GrainRadiusAux

Computes grain evolution using an empirical model.

Description

When a polycrystalline material is subject to high temperatures, larger grains tend to grow at the expense of the smaller ones. As a consequence, the latter gradually disappear, thus reducing the total number of grains per unit volume and increasing the average grain size. This phenomenon is known as grain growth. The granular structure of the fuel affects physical processes such as fission gas behavior.

A simple empirical model (Ainscough et al., 1973) is implemented in BISON for calculating grain growth in UO fuel. According to this model, the kinetics of grain growth is described by the equation: where (m) is the two-dimensional (linear intercept) average grain diameter, (h) the time, (m/h) the rate constant, and (m) is the limiting grain size. The rate constant is given as when = 8.314 J/(mol-K). The limiting grain size is a function of the temperature such that To obtain the three-dimensional grain diameter, is multiplied by a factor of 1.56 (Mendelson, 1969).

An option is also available to allow for the recrystallization during the high burner structure (HBS) formation and the associated shrinkage of grain size. Once the HBS is established, the grain size evolution behaves according to Eq. (1), which depends on the local effective burnup, (GWd/tU) (see EffectiveBurnupAux). (1) In this formulation (m) is the grain radius, and the fit parameters, and , are 7.0 0.8 GWd/tU and 0.15 0.03 m respectively (Pizzocri et al., 2017).

A alternative mechanistic model for grain growth is available in GrainRadiusMechanistic.

Example Input Syntax

[AuxKernels<<<{"href": "../../syntax/AuxKernels/index.html"}>>>]
  [grain_radius]
    type = GrainRadiusAux<<<{"description": "Computes grain evolution using an empirical model.", "href": "GrainRadiusAux.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = pellet_type_1
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = grain_radius
    temperature<<<{"description": "Coupled temperature (K)"}>>> = temp
    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."}>>> = linear
  []
[]
(examples/2D-RZ_rodlet_10pellets/fuel_pin_geometry/fuelpingeo.i)

Input Parameters

  • temperatureCoupled temperature (K)

    C++ Type:std::vector<VariableName>

    Unit:(no unit assumed)

    Controllable:No

    Description:Coupled temperature (K)

  • 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

  • burnup_effCoupled Effective Burnup.

    C++ Type:std::vector<VariableName>

    Unit:(no unit assumed)

    Controllable:No

    Description:Coupled Effective Burnup.

  • burnup_eff_threshold50HBS Threshold (GWD/tU).

    Default:50

    C++ Type:double

    Unit:(no unit assumed)

    Controllable:No

    Description:HBS Threshold (GWD/tU).

  • 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

  • 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.

  • include_hbsFalseImplement Shrinking Grain Radius Model.

    Default:False

    C++ Type:bool

    Controllable:No

    Description:Implement Shrinking Grain Radius Model.

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

References

  1. J.B. Ainscough, B.W. Oldfield, and J.O. Ware. Isothermal grain growth kinetics in sintered UO$_2$ pellets. Journal of Nuclear Materials, 49:117–128, 1973.[BibTeX]
  2. M.I. Mendelson. Average grain size in polycrystalline ceramics. Journal of the American Ceramic Society, 52:443–446, 1969.[BibTeX]
  3. D. Pizzocri, F. Cappia, L. Luzzi, G. Pastore, V.V. Rondinella, and P. Van Uffelen. A semi-empirical model for the formation and depletion of the high burnup structure in uo2. Journal of Nuclear Materials, 487:23–29, 2017.[BibTeX]