BISON Overview

Fuel Behavior: Introduction

At beginning of life, a fuel element is quite simple...

Nakajima et al., Nuc. Eng. Des., 148, 41 (1994)

but irradiation brings about substantial complexity...

Michel et al., Eng. Frac. Mech., 75, 3581 (2008)

Fuel Fracture

Olander, p. 584 (1978)

Multidimensional Contact
and Deformation

Olander, p. 584 (1978)

Fission Gas

Bentejac et al., PCI Seminar (2004)

Stress Corrosion
Cracking Cladding
Failure

Fuel Behavior Modeling: Coupled Multiphysics

Multiphysics

• Fully coupled nonlinear thermo-mechanics

• Multiple species diffusion

• Neutronics

• Thermal-hydraulics

• Chemistry

Multi-space scale

• Important physics at the atomistic and micro-structural levels

• Practical engineering simulations require the continuum level

Multi-time scale

• Steady operation ( week)

• Power ramps/accidents
  ( s)

BISON - Nuclear Fuel Performance Analysis

• BISON is a nuclear fuel performance analysis tool. It is used primarily for analysis of fuel but has also been used to model TRISO fuel, both rod and plate metal fuel, and accident tolerant fuel. BISON is built on top of MOOSE.

• BISON is implicit

  • Large time steps

• BISON runs in parallel

  • Runs naturally on one or many processors

• BISON is fully coupled

  • No operator splitting or staggered scheme necessary

  • All unknowns are solved for simultaneously

• BISON is under development; there is still much to do

  • Fission gas release model continues to improve

  • Contact can be a challenge; friction needs improvement

  • Automatic time-stepping needs improvement

  • Documentation and validation is evolving

BISON's Relationship to MOOSE

Code too specific for MOOSE but useful for multiple applications is collected in libraries.

BISON depends on:

• MOOSE modules (solid mechanics, fluid dynamics, etc.) depends on:

• MOOSE (multiphysics application framework) depends on:

• libMesh (numerical PDE solution framework out of UT Austin) depends on:

• PETSc, Exodus II, MPI, etc.

BISON LWR Capabilities

General Capabilities

• 3D, 2D-RZ, 1D fully coupled thermo-mechanics

• Large deformations

• Parallel

• Meso-scale informed

Oxide Fuel Behavior

• Temperature/burnup/porosity dependent material properties

• Volumetric heat generation

• Thermal and fission product swelling, and densification strains

• Thermal and irradiation creep

• Fuel fracture via relocation and smeared cracking

• Fission gas release (2 stages)

  • transient release

  • grain growth/sweeping

  • athermal release

Temperature

Gap/Plenum Behavior

• Gap heat transfer with

• Mechanical contact

• Plenum pressure as a function of:

  • evolving gas volume (from mechanics)

  • gas mixture (FGR)

  • gas temperature approximation

Cladding Behavior

• Thermal and irradiation creep

• Thermal expansion

• Irradiation growth

• Plasticity

• Hydride damage

Coolant Channel

• Closed channel thermal hydraulics with heat transfer coefficients

BISON Example - Axisymmetric LWR Fuel Rodlet

BISON Results - Axisymmetric LWR Fuel Rodlet

• Thermal expansion, fuel densification, clad creep-down, fission gas release, contact, and burnup dependent fuel thermal conductivity all affect fuel temperatures

• Hourglass shape of pellets is evident in gap closure histories

BISON Results - Axisymmetric LWR Fuel Rodlet

• Fission gas release begins at a burnup of 10 MWd/kgU

• Hourglass shape of pellets creates ridges in clad during PCMI

BISON Example - Missing Pellet Surface

• High-resolution 3D calculation (25,000 elements, 1.1 dof) run on 120 processors

• Simulation starting from a fresh fuel state with a typical power history, followed by a late-life power ramp

BISON Results - Missing Pellet Surface

Fuel Temperature

Clad Temperature

• Missing pellet surface has a very significant effect on the temperature and stress state in the rod

• Model can be used to examine source of rod failures

Clad Stress

BISON Coated-Particle Fuel Capabilities

General Capabilities

• 3D, 2D-RZ, 1D fully coupled thermomechanics with species diffusion

• Large deformation

• Elasticity with thermal expansion

• Steady and transient

• Massively parallel

Fuel Kernel

• Temperature, burnup, porosity dependent conductivity

• Solid and gaseous fission product swelling

• Densification

• Thermal/irradiation creep

• Fission gas release

• CO production

• Radioactive decay

Tangential Stress

Gap Behavior

• Gap heat transfer with

• Gap mass transfer

• Mechanical contact

• Plenum pressure as a function of:

  • evolving gas volume (from mechanics)

  • gas mixture (FGR and CO)

  • gas temperature approximation

Silicon Carbide

• Irradiation creep

Pyrolytic Carbon

• Anisotropic irradiation-induced strain

• Irradiation creep

BISON Results - TRISO Particle

• Validated against PARFUME, ATLAS, STRESS3

• Code comparisons are excellent

• Run times of 1 s are typical

PBR cyclic particle temperature

• Aspherical particles are common

• Raises peak tensile stress by 4x

• Runs in a few minutes (8 procs)

BISON Results - 3D Simulation of Thinned SiC Layer

• Localized SiC thinning due to soot inclusions or fission product interaction

• 3D capability demonstrated on eighth particle with random thinning

• Significantly higher tensile stress and cesium release; impossible to predict with state-of-the-art 1D or 2D analyses

• Typical run times of a few hours on 8 procs

Fuels Specific Models

Fuels Specific Models

• Bison consists, in addition to the capability in MOOSE, of material models specific to nuclear fuels:

  • Fission gas release

  • Material models that are functions of irradiation

    • Creep

    • Thermal Conductivity

    • Relocation

  • Other models that capture fuel behavior, like radial and axial power profiles

  • Gap heat transfer in LWR fuel

• This section highlights some of these models.

Fission Gas Behavior

Bison Fission Gas Model

• Physics-based model that describes the different stages of fission gas behavior

  • Gas generation

  • Intra-granular diffusion to grain boundaries

  • Bubble development at grain boundaries and associated fuel swelling

  • Fission gas release due to grain boundary saturation

  • Fission gas release due to micro-cracking

• Current results are state-of-the-art or better

Material Models that Depend on Irradiation or Power

Power Profiles

Radial power profile example:

Don't forget the axial profile.

LWR Gap Heat Transfer

• In BISON, and are described using the form proposed by Ross and Stoute (1962). is defined as

  where is the conductivity of the gas in the gap, is the gap width, is a roughness coefficient, and are roughnesses of the surfaces, and and are jump distances, which become important for small gap widths and low gas pressures. The jump distances provide a reduction in gap conductance when the mean free path of the gas molecules is significant in comparison to the gap width, and the continuum approximation is no longer valid. The gas temperature () is the average of the two surfaces.

LWR Gap Heat Transfer

• is defined as

  where is an empirical constant, and are the thermal conductivities of the two materials, is the contact pressure, is the average gas film thickness, and is the Meyer hardness of the softer material.

Bison Gap Heat Transfer (continued)

• In BISON, is computed using a diffusion approximation. Based on the Stefan-Boltzmann law,

  where is the Stefan-Boltzmann constant, is an emissivity function, and and are the temperatures of the radiating surfaces.

• The radiant conductance is approximated as

  which can be reduced to

  For infinite parallel plates,

  where and are the emissivities of the radiating surfaces. This is the specific function implemented in BISON.

MOOSE, a Partial Differential Equation Solver

• We are interested in solving a set of partial differential equations (PDEs) that represent physical processes, such as heat transfer and solid mechanics.

• MOOSE is a general solver that uses the finite element method (FEM) to solve arbitrary sets of PDEs for specific applications.

• FEM converts complex PDEs into a set of coupled algebraic equations which can be readily solved on a computer.

• FEM is applicable to a wide range of PDEs and can represent problems with arbitrary geometry.

FEM Vocabulary

The following list contains terms commonly used when discussing the finite element approach. These definitions are NOT COMPREHENSIVE. This list is just to get the conversation started.

• Domain - The space or geometry of your problem.

• Element - To obtain the approximate solution, the domain must be subdivided (discretized) into simpler smaller regions. These are called elements.

• Node - The points at which the elements are connected. We typically compute the value of primary solution variables (temperature, displacement) at nodes. Also where Dirichlet boundary conditions are applied.

• Boundary Condition - A constraint, or 'load' applied to the domain.

• Quadrature Point - One of the steps to finding the approximate solution to the PDE is integration. Quadrature points are where this integration happens. They are located within the elements.

• Test or Shape Function - Functions that help form the approximate solution to the PDE.

Heat Conduction

• MOOSE Modules' heat conduction routines are built to help solve

  where is the mass density, is the specific heat, is the temperature, is the thermal conductivity, and is the volumetric heat generation rate.

• MOOSE Modules provides spherically symmetric 1D, axisymmetric 2D, and 3D formulations. Either first or second order elements may be used (QUAD4 or QUAD8 for RZ, HEX8 or HEX20 for 3D).

Heat Conduction Continued

• Multiply by test function, integrate

• Integrate by parts

• Jacobian

The Input File

• To solve these PDEs, we need to create an input file that contains all the necessary information.

• By default MOOSE uses a hierarchical, block-structured input file.

• Within each block, any number of name/value pairs can be listed.

• The syntax is completely customizable, or replaceable.

• To specify a simple problem, you will need to populate five or six top-level blocks.

• We will briefly cover a few of these blocks in this section and will illustrate the usage of the remaining blocks throughout this manual.

The Required Blocks of an Input File

• Mesh - the domain of the problem

• Variables - temperature and displacement

• Kernels - heat conduction, solid mechanics

• Materials - used by kernels, e.g. thermal conductivity

• BCs - specify Dirichlet or Neumann

• Executioner - steady state or transient

• Outputs - set options for how you want the output to look.

Example Input File

The following input file is an example of how to solve the heat conduction equation with a source term.

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
[]

[Variables]
  [./temp]
  [../]
[]

[Kernels]
  [./heat_conduction]
    type = HeatConduction
    variable = temp
  [../]
  [./heat_source]
    type = HeatSource
    variable = temp
    value = 10000
  [../]
[]

[Materials]
  [./heat_conductor]
    type = HeatConductionMaterial
    thermal_conductivity = 1
    block = 0
  [../]
[]

[BCs]
  [./leftright]
    type = DirichletBC
    variable = temp
    boundary = 'left right'
    value = 200
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'
  dt = 1.0
  end_time = 1.0
[]

[Outputs]
  exodus = true
  [./console]
    type = Console
    perf_log = true
  [../]
[]

[Postprocessors]
  [./peak_temp]
    type = NodalExtremeValue
    variable = temp
  [../]
[]

Mesh Block

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
[]

• The FEM mesh is defined in the block.

• A mesh can be read in from a file. There are many accepted formats (see the MOOSE manual). We typically use the exodus file format and create meshes with CUBIT.

• Simple meshes can also be generated within the input file. We'll use this approach for our first examples.

• The sides of a GeneratedMesh are named in a logical way (bottom, top, left, right, front, and back).

Variables Block

[Variables]
  [./temp]
  [../]
[]

• The primary or dependent variables in the PDEs (temperature, displacement) are defined in the Variables block.

• A user-selected unique name is assigned for each variable.

Kernels Block

[Kernels]
  [./heat_conduction]
    type = HeatConduction
    variable = temp
  [../]
  [./heat_source]
    type = HeatSource
    variable = temp
    value = 10000
  [../]
[]

• The kernels (individual terms in the PDEs being solved) are listed in the Kernels block.

• Each kernel is assigned a specific variable (in this case, temp or temperature).

Materials Block

[Materials]
  [./heat_conductor]
    type = HeatConductionMaterial
    thermal_conductivity = 1
    block = 0
  [../]

• Material properties are defined in the Materials block. Information from the materials block is used by some kernels.

• Here, thermal conductivity is defined to be used by the HeatConduction kernel.

Boundary Conditions (BCs) Block

[BCs]
  [./leftright]
    type = DirichletBC
    variable = temp
    boundary = 'left right'
    value = 200
  [../]
[]

Define temperature on boundary

• Boundary conditions are defined in the BCs block.

• Many types of boundary conditions can be applied.

• For this simple example, the temperature is set on the left and right sides of the domain.

Executioner Block

[Executioner]
  type = Transient

  solve_type = 'PJFNK'
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'
  dt = 1.0
  end_time = 1.0
[]

• The Executioner block defines how the problem is solved.

• The parameters solve_type and petsc_options will be discussed later.

Outputs Block

[Outputs]
  exodus = true
  [./console]
    type = Console
    perf_log = true
  [../]
[]

• The results you will output from your simulation are defined in the Outputs block.

• This includes defining the file type (exodus file here).

• Performance logs are also defined.

Postprocessors Block

[Postprocessors]
  [./peak_temp]
    type = NodalExtremeValue
    variable = temp
  [../]
[]

• Analysis results in the form of single scalar values are defined in the Postprocessors block.

• May operate on elements, nodes, or sides of the model.

• Examples include NodalExtremeValue, AverageElementSize, and SideAverageValue.

Run Problem and Look at Results with Paraview

• The problems shown here can be run either with an application such as Bison that links in the heat_conduction module, or with the MOOSE combined module executable.

• To run with the MOOSE combined modules executable, run:

~/projects/moose/modules/combined/combined-opt -i heat_cond.i

• To run with an application (Bison example shown here), run:

~/projects/bison/bison-opt -i heat_cond.i

• These examples assume your code is in the ~/projects directory. Substitute in an appropriate path if it is located elsewhere.

Heat Conduction with Source: Results

Mechanics

• MOOSE modules' mechanics routines are built to help solve:

  where is the stress and is a body force.

• MOOSE modules also supplies boundary conditions useful for mechanics (such as pressure).

• MOOSE modules provides spherically symmetric 1D, axisymmetric 2D (typically linear), and 3D fully nonlinear formulations. Either first or second order elements may be used (QUAD4 or QUAD8 for RZ; HEX8 or HEX20 for 3D).

Mechanics (cont.)

• Multiply by test function, integrate

• Integrate by parts

Mechanics: Spherically Symmetric 1D

• The 1D, 2D, and 3D classes have much in common.

• The calculation of the strain is of course different for the three formulations. However, they share material models.

• The spherically symmetric 1D strain is

• The mesh for spherically symmetric 1D is defined such that the x coordinate corresponds to the radial direction.

• No displacement in the x (radial) direction must be explicitly enforced in the input file for nodes at x=0.

Mechanics: Axisymmetric 2D

• The axisymmetric 2D strain is

• The mesh for RZ is defined such that the x coordinate corresponds to the radial direction and the y coordinate with the axial direction.

• No displacement in the x (radial) direction must be explicitly enforced in the input file for nodes at x=0.

Mechanics: Nonlinear 3D

• The nonlinear kinematics formulation in MOOSE modules accommodates both large strains and large rotations.

• The deformation gradient can be viewed as the derivative of the current coordinates with respect to the original coordinates.

• can be decomposed into pure rotation and pure stretch .

Mechanics: 3D

• We begin with a complete set of data for step and seek the displacements and stresses at step . We first compute an incremental deformation gradient;

• With , we next compute a strain increment that represents the rotation-free deformation from the configuration at to the configuration at . Following Rashid (1993), we seek the stretching rate :

• Here, is the incremental stretch tensor, and is the incremental Green deformation tensor. Through a Taylor series expansion, this can be determined in a straightforward, efficient manner.

Mechanics: 3D (cont.)

• is passed to the constitutive model as an input for computing at .

• The next step is computing the incremental rotation, , where . Like for , an efficient algorithm exists for computing . It is also possible to compute these quantities using an eigenvalue/eigenvector routine.

• With and , we rotate the stress to the current configuration.

Mechanics: Material Models

• The material models for 1D, axisymmetric 2D, and 3D are formulated in an incremental fashion (think hypo-elastic).

• Thus, the stress at the new step is the old stress plus a stress increment:

• The incremental formulation is particularly useful for plasticity and creep models.

Let's add some more physics... Mechanics!

The following blocks have to be added to or modified in our input file if we want to include mechanics behavior.

[Variables]
  [./temp]
  [../]
  [./disp_x]
  [../]
  [./disp_y]
  [../]
[]

[Kernels]
  [./TensorMechanics]
    use_displaced_mesh = true
  [../]
  [./heat_conduction]
    type = HeatConduction
    variable = temp
  [../]
  [./heat_source]
    type = HeatSource
    variable = temp
    value = 10000
    function = source
  [../]
[]

Let's add some more physics... Mechanics!

The following blocks have to be added to or modified in our input file if we want to include mechanics behavior.

[Materials]
  [./heat_conductor]
    type = HeatConductionMaterial
    thermal_conductivity = 1
    block = 0
  [../]
  [./elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = 0
    youngs_modulus = 1e6
    poissons_ratio = 0.3
  [../]
  [./thermal_expansion_strain]
    type = ComputeThermalExpansionEigenstrain
    stress_free_temperature = 200
    thermal_expansion_coeff = 1.0e-4
    temperature = temp
    eigenstrain_name = thermal_eigenstrain
    block = 0
  [../]
  [./strain]
    type = ComputeFiniteStrain
    block = 0
    eigenstrain_names = thermal_eigenstrain
  [../]
  [./stress]
    type = ComputeFiniteStrainElasticStress
    block = 0
  [../]
[]

Let's add some more physics... Mechanics!

The following blocks have to be added to modified in our input file if we want to include mechanics behavior.

[BCs]
  [./leftright_temp]
    type = DirichletBC
    variable = temp
    boundary = 'left right'
    value = 200
  [../]
  [./leftright_disp_x]
    type = DirichletBC
    variable = disp_x
    boundary = 'left right'
    value = 0
  [../]
  [./bottom_disp_y]
    type = DirichletBC
    variable = disp_y
    boundary = bottom
    value = 0
  [../]
[]

Heat Conduction + Mechanics: Results

Modules: Contact: Finite Element Contact Basics

• A contact capability in a solid mechanics finite element code prevents the penetration of one domain into another, or part of one domain into itself.

Modules: Contact: Required Capabilites

A necessary but insufficient list:

Contact: Overview

• In node-face contact, nodes (green) may not penetrate faces (defined by orange nodes).

• Forces must be determined to push against the two contacting bodies.

• No force should be applied where the bodies are not in contact.

• The contact forces must increase from zero as the bodies first come into contact.

Contact: Constraints

• ; the gap (penetration distance) must be non-positive

• ; the contact force must push bodies apart

• ; the contact force must be zero if the bodies are not in contact

• ; the contact force must be zero when constraints are formed and released

• The gap in the normal direction for constraint is ( is the normal, denotes normal direction, is position of the slave node, is position of the contact point, and is a matrix):

Contact: Contact Options

Even more physics... CONTACT

The following blocks have to be added to or modified in our input file if we want to include the effects of mechanical contact.

[Mesh]
  file = contact.e
  displacements = 'disp_x disp_y'
[]

[Functions]
  [./source]
  type = PiecewiseLinear
  x = '0 1'
  y = '0 1'
  [../]
[]

[Kernels]
.
.
  [./heat_source]
    type = HeatSource
    variable = temp
    value = 1500
    function = source
    block = 2
  [../]
.
.
[Contact]
  [./mechanical]
    master = 1
    slave = 7
    disp_x = disp_x
    disp_y = disp_y
    penalty = 1e7
    tangential_tolerance = 0.1
  [../]
[]

[BCs]
.
.
  [./bottom_disp_y]
    type = DirichletBC
    variable = disp_y
    boundary = 3
    value = 0
  [../]
  [./bottom_disp_y_upper]
    type = DirichletBC
    variable = disp_y
    boundary = '5 6 8'
    value = 0
  [../]
.
.
[]
[Preconditioning]
  [./smp]
    type = SMP
    full = true
  [../]
[]
[Executioner]
  type = Transient
  solve_type = 'PJFNK'
  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'
  line_search = none
  dt = 0.1
  dtmin = 0.01
  num_steps = 10
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-8
[]

Heat Conduction + Mechanics + Contact: Results

• q = 600

• Bottom block heats and expands upward, but is not yet in contact

• Blocks do not communicate thermally (no gap heat transfer)

Heat Conduction + Mechanics + Contact: Results

• q = 600

• Bottom block heats and expands upward, but is not yet in contact

• Vertical displacement plots show curvature of top surface

Heat Conduction + Mechanics + Contact: Results

• q = 1500

• Further heating and upward expansion brings blocks into contact; first at the center where the bottom block is hottest

• Still, blocks do not communicate thermally (no gap heat transfer)

Heat Conduction + Mechanics + Contact: Results

• q = 1500

• Contour scale is set to show displacement in top block resulting from mechanical contact

Modules: Heat Conduction: Gap Heat Transfer

• The principle is that the heat leaving one body must equal that entering another. For bodies and with heat transfer surface :

• Gap heat transfer is modeled using the relation:

  where is the total conductance across the gap, is the gas conductance, is the increased conductance due to solid-solid contact, and is the conductance due to radiant heat transfer.

• In MOOSE modules, only the gas conductance is active by default.

• The form of in MOOSE modules is:

  where is the conductivity in the gap and is the gap distance.

Adding Thermal Contact

[ThermalContact]
  [./thermal_contact]
    type = GapHeatTransfer
    variable = temp
    master = 1
    slave = 7
    gap_conductivity = 1
  [../]
[]

Heat Conduction + Mechanics + Contact + Thermal Contact: Results

• q = 750

• Heat tranfer occurs through the gap medium prior to mechanical contact

Heat Conduction + Mechanics + Contact + Thermal Contact: Results

• q = 1330

• Combined thermal and mechanical contact

Running Bison

Running Bison

• This section walks through the steps of running Bison on a new problem.

• We will build upon the sections describing the input file and mesh generation.

Running Bison ... continued

Let's assume that we want to run a problem similar to the example problem but with the following differences:

• Smeared fuel pellet mesh

• Coolant pressure of 16 MPa

• Rod averaged linear power of 21 kW/m

• Clad properties:

  - Thermal conductivity of 21.5 W/m/K

  - Specific heat capacity of 285 J/kg/K

  - Density of 6560 kg/m

  - Young's modulus of 99.3 GPa

  - Poisson's ratio of 0.37

• First, copy the example problem to a new file:

  - mkdir bison/sandbox - cd bison/sandbox - cp ../tensor_mechanics/examples/2D-RZ_rodlet_10pellets/inputQuad8.i myProblem.i

• Now, in a text editor, we can change the input file.

Editing the Input File: Mesh

# Import mesh file
[Mesh]
  file = quad8Medium10_rz.e
  displacements = 'disp_x disp_y'
  patch_size = 1000 # For contact algorithm
[]

# Import mesh file
[Mesh]
  file = $\alert{coarse1\_rz.e}$
  displacements = 'disp_x disp_y'
  patch_size = 1000
[]

Editing the Input File: Functions

# Define functions to control power, etc.
[Functions]

  [./power_history]
    type = PiecewiseLinear
    data_file = powerhistory.csv
    scale_factor = 1
  [../]

  [./axial_peaking_factors]
    type = PiecewiseBilinear
    data_file = peakingfactors.csv
    scale_factor = 1
    axis = 1 # (0,1,2) => (x,y,z)
  [../]

  [./pressure_ramp]
    type = PiecewiseLinear
    x = '-200 0'
    y = '   0 1'
  [../]

  [./q]
    type = CompositeFunction
    functions = 'power_history
                 axial_peaking_factors'
  [../]
[]

# Define functions to control power, etc.
[Functions]

  [./power_history]
    type = PiecewiseLinear
    $\alert{x = '0 1e4'}$
    $\alert{y = '0 21000'}$
  [../]

  [./axial_peaking_factors]
    type = PiecewiseBilinear
    data_file = peakingfactors.csv
    scale_factor = 1
    axis = 1 # (0,1,2) => (x,y,z)
  [../]

  [./pressure_ramp]
    type = PiecewiseLinear
    x = '-200 0'
    y = '   0 1'
  [../]

  [./q]
    type = CompositeFunction
    functions = 'power_history
                 axial_peaking_factors'
  [../]
[]

Editing the Input File: Coolant Pressure

[./Pressure]
#  apply coolant pressure on clad outer walls
    [./coolantPressure]
      boundary = '1 2 3'
      factor = 15.5e6
      function = pressure_ramp
    [../]
  [../]

[./Pressure]
#  apply coolant pressure on clad outer walls
    [./coolantPressure]
      boundary = '1 2 3'
      factor = $\alert{16e6}$
      function = pressure_ramp
    [../]
  [../]

Editing the Input File: Cladding

[./clad_thermal]
    type = HeatConductionMaterial
    block = clad
    thermal_conductivity = 16.0
    specific_heat = 330.0
  [../]

[./clad_thermal]
    type = HeatConductionMaterial
    block = clad
    thermal_conductivity = $\alert{21.5}$
    specific_heat = $\alert{285.0}$
  [../]

Editing the Input File: Cladding Continued

[./clad_elasticity_tensor]
    type = ZryElasticityTensor
    block = clad
  [../]

[./clad_elasticity_tensor]
    type = $\alert{ComputeIsotropicElasticityTensor}$
    block = clad
    youngs_modulus = $\alert{9.93e10}$
    poissons_ratio = $\alert{0.37}$
  [../]

Editing the Input File: Cladding Continued

[./clad_density]
    type = StrainAdjustedDensity
    block = clad
    strain_free_density = 6551.0
  [../]

[./clad_density]
    type = StrainAdjustedDensity
    block = clad
    strain_free_density = $\alert{6560.0}$
  [../]

Copy Input Data Files

• The input file uses a PiecewiseBilinear function (axial_peaking_factors) that requires a comma separated value (csv) file. PiecewiseBilinear functions allow data lookup in a table.

  - cp ../tensor_mechanics/examples/2D-RZ*/peakingfactors.csv .

• The format of this csv file is as follows:

Generate Smeared Pellet Mesh

• With the input file (myProject.i) complete and the csv file in place, all that remains is to generate the mesh file:

  - cp ../tools/UO2/mesh_script.sh . - cp ../tools/UO2/mesh_script.py . - cp ../tools/UO2/mesh_script_input.py coarse1_rz.py - ./mesh_script.sh -i coarse1_rz.py

Note, you'll also have to modify the burnup block and axial profile to account for the change in fuel height from 10 pellets to one pellet.

Run Bison

• We will now analyze this problem using Bison.

• We will use four processors with MPI (Message Passing Interface):

  - mpiexec -n 4 ../bison-opt -i myProblem.i

• To run with a single processor:

  - ../bison-opt -i myProblem.i