UMoBurnup

Computes burnup and fission density given fission rate density, initial density, and initial enrichment of the fuel.

Description

This model computes the burnup (fission per initial heavy-metal atom - FIMA) of UMo fuel along with the fission density.

Automatic differentiation (AD) version is also available by adding the prefix AD to the name for the "type" parameter.

Burnup

The burnup increment, $var element = document.getElementById("moose-equation-aef30330-e0fe-4f26-9bc6-4e3615bdaf5f");katex.render("{\\Delta}B_{u}", element, {displayMode:false,throwOnError:false});$ (FIMA), during a time interval, $var element = document.getElementById("moose-equation-52c567d8-969b-4877-ad04-c9597b0104b4");katex.render("{\\Delta}t", element, {displayMode:false,throwOnError:false});$ (s), is calculated as:

$var element = document.getElementById("moose-equation-efcda3a1-1dd4-4758-a692-b6df619fd633");katex.render(" {\\Delta}B_{u} = \\frac{f''' {\\Delta}t}{\\rho_{atU}}", element, {displayMode:true,throwOnError:false});$

where $var element = document.getElementById("moose-equation-295201ca-8f67-4ef3-bb43-8326ccd8961a");katex.render("f'''", element, {displayMode:false,throwOnError:false});$ (fission/m $var element = document.getElementById("moose-equation-2fc17f38-8bc8-4022-9ab1-e84874c51599");katex.render("^{3}", element, {displayMode:false,throwOnError:false});$ -s) is the fission rate density and $var element = document.getElementById("moose-equation-b8b81c84-61d5-49c0-aa41-c1e99a86ae4e");katex.render("\\rho_{atU}", element, {displayMode:false,throwOnError:false});$ (at/m $var element = document.getElementById("moose-equation-e0cb9810-87b4-4a46-b7e5-a19efd537ecc");katex.render("^{3}", element, {displayMode:false,throwOnError:false});$ ) is the density of uranium (heavy-metal) atoms.

The option to use the current fission rate or a fission rate that is an average of the current and previous timestep is controllable with the time_average_fission_rate parameter. This is set to True by default which enables the averaged approach. Averaging the fission rate assures that the burnup calculation is not an over-estimate.

The burnup increment is then added to the burnup calculated from the previous timestep to obtain the total burnup.

The density of uranium atoms is given by:

$var element = document.getElementById("moose-equation-80e22352-5067-47fd-a42f-1fc00e2473f0");katex.render(" \\rho_{atU} = \\frac{f_{wtU} rho_{\\text{init}}{M} N_{avo}}{aw_U}", element, {displayMode:true,throwOnError:false});$

where $var element = document.getElementById("moose-equation-eff84d90-4b47-4923-b66a-030434a10310");katex.render("f_{wtU}", element, {displayMode:false,throwOnError:false});$ is the weight fraction of uranium, $var element = document.getElementById("moose-equation-8b9f7cd7-8456-4b99-aa18-6125156b04dd");katex.render("\\rho_{\\text{init}}", element, {displayMode:false,throwOnError:false});$ (kg/m $var element = document.getElementById("moose-equation-af92b7ff-67a7-49b0-91c6-182cfe253baa");katex.render("^{3}", element, {displayMode:false,throwOnError:false});$ ) is the initial density of the fuel, $var element = document.getElementById("moose-equation-d0ada65a-d363-4db8-bad8-c12d04db5daf");katex.render("N_{avo}", element, {displayMode:false,throwOnError:false});$ is Avogadro's number, and $var element = document.getElementById("moose-equation-9e072440-a9ab-42b0-a7e2-9b6691a95e5c");katex.render("aw_U", element, {displayMode:false,throwOnError:false});$ (kg/mol) is the atomic weight of uranium.

The atomic weight of uranium depends on the initial U-235 enrichment, $var element = document.getElementById("moose-equation-2fa854f9-7ad9-4667-94ef-3dd805e9dea3");katex.render("\\epsilon", element, {displayMode:false,throwOnError:false});$ (mole fraction), and on the atomic weights $var element = document.getElementById("moose-equation-e04c5a07-f1dc-42fe-810b-7d514e2dcf36");katex.render("aw_{U235}", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-438c162f-fbf4-4dff-81d6-9d845eb6e008");katex.render("aw_{U238}", element, {displayMode:false,throwOnError:false});$ (kg/mol) of U-235 and U-238:

$var element = document.getElementById("moose-equation-f44def4e-eea4-4fb4-9929-94f4b861da37");katex.render(" aw_{U} = aw_{U235} {\\epsilon} + (1.0 - {\\epsilon}) aw_{U238}", element, {displayMode:true,throwOnError:false});$

Fission Density

Fission density, $var element = document.getElementById("moose-equation-45c65229-e277-4a2b-a96d-87ba35c570b5");katex.render("\\rho_f", element, {displayMode:false,throwOnError:false});$ (fission/m $var element = document.getElementById("moose-equation-e20f4fe3-d6f3-4b15-bd37-823c331673e2");katex.render("^3", element, {displayMode:false,throwOnError:false});$ ), is calculated as $var element = document.getElementById("moose-equation-fa5b4c6d-ec6f-459f-a2d1-d907dd2bb558");katex.render(" \\rho_f = \\int f''' \\;\\; dt", element, {displayMode:true,throwOnError:false});$ and is needed by some UMo material models.

Example Input Syntax

[Materials<<<{"href": "../../syntax/Materials/index.html"}>>>]
  [UMo_burnup]
    type = UMoBurnup<<<{"description": "Computes burnup and fission density given fission rate density, initial density, and initial enrichment of the fuel.", "href": "UMoBurnup.html"}>>>
    initial_density<<<{"description": "initial density of the fuel (kg/m^3)"}>>> = 17000
    initial_enrichment<<<{"description": "initial enrichment fraction of U235 (mole fraction)"}>>> = 0.15
    weight_fraction_Mo<<<{"description": "Weight fraction of molybdenum"}>>> = 0.1
    outputs<<<{"description": "Vector of output names where you would like to restrict the output of variables(s) associated with this object"}>>> = all
  []
[]

Input Parameters

initial_densityinitial density of the fuel (kg/m^3)
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:initial density of the fuel (kg/m^3)
initial_enrichmentinitial enrichment fraction of U235 (mole fraction)
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:initial enrichment fraction of U235 (mole fraction)
weight_fraction_MoWeight fraction of molybdenum
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Weight fraction of molybdenum

Required Parameters

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
burnup_nameburnupName of the created burnup material property.
Default:burnup
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:Name of the created burnup material property.
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
Options:NONE, ELEMENT, SUBDOMAIN
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.
fission_density_namefission_densityName of the created fission density material property.
Default:fission_density
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:Name of the created fission density material property.
fission_ratefission_rateFission rate material name
Default:fission_rate
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:Fission rate material name
time_average_fission_rateTrueFlag to average the fission rate with the previous time step instead of only using the current fission rate
Default:True
C++ Type:bool
Controllable:No
Description:Flag to average the fission rate with the previous time step instead of only using the current fission rate

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
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

(test/tests/umo_burnup/UMoBurnup.i)

#
# Tests burnup and fission density calculation for UMo
#
[Mesh]
  [meshgenerator]
    type = GeneratedMeshGenerator
    dim = 1
  []
[]

[Problem]
  solve = false
[]

[Materials]
  [fission_rate]
    type = GenericFunctionMaterial
    prop_names = 'fission_rate'
    prop_values = '1e19*t'
    outputs = all
  []
  [UMo_burnup]
    type = UMoBurnup
    initial_density = 17000
    initial_enrichment = 0.15
    weight_fraction_Mo = 0.1
    outputs = all
  []
[]

[Executioner]
   type = Transient
   num_steps = 10
   dt = 100
[]

[Postprocessors]
   [fission_rate]
     type = ElementAverageValue
     variable = fission_rate
   []
   [burnup]
     type = ElementAverageValue
     variable = burnup
   []
   [fission_density]
     type = ElementAverageValue
     variable = fission_density
   []
   [dt]
     type = TimestepSize
   []
[]

[Outputs]
  csv = true
[]

(test/tests/umo_burnup/ad_UMoBurnup.i)

#
# Tests burnup and fission density calculation for UMo
#
[Mesh]
  [meshgenerator]
    type = GeneratedMeshGenerator
    dim = 1
  []
[]

[Problem]
  solve = false
[]

[Materials]
  [fission_rate]
    type = ADGenericFunctionMaterial
    prop_names = 'fission_rate'
    prop_values = '1e19*t'
    outputs = all
  []
  [UMo_burnup]
    type = ADUMoBurnup
    initial_density = 17000
    initial_enrichment = 0.15
    weight_fraction_Mo = 0.1
    outputs = all
  []
[]

[Executioner]
   type = Transient
   num_steps = 10
   dt = 100
[]

[Postprocessors]
   [fission_rate]
     type = ElementAverageValue
     variable = fission_rate
   []
   [burnup]
     type = ElementAverageValue
     variable = burnup
   []
   [fission_density]
     type = ElementAverageValue
     variable = fission_density
   []
   [dt]
     type = TimestepSize
   []
[]

[Outputs]
  csv = true
[]

(test/tests/umo_burnup/UMoBurnup.i)

#
# Tests burnup and fission density calculation for UMo
#
[Mesh]
  [meshgenerator]
    type = GeneratedMeshGenerator
    dim = 1
  []
[]

[Problem]
  solve = false
[]

[Materials]
  [fission_rate]
    type = GenericFunctionMaterial
    prop_names = 'fission_rate'
    prop_values = '1e19*t'
    outputs = all
  []
  [UMo_burnup]
    type = UMoBurnup
    initial_density = 17000
    initial_enrichment = 0.15
    weight_fraction_Mo = 0.1
    outputs = all
  []
[]

[Executioner]
   type = Transient
   num_steps = 10
   dt = 100
[]

[Postprocessors]
   [fission_rate]
     type = ElementAverageValue
     variable = fission_rate
   []
   [burnup]
     type = ElementAverageValue
     variable = burnup
   []
   [fission_density]
     type = ElementAverageValue
     variable = fission_density
   []
   [dt]
     type = TimestepSize
   []
[]

[Outputs]
  csv = true
[]

Description
Burnup
Fission Density
Example Input Syntax
Input Parameters
Input Files