# MOX Pore Velocity Calculation

Calculates pore speed from author Kato. Used with vapor pressure calculations from MOXVaporPressure.

## Description

Pore speed is calculated in this class, which is used in the kernel MOXPoreContinuity shown in the second term of the following equation: (1) where is the porosity, is the pore velocity, is the temperature, and is the diffusion coefficient MOX Pore Restructuring: Diffusion. Usually, the temperature gradient is included in the pore velocity term, but here, the temperature gradient is written separately to emphasize the dependence of pore migration on temperature gradient. The difference between the equation for pore speed found here and in MOXPoreVelocity is vapor pressure terms for UO, PuO, UO, U, UO, PuO, Pu, AmO, Am, AmO, and O.

From Ikusawa et al. (2014) (2) is fuel molecular volume in cm, is the mol fraction of PuO, is the mol fraction of UO, is the lattice parameter of PuO (5.396E-8 cm), is the lattice parameter of UO (5.4704E-8 cm), D is the diffusion coefficient of PuO and UO gas in the void, is the Boltzmann constant (1.3708E-16 cmg/sK), m is a mass conversion factor, is the number of gas molecules captured within voids during sintering, is the gas molecule diameter (4.33E-8 cm), is the concentration gradient of gas molecules in a void, is temperature in K, is the correction factor of void migration velocity, and is calculated from correlations between vapor pressure of vapor species and Gibbs free energy. Specifically, is the summation of the vapor pressure terms from the following fuel constituents: UO, PuO2, UO, U, UO, PuO, Pu, AmO, Am, AmO, and O. The term corresponds to a factor to assume the temperature gradient in a pore from that in fuel.

For = Pu concentration, = Am concentration, = deviation from stoichiometry of the metal oxide (MO), = partial pressure of oxygen, and Gibbs free energy via the Rand-Markin model (s defined subsequently), the following equations are the vapor pressure terms as a function of temperature ():

(3) Oxygen partial pressure, p, can be calculated from the following equation: (4) where (5) Again, the pressure in the velocity equation is the sum of all these individual vapor pressures: (6)

The vapor pressure and come from the class MOXVaporPressure.

under construction

This class is still under development!

See bison/test/mox_pore_velocity/ for examples of how this class should be used.

## Input Parameters

• temperatureCoupled Temperature

C++ Type:std::vector

Description:Coupled Temperature

### Required Parameters

• scale_factor1scale the velocity to account for uncertainty

Default:1

C++ Type:double

Description:scale the velocity to account for uncertainty

• 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

• computeTrueWhen false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the Material via MaterialPropertyInterface::getMaterial(). Non-computed Materials are not sorted for dependencies.

Default:True

C++ Type:bool

Description:When false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the Material via MaterialPropertyInterface::getMaterial(). Non-computed Materials are not sorted for dependencies.

• 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

### Optional Parameters

• enableTrueSet the enabled status of the MooseObject.

Default:True

C++ Type:bool

Description:Set the enabled status of the MooseObject.

• 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.

• 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.

• seed0The seed for the master random number generator

Default:0

C++ Type:unsigned int

Description:The seed for the master random number generator

• implicitTrueDetermines whether this object is calculated using an implicit or explicit form

Default:True

C++ Type:bool

Description:Determines whether this object is calculated using an implicit or explicit form

• 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 computeSubdomainProperties() 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

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 computeSubdomainProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped

• output_propertiesList of material properties, from this material, to output (outputs must also be defined to an output type)

C++ Type:std::vector

Description:List of material properties, from this material, to output (outputs must also be defined to an output type)

• outputsnone Vector of output names were you would like to restrict the output of variables(s) associated with this object

Default:none

C++ Type:std::vector

Description:Vector of output names were you would like to restrict the output of variables(s) associated with this object

## References

1. Yoshihisa Ikusawa, Takayuki Ozawa, Shun Hirooka, Koji Maeda, Masato Kato, and Seiichiro Maeda. Development and verification of the thermal behavior analysis code for ma containing mox fuels. In International Conference on Nuclear Engineering. Prague, Czech Republic, July 7â€“11 2014.[BibTeX]