- temperatureCoupled temperature
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Coupled temperature
- vacancy_GB_diffusivityMaterial property for vacancy diffusion in grain boundaries.
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:Material property for vacancy diffusion in grain boundaries.
UNSifgrs
Computes fission gas release and swelling in UN through a mechanistic model.
Description
The processes induced by the generation of the fission gases xenon and krypton in nuclear fuel have a strong impact on the thermo-mechanical performance of the fuel rods. On the one hand, the fission gases tend to precipitate into bubbles resulting in fuel swelling, which promotes pellet-cladding gap closure and the ensuing pellet-cladding mechanical interaction (PCMI). On the other hand, fission gas release (FGR) to the fuel rod free volume causes pressure build-up and thermal conductivity degradation of the rod filling gas.
The fundamental physical processes, which control the kinetics of fission gas swelling and release in irradiated fuel, may be summarized as follows; fission gas atoms generated in the fuel grains diffuse towards the grain boundaries through repeated trapping in and irradiation-induced resolution from nanometre-size intra-granular gas bubbles. Although a part of the gas atoms that reach the grain boundaries is dissolved back to the grain interior by irradiation, the majority of the gas diffuses into grain-face gas bubbles, giving rise to grain-face swelling. Bubble growth brings about bubble coalescence and inter-connection, eventually leading to the formation of a tunnel network through which a fraction of the gas is released to the fuel rod free volume.
In BISON, fission gas behavior is computed for each integration point in the fuel finite element mesh. The gas produced at each integration point is computed by a numerical time integration of the gas production rate, given as the product of the fission rate and fractional yield of gas atoms per fission.
Coupled fission gas release and swelling model
The UNSifgrs model handles fission gas swelling and release in UN under power reactor conditions. The model calculates the coupled fission gas swelling and release concurrently Rizk et al. (2023). The same basic structure of the UO Sifgrs model (UO2Sifgrs) model is applied in this model, with a two-stage description of intra-granular and inter-granular processes. The intra-granular bubble part of the UN model shares similarities with both USi Sifgrs model (U3Si2Sifgrs) and UO Sifgrs model. Similarly to USi, bulk intra-granular bubble nucleation and intra-granular bubble gas atom re-solution are modeled based on the homogeneous mechanisms, and the growth model for intra-granular bubbles considers the absorptions of vacancies by the bubbles based on an adaptation of the Speight-Beere model driven by the overpressurization of gas in the bubbles compared to the surface tension of the surrounding lattice. Like with UO, there is a second population of intra-granular bubbles located on dislocations. Nucleation of these bubbles occurs as the dislocation density increases, and additional trapping of gas atoms and vacancies occurs along dislocations lines. Otherwise, the intragranular dislocation bubbles are modeled similarly to the intragranular bulk bubbles in terms of resolution and growth.
Lower-length scale modeling is used to determine UN-specific parameters where needed. A combination of density functional theory (DFT) calculations, empirical potential calculations, and free energy cluster dynamics calculations estimated the thermal-equilibrium and irradiation-enhanced diffusivities of gas atoms and vacancies Cooper et al. (2023), and molecular dynamics simulations estimated the athermal diffusion of gas atoms due to ballistic mixing. Analytical expressions are used to calculate diffusion coefficients. For vacancy diffusion, the minimum of uranium vacancy and nitrogen vacancy diffusivity is used to calculate bubble growth. The re-solution rate of gas atoms from intra-granular bubbles were estimated from binary collision approximation calculations in Matthews et al. (2016). The UN-gas surface energy was estimated by averaging literature values estimated using DFT Bocharov (2012).
Parameters for which specific UN values are not yet available are adopted from either USi or UO. The UNSifgrs model will be progressively updated as new data become available.
Intra-granular gas behavior
The intra-granular module computes gas generation and bubble evolution in the grains and the coupled diffusion of gas atoms to grain boundaries. The description includes bubble nucleation, irradiation-induced re-solution of gas atoms from bubbles back into the lattice, absorption of gas atoms and vacancies at the bubbles, and diffusion of single gas atoms.
The model for intragranular bubble growth and evolution makes the simplifying assumption of an average bubble size, (m), and an average bubble concentration, (m), for the two bubble types, bulk (subscripted with "") and dislocation (subscripted with "") Pizzocri et al. (2018), Barani et al. (2019), and Barani et al. (2020). This assumption allows for the bubble behavior to be expressed by five equations, (1)
where (m) is the concentration of gas atoms in the matrix, (m) is the concentration of gas atoms in the bubbles, (ms) is the nucleation rate given for dislocation bubbles by Eq. (5), (s) is the resolution rate given by Eq. (8), (m/s) is the gas atom diffusion coefficient, (s) is the trapping rate for dislocation bubbles given by Eq. (6), (s) is the trapping rate for bulk bubbles, and () is the generation rate of fission gas atoms. When calculating the number of bubbles, resolution destroys only the smallest bubbles with a size of two atoms. So the correction factor is applied, which is the fraction of dimers out of the total number of bubbles, estimated as, (2) where is the average number of gas atoms per bubble, defined as, (3)
The nucleation rate for bulk bubbles is calculated as: (4) where (m) is the radius of a single fission gas atom and is the nucleation factor (dimensionless), equal to (e.g., Veshchunov (2000)).
Dislocation bubbles nucleate along new dislocation lines by a factor bubbles/m, which is the number of bubbles nucleated per dislocation line length. Nucleation is given by, (5) The value of comes from previous modeling work for UO Barani et al. (2020), and from bubble density and dislocation density measurements in carbide fuel Ray and Blank (1984), where the bubble density was found to increase linearly with dislocation density by (bubbles/m) at 1025 K. In the same experiment, bubbles were also found to nucleate on needle-shaped precipitates, which demonstrated no temperature-dependence of this nucleation factor.
The trapping of gas atoms at bubbles is considered to be driven by diffusion of gas atoms within the interaction vicinity of the bubbles. The trapping rate is given by, (6) where (m) is the average radius of the bubbles. The nucleation factor is a calibration term equal to 1 or greater to account for an extended interaction distance between gas atoms and bubbles.
Gas can also be trapped and travel along dislocation line to reach dislocation bubbles. The trapping rate at dislocations is given by, (7) where (m) is the radius of the Wigner-Seitz cell associated with a dislocation, and (m) is the dislocation core radius, which is roughly the length of the Burger's vector. is a trapping radius factor to account for the elastic strain field around the dislocation core causing gas atoms to imminently absorb from greater distances. Trapping at dislocation bubbles is given as the sum of trapping at the bubbles and the dislocations, . This formulation should be updated to exclude the fraction of the dislocation line covered by the dislocation bubbles, because the part of the dislocation line that is covered by a bubble that already traps gas at its surface cannot also contribute to gas trapping. If a large fraction of the dislocation line is covered, then that fraction is contributing nonphysically to the trapping by what may be a non-negligible amount.
The re-solution rate for both bulk and dislocation bubbles is expressed as: (8) where is the fission rate density (ms). The trapping rate is calculated as Ham (1958): (9) where is the average bubble radius (m).
The dislocation bubbles may reach sufficiently large sizes that their radii are comparable to the inter-bubble distance. In such a senario, dislocation bubbles are allowed to coalescence, decreasing their number density, but maintaining the bubble gas content. The equation for the variation of the number density of dislocation bubbles as the size changes is based on the nearest-neighbor distribution of hard sphere Torquato (1995) and is given by, (10) where is a correction factor for the hard sphere assumption, and is the porosity associated with dislocation bubbles.
The system of equations Eq. (1) is solved using the Polypole-1 algorithm. Due to the relatively low resolution parameter in UN, the quasi-stationary approximation used to compute in Polypole-1 may not necessarily hold. The Polypole-2 alorithm cannot yet handle the population of dislocation bubbles.
Intra-granular bubble growth is computed based on the evolution of the gas atom content from Eq. (9) and the rate of absorption of vacancies at the bubble. The latter is computed using a modified Speight and Beere (1975) model, as follows:
The mechanical equilibrium of an intra-granular bubble, assumed to be spherical, is governed by the Young-Laplace equation (11) where (Pa) is the equilibrium pressure, (J ) is the UN/gas surface energy and (Pa) is the hydrostatic stress. In general, the bubbles are in a non-equilibrium state and tend to the equilibrium condition absorbing or emitting vacancies. The vacancy absorption/emission rate can be calculated starting from the approach in Speight and Beere (1975) as (12) being (dimensionless) the number of vacancies per intra-granular bubble, ( ) the intra-granular vacancy diffusion coefficient, (m) is the radius of the equivalent Wigner-Seitz cell surrounding a bubble and influenced by the vacancy absorption/emission, (J K) is the Boltzmann constant, (K) is the local temperature, and (dimensionless) is an dimensionless factor, which is calculated as (Pizzocri et al., 2016) (13) where is the ratio between the bubble and the cell radii. The present model for vacancy absorption/emission at intra-granular bubbles is a reformulation of the Speight and Beere model for behavior at grain boundaries of bubbles of circular projection (2D problem) (Speight and Beere, 1975). In particular, Eq. (12) and Eq. (13) represent the equivalent model for vacancy absorption/emission at spherical bubbles in the bulk (3D problem). Considering a van der Waals gas, the pressure of the bubble is expressed as (14) where () is the vacancy volume, (dimensionless) is the ratio between and , and () is the van der Waals atomic volume for xenon.
The volume of intra-granular bubbles is calculated as
The fractional volume intra-granular fission gas swelling is given by (15)
Grain-boundary gas behavior
The numerical solution of Eq. (1) allows calculation of the arrival rate of gas at the grain boundaries, providing the source term for the grain-boundary gas behavior module. This computes both grain-boundary fission gas swelling and fission gas release through a direct description of the grain-face bubble development, including bubble growth, coalescence, and eventual inter-connection leading to fission gas release. The concept of the grain-boundary model is identical to that of the UO ( UO2Sifgrs) model. However, the material parameters are specific to the UNSifgrs model.
The fractional volume grain-boundary fission gas swelling is given by (16) where is the number density of grain-face bubbles per unit surface, the grain radius, and the bubble volume. The factor 1/2 is introduced in Eq. (16) because a grain-face bubble is shared by two neighboring grains.
Bubble growth is calculated with the model from Speight and Beere (1975) to describe the growth (or shrinkage) of grain-face bubbles as proceeding by absorption (or emission) of vacancies in grain boundaries, induced by the difference between the pressure of the gas in the bubble, (Pa), and the mechanical equilibrium pressure, (Pa). The approach is conceptually analogous to that applied in for the growth and shrinkage of intra-granular bubbles and is described in UO2Sifgrs. The grain-boundary diffusion coefficient of vacancies is estimated by multiplying the intra-granular diffusion coefficient of vacancies by a factor of . Ultimately, the volume of a bubble comprising fission gas atoms and vacancies is given by (17)
An initial concentration of grain-face bubbles equal to (bub/m) is employed. The process of grain-face bubble coalescence, which leads to a progressive decrease of the bubble number density throughout irradiation, is described with a model based on Pastore et al. (2013) and White (2004). According to this model, the evolution of the number density of grain-boundary bubbles is given by where and represent the number density and projected area of grain-face bubbles, respectively.
The release of fission gas to the fuel rod free volume after the inter-connection of grain-face bubbles and the consequent formation of pathways for gas venting to the fuel exterior (thermal release) is based on the principle of grain face saturation. More precisely, after the fractional coverage, , attains a saturation value, , further bubble growth is compensated by gas release in order to maintain the constant coverage condition: (18) where is the bubble number density and is the bubble projected area on the grain face. In the absence of experimental data or calculations on the maximum grain-face bubble coverage in UN, the same value used for UO, i.e., , is considered.
Fission rate cutoff
warningwarning:Zero power annealing
Due to the quasi-static approximation required by Polypole1, high temperature annealing in the absence if fission rate will not be captured correctly.
Due to the quasi-static approximation required by Polypole1, the intragranular solve will be skipped altogether if the fission rate is less than or equal to the user value, "fission_rate_cutoff". To prevent weird fission gas behavior during low power transients, it's assumed that if fission rate is zero, then temperature is likely low enough that diffusion does not occur, thus fission gas concentrations are do not evolve in the grain. This approxmiation does not work for high temperature annealing, but is likely adequate to capture the behavior as the reactor shuts down.
Example Input Syntax
[Materials<<<{"href": "../../syntax/Materials/index.html"}>>>]
[fission_gas_behavior]
type = UNSifgrs<<<{"description": "Computes fission gas release and swelling in UN through a mechanistic model.", "href": "UNSifgrs.html"}>>>
temperature<<<{"description": "Coupled temperature"}>>> = temp
fission_rate<<<{"description": "Coupled fission rate variable (fiss/m^3/s)"}>>> = fission_rate
outputs<<<{"description": "Vector of output names where you would like to restrict the output of variables(s) associated with this object"}>>> = all
ig_bubble_coarsening<<<{"description": "Select intra-granular diffusion algorithm"}>>> = WITH_COARSENING
dislocation_density<<<{"description": "Coupled dislocation density (m/m^3)"}>>> = dislocation_density
vacancy_GB_diffusivity<<<{"description": "Material property for vacancy diffusion in grain boundaries."}>>> = vacancy_GB_diffusivity
[]
[]Input Parameters
- atomic_covolume8.47705e-29Van der Waals covolume for Xe (m^3/atm)
Default:8.47705e-29
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Van der Waals covolume for Xe (m^3/atm)
- 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
- bubble_gb_limit1e+10grain-boundary bubble number density limit (bbl/m**2)
Default:1e+10
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:grain-boundary bubble number density limit (bbl/m**2)
- burnupCoupled burnup
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Coupled burnup
- burnup_functionBurnup function
C++ Type:BurnupFunctionName
Unit:(no unit assumed)
Controllable:No
Description:Burnup function
- 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_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
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.
- dislocation_bubble_nucleation_factor1e+06dislocation bubble nucleation factor, i.e., number of bubbles per dislocation line density (bubbles/(m/m2))
Default:1e+06
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:dislocation bubble nucleation factor, i.e., number of bubbles per dislocation line density (bubbles/(m/m2))
- dislocation_core_radius3.45705e-10dislocation core radius (m), burgers vector length
Default:3.45705e-10
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:dislocation core radius (m), burgers vector length
- dislocation_density40000000000000.0Coupled dislocation density (m/m^3)
Default:40000000000000.0
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Coupled dislocation density (m/m^3)
- dislocation_density_materialdislocation density material property (m/m^3)
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:dislocation density material property (m/m^3)
- dislocation_punchingFalseFlag to allow dislocation punching, effectively limiting bubble pressures and tracking the rate of dislocation production.
Default:False
C++ Type:bool
Controllable:No
Description:Flag to allow dislocation punching, effectively limiting bubble pressures and tracking the rate of dislocation production.
- dislocation_trap_Zfactor25Z * dislocation core radius = dislocation_trap_radius (m)
Default:25
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Z * dislocation core radius = dislocation_trap_radius (m)
- effdiffcoeff_scalef1Scaling factor for intragranular effective diffusion coefficient
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Scaling factor for intragranular effective diffusion coefficient
- eos_optionORIGINAL_MODELSelect Equation of State
Default:ORIGINAL_MODEL
C++ Type:MooseEnum
Controllable:No
Description:Select Equation of State
- fission_gas_concCoupled fission gas concentration
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Coupled fission gas concentration
- fission_rateCoupled fission rate variable (fiss/m^3/s)
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Coupled fission rate variable (fiss/m^3/s)
- fission_rate_cutoff0Value of fission rate at which or below the intragranular solve is not computed. This is required due to the quasi-static approximation utilized by Polypole1.
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Value of fission rate at which or below the intragranular solve is not computed. This is required due to the quasi-static approximation utilized by Polypole1.
- fission_rate_materialFission rate material property (fiss/m^3/s)
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:Fission rate material property (fiss/m^3/s)
- fract_yield0.3017fractional yield of fission gas atoms (Xe + Kr) (/)
Default:0.3017
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:fractional yield of fission gas atoms (Xe + Kr) (/)
- gas_atom_dislocation_diffusion_multiplier1Factor by which gas atom diffusion is multiplied along dislocations compared to the bulk to capture pipe diffusion
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Factor by which gas atom diffusion is multiplied along dislocations compared to the bulk to capture pipe diffusion
- gas_diffusivity_functionOptional function for gas atomic diffusivity (m^2/s). For implementation of the function, the x-axis corresponds to temperature and y-axis corresponds to fission rate. The z-axis is unused, and time is the standard current time.
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:Optional function for gas atomic diffusivity (m^2/s). For implementation of the function, the x-axis corresponds to temperature and y-axis corresponds to fission rate. The z-axis is unused, and time is the standard current time.
- gbdiffcoeff_scalef1Scaling factor for grain-boundary vacancy diffusion coefficient
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Scaling factor for grain-boundary vacancy diffusion coefficient
- grain_radiusCoupled grain Radius
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Coupled grain Radius
- grain_radius_const6e-06Constant grain radius (m)
Default:6e-06
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Constant grain radius (m)
- grainradius_scalef1Scaling factor for grain radius
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Scaling factor for grain radius
- hydrostatic_stressCoupled hydrostatic Stress
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Coupled hydrostatic Stress
- hydrostatic_stress_const0constant hydrostatic stress (Pa)
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:constant hydrostatic stress (Pa)
- ig_bubble_coarseningNO_COARSENINGSelect intra-granular diffusion algorithm
Default:NO_COARSENING
C++ Type:MooseEnum
Controllable:No
Description:Select intra-granular diffusion algorithm
- ig_bubble_modelNUCLEATION_RESOLUTIONSelect bubble evolution model
Default:NUCLEATION_RESOLUTION
C++ Type:MooseEnum
Controllable:No
Description:Select bubble evolution model
- ig_diff_algorithmPOLYPOLE1Select intra-granular diffusion algorithm
Default:POLYPOLE1
C++ Type:MooseEnum
Controllable:No
Description:Select intra-granular diffusion algorithm
- ig_fully_coupledLOOSELY_COUPLEDSolving diffusion coupled to bubble evolution
Default:LOOSELY_COUPLED
C++ Type:MooseEnum
Controllable:No
Description:Solving diffusion coupled to bubble evolution
- igdiffcoeff_scalef1Scaling factor for intragranular diffusion coefficients
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Scaling factor for intragranular diffusion coefficients
- initial_porosity0Initial fuel porosity (/)
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Initial fuel porosity (/)
- intergranular_bubble_coalescence_optionWHITE2004Select intergranular bubble coalescence model
Default:WHITE2004
C++ Type:MooseEnum
Controllable:No
Description:Select intergranular bubble coalescence model
- minimum_pressure_ratio1Factor to limit the equilibrium pressure of bubbles by enforcing a minimum ratio of the equilibrium pressure to the pressure due to surface energies alone. If greater than one, tensile stresses do not impact the equilibrium bubble size. This factor is not allowed to be below 0 since it can result in negative equilibrium pressures. A value of of 0.1 - 0.5 is reasonable for capturing tensile stress impacts on the equilibrium bubble pressure.
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Factor to limit the equilibrium pressure of bubbles by enforcing a minimum ratio of the equilibrium pressure to the pressure due to surface energies alone. If greater than one, tensile stresses do not impact the equilibrium bubble size. This factor is not allowed to be below 0 since it can result in negative equilibrium pressures. A value of of 0.1 - 0.5 is reasonable for capturing tensile stress impacts on the equilibrium bubble pressure.
- nucleation_optionHOMOGENEOUSSelect intragranular bubble nucleation model
Default:HOMOGENEOUS
C++ Type:MooseEnum
Controllable:No
Description:Select intragranular bubble nucleation model
- nuclerate_scalef1Scaling factor for nucleation rate
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Scaling factor for nucleation rate
- percolation_to_surface1.0Optional AuxVariable that indicates whether the local position is connected by a percolated path to a free surface to allow gas release. If this parameter is not set, path to free surface is not considered in the gas release calculation.
Default:1.0
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Optional AuxVariable that indicates whether the local position is connected by a percolated path to a free surface to allow gas release. If this parameter is not set, path to free surface is not considered in the gas release calculation.
- resolutionp_scalef1Scaling factor for resolution parameter
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Scaling factor for resolution parameter
- resolutionp_scalef_dislocation1Scaling factor for resolution parameter in dislocations
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Scaling factor for resolution parameter in dislocations
- saturation_coverage0.5initial grain boundary saturation coverage (/)
Default:0.5
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:initial grain boundary saturation coverage (/)
- semidihedral_angle1.032Semi-dihedral angle of grain-boundary bubbles (rad)
Default:1.032
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Semi-dihedral angle of grain-boundary bubbles (rad)
- shear_modulusShear modulus material property (Pa). Required if dislocation_punching=true
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:Shear modulus material property (Pa). Required if dislocation_punching=true
- surface_energy1.11UN-gas surface energy (J/m^2)
Default:1.11
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:UN-gas surface energy (J/m^2)
- temperature_scalef1Scaling factor for temperature
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Scaling factor for temperature
- trap_param_optionDEFAULTSelect trapping parameter
Default:DEFAULT
C++ Type:MooseEnum
Controllable:No
Description:Select trapping parameter
- trappingp_scalef1Scaling factor for trapping parameter
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Scaling factor for trapping parameter
- trappingp_scalef_dislocation1Scaling factor for trapping parameter in dislocation bubbles
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Scaling factor for trapping parameter in dislocation bubbles
- trappingp_scalef_dislocation_line1Scaling factor for trapping parameter in dislocation lines
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Scaling factor for trapping parameter in dislocation lines
- vacancies_per_atom_diffusion_functionOptional function for the number of vacancies assisting gas atom diffusion.
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:Optional function for the number of vacancies assisting gas atom diffusion.
- vacancy_diffusivity_functionOptional function for vacancy diffusivity (m^2/s). For implementation of the function, the x-axis corresponds to temperature and y-axis corresponds to fission rate. The z-axis is unused, and time is the standard current time.
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:Optional function for vacancy diffusivity (m^2/s). For implementation of the function, the x-axis corresponds to temperature and y-axis corresponds to fission rate. The z-axis is unused, and time is the standard current time.
- vacancy_dislocation_diffusion_multiplier100Factor by which vacancy diffusion is multiplied along dislocations compared to the bulk to capture pipe diffusion
Default:100
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Factor by which vacancy diffusion is multiplied along dislocations compared to the bulk to capture pipe diffusion
- vacancy_volume2.92e-29Atomic (vacancy) volume in bubbles (m^3)
Default:2.92e-29
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Atomic (vacancy) volume in bubbles (m^3)
- verboseFalseFlag to optionally output verbose information
Default:False
C++ Type:bool
Controllable:No
Description:Flag to optionally output verbose information
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
- skip_bdr_modelFalseSkips the grain-boundary model
Default:False
C++ Type:bool
Controllable:No
Description:Skips the grain-boundary model
- testing_outputFalseProvides an analytic reference for the value of the intra-granular fission gas release
Default:False
C++ Type:bool
Controllable:No
Description:Provides an analytic reference for the value of the intra-granular fission gas release
- 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
References
- T. Barani, G. Pastore, A. Magni, D. Pizzocri, P. Van Uffelen, and L. Luzzi.
Modeling intra-granular fission gas bubble evolution and coarsening in uranium dioxide during in-pile transients.
Journal of Nuclear Materials, 538:152195, 2020.[BibTeX]
- T. Barani, G. Pastore, D. Pizzocri, D.A. Andersson, C. Matthews, A. Alfonsi, K.A. Gamble, P. Van Uffelen, L. Luzzi, and J.D. Hales.
Multiscale modeling of fission gas behavior in U3Si2 under LWR conditions.
Journal of Nuclear Materials, 522:97 – 110, 2019.
doi:10.1016/j.jnucmat.2019.04.037.[BibTeX]
- Dmitry Bocharov.
First Principles Simulations on Surface Properties and Reactivity of Sustainable Nitride Nuclear Fuels.
PhD thesis, University of Latvia, 2012.[BibTeX]
- M.W.D. Cooper, J. Rizk, C. Matthews, V. Kocevski, G.T. Craven, T. Gibson, and D.A. Andersson.
Simulations of self- and xe diffusivity in uranium mononitride including chemistry and irradiation effects.
Journal of Nuclear Materials, 587:154685, 2023.[BibTeX]
- F.S. Ham.
Theory of diffusion-limited precipitation.
J. Phys. Chem. Solids, 6:335–351, 1958.[BibTeX]
- C. Matthews, D.A. Andersson, and C. Unal.
Radiation re-solution calculation in uranium-silicide fuels.
Technical Report, Los Alamos National Laboratory, 2016.[BibTeX]
- G. Pastore, L. Luzzi, V. Di Marcello, and P. Van Uffelen.
Physics-based modelling of fission gas swelling and release in UO$_2$ applied to integral fuel rod analysis.
Nuclear Engineering and Design, 256:75–86, 2013.[BibTeX]
- D. Pizzocri, F. Cappia, V. V. Rondinella, and P. Van Uffelen.
Preliminary model for the pore growth in the HBS.
Technical Report, JRC103064, European Commission, Directorate for Nuclear Safety and Security, JRC-Karlsruhe, 2016.[BibTeX]
- D. Pizzocri, G. Pastore, T. Barani, A. Magni, L. Luzzi, P. Van Uffelen, S.A. Pitts, A. Alfonsi, and J.D. Hales.
A model describing intra-granular fission gas behaviour in oxide fuel for advanced engineering tools.
Journal of Nuclear Materials, 502:323 – 330, 2018.
doi:10.1016/j.jnucmat.2018.02.024.[BibTeX]
- I.L.F. Ray and H. Blank.
Microstructure and fission gas bubbles in irradiated mixed carbide fuels at 2 to 11 a/o burnup.
Journal of Nuclear Materials, 124:159–174, 1984.[BibTeX]
- Jason Rizk, Anton Schneider, Michael Cooper, Anders David Andersson, and Christopher Matthews.
Development of mechanistic fission gas release and swelling models for un fuels in bison.
Technical Report LA-UR-23-29157, Los Alamos National Laboratory, 8 2023.[BibTeX]
- M.V. Speight and W. Beere.
Vacancy potential and void growth on grain boundaries.
Metal Science, 9:190–191, 1975.[BibTeX]
- S. Torquato.
Nearest-neighbor statistics for packings of hard spheres and disks.
Physical Review E, 51(4):3170–3182, 1995.[BibTeX]
- M. S. Veshchunov.
On the theory of fission gas bubble evolution in irradiated UO$_2$ fuel.
Journal of Nuclear Materials, 277:67–81, 2000.[BibTeX]
- R.J. White.
The development of grain-face porosity in irradiated oxide fuel.
Journal of Nuclear Materials, 325:61–77, 2004.[BibTeX]