Burnup Function

Compute burnup and radial power factor. Built by an Action.

note:Often Created by an Action

This object can be set up automatically by using the Burnup action.

Description

The power density in a fuel pellet varies radially as a function of geometry, initial fuel characteristics, and irradiation history. At the beginning of irradiation (low burnup), the concentration of fissile material is uniform, which means that the radial power has a relatively small variation across the radius. With increasing burnup, the Pu concentration markedly increases near the fuel surface due to the capture of epithermal neutrons in the resonances of U. Consequently, the concentration of fissile material and the power density profile are steeper near the pellet surface. These aspects need to be captured in order to calculate the heat generation and temperature distribution in the pellet accurately.

For this purpose, Bison uses the DIONISIO model from Soba et al. (2013), Soba et al. (2014), and Soba and Denis (2017). This model computes the evolution of the concentrations of various heavy metal isotopes (specifically, U, U, U, Pu, Pu, Pu, Pu) locally across the radius of the fuel pellet and the coupled evolution of the radial power and burnup distributions. The model uses one-group cross sections that are function of radial position, U enrichment and radially averaged burnup, and are fitted to the results of extensive neutronics calculations performed with the CONDOR and HUEMUL codes. Neutronics calculations covered LWR-UO fuel rods with inital U enrichments from 0.7% to 12% and average burnups ranging from fresh fuel to 120 MWd/kgU (Soba et al., 2013; Soba et al., 2014; Soba and Denis, 2017).

The rate equations describing the evolution of the concentrations of each heavy metal isotope are (1) (2) (3) (4) (5) (6) (7) where is the local concentration (number of atoms per unit volume), is the absorption cross section, is the capture cross section, and is the neutron flux. Note that decay terms are neglected in the Bison implementation.

Figure 1: Example of calculated radial power form factors (normalized) at various radial average burnups.

The neutron flux, , is calculated in an approximate way using one-group diffusion theory. The neutron diffusion equation is solved in 1D cylindrical coordinates by finite difference. The local power density at radial position , , which is needed for the thermal analysis is proportional to the neutron flux and the macroscopic cross section for fission, (8) where is the fission cross section for isotope and is the concentration of isotope . The model computes the radial power profile in the fuel pellet based on Eq. 8. The radial power from factor at radial position is (9) with (10) where and are the inner and outer fuel radii, respectively. The local burnup is computed based on the time integral of the local power density.

An example of model results is given in Figure 1, which illustrates radial power factor distributions at various burnup levels for a UO fuel pellet irradiated under typical PWR conditions.

USi Radial Power Profile

Bison also contains the ability to estimate the radial power profile in USi fuel. The same formulation given above for UO is used with different cross sections and mass ratios. The cross sections for USi were generated using the DRAGON neutronics code by Javier Ortensi at INL.

Example Input Syntax

The burnup function is often created by the Burnup action, as shown below:


[./burnup2]
  block = 2
  base_name = action_block2
  rod_ave_lin_pow = power_profile
  axial_power_profile = axial_peaking_factors
  num_radial = 80
  num_axial = 20
  a_upper = 0.0205
  a_lower = 0.0105
  fuel_inner_radius = 0.0
  fuel_outer_radius = 0.01
[../]
(test/tests/burnup_action/burnup_with_actions.i)

It is also possible to directly use the BurnupFunction in an input file:


[./burnup2]
  type = BurnupFunction
  rod_ave_lin_pow = power_profile
  axial_power_profile = axial_peaking_factors
  num_radial = 80
  num_axial = 20
  a_upper = 0.0205
  a_lower = 0.0105
  fuel_inner_radius = 0.0
  fuel_outer_radius = 0.01
[../]
(test/tests/burnup_action/burnup_without_actions.i)

Input Parameters

  • densityThe initial fuel density.

    C++ Type:double

    Description:The initial fuel density.

Required Parameters

  • fuel_outer_radius0.0041The outer radius of the fuel.

    Default:0.0041

    C++ Type:double

    Description:The outer radius of the fuel.

  • i_enrich0.05 0.95 0 0 0 0 The initial enrichments for U-235, U-238, Pu-239, Pu-240, Pu-241, Pu-242.

    Default:0.05 0.95 0 0 0 0

    C++ Type:std::vector

    Description:The initial enrichments for U-235, U-238, Pu-239, Pu-240, Pu-241, Pu-242.

  • axial_power_profileAxial power peaking function.

    C++ Type:FunctionName

    Description:Axial power peaking function.

  • num_axial20Number of axial divisions in secondary grid used to compute radial power profile.

    Default:20

    C++ Type:unsigned int

    Description:Number of axial divisions in secondary grid used to compute radial power profile.

  • rpf_inputThe radial power profile function. Used to specify the rpf from input

    C++ Type:FunctionName

    Description:The radial power profile function. Used to specify the rpf from input

  • fuel_typeUO2Fuel type. Choices are UO2 U3Si2

    Default:UO2

    C++ Type:MooseEnum

    Description:Fuel type. Choices are UO2 U3Si2

  • fuel_volume_ratio1Reduction factor for deviation from right circular cylinder fuel. The ratio of actual volume to right circular cylinder volume.

    Default:1

    C++ Type:double

    Description:Reduction factor for deviation from right circular cylinder fuel. The ratio of actual volume to right circular cylinder volume.

  • initial_burnup0Initial burnup to be applied in units of MWd/kgU

    Default:0

    C++ Type:double

    Description:Initial burnup to be applied in units of MWd/kgU

  • value1Default/scaling value.

    Default:1

    C++ Type:double

    Description:Default/scaling value.

  • a_upperThe upper axial coordinate of the fuel stack. Required if fuel_pin_geometry is not specified.

    C++ Type:double

    Description:The upper axial coordinate of the fuel stack. Required if fuel_pin_geometry is not specified.

  • fuel_pin_geometryName of the UserObject that reads the pin geometry from the mesh.

    C++ Type:UserObjectName

    Description:Name of the UserObject that reads the pin geometry from the mesh.

  • bias1Bias for radial point spacing. Must be between 0.5 and 2.0

    Default:1

    C++ Type:double

    Description:Bias for radial point spacing. Must be between 0.5 and 2.0

  • num_radial80Number of radial divisions in secondary grid used to compute radial power profile.

    Default:80

    C++ Type:unsigned int

    Description:Number of radial divisions in secondary grid used to compute radial power profile.

  • rod_ave_lin_powRod average linear power function.

    C++ Type:FunctionName

    Description:Rod average linear power function.

  • energy_per_fission3.28451e-11The energy released per fission in J/fission.

    Default:3.28451e-11

    C++ Type:double

    Description:The energy released per fission in J/fission.

  • axial_axis1Coordinate axis of the axial direction of the fuel stack (0, 1, or 2 for x, y, or z

    Default:1

    C++ Type:unsigned int

    Description:Coordinate axis of the axial direction of the fuel stack (0, 1, or 2 for x, y, or z

  • a_lowerThe lower axial coordinate of the fuel stack. Required if fuel_pin_geometry is not specified.

    C++ Type:double

    Description:The lower axial coordinate of the fuel stack. Required if fuel_pin_geometry is not specified.

  • rpf_activeTrueFlag for turning calculation of radial power factor on.

    Default:True

    C++ Type:bool

    Description:Flag for turning calculation of radial power factor on.

  • fuel_inner_radius0The inner radius of the fuel.

    Default:0

    C++ Type:double

    Description:The inner radius of the fuel.

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.

  • heavy_metal_molar_massThe molar mass of the heavy metal

    C++ Type:double

    Description:The molar mass of the heavy metal

  • enableTrueSet the enabled status of the MooseObject.

    Default:True

    C++ Type:bool

    Description:Set the enabled status of the MooseObject.

  • fuel_molar_massThe molar mass of the entire fuel

    C++ Type:double

    Description:The molar mass of the entire fuel

  • built_by_action

    C++ Type:std::string

Advanced Parameters

Input Files

References

  1. A. Soba and A. Denis. Personal communication, 2017.[BibTeX]
  2. A. Soba, A. Denis, L. Romero, E. Villarino, and F. Sardella. A high burnup model developed for the DIONISIO code. Journal of Nuclear Materials, 433:160–166, 2013.[BibTeX]
  3. A. Soba, M. Lemes, M.E. González, A. Denis, and L. Romero. Simulation of the behaviour of nuclear fuel under high burnup conditions. Annals of Nuclear Energy, 70:147–156, 2014.[BibTeX]