.
  []
  [failure_criterion]
    type = ZryRIACladdingFailure
    block = 0
    peak_radial_average_enthalpy = peak_radial_average_enthalpy
    total_hydrogen_in_hydride = total_hydrogen_in_hydride
    temperature = temperature
  []
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'

  petsc_options       = '-snes_ksp_ew'
  petsc_options_iname = '-ksp_gmres_restart'
  petsc_options_value = '101'

  line_search = 'none'

  l_max_its  = 100
  nl_max_its = 100
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-6
  l_tol      = 1e-5
  start_time = 0.0
  end_time   = 57

  [TimeStepper]
    type = ConstantDT
    dt = 1
  []
[]

[UserObjects]
  [arnold]
    type = Terminator
    expression = 'burst > 0'
  []
[]

[Postprocessors]
  [burst]
    type = ElementalVariableValue
    elementid = 0
    variable = burst
  []
  [peak_radial_average_enthalpy]
    type = FunctionValuePostprocessor
    function = radial_average_enthalpy_function
    execute_on = linear
  []
  [total_hydrogen_in_hydride]
    type = FunctionValuePostprocessor
    function = hydride_function
    execute_on = linear
  []
[]

[Outputs]
  csv = true
[]

(test/tests/zry_ria_clad_failure/zry_ria_clad_failure.i)

#--------------------------------------------------------------------------------
#
# This test case is prepared to test the LOCA RIA criterion for Zirconium alloy
# using the ZryRIACladdingFailure materials for Zircaloy-4. Command line
# arguments are used in the tests file to additionally test both lined and
# unlined Zircaloy-2.
#
# The temperature is held constant at 500 K and the peak radial average enthalpy
# in the fuel is linearly increased in time from 0 to 100 J/kg over 100 seconds
# with a constant hydrogen excess of 600 wppm.
#
# Failure is assumed when the peak radial average enthalpy exceeds:
#
# H_{fail} = min (150, 1.6e5 C_{prec}^{-1.5} + 45)
# H_{fail} = 55.89 cal/g
#
# where  C_{prec} is the amount of hydrogen in hydrides wt. ppm with the linear
# increase in peak radial average enthalpy failure is analytically expected at a
# time of 56 seconds. This is confirmed by looking at the burst AuxVariable.
#
#--------------------------------------------------------------------------------

[Mesh]
  coord_type = RZ
  [generated_mesh]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 1
    ny = 1
    xmin = 0.005
    xmax = 0.0055
    ymin = 0.0
    ymax = 0.01
  []
[]

[Variables]
  [temperature]
    order = FIRST
    family = LAGRANGE
    initial_condition = 500.0
  []
[]

[AuxVariables]
  [burst]          # Did cladding burst occur?
    order  = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [hydride_function]
    type = ConstantFunction
    value = 600.0
  []
  [radial_average_enthalpy_function]
    type = PiecewiseLinear
    x = '0 100'
    y = '0 418400'
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = temperature
  []
[]

[AuxKernels]
  [hasburst]
    type = MaterialRealAux
    variable = burst
    property = failed
    block = 0
    execute_on = timestep_end
  []
[]

[BCs]
  [temp_bc_1]
    type = DirichletBC
    variable = temperature
    boundary = 'left right top bottom'
    value = 500
  []
[]

[Materials]
  [thermal]
    type = HeatConductionMaterial
    block = 0
    specific_heat = 1.0
    thermal_conductivity = 100.
  []
  [failure_criterion]
    type = ZryRIACladdingFailure
    block = 0
    peak_radial_average_enthalpy = peak_radial_average_enthalpy
    total_hydrogen_in_hydride = total_hydrogen_in_hydride
    temperature = temperature
  []
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'

  petsc_options       = '-snes_ksp_ew'
  petsc_options_iname = '-ksp_gmres_restart'
  petsc_options_value = '101'

  line_search = 'none'

  l_max_its  = 100
  nl_max_its = 100
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-6
  l_tol      = 1e-5
  start_time = 0.0
  end_time   = 57

  [TimeStepper]
    type = ConstantDT
    dt = 1
  []
[]

[UserObjects]
  [arnold]
    type = Terminator
    expression = 'burst > 0'
  []
[]

[Postprocessors]
  [burst]
    type = ElementalVariableValue
    elementid = 0
    variable = burst
  []
  [peak_radial_average_enthalpy]
    type = FunctionValuePostprocessor
    function = radial_average_enthalpy_function
    execute_on = linear
  []
  [total_hydrogen_in_hydride]
    type = FunctionValuePostprocessor
    function = hydride_function
    execute_on = linear
  []
[]

[Outputs]
  csv = true
[]

Description
Examples
Input Parameters
Input Files
References