SodiumCoolantChannelMaterial

Computes the coolant temperature and heat transfer coefficient for sodium in a typical sodium fast reactor assembly. This material is to be used in conjunction with the ConvectiveHeatFluxBC boundary condition, This material can only be applied to boundaries.

Description

SodiumCoolantChannelMaterial computes two material properties, coolant_channel_htc and coolant_temperature, on a boundary. These two properties are then passed to ConvectiveHeatFluxBC or ADConvectiveHeatFluxBC to compute the heat flux and apply the proper boundary condition to the temperature variable. SodiumCoolantChannelMaterial is not an AD material as it does not depend on any other field variables such as temperature or displacements. Instead, SodiumCoolantChanelMaterial uses the flow channel parameters to compute the coolant channel temperature due to heat up of the coolant from the fuel pin, and the heat transfer coefficient of the sodium.

Sodium properties

SodiumCoolantChannelMaterial utilizes the SodiumProperties user object from the Fluid Properties module. This allows for a consistant set of properties for utilization in this, and other models, although SodiumCoolantChannelMaterial will only utilize the formulations for specific heat, $var element = document.getElementById("moose-equation-83c188b4-fd62-4a18-b8ca-d91a3ba0050c");katex.render("c_p(T)", element, {displayMode:false,throwOnError:false});$ , and thermal conductivity, $var element = document.getElementById("moose-equation-337124af-a7ea-416c-ab0e-d1964a98d6a3");katex.render("\\lambda(T)", element, {displayMode:false,throwOnError:false});$ .

Flow channel geometry

Several important parameters are required for calculation of the coolant temperature and heat transfer coefficient based on the pin geometry. In general, the assembly geometry can be defined using the rod diameter, $var element = document.getElementById("moose-equation-44132fac-d587-43ae-a173-b8a5a7f957cf");katex.render("D", element, {displayMode:false,throwOnError:false});$ , and wire wrap around the pin, $var element = document.getElementById("moose-equation-caf1d17e-c97e-441c-82bb-11855fc0f988");katex.render("s", element, {displayMode:false,throwOnError:false});$ . Following the formulations in Waltar et al. (2011), the flow area and wetted perimeters will be different depending on the location of the pin in the assembly (see Figure 1).

Figure 1: Schematic of flow channels in a typical sodium fast reactor (Waltar et al., 2011).

In a typical sodium fast reactor assembly, fuel rods are bundled, with their spacing enforced by the wire spacing. This results in a hexagonal pitch, or distance between the center of adjacent pins, that can be determined as, $(1) var element = document.getElementById("moose-equation-b6e8ef90-77f5-4ae3-af18-34b86725e75f");katex.render(" P = D + s ", element, {displayMode:true,throwOnError:false});$ This bundle of pins is then surrounded by a hexagonal steel duct that restricts sodium cross-flow between assemblies and mechanically constrains the pins. This results in three types of flow channels: interior, edge, and corner flow channels. The majority of the sodium flow passes through the "interior" channels within the assembly, in which a flow channel passes between three rods. A small subsection of the sodium will pass through the "edge" flow channels pins in which sodium flows between fuel pins and the side of the duct. An even smaller amount of sodium will flow through the "corner" of the duct in which the flow channel is comprised of the duct corner and one fuel pin.

Each of these flow channels will have different flow areas, $var element = document.getElementById("moose-equation-019d94f1-da20-4c5d-a616-f7bf01c172e4");katex.render("A", element, {displayMode:false,throwOnError:false});$ and wetted perimeters, $var element = document.getElementById("moose-equation-5026d186-2b92-4bc5-9bb3-ad4c47041137");katex.render("W", element, {displayMode:false,throwOnError:false});$ :

For interior flow channels, $(2)var element = document.getElementById("moose-equation-9962f5cd-bd96-4295-9e17-41a1310315e0");katex.render(" \\begin{aligned} &A_{i} = \\frac{\\sqrt{3}}{4}P^2 - \\frac{\\pi}{8}\\left(D^2 + s^2\\right), \\\\ &W_{i} = \\frac{\\pi}{2} P. \\end{aligned} ", element, {displayMode:true,throwOnError:false});$

For edge flow channels, $(3)var element = document.getElementById("moose-equation-364d8abd-f4c5-4d1c-a51b-e966dc4b5403");katex.render(" \\begin{aligned} &A_{e} = P \\left(\\frac{D}{2} + s\\right) - \\frac{\\pi}{8}\\left(D^2 + s^2\\right), \\\\ &W_{e} = P(1 + \\frac{\\pi}{2}). \\end{aligned} ", element, {displayMode:true,throwOnError:false});$

For corner flow channels, $(4)var element = document.getElementById("moose-equation-9bc9ae59-133c-4f39-9abd-f6ffbb026800");katex.render(" \\begin{aligned} &A_{c} = \\frac{1}{\\sqrt{3}} \\left(\\frac{D}{2} + s\\right)^2 - \\frac{\\pi}{24}\\left(D^2 + s^2\\right), \\\\ &W_{c} = D + 2s + \\frac{\\pi}{6} P. \\end{aligned} ", element, {displayMode:true,throwOnError:false});$

Each pin will impart energy to a combination of flow channels and areas, resulting in a fuel pin-centric flow area, $var element = document.getElementById("moose-equation-661db141-3ca5-4385-84f8-01e838231629");katex.render("a", element, {displayMode:false,throwOnError:false});$ and fuel pin-centric wetted perimeter, $var element = document.getElementById("moose-equation-23847117-642b-47e7-bece-1557e09b5b75");katex.render("w", element, {displayMode:false,throwOnError:false});$ unique for "interior", "edge", and "corner" fuel pins:

For interior pins, $(5)var element = document.getElementById("moose-equation-3b5b11c6-7c85-48e5-bc6a-584648964e98");katex.render(" \\begin{aligned} & a_{i} = 2A_i, \\\\ & w_{i} = 2W_i. \\end{aligned} ", element, {displayMode:true,throwOnError:false});$

For edge pins, $(6)var element = document.getElementById("moose-equation-74288bff-214c-46dc-9c1f-28aff4a408b6");katex.render(" \\begin{aligned} & a_{e} = A_i + A_e, \\\\ & w_{e} = W_i + W_e. \\end{aligned} ", element, {displayMode:true,throwOnError:false});$

For corner pins, $(7)var element = document.getElementById("moose-equation-dd7864b3-e6ec-4a58-ae8e-4949f15236a6");katex.render(" \\begin{aligned} & a_{c} = \\frac{2}{3}A_i + A_e + A_c, \\\\ & w_{c} = \\frac{2}{3}W_i + W_e + W_c. \\end{aligned} ", element, {displayMode:true,throwOnError:false});$

From these, the hydraulic diameter can be computed for the given pin location, $(8)var element = document.getElementById("moose-equation-335787f7-33f8-4deb-ae1b-7231be728c0a");katex.render(" D_h = \\frac{4a}{w}, ", element, {displayMode:true,throwOnError:false});$ using the formulations in Eq. (5), Eq. (6), and Eq. (7).

Coolant Temperature

The coolant temperature, $var element = document.getElementById("moose-equation-dc17cf35-102d-42c8-9637-594f6347b240");katex.render("T", element, {displayMode:false,throwOnError:false});$ , at a given axial position $var element = document.getElementById("moose-equation-ae6456f5-68dd-4235-a0b0-79fcd53109c3");katex.render("Z", element, {displayMode:false,throwOnError:false});$ is computed from the inlet temperature $var element = document.getElementById("moose-equation-b6a316a2-215c-4057-9496-a9139261a5b7");katex.render("T_{in}", element, {displayMode:false,throwOnError:false});$ as a function of the integrated linear power of the rod $var element = document.getElementById("moose-equation-fe288fb0-ed75-4b35-937b-6f8b38e905dd");katex.render("\\chi", element, {displayMode:false,throwOnError:false});$ , the mass flow rate, $var element = document.getElementById("moose-equation-5cd21dd1-fa25-480f-9d50-2eea4f744f43");katex.render("\\dot{m}", element, {displayMode:false,throwOnError:false});$ , and the specific heat of the sodium, $(9)var element = document.getElementById("moose-equation-cee5a2ce-6423-495d-bfad-a468d3253f53");katex.render(" T(z) = T_{in} + \\begin{cases} 0 & \\text{if } Z \\le z_{bottom} \\\\ \\frac{1}{\\dot{m}c_p(T_{in})} \\int_0^Z \\chi(z) &\\text{if } z_{bottom} < Z < z_{top} \\\\ \\frac{1}{\\dot{m}c_p(T_{in})} &\\text{if } z_{top} \\le Z \\\\ \\end{cases} ", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-67b9ddba-2b44-447b-a774-4abe72c09474");katex.render("z_{top}", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-248df2d4-ab28-4019-915b-3253d18e822b");katex.render("z_{bottom}", element, {displayMode:false,throwOnError:false});$ are the axial coordinates of the top and bottom of the fuel respectively, and $var element = document.getElementById("moose-equation-3f4a5013-c724-4c2a-aa73-3eea09322d8e");katex.render("c_p", element, {displayMode:false,throwOnError:false});$ is evaluated at the inlet temperature in order to simplify the integral as it is only weakly dependent on temperature. Here, the mass flow rate is calculated from the mass flux, $var element = document.getElementById("moose-equation-a08ab189-f97c-4680-8332-1fcdde6c928a");katex.render("m_f", element, {displayMode:false,throwOnError:false});$ , and flow area, $var element = document.getElementById("moose-equation-4b2cdfcf-08c9-42c1-a5f6-97bfe52b6eaa");katex.render("A", element, {displayMode:false,throwOnError:false});$ , $(10)var element = document.getElementById("moose-equation-548e9c67-1926-4258-8461-1b295bbbed8e");katex.render(" \\dot{m} = m_f A. ", element, {displayMode:true,throwOnError:false});$ The integrated rod power in Eq. (9) is calculated by multiplying the rod linear power, $var element = document.getElementById("moose-equation-655b47e8-a20e-4db1-99bd-05558caa11d6");katex.render("P^l_{rod}", element, {displayMode:false,throwOnError:false});$ , by the fuel pellet length, and the integrated axial power profile up to $var element = document.getElementById("moose-equation-35558fea-417b-43e2-9b6e-4c29960e150e");katex.render("Z", element, {displayMode:false,throwOnError:false});$ , $(11)var element = document.getElementById("moose-equation-7b48dc94-2c11-4607-a30a-784cd5138770");katex.render(" \\int_0^Z \\chi(z) = (z_{top} - z_{bottom}) P^l_{rod} \\int_0^Z P_{axial}(z) ", element, {displayMode:true,throwOnError:false});$ In SodiumCoolantChanelMaterial, the mass flux and total rod power are provided as time varying functions. While the axial power profile is also a function, it must be provided by PowerPeakingFunction using the cdf = true input parameter in order to correctly calculate the integral in Eq. (11).

Below the bottom of the fuel pellet, the integral in Eq. (9) is forced to be zero, thus there is no temperature rise. Above the top of the fuel pellet, the integral in Eq. (9) is forced to be one, resulting in an outlet coolant temperature at the top of the cladding to be the same as the coolant temperature at the top of the fuel pellet.

Heat Transfer Coefficient

The heat transfer coefficient can be computed externally from a function, or internally using either the Fast Flux Test Reactor (FFTF) correlation, or the Borishanskii, Gotovskii, and Firsova (BGF) correlation. For the FFTF and BGF correlation, the model specific Nusselt number $var element = document.getElementById("moose-equation-3a20fa4f-1028-42a6-9ef3-00ab6a99d1c9");katex.render("Nu", element, {displayMode:false,throwOnError:false});$ is used to compute the local heat transfer coefficient $var element = document.getElementById("moose-equation-9af81192-f20d-421d-a168-8e9d9944b7f4");katex.render("h", element, {displayMode:false,throwOnError:false});$ by, $(12)var element = document.getElementById("moose-equation-d1c8739a-7551-4143-b8d6-e8a0a332dad0");katex.render(" h(T) = \\frac{Nu(Pe) k(T)}{D_h}, ", element, {displayMode:true,throwOnError:false});$ where the hydraulic diameter is calculated via Eq. (8). Here, each Nusselt number is determined by the local Peclet number: $(13)var element = document.getElementById("moose-equation-2e598fd5-b29b-4904-83ed-26d2b714abe6");katex.render(" Pe(T) = \\frac{m_f c_p(T) D_h}{k(T)}, ", element, {displayMode:true,throwOnError:false});$ where the specific heat and thermal conductivity are computed using the local coolant temperature.

FFTF Correlation

The FFTF correlation from Calamai et al. (1974) is valid for Peclet numbers between $var element = document.getElementById("moose-equation-3ec5404c-c7b3-427c-b64b-7ab482db09ca");katex.render("20 \\le Pe \\le 1000", element, {displayMode:false,throwOnError:false});$ , for any pitch to diameter ratio: $(14)var element = document.getElementById("moose-equation-5adf50ca-37cc-42d2-9e1b-a621130a2209");katex.render(" Nu_{FFTF} = 4 + 0.16 (P / D)^{5} + 0.33 (P / D)^{3.8}(Pe / 100)^{0.86}. ", element, {displayMode:true,throwOnError:false});$ In general, $var element = document.getElementById("moose-equation-3f23fcd4-df65-4f8c-aa39-f3e023fdd83a");katex.render("Nu_{FFTF}", element, {displayMode:false,throwOnError:false});$ tends to be conservative by underestimating the $var element = document.getElementById("moose-equation-1d2e6f6b-a7a6-4344-9170-0090da03ce96");katex.render("Nu", element, {displayMode:false,throwOnError:false});$ number when compared to experimental data points and other correlations.

BFG correlation

The BGF correlation from Borishanskii et al. (1969) is valid for Peclet numbers between $var element = document.getElementById("moose-equation-dad276d2-40a1-4fe5-8aa1-ed8a256696c3");katex.render("0 \\le Pe \\le 2000", element, {displayMode:false,throwOnError:false});$ , and for pitch to diameter ratios between $var element = document.getElementById("moose-equation-599bde23-c6a2-4e18-b8a6-2d27807a39a8");katex.render("1.1 \\le P/D \\le 1.5", element, {displayMode:false,throwOnError:false});$ : $(15)var element = document.getElementById("moose-equation-b2b7bcbc-34e0-42a6-90d2-db98285beb1a");katex.render(" Nu_{BFG} = \\begin{cases} Nu_{BFG}^0 &\\text{if} & Pe \\le 200 \\\\ Nu_{BFG}^0 + 0.0174\\left[1-\\exp(-6(P/D)-6) \\right](Pe - 200)^{0.9} &\\text{if} & 200 < Pe \\le 2000 \\end{cases} ", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-3c41176e-b2ee-49bb-b28f-36d6f3f2f01c");katex.render(" Nu_{BFG}^0 = 24.15 \\log_{10}\\left[-8.12 + 12.76 (P/D) - 3.65 (P/D)^2\\right]", element, {displayMode:true,throwOnError:false});$ From the discussion in Waltar et al. (2011), the BFG seems to be the most realistic heat transfer correlation.

Example Input Syntax

A typical implementation of SodiumCoolantChanelMaterial with the FFTF correlation is:

[Materials<<<{"href": "../../syntax/Materials/index.html"}>>>]
  [coolant]
    type = SodiumCoolantChannelMaterial<<<{"description": "Computes the coolant temperature and heat transfer coefficient for sodium in a typical sodium fast reactor assembly. This material is to be used in conjunction with the ConvectiveHeatFluxBC boundary condition, This material can only be applied to boundaries.", "href": "SodiumCoolantChannelMaterial.html"}>>>
    inlet_temperature_function<<<{"description": "Function for inlet temperature in K as a function of time."}>>> = 648.0
    rod_linear_power<<<{"description": "Function describing linear power in W/m as a function of time."}>>> = dp16_power
    inlet_massflux_function<<<{"description": "Function for inlet mass flux in kg/m2/s as a function of time."}>>> = 5262.0
    axial_power_profile_cdf<<<{"description": "Function describing cumulative distribution function of the axial power profile as a function of time and position."}>>> = row_4_cdf
    pellet_height<<<{"description": "Height of fuel pellet in m."}>>> = 3.442e-01
    cladding_radius<<<{"description": "Cladding outer radius in m."}>>> = 2.921e-03
    boundary<<<{"description": "The list of boundary IDs from the mesh where this material applies"}>>> = clad_outside_right
    wire_wrap_diameter<<<{"description": "Diameter of wire wrap in m."}>>> = 1.067e-03
    temperature<<<{"description": "Coupled temperature variable. Only used in computing the heat flux for visualization and not in computation of coolant channel properties."}>>> = temp
    sodium_user_object<<<{"description": "Name of the sodium user object"}>>> = sodium_uo
    htc_model<<<{"description": "Thermal conductivity model. Choices are: BGF FFTF function"}>>> = BGF
    update_temperature<<<{"description": "Flag to update temperature due to heating. If false, the coolant temperature will always equal the inlet temperature."}>>> = true
    pin_location<<<{"description": "Pin location in the assembly. Choices are: interior edge corner"}>>> = interior
    peclet_limit_behavior<<<{"description": "Behavior when Peclet number is outside bounds of current htc model. Choices are: nothing warning error"}>>> = error
    outputs<<<{"description": "Vector of output names where you would like to restrict the output of variables(s) associated with this object"}>>> = all
  []
[]

As discussed above, SodiumCoolantChanelMaterial requires a PowerPeakingFunction using the cdf = true input parameter:

[Functions<<<{"href": "../../syntax/Functions/index.html"}>>>]
  [row_4_cdf]
    type = PowerPeakingFunction<<<{"description": "Computes an axial power profile applied to the fuel from a third order polynomial.", "href": "../functions/PowerPeakingFunction.html"}>>>
    fit<<<{"description": "Fitting parameters for the 3rd order power peaking factor equation. Use EBR-II_ROW_3 for irradiaiton in rows 1-3, EBR-II_ROW_4 for irradiation in rows 4-6, and custom to manually input coefficients."}>>> = EBRII_ROW_4
    pellet_length<<<{"description": "Length of fuel pellet."}>>> = 3.442e-01
    pellet_y_start<<<{"description": "y position of start of fuel pellet."}>>> = 2.24e-3
    zero_beyond_top_and_bottom<<<{"description": "Set the function to zero above and below the y position start and end. Note that this parameter will not ensure normalization of the function."}>>> = true
    cdf<<<{"description": "Flag to return the cumulative distribution function."}>>> = true
  []
[]

In addition, the material properties computed by SodiumCoolantChanelMaterial can be passed to ConvectiveHeatFluxBC

[BCs<<<{"href": "../../syntax/NuclearMaterials/BCs/index.html"}>>>]
  [temp]
    type = ConvectiveHeatFluxBC<<<{"description": "Convective heat transfer boundary condition with temperature and heat transfer coefficent given by material properties.", "href": "../bcs/ConvectiveHeatFluxBC.html"}>>>
    T_infinity<<<{"description": "Material property for far-field temperature"}>>> = coolant_temperature
    heat_transfer_coefficient<<<{"description": "Material property for heat transfer coefficient"}>>> = coolant_channel_htc
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = temp
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = 'right'
  []
[]

Input Parameters

axial_power_profile_cdfFunction describing cumulative distribution function of the axial power profile as a function of time and position.
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:Function describing cumulative distribution function of the axial power profile as a function of time and position.
boundaryThe list of boundary IDs from the mesh where this material applies
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:The list of boundary IDs from the mesh where this material applies
inlet_massflux_functionFunction for inlet mass flux in kg/m2/s as a function of time.
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:Function for inlet mass flux in kg/m2/s as a function of time.
inlet_temperature_functionFunction for inlet temperature in K as a function of time.
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:Function for inlet temperature in K as a function of time.
rod_linear_powerFunction describing linear power in W/m as a function of time.
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:Function describing linear power in W/m as a function of time.
temperatureCoupled temperature variable. Only used in computing the heat flux for visualization and not in computation of coolant channel properties.
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Coupled temperature variable. Only used in computing the heat flux for visualization and not in computation of coolant channel properties.

Required Parameters

cladding_radius-1Cladding outer radius in m.
Default:-1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Cladding outer radius in m.
cladding_radius_mesh_property_namecladding_radiusThe mesh metadata name of cladding radius.
Default:cladding_radius
C++ Type:std::string
Controllable:No
Description:The mesh metadata name of cladding radius.
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.
htc_functionFunction describing heat transfer coefficient as a function of temperature and position. Required if htc_model = function.
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:Function describing heat transfer coefficient as a function of temperature and position. Required if htc_model = function.
htc_modelBGFThermal conductivity model. Choices are: BGF FFTF function
Default:BGF
C++ Type:MooseEnum
Options:BGF, FFTF, function
Controllable:No
Description:Thermal conductivity model. Choices are: BGF FFTF function
htc_scalar1Scalar multiplied against the heat transfer coefficient
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Scalar multiplied against the heat transfer coefficient
mesh_generatorThe name of the generator to use as the prefix for mesh meta data properties.
C++ Type:MeshGeneratorName
Controllable:No
Description:The name of the generator to use as the prefix for mesh meta data properties.
peclet_limit_behaviorerrorBehavior when Peclet number is outside bounds of current htc model. Choices are: nothing warning error
Default:error
C++ Type:MooseEnum
Options:nothing, warning, error
Controllable:No
Description:Behavior when Peclet number is outside bounds of current htc model. Choices are: nothing warning error
pellet_height-1Height of fuel pellet in m.
Default:-1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Height of fuel pellet in m.
pellet_height_mesh_property_namefuel_heightThe mesh metadata name of pellet height.
Default:fuel_height
C++ Type:std::string
Controllable:No
Description:The mesh metadata name of pellet height.
pin_locationinteriorPin location in the assembly. Choices are: interior edge corner
Default:interior
C++ Type:MooseEnum
Options:interior, edge, corner
Controllable:No
Description:Pin location in the assembly. Choices are: interior edge corner
sodium_user_objectsodiumName of the sodium user object
Default:sodium
C++ Type:UserObjectName
Controllable:No
Description:Name of the sodium user object
update_temperatureTrueFlag to update temperature due to heating. If false, the coolant temperature will always equal the inlet temperature.
Default:True
C++ Type:bool
Controllable:No
Description:Flag to update temperature due to heating. If false, the coolant temperature will always equal the inlet temperature.
use_metadataFalseWhether to use the cladding radius, wire wrap diameter, and pellet height value from MeshMetaDataInterface.
Default:False
C++ Type:bool
Controllable:No
Description:Whether to use the cladding radius, wire wrap diameter, and pellet height value from MeshMetaDataInterface.
wire_wrap_diameter-1Diameter of wire wrap in m.
Default:-1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Diameter of wire wrap in m.
wire_wrap_diameter_mesh_property_namewire_wrap_diameterThe mesh metadata name of wire wrap diameter.
Default:wire_wrap_diameter
C++ Type:std::string
Controllable:No
Description:The mesh metadata name of wire wrap diameter.

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

Input Files

(test/tests/sodium_coolant_channel/htc_fftf_edge.i)
(test/tests/sodium_coolant_channel/heated.i)
(test/tests/metallic_fuel_coolant_wastage/cc_wastage_ht9_eff_full_pin.i)
(test/tests/sodium_coolant_channel/dp16.i)
(test/tests/sodium_coolant_channel/htc_fftf.i)
(test/tests/ad_metallic_fuel_coolant_wastage/cc_wastage_ht9_eff_full_pin.i)
(test/tests/sodium_coolant_channel/htc_function.i)
(test/tests/sodium_coolant_channel/htc_fftf_corner.i)
(test/tests/sodium_coolant_channel/htc_bgf.i)
(test/tests/sodium_coolant_channel/dp11.i)
(assessment/metallic_fuel/FBTA/analysis/steady_state/AK181/181193/IFR1_181193.i)

References

V M Borishanskii, M A Gotovskii, and É V Firsova. Heat transfer to liquid metals in longitudinally wetted bundles of rods. Soviet Atomic Energy, 27(6):1347–1350, 1969.

@article{Borishanskii:1969tu,
    author = "Borishanskii, V M and Gotovskii, M A and Firsova, {\'E} V",
    title = "{Heat transfer to liquid metals in longitudinally wetted bundles of rods}",
    journal = "Soviet Atomic Energy",
    year = "1969",
    volume = "27",
    number = "6",
    pages = "1347-1350"
}

GJ Calamai, RD Coffield, L Jossens, JL Kerian, JV Miller, EH Novendstern, GH Ursim, H West, and PJ Wood. Steady state thermal and hydraulic characteristics of the fftf fuel assemblies. FRT-1582, June, 1974.

@article{calamai1974steady,
    author = "Calamai, GJ and Coffield, RD and Jossens, L and Kerian, JL and Miller, JV and Novendstern, EH and Ursim, GH and West, H and Wood, PJ",
    title = "Steady State Thermal and Hydraulic Characteristics of the FFTF Fuel Assemblies",
    journal = "FRT-1582, June",
    year = "1974"
}

A.E. Waltar, D.R. Todd, and P.V. Tsvetkov. Fast Spectrum Reactors. Springer US, 2011. ISBN 9781441995728. URL: https://books.google.com/books?id=z8z\_RNUZSbEC.

@book{waltar2011fast,
    author = "Waltar, A.E. and Todd, D.R. and Tsvetkov, P.V.",
    title = "Fast Spectrum Reactors",
    isbn = "9781441995728",
    lccn = "2011935931",
    url = "https://books.google.com/books?id=z8z\\_RNUZSbEC",
    year = "2011",
    publisher = "Springer US"
}

(test/tests/sodium_coolant_channel/dp16.i)

# This test applies the new coolant channel model to a realistic geometry, e.g. dp16 from EBR-II.

[Problem]
  type = ReferenceResidualProblem
  reference_vector = 'ref'
  extra_tag_vectors = 'ref'
[]

[Mesh]
  coord_type = RZ
  # rod specific parameters
  [smeared_pellet_mesh]
    type = FuelPinMeshGenerator
    clad_thickness = 0.381e-03
    pellet_outer_radius = 2.184e-03
    pellet_height = 3.442e-01
    clad_top_gap_height = 2.949e-01
    clad_gap_width = 3.556e-04
    bottom_clad_height = 2.24e-3 # arbitrary
    top_clad_height = 2.24e-3 # arbitrary
    clad_bot_gap_height = 0.31e-3 # arbitrary
    # meshing parameters
    clad_mesh_density = customize
    pellet_mesh_density = customize
    nx_p = 10
    ny_p = 10
    nx_c = 10
    ny_c = 30
    ny_cu = 3
    ny_cl = 3
    pellet_quantity = 1
  []
  # mesh options
  partitioner = centroid
  centroid_partitioner_direction = y
[]

[DefaultElementQuality]
  failure_type = Warning
[]

[Variables]
  [temp]
    initial_condition = 300
  []
[]

[Kernels]
  [heat]
    type = ADHeatConduction
    variable = temp
    extra_vector_tags = 'ref'
  []
  [heat_ie_fuel]
    type = ADHeatConductionTimeDerivative
    variable = temp
    extra_vector_tags = 'ref'
    block = pellet
    density_name = 15800
  []
  [heat_ie_clad]
    type = ADHeatConductionTimeDerivative
    variable = temp
    extra_vector_tags = 'ref'
    block = clad
    density_name = 7876
  []
  [heat_source]
    type = ADFissionRateHeatSource
    variable = temp
    block = pellet
    fission_rate = fission_rate
    extra_vector_tags = 'ref'
  []
[]

[BCs]
  [convection]
    type = ConvectiveHeatFluxBC
    variable = temp
    boundary = clad_outside_right
    T_infinity = coolant_temperature
    heat_transfer_coefficient = coolant_channel_htc
  []
[]

[AuxVariables]
  [cdf]
  []
[]

[AuxKernels]
  [cdf_aux]
    type = FunctionAux
    variable = cdf
    function = row_4_cdf
  []
[]

[Functions]
  [dp16_power]
    type = PiecewiseLinear
    # min power, weighted avg, max power
    x = '0 1'
    y = '44734 44734'
  []
  [row_4]
    type = PowerPeakingFunction
    fit = EBRII_ROW_4
    pellet_length = 3.442e-01
    pellet_y_start = 2.24e-3
    zero_beyond_top_and_bottom = true
  []
  [row_4_cdf]
    type = PowerPeakingFunction
    fit = EBRII_ROW_4
    pellet_length = 3.442e-01
    pellet_y_start = 2.24e-3
    zero_beyond_top_and_bottom = true
    cdf = true
  []
[]

[ThermalContact]
  [thermal_contact]
    type = GapHeatTransfer
    variable = temp
    primary = 'clad_inside_right'
    secondary = 'pellet_outer_radial_surface'
    quadrature = true
    gap_conductivity = 61.0
    min_gap = 3.556E-04
  []
[]

[FluidProperties]
  [sodium_uo]
    type = SodiumProperties
  []
[]

[Materials]
  [coolant]
    type = SodiumCoolantChannelMaterial
    inlet_temperature_function = 648.0
    rod_linear_power = dp16_power
    inlet_massflux_function = 5262.0
    axial_power_profile_cdf = row_4_cdf
    pellet_height = 3.442e-01
    cladding_radius = 2.921e-03
    boundary = clad_outside_right
    wire_wrap_diameter = 1.067e-03
    temperature = temp
    sodium_user_object = sodium_uo
    htc_model = BGF
    update_temperature = true
    pin_location = interior
    peclet_limit_behavior = error
    outputs = all
  []
  [fission_rate]
    type = ADUPuZrFissionRate
    rod_linear_power = dp16_power
    axial_power_profile = row_4
    pellet_radius = 2.184e-03
    X_Zr = 0.225
    block = pellet
    outputs = all
  []

  [metal_fuel_thermal]
    type = ADUPuZrThermal
    block = pellet
    X_Zr = 0.225
    X_Pu = 0
    spheat_model = savage
    thcond_model = lanl
    porosity = 0
    temperature = temp
  []
  [clad_thermal]
    type = ADHT9Thermal
    block = clad
    temperature = temp
  []
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu       superlu_dist'
  line_search = 'none'

  l_max_its = 60
  l_tol = 8e-3
  nl_max_its = 40
  nl_rel_tol = 5e-4
  nl_abs_tol = 1e-7

  end_time = 1
  dt = .1
[]

[Postprocessors]
  [temp_fuel_avg]
    type = ElementAverageValue
    variable = temp
    block = pellet
  []
  [temp_fuel_max]
    type = ElementExtremeValue
    variable = temp
    block = pellet
  []
  [temp_clad_avg]
    type = ElementAverageValue
    variable = temp
    block = clad
  []
  [temp_clad_max]
    type = ElementExtremeValue
    variable = temp
    block = clad
  []
  [temp_oulet]
    type = ElementExtremeValue
    variable = coolant_temperature
  []
[]

[VectorPostprocessors]
  [cladding]
    type = SideValueSampler
    boundary = clad_outside_right
    sort_by = y
    variable = 'temp coolant_temperature coolant_channel_htc'
  []
  [centerline]
    type = SideValueSampler
    boundary = centerline
    sort_by = y
    variable = 'temp'
  []
[]

[Outputs]
  [out]
    type = CSV
    execute_on = final
  []
[]

(test/tests/sodium_coolant_channel/dp16.i)

# This test applies the new coolant channel model to a realistic geometry, e.g. dp16 from EBR-II.

[Problem]
  type = ReferenceResidualProblem
  reference_vector = 'ref'
  extra_tag_vectors = 'ref'
[]

[Mesh]
  coord_type = RZ
  # rod specific parameters
  [smeared_pellet_mesh]
    type = FuelPinMeshGenerator
    clad_thickness = 0.381e-03
    pellet_outer_radius = 2.184e-03
    pellet_height = 3.442e-01
    clad_top_gap_height = 2.949e-01
    clad_gap_width = 3.556e-04
    bottom_clad_height = 2.24e-3 # arbitrary
    top_clad_height = 2.24e-3 # arbitrary
    clad_bot_gap_height = 0.31e-3 # arbitrary
    # meshing parameters
    clad_mesh_density = customize
    pellet_mesh_density = customize
    nx_p = 10
    ny_p = 10
    nx_c = 10
    ny_c = 30
    ny_cu = 3
    ny_cl = 3
    pellet_quantity = 1
  []
  # mesh options
  partitioner = centroid
  centroid_partitioner_direction = y
[]

[DefaultElementQuality]
  failure_type = Warning
[]

[Variables]
  [temp]
    initial_condition = 300
  []
[]

[Kernels]
  [heat]
    type = ADHeatConduction
    variable = temp
    extra_vector_tags = 'ref'
  []
  [heat_ie_fuel]
    type = ADHeatConductionTimeDerivative
    variable = temp
    extra_vector_tags = 'ref'
    block = pellet
    density_name = 15800
  []
  [heat_ie_clad]
    type = ADHeatConductionTimeDerivative
    variable = temp
    extra_vector_tags = 'ref'
    block = clad
    density_name = 7876
  []
  [heat_source]
    type = ADFissionRateHeatSource
    variable = temp
    block = pellet
    fission_rate = fission_rate
    extra_vector_tags = 'ref'
  []
[]

[BCs]
  [convection]
    type = ConvectiveHeatFluxBC
    variable = temp
    boundary = clad_outside_right
    T_infinity = coolant_temperature
    heat_transfer_coefficient = coolant_channel_htc
  []
[]

[AuxVariables]
  [cdf]
  []
[]

[AuxKernels]
  [cdf_aux]
    type = FunctionAux
    variable = cdf
    function = row_4_cdf
  []
[]

[Functions]
  [dp16_power]
    type = PiecewiseLinear
    # min power, weighted avg, max power
    x = '0 1'
    y = '44734 44734'
  []
  [row_4]
    type = PowerPeakingFunction
    fit = EBRII_ROW_4
    pellet_length = 3.442e-01
    pellet_y_start = 2.24e-3
    zero_beyond_top_and_bottom = true
  []
  [row_4_cdf]
    type = PowerPeakingFunction
    fit = EBRII_ROW_4
    pellet_length = 3.442e-01
    pellet_y_start = 2.24e-3
    zero_beyond_top_and_bottom = true
    cdf = true
  []
[]

[ThermalContact]
  [thermal_contact]
    type = GapHeatTransfer
    variable = temp
    primary = 'clad_inside_right'
    secondary = 'pellet_outer_radial_surface'
    quadrature = true
    gap_conductivity = 61.0
    min_gap = 3.556E-04
  []
[]

[FluidProperties]
  [sodium_uo]
    type = SodiumProperties
  []
[]

[Materials]
  [coolant]
    type = SodiumCoolantChannelMaterial
    inlet_temperature_function = 648.0
    rod_linear_power = dp16_power
    inlet_massflux_function = 5262.0
    axial_power_profile_cdf = row_4_cdf
    pellet_height = 3.442e-01
    cladding_radius = 2.921e-03
    boundary = clad_outside_right
    wire_wrap_diameter = 1.067e-03
    temperature = temp
    sodium_user_object = sodium_uo
    htc_model = BGF
    update_temperature = true
    pin_location = interior
    peclet_limit_behavior = error
    outputs = all
  []
  [fission_rate]
    type = ADUPuZrFissionRate
    rod_linear_power = dp16_power
    axial_power_profile = row_4
    pellet_radius = 2.184e-03
    X_Zr = 0.225
    block = pellet
    outputs = all
  []

  [metal_fuel_thermal]
    type = ADUPuZrThermal
    block = pellet
    X_Zr = 0.225
    X_Pu = 0
    spheat_model = savage
    thcond_model = lanl
    porosity = 0
    temperature = temp
  []
  [clad_thermal]
    type = ADHT9Thermal
    block = clad
    temperature = temp
  []
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu       superlu_dist'
  line_search = 'none'

  l_max_its = 60
  l_tol = 8e-3
  nl_max_its = 40
  nl_rel_tol = 5e-4
  nl_abs_tol = 1e-7

  end_time = 1
  dt = .1
[]

[Postprocessors]
  [temp_fuel_avg]
    type = ElementAverageValue
    variable = temp
    block = pellet
  []
  [temp_fuel_max]
    type = ElementExtremeValue
    variable = temp
    block = pellet
  []
  [temp_clad_avg]
    type = ElementAverageValue
    variable = temp
    block = clad
  []
  [temp_clad_max]
    type = ElementExtremeValue
    variable = temp
    block = clad
  []
  [temp_oulet]
    type = ElementExtremeValue
    variable = coolant_temperature
  []
[]

[VectorPostprocessors]
  [cladding]
    type = SideValueSampler
    boundary = clad_outside_right
    sort_by = y
    variable = 'temp coolant_temperature coolant_channel_htc'
  []
  [centerline]
    type = SideValueSampler
    boundary = centerline
    sort_by = y
    variable = 'temp'
  []
[]

[Outputs]
  [out]
    type = CSV
    execute_on = final
  []
[]

(test/tests/sodium_coolant_channel/htc_function.i)

# This test is for comparing the heat transfer coefficient defined as a function to a hand calculation

[Mesh]
  coord_type = RZ
  [mesh]
    type = GeneratedMeshGenerator
    dim = 2
    xmax = 0.5
  []
[]

[Variables]
  [temp]
    initial_condition = 100
  []
[]

[Kernels]
  [heat]
    type = Diffusion
    variable = temp
  []
  [heat_dt]
    type = TimeDerivative
    variable = temp
  []
[]

[BCs]
  [temp]
    type = ConvectiveHeatFluxBC
    T_infinity = coolant_temperature
    heat_transfer_coefficient = coolant_channel_htc
    variable = temp
    boundary = 'right'
  []
[]

[FluidProperties/sodium]
  type = SodiumProperties
[]

[Functions]
  [htc_fcn]
    type = PiecewiseLinear
    x = '0 10'
    y = '0.5 0.25'
  []
  [areal_heat_loss]
    type = ParsedFunction
    symbol_names = 'temp_avg radius'
    symbol_values = 'temp_avg 0.5'
    expression = 'pi * radius^2 * (100 - temp_avg)'
  []
  [surface_net_heat_flux]
    type = ParsedFunction
    symbol_names = 'flux_sum radius'
    symbol_values = 'flux_sum 0.5'
    expression = '2 * pi * radius * flux_sum'
  []
  [diff]
    type = ParsedFunction
    symbol_names = 'areal_heat_loss surface_net_heat_flux'
    symbol_values = 'areal_heat_loss surface_net_heat_flux'
    expression = 'areal_heat_loss - surface_net_heat_flux'
  []
[]

[Materials]
  [coolant]
    type = SodiumCoolantChannelMaterial
    inlet_temperature_function = 200
    rod_linear_power = 0
    inlet_massflux_function = 0
    axial_power_profile_cdf = 0
    pellet_height = 1
    cladding_radius = 1
    boundary = right
    wire_wrap_diameter = 0
    temperature = temp
    sodium_user_object = sodium
    htc_model = function
    htc_function = htc_fcn
    update_temperature = false
    htc_scalar = 0.05
    outputs = all
  []
[]

[Executioner]
  type = Transient

  end_time = 10
[]

[Postprocessors]
  [temp_centerline]
    type = AxisymmetricCenterlineAverageValue
    variable = temp
    boundary = left
    outputs = console
  []
  [temp_avg]
    type = ElementAverageValue
    variable = temp
    outputs = console
  []
  [temp_surf]
    type = SideAverageValue
    variable = temp
    boundary = right
    outputs = console
  []
  [temp_coolant_avg]
    type = ElementAverageValue
    variable = coolant_temperature
    outputs = console
  []
  [heat_flux_avg]
    type = SideAverageValue
    variable = heat_flux
    boundary = right
    outputs = console
  []
  [flux_sum]
    type = CumulativeValuePostprocessor
    postprocessor = heat_flux_avg
    outputs = console
  []
  [diff]
    type = FunctionValuePostprocessor
    function = diff
    outputs = none
  []
  [max_diff]
    type = TimeExtremeValue
    postprocessor = diff
  []
[]

[Outputs]
  csv = true
[]

(test/tests/sodium_coolant_channel/htc_fftf_edge.i)

# This test is for comparing the heat transfer coefficient for the FFTF model to a hand calculation
# for a pin in an edge location.

[Mesh]
  coord_type = RZ
  [mesh]
    type = GeneratedMeshGenerator
    dim = 2
    ny = 10
    xmax = 0.01
  []
[]

[Problem]
  solve = false
[]

[Functions]
  [axial_power_profile]
    type = PowerPeakingFunction
    pellet_length = 1
    pellet_y_start = 0
    fit = FLAT
    cdf = false
  []
  [axial_power_profile_cdf]
    type = PowerPeakingFunction
    pellet_length = 1
    pellet_y_start = 0
    fit = FLAT
    cdf = true
  []
  [inlet_massflux]
    type = PiecewiseLinear
    x = '0 100'
    y = '1e3 0.5e4'
  []
  [inlet_temp]
    type = PiecewiseLinear
    x = '0 100'
    y = '200 1000'
  []
  [rod_linear_power]
    type = PiecewiseLinear
    x = '0 1'
    y = '1e9 1e9'
  []
  [cp]
    type = ParsedFunction
    symbol_names = inlet_temp
    symbol_values = inlet_temp
    expression = '1.6582e3 - 8.4790e-1 * inlet_temp + 4.4541e-4 * inlet_temp^2 - 2992.6e3 / inlet_temp^2'
  []
  [thcond]
    type = ParsedFunction
    symbol_names = inlet_temp
    symbol_values = inlet_temp
    expression = '124.67 - 0.11381 * inlet_temp + 5.5226e-5 * inlet_temp^2 - 1.1842e-8 * inlet_temp^3'
  []

  [interior_flow_channel_area]
    type = ParsedFunction
    symbol_names = 'D s P'
    symbol_values = '2e-2 1e-3 2.1e-2'
    expression = 'sqrt(3) / 4 * P^2 - pi / 8 * D^2 -  pi / 8 * s^2'
  []
  [edge_flow_channel_area]
    type = ParsedFunction
    symbol_names = 'D s P'
    symbol_values = '2e-2 1e-3 2.1e-2'
    expression = 'P * (D / 2 + s) - pi / 8 * D^2 -  pi / 8 * s^2'
  []
  [corner_flow_channel_area]
    type = ParsedFunction
    symbol_names = 'D s P'
    symbol_values = '2e-2 1e-3 2.1e-2'
    expression = '1.0 / sqrt(3.0) * (D / 2.0 + s)^2 - pi / 24.0 * D^2 -  pi / 24.0 * s^2'
  []

  [interior_channel_wetted]
    type = ParsedFunction
    symbol_names = 'D s P'
    symbol_values = '2e-2 1e-3 2.1e-2'
    expression = 'P * pi / 2'
  []
  [edge_channel_wetted]
    type = ParsedFunction
    symbol_names = 'D s P'
    symbol_values = '2e-2 1e-3 2.1e-2'
    expression = '(1 + pi / 2) * P'
  []
  [corner_channel_wetted]
    type = ParsedFunction
    symbol_names = 'D s P'
    symbol_values = '2e-2 1e-3 2.1e-2'
    expression = '(D + 2 * s) + pi / 6 * P'
  []

  [flow_area]
    type = ParsedFunction
    symbol_names = 'interior_flow_channel_area edge_flow_channel_area corner_flow_channel_area'
    symbol_values = 'interior_flow_channel_area edge_flow_channel_area corner_flow_channel_area'
    expression = 'interior_flow_channel_area + edge_flow_channel_area'
  []
  [wetted_perimeter]
    type = ParsedFunction
    symbol_names = 'interior_channel_wetted edge_channel_wetted corner_channel_wetted'
    symbol_values = 'interior_channel_wetted edge_channel_wetted corner_channel_wetted'
    expression = 'interior_channel_wetted + edge_channel_wetted'
  []

  [hydraulic_diameter]
    type = ParsedFunction
    symbol_names = 'flow_area wetted_perimeter'
    symbol_values = 'flow_area wetted_perimeter'
    expression = '4.0 * flow_area / wetted_perimeter'
  []

  [peclet]
    type = ParsedFunction
    symbol_names = 'cp thcond inlet_massflux hydraulic_diameter'
    symbol_values = 'cp thcond inlet_massflux hydraulic_diameter'
    expression = 'inlet_massflux * cp * hydraulic_diameter / thcond'
  []
  [nusselt]
    type = ParsedFunction
    symbol_names = 'pitch diameter peclet'
    symbol_values = '2.1e-2 2e-2    peclet'
    expression = 'p_over_d := pitch / diameter;
             4 + 0.16 * p_over_d^5 + 0.33 * p_over_d^3.8 * (peclet / 100)^0.86'
  []
  [htc_exact]
    type = ParsedFunction
    symbol_names = 'nusselt thcond hydraulic_diameter scalar'
    symbol_values = 'nusselt thcond hydraulic_diameter 0.01'
    expression = 'scalar * nusselt * thcond / hydraulic_diameter'
  []
[]

[FluidProperties]
  [sodium_uo]
    type = SodiumProperties
  []
[]

[Materials]
  [coolant]
    type = SodiumCoolantChannelMaterial
    inlet_temperature_function = inlet_temp
    rod_linear_power = rod_linear_power
    inlet_massflux_function = inlet_massflux
    axial_power_profile_cdf = axial_power_profile_cdf
    pellet_height = 1
    cladding_radius = 0.01
    boundary = right
    wire_wrap_diameter = 0.001
    temperature = 200
    sodium_user_object = sodium_uo
    htc_model = FFTF
    update_temperature = false
    htc_scalar = 0.01
    pin_location = edge
    peclet_limit_behavior = nothing
    outputs = all
  []
[]

[Executioner]
  type = Transient
  dt = 1
  end_time = 100
[]

[Postprocessors]
  [temp_coolant_avg]
    type = SideAverageValue
    boundary = right
    variable = coolant_temperature
  []

  [htc_avg]
    type = SideAverageValue
    boundary = right
    variable = coolant_channel_htc
  []
  [htc_exact]
    type = FunctionValuePostprocessor
    function = htc_exact
    indirect_dependencies = 'peclet'
  []
  [htc_diff]
    type = DifferencePostprocessor
    value1 = htc_avg
    value2 = htc_exact
    outputs = none
  []
  [htc_max_diff]
    type = TimeExtremeValue
    postprocessor = htc_diff
    value_type = abs_max
  []
  [peclet]
    type = FunctionValuePostprocessor
    function = peclet
  []

[]

[Outputs]
  csv = true
[]

(test/tests/sodium_coolant_channel/heated.i)

# This test is for comparing the heatup in the coolant channel around a fuel pin to  in interior, edge,
# and corner pin locations, to a hand calculation.

[Mesh]
  coord_type = RZ
  [mesh]
    type = GeneratedMeshGenerator
    dim = 2
    ny = 10
    xmax = 0.01
  []
[]

[Variables]
  [temp]
    initial_condition = 200
  []
[]

[Kernels]
  [heat]
    type = Diffusion
    variable = temp
  []
  [heat_dt]
    type = TimeDerivative
    variable = temp
  []
  [heat_source]
    type = BodyForce
    value = 1
    variable = temp
    function = power
  []
[]

[BCs]
  [temp]
    type = ConvectiveHeatFluxBC
    T_infinity = coolant_temperature
    heat_transfer_coefficient = coolant_channel_htc
    variable = temp
    boundary = 'right'
  []
[]

[Functions]
  [power]
    type = ParsedFunction
    symbol_names = 'axial_power_profile rod_linear_power'
    symbol_values = 'axial_power_profile rod_linear_power'
    expression = 'axial_power_profile * rod_linear_power'
  []
  [axial_power_profile]
    type = PowerPeakingFunction
    pellet_length = 1
    pellet_y_start = 0
    fit = FLAT
    cdf = false
  []
  [axial_power_profile_cdf]
    type = PowerPeakingFunction
    pellet_length = 1
    pellet_y_start = 0
    fit = FLAT
    cdf = true
  []
  [inlet_massflux]
    type = PiecewiseLinear
    x = '0 100'
    y = '1e-5 1e-5'
  []
  [rod_linear_power]
    type = PiecewiseLinear
    x = '0 1'
    y = '100 100'
  []
  [cp]
    type = ParsedFunction
    expression = '1.6582e3 - 8.4790e-1 * 200 + 4.4541e-4 * 200^2 - 2992.6e3 / 200^2'
  []

  [interior_flow_channel_area]
    type = ParsedFunction
    symbol_names = 'D s P'
    symbol_values = '2e-2 1e-3 2.1e-2'
    expression = 'sqrt(3) / 4 * P^2 - pi / 8 * D^2 -  pi / 8 * s^2'
  []
  [edge_flow_channel_area]
    type = ParsedFunction
    symbol_names = 'D s P'
    symbol_values = '2e-2 1e-3 2.1e-2'
    expression = 'P * (D / 2 + s) - pi / 8 * D^2 -  pi / 8 * s^2'
  []
  [corner_flow_channel_area]
    type = ParsedFunction
    symbol_names = 'D s P'
    symbol_values = '2e-2 1e-3 2.1e-2'
    expression = '1.0 / sqrt(3.0) * (D / 2.0 + s)^2 - pi / 24.0 * D^2 -  pi / 24.0 * s^2'
  []

  [flow_area]
    type = ParsedFunction
    symbol_names = 'interior_flow_channel_area edge_flow_channel_area corner_flow_channel_area'
    symbol_values = 'interior_flow_channel_area edge_flow_channel_area corner_flow_channel_area'
    expression = '2 * interior_flow_channel_area'
  []

  [T_exact]
    type = ParsedFunction
    symbol_names = 'flow_area cp inlet_massflux axial_power_profile rod_linear_power'
    symbol_values = 'flow_area cp inlet_massflux axial_power_profile rod_linear_power'
    expression = '200 + 0.5 * rod_linear_power / inlet_massflux / flow_area / cp'
  []
[]

[FluidProperties]
  [sodium_uo]
    type = SodiumProperties
  []
[]

[Materials]
  [coolant]
    type = SodiumCoolantChannelMaterial
    inlet_temperature_function = 200
    rod_linear_power = rod_linear_power
    inlet_massflux_function = inlet_massflux
    axial_power_profile_cdf = axial_power_profile_cdf
    pellet_height = 1
    cladding_radius = 0.01
    boundary = right
    wire_wrap_diameter = 0.001
    temperature = temp
    sodium_user_object = sodium_uo
    htc_model = function
    htc_function = 1
    update_temperature = true
    htc_scalar = 0.01
    pin_location = interior
    peclet_limit_behavior = error
    outputs = all
  []
[]

[Executioner]
  type = Transient
  dt = 1
  end_time = 2
[]

[Postprocessors]
  [temp_centerline]
    type = AxisymmetricCenterlineAverageValue
    variable = temp
    boundary = left
    outputs = console
  []
  [temp_avg]
    type = ElementAverageValue
    variable = temp
    outputs = console
  []
  [temp_surf]
    type = SideAverageValue
    variable = temp
    boundary = right
    outputs = console
  []
  [temp_coolant_avg]
    type = ElementAverageValue
    variable = coolant_temperature
  []
  [temp_coolant_exact]
    type = FunctionValuePostprocessor
    function = T_exact
    outputs = none
  []
  [temp_coolant_diff]
    type = DifferencePostprocessor
    value1 = temp_coolant_avg
    value2 = temp_coolant_exact
    outputs = none
  []
  [temp_coolant_max_diff]
    type = TimeExtremeValue
    postprocessor = temp_coolant_diff
    value_type = abs_max
  []
[]

[Outputs]
  csv = true
  file_base = 'heated_interior_out'
[]

(test/tests/metallic_fuel_coolant_wastage/cc_wastage_ht9_eff_full_pin.i)

# This test is to verify the calculation for HT9 Coolant Wastage in a simplified pin mesh (non-AD)

[GlobalParams]
  order = FIRST
  family = LAGRANGE
  energy_per_fission = 3.2e-11  # J/fission
  X_Zr = 0.225
  X_Pu = 0.0
[]

[Problem]
  type = ReferenceResidualProblem
  reference_vector = 'ref'
  extra_tag_vectors = 'ref'
[]

[Mesh]
  coord_type = RZ
  [smeared_pellet_mesh]
    type = FuelPinMeshGenerator
    clad_thickness = 0.381e-03
    pellet_outer_radius = 2.158e-03
    pellet_height = 342.5e-3
    clad_top_gap_height = 479.5e-3
    clad_gap_width = 0.382e-03
    bottom_clad_height = 2.24e-3
    top_clad_height = 2.24e-3
    clad_bot_gap_height = 0.31e-3
    clad_mesh_density = customize
    pellet_mesh_density = customize
    nx_p = 1
    ny_p = 1
    nx_c = 1
    ny_c = 20
    ny_cu = 1
    ny_cl = 1
    pellet_quantity = 1
    elem_type = QUAD4
  []
  patch_size = 20
  patch_update_strategy = auto
  partitioner = centroid
  centroid_partitioner_direction = y
[]

[Variables]
  [temp]
    initial_condition = 298
  []
[]

[Functions]
  [power_history]
    type = PiecewiseLinear
    x = '0 1E6 1E7'
    y = '0 2E4 3E4'
  []
  [pwr_axial_peaking_factors]
    type = ConstantFunction
    value = 1.0
  []
  [pwr_cdf]
    type = PiecewiseLinear
    axis = y
    x = '0 2.55e-3 342.5e-3'
    y = '0 0 1'
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = temp
    extra_vector_tags = 'ref'
  []
  [heat_ie_f]
    type = HeatConductionTimeDerivative
    variable = temp
    extra_vector_tags = 'ref'
    block = pellet
    density_name = 16000
  []
  [heat_ie_c]
    type = HeatConductionTimeDerivative
    variable = temp
    extra_vector_tags = 'ref'
    block = clad
    density_name = 7890
  []
  [heat_source]
    type = FissionRateHeatSource
    variable = temp
    block = pellet
    fission_rate = fission_rate
    extra_vector_tags = 'ref'
  []
[]

[ThermalContact]
  [thermal_contact]
    type = GapHeatTransfer
    variable = temp
    primary = 5
    secondary = 10
    quadrature = true
    gap_conductivity = 61.0
    min_gap = 1e-6
    emissivity_primary = 0
    emissivity_secondary = 0
  []
[]

[FluidProperties]
  [sodium_uo]
    type = SodiumProperties
  []
[]

[BCs]
  [convection]
    type = ConvectiveHeatFluxBC
    variable = temp
    boundary = 2
    T_infinity = coolant_temperature
    heat_transfer_coefficient = coolant_channel_htc
  []
[]

[Materials]
  [coolant]
    type = SodiumCoolantChannelMaterial
    inlet_temperature_function = 648.0
    rod_linear_power = power_history
    inlet_massflux_function = 2300
    axial_power_profile_cdf = pwr_cdf
    pellet_height = 3.425e-01
    cladding_radius = 2.921e-03
    boundary = clad_outside_right
    wire_wrap_diameter = 1.067e-03
    temperature = temp
    sodium_user_object = sodium_uo
    htc_model = BGF
    update_temperature = true
    pin_location = interior
    peclet_limit_behavior = error
    outputs = all
  []
  [fission_rate]
    type = UPuZrFissionRate
    rod_linear_power = power_history
    axial_power_profile = pwr_axial_peaking_factors
    pellet_radius = 2.158e-3
    outputs = all
  []
  [burnup]
    type = UPuZrBurnup
    density = 16000
    outputs = all
  []
  [cc_wastage_thickness]
    type = MetallicFuelCoolantWastage
    clad_material = HT9
    use_effective_method = true
    temperature = temp
    boundary = 2
    outputs = all
  []
  [metal_fuel_thermal]
    type = UPuZrThermal
    block = pellet
    spheat_model = savage
    thcond_model = lanl
    porosity = 0
    temperature = temp
  []
  [clad_thermal]
    type = HT9Thermal
    block = clad
    temperature = temp
  []
[]

[Dampers]
  [limitT]
    type = MaxIncrement
    max_increment = 50
    variable = temp
  []
[]

[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 -ksp_gmres_restart'
  petsc_options_value = 'lu       superlu_dist                  51'
  line_search = 'none'

  l_max_its = 100
  l_tol = 1e-3

  nl_max_its = 50
  nl_rel_tol = 1e-4
  nl_abs_tol = 1e-8

  end_time = 1E7
  dt = 5E5

  [Quadrature]
    order = fifth
    side_order = seventh
  []
[]

[Postprocessors]
  [peak_clad_outer_temp]
    type = NodalExtremeValue
    variable = temp
    value_type = max
    boundary = 2
    outputs = 'console'
  []
  [time_max_clad_outer_temp]
    type = TimeExtremeValue
    postprocessor = peak_clad_outer_temp
    outputs = 'console'
  []
  [max_wastagethickness]
    type = ElementExtremeValue
    value_type = max
    variable = cc_wastage_thickness
    outputs = 'console'
  []
[]

[VectorPostprocessors]
  [cc_wastage_profile]
    type = SideValueSampler
    boundary = 2
    sort_by = y
    variable = cc_wastage_thickness
  []
[]

[Outputs]
  perf_graph = true
  console = true
  [csv_vec]
    type = CSV
    file_base = cc_wastage_ht9_eff_full_pin_profile
    execute_on = final
  []
[]

(test/tests/sodium_coolant_channel/dp16.i)

# This test applies the new coolant channel model to a realistic geometry, e.g. dp16 from EBR-II.

[Problem]
  type = ReferenceResidualProblem
  reference_vector = 'ref'
  extra_tag_vectors = 'ref'
[]

[Mesh]
  coord_type = RZ
  # rod specific parameters
  [smeared_pellet_mesh]
    type = FuelPinMeshGenerator
    clad_thickness = 0.381e-03
    pellet_outer_radius = 2.184e-03
    pellet_height = 3.442e-01
    clad_top_gap_height = 2.949e-01
    clad_gap_width = 3.556e-04
    bottom_clad_height = 2.24e-3 # arbitrary
    top_clad_height = 2.24e-3 # arbitrary
    clad_bot_gap_height = 0.31e-3 # arbitrary
    # meshing parameters
    clad_mesh_density = customize
    pellet_mesh_density = customize
    nx_p = 10
    ny_p = 10
    nx_c = 10
    ny_c = 30
    ny_cu = 3
    ny_cl = 3
    pellet_quantity = 1
  []
  # mesh options
  partitioner = centroid
  centroid_partitioner_direction = y
[]

[DefaultElementQuality]
  failure_type = Warning
[]

[Variables]
  [temp]
    initial_condition = 300
  []
[]

[Kernels]
  [heat]
    type = ADHeatConduction
    variable = temp
    extra_vector_tags = 'ref'
  []
  [heat_ie_fuel]
    type = ADHeatConductionTimeDerivative
    variable = temp
    extra_vector_tags = 'ref'
    block = pellet
    density_name = 15800
  []
  [heat_ie_clad]
    type = ADHeatConductionTimeDerivative
    variable = temp
    extra_vector_tags = 'ref'
    block = clad
    density_name = 7876
  []
  [heat_source]
    type = ADFissionRateHeatSource
    variable = temp
    block = pellet
    fission_rate = fission_rate
    extra_vector_tags = 'ref'
  []
[]

[BCs]
  [convection]
    type = ConvectiveHeatFluxBC
    variable = temp
    boundary = clad_outside_right
    T_infinity = coolant_temperature
    heat_transfer_coefficient = coolant_channel_htc
  []
[]

[AuxVariables]
  [cdf]
  []
[]

[AuxKernels]
  [cdf_aux]
    type = FunctionAux
    variable = cdf
    function = row_4_cdf
  []
[]

[Functions]
  [dp16_power]
    type = PiecewiseLinear
    # min power, weighted avg, max power
    x = '0 1'
    y = '44734 44734'
  []
  [row_4]
    type = PowerPeakingFunction
    fit = EBRII_ROW_4
    pellet_length = 3.442e-01
    pellet_y_start = 2.24e-3
    zero_beyond_top_and_bottom = true
  []
  [row_4_cdf]
    type = PowerPeakingFunction
    fit = EBRII_ROW_4
    pellet_length = 3.442e-01
    pellet_y_start = 2.24e-3
    zero_beyond_top_and_bottom = true
    cdf = true
  []
[]

[ThermalContact]
  [thermal_contact]
    type = GapHeatTransfer
    variable = temp
    primary = 'clad_inside_right'
    secondary = 'pellet_outer_radial_surface'
    quadrature = true
    gap_conductivity = 61.0
    min_gap = 3.556E-04
  []
[]

[FluidProperties]
  [sodium_uo]
    type = SodiumProperties
  []
[]

[Materials]
  [coolant]
    type = SodiumCoolantChannelMaterial
    inlet_temperature_function = 648.0
    rod_linear_power = dp16_power
    inlet_massflux_function = 5262.0
    axial_power_profile_cdf = row_4_cdf
    pellet_height = 3.442e-01
    cladding_radius = 2.921e-03
    boundary = clad_outside_right
    wire_wrap_diameter = 1.067e-03
    temperature = temp
    sodium_user_object = sodium_uo
    htc_model = BGF
    update_temperature = true
    pin_location = interior
    peclet_limit_behavior = error
    outputs = all
  []
  [fission_rate]
    type = ADUPuZrFissionRate
    rod_linear_power = dp16_power
    axial_power_profile = row_4
    pellet_radius = 2.184e-03
    X_Zr = 0.225
    block = pellet
    outputs = all
  []

  [metal_fuel_thermal]
    type = ADUPuZrThermal
    block = pellet
    X_Zr = 0.225
    X_Pu = 0
    spheat_model = savage
    thcond_model = lanl
    porosity = 0
    temperature = temp
  []
  [clad_thermal]
    type = ADHT9Thermal
    block = clad
    temperature = temp
  []
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu       superlu_dist'
  line_search = 'none'

  l_max_its = 60
  l_tol = 8e-3
  nl_max_its = 40
  nl_rel_tol = 5e-4
  nl_abs_tol = 1e-7

  end_time = 1
  dt = .1
[]

[Postprocessors]
  [temp_fuel_avg]
    type = ElementAverageValue
    variable = temp
    block = pellet
  []
  [temp_fuel_max]
    type = ElementExtremeValue
    variable = temp
    block = pellet
  []
  [temp_clad_avg]
    type = ElementAverageValue
    variable = temp
    block = clad
  []
  [temp_clad_max]
    type = ElementExtremeValue
    variable = temp
    block = clad
  []
  [temp_oulet]
    type = ElementExtremeValue
    variable = coolant_temperature
  []
[]

[VectorPostprocessors]
  [cladding]
    type = SideValueSampler
    boundary = clad_outside_right
    sort_by = y
    variable = 'temp coolant_temperature coolant_channel_htc'
  []
  [centerline]
    type = SideValueSampler
    boundary = centerline
    sort_by = y
    variable = 'temp'
  []
[]

[Outputs]
  [out]
    type = CSV
    execute_on = final
  []
[]

(test/tests/sodium_coolant_channel/htc_fftf.i)

# This test is for comparing the heat transfer coefficient for the FFTF model to a hand calculation
# for a pin in an interior location.

[Mesh]
  coord_type = RZ
  [mesh]
    type = GeneratedMeshGenerator
    dim = 2
    ny = 10
    xmax = 0.01
  []
[]

[Problem]
  solve = false
[]

[Functions]
  [axial_power_profile]
    type = PowerPeakingFunction
    pellet_length = 1
    pellet_y_start = 0
    fit = FLAT
    cdf = false
  []
  [axial_power_profile_cdf]
    type = PowerPeakingFunction
    pellet_length = 1
    pellet_y_start = 0
    fit = FLAT
    cdf = true
  []
  [inlet_massflux]
    type = PiecewiseLinear
    x = '0 100'
    y = '1e3 1e4'
  []
  [inlet_temp]
    type = PiecewiseLinear
    x = '0 100'
    y = '200 1000'
  []
  [rod_linear_power]
    type = PiecewiseLinear
    x = '0 1'
    y = '1e9 1e9'
  []
  [cp]
    type = ParsedFunction
    symbol_names = inlet_temp
    symbol_values = inlet_temp
    expression = '1.6582e3 - 8.4790e-1 * inlet_temp + 4.4541e-4 * inlet_temp^2 - 2992.6e3 / inlet_temp^2'
  []
  [thcond]
    type = ParsedFunction
    symbol_names = inlet_temp
    symbol_values = inlet_temp
    expression = '124.67 - 0.11381 * inlet_temp + 5.5226e-5 * inlet_temp^2 - 1.1842e-8 * inlet_temp^3'
  []

  [interior_flow_channel_area]
    type = ParsedFunction
    symbol_names = 'D s P'
    symbol_values = '2e-2 1e-3 2.1e-2'
    expression = 'sqrt(3) / 4 * P^2 - pi / 8 * D^2 -  pi / 8 * s^2'
  []
  [edge_flow_channel_area]
    type = ParsedFunction
    symbol_names = 'D s P'
    symbol_values = '2e-2 1e-3 2.1e-2'
    expression = 'P * (D / 2 + s) - pi / 8 * D^2 -  pi / 8 * s^2'
  []
  [corner_flow_channel_area]
    type = ParsedFunction
    symbol_names = 'D s P'
    symbol_values = '2e-2 1e-3 2.1e-2'
    expression = '1.0 / sqrt(3.0) * (D / 2.0 + s)^2 - pi / 24.0 * D^2 -  pi / 24.0 * s^2'
  []

  [interior_channel_wetted]
    type = ParsedFunction
    symbol_names = 'D s P'
    symbol_values = '2e-2 1e-3 2.1e-2'
    expression = 'P * pi / 2'
  []
  [edge_channel_wetted]
    type = ParsedFunction
    symbol_names = 'D s P'
    symbol_values = '2e-2 1e-3 2.1e-2'
    expression = '(1 + pi / 2) * P'
  []
  [corner_channel_wetted]
    type = ParsedFunction
    symbol_names = 'D s P'
    symbol_values = '2e-2 1e-3 2.1e-2'
    expression = '(D + 2 * s) + pi / 6 * P'
  []

  [flow_area]
    type = ParsedFunction
    symbol_names = 'interior_flow_channel_area edge_flow_channel_area corner_flow_channel_area'
    symbol_values = 'interior_flow_channel_area edge_flow_channel_area corner_flow_channel_area'
    expression = '2 * interior_flow_channel_area'
  []
  [wetted_perimeter]
    type = ParsedFunction
    symbol_names = 'interior_channel_wetted edge_channel_wetted corner_channel_wetted'
    symbol_values = 'interior_channel_wetted edge_channel_wetted corner_channel_wetted'
    expression = '2 * interior_channel_wetted'
  []

  [hydraulic_diameter]
    type = ParsedFunction
    symbol_names = 'flow_area wetted_perimeter'
    symbol_values = 'flow_area wetted_perimeter'
    expression = '4.0 * flow_area / wetted_perimeter'
  []

  [peclet]
    type = ParsedFunction
    symbol_names = 'cp thcond inlet_massflux hydraulic_diameter'
    symbol_values = 'cp thcond inlet_massflux hydraulic_diameter'
    expression = 'inlet_massflux * cp * hydraulic_diameter / thcond'
  []
  [nusselt]
    type = ParsedFunction
    symbol_names = 'pitch diameter peclet'
    symbol_values = '2.1e-2 2e-2    peclet'
    expression = 'p_over_d := pitch / diameter;
             4 + 0.16 * p_over_d^5 + 0.33 * p_over_d^3.8 * (peclet / 100)^0.86'
  []
  [htc_exact]
    type = ParsedFunction
    symbol_names = 'nusselt thcond hydraulic_diameter scalar'
    symbol_values = 'nusselt thcond hydraulic_diameter 0.01'
    expression = 'scalar * nusselt * thcond / hydraulic_diameter'
  []
[]

[FluidProperties]
  [sodium_uo]
    type = SodiumProperties
  []
[]

[Materials]
  [coolant]
    type = SodiumCoolantChannelMaterial
    inlet_temperature_function = inlet_temp
    rod_linear_power = rod_linear_power
    inlet_massflux_function = inlet_massflux
    axial_power_profile_cdf = axial_power_profile_cdf
    pellet_height = 1
    cladding_radius = 0.01
    boundary = right
    wire_wrap_diameter = 0.001
    temperature = 200
    sodium_user_object = sodium_uo
    htc_model = FFTF
    update_temperature = false
    htc_scalar = 0.01
    pin_location = interior
    peclet_limit_behavior = error
    outputs = all
  []
[]

[Executioner]
  type = Transient
  dt = 1
  end_time = 100
[]

[Postprocessors]
  [temp_coolant_avg]
    type = SideAverageValue
    boundary = right
    variable = coolant_temperature
  []

  [htc_avg]
    type = SideAverageValue
    boundary = right
    variable = coolant_channel_htc
  []
  [htc_exact]
    type = FunctionValuePostprocessor
    function = htc_exact
    indirect_dependencies = 'peclet'
  []
  [htc_diff]
    type = DifferencePostprocessor
    value1 = htc_avg
    value2 = htc_exact
    outputs = none
  []
  [htc_max_diff]
    type = TimeExtremeValue
    postprocessor = htc_diff
    value_type = abs_max
  []
  [peclet]
    type = FunctionValuePostprocessor
    function = peclet
  []
[]

[Outputs]
  csv = true
[]

(test/tests/ad_metallic_fuel_coolant_wastage/cc_wastage_ht9_eff_full_pin.i)

# This test is to verify the calculation for HT9 Coolant Wastage in a simplified pin mesh (non-AD)

[GlobalParams]
  order = FIRST
  family = LAGRANGE
  energy_per_fission = 3.2e-11  # J/fission
  X_Zr = 0.225
  X_Pu = 0.0
[]

[Problem]
  type = ReferenceResidualProblem
  reference_vector = 'ref'
  extra_tag_vectors = 'ref'
[]

[Mesh]
  coord_type = RZ
  [smeared_pellet_mesh]
    type = FuelPinMeshGenerator
    clad_thickness = 0.381e-03
    pellet_outer_radius = 2.158e-03
    pellet_height = 342.5e-3
    clad_top_gap_height = 479.5e-3
    clad_gap_width = 0.382e-03
    bottom_clad_height = 2.24e-3
    top_clad_height = 2.24e-3
    clad_bot_gap_height = 0.31e-3
    clad_mesh_density = customize
    pellet_mesh_density = customize
    nx_p = 1
    ny_p = 1
    nx_c = 1
    ny_c = 20
    ny_cu = 1
    ny_cl = 1
    pellet_quantity = 1
    elem_type = QUAD4
  []
  patch_size = 20
  patch_update_strategy = auto
  partitioner = centroid
  centroid_partitioner_direction = y
[]

[Variables]
  [temp]
    initial_condition = 298
  []
[]

[Functions]
  [power_history]
    type = PiecewiseLinear
    x = '0 1E6 1E7'
    y = '0 2E4 3E4'
  []
  [pwr_axial_peaking_factors]
    type = ConstantFunction
    value = 1.0
  []
  [pwr_cdf]
    type = PiecewiseLinear
    axis = y
    x = '0 2.55e-3 342.5e-3'
    y = '0 0 1'
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = temp
    extra_vector_tags = 'ref'
  []
  [heat_ie_f]
    type = HeatConductionTimeDerivative
    variable = temp
    extra_vector_tags = 'ref'
    block = pellet
    density_name = 16000
  []
  [heat_ie_c]
    type = HeatConductionTimeDerivative
    variable = temp
    extra_vector_tags = 'ref'
    block = clad
    density_name = 7890
  []
  [heat_source]
    type = FissionRateHeatSource
    variable = temp
    block = pellet
    fission_rate = fission_rate
    extra_vector_tags = 'ref'
  []
[]

[ThermalContact]
  [thermal_contact]
    type = GapHeatTransfer
    variable = temp
    primary = 5
    secondary = 10
    quadrature = true
    gap_conductivity = 61.0
    min_gap = 1e-6
    emissivity_primary = 0
    emissivity_secondary = 0
  []
[]

[FluidProperties]
  [sodium_uo]
    type = SodiumProperties
  []
[]

[BCs]
  [convection]
    type = ConvectiveHeatFluxBC
    variable = temp
    boundary = 2
    T_infinity = coolant_temperature
    heat_transfer_coefficient = coolant_channel_htc
  []
[]

[Materials]
  [coolant]
    type = SodiumCoolantChannelMaterial
    inlet_temperature_function = 648.0
    rod_linear_power = power_history
    inlet_massflux_function = 2300
    axial_power_profile_cdf = pwr_cdf
    pellet_height = 3.425e-01
    cladding_radius = 2.921e-03
    boundary = clad_outside_right
    wire_wrap_diameter = 1.067e-03
    temperature = temp
    sodium_user_object = sodium_uo
    htc_model = BGF
    update_temperature = true
    pin_location = interior
    peclet_limit_behavior = error
    outputs = all
  []
  [fission_rate]
    type = UPuZrFissionRate
    rod_linear_power = power_history
    axial_power_profile = pwr_axial_peaking_factors
    pellet_radius = 2.158e-3
    outputs = all
  []
  [burnup]
    type = UPuZrBurnup
    density = 16000
    outputs = all
  []
  [cc_wastage_thickness]
    type = MetallicFuelCoolantWastage
    clad_material = HT9
    use_effective_method = true
    temperature = temp
    boundary = 2
    outputs = all
  []
  [metal_fuel_thermal]
    type = UPuZrThermal
    block = pellet
    spheat_model = savage
    thcond_model = lanl
    porosity = 0
    temperature = temp
  []
  [clad_thermal]
    type = HT9Thermal
    block = clad
    temperature = temp
  []
[]

[Dampers]
  [limitT]
    type = MaxIncrement
    max_increment = 50
    variable = temp
  []
[]

[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 -ksp_gmres_restart'
  petsc_options_value = 'lu       superlu_dist                  51'
  line_search = 'none'

  l_max_its = 100
  l_tol = 1e-3

  nl_max_its = 50
  nl_rel_tol = 1e-4
  nl_abs_tol = 1e-8

  end_time = 1E7
  dt = 5E5

  [Quadrature]
    order = fifth
    side_order = seventh
  []
[]

[Postprocessors]
  [peak_clad_outer_temp]
    type = NodalExtremeValue
    variable = temp
    value_type = max
    boundary = 2
    outputs = 'console'
  []
  [time_max_clad_outer_temp]
    type = TimeExtremeValue
    postprocessor = peak_clad_outer_temp
    outputs = 'console'
  []
  [max_wastagethickness]
    type = ElementExtremeValue
    value_type = max
    variable = cc_wastage_thickness
    outputs = 'console'
  []
[]

[VectorPostprocessors]
  [cc_wastage_profile]
    type = SideValueSampler
    boundary = 2
    sort_by = y
    variable = cc_wastage_thickness
  []
[]

[Outputs]
  perf_graph = true
  console = true
  [csv_vec]
    type = CSV
    file_base = cc_wastage_ht9_eff_full_pin_profile
    execute_on = final
  []
[]

(test/tests/sodium_coolant_channel/htc_function.i)

# This test is for comparing the heat transfer coefficient defined as a function to a hand calculation

[Mesh]
  coord_type = RZ
  [mesh]
    type = GeneratedMeshGenerator
    dim = 2
    xmax = 0.5
  []
[]

[Variables]
  [temp]
    initial_condition = 100
  []
[]

[Kernels]
  [heat]
    type = Diffusion
    variable = temp
  []
  [heat_dt]
    type = TimeDerivative
    variable = temp
  []
[]

[BCs]
  [temp]
    type = ConvectiveHeatFluxBC
    T_infinity = coolant_temperature
    heat_transfer_coefficient = coolant_channel_htc
    variable = temp
    boundary = 'right'
  []
[]

[FluidProperties/sodium]
  type = SodiumProperties
[]

[Functions]
  [htc_fcn]
    type = PiecewiseLinear
    x = '0 10'
    y = '0.5 0.25'
  []
  [areal_heat_loss]
    type = ParsedFunction
    symbol_names = 'temp_avg radius'
    symbol_values = 'temp_avg 0.5'
    expression = 'pi * radius^2 * (100 - temp_avg)'
  []
  [surface_net_heat_flux]
    type = ParsedFunction
    symbol_names = 'flux_sum radius'
    symbol_values = 'flux_sum 0.5'
    expression = '2 * pi * radius * flux_sum'
  []
  [diff]
    type = ParsedFunction
    symbol_names = 'areal_heat_loss surface_net_heat_flux'
    symbol_values = 'areal_heat_loss surface_net_heat_flux'
    expression = 'areal_heat_loss - surface_net_heat_flux'
  []
[]

[Materials]
  [coolant]
    type = SodiumCoolantChannelMaterial
    inlet_temperature_function = 200
    rod_linear_power = 0
    inlet_massflux_function = 0
    axial_power_profile_cdf = 0
    pellet_height = 1
    cladding_radius = 1
    boundary = right
    wire_wrap_diameter = 0
    temperature = temp
    sodium_user_object = sodium
    htc_model = function
    htc_function = htc_fcn
    update_temperature = false
    htc_scalar = 0.05
    outputs = all
  []
[]

[Executioner]
  type = Transient

  end_time = 10
[]

[Postprocessors]
  [temp_centerline]
    type = AxisymmetricCenterlineAverageValue
    variable = temp
    boundary = left
    outputs = console
  []
  [temp_avg]
    type = ElementAverageValue
    variable = temp
    outputs = console
  []
  [temp_surf]
    type = SideAverageValue
    variable = temp
    boundary = right
    outputs = console
  []
  [temp_coolant_avg]
    type = ElementAverageValue
    variable = coolant_temperature
    outputs = console
  []
  [heat_flux_avg]
    type = SideAverageValue
    variable = heat_flux
    boundary = right
    outputs = console
  []
  [flux_sum]
    type = CumulativeValuePostprocessor
    postprocessor = heat_flux_avg
    outputs = console
  []
  [diff]
    type = FunctionValuePostprocessor
    function = diff
    outputs = none
  []
  [max_diff]
    type = TimeExtremeValue
    postprocessor = diff
  []
[]

[Outputs]
  csv = true
[]

(test/tests/sodium_coolant_channel/htc_fftf_corner.i)

# This test is for comparing the heat transfer coefficient for the FFTF model to a hand calculation
# for a pin in a corner location.

[Mesh]
  coord_type = RZ
  [mesh]
    type = GeneratedMeshGenerator
    dim = 2
    ny = 10
    xmax = 0.01
  []
[]

[Problem]
  solve = false
[]

[Functions]
  [axial_power_profile]
    type = PowerPeakingFunction
    pellet_length = 1
    pellet_y_start = 0
    fit = FLAT
    cdf = false
  []
  [axial_power_profile_cdf]
    type = PowerPeakingFunction
    pellet_length = 1
    pellet_y_start = 0
    fit = FLAT
    cdf = true
  []
  [inlet_massflux]
    type = PiecewiseLinear
    x = '0 100'
    y = '1e3 1e4'
  []
  [inlet_temp]
    type = PiecewiseLinear
    x = '0 100'
    y = '200 1000'
  []
  [rod_linear_power]
    type = PiecewiseLinear
    x = '0 1'
    y = '1e9 1e9'
  []
  [cp]
    type = ParsedFunction
    symbol_names = inlet_temp
    symbol_values = inlet_temp
    expression = '1.6582e3 - 8.4790e-1 * inlet_temp + 4.4541e-4 * inlet_temp^2 - 2992.6e3 / inlet_temp^2'
  []
  [thcond]
    type = ParsedFunction
    symbol_names = inlet_temp
    symbol_values = inlet_temp
    expression = '124.67 - 0.11381 * inlet_temp + 5.5226e-5 * inlet_temp^2 - 1.1842e-8 * inlet_temp^3'
  []

  [interior_flow_channel_area]
    type = ParsedFunction
    symbol_names = 'D s P'
    symbol_values = '2e-2 1e-3 2.1e-2'
    expression = 'sqrt(3) / 4 * P^2 - pi / 8 * D^2 -  pi / 8 * s^2'
  []
  [edge_flow_channel_area]
    type = ParsedFunction
    symbol_names = 'D s P'
    symbol_values = '2e-2 1e-3 2.1e-2'
    expression = 'P * (D / 2 + s) - pi / 8 * D^2 -  pi / 8 * s^2'
  []
  [corner_flow_channel_area]
    type = ParsedFunction
    symbol_names = 'D s P'
    symbol_values = '2e-2 1e-3 2.1e-2'
    expression = '1.0 / sqrt(3.0) * (D / 2.0 + s)^2 - pi / 24.0 * D^2 -  pi / 24.0 * s^2'
  []

  [interior_channel_wetted]
    type = ParsedFunction
    symbol_names = 'D s P'
    symbol_values = '2e-2 1e-3 2.1e-2'
    expression = 'P * pi / 2'
  []
  [edge_channel_wetted]
    type = ParsedFunction
    symbol_names = 'D s P'
    symbol_values = '2e-2 1e-3 2.1e-2'
    expression = '(1 + pi / 2) * P'
  []
  [corner_channel_wetted]
    type = ParsedFunction
    symbol_names = 'D s P'
    symbol_values = '2e-2 1e-3 2.1e-2'
    expression = '(D + 2 * s) + pi / 6 * P'
  []

  [flow_area]
    type = ParsedFunction
    symbol_names = 'interior_flow_channel_area edge_flow_channel_area corner_flow_channel_area'
    symbol_values = 'interior_flow_channel_area edge_flow_channel_area corner_flow_channel_area'
    expression = 'interior_flow_channel_area * 2 / 3 + edge_flow_channel_area + corner_flow_channel_area'
  []
  [wetted_perimeter]
    type = ParsedFunction
    symbol_names = 'interior_channel_wetted edge_channel_wetted corner_channel_wetted'
    symbol_values = 'interior_channel_wetted edge_channel_wetted corner_channel_wetted'
    expression = 'interior_channel_wetted * 2 / 3 + edge_channel_wetted + corner_channel_wetted'
  []

  [hydraulic_diameter]
    type = ParsedFunction
    symbol_names = 'flow_area wetted_perimeter'
    symbol_values = 'flow_area wetted_perimeter'
    expression = '4.0 * flow_area / wetted_perimeter'
  []

  [peclet]
    type = ParsedFunction
    symbol_names = 'cp thcond inlet_massflux hydraulic_diameter'
    symbol_values = 'cp thcond inlet_massflux hydraulic_diameter'
    expression = 'inlet_massflux * cp * hydraulic_diameter / thcond'
  []
  [nusselt]
    type = ParsedFunction
    symbol_names = 'pitch diameter peclet'
    symbol_values = '2.1e-2 2e-2    peclet'
    expression = 'p_over_d := pitch / diameter;
             4 + 0.16 * p_over_d^5 + 0.33 * p_over_d^3.8 * (peclet / 100)^0.86'
  []
  [htc_exact]
    type = ParsedFunction
    symbol_names = 'nusselt thcond hydraulic_diameter scalar'
    symbol_values = 'nusselt thcond hydraulic_diameter 0.01'
    expression = 'scalar * nusselt * thcond / hydraulic_diameter'
  []
[]

[FluidProperties]
  [sodium_uo]
    type = SodiumProperties
  []
[]

[Materials]
  [coolant]
    type = SodiumCoolantChannelMaterial
    inlet_temperature_function = inlet_temp
    rod_linear_power = rod_linear_power
    inlet_massflux_function = inlet_massflux
    axial_power_profile_cdf = axial_power_profile_cdf
    pellet_height = 1
    cladding_radius = 0.01
    boundary = right
    wire_wrap_diameter = 0.001
    temperature = 200
    sodium_user_object = sodium_uo
    htc_model = FFTF
    update_temperature = false
    htc_scalar = 0.01
    pin_location = corner
    peclet_limit_behavior = nothing
    outputs = all
  []
[]

[Executioner]
  type = Transient
  dt = 1
  end_time = 100
[]

[Postprocessors]
  [temp_coolant_avg]
    type = SideAverageValue
    boundary = right
    variable = coolant_temperature
  []

  [htc_avg]
    type = SideAverageValue
    boundary = right
    variable = coolant_channel_htc
  []
  [htc_exact]
    type = FunctionValuePostprocessor
    function = htc_exact
    indirect_dependencies = 'peclet'
  []
  [htc_diff]
    type = DifferencePostprocessor
    value1 = htc_avg
    value2 = htc_exact
    outputs = none
  []
  [htc_max_diff]
    type = TimeExtremeValue
    postprocessor = htc_diff
    value_type = abs_max
  []
  [peclet]
    type = FunctionValuePostprocessor
    function = peclet
  []
[]

[Outputs]
  csv = true
[]

(test/tests/sodium_coolant_channel/htc_bgf.i)

# This test is for comparing the heat transfer coefficient for the BGF model to a hand calculation.

[Mesh]
  coord_type = RZ
  [mesh]
    type = GeneratedMeshGenerator
    dim = 2
    ny = 10
    xmax = 0.01
  []
[]

[Problem]
  solve = false
[]

[Functions]
  [axial_power_profile]
    type = PowerPeakingFunction
    pellet_length = 1
    pellet_y_start = 0
    fit = FLAT
    cdf = false
  []
  [axial_power_profile_cdf]
    type = PowerPeakingFunction
    pellet_length = 1
    pellet_y_start = 0
    fit = FLAT
    cdf = true
  []
  [inlet_massflux]
    type = PiecewiseLinear
    x = '0 100'
    y = '1e3 1e4'
  []
  [inlet_temp]
    type = PiecewiseLinear
    x = '0 100'
    y = '200 1000'
  []
  [rod_linear_power]
    type = PiecewiseLinear
    x = '0 1'
    y = '1e9 1e9'
  []
  [cp]
    type = ParsedFunction
    symbol_names = inlet_temp
    symbol_values = inlet_temp
    expression = '1.6582e3 - 8.4790e-1 * inlet_temp + 4.4541e-4 * inlet_temp^2 - 2992.6e3 / inlet_temp^2'
  []
  [thcond]
    type = ParsedFunction
    symbol_names = inlet_temp
    symbol_values = inlet_temp
    expression = '124.67 - 0.11381 * inlet_temp + 5.5226e-5 * inlet_temp^2 - 1.1842e-8 * inlet_temp^3'
  []

  [interior_flow_channel_area]
    type = ParsedFunction
    symbol_names = 'D s P'
    symbol_values = '2e-2 1e-3 2.1e-2'
    expression = 'sqrt(3) / 4 * P^2 - pi / 8 * D^2 -  pi / 8 * s^2'
  []
  [edge_flow_channel_area]
    type = ParsedFunction
    symbol_names = 'D s P'
    symbol_values = '2e-2 1e-3 2.1e-2'
    expression = 'P * (D / 2 + s) - pi / 8 * D^2 -  pi / 8 * s^2'
  []
  [corner_flow_channel_area]
    type = ParsedFunction
    symbol_names = 'D s P'
    symbol_values = '2e-2 1e-3 2.1e-2'
    expression = '1.0 / sqrt(3.0) * (D / 2.0 + s)^2 - pi / 24.0 * D^2 -  pi / 24.0 * s^2'
  []

  [interior_channel_wetted]
    type = ParsedFunction
    symbol_names = 'D s P'
    symbol_values = '2e-2 1e-3 2.1e-2'
    expression = 'P * pi / 2'
  []
  [edge_channel_wetted]
    type = ParsedFunction
    symbol_names = 'D s P'
    symbol_values = '2e-2 1e-3 2.1e-2'
    expression = '(1 + pi / 2) * P'
  []
  [corner_channel_wetted]
    type = ParsedFunction
    symbol_names = 'D s P'
    symbol_values = '2e-2 1e-3 2.1e-2'
    expression = '(D + 2 * s) + pi / 6 * P'
  []

  [flow_area]
    type = ParsedFunction
    symbol_names = 'interior_flow_channel_area edge_flow_channel_area corner_flow_channel_area'
    symbol_values = 'interior_flow_channel_area edge_flow_channel_area corner_flow_channel_area'
    expression = '2 * interior_flow_channel_area'
  []
  [wetted_perimeter]
    type = ParsedFunction
    symbol_names = 'interior_channel_wetted edge_channel_wetted corner_channel_wetted'
    symbol_values = 'interior_channel_wetted edge_channel_wetted corner_channel_wetted'
    expression = '2 * interior_channel_wetted'
  []

  [hydraulic_diameter]
    type = ParsedFunction
    symbol_names = 'flow_area wetted_perimeter'
    symbol_values = 'flow_area wetted_perimeter'
    expression = '4.0 * flow_area / wetted_perimeter'
  []

  [peclet]
    type = ParsedFunction
    symbol_names = 'cp thcond inlet_massflux hydraulic_diameter'
    symbol_values = 'cp thcond inlet_massflux hydraulic_diameter'
    expression = 'inlet_massflux * cp * hydraulic_diameter / thcond'
  []
  [nusselt]
    type = ParsedFunction
    symbol_names = 'pitch diameter peclet'
    symbol_values = '2.1e-2 2e-2    peclet'
    expression = 'p_over_d := pitch / diameter;
             nu := 24.15 * log10(-8.12 + 12.72 * p_over_d - 3.65 * p_over_d^2);
             if (peclet > 200,
                 nu + 0.0174 * (1 - exp(-6 * (p_over_d - 1))) * (peclet - 200)^(0.9),
                 nu)'
  []
  [htc_exact]
    type = ParsedFunction
    symbol_names = 'nusselt thcond hydraulic_diameter scalar'
    symbol_values = 'nusselt thcond hydraulic_diameter 0.01'
    expression = 'scalar * nusselt * thcond / hydraulic_diameter'
  []
[]

[FluidProperties]
  [sodium_uo]
    type = SodiumProperties
  []
[]

[Materials]
  [coolant]
    type = SodiumCoolantChannelMaterial
    inlet_temperature_function = inlet_temp
    rod_linear_power = rod_linear_power
    inlet_massflux_function = inlet_massflux
    axial_power_profile_cdf = axial_power_profile_cdf
    pellet_height = 1
    cladding_radius = 0.01
    boundary = right
    wire_wrap_diameter = 0.001
    temperature = 200
    sodium_user_object = sodium_uo
    htc_model = BGF
    update_temperature = false
    htc_scalar = 0.01
    pin_location = interior
    peclet_limit_behavior = error
    outputs = all
  []
[]

[Executioner]
  type = Transient
  dt = 1
  end_time = 100
[]

[Postprocessors]
  [temp_coolant_avg]
    type = SideAverageValue
    boundary = right
    variable = coolant_temperature
  []

  [htc_avg]
    type = SideAverageValue
    boundary = right
    variable = coolant_channel_htc
  []
  [htc_exact]
    type = FunctionValuePostprocessor
    function = htc_exact
    indirect_dependencies = 'peclet'
  []
  [htc_diff]
    type = DifferencePostprocessor
    value1 = htc_avg
    value2 = htc_exact
    outputs = none
  []
  [htc_max_diff]
    type = TimeExtremeValue
    postprocessor = htc_diff
    value_type = abs_max
  []
  [peclet]
    type = FunctionValuePostprocessor
    function = peclet
  []
[]

[Outputs]
  csv = true
[]

(test/tests/sodium_coolant_channel/dp11.i)

# This test applies the new coolant channel model to a realistic geometry, e.g. dp11 from EBR-II.
# It directly adopts geometry parameters from Mesh Generator through MeshMetaDataInterface

[GlobalParams]
  order = FIRST
  family = LAGRANGE
  energy_per_fission = 3.2e-11 # J/fission
[]

[Problem]
  type = ReferenceResidualProblem
  extra_tag_vectors = 'ref'
  reference_vector = 'ref'
[]

[Mesh]
  coord_type = RZ
  [gen]
    type = FIPDRodletMeshGenerator
    fipd_geom_file = ../fipd_rodlet_mesh_generator/fipd_pin_design/DP11_design.csv
    gap_bottom_length = 0.31e-3 # arbitrary
    cladding_bottom_plug_length = 2.24e-3 # arbitrary
    cladding_top_plug_length = 2.24e-3 # arbitrary
    cladding_sidewall_radial_elements = 4
    cladding_sidewall_axial_element_numbers = '2 20 20'
    cladding_top_plug_radial_elements = 4
    cladding_top_plug_axial_elements = 2
    cladding_bottom_plug_radial_elements = 4
    cladding_bottom_plug_axial_elements = 2
    fuel_radial_elements = 4
    fuel_axial_element_intervals = '0 1'
    fuel_axial_element_numbers = '20'
    use_default_cladding_sidewall_axial_element_intervals = true
    elem_type = QUAD4
  []
[]

[Variables]
  [temp]
    initial_condition = 298
  []
[]

[Functions]
  [power_history]
    type = PiecewiseLinear
    x = '0 3000'
    y = '0 32500'
  []
  [flow_rate_history]
    type = ConstantFunction
    value = 2255
  []
  [pwr_axial_peaking_factors]
    type = PiecewiseBilinear
    data_file = fipd_csv/peakingfactor_power_DP11.csv
    axis = 1
  []
  [ppf_cdf]
    type = PiecewiseBilinear
    data_file = fipd_csv/peakingfactor_power_cdf_DP11.csv
    axis = 1
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = temp
    extra_vector_tags = 'ref'
  []
  [heat_ie_f]
    type = HeatConductionTimeDerivative
    variable = temp
    block = fuel
    density_name = 16000
    extra_vector_tags = 'ref'
  []
  [heat_ie_c]
    type = HeatConductionTimeDerivative
    variable = temp
    block = cladding
    density_name = 7890
    extra_vector_tags = 'ref'
  []
  [heat_source]
    type = FissionRateHeatSource
    variable = temp
    block = fuel
    fission_rate = fission_rate
    extra_vector_tags = 'ref'
  []
[]

[ThermalContact]
  [thermal_contact]
    type = GapHeatTransfer
    variable = temp
    primary = cladding_inside_right
    secondary = fuel_outer_radial_surface
    quadrature = true
    gap_conductivity = 61.0
    min_gap = 1e-6
  []
[]

[BCs]
  [convection]
    type = ConvectiveHeatFluxBC
    variable = temp
    boundary = cladding_outside_right
    T_infinity = coolant_temperature
    heat_transfer_coefficient = coolant_channel_htc
  []
[]

[FluidProperties]
  [sodium_uo]
    type = SodiumProperties
  []
[]

[Materials]
  [coolant]
    type = SodiumCoolantChannelMaterial
    inlet_temperature_function = 648.0
    rod_linear_power = power_history
    inlet_massflux_function = flow_rate_history
    axial_power_profile_cdf = ppf_cdf
    use_metadata = true
    mesh_generator = gen
    boundary = cladding_outside_right
    temperature = temp
    sodium_user_object = sodium_uo
    htc_model = BGF
    update_temperature = true
    pin_location = interior
    peclet_limit_behavior = error
    outputs = all
  []
  [fission_rate]
    type = UPuZrFissionRate
    X_Zr = 0.225
    X_Pu_function = 0
    rod_linear_power = power_history
    axial_power_profile = pwr_axial_peaking_factors
    use_metadata = true
    mesh_generator = gen
    outputs = all
  []
  [metal_fuel_thermal]
    type = UPuZrThermal
    block = fuel
    X_Zr = 0.225
    X_Pu = 0
    spheat_model = savage
    thcond_model = lanl
    porosity = 0
    temperature = temp
  []
  [clad_thermal]
    type = HT9Thermal
    block = cladding
    temperature = temp
  []
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu       superlu_dist'
  line_search = 'none'
  dt = 500
  num_steps = 6
[]

[Postprocessors]
  [temp_fuel_avg]
    type = ElementAverageValue
    variable = temp
    block = fuel
  []
  [temp_fuel_max]
    type = ElementExtremeValue
    variable = temp
    block = fuel
  []
  [temp_clad_avg]
    type = ElementAverageValue
    variable = temp
    block = cladding
  []
  [temp_clad_max]
    type = ElementExtremeValue
    variable = temp
    block = cladding
  []
  [temp_oulet]
    type = ElementExtremeValue
    variable = coolant_temperature
  []
[]

[Outputs]
  csv = true
[]

(assessment/metallic_fuel/FBTA/analysis/steady_state/AK181/181193/IFR1_181193.i)

# IFR-1 Pin 181193
# Inspired by BISON IFR-1 Assessment Case and BISON X441 Assessment Case

exp_id = AK181
pin_id = 181193
fipd_submodule_dir = '../../../../../../../fipd-bison-integration-data/'

cladding_ir = '${fparse 0.226*0.5*0.0254}'
cladding_thickness = '${fparse 0.022*0.0254}'
fuel_radius = ${fparse 0.196*0.5*0.0254}

# Fuel length is 6.5 + 36.0 + 6.5 = 49.0 inch
# Which is 0.13265 0.73470 0.13265

reflector_frac = 0.13265
active_frac = 0.73470
transition_frac = 0.001
fuel_intervals = '0 ${fparse reflector_frac-transition_frac} ${reflector_frac} ${fparse reflector_frac+active_frac} ${fparse reflector_frac+active_frac+transition_frac} 1.0'

reflector_height = '${fparse 6.5*0.0254}'
active_fuel_height = '${fparse 36.0*0.0254}'
transition_height = '${fparse reflector_height/reflector_frac*transition_frac}'

clad_plug_thick = 2.24e-3
bot_gap_thick = 0.31e-3

bottom_blanket_start = '${fparse clad_plug_thick+bot_gap_thick}'
bottom_transition_layer_start = '${fparse bottom_blanket_start+reflector_height-transition_height}'
active_fuel_start = '${fparse bottom_blanket_start+reflector_height}'
active_fuel_end = '${fparse active_fuel_start+active_fuel_height}'
top_transition_layer_end = '${fparse active_fuel_end+transition_height}'
top_blanket_end = '${fparse active_fuel_end+reflector_height}'
gas_plenum_height = '${fparse 39.0*0.0254}'
sodium_cap_height = '${fparse 1.0*0.0254}'

time_last = 53611920
max_dt = 1e5

magic_factor = 5e-1 #1.00e-01

A_U = 0.23803 # [kg/mol]
A_Pu = 0.240 # [kg/mol]
A_Zr = 0.091224 # [kg/mol]
W_Pu = 0.19
W_Zr = 0.1
W_U = '${fparse 1 - W_Pu - W_Zr}'
A_tot = '${fparse 1 / (W_U / A_U + W_Pu / A_Pu + W_Zr / A_Zr)}'
X_Pu = '${fparse W_Pu / A_Pu * A_tot}'
fuel_pu = ${X_Pu}
initial_X_Zr = '${fparse W_Zr / A_Zr * A_tot}'

fuel_density = 15.73e3

alpha_start = 877
alpha_end = 936
bubble_concentration = 1e15

cladding_block = 'cladding'

[GlobalParams]
  density = ${fuel_density}
  order = FIRST
  family = LAGRANGE
  energy_per_fission = 3.2e-11  # J/fission
  volumetric_locking_correction = false
  displacements = 'disp_x disp_y'
  alpha_transition_end = ${alpha_end}
  alpha_transition_start = ${alpha_start}
[]

[Problem]
  type = ReferenceResidualProblem
  extra_tag_vectors = 'ref'
  reference_vector = 'ref'
  group_variables = 'disp_x disp_y'
  converge_on = 'disp_x disp_y temp'
[]

[Mesh]
  [gen]
    type = FIPDRodletMeshGenerator
    fipd_geom_file = ${raw ' ${fipd_submodule_dir} / ${exp_id} / ${pin_id} / ${pin_id} _design.csv'}

    gap_bottom_length = ${bot_gap_thick}
    cladding_bottom_plug_length = ${clad_plug_thick}
    cladding_top_plug_length = ${clad_plug_thick}

    cladding_sidewall_radial_elements = 10
    cladding_sidewall_axial_element_numbers = '2 400 400'
    cladding_top_plug_radial_elements = 10
    cladding_top_plug_axial_elements = 5
    cladding_bottom_plug_axial_elements = 5
    fuel_radial_elements = 10
    fuel_axial_element_intervals = ${fuel_intervals}
    fuel_axial_element_numbers = '30 1 400 1 30'
    use_default_cladding_sidewall_axial_element_intervals = true
    elem_type = QUAD4

    make_stand = true
    make_cap = true
    cap_axial_elements = 15
    stand_axial_elements = 15
  []
  # As RodletMeshGenerator does not support axial blankets
  # We need to define them ourselves
  [upper_blanket]
    type = ParsedSubdomainMeshGenerator
    input = gen
    excluded_subdomains = 'cladding cap stand'
    combinatorial_geometry = 'y>=y0'
    constant_names = 'y0'
    constant_expressions = '${top_transition_layer_end}'
    block_id = 11
    block_name = 'upper_blanket'
  []
  [lower_blanket]
    type = ParsedSubdomainMeshGenerator
    input = upper_blanket
    excluded_subdomains = 'cladding cap stand upper_blanket'
    combinatorial_geometry = 'y<=y0'
    constant_names = 'y0'
    constant_expressions = '${bottom_transition_layer_start}'
    block_id = 12
    block_name = 'lower_blanket'
  []
  [upper_transition]
    type = ParsedSubdomainMeshGenerator
    input = lower_blanket
    excluded_subdomains = 'cladding cap stand upper_blanket'
    combinatorial_geometry = 'y>=y0'
    constant_names = 'y0'
    constant_expressions = '${active_fuel_end}'
    block_id = 13
    block_name = 'upper_transition'
  []
  [lower_transition]
    type = ParsedSubdomainMeshGenerator
    input = upper_transition
    excluded_subdomains = 'cladding cap stand lower_blanket'
    combinatorial_geometry = 'y<=y0'
    constant_names = 'y0'
    constant_expressions = '${active_fuel_start}'
    block_id = 14
    block_name = 'lower_transition'
  []

  [sodium_height]
    type = SideSetsFromBoundingBoxGenerator
    input = lower_transition
    bottom_left = '0 0 0'
    top_right = '${fparse cladding_ir + cladding_thickness} ${top_blanket_end} 0'
    included_boundaries = 'cladding_inside_right'
    boundary_new = '1005'
  []
  [gas_height]
    type = SideSetsFromBoundingBoxGenerator
    input = sodium_height
    bottom_left = '0 ${top_blanket_end} 0'
    top_right = '${fparse cladding_ir + cladding_thickness} ${fparse top_blanket_end + sodium_cap_height + gas_plenum_height + clad_plug_thick} 0'
    included_boundaries = 'cladding_inside_right'
    boundary_new = '1006'
  []
  [sodium_plenum_rename]
    type = RenameBoundaryGenerator
    input = gas_height
    old_boundary = '1005 1006'
    new_boundary = 'sodium_height gas_height'
  []

  patch_size = 40
  patch_update_strategy = always
  partitioner = centroid
  centroid_partitioner_direction = y
  coord_type = RZ
[]

[Variables]
  [temp]
    initial_condition = 298
    block = 'fuel cladding cap stand upper_blanket lower_blanket upper_transition lower_transition'
  []
  [disp_x]
    block = 'fuel cladding cap stand upper_blanket lower_blanket upper_transition lower_transition'
  []
  [disp_y]
    block = 'fuel cladding cap stand upper_blanket lower_blanket upper_transition lower_transition'
  []
[]

[Functions]
  # We do not have SE2P data for IFR-1
  # [clad_od_temp]
  #   type =  FIPDAxialProfileFunction
  #   data_file = ${raw 'fipd /clad_od_temp_history_ ${pin_id} .csv'}

  #   bottom_clad_height = ${clad_plug_thick}
  #   clad_bottom_gap_height = ${fparse bot_gap_thick+reflector_height}
  #   fuel_slug_length = ${active_fuel_height}
  # []
  [coolant_flux_function]
    type = PiecewiseLinear
    data_file = ${raw ' ${fipd_submodule_dir} / ${exp_id} / ${pin_id} / flow_history_ ${pin_id} .csv'}
  []
  [coolant_pressure_function]
    # Constant coolant inlet pressure (Pa) taken from [Cabell, 1980].
    # From IFR-1 Assessment Case
    type = ConstantFunction
    value = 1018327
  []
  [coolant_T_in_function]
    # Sodium coolant inlet temperature (K). See [Porter and Tsai, 2011]
    # We would like to always use 633.15 K
    type = ConstantFunction
    value = 633.15
  []
  [ab_sodium_vol]
    type = MeshPropertyFunction
    mesh_generator = gen
    mesh_property_name = sodium_volume
    scale_factor = -1.0
  []
  [sodium_volume]
    type = ParsedFunction
    symbol_names = 'porosity_sodium_logging_avg volume_fuel raw_sodium_vol temp_sodium_avg'
    symbol_values = 'porosity_sodium_logging_avg volume_fuel ab_sodium_vol temp_sodium_avg'
    expression = 'raw_sodium_vol * 954 / (1102 - 0.23 * temp_sodium_avg) - volume_fuel * porosity_sodium_logging_avg'
  []
  [power_history]
    type = PiecewiseLinear
    data_file = ${raw ' ${fipd_submodule_dir} / ${exp_id} / ${pin_id} / power_history_ ${pin_id} .csv'}
  []
  [power_history_avg]
    type = PiecewiseLinear
    data_file = ${raw ' ${fipd_submodule_dir} / ${exp_id} / ${pin_id} / power_history_ ${pin_id} .csv'}
    scale_factor = 0.811078523
  []
  [pwr_axial_peaking_factors]
    type = FIPDAxialProfileFunction
    data_file = ${raw ' ${fipd_submodule_dir} / ${exp_id} / ${pin_id} / peakingfactor_power_relative_ ${pin_id} .csv'}
    zero_ends = true
    data_shift_type = peaking

    bottom_clad_height = ${clad_plug_thick}
    clad_bottom_gap_height = ${fparse bot_gap_thick+reflector_height}
    fuel_slug_length = ${active_fuel_height}
  []
  [pwr_axial_peaking_factors_cdf]
    type = FIPDAxialProfileFunction
    data_file = ${raw ' ${fipd_submodule_dir} / ${exp_id} / ${pin_id} / peakingfactor_power_cdf_relative_ ${pin_id} .csv'}
    data_shift_type = peaking

    bottom_clad_height = ${clad_plug_thick}
    clad_bottom_gap_height = ${fparse bot_gap_thick+reflector_height}
    fuel_slug_length = ${active_fuel_height}
  []
  [pwr_axial_peaking_factors_elongate]
    type = FIPDAxialProfileFunction
    data_file = ${raw ' ${fipd_submodule_dir} / ${exp_id} / ${pin_id} / peakingfactor_power_relative_ ${pin_id} .csv'}
    zero_ends = true
    data_shift_type = peaking
    fuel_elongation_pp = max_fuel_elongation

    bottom_clad_height = ${clad_plug_thick}
    clad_bottom_gap_height = ${fparse bot_gap_thick+reflector_height}
    fuel_slug_length = ${active_fuel_height}
  []
  [fflux_axial_peaking_factors]
    type = FIPDAxialProfileFunction
    data_file = ${raw ' ${fipd_submodule_dir} / ${exp_id} / ${pin_id} / peakingfactor_flux_relative_ ${pin_id} .csv'}
    zero_ends = true
    data_shift_type = peaking
    extrapolate_to_zero = true

    bottom_clad_height = ${clad_plug_thick}
    clad_bottom_gap_height = ${fparse bot_gap_thick+reflector_height}
    fuel_slug_length = ${active_fuel_height}
  []
  [fflux_axial_peaking_factors_elongate]
    type = FIPDAxialProfileFunction
    data_file = ${raw ' ${fipd_submodule_dir} / ${exp_id} / ${pin_id} / peakingfactor_flux_relative_ ${pin_id} .csv'}
    zero_ends = true
    data_shift_type = peaking
    extrapolate_to_zero = true
    fuel_elongation_pp = max_fuel_elongation

    bottom_clad_height = ${clad_plug_thick}
    clad_bottom_gap_height = ${fparse bot_gap_thick+reflector_height}
    fuel_slug_length = ${active_fuel_height}
  []
  [flux_history]
    type = PiecewiseLinear
    data_file = ${raw ' ${fipd_submodule_dir} / ${exp_id} / ${pin_id} / flux_history_ ${pin_id} .csv'}
  []
  [id_vpp_func]
    type = MetallicFuelWastageDegradationFunction
    vectorpostprocessor_name = id_wastage
    argument_column = y
    wastage_type = ID
    value_column = wastage_thickness
    use_metadata = true
    degradation_factor = 0.001
    mesh_generator = 'gen'
    transition_width = 1E-4
  []
  [od_vpp_func]
    type = MetallicFuelWastageDegradationFunction
    vectorpostprocessor_name = od_wastage
    argument_column = y
    wastage_type = OD
    value_column = cc_wastage_thickness
    use_metadata = true
    degradation_factor = 0.001
    mesh_generator = 'gen'
    transition_width = 1E-4
  []
  [anisotropic_swelling_factor]
    type = ParsedFunction
    symbol_names = 'disp_x_fuel_radial_surface_avg disp_y_fuel_top_surface_avg fuel_height fuel_radius'
    symbol_values = 'disp_x_fuel_radial_surface_avg disp_y_fuel_top_surface_avg ${active_fuel_height} ${fuel_radius}'
    expression = '(disp_x_fuel_radial_surface_avg / fuel_radius) / (disp_y_fuel_top_surface_avg / fuel_height)'
  []
  [gap_thermal_conductivity]
    type = ParsedFunction
    expression = '124.67 - 0.11381 * t + 5.5226e-5 * t^2 - 1.1842e-8 * t^3'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [fuel]
    strain = FINITE
    add_variables = false
    generate_output = 'firstinv_strain stress_xx stress_yy stress_zz vonmises_stress '
                      'hydrostatic_stress creep_strain_xx creep_strain_yy creep_strain_zz '
                      'elastic_strain_xx elastic_strain_yy elastic_strain_zz strain_xx strain_yy '
                      'strain_zz'
    extra_vector_tags = 'ref'
    block = 'fuel upper_blanket lower_blanket'
    eigenstrain_names = 'fuel_thermal_strain solid_swelling_eigenstrain'
    use_automatic_differentiation = true
  []
[]

[Kernels]
  [gravity]
    type = ADGravity
    block = 'fuel cladding upper_blanket lower_blanket'
    variable = disp_y
    value = -9.81
    extra_vector_tags = 'ref'
  []
  [heat]
    type = ADHeatConduction
    block = 'fuel cladding cap stand upper_blanket lower_blanket upper_transition lower_transition'
    variable = temp
    extra_vector_tags = 'ref'
  []
  [heat_ie]
    type = ADHeatConductionTimeDerivative
    block = 'fuel cladding cap stand upper_blanket lower_blanket upper_transition lower_transition'
    variable = temp
    extra_vector_tags = 'ref'
  []
  [heat_source]
    type = ADFissionRateHeatSource
    variable = temp
    block = 'fuel upper_blanket lower_blanket upper_transition lower_transition'
    fission_rate = fission_rate
    extra_vector_tags = 'ref'
    energy_deposited_in_fuel = 0.95
  []
  [disp_x_dt]
    type = ADTimeDerivative
    variable = disp_x
    block = 'cap stand upper_transition lower_transition'
    extra_vector_tags = 'ref'
  []
  [disp_y_dt]
    type = ADTimeDerivative
    variable = disp_y
    block = 'cap stand upper_transition lower_transition'
    extra_vector_tags = 'ref'
  []
  [disp_x_diff]
    type = ADMatAnisoDiffusion
    variable = disp_x
    block = 'cap stand upper_transition lower_transition'
    diffusivity = d_x
    extra_vector_tags = 'ref'
  []
  [disp_y_diff]
    type = ADMatDiffusion
    variable = disp_y
    block = 'cap stand upper_transition lower_transition'
    diffusivity = 1e8
    extra_vector_tags = 'ref'
  []
[]

[UserObjects]
  [fuel_thm_exp]
    type = LayeredAverage
    variable = fuel_thermal_strain_xx
    direction = y
    num_layers = 1000
    block = 'fuel upper_blanket lower_blanket'
  []
  [pin_geometry]
    type = FuelPinGeometry
    clad_bottom = cladding_outside_bottom
    clad_inner_wall = cladding_inside_right
    clad_outer_wall = cladding_outside_right
    clad_top = cladding_outside_top
    pellet_exteriors = fuel_outside_all
  []
  [clad_thm_exp]
    type = LayeredAverage
    variable = clad_thermal_eigenstrain_xx
    direction = y
    num_layers = 1000
    block = cladding
  []
[]

[Contact]
  [fuel_cladding_mechanical]
    primary = cladding_inside_right
    secondary = fuel_outer_radial_surface
    model = coulomb
    friction_coefficient = 0.1
    formulation = mortar
    c_normal = ${fparse 1e17 * magic_factor}
    c_tangential = ${fparse 1e19 * magic_factor}
    tangential_lm_scaling = 1.0e-22
    normal_lm_scaling = 1.0e-4
    correct_edge_dropping = true
  []
[]

[MortarGapHeatTransfer]
  [inside2outside]
    temperature = temp
    primary_emissivity = 0
    secondary_emissivity = 0
    boundary = 'cladding_inside_right'
    gap_conductivity_function = gap_thermal_conductivity
    gap_conductivity_function_variable = temp
    primary_boundary = cladding_inside_right
    secondary_boundary = fuel_contact_surfaces
    gap_flux_options = 'CONDUCTION'
    thermal_lm_scaling = 1e-4
  []
[]

[BCs]
  [no_x_all]
    type = ADDirichletBC
    variable = disp_x
    boundary = 'centerline cap_top'
    value = 0.0
    preset = false
  []
  [no_y_clad]
    type = ADDirichletBC
    variable = disp_y
    boundary = 'cladding_inside_bottom'
    value = 0.0
    preset = false
  []
  [Pressure]
    [coolantPressure]
      boundary = 'cladding_outside_right'
      factor = 0.151e6
      use_automatic_differentiation = true
    []
  []
  [PlenumPressure]
    [plenumPressure]
      boundary = 'inside_surfaces'
      initial_pressure = 84116 # in Pa, 12.2 psi
      startup_time = 0
      R = 8.3143
      temperature = temp_gas_avg
      volume = volume_plenum
      output = plenum_pressure
      material_input = fg_released
      use_automatic_differentiation = true
    []
  []

  [convection]
    type = ConvectiveHeatFluxBC
    variable = temp
    boundary = cladding_outside_right
    T_infinity = coolant_temperature
    heat_transfer_coefficient = coolant_channel_htc
  []
[]

[FluidProperties]
  [sodium_uo]
    type = SodiumProperties
  []
[]

[AuxVariables]
  [cumulative_damage_index]
    order = CONSTANT
    family = MONOMIAL
  []
  [relx]
  []
  [clad_thm_exp]
    order = CONSTANT
    family = MONOMIAL
    block = cladding
  []
  [fuel_thermal_strain_xx]
    order = CONSTANT
    family = MONOMIAL
    block = 'fuel upper_blanket lower_blanket'
  []
  [fuel_thermal_strain_yy]
    order = CONSTANT
    family = MONOMIAL
    block = 'fuel upper_blanket lower_blanket'
  []
  [fuel_thm_exp]
    order = CONSTANT
    family = MONOMIAL
    block = 'fuel upper_blanket lower_blanket'
  []
  [clad_thermal_eigenstrain_xx]
    order = CONSTANT
    family = MONOMIAL
    block = cladding
  []
  [func_val1]
  []
  [func_val2]
  []
  [fast_neutron_fluence_aux]
    order = CONSTANT
    family = MONOMIAL
    block = 'cladding'
  []
[]

[AuxKernels]
  [func_val1]
    type = FunctionAux
    function = id_vpp_func
    variable = func_val1
    block = 'cladding'
  []
  [func_val2]
    type = FunctionAux
    function = od_vpp_func
    variable = func_val2
    block = 'cladding'
  []
  [cdf_amount]
    block = cladding
    type = MaterialRealAux
    property = cdf_failure
    variable = cumulative_damage_index
    execute_on = timestep_end
  []
  [relx_aux]
    type = ParsedAux
    variable = relx
    block = 'fuel upper_blanket lower_blanket upper_transition lower_transition'
    use_xyzt = true
    expression = 'x / ${fuel_radius}'
  []
  [clad_thm_exp]
    type = SpatialUserObjectAux
    variable = clad_thm_exp
    execute_on = 'initial timestep_end'
    user_object = clad_thm_exp
    block = cladding
  []
  [clad_thermal_eigenstrain_xx]
    type = ADRankTwoAux
    rank_two_tensor = cladding_thermal_eigenstrain
    variable = clad_thermal_eigenstrain_xx
    index_j = 0
    index_i = 0
    execute_on = 'initial timestep_end'
    block = cladding
  []
  [fuel_thermal_strain_xx]
    type = ADRankTwoAux
    rank_two_tensor = fuel_thermal_strain
    variable = fuel_thermal_strain_xx
    index_j = 0
    index_i = 0
    execute_on = 'initial timestep_end'
    block = 'fuel upper_blanket lower_blanket'
  []
  [fuel_thermal_strain_yy]
    type = ADRankTwoAux
    rank_two_tensor = fuel_thermal_strain
    variable = fuel_thermal_strain_yy
    index_j = 1
    index_i = 1
    execute_on = 'initial timestep_end'
    block = 'fuel upper_blanket lower_blanket'
  []
  [fuel_thm_exp]
    type = SpatialUserObjectAux
    variable = fuel_thm_exp
    execute_on = 'initial timestep_end'
    user_object = fuel_thm_exp
    block = 'fuel upper_blanket lower_blanket'
  []
[]

[Materials]
  [coolant]
    type = SodiumCoolantChannelMaterial
    boundary = cladding_outside_right
    inlet_temperature_function = coolant_T_in_function
    rod_linear_power = power_history_avg
    inlet_massflux_function = coolant_flux_function
    axial_power_profile_cdf = pwr_axial_peaking_factors_cdf
    pellet_height = ${active_fuel_height}
    cladding_radius = '${fparse cladding_ir + cladding_thickness}'
    wire_wrap_diameter = ${fparse 0.054*0.0254}
    temperature = temp
    sodium_user_object = sodium_uo
    htc_model = BGF
    update_temperature = true
    pin_location = interior
    peclet_limit_behavior = error
    outputs = all
  []

  [d_x]
    type = ADConstantAnisotropicMobility
    tensor = '1e3 0 0
              0   1e6 0
              0   0 0'
    M_name = d_x
  []
  [cap_thcond]
    type = ADGenericConstantMaterial
    prop_names = 'thermal_conductivity specific_heat density'
    prop_values = '65 1200 830'
    block = 'cap stand'
    outputs = all
  []
  [interconnected_porosity]
    type = ADParsedMaterial
    property_name = interconnected_porosity
    material_property_names = 'porosity interconnectivity'
    expression = 'porosity * interconnectivity'
    outputs = all
    block = 'fuel upper_blanket lower_blanket'
  []
  [fission_rate]
    type = ADUPuZrFissionRate
    rod_linear_power = power_history
    axial_power_profile = pwr_axial_peaking_factors
    pellet_radius = ${fuel_radius}
    X_Zr = ${initial_X_Zr}
    X_Pu_function = ${fuel_pu}
    block = 'fuel upper_blanket lower_blanket upper_transition lower_transition'
    outputs = all
  []
  [fission_rate_elongate]
    type = ADUPuZrFissionRate
    rod_linear_power = power_history
    axial_power_profile = pwr_axial_peaking_factors_elongate
    pellet_radius = ${fuel_radius}
    X_Zr = ${initial_X_Zr}
    X_Pu_function = ${fuel_pu}
    block = 'cladding'
    outputs = all
    fission_rate_name = fission_rate
  []
  [burnup]
    type = ADUPuZrBurnup
    initial_X_Zr = ${initial_X_Zr}
    initial_X_Pu = ${fuel_pu}
    density = ${fuel_density}
    block = 'fuel upper_blanket lower_blanket upper_transition lower_transition'
    outputs = all
  []
  [burnup_elongate]
    type = ADUPuZrBurnup
    initial_X_Pu = ${fuel_pu}
    initial_X_Zr = ${initial_X_Zr}
    outputs = all
    block = cladding
    density = ${fuel_density}
    burnup_name = burnup
  []
  [fuel_elastic_stress]
    type = ADComputeMultipleInelasticStress
    inelastic_models = 'hotpress fuel_upuzrcreep gas_swelling'
    block = 'fuel upper_blanket lower_blanket'
    outputs = all
  []
  [hotpress]
    type = ADUPuZrHotPressingStressUpdate
    block = 'fuel upper_blanket lower_blanket'
    outputs = all
    surface_energy = 1.6
    plenum_pressure = plenum_pressure
    porosity_name = porosity
    max_inelastic_increment = 1e-3 #1e-1
    interconnectivity = interconnectivity
    bubble_concentration = ${bubble_concentration}
    temperature = temp
    creep_model = MFH
    fission_rate = fission_rate
    atomic_volume = 2.15e-29
    porosity_start = 0.01
    porosity_end = 0
    grain_boundary_D0 = 4e-29
    grain_boundary_Q = 0
    absolute_tolerance = 1e-9
  []
  [porosity]
    type = ADPorosityFromStrain
    block = 'fuel upper_blanket lower_blanket'
    initial_porosity = 1e-10
    inelastic_strain = 'combined_inelastic_strain'
    outputs = all
  []
  [porosity_transition]
    type = ADGenericConstantMaterial
    prop_names = 'porosity interconnectivity'
    prop_values = '0.0 0.0'
    block = 'upper_transition lower_transition'
  []
  [fuel_elasticity_tensor]
    type = ADUPuZrElasticityTensor
    X_Zr = ${initial_X_Zr}
    X_Pu = ${fuel_pu}
    youngs_model = LANL
    block = 'fuel upper_blanket lower_blanket'
    temperature = temp
    use_old_porosity = true
    outputs = all
    output_properties = 'youngs_modulus poissons_ratio'
  []
  [fuel_upuzrcreep]
    type = ADUPuZrCreepUpdate
    block = 'fuel upper_blanket lower_blanket'
    temperature = temp
    porosity = porosity
    max_inelastic_increment=1e-1
    use_old_porosity = true
    automatic_differentiation_return_mapping = false
  []
  [fuel_thermal_expansion]
    type = ADUPuZrThermalExpansionEigenstrain
    block = 'fuel upper_blanket lower_blanket'
    temperature = temp
    stress_free_temperature = 298.0
    eigenstrain_name = fuel_thermal_strain
    outputs = all
    thermal_expansion_model = LANL
    X_Zr = ${initial_X_Zr}
    X_Pu = ${fuel_pu}
  []
  [gas_swelling]
    type = ADSimpleFissionGasViscoplasticityStressUpdate
    temperature = temp
    outputs = all
    block = 'fuel upper_blanket lower_blanket'
    bubble_concentration = ${bubble_concentration}
    initial_bubble_concentration = ${bubble_concentration}
    compute_interconnectivity = true
    fission_gas_yield = 0.25
    fission_rate = fission_rate
    initial_atoms_per_bubble = 1e-05
    initial_bubble_radius = 1e-15
    initial_fgm_dissolved = 0
    interconnection_cutoff = 0.99
    interconnection_initiating_porosity = 0.23
    interconnection_terminating_porosity = 0.25
    max_inelastic_increment = 1e-2
    retained_gas_fraction = 0.25
    interconnection_dependent_retained_gas_fraction = 0.5
    surface_energy = 1.6
    anisotropic_factor = 0.26
    initial_porosity = 1e-10
  []
  [solid_swelling]
    type = ADBurnupDependentEigenstrain
    eigenstrain_name = solid_swelling_eigenstrain
    block = 'fuel upper_blanket lower_blanket'
    swelling_name = 'solid_swelling'
    outputs = all
    anisotropic_factor = 0.26
  []
  [metal_fuel_thermal]
    type = ADUPuZrThermal
    block = 'fuel upper_blanket lower_blanket upper_transition lower_transition'
    X_Zr = ${initial_X_Zr}
    X_Pu = ${fuel_pu}
    spheat_model = savage
    porosity = porosity
    temperature = temp
    outputs = all
    porosity_model = logged
    sodium_logged_porosity = sodium_logged_porosity
  []
  [sodium_logging]
    type = ADUPuZrSodiumLogging
    block = 'fuel upper_blanket lower_blanket upper_transition lower_transition'
    porosity = porosity
    interconnectivity = interconnectivity
    sodium_infiltration_fraction = 0.28
    outputs = all
  []
  [fuel_density]
    type = ADStrainAdjustedDensity
    strain_free_density = ${fuel_density}
    block = 'fuel upper_blanket lower_blanket upper_transition lower_transition'
  []
  [fast_neutron_flux]
    type = ADFastNeutronFlux
    calculate_fluence = true
    axial_power_profile = fflux_axial_peaking_factors
    rod_ave_lin_pow = flux_history
    block = 'fuel upper_blanket lower_blanket upper_transition lower_transition'
    factor = 1.0
    outputs = all
  []
  [fast_neutron_flux_elongate]
    type = ADFastNeutronFlux
    calculate_fluence = true
    axial_power_profile = fflux_axial_peaking_factors_elongate
    rod_ave_lin_pow = flux_history
    block = cladding
    factor = 1.0
    outputs = all
  []
[]

[Dampers]
  [disp_x]
    type = MaxIncrement
    variable = disp_x
    max_increment = 1e-4
  []
  [disp_y]
    type = MaxIncrement
    variable = disp_y
    max_increment = 1e-3
  []
  [temp]
    type = MaxIncrement
    variable = temp
    max_increment = 50
  []
[]

[Preconditioning]
  [vcp]
    type = VCP
    full = true
    primary_variable = 'disp_x disp_y temp'
    preconditioner = 'LU'
    adaptive_condensation = true
    lm_variable = 'fuel_cladding_mechanical_normal_lm fuel_cladding_mechanical_tangential_lm inside2outside_thermal_lm'
    is_lm_coupling_diagonal = true
  []
[]

[Executioner]
  type = Transient
  solve_type = 'NEWTON'
  petsc_options = '-snes_ksp_ew -snes_converged_reason -ksp_converged_reason'
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_type -mat_mffd_err -pc_factor_shift_type -pc_factor_shift_amount -snes_force_iteration'
  petsc_options_value = 'lu    superlu_dist   1e-5          NONZERO               1e-15 1'
  line_search = 'none'
  snesmf_reuse_base = false
  verbose = true

  l_max_its = 60
  nl_max_its = 30
  nl_rel_tol = 1e-4 #5e-6
  nl_abs_tol = 1e-8 #5e-9

  end_time = ${time_last}
  dtmin = 1
  dtmax = ${max_dt}

  automatic_scaling = true
  compute_scaling_once = false
  off_diagonals_in_auto_scaling = true
  ignore_variables_for_autoscaling = 'fuel_cladding_mechanical_normal_lm fuel_cladding_mechanical_tangential_lm inside2outside_thermal_lm'

  [TimeStepper]
    type = IterationAdaptiveDT
    timestep_limiting_function = power_history
    dt = 100
    iteration_window = 4
    optimal_iterations = 20
    force_step_every_function_point = true

    timestep_limiting_postprocessor = creep_timestep
  []
[]

[Postprocessors]
  [creep_timestep]
    type = MaterialTimeStepPostprocessor
    block = 'fuel cladding'
  []

  [_dt]
    type=TimestepSize
  []
  # elemental temperatures
  [temp_fuel_avg]
    type = ElementAverageValue
    variable = temp
    block = 'fuel'
    execute_on = 'initial timestep_end'
  []
  [temp_fuel_max]
    type = ElementExtremeValue
    variable = temp
    block = 'fuel'
  []
  [temp_fuel_min]
    type = ElementExtremeValue
    variable = temp
    block = 'fuel'
    value_type = min
  []
  [temp_cladding_avg]
    type = ElementAverageValue
    variable = temp
    block = 'cladding'
  []
  [temp_cladding_max]
    type = ElementExtremeValue
    variable = temp
    block = 'cladding'
  []
  [temp_cladding_min]
    type = ElementExtremeValue
    variable = temp
    block = 'cladding'
    value_type = min
  []

  # boundary temperatures
  [temp_gas_avg]
    type = SideAverageValue
    boundary = 'gas_height cladding_inside_top'
    variable = temp
    execute_on = 'initial timestep_end'
  []
  [temp_sodium_avg]
    type = SideAverageValue
    boundary = 'sodium_height fuel_bottom cladding_inside_bottom fuel_top'
    variable = temp
    execute_on = 'initial timestep_end'
  []
  [temp_inside_surfaces_avg]
    type = SideAverageValue
    boundary = 'inside_surfaces'
    variable = temp
    execute_on = 'initial timestep_end'
  []
  [temp_fuel_centerline_avg]
    type = AxisymmetricCenterlineAverageValue
    boundary = 'centerline'
    variable = temp
  []
  [temp_fuel_centerline_max]
    type = NodalExtremeValue
    boundary = 'centerline'
    variable = temp
  []
  [temp_fuel_centerline_min]
    type = NodalExtremeValue
    boundary = 'centerline'
    variable = temp
    value_type = min
  []
  [temp_fuel_surface_avg]
    type = SideAverageValue
    boundary = 'fuel_outer_radial_surface'
    variable = temp
  []
  [temp_fuel_surface_max]
    type = NodalExtremeValue
    boundary = 'fuel_outer_radial_surface'
    variable = temp
  []
  [temp_fuel_surface_min]
    type = NodalExtremeValue
    boundary = 'fuel_outer_radial_surface'
    variable = temp
    value_type = min
  []
  [temp_cladding_inside_right_avg]
    type = SideAverageValue
    boundary = 'cladding_inside_right'
    variable = temp
  []
  [temp_cladding_inside_right_max]
    type = NodalExtremeValue
    boundary = 'cladding_inside_right'
    variable = temp
  []
  [temp_cladding_outside_right_avg]
    type = SideAverageValue
    boundary = 'cladding_outside_right'
    variable = temp
  []

  # stresses
  [stress_vonmises_fuel_avg]
    type = ElementAverageValue
    variable = vonmises_stress
    block = 'fuel'
  []
  [stress_vonmises_fuel_max]
    type = ElementExtremeValue
    variable = vonmises_stress
    block = 'fuel'
  []
  [stress_vonmises_fuel_min]
    type = ElementExtremeValue
    variable = vonmises_stress
    value_type = min
    block = 'fuel'
  []
  [stress_hydro_fuel_avg]
    type = ElementAverageValue
    variable = hydrostatic_stress
    block = 'fuel'
  []
  [stress_hydro_fuel_max]
    type = ElementExtremeValue
    variable = hydrostatic_stress
    block = 'fuel'
  []
  [stress_hydro_fuel_min]
    type = ElementExtremeValue
    variable = hydrostatic_stress
    value_type = min
    block = 'fuel'
  []
  [stress_vonmises_cladding_avg]
    type = ElementAverageValue
    variable = vonmises_stress
    block = 'cladding'
  []
  [stress_vonmises_cladding_max]
    type = ElementExtremeValue
    variable = vonmises_stress
    block = 'cladding'
  []
  [stress_vonmises_cladding_min]
    type = ElementExtremeValue
    variable = vonmises_stress
    value_type = min
    block = 'cladding'
  []
  [stress_hydro_cladding_avg]
    type = ElementAverageValue
    variable = hydrostatic_stress
    block = 'cladding'
  []
  [stress_hydro_cladding_max]
    type = ElementExtremeValue
    variable = hydrostatic_stress
    block = 'cladding'
  []
  [stress_hydro_cladding_min]
    type = ElementExtremeValue
    variable = hydrostatic_stress
    value_type = min
    block = 'cladding'
  []

  # strain information
  [strain_solid_swelling_fuel_avg]
    type = ElementAverageValue
    variable = solid_swelling
    block = 'fuel'
  []
  [strain_gas_swelling_fuel_avg]
    type = ElementAverageValue
    variable = effective_fission_gas_strain
    block = 'fuel'
  []
  [strain_hot_pressing_fuel_avg]
    type = ElementAverageValue
    variable = effective_hot_pressing_strain
    block = 'fuel'
  []
  [strain_volumetric_fuel_avg]
    type = ElementAverageValue
    variable = firstinv_strain
    block = 'fuel'
  []
  [strain_axial_fuel_avg]
    type = ParsedPostprocessor
    pp_names = 'disp_y_fuel_top_surface_avg disp_y_fuel_bottom_surface_avg'
    expression = '(disp_y_fuel_top_surface_avg - disp_y_fuel_bottom_surface_avg) / ${active_fuel_height}'
  []
  [disp_y_fuel_top_surface_avg]
    type = SideAverageValue
    variable = disp_y
    boundary = 'fuel_top'
  []
  [disp_y_fuel_top_surface_max]
    type = NodalExtremeValue
    variable = disp_y
    boundary = 'fuel_top'
  []
  [disp_y_fuel_bottom_surface_avg]
    type = SideAverageValue
    variable = disp_y
    boundary = 'fuel_bottom'
  []
  [disp_y_fuel_bottom_surface_max]
    type = NodalExtremeValue
    variable = disp_y
    boundary = 'fuel_bottom'
  []
  [disp_x_fuel_radial_surface_max]
    type = NodalExtremeValue
    variable = disp_x
    boundary = 'fuel_outer_radial_surface'
  []
  [disp_x_fuel_radial_surface_avg]
    type = SideAverageValue
    variable = disp_x
    boundary = 'fuel_outer_radial_surface'
  []
  [disp_x_cladding_interior_max]
    type = NodalExtremeValue
    variable = disp_x
    boundary = 'cladding_inside_right'
  []
  [disp_x_cladding_interior_min]
    type = NodalExtremeValue
    variable = disp_x
    boundary = 'cladding_inside_right'
    value_type = min
  []
  [disp_x_cladding_interior_avg]
    type = SideAverageValue
    variable = disp_x
    boundary = 'cladding_inside_right'
  []
  [disp_x_cladding_exterior_max]
    type = NodalExtremeValue
    variable = disp_x
    boundary = 'cladding_outside_right'
  []
  [disp_x_cladding_exterior_avg]
    type = SideAverageValue
    variable = disp_x
    boundary = 'cladding_outside_right'
  []
  [anisotropic_swelling_factor]
    type = FunctionValuePostprocessor
    function = anisotropic_swelling_factor
  []
  [max_fuel_elongation]
    type = NodalExtremeValue
    variable = disp_y
    boundary = fuel_outside_all
  []

  # geometric information
  [volume_cladding_interior]
    type = InternalVolume
    boundary = 'cladding_inside_all'
  []
  [volume_fuel]
    type = InternalVolume
    boundary = 'fuel_outside_all'
    execute_on = 'initial timestep_end'
  []
  [volume_plenum]
    type = InternalVolume
    boundary = 'inside_surfaces'
    execute_on = 'initial timestep_end'
    addition = sodium_volume
  []
  [plenum_ratio]
    type = ParsedPostprocessor
    pp_names = 'volume_plenum volume_fuel'
    expression = 'volume_plenum / volume_fuel'
    execute_on = 'initial timestep_end'
  []
  [volume_sodium]
    type = FunctionValuePostprocessor
    function = sodium_volume
    execute_on = 'initial timestep_end'
  []

  # energy information
  [flux_clad]
    type = ADSideDiffusiveFluxIntegral
    variable = temp
    boundary = 'cladding_inside_right'
    diffusivity = thermal_conductivity
  []
  [flux_fuel]
    type = ADSideDiffusiveFluxIntegral
    variable = temp
    boundary = 'fuel_contact_surfaces'
    diffusivity = thermal_conductivity
  []
  [power_integral]
    type = ADElementIntegralPower
    variable = temp
    use_material_fission_rate = true
    fission_rate_material = fission_rate
    block = fuel
  []
  [linear_heat_generation_rate]
    type = FunctionValuePostprocessor
    function = power_history
    scale_factor = 0.01
  []
  [burnup_avg]
    type = ElementAverageValue
    block = fuel
    variable = burnup
  []
  [burnup_max]
    type = ElementExtremeValue
    block = fuel
    variable = burnup
  []
  [fission_rate_avg]
    type = ElementAverageValue
    variable = fission_rate
    block = fuel
  []

  # fission gas information
  [fg_produced]
    type = ADElementIntegralMaterialProperty
    mat_prop = fgm_produced
    block = fuel
  []
  [fg_released]
    type = ADElementIntegralMaterialProperty
    mat_prop = fgm_released
    block = fuel
    execute_on = 'initial timestep_end'
  []
  [fg_percent]
    type = FGRPercent
    fission_gas_released = fg_released
    fission_gas_generated = fg_produced
  []
  [interconnected_porosity_fuel_avg]
    type = ElementAverageValue
    variable = interconnected_porosity
    block = fuel
    execute_on = 'initial timestep_end'
  []
  [porosity_fuel_avg]
    type = ElementAverageValue
    variable = porosity
    block = fuel
  []
  [porosity_fuel_max]
    type = ElementExtremeValue
    variable = porosity
    block = fuel
  []
  [porosity_fuel_min]
    type = ElementExtremeValue
    variable = porosity
    value_type = min
    block = fuel
  []
  [porosity_sodium_logging_avg]
    type = ElementAverageValue
    variable = sodium_logged_porosity
    block = fuel
  []

  # extras
  [actual_time_step_limit]
    type = MaterialTimeStepPostprocessor
    block = 'fuel cladding'
    outputs = none
  []
  [time_step_limit]
    type = ParsedPostprocessor
    expression = 'if(actual_time_step_limit > 1e6, 1e6, actual_time_step_limit)'
    pp_names = 'actual_time_step_limit'
  []
  [max_wastagethickness]
    type = ElementExtremeValue
    value_type = max
    variable = wastage_thickness
  []
  [max_wst_temp]
    type=ElementExtremeValue
    value_type=max
    variable=temp
    proxy_variable=wastage_thickness
    block='cladding'
  []
  [max_wst_burnup]
    type=ElementExtremeValue
    value_type=max
    variable=burnup
    proxy_variable=wastage_thickness
    block='cladding'
  []
  [max_cdf]
    type = ElementExtremeValue
    value_type = max
    variable = cumulative_damage_index
  []
[]

[VectorPostprocessors]
  [id_wastage]
    type = FuelRodLineValueSampler
    variable = wastage_thickness
    material = 'clad'
    fraction = 0.0
    num_points = 600
    orientation = 'vertical'
    fuel_pin_geometry = 'pin_geometry'
    execute_on = 'initial timestep_end'
    allow_duplicate_execution_on_initial = true
    outputs = none
  []
  [od_wastage]
    type = FuelRodLineValueSampler
    variable = cc_wastage_thickness
    material = 'clad'
    fraction = 1.0
    num_points = 600
    orientation = 'vertical'
    fuel_pin_geometry = 'pin_geometry'
    execute_on = 'initial timestep_end'
    allow_duplicate_execution_on_initial = true
    outputs = none
  []
[]

[Outputs]
  perf_graph = true
  color = true
  [console]
    type = Console
    max_rows = 25
  []
  [csv_general]
    type = CSV
    execute_on = FINAL
  []
  [exodus]
    type = Exodus
    enable = false
    additional_execute_on = 'FAILED'
  []
  [params_exodus_final]
    type = Exodus
    execute_on = 'FINAL'
  []
[]

!include d9_clad_base.i

Description
Example Input Syntax
Input Parameters
Input Files
References