# UOvar element = document.getElementById("moose-equation-cf712ccd-f283-4539-a863-cdfee90ead9a");katex.render("_2", element, {displayMode:false,throwOnError:false}); Volumetric Swelling Eigenstrain

Calculates and sums the change in fuel pellet volume due to densification and fission product release. This class applies a volumetric strain correction before adding the strain from this class to the diagonal entries of the eigenstrain tensor.

## Description

Swelling due to solid fission products, gaseous fission products, and densification all contribute to the change in volume of a UO fuel pellet. The contributions from all three of these components are modeled in UO2VolumetricSwellingEigenstrain.

## Densification of the Fuel

Fuel densification is computed using the ESCORE empirical model (Rashid et al., 2004) given by: (1) where is the densification strain, is the total densification that can occur (given as a fraction of theoretical density), Bu is the burnup, and Bu is the burnup at which densification is complete. (2) In Eq. 2 the variable for temperature, , is defined in Celcius. Note that the parameter given in (Rashid et al., 2004) for temperatures below 750C; the values in Eq. 2 are used in Bison to eliminate the discontinuity in .

### Application to MOX Fuel

In MATPRO (Allison et al., 1993), the same model is provided for UO and MOX. Because this correlation relies on a wide database, this model is also used in Bison for MOX densification.

## Fission Product Swelling

Empirical relations from MATPRO (Allison et al., 1993) are available in Bison for calculating the swelling due to both solid and gaseous fission products. The same model is provided for both UO and MOX.

Solid fission product swelling is expressed as a simple linear function of burnup: (3) where is the volumetric solid swelling increment, Bu the burnup increment (fissions/atoms-U), and is the density (kg/m).

Swelling due to gaseous fission products is approximated by a semi-empirical model: (4) where is the volumetric gas swelling increment, and are the burnup and burnup increment (fissions/atoms-U), respectively, is the density (kg/m) and is the temperature (K).

Figure 1: UO gaseous and total swelling, as a function of temperature and burnup, based on the MATPRO correlations.

Figure 1 shows a plot of the gaseous and total fission product swelling as a function of temperature and burnup. The MATPRO correlations (Allison et al., 1993) indicate that gaseous swelling does not become significant until above 1500 K and is saturated at a burnup of 20 MWd/kgU.

Alternatively the gaseous fission product swelling can be calculated using a physics-based model that takes into account the coupling with the fission gas release (see Sifgrs ).

## Example Input Syntax


[./fuel_swelling]
type = UO2VolumetricSwellingEigenstrain
gas_swelling_model_type = MATPRO
block = '1 2 3 4 5 6 7'
temperature = temp
burnup = burnup
complete_burnup = 5
total_densification = 0.01
eigenstrain_name = swell
initial_fuel_density = 10430.0
save_densification = true
save_solid_swelling = true
[../]
(test/tests/tensor_mechanics/uo2_eigenstrains/uo2_vswelling/swelling_tm.i)

The eigenstrain_name parameter value must also be set for the strain calculator, and an example parameter setting is shown below:


[./fuel_strain]
type = ComputeFiniteStrain
block = '1 2 3 4 5 6 7'
eigenstrain_names = 'fuelthermal_strain swell'
[../]
(test/tests/tensor_mechanics/uo2_eigenstrains/uo2_vswelling/swelling_tm.i)

## Input Parameters

• temperatureCoupled Temperature in Kelvin

C++ Type:std::vector

Description:Coupled Temperature in Kelvin

• initial_fuel_densityInitial fuel density in kg-UO2/m^3

C++ Type:double

Description:Initial fuel density in kg-UO2/m^3

• eigenstrain_nameMaterial property name for the eigenstrain tensor computed by this model. IMPORTANT: The name of this property must also be provided to the strain calculator.

C++ Type:std::string

Description:Material property name for the eigenstrain tensor computed by this model. IMPORTANT: The name of this property must also be provided to the strain calculator.

### Required Parameters

• initial_porosity0.05initial fuel porosity (dimensionless)

Default:0.05

C++ Type:double

Description:initial fuel porosity (dimensionless)

• 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.

• base_nameOptional parameter that allows the user to define multiple mechanics material systems on the same block, i.e. for multiple phases

C++ Type:std::string

Description:Optional parameter that allows the user to define multiple mechanics material systems on the same block, i.e. for multiple phases

• include_solid_swellingTrueShould the calculation of volumetric swelling include swelling due to solid fision products

Default:True

C++ Type:bool

Description:Should the calculation of volumetric swelling include swelling due to solid fision products

• save_solid_swellingFalseShould the solid swelling be saved in a material property

Default:False

C++ Type:bool

Description:Should the solid swelling be saved in a material property

• complete_burnup5The burnup at which densification is complete input in units of MWd/kgU

Default:5

C++ Type:double

Description:The burnup at which densification is complete input in units of MWd/kgU

• constant_dens_c_dFalseWhether to use a constant C_d (1.0)

Default:False

C++ Type:bool

Description:Whether to use a constant C_d (1.0)

• total_densification0.01The densification that will occur given as a fraction of theoretical density

Default:0.01

C++ Type:double

Description:The densification that will occur given as a fraction of theoretical density

• include_gas_swellingTrueShould the calculation of volumetric swelling include swelling due to gas fision products

Default:True

C++ Type:bool

Description:Should the calculation of volumetric swelling include swelling due to gas fision products

• 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

• gas_swelling_model_typeSIFGRSWhich type of model to use to calculate the gaseous swelling. Choices are SIFGRS MATPRO. If you select SIFGRS, the SIFGRS model must be included in the input file.

Default:SIFGRS

C++ Type:MooseEnum

Description:Which type of model to use to calculate the gaseous swelling. Choices are SIFGRS MATPRO. If you select SIFGRS, the SIFGRS model must be included in the input file.

• include_densificationTrueShould the calculation of volumetric swelling include volumetric changes due to densification

Default:True

C++ Type:bool

Description:Should the calculation of volumetric swelling include volumetric changes due to densification

• save_densificationFalseShould the densification be saved in a material property

Default:False

C++ Type:bool

Description:Should the densification be saved in a material property

• 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_functionBurnup function

C++ Type:BurnupFunctionName

Description:Burnup function

• burnupCoupled Burnup

C++ Type:std::vector

Description:Coupled Burnup

### 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

• gaseous_swelling_scale_factor1Scale factor to be applied to the gaseous swelling strain when gas swelling model type is MATPRO. Used for calibration and sensitivity studies

Default:1

C++ Type:double

Description:Scale factor to be applied to the gaseous swelling strain when gas swelling model type is MATPRO. Used for calibration and sensitivity studies

• solid_swelling_scale_factor1Scale factor to be applied to the solid swelling strain. Used for calibration and sensitivity studies

Default:1

C++ Type:double

Description:Scale factor to be applied to the solid swelling strain. Used for calibration and sensitivity studies

• 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. C. M. Allison, G. A. Berna, R. Chambers, E. W. Coryell, K. L. Davis, D. L. Hagrman, D. T. Hagrman, N. L. Hampton, J. K. Hohorst, R. E. Mason, M. L. McComas, K. A. McNeil, R. L. Miller, C. S. Olsen, G. A. Reymann, and L. J. Siefken. SCDAP/RELAP5/MOD3.1 code manual, volume IV: MATPROâ€“A library of materials properties for light-water-reactor accident analysis. Technical Report NUREG/CR-6150, EGG-2720, Idaho National Engineering Laboratory, 1993.[BibTeX]
2. Y Rashid, R Dunham, and R Montgomery. Fuel Analysis and Licensing Code: FALCON MOD01. Technical Report, Electric Power Research Institute, December 2004.[BibTeX]