Empirical model for calculating grain evolution

## 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: (1) where (m) is the 2-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 (2) when = 8.314 J/(molK). The limiting grain size is a function of the temperature such that (3) To obtain the 3-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. 4, which depends on the local effective burnup, (GWd/tU) (see EffectiveBurnupAux). (4) 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).

## Example Input Syntax


block = pellet_type_1
temp = temp
execute_on = linear
[../]
(examples/2D-RZ_rodlet_10pellets/Smeared.i)

## Input Parameters

• variableThe name of the variable that this object applies to

C++ Type:AuxVariableName

Description:The name of the variable that this object applies to

• tempCoupled Temperature

C++ Type:std::vector

Description:Coupled Temperature

### Required Parameters

• burnup_eff_threshold50HBS Threshold (GWD/tU)

Default:50

C++ Type:double

Description:HBS Threshold (GWD/tU)

• include_hbsFalseImplement Shrinking Grain Radius Model

Default:False

C++ Type:bool

• blockThe list of block ids (SubdomainID) that this object will be applied

C++ Type:std::vector

Description:The list of block ids (SubdomainID) that this object will be applied

• execute_onLINEARThe list of flag(s) indicating when this object should be executed, the available options include NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, FINAL, CUSTOM.

Default:LINEAR

C++ Type:ExecFlagEnum

Description:The list of flag(s) indicating when this object should be executed, the available options include NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, FINAL, CUSTOM.

• boundaryThe list of boundary IDs from the mesh where this boundary condition applies

C++ Type:std::vector

Description:The list of boundary IDs from the mesh where this boundary condition applies

• burnup_effCoupled Effective Burnup

C++ Type:std::vector

Description:Coupled Effective Burnup

### Optional Parameters

• control_tagsAdds user-defined labels for accessing object parameters via control logic.

C++ Type:std::vector

Description:Adds user-defined labels for accessing object parameters via control logic.

• enableTrueSet the enabled status of the MooseObject.

Default:True

C++ Type:bool

Description:Set the enabled status of the MooseObject.

• seed0The seed for the master random number generator

Default:0

C++ Type:unsigned int

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

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.

1. J.B. Ainscough, B.W. Oldfield, and J.O. Ware. Isothermal grain growth kinetics in sintered UO$_2$ pellets. Journal of Nuclear Materials, 49:117Ã¢â‚¬â€œ128, 1973.[BibTeX]