SilicideFuelThermal

Computes the specific heat and thermal conductivity for different phases of uranium silicide fuel.

Description

The SilicideFuelThermal model computes the specific heat and thermal conductivity for different phases of uranium silicide fuel including pure silicon, pure uranium metal, U $var element = document.getElementById("moose-equation-55b7e924-818e-4837-9552-18453f7cc117");katex.render("_3", element, {displayMode:false,throwOnError:false});$ Si $var element = document.getElementById("moose-equation-2c393ba7-5fac-4146-ba3f-9e925f0b74f5");katex.render("_2", element, {displayMode:false,throwOnError:false});$ , U $var element = document.getElementById("moose-equation-e2fc1393-8a19-4aa9-a4c5-7a10a5dcfe34");katex.render("_3", element, {displayMode:false,throwOnError:false});$ Si, and U $var element = document.getElementById("moose-equation-d974d01f-593c-4eff-9d4e-de494d96f50c");katex.render("_3", element, {displayMode:false,throwOnError:false});$ Si $var element = document.getElementById("moose-equation-b7357281-bb0f-4744-83d5-7a2ca14aebe0");katex.render("_5", element, {displayMode:false,throwOnError:false});$ . The SilicideFuelThermal material model contains four different options to model thermal conductivity of U $var element = document.getElementById("moose-equation-1e8b3af5-274d-4c18-a5a2-f7d9beba01ab");katex.render("_3", element, {displayMode:false,throwOnError:false});$ Si $var element = document.getElementById("moose-equation-9bc09518-4fa0-4d6c-8fa1-7645039d0c74");katex.render("_2", element, {displayMode:false,throwOnError:false});$ :

and three different options to model the specific heat of U $var element = document.getElementById("moose-equation-02983432-9aa0-488e-b45a-b8e9dca68bfa");katex.render("_3", element, {displayMode:false,throwOnError:false});$ Si $var element = document.getElementById("moose-equation-8702e21b-386b-4f33-a9eb-2077246814a5");katex.render("_2", element, {displayMode:false,throwOnError:false});$ :

Thermal Conductivity Models

(Default) WHITE Model

The default model (WHITE) for thermal conductivity is given by equation 4 in White et al. (2015): $var element = document.getElementById("moose-equation-846a863d-583e-4112-8cf3-e757aa0f65a1");katex.render(" k = 4.996 + 0.0118 T", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-7c29d6f0-83a1-465d-b3d8-a57a3472519c");katex.render("T", element, {displayMode:false,throwOnError:false});$ is temperature in K. This expression is valid for temperatures up to 1773 K.

SHIMIZU Model

An alternative model (SHIMIZU) is available for use in ThermalSilicide by using experimental data from figure 4 of Shimizu (1965). The conservative expression for thermal conductivity k (W/m-K) of arc cast U $var element = document.getElementById("moose-equation-e6b11041-83ee-44fc-8374-cee929cac115");katex.render("_3", element, {displayMode:false,throwOnError:false});$ Si $var element = document.getElementById("moose-equation-76168e42-87a9-45c5-8976-947e86535b52");katex.render("_2", element, {displayMode:false,throwOnError:false});$ pellets is: $var element = document.getElementById("moose-equation-fb0ddfbf-6b8a-4c79-a105-3f9ca8fe5959");katex.render("k = 7.98+0.0051\\left(T-273.15\\right)", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-ccf18d1d-f12d-428d-b6a4-a5bfaeb3c0f8");katex.render("T", element, {displayMode:false,throwOnError:false});$ is temperature in K. This expression is valid for temperatures from room temperature to 1473.15 K. This expression may underestimate the true thermal conductivity of U $var element = document.getElementById("moose-equation-37076a92-45e4-4ace-99fe-e45c393bf8ed");katex.render("_3", element, {displayMode:false,throwOnError:false});$ Si $var element = document.getElementById("moose-equation-2cf8b75c-0376-4c1e-b354-8197de7a7fde");katex.render("_2", element, {displayMode:false,throwOnError:false});$ .

ZHANG Model

The third thermal conductivity option known as the ZHANG model is more sophisticated because it is able to determine the thermal conductivity of pure uranium metal, pure silicon, U $var element = document.getElementById("moose-equation-e1434947-db06-4a10-a901-93e069c22865");katex.render("_3", element, {displayMode:false,throwOnError:false});$ Si $var element = document.getElementById("moose-equation-9b8ae5a0-1f37-4754-a3c0-bb2159ee5569");katex.render("_2", element, {displayMode:false,throwOnError:false});$ , U $var element = document.getElementById("moose-equation-b958910c-89cf-4847-b6e7-411e850f61ee");katex.render("_3", element, {displayMode:false,throwOnError:false});$ Si $var element = document.getElementById("moose-equation-6302faef-fd1f-49ae-a99b-e53f16025741");katex.render("_5", element, {displayMode:false,throwOnError:false});$ , and U $var element = document.getElementById("moose-equation-e4ab6c17-c4f0-4b4a-94d4-df674e5a2d3d");katex.render("_3", element, {displayMode:false,throwOnError:false});$ Si. By utilizing details from Ho et al. (1978), Tsiovkin et al. (2010), and Glassbrenner and Slack (1964), Zhang arrived at an equation of the form: $var element = document.getElementById("moose-equation-de8a9a67-04b3-4e71-8693-3cede14e5e2d");katex.render("k\\left(c\\right) = \\frac{(1-c)/w_e^U + c/w_e^{Si}}{1+ c(1-c)\\left\\{L_1+L_2\\left[c^2-(1-c)^2\\right]\\right\\}}", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-6f86068f-1249-4017-91cf-4e7e97325cf8");katex.render("c", element, {displayMode:false,throwOnError:false});$ is the silicon concentration (given as mole fraction in the fuel). For example, for U $var element = document.getElementById("moose-equation-6ec6f282-d533-42cc-91b9-6c307e6f1086");katex.render("_3", element, {displayMode:false,throwOnError:false});$ Si $var element = document.getElementById("moose-equation-f0ad24b7-9062-4a67-8e97-0161f2b5456d");katex.render("_2", element, {displayMode:false,throwOnError:false});$ $var element = document.getElementById("moose-equation-f71cc6a6-b025-4fa0-885b-47ad66b08e11");katex.render("c", element, {displayMode:false,throwOnError:false});$ =0.4. $var element = document.getElementById("moose-equation-7b3a08f5-8782-4e4d-a3ca-24f7b3343a5e");katex.render("1/w_e^U", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-487a6a63-0dc7-4197-8aac-d3d712605db4");katex.render("1/w_e^{Si}", element, {displayMode:false,throwOnError:false});$ are the conductivities of U and Si, respectively. $var element = document.getElementById("moose-equation-1175312b-fad5-43f7-82e9-3c2db4b78ecb");katex.render("L_1", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-5ea5457a-bcbd-4046-aad1-7a8ec4d3f1ab");katex.render("L_2", element, {displayMode:false,throwOnError:false});$ are fitting parameters. The first step is to find the values of $var element = document.getElementById("moose-equation-fd2ace3f-2faa-4a78-a3b7-3388dfd23fb6");katex.render("w_e^U", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-0e984f9d-9f1c-47d7-be43-c7362e17b0b6");katex.render("w_e^{Si}", element, {displayMode:false,throwOnError:false});$ . Zhang found that the exponential decay function can be used to reproduce these values well: $var element = document.getElementById("moose-equation-a4ddc441-70ab-4eaf-b0e9-052f0d45b4c9");katex.render(" w_e = m_0 + m_1 \\exp{\\left(-\\frac{T-T_0}{T_1}\\right)} + m_2 \\exp{\\left(-\\frac{T-T_0}{T_2}\\right)}", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-1342ac18-7f8f-45cc-b831-8e468b273b4c");katex.render("T", element, {displayMode:false,throwOnError:false});$ is the temperature in K and, $var element = document.getElementById("moose-equation-631cc38b-35da-4498-9abe-506175534854");katex.render("m_0", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-a35c7cd0-bb10-405d-95e4-7e8b4df15da3");katex.render("m_1", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-92e2b363-224d-446e-a307-811d5ad64dd2");katex.render("m_2", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-5ed22e0d-cb56-4912-84cc-2beaaff86a35");katex.render("T_0", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-0dba4715-f5b2-4c26-a12a-239a6ed76db0");katex.render("T_1", element, {displayMode:false,throwOnError:false});$ , and $var element = document.getElementById("moose-equation-472f646f-9613-4250-a381-e57e4dcafdec");katex.render("T_2", element, {displayMode:false,throwOnError:false});$ are parameters unique to U or Si. The values of these parameters are summarized in Table 1.

Table 1: Parameters used to fit the intrinsic thermal resistivity of U and Si

Parameters	$var element = document.getElementById("moose-equation-7355d11b-e530-4a20-883c-358fe6861a6f");katex.render("m_0", element, {displayMode:false,throwOnError:false});$	$var element = document.getElementById("moose-equation-163aa132-0453-4761-a9fa-dad3f617e57a");katex.render("m_1", element, {displayMode:false,throwOnError:false});$	$var element = document.getElementById("moose-equation-35c4ef28-3fe2-4ab8-8b0e-713985dc761b");katex.render("m_2", element, {displayMode:false,throwOnError:false});$	$var element = document.getElementById("moose-equation-4c1a0b4d-ed5a-4e93-9b00-84c16e10302f");katex.render("T_0", element, {displayMode:false,throwOnError:false});$	$var element = document.getElementById("moose-equation-72905598-ea22-46cb-8598-dac3ee19ce78");katex.render("T_1", element, {displayMode:false,throwOnError:false});$	$var element = document.getElementById("moose-equation-f7b39f85-d287-4e31-b5db-a15011991529");katex.render("T_2", element, {displayMode:false,throwOnError:false});$
U	0.00448	0.0089	0.03267	0.0	500.76917	1555.4716
Si	0.08303	29.152	3.88841	645	87.48315	252.19318

Next, Zhang used the data from White et al.'s references for U $var element = document.getElementById("moose-equation-b6d9a275-9486-4a4d-8ec2-ccfcc3300329");katex.render("_3", element, {displayMode:false,throwOnError:false});$ Si $var element = document.getElementById("moose-equation-81246716-e751-424f-b69d-d4d05392b6fc");katex.render("_2", element, {displayMode:false,throwOnError:false});$ (White et al., 2015) and U $var element = document.getElementById("moose-equation-bee3c6f9-54a6-4307-86a8-dde6ffb6c302");katex.render("_3", element, {displayMode:false,throwOnError:false});$ Si $var element = document.getElementById("moose-equation-29c51c88-44ea-42da-97f0-4f1ac38ee2d3");katex.render("_5", element, {displayMode:false,throwOnError:false});$ (White et al., 2015) to fit the parameters $var element = document.getElementById("moose-equation-b2be63a7-d56c-490d-862b-da6c539f5ee5");katex.render("L_1", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-5a349ee7-a335-4eca-ae52-1e04f25416bb");katex.render("L_2", element, {displayMode:false,throwOnError:false});$ . The equation for these parameters are 5th order polynomials of temperature given by: $var element = document.getElementById("moose-equation-5870d7f2-6af7-4fa6-bc26-cb4f7a9d8aa5");katex.render(" \\begin{aligned} L_1 = 6.0959 - 0.01457T +1.75527\\times 10^{-5}T^2 - 1.13428\\times 10^{-8}T^3 \\\\ + 4.05139\\times 10^{-12}T^4 - 6.04924\\times 10^{-16}T^5 \\end{aligned}", element, {displayMode:true,throwOnError:false});$ $var element = document.getElementById("moose-equation-64af3de2-e77e-4d71-9cd3-7326005586d8");katex.render(" \\begin{aligned} L_2 = -1.82488 + 0.0148T -2.92953\\times 10^{-5}T^2 + 2.68933\\times 10^{-8}T^3 \\\\ -1.15846\\times 10^{-11}T^4 + 1.90712\\times 10^{-15}T^5 \\end{aligned}", element, {displayMode:true,throwOnError:false});$

HANDBOOK Model

A fourth option is available form the updated U $var element = document.getElementById("moose-equation-a22e3a14-8660-4e54-9206-ef1d2362a70f");katex.render("_3", element, {displayMode:false,throwOnError:false});$ Si $var element = document.getElementById("moose-equation-0e9be86d-b499-48c9-99a9-dd9e53df51f9");katex.render("_2", element, {displayMode:false,throwOnError:false});$ handbook (White, 2018). $var element = document.getElementById("moose-equation-87935add-d942-4fde-af7b-a5c30e1802ad");katex.render("k = 9.029\\times10^{-15}T^5 - 4.609\\times10^{-11}T^4 + 8.676\\times10^{-8}T^3 - 7.485\\times10^{-5}T^2 + 4.166\\times10^{-2}T + 0.5211", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-74ad2ec8-92ea-4502-afed-6c9bc2274302");katex.render("T", element, {displayMode:false,throwOnError:false});$ is temperature in K and $var element = document.getElementById("moose-equation-dc1e2763-143d-4605-80d1-cce20acf6525");katex.render("k", element, {displayMode:false,throwOnError:false});$ is the thermal conductivity in W/m-K.

Thermal Conductivity Degradation

The degradation of thermal conductivity in U $var element = document.getElementById("moose-equation-2ca609e5-e45a-4e07-a15c-f90d1aaf6caa");katex.render("_3", element, {displayMode:false,throwOnError:false});$ Si $var element = document.getElementById("moose-equation-a91a261b-29a7-439d-b295-e15d7ceaa875");katex.render("_2", element, {displayMode:false,throwOnError:false});$ can be captured using the U3Si2TricubicInterpolationUserObject to calculate temperature, temperature gradient, and fission density (burnup) dependent degradation factors applied to the intrinsic thermal conductivity calculated from any of the unirradiated thermal conductivity models described previously. The ranges of applicability of the model are temperatures from 390 K to 1190 K, temperature gradients from 0 to 160 K/mm, and fission densities from 0 to 2.5755 $var element = document.getElementById("moose-equation-bd06c462-3f00-4553-9fa1-79fbe68ed8c2");katex.render("\\times", element, {displayMode:false,throwOnError:false});$ 10 $var element = document.getElementById("moose-equation-d0475f08-0a0b-47f5-abf9-c3df4295524f");katex.render("^{21}", element, {displayMode:false,throwOnError:false});$ fissions/cm $var element = document.getElementById("moose-equation-a5d495ba-747f-45bf-821e-c9efd228007d");katex.render("^3", element, {displayMode:false,throwOnError:false});$ .

The intrinsic thermal conductivity is calculated as follows:

$var element = document.getElementById("moose-equation-a778f3c7-3364-4359-af47-b2848e39f335");katex.render("k_{in} = \\frac{k_{unirr}}{1 - k_{unirr}\\frac{R}{g}}", element, {displayMode:true,throwOnError:false});$

where $var element = document.getElementById("moose-equation-da6bf325-e46d-4ed8-8166-efc1d20a0317");katex.render("k_{unirr}", element, {displayMode:false,throwOnError:false});$ is the unirradiated thermal conductivity calculated by any of the models described above (WHITE, SHIMIZU, ZHANG, or HANDBOOK), $var element = document.getElementById("moose-equation-d944eb2e-a23b-46ce-90c1-bee95f77833f");katex.render("R", element, {displayMode:false,throwOnError:false});$ is the Kapitza resistance (2.5e-8 m $var element = document.getElementById("moose-equation-10ac06e2-002a-40e8-ba15-2c65b9a06cdc");katex.render("^2", element, {displayMode:false,throwOnError:false});$ -K/W), and $var element = document.getElementById("moose-equation-4823314a-cd36-4f24-9ef0-be419b6c3f0f");katex.render("g", element, {displayMode:false,throwOnError:false});$ is the grain size (taken as 35 $var element = document.getElementById("moose-equation-617147db-a125-4258-8524-c53aa38e8b86");katex.render("\\mu", element, {displayMode:false,throwOnError:false});$ m).

The modified Kapitza resistance is determined based upon the amount of grain boundary coverage: $var element = document.getElementById("moose-equation-c76e27c0-356a-4aab-b6ce-0b6c11d08570");katex.render("GB_{cov} = FCOV / 3000.0", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-bfe3544e-05e8-4d3a-b153-bcc1dcb4edc0");katex.render("GB_{cov}", element, {displayMode:false,throwOnError:false});$ is the grain boundary coverage, and $var element = document.getElementById("moose-equation-df1e9b1f-885d-4857-bc61-7246469c45bf");katex.render("FCOV", element, {displayMode:false,throwOnError:false});$ is computed by U3Si2TricubicInterpolationUserObject. The modified Kapitza resistance is then determined by: $var element = document.getElementById("moose-equation-ad168ec8-65a2-4df3-b1a8-01173ca9d790");katex.render("R' = R \\left( 1 - GB_{cov}\\right)^{0.86 + 0.3 ln\\left(R\\right)}", element, {displayMode:true,throwOnError:false});$

The first degradation factor known as the intergranular factor is then computed by: $var element = document.getElementById("moose-equation-65d0ff54-289b-477b-b6b9-b956297a016b");katex.render("f_{inter} = \\frac{1.0}{1.0 - k_{in}\\dfrac{R'}{g_g}}", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-dc8eb459-2865-4239-9ce5-b35be854d679");katex.render("g_g", element, {displayMode:false,throwOnError:false});$ is the grain size specified in the GRASS-SST rate theory calculation. This value is taken as 5.0 $var element = document.getElementById("moose-equation-629417f0-1fab-4223-a377-a0e0b7e2f4f4");katex.render("\\mu", element, {displayMode:false,throwOnError:false});$ m. The second degradation factor known as the intragranular factor is calculated by: $var element = document.getElementById("moose-equation-00844f74-cdbf-43f7-b973-ee5a49744127");katex.render("f_{intra} = \\frac{1.0 - GSWb}{1.0 + 0.9GSWb}", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-760f2cd5-d423-4f54-b870-db9bbe19f501");katex.render("GSWb", element, {displayMode:false,throwOnError:false});$ is the intragranular gaseous swelling strain due to intragranular bubbles calculated by U3Si2TricubicInterpolationUserObject. Finally the thermal conductivity is then given as: $var element = document.getElementById("moose-equation-d6d93f12-0529-4eeb-a619-1a70503745a9");katex.render("k = k_{in} f_{inter} f_{intra}", element, {displayMode:true,throwOnError:false});$

Specific Heat Capacity

(Default) WHITE model

The default correlation for the specific heat of C $var element = document.getElementById("moose-equation-f81f5a68-9c85-4913-81f8-0192f8363078");katex.render("_p", element, {displayMode:false,throwOnError:false});$ (J/kg-K) of U $var element = document.getElementById("moose-equation-c692cd74-b6aa-4083-9abd-4bfdedd5dd93");katex.render("_3", element, {displayMode:false,throwOnError:false});$ Si $var element = document.getElementById("moose-equation-a4016d2e-e31a-460e-a1a5-f9514b504357");katex.render("_2", element, {displayMode:false,throwOnError:false});$ is equation 2 from White et al. (2015): $var element = document.getElementById("moose-equation-9ed80ff8-bd9b-4201-abc8-e732e6d3e552");katex.render(" C_p = 140.5 + 0.02582 T", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-86086545-cc16-4870-a930-e68bcb924f70");katex.render("T", element, {displayMode:false,throwOnError:false});$ is temperature in K.

IAEA model

An alternative correlation that can be used is taken from Matos and Snelgrove (1992): $var element = document.getElementById("moose-equation-2cce4eea-1b4a-49f6-bb71-ea144b8cdec2");katex.render("C_p = 199 + 0.104\\left(T-273.15\\right)", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-cd838722-cda3-4538-bb2f-236178a86f9a");katex.render("T", element, {displayMode:false,throwOnError:false});$ is temperature in K and C $var element = document.getElementById("moose-equation-64b3cfbe-c0c8-4329-8008-cbcb7a9ce22d");katex.render("_p", element, {displayMode:false,throwOnError:false});$ is the specific heat capacity is in J/kg-K. The reference does not state the validity range of this expression.

HANDBOOK model

A third option is available from the U $var element = document.getElementById("moose-equation-3f037465-a4e4-4044-8cc5-f7dcb410baa0");katex.render("_3", element, {displayMode:false,throwOnError:false});$ Si $var element = document.getElementById("moose-equation-15f885c3-6e63-4a5d-bbe9-dcc26563d885");katex.render("_2", element, {displayMode:false,throwOnError:false});$ handbook (White, 2017). $var element = document.getElementById("moose-equation-b174bb6b-ce5a-4b44-ab59-e3e3d3b4a785");katex.render("C_p = 1000.0 \\left(3.52 \\times 10^{-5} T + 0.18\\right)", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-1a0e3b98-c216-4667-900b-b749adb46d5f");katex.render("T", element, {displayMode:false,throwOnError:false});$ is temperature in K and C $var element = document.getElementById("moose-equation-bb732398-134c-46d3-a43b-be3a98da08b5");katex.render("_p", element, {displayMode:false,throwOnError:false});$ is the specific heat capacity is in J/kg-K.

Example Input Syntax

[Materials<<<{"href": "../../syntax/Materials/index.html"}>>>]
  [fuel_thermalU3Si2]
    type = SilicideFuelThermal<<<{"description": "Computes the specific heat and thermal conductivity for different phases of uranium silicide fuel.", "href": "SilicideFuelThermal.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = 1
    temperature<<<{"description": "Coupled temperature"}>>> = T
    specific_heat_model<<<{"description": "The chosen model to use for specific heat: WHITE, IAEA or HANDBOOK"}>>> = WHITE # This is the default
    thermal_conductivity_model<<<{"description": "The chosen model to use for thermal conductivity: WHITE, SHIMIZU, ZHANG or HANDBOOK"}>>> = WHITE # This is the default
  []
[]

Input Parameters

temperatureCoupled temperature
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Coupled temperature

Required Parameters

axis_vectorVector defining direction of cylindrical axis (3D Cartesian models) when using the Argonne thermal conductivity model.
C++ Type:libMesh::VectorValue<double>
Unit:(no unit assumed)
Controllable:No
Description:Vector defining direction of cylindrical axis (3D Cartesian models) when using the Argonne thermal conductivity model.
blockThe list of blocks (ids or names) that this object will be applied
C++ Type:std::vector<SubdomainName>
Controllable:No
Description:The list of blocks (ids or names) that this object will be applied
boundaryThe list of boundaries (ids or names) from the mesh where this object applies
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:The list of boundaries (ids or names) from the mesh where this object applies
burnupCoupled Burnup
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Coupled Burnup
burnup_functionBurnup function
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:Burnup function
computeTrueWhen false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
Default:True
C++ Type:bool
Controllable:No
Description:When false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
constant_onNONEWhen ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
Default:NONE
C++ Type:MooseEnum
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.
originOrigin of cylinder axis of rotation for 2D and 3D Cartesian models when using the Argonne thermal conductivity model.
C++ Type:libMesh::VectorValue<double>
Unit:(no unit assumed)
Controllable:No
Description:Origin of cylinder axis of rotation for 2D and 3D Cartesian models when using the Argonne thermal conductivity model.
silicon_mole_fraction0.4The mole fraction of silicon in the fuel. For example for U3Si2 this parameter would be 0.4
Default:0.4
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The mole fraction of silicon in the fuel. For example for U3Si2 this parameter would be 0.4
specific_heat_modelWHITEThe chosen model to use for specific heat: WHITE, IAEA or HANDBOOK
Default:WHITE
C++ Type:MooseEnum
Options:WHITE, IAEA, HANDBOOK
Controllable:No
Description:The chosen model to use for specific heat: WHITE, IAEA or HANDBOOK
specific_heat_scale_factor1The scaling factor on the specific heat.
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The scaling factor on the specific heat.
thermal_conductivity_degradationName of the UserObject that is used to calculate the intergranular and intragranular degradation of thermal conductivity. Must be supplied when modeling thermal conductivity degradation.
C++ Type:UserObjectName
Controllable:No
Description:Name of the UserObject that is used to calculate the intergranular and intragranular degradation of thermal conductivity. Must be supplied when modeling thermal conductivity degradation.
thermal_conductivity_modelWHITEThe chosen model to use for thermal conductivity: WHITE, SHIMIZU, ZHANG or HANDBOOK
Default:WHITE
C++ Type:MooseEnum
Options:WHITE, SHIMIZU, ZHANG, HANDBOOK
Controllable:No
Description:The chosen model to use for thermal conductivity: WHITE, SHIMIZU, ZHANG or HANDBOOK
thermal_conductivity_scale_factor1The scaling factor on the thermal conductivity.
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The scaling factor on the thermal conductivity.

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/solid_mechanics/u3si2_eigenstrains/u3si2_vswelling/swelling.i)
(test/tests/thermalSilicideFuel/thermalU3Si2_degradation.i)
(test/tests/thermalSilicideFuel/thermal_silicide_negative_temperature_exception.i)
(test/tests/thermalSilicideFuel/thermalU3Si5_zhang.i)
(test/tests/thermalSilicideFuel/thermalU3Si2_zhang.i)
(test/tests/thermalSilicideFuel/thermalU3Si2_zhang_error.i)
(test/tests/thermalSilicideFuel/thermalU3Si2_white.i)
(test/tests/thermalSilicideFuel/thermalU3Si2_shimizu_IAEA.i)
(examples/accident_tolerant_fuel/u3si2_zircaloy/u3si2_zircaloy.i)
(test/tests/solid_mechanics/u3si2_eigenstrains/u3si2_vswelling/argonne_rz.i)
(test/tests/thermalSilicideFuel/thermalU3Si2_handbook.i)
(examples/accident_tolerant_fuel/u3si2_sic/u3si2_outer_monolith_1.5D.i)
(test/tests/thermalSilicideFuel/thermalU3Si_zhang.i)

References

C.J. Glassbrenner and G.A. Slack. Thermal conductivity of silicon and germanium from 3k to the melting point. Journal of Physical Review, 134:A1059, 1964.

@article{glassbrenner1964,
    author = "Glassbrenner, C.J. and Slack, G.A.",
    title = "Thermal Conductivity of Silicon and Germanium from 3K to the Melting Point",
    journal = "Journal of Physical Review",
    volume = "134",
    pages = "A1059",
    year = "1964"
}

C.Y. Ho, M.W. Ackerman, K.Y. Wu, S.G. Oh, and T.N. Havill. Thermal conductivity of ten selected binary alloy systems. Journal of Physical and Chemical Reference Data, 7:959, 1978.

@article{ho1978,
    author = "Ho, C.Y. and Ackerman, M.W. and Wu, K.Y. and Oh, S.G. and Havill, T.N.",
    title = "Thermal Conductivity of Ten Selected Binary Alloy Systems",
    journal = "Journal of Physical and Chemical Reference Data",
    volume = "7",
    pages = "959",
    year = "1978"
}

J. E. Matos and J. L. Snelgrove. Research reactor core conversion guidebook-Vol 4: Fuels (Appendices I-K). Technical Report IAEA-TECDOC-643, IAEA, 1992.

@TECHREPORT{IAEA_tecdoc643,
    author = "Matos, J. E. and Snelgrove, J. L.",
    title = "{Research reactor core conversion guidebook-Vol 4: Fuels (Appendices I-K)}",
    institution = "IAEA",
    year = "1992",
    number = "IAEA-TECDOC-643"
}

H. Shimizu. The properties and irradiation behavior of U$_3$Si$_2$. Technical Report NAA-SR-10621, Atomics International, 1965.

@TECHREPORT{Shimizu_1965,
    author = "Shimizu, H.",
    title = "{The properties and irradiation behavior of U$\_3$Si$\_2$}",
    institution = "Atomics International",
    year = "1965",
    number = "NAA-SR-10621"
}

Yu. Tsiovkin, V.V. Dremov, E.S. Koneva, A.A. Povzner, A.N. Filanovich, and A.N. Petrova. Theory of the residual electrical resistivity of binary actinide alloys. Journal of Physics of the Solid State, 52:1–5, 2010.

@article{tsiovkin2010,
    author = "Tsiovkin, Yu. and Dremov, V.V. and Koneva, E.S. and Povzner, A.A. and Filanovich, A.N. and Petrova, A.N.",
    title = "Theory of the Residual Electrical Resistivity of Binary Actinide Alloys",
    journal = "Journal of Physics of the Solid State",
    volume = "52",
    pages = "1-5",
    year = "2010"
}

J. T. White. Issue draft U$_3$Si$_2$ fuel property handbook. Technical Report LA-UR-17-20609, Los Alamos National Laboratory, 2017.

@TECHREPORT{u3si2_handbook,
    author = "White, J. T.",
    title = "Issue draft {U}$\_3${Si}$\_2$ fuel property handbook",
    institution = "Los Alamos National Laboratory",
    number = "LA-UR-17-20609",
    year = "2017"
}

J. T. White. Update to the U$_3$Si$_2$ property handbook. Technical Report LA-UR-18-28719, Los Alamos National Laboratory, 2018.

@TECHREPORT{u3si2_handbook2,
    author = "White, J. T.",
    title = "Update to the {U}$\_3${Si}$\_2$ property handbook",
    institution = "Los Alamos National Laboratory",
    number = "LA-UR-18-28719",
    year = "2018"
}

J. T. White, A. T. Nelson, D. D. Byler, D. J. Safarik, J.T. Dunwoody, and K. J. McClellan. Thermophysical properties of U$_3$Si$_5$ to 1773K. Journal of Nuclear Materials, 456:442–448, 2015.

@ARTICLE{white2015b,
    author = "White, J. T. and Nelson, A. T. and Byler, D. D. and Safarik, D. J. and Dunwoody, J.T. and McClellan, K. J.",
    title = "Thermophysical properties of {U}$\_3${Si}$\_5$ to 1773{K}",
    journal = "Journal of Nuclear Materials",
    year = "2015",
    volume = "456",
    pages = "442-448"
}

J. T. White, A. T. Nelson, J. T. Dunwoody, D. D. Byler, D. J. Safarik, and K. J. McClellan. Thermophysical properties of U$_3$Si$_2$ to 1773K. Journal of Nuclear Materials, 464:275–280, 2015.

@ARTICLE{white2015,
    author = "White, J. T. and Nelson, A. T. and Dunwoody, J. T. and Byler, D. D. and Safarik, D. J. and McClellan, K. J.",
    title = "Thermophysical properties of {U}$\_3${Si}$\_2$ to 1773{K}",
    journal = "Journal of Nuclear Materials",
    year = "2015",
    volume = "464",
    pages = "275-280"
}

(test/tests/thermalSilicideFuel/thermalU3Si2_white.i)

# The mesh is a 1x1x1 cube (single element).
# The temperature is ramped on all faces of the cube from 300 K to 1200K
#       over 100 Ms.
#
# Thermal conductivity and specific heat are computed using the U3Si2 thermal
# model from White et al.
#
# Thermal conductivity expression from eq. 4 in White et al.:
#   1)  White et al. Corrigendum to "Thermophysical properties of U3Si2 to 1773 K.
#       J. Nucl. Materials, 464, pp. 275-280, 2015", J. Nucl. Material, 484,
#       pp. 386-387, 2017.
#
# Specific heat expression from eq. 2 in:
#   2)  White et al. Thermophysical properties of U3Si2 to 1773 K.
#       J. Nucl. Materials, 464, pp. 275-280, 2015.
#
# The thermal conductivity and specific heat computed by BISON for the
# temperatures shown below and compared with analytical solution.
#
# The results are as follows:
#                  Thermal Conductivity             Specific Heat
#               -------------------------       ---------------------
#               BISON           Analytical     BISON        Analytical
# Temp(K)      (W/m-K)          (W/m-K)        J/(kgK)      J/(kgK)
#  300         8.53600          8.53600        192.463      192.463
#  408         9.81040          9.81040        196.083      196.083
#  570         11.7220          11.7220        201.514      201.514
# 1002         16.8196          16.8196        215.995      215.995
# 1137         18.4126          18.4126        220.520      220.520
# 1200         19.1560          19.1560        222.632      222.632


[Mesh]
  [mesh]
    type = FileMeshGenerator
    file = 1x1x1cube.e
  []
[]


[Variables]
  [T]
    order = FIRST
    family = LAGRANGE
    initial_condition = 300     # set initial T to 300 K
  []
[]


[AuxVariables]
  [th_cond]
    order = CONSTANT
    family = MONOMIAL
  []
  [cp]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = T
  []

  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = T
  []

[]


[AuxKernels]
  [th_cond]
    type = MaterialRealAux
    variable = th_cond
    property = thermal_conductivity
    block = 1
    execute_on = 'initial linear'
  []

  [cp]
    type = MaterialRealAux
    variable = cp
    property = specific_heat
    block = 1
    execute_on = 'initial linear'
  []

[]

[Functions]
  [temp_ramp]
    type = PiecewiseLinear
    x = '0.0 100.e6'
    y = '300 1200'
  []
[]

[BCs]

   [VariableT]
     type = FunctionDirichletBC
     boundary = 2      # All cube faces
     variable = T
     function = temp_ramp
   []

[]


[Materials]

  [fuel_thermalU3Si2]
    type = SilicideFuelThermal
    block = 1
    temperature = T
    specific_heat_model = WHITE   # This is the default
    thermal_conductivity_model = WHITE # This is the default
  []

  [density]
    type = ParsedMaterial
    block = 1
    property_name = density
    expression = 1200.0
  []
[]

[Executioner]

   type = Transient


   solve_type = PJFNK

   petsc_options = '-snes_ksp_ew'
   petsc_options_iname = '-ksp_gmres_restart'
   petsc_options_value = '101'

  line_search = 'none'


   l_max_its = 100
   nl_max_its = 100
   nl_rel_tol = 1e-4
   nl_abs_tol = 1e-6
   l_tol = 1e-5
   start_time = 0.0
#  num_steps = 50
   num_steps = 100
#  dt = 1.163e6
   dt = 1.0e6


[]

[Postprocessors]
   [ave_temp_interior]
     # average temperature of the cladding interior and all pellet exteriors
     type = SideAverageValue
     boundary = 2
     variable = T
     execute_on = 'initial linear'
   []
   [avg_th_cond]
     type = ElementAverageValue
     block = 1
     variable = th_cond
     execute_on = 'initial linear'
   []
   [avg_cp]
     type = ElementAverageValue
     block = 1
     variable = cp
     execute_on = 'initial linear'
   []
   [average_fuel_T]
     type = ElementAverageValue
     block = 1
     variable = T
     execute_on = 'initial linear'
   []
 []

[Outputs]
  exodus = true
[]

(test/tests/solid_mechanics/u3si2_eigenstrains/u3si2_vswelling/swelling.i)

#
# Test of combined swelling and densification of U3Si2 (1000K)
#
# With a burnup of 0.05, the volumetric strain should be 0.0396075; the strain due to swelling alone is 0.04960750; and the strain due to densification alone is -0.01.
# This is easily checked with the 'swelling', 'densification', and 'volume' postprocessor values.  The current volumetric_strain postprocessor calculates the first invariant of the volumetric strain not the volumetric strain itself.  Therefore, use the volume change as the volumetric strain.
#
# Volume swelling of U3Si2 is an emprical fit of experimental data from M.R. Finlay.
# The Finlay data is for fuel particle swelling and was calculated by the author
# based on miniplate swelling.
#
# See Figure 3 in article:
#   1.)  M.R. Finlay.  Irradiation behavior of uranium silicide compounds. Journal
#   of Nuclear Materials.  Vol 325 (2004) p. 118-128.
#
#  Empirical fit to data:  dV/Vo=3.88008*BU^2+0.79811*BU
#  Where dV/Vo is a fraction relative to the initial volume and BU is in FIMA.
#
#  The above empirical fit is further separated into gaseous and solid swelling components using the data from Hofman 1989.
#
# Fuel densification is computed using the ESCORE emprical model.  This is the same fuel densification used in VSwellingUO2.
# For further information, see:
#   2) Y. Rashid, R. Dunham, and R. Montgomery.  Fuel analysis and licensing code: FALCON MOD01.
#   Technical Report EPRI 1011308, Electric Power Research Institute, December 2004.
#
# For this problem, temperature is fixed at 1000K and burnup is increased from 0 to 0.05 over a time of t=0 to t=1.  There are 10 steps.
# The swelling columns below represent the sum of the gaseous and solid swelling components and is calculated by subtracting the densification
# postprocessor from the swelling postprocessor.
#
# The results are as follows:
#                            BISON                         Analytical Swelling
#                                                              Strain Calc
#             --------------------------------------      ---------------------
#                Gas. + Solid                                   Gas. + Solid
# Burnup          Swelling         Densification                  Swelling
# (FIMA)           (dV/V)             (dV/V)                       (dV/V)
#  0                  0                 0                            0
#  0.005         0.00408757        -0.008472744                  0.00408757
#  0.010         0.00836918        -0.009766749                  0.00836918
#  0.015         0.01284483        -0.009964377                  0.01284483
#  0.020         0.01751452        -0.009994559                  0.01751452
#  0.025         0.02237825        -0.009999169                  0.02237825
#  0.030         0.02743602        -0.009999981                  0.02743602
#  0.035         0.03268783        -0.009999981                  0.03268783
#  0.040         0.03813368        -0.009999997                  0.03813368
#  0.045         0.04377357        -0.010000000                  0.04377357
#  0.050         0.04960750        -0.010000000                  0.04960750
#

initial_fuel_density = 11590.0

[GlobalParams]
  density = ${initial_fuel_density}
  displacements = 'disp_x disp_y disp_z'
[]

[Mesh]
  [mesh]
    type = FileMeshGenerator
    file = patch.e
  []
[]

[Variables]
  active = 'disp_x disp_y disp_z temp'

  [disp_x]
    order = FIRST
    family = LAGRANGE
  []

  [disp_y]
    order = FIRST
    family = LAGRANGE
  []

  [disp_z]
    order = FIRST
    family = LAGRANGE
  []

  [temp]
    order = FIRST
    family = LAGRANGE
    initial_condition = 1000.0
  []
[]

[AuxVariables]

  [burnup]
    order = FIRST
    family = LAGRANGE
  []

  [total_swell]
    order = CONSTANT
    family = MONOMIAL
  []

  [densification]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = finite
    eigenstrain_names = 'fuelthermal_strain swell'
    temperature = temp
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = temp
  []

  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temp
  []

[]

[Functions]
  [burnupFunc]
    type = PiecewiseLinear
    x = '0 1'
    y = '0 0.05'
  []
[]

[AuxKernels]

  [burnup]
    type = FunctionAux
    variable = burnup
    function = burnupFunc
    execute_on = timestep_begin
  []

  [total_swelling]
    type = MaterialRealAux
    variable = total_swell
    property = volumetric_swelling_strain
    block = '1 2 3 4 5 6 7'
  []

  [densification]
    type = MaterialRealAux
    variable = densification
    property = densification
    block = ' 1 2 3 4 5 6 7'
  []
[]

[BCs]

  [bottom_x]
    type = DirichletBC
    variable = disp_x
    boundary = 10
    value = 0.0
  []

  [bottom_y]
    type = DirichletBC
    variable = disp_y
    boundary = 9
    value = 0.0
  []

  [bottom_z]
    type = DirichletBC
    variable = disp_z
    boundary = 14
    value = 0.0
  []

  [bottom_temp]
    type = DirichletBC
    variable = temp
    boundary = 3
    value = 1000.0
  []

  [top_temp]
    type = DirichletBC
    variable = temp
    boundary = 5
    value = 1000.0
  []

[]

[Materials]

  [fuel_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = '1 2 3 4 5 6 7'
    youngs_modulus = 1e11
    poissons_ratio = 0.17
  []
  [fuel_swelling]
    type = U3Si2VolumetricSwellingEigenstrain
    block = '1 2 3 4 5 6 7'
    temperature = temp
    burnup = burnup
    complete_burnup = 10
    eigenstrain_name = swell
  []
  [fuel_thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    block = '1 2 3 4 5 6 7'
    thermal_expansion_coeff = 1.5e-5
    temperature = temp
    stress_free_temperature = 1000.0
    eigenstrain_name = fuelthermal_strain
  []
  [fuel_stress]
    type = ComputeFiniteStrainElasticStress
    block = '1 2 3 4 5 6 7'
  []

  [thermal]
    type = SilicideFuelThermal
    block = '1 2 3 4 5 6 7'
    temperature = temp
  []

  [density]
    type = StrainAdjustedDensity
    block = '1 2 3 4 5 6 7'
    strain_free_density = ${initial_fuel_density}
  []

[]

[Executioner]
   type = Transient

  solve_type = 'PJFNK'


   petsc_options = '-snes_ksp_ew '
   petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type'
   petsc_options_value = '70 hypre boomeramg'
   l_max_its = 60
   nl_rel_tol = 1e-8
   nl_abs_tol = 1e-10
   l_tol = 1e-5

   start_time = 0.0
   dt = 0.1
   num_steps = 10

[]

[Postprocessors]
  [avgFuelTemp]
    type = ElementAverageValue
    variable = temp
    block = 4
    execute_on = 'initial linear'
  []
  [volume]
    type = VolumePostprocessor
    use_displaced_mesh = true
    execute_on = 'initial timestep_end'
  []

  [ave_burnup]
    type = ElementAverageValue
    variable = burnup
    block = 4
  []

  [swelling]
    type = ElementAverageValue
    variable = total_swell
    block = 4
  []

  [densification]
    type = ElementAverageValue
    variable = densification
    block = 4
  []
[]

[Outputs]
  exodus = true
  hide = 'disp_x disp_y disp_z temp'
[]

(test/tests/thermalSilicideFuel/thermalU3Si2_degradation.i)

#
# This input file is used to test the thermal conductivity degradation
# model for U3Si2 fuel in an axisymmetric RZ geometry.
#
# The thermal conductivity model was developed using rate theory calculations at
# the Argonne National Laboratory:
#
# Y. Miao, K. A. Gamble, D. Andersson, B. Ye, Z. Mei, G. Hofman and A. M. Yacout,
# "Gaseous swelling of U3Si2 during steady-state LWR operation: A rate theory
# investigation," Nuclear Engineering and Design, 322, 2017, p. 336-344.
#
# Note that for this test the input CSV files are made up for testing the
# algorithm.  The full CSV data set developed using the rate theory calculations
# from Argonne National Laboratory can be obtained by contacted a BISON
# developer.
#
# For this problem, a 1x1 mm square is simulated. The temperature is fixed at
# 450 K and the burnup is fixed at 9.086425e-3 FIMA which corresponds to a
# fission density of 0.25e21 fissions/cm^3.
#
# The thermal conductivity degradation calculation is complex and outlined
# in the documentation.  Given the supplied input CSVs the parameters FCOV and GSWb
# calculated from the tricubic interpolation userobject should be 7.5 and 0.00375
# respectively.  Then, using these values and the given temperature and burnup
# above the analytically calculated thermal conductivity is given as: 9.79462 W/m-K
#
# This value is confirmed when looking at the avg_th_cond postprocessor.
#

[GlobalParams]
  displacements = 'disp_x disp_y'
  volumetric_locking_correction = true
[]

[Mesh]
  coord_type = RZ
  [mesh]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 1e-3
    ymin = 0
    ymax = 1e-3
    nx = 1
    ny = 1
  []
[]

[UserObjects]
  [thermal_conductivity_degradation]
    type = U3Si2TricubicInterpolationUserObject
    execute_on = 'initial nonlinear'
    temperature_grid_points_file = temperature.csv
    temperature_gradient_grid_points_file = temperature_gradient.csv
    fission_density_grid_points_file = fission_density.csv
    grain_boundary_coverage_file = fcov.csv
    intragranular_gaseous_swelling_file = gswb.csv
    total_gaseous_swelling_file = gsw.csv
  []
[]

[Variables]
  [temp]
    order = FIRST
    family = LAGRANGE
    initial_condition = 450.0
  []
[]

[AuxVariables]
  [th_cond]
    order = CONSTANT
    family = MONOMIAL
  []
  [burnup]
    order = FIRST
    family = LAGRANGE
  []
[]

[Physics]
  [SolidMechanics]
    [QuasiStatic]
      [all]
        strain = FINITE
        block = 0
        incremental = true
        add_variables = true
      []
    []
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = temp
  []
  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temp
  []
[]

[Functions]
  [burnupFunc]
    type = ConstantFunction
    value = 9.086425e-3  # Corresponds to a fission density of 0.25e21 fissions/cm^3
  []
[]

[AuxKernels]
  [th_cond]
    type = MaterialRealAux
    variable = th_cond
    property = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [burnup]
    type = FunctionAux
    variable = burnup
    function = burnupFunc
    execute_on = timestep_begin
  []
[]

[BCs]
  [left_x]
    type = DirichletBC
    variable = disp_x
    boundary = left
    value = 0.0
  []
  [bottom_y]
    type = DirichletBC
    variable = disp_y
    boundary = bottom
    value = 0.0
  []
  [left_temp]
    type = DirichletBC
    variable = temp
    boundary = left
    value = 450.0
  []
  [right_temp]
    type = DirichletBC
    variable = temp
    boundary = right
    value = 450.0
  []
[]

[Materials]
  [stress]
    type = ComputeFiniteStrainElasticStress
  []
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = 0
    youngs_modulus = 1.0e11
    poissons_ratio = 0.17
  []
  [thermal]
    type = SilicideFuelThermal
    block = 0
    thermal_conductivity_degradation = 'thermal_conductivity_degradation'
    thermal_conductivity_model = WHITE
    burnup = burnup
    temperature = temp
  []
  [density]
    type = ParsedMaterial
    block = 0
    property_name = density
    expression = 11590.0
  []
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'

  petsc_options = '-snes_ksp_ew '
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu       superlu_dist'
  l_max_its = 60
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-9
  l_tol = 1e-5

  start_time = 0.0
  end_time = 1.0
  num_steps = 1
[]

[Postprocessors]
  [ave_burnup]
    type = ElementAverageValue
    variable = burnup
    block = 0
  []
  [avg_th_cond]
    type = ElementAverageValue
    variable = th_cond
    execute_on = 'initial timestep_end'
  []
  [avg_temp]
    type = AverageNodalVariableValue
    variable = temp
    block = 0
  []
[]

[Outputs]
  exodus = true
[]

(test/tests/thermalSilicideFuel/thermal_silicide_negative_temperature_exception.i)

# This test ensures that the moose exception to cut the timestep when a
# negative temperature is detected in SilicideFuelThermal is properly executed.

[Mesh]
  [line]
    type = GeneratedMeshGenerator
    dim = 1
  []
[]

[Functions]
  [temperature_func]
    type = PiecewiseLinear
    x = '0 2'
    y = '300 -100.0'
  []
[]

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

[AuxVariables]
  [burnup]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = temp
  []
[]

[AuxKernels]
  [burnup]
    type = ConstantAux
    variable = burnup
    value = 0
  []
[]

[BCs]
  [fixed_temp]
    type = FunctionDirichletBC
    variable = temp
    boundary = 'left right'
    function = temperature_func
  []
[]

[Materials]
  [thermal]
    type = SilicideFuelThermal
    thermal_conductivity_model = WHITE
    temperature = temp
    burnup = burnup
  []
[]

[Executioner]
  type = Transient
  num_steps = 2
  dt = 2
[]

[Postprocessors]
  [dt]
   type = TimestepSize
  []
[]

[UserObjects]
  [terminator]
    type = Terminator
    expression = 'dt = 1'
    execute_on = timestep_end
  []
[]

[Outputs]
  csv = true
[]

(test/tests/thermalSilicideFuel/thermalU3Si5_zhang.i)

# The mesh is a 1x1x1 cube (single element).
# The temperature is ramped on all faces of the cube from 300 K to 1800K
#       over 800 seconds.
#
# Thermal conductivity is computed using the Zhang model.
#
# The thermal conductivity calculated by BISON is compared against the analytical
# thermal conductivity.
#
# The results are as follows:
#                  Thermal Conductivity
#               -------------------------
#               BISON           Analytical
# Temp(K)      (W/m-K)          (W/m-K)
#  300         5.91090          5.91090
#  500         7.79617          7.79617
#  700         9.72824          9.72824
#  900         11.6365          11.6365
# 1100         13.5816          13.5816
# 1300         15.5783          15.5783
# 1500         17.6173          17.6173
# 1700         19.5742          19.5742
# 1800         20.4491          20.4491

[Mesh]
  [mesh]
    type = FileMeshGenerator
    file = 1x1x1cube.e
  []
[]


[Variables]
  [T]
    order = FIRST
    family = LAGRANGE
    initial_condition = 300     # set initial T to 300 K
  []
[]


[AuxVariables]
  [th_cond]
    order = CONSTANT
    family = MONOMIAL
  []
  [cp]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = T
  []

  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = T
  []
[]


[AuxKernels]
  [th_cond]
    type = MaterialRealAux
    variable = th_cond
    property = thermal_conductivity
    block = 1
    execute_on = 'initial linear'
  []

  [cp]
    type = MaterialRealAux
    variable = cp
    property = specific_heat
    block = 1
    execute_on = 'initial linear'
  []
[]

[Functions]
  [temp_ramp]
    type = PiecewiseLinear
    x = '0.0 100 200 300 400 500 600 700 800'
    y = '300 500 700 900 1100 1300 1500 1700 1800'
  []
[]

[BCs]
  [VariableT]
    type = FunctionDirichletBC
    boundary = 2      # All cube faces
    variable = T
    function = temp_ramp
  []
[]


[Materials]
  [fuel_thermalU3Si5]
    type = SilicideFuelThermal
    block = 1
    temperature = T
    silicon_mole_fraction = 0.625
    specific_heat_model = WHITE   # This is the default
    thermal_conductivity_model = ZHANG
  []

  [density]
    type = ParsedMaterial
    block = 1
    property_name = density
    expression = 1200.0
  []
[]

[Executioner]

  type = Transient

  solve_type = PJFNK

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-ksp_gmres_restart'
  petsc_options_value = '101'

  line_search = 'none'


  l_max_its = 100
  nl_max_its = 100
  nl_rel_tol = 1e-4
  nl_abs_tol = 1e-6
  l_tol = 1e-5
  start_time = 0.0
  num_steps = 8
  dt = 100
[]

[Postprocessors]
  [ave_temp_interior]
    # average temperature of the cladding interior and all pellet exteriors
    type = SideAverageValue
    boundary = 2
    variable = T
    execute_on = 'initial linear'
  []
  [avg_th_cond]
    type = ElementAverageValue
    block = 1
    variable = th_cond
    execute_on = 'initial linear'
  []
  [average_fuel_T]
    type = ElementAverageValue
    block = 1
    variable = T
    execute_on = 'initial linear'
  []
[]

[Outputs]
  exodus = true
[]

(test/tests/thermalSilicideFuel/thermalU3Si2_zhang.i)

# The mesh is a 1x1x1 cube (single element).
# The temperature is ramped on all faces of the cube from 300 K to 1800K
#       over 800 seconds.
#
# Thermal conductivity is computed using the Zhang model.
#
# The thermal conductivity calculated by BISON is compared against the analytical
# thermal conductivity.
#
# The results are as follows:
#                  Thermal Conductivity
#               -------------------------
#               BISON           Analytical
# Temp(K)      (W/m-K)          (W/m-K)
#  300         9.74039          9.74039
#  500         13.2832          13.2832
#  700         16.7020          16.7020
#  900         19.8831          19.8831
# 1100         22.9247          22.9247
# 1300         25.8465          25.8465
# 1500         28.5840          28.5840
# 1700         31.0546          31.0546
# 1800         32.2090          32.2090

[Mesh]
  [mesh]
    type = FileMeshGenerator
    file = 1x1x1cube.e
  []
[]


[Variables]
  [T]
    order = FIRST
    family = LAGRANGE
    initial_condition = 300     # set initial T to 300 K
  []
[]


[AuxVariables]
  [th_cond]
    order = CONSTANT
    family = MONOMIAL
  []
  [cp]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = T
  []

  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = T
  []
[]


[AuxKernels]
  [th_cond]
    type = MaterialRealAux
    variable = th_cond
    property = thermal_conductivity
    block = 1
    execute_on = 'initial linear'
  []

  [cp]
    type = MaterialRealAux
    variable = cp
    property = specific_heat
    block = 1
    execute_on = 'initial linear'
  []
[]

[Functions]
  [temp_ramp]
    type = PiecewiseLinear
    x = '0.0 100 200 300 400 500 600 700 800'
    y = '300 500 700 900 1100 1300 1500 1700 1800'
  []
[]

[BCs]
  [VariableT]
    type = FunctionDirichletBC
    boundary = 2      # All cube faces
    variable = T
    function = temp_ramp
  []
[]


[Materials]
  [fuel_thermalU3Si2]
    type = SilicideFuelThermal
    block = 1
    temperature = T
    silicon_mole_fraction = 0.4
    specific_heat_model = WHITE   # This is the default
    thermal_conductivity_model = ZHANG
  []

  [density]
    type = ParsedMaterial
    block = 1
    property_name = density
    expression = 1200.0
  []
[]

[Executioner]

  type = Transient

  solve_type = PJFNK

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-ksp_gmres_restart'
  petsc_options_value = '101'

  line_search = 'none'


  l_max_its = 100
  nl_max_its = 100
  nl_rel_tol = 1e-4
  nl_abs_tol = 1e-6
  l_tol = 1e-5
  start_time = 0.0
  num_steps = 8
  dt = 100
[]

[Postprocessors]
  [ave_temp_interior]
    # average temperature of the cladding interior and all pellet exteriors
    type = SideAverageValue
    boundary = 2
    variable = T
    execute_on = 'initial linear'
  []
  [avg_th_cond]
    type = ElementAverageValue
    block = 1
    variable = th_cond
    execute_on = 'initial linear'
  []
  [average_fuel_T]
    type = ElementAverageValue
    block = 1
    variable = T
    execute_on = 'initial linear'
  []
[]

[Outputs]
  exodus = true
[]

(test/tests/thermalSilicideFuel/thermalU3Si2_zhang_error.i)

# This regression tests verifies that the silicon mole fraction
# error checking is working as expected.  When using the Zhang
# model the given silicon mole fraction must be between 0 and 1.
#
# In this test a value of 1.5 is specified and the testing system
# checks that the following error message is printed:
#
# "Range check failed for parameter Materials/fuel_thermalU3Si2/silicon_mole_fraction"
#
# The check only occurs if the Zhang model is specified.
#
[Mesh]
  [mesh]
    type = FileMeshGenerator
    file = 1x1x1cube.e
  []
[]


[Variables]
  [T]
    order = FIRST
    family = LAGRANGE
    initial_condition = 300     # set initial T to 300 K
  []
[]


[AuxVariables]
  [th_cond]
    order = CONSTANT
    family = MONOMIAL
  []
  [cp]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = T
  []

  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = T
  []
[]


[AuxKernels]
  [th_cond]
    type = MaterialRealAux
    variable = th_cond
    property = thermal_conductivity
    block = 1
  []

  [cp]
    type = MaterialRealAux
    variable = cp
    property = specific_heat
    block = 1
  []
[]

[Functions]
  [temp_ramp]
    type = PiecewiseLinear
    x = '0.0 100 200 300 400 500 600 700 800'
    y = '300 500 700 900 1100 1300 1500 1700 1800'
  []
[]

[BCs]
  [VariableT]
    type = FunctionDirichletBC
    boundary = 2      # All cube faces
    variable = T
    function = temp_ramp
  []
[]


[Materials]
  [fuel_thermalU3Si2]
    type = SilicideFuelThermal
    block = 1
    temperature = T
    silicon_mole_fraction = 1.5
    specific_heat_model = WHITE   # This is the default
    thermal_conductivity_model = ZHANG
  []

  [density]
    type = StrainAdjustedDensity
    block = 1
    strain_free_density = 1200.0
  []
[]

[Executioner]

  type = Transient

  solve_type = PJFNK

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-ksp_gmres_restart'
  petsc_options_value = '101'

  line_search = 'none'


  l_max_its = 100
  nl_max_its = 100
  nl_rel_tol = 1e-4
  nl_abs_tol = 1e-6
  l_tol = 1e-5
  start_time = 0.0
  num_steps = 8
  dt = 100
[]

[Postprocessors]
  [ave_temp_interior]
    # average temperature of the cladding interior and all pellet exteriors
    type = SideAverageValue
    boundary = 2
    variable = T
  []
  [avg_th_cond]
    type = ElementAverageValue
    block = 1
    variable = th_cond
  []
  [average_fuel_T]
    type = ElementAverageValue
    block = 1
    variable = T
  []
[]

[Outputs]
  exodus = true
[]

(test/tests/thermalSilicideFuel/thermalU3Si2_white.i)

# The mesh is a 1x1x1 cube (single element).
# The temperature is ramped on all faces of the cube from 300 K to 1200K
#       over 100 Ms.
#
# Thermal conductivity and specific heat are computed using the U3Si2 thermal
# model from White et al.
#
# Thermal conductivity expression from eq. 4 in White et al.:
#   1)  White et al. Corrigendum to "Thermophysical properties of U3Si2 to 1773 K.
#       J. Nucl. Materials, 464, pp. 275-280, 2015", J. Nucl. Material, 484,
#       pp. 386-387, 2017.
#
# Specific heat expression from eq. 2 in:
#   2)  White et al. Thermophysical properties of U3Si2 to 1773 K.
#       J. Nucl. Materials, 464, pp. 275-280, 2015.
#
# The thermal conductivity and specific heat computed by BISON for the
# temperatures shown below and compared with analytical solution.
#
# The results are as follows:
#                  Thermal Conductivity             Specific Heat
#               -------------------------       ---------------------
#               BISON           Analytical     BISON        Analytical
# Temp(K)      (W/m-K)          (W/m-K)        J/(kgK)      J/(kgK)
#  300         8.53600          8.53600        192.463      192.463
#  408         9.81040          9.81040        196.083      196.083
#  570         11.7220          11.7220        201.514      201.514
# 1002         16.8196          16.8196        215.995      215.995
# 1137         18.4126          18.4126        220.520      220.520
# 1200         19.1560          19.1560        222.632      222.632


[Mesh]
  [mesh]
    type = FileMeshGenerator
    file = 1x1x1cube.e
  []
[]


[Variables]
  [T]
    order = FIRST
    family = LAGRANGE
    initial_condition = 300     # set initial T to 300 K
  []
[]


[AuxVariables]
  [th_cond]
    order = CONSTANT
    family = MONOMIAL
  []
  [cp]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = T
  []

  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = T
  []

[]


[AuxKernels]
  [th_cond]
    type = MaterialRealAux
    variable = th_cond
    property = thermal_conductivity
    block = 1
    execute_on = 'initial linear'
  []

  [cp]
    type = MaterialRealAux
    variable = cp
    property = specific_heat
    block = 1
    execute_on = 'initial linear'
  []

[]

[Functions]
  [temp_ramp]
    type = PiecewiseLinear
    x = '0.0 100.e6'
    y = '300 1200'
  []
[]

[BCs]

   [VariableT]
     type = FunctionDirichletBC
     boundary = 2      # All cube faces
     variable = T
     function = temp_ramp
   []

[]


[Materials]

  [fuel_thermalU3Si2]
    type = SilicideFuelThermal
    block = 1
    temperature = T
    specific_heat_model = WHITE   # This is the default
    thermal_conductivity_model = WHITE # This is the default
  []

  [density]
    type = ParsedMaterial
    block = 1
    property_name = density
    expression = 1200.0
  []
[]

[Executioner]

   type = Transient


   solve_type = PJFNK

   petsc_options = '-snes_ksp_ew'
   petsc_options_iname = '-ksp_gmres_restart'
   petsc_options_value = '101'

  line_search = 'none'


   l_max_its = 100
   nl_max_its = 100
   nl_rel_tol = 1e-4
   nl_abs_tol = 1e-6
   l_tol = 1e-5
   start_time = 0.0
#  num_steps = 50
   num_steps = 100
#  dt = 1.163e6
   dt = 1.0e6


[]

[Postprocessors]
   [ave_temp_interior]
     # average temperature of the cladding interior and all pellet exteriors
     type = SideAverageValue
     boundary = 2
     variable = T
     execute_on = 'initial linear'
   []
   [avg_th_cond]
     type = ElementAverageValue
     block = 1
     variable = th_cond
     execute_on = 'initial linear'
   []
   [avg_cp]
     type = ElementAverageValue
     block = 1
     variable = cp
     execute_on = 'initial linear'
   []
   [average_fuel_T]
     type = ElementAverageValue
     block = 1
     variable = T
     execute_on = 'initial linear'
   []
 []

[Outputs]
  exodus = true
[]

(test/tests/thermalSilicideFuel/thermalU3Si2_shimizu_IAEA.i)

# The mesh is a 1x1x1 cube (single element).
# The temperature is ramped on all faces of the cube from 300 K to 1200K
#       over 100 Ms.
#
# Thermal conductivity and specific heat are computed using the U3Si2 thermal
# conductivity model.
#
# Thermal conductivity expression derived from the induction cast data set in
# figure 4 from Shimizu.  See:
#   1)  Shimizu, H. The properties and irradiation behavior of U3Si2.
#       NAA-SR-10621, Atomics International. July 25, 1965.
#   *****ONLY VALID FOR ROOM TEMPERATURE UP TO 1200 DEG CELCIUS*********
#
# Specific heat expression taken from page 26 of:
#   2)  IAEA-TECDOC-643, Research reactor core conversion guidebook- Volume 4:
#       Fuel(Appendices -I-K).
#
# The thermal conductivity and specific heat computed by BISON for the
# temperatures shown below and compared with analytical solution.
#
# The results are as follows:
#                  Thermal Conductivity             Specific Heat
#               -------------------------       ---------------------
#               BISON           Analytical     BISON        Analytical
# Temp(K)      (W/m-K)          (W/m-K)        J/(kgK)      J/(kgK)
#  300         8.116935         8.116935       201.7924     201.7924
#  408         8.667735         8.667735       213.0244     213.0244
#  570         9.493935         9.493935       229.8724     229.8724
# 1002         11.697135        11.697135      274.8004     274.8004
# 1137         12.385635        12.385635      288.8404     288.8404
# 1200         12.706935        12.706935      295.3924     295.3924


[Mesh]
  [mesh]
    type = FileMeshGenerator
    file = 1x1x1cube.e
  []
[]


[Variables]
  [T]
    order = FIRST
    family = LAGRANGE
    initial_condition = 300     # set initial T to 300 K
  []
[]


[AuxVariables]
  [th_cond]
    order = CONSTANT
    family = MONOMIAL
  []
  [cp]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = T
  []

  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = T
  []

[]


[AuxKernels]
  [th_cond]
    type = MaterialRealAux
    variable = th_cond
    property = thermal_conductivity
    block = 1
    execute_on = 'initial linear'
  []

  [cp]
    type = MaterialRealAux
    variable = cp
    property = specific_heat
    block = 1
    execute_on = 'initial linear'
  []

[]

[Functions]
  [temp_ramp]
    type = PiecewiseLinear
    x = '0.0 100.e6'
    y = '300 1200'
  []
[]

[BCs]

   [VariableT]
     type = FunctionDirichletBC
     boundary = 2      # All cube faces
     variable = T
     function = temp_ramp
   []

[]


[Materials]

  [fuel_thermalU3Si2]
    type = SilicideFuelThermal
    block = 1
    temperature = T
    specific_heat_model = IAEA
    thermal_conductivity_model = SHIMIZU
  []

  [density]
    type = ParsedMaterial
    block = 1
    property_name = density
    expression = 1200.0
  []
[]

[Executioner]

   type = Transient


   solve_type = PJFNK

   petsc_options = '-snes_ksp_ew'
   petsc_options_iname = '-ksp_gmres_restart'
   petsc_options_value = '101'

  line_search = 'none'


   l_max_its = 100
   nl_max_its = 100
   nl_rel_tol = 1e-4
   nl_abs_tol = 1e-6
   l_tol = 1e-5
   start_time = 0.0
#  num_steps = 50
   num_steps = 100
#  dt = 1.163e6
   dt = 1.0e6


[]

[Postprocessors]
   [ave_temp_interior]
     # average temperature of the cladding interior and all pellet exteriors
     type = SideAverageValue
     boundary = 2
     variable = T
     execute_on = 'initial linear'
   []
   [avg_th_cond]
     type = ElementAverageValue
     block = 1
     variable = th_cond
     execute_on = 'initial linear'
   []
   [avg_cp]
     type = ElementAverageValue
     block = 1
     variable = cp
     execute_on = 'initial linear'
   []
   [average_fuel_T]
     type = ElementAverageValue
     block = 1
     variable = T
     execute_on = 'initial linear'
   []
 []

[Outputs]
  file_base = thermalU3Si2_shimizu_IAEA_out
  exodus = true
[]

(examples/accident_tolerant_fuel/u3si2_zircaloy/u3si2_zircaloy.i)


initial_fuel_density = 11590.0

[GlobalParams]
  # Set initial fuel density, other global parameters
  density = ${initial_fuel_density}
  order = SECOND
  family = LAGRANGE
  energy_per_fission = 3.2e-11 # J/fission
  volumetric_locking_correction = false
  displacements = 'disp_x disp_y'
[]

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

[Mesh]
  coord_type = RZ
  # Import mesh file
  patch_size = 10 # For contact algorithm
  patch_update_strategy = auto
  partitioner = centroid
  centroid_partitioner_direction = y
  [mesh]
    type = FileMeshGenerator
    file = u3si2_zircaloy_smeared.e
  []
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [temp]
    initial_condition = 293.0
  []
[]

[UserObjects]
  [pin_geometry]
    type = FuelPinGeometry
    clad_inner_wall = 5
    clad_outer_wall = 2
    clad_top = 3
    clad_bottom = 1
    pellet_exteriors = 8
  []
[]

[AuxVariables]
  # Define auxilary variables
  [fast_neutron_flux]
    block = clad
  []
  [fast_neutron_fluence]
    block = clad
  []
  [gap_cond]
    order = CONSTANT
    family = MONOMIAL
  []
  [hoop_stress]
    order = CONSTANT
    family = MONOMIAL
  []
  [coolant_htc]
    order = CONSTANT
    family = MONOMIAL
  []
  [oxide_thickness]
    order = CONSTANT
    family = MONOMIAL
  []
  [total_hoop_strain]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_rate]
    order = CONSTANT
    family = MONOMIAL
  []
  [densification]
    order = CONSTANT
    family = MONOMIAL
  []
  [solid_swell]
    order = CONSTANT
    family = MONOMIAL
  []
  [gaseous_swell]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [power_history]
    type = PiecewiseLinear
    x = '0 1e4 1e8'
    y = '0 2.5e4 2.5e4'
    scale_factor = 1
  []
  [axial_peaking_factors]
    type = ParsedFunction
    expression = 1
  []
  [pressure_ramp]
    type = PiecewiseLinear
    x = '-200 0 1e8'
    y = '6.537e-3 1 1'
    scale_factor = 15.5e6
  []
  [mass_flux_func]
    type = PiecewiseLinear
    x = '-200 0 1e8'
    y = '3800 3800 3800'
  []
  [q]
    type = CompositeFunction
    functions = 'power_history axial_peaking_factors'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [pellets]
    block = pellet_type_1
    strain = FINITE
    eigenstrain_names = 'fuel_thermal_strain fuel_volumetric_strain'
    generate_output = 'vonmises_stress stress_xx stress_yy stress_zz'
    extra_vector_tags = 'ref'
  []
  [clad]
    block = clad
    strain = FINITE
    eigenstrain_names = 'clad_thermal_eigenstrain clad_irradiation_strain'
    generate_output = 'vonmises_stress stress_xx stress_yy stress_zz'
    extra_vector_tags = 'ref'
  []
[]

[Kernels]
  [gravity]
    type = Gravity
    variable = disp_y
    value = -9.81
    extra_vector_tags = 'ref'
  []
  [heat]
    type = HeatConduction
    variable = temp
    extra_vector_tags = 'ref'
  []
  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temp
    extra_vector_tags = 'ref'
  []
  [heat_source]
    type = NeutronHeatSource
    variable = temp
    block = pellet_type_1
    burnup_function = burnup
    extra_vector_tags = 'ref'
  []
[]

[Burnup]
  [burnup]
    block = pellet_type_1
    rod_ave_lin_pow = power_history
    axial_power_profile = axial_peaking_factors
    num_radial = 81
    num_axial = 11
    fuel_pin_geometry = pin_geometry
    fuel_volume_ratio = 1.0
    RPF = RPF
    fuel_type = U3Si2
  []
[]

[AuxKernels]
  [fast_neutron_flux]
    type = FastNeutronFluxAux
    variable = fast_neutron_flux
    block = clad
    rod_ave_lin_pow = power_history
    axial_power_profile = axial_peaking_factors
    factor = 3e13
    execute_on = timestep_begin
  []
  [fast_neutron_fluence]
    type = FastNeutronFluenceAux
    variable = fast_neutron_fluence
    block = clad
    fast_neutron_flux = fast_neutron_flux
    execute_on = timestep_begin
  []
  [hoop_stress]
    type = RankTwoScalarAux
    rank_two_tensor = stress
    variable = hoop_stress
    scalar_type = HoopStress
    execute_on = timestep_end
  []
  [total_hoop_strain]
    type = RankTwoScalarAux
    rank_two_tensor = total_strain
    variable = total_hoop_strain
    scalar_type = HoopStress
    execute_on = timestep_end
  []
  [conductance]
    type = MaterialRealAux
    property = gap_conductance
    variable = gap_cond
    boundary = 10
  []
  [coolant_htc]
    type = MaterialRealAux
    property = coolant_channel_htc
    variable = coolant_htc
    boundary = 2
  []
  [oxide]
    type = MaterialRealAux
    variable = oxide_thickness
    property = oxide_scale_thickness
    boundary = 2
  []
  [creep_rate]
    type = MaterialRealAux
    variable = creep_rate
    property = creep_rate
    execute_on = timestep_end
    block = clad
  []
  [densfication]
    type = MaterialRealAux
    property = densification
    variable = densification
    block = pellet_type_1
  []
  [solid_swell]
    type = MaterialRealAux
    property = solid_swelling
    variable = solid_swell
    block = pellet_type_1
  []
  [gaseous_swell]
    type = MaterialRealAux
    property = gaseous_swelling
    variable = gaseous_swell
    block = pellet_type_1
  []
[]

[Contact]
  [pellet_clad_mechanical]
    primary = 5
    secondary = 10
    normal_smoothing_distance = 0.1
    penalty = 1e7
  []
[]

[ThermalContact]
  [thermal_contact]
    type = GasGapHeatTransfer
    variable = temp
    primary = 5
    secondary = 10
    initial_moles = initial_moles
    gas_released = fis_gas_released
    contact_pressure = contact_pressure
    quadrature = true
  []
[]

[BCs]
  [no_x_all] # pin pellets and clad along axis of symmetry (y)
    type = DirichletBC
    variable = disp_x
    boundary = 12
    value = 0.0
  []
  [no_y_clad_bottom] # pin clad bottom in the axial direction (y)
    type = DirichletBC
    variable = disp_y
    boundary = '1'
    value = 0.0
  []
  [no_y_fuel_bottom] # pin fuel bottom in the axial direction (y)
    type = DirichletBC
    variable = disp_y
    boundary = '1020'
    value = 0.0
  []
  [Pressure]
    [coolantPressure]
      boundary = '1 2 3'
      function = pressure_ramp
    []
  []
  [PlenumPressure]
    [plenumPressure]
      boundary = 9
      initial_pressure = 2.0e6
      startup_time = 0
      R = 8.3143
      output_initial_moles = initial_moles
      temperature = ave_temp_interior
      volume = gas_volume
      material_input = fis_gas_released
      output = plenum_pressure
    []
  []
[]

[CoolantChannel]
  [convective_clad_surface]
    boundary = '1 2 3'
    variable = temp
    inlet_temperature = 580 # K
    inlet_pressure = pressure_ramp # Pa
    inlet_massflux = mass_flux_func # kg/m^2-sec
    rod_diameter = 9.4996e-3 # m
    rod_pitch = 1.26e-2 # m
    linear_heat_rate = power_history
    axial_power_profile = axial_peaking_factors
  []
[]

[Materials]
  [fuel_thermal]
    type = SilicideFuelThermal
    block = pellet_type_1
    thermal_conductivity_model = WHITE
    silicon_mole_fraction = 0.4
    temperature = temp
  []
  [fuel_elasticity_tensor]
    type = U3Si2ElasticityTensor
    block = pellet_type_1
  []
  [fuel_stress]
    type = ComputeMultipleInelasticStress
    block = pellet_type_1
    tangent_operator = elastic
    inelastic_models = 'fuel_creep'
  []
  [fuel_creep]
    type = U3Si2CreepUpdate
    block = pellet_type_1
    temperature = temp
  []
  [fuel_thermal_expansion]
    type = U3Si2ThermalExpansionEigenstrain
    block = pellet_type_1
    temperature = temp
    stress_free_temperature = 295.0
    eigenstrain_name = fuel_thermal_strain
  []
  [fuel_volumetric_swelling]
    type = U3Si2VolumetricSwellingEigenstrain
    block = pellet_type_1
    gaseous_swelling_type = U3SI2FG
    temperature = temp
    burnup_function = burnup
    eigenstrain_name = fuel_volumetric_strain
  []

  [clad_thermal]
    type = ZryThermal
    temperature = temp
    block = clad
  []
  [clad_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 7.5e10
    poissons_ratio = 0.3
    block = clad
  []
  [clad_stress]
    type = ComputeMultipleInelasticStress
    tangent_operator = elastic
    inelastic_models = 'clad_zrycreep clad_plasticity'
    relative_tolerance = 1e-5
    block = clad
  []
  [clad_zrycreep]
    type = ZryCreepLimbackHoppeUpdate
    block = clad
    temperature = temp
    fast_neutron_flux = fast_neutron_flux
    fast_neutron_fluence = fast_neutron_fluence
    model_irradiation_creep = true
    model_primary_creep = true
    model_thermal_creep = true
    relative_tolerance = 1e-5
    max_inelastic_increment = 1e-4
    zircaloy_material_type = stress_relief_annealed
  []
  [thermal_expansion]
    type = ZryThermalExpansionMATPROEigenstrain
    block = clad
    temperature = temp
    stress_free_temperature = 295.0
    eigenstrain_name = clad_thermal_eigenstrain
  []
  [irradiation_swelling]
    type = ZryIrradiationGrowthEigenstrain
    block = clad
    fast_neutron_fluence = fast_neutron_fluence
    zircaloy_material_type = stress_relief_annealed
    eigenstrain_name = clad_irradiation_strain
  []
  [clad_plasticity]
    type = ZryPlasticityUpdate
    block = clad
    temperature = temp
    fast_neutron_flux = fast_neutron_flux
    fast_neutron_fluence = fast_neutron_fluence
    relative_tolerance = 1e-5
    cold_work_factor = 0.5
    plasticity_model_type = MATPRO
    zircaloy_alloy_type = 4
  []
  [fission_gas_behavior]
    type = U3Si2Sifgrs
    block = pellet_type_1
    temperature = temp
    burnup_function = burnup
    saturation_coverage = 0.5
  []
  [clad_density]
    type = StrainAdjustedDensity
    block = clad
    strain_free_density = 6511.0
  []
  [fuel_density]
    type = StrainAdjustedDensity
    block = pellet_type_1
    strain_free_density = ${initial_fuel_density}
  []
  [ZryOxidation]
    type = ZryOxidation
    boundary = 2
    clad_inner_radius = 4.1783e-3
    clad_outer_radius = 4.7498e-3
    normal_operating_temperature_model = epri_kwu_ce
    temperature = temp
    fast_neutron_flux = fast_neutron_flux
    use_coolant_channel = true
    oxygen_weight_fraction_initial = 0.0012
  []
[]

[Dampers]
  [limitT]
    type = MaxIncrement
    max_increment = 100.0
    variable = temp
  []
  [limitX]
    type = MaxIncrement
    max_increment = 1e-5
    variable = disp_x
  []
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  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 = 8e-3

  nl_max_its = 25
  nl_rel_tol = 1e-5
  nl_abs_tol = 1e-10

  start_time = -200
  n_startup_steps = 1
  end_time = 1e8

  dtmax = 1e6
  dtmin = 1e-3

  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 2.0e2
    force_step_every_function_point = true
    timestep_limiting_function = power_history
    max_function_change = 3e20
    optimal_iterations = 10
    iteration_window = 2
    linear_iteration_ratio = 100
    timestep_limiting_postprocessor = material_timestep
  []
  [Quadrature]
    order = FIFTH
    side_order = SEVENTH
  []
[]

[Postprocessors]
  [avg_fuel_surface]
    type = SideAverageValue
    boundary = 10
    variable = temp
  []
  [ave_temp_interior]
    type = SideAverageValue
    boundary = 9
    variable = temp
    execute_on = 'initial linear'
  []
  [clad_inner_vol]
    type = InternalVolume
    boundary = 7
  []
  [pellet_volume]
    type = InternalVolume
    boundary = 8
  []
  [avg_clad_temp]
    type = SideAverageValue
    boundary = 7
    variable = temp
  []
  [fis_gas_produced]
    type = ElementIntegralFisGasGeneratedSifgrs
    block = pellet_type_1
  []
  [fis_gas_released]
    type = ElementIntegralFisGasReleasedSifgrs
    block = pellet_type_1
  []
  [fis_gas_grain]
    type = ElementIntegralFisGasGrainSifgrs
    block = pellet_type_1
  []
  [fis_gas_boundary]
    type = ElementIntegralFisGasBoundarySifgrs
    block = pellet_type_1
  []
  [gas_volume]
    type = InternalVolume
    boundary = 9
    execute_on = 'initial linear'
  []
  [flux_from_clad]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 5
    diffusivity = thermal_conductivity
  []
  [flux_from_fuel]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 10
    diffusivity = thermal_conductivity
  []
  [_dt]
    type = TimestepSize
  []
  [num_lin_it]
    type = NumLinearIterations
  []
  [num_nonlin_it]
    type = NumNonlinearIterations
  []
  [tot_lin_it]
    type = CumulativeValuePostprocessor
    postprocessor = num_lin_it
  []
  [tot_nonlin_it]
    type = CumulativeValuePostprocessor
    postprocessor = num_nonlin_it
  []
  [alive_time]
    type = PerfGraphData
    section_name = Root
    data_type = TOTAL
  []
  [rod_total_power]
    type = ElementIntegralPower
    variable = temp
    burnup_function = burnup
    block = pellet_type_1
  []
  [rod_input_power]
    type = FunctionValuePostprocessor
    function = power_history
    scale_factor = 0.1186
  []
  [average_burnup]
    type = ElementAverageValue
    block = pellet_type_1
    variable = burnup
  []
  [oxide_thickness]
    type = ElementExtremeValue
    block = clad
    variable = oxide_thickness
  []
  [fis_gas_percent]
    type = FGRPercent
    fission_gas_released = fis_gas_released
    fission_gas_generated = fis_gas_produced
  []
  [material_timestep]
    type = MaterialTimeStepPostprocessor
    block = clad
  []
[]

[Outputs]
  perf_graph = true
  time_step_interval =  1
  exodus = true
  color = false
  csv = true
  print_linear_residuals = true
  [console]
    type = Console
    max_rows = 25
  []
[]

(test/tests/solid_mechanics/u3si2_eigenstrains/u3si2_vswelling/argonne_rz.i)

#
# This input file is used to test the Argonne gaseous swelling model for U3Si2 fuel
# in an axisymmetric RZ geometry.
#
# The gaseous swelling model was developed using rate theory calculations at
# the Argonne National Laboratory:
#
# Y. Miao, K. A. Gamble, D. Andersson, B. Ye, Z. Mei, G. Hofman and A. M. Yacout,
# "Gaseous swelling of U3Si2 during steady-state LWR operation: A rate theory
# investigation," Nuclear Engineering and Design, 322, 2017, p. 336-344.
#
# Note that for this test the input CSV files are made up for testing the
# algorithm.  The full CSV data set developed using the rate theory calculations
# from Argonne National Laboratory can be obtained by contacted a BISON
# developer.
#
# For this problem, a 1x1 mm square is simulated. The temperature is fixed at
# 450 K and the burnup is fixed at 9.086425e-3 FIMA which corresponds to a
# fission density of 0.25e21 fissions/cm^3.
#
# Given the input csv used in the U3Si2TricubicInterpolationUserObject the
# interpolated value for gaseous swelling should be 0.0075. Comparing to the
# value reported by the gas_swell postprocessor confirms the correct implementation
# of the tricubic interpolation scheme.
#

initial_fuel_density = 11590.0

[GlobalParams]
  density = ${initial_fuel_density}
  displacements = 'disp_x disp_y'
  volumetric_locking_correction = true
[]

[Mesh]
  coord_type = RZ
  [mesh]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 1e-3
    ymin = 0
    ymax = 1e-3
    nx = 1
    ny = 1
  []
[]

[Variables]
  [temp]
    order = FIRST
    family = LAGRANGE
    initial_condition = 450.0
  []
[]

[UserObjects]
  [gaseous_swelling]
    type = U3Si2TricubicInterpolationUserObject
    execute_on = 'initial nonlinear'
    temperature_grid_points_file = temperature.csv
    temperature_gradient_grid_points_file = temperature_gradient.csv
    fission_density_grid_points_file = fission_density.csv
    grain_boundary_coverage_file = fcov.csv
    intragranular_gaseous_swelling_file = gswb.csv
    total_gaseous_swelling_file = gsw.csv
  []
[]

[Physics]
  [SolidMechanics]
    [QuasiStatic]
      [all]
        strain = FINITE
        block = 0
        incremental = true
        add_variables = true
        eigenstrain_names = 'swell'
      []
    []
  []
[]

[Kernels]
  [heat]         # gradient term in heat conduction equation
    type = HeatConduction
    variable = temp
  []

  [heat_ie]       # time term in heat conduction equation
    type = HeatConductionTimeDerivative
    variable = temp
  []
[]

[AuxVariables]
 [burnup]
    order = FIRST
    family = LAGRANGE
 []
 [gaseous_swelling]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [burnupFunc]
    type = ConstantFunction
    value = 9.086425e-3  # Corresponds to a fission density of 0.25e21 fissions/cm^3
  []
[]

[AuxKernels]
  [burnup]
    type = FunctionAux
    variable = burnup
    function = burnupFunc
    execute_on = timestep_begin
  []
  [gaseous_swelling]
    type = MaterialRealAux
    property = gaseous_swelling
    variable = gaseous_swelling
    block = 0
    execute_on = timestep_end
  []
[]

[BCs]
  [left_x]
    type = DirichletBC
    variable = disp_x
    boundary = left
    value = 0.0
  []
  [bottom_y]
    type = DirichletBC
    variable = disp_y
    boundary = bottom
    value = 0.0
  []
  [left_temp]
    type = DirichletBC
    variable = temp
    boundary = left
    value = 450.0
  []
  [right_temp]
    type = DirichletBC
    variable = temp
    boundary = right
    value = 450.0
  []
[]

[Materials]
  [fuel_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = 0
    youngs_modulus = 1e11
    poissons_ratio = 0.17
  []
  [fuel_swelling]
    type = U3Si2VolumetricSwellingEigenstrain
    block = 0
    temperature = temp
    burnup = burnup
    complete_burnup = 10
    gaseous_swelling_type = ARGONNE
    gaseous_swelling_object = gaseous_swelling
    eigenstrain_name = swell
    include_densification = false
    include_solid_swelling = false
  []
  [fuel_stress]
    type = ComputeFiniteStrainElasticStress
    block = 0
  []
  [thermal]
    type = SilicideFuelThermal
    block = 0
    temperature = temp
  []
  [density]
    type = StrainAdjustedDensity
    block = 0
    strain_free_density = ${initial_fuel_density}
  []
[]

[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'
  l_max_its = 60
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-10
  l_tol = 1e-5

  start_time = 0.0
  end_time = 1.0
  num_steps = 1
[]

[Postprocessors]
  [ave_burnup]
    type = ElementAverageValue
    variable = burnup
    block = 0
  []
  [gas_swell]
    type = ElementAverageValue
    variable = gaseous_swelling
    block = 0
  []
  [avg_temp]
    type = AverageNodalVariableValue
    variable = temp
    block = 0
  []
[]

[Outputs]
  exodus = true
[]

(test/tests/thermalSilicideFuel/thermalU3Si2_handbook.i)

# The mesh is a 1x1x1 cube (single element).
# The temperature is ramped on all faces of the cube from 300 K to 1200K
# over 100 Ms.
#
# This test is for the specific heat and thermal conductivity calculation from
# the U3Si2 handbook:
#
# J. T. White, "Issue Draft U3Si2 Fuel Property Handbook," Los Alamos National
# Laboratory, LA-UR17-20609, 2017.
#
# J.T. White "UPdate to ther U3Si2 property handbook," Los Alamos National
# Laboratory, LA-UR-18-28719, 2018.
#
# The specific heat and thermal conductivity computed by BISON for the
# temperatures shown below are
# compared with analytical solution.
#
# The results are as follows:
#               Thermal Conductivity            Specific Heat
#            -------------------------      ---------------------
#            BISON           Analytical    BISON        Analytical
# Temp(K)   (W/m-K)          (W/m-K)      J/(kg-K)      J/(kg-K)
#  300      8.27373         8.27373       190.560       190.560
#  408      9.77597         9.77597       194.362       194.362
#  570      11.6939         11.6939       200.064       200.064
# 1002      17.0562         17.0562       215.270       215.270
# 1137      18.7804         18.7804       220.022       220.022
# 1200      19.5452         19.5452       222.240       222.240

[Mesh]
  [mesh]
    type = FileMeshGenerator
    file = 1x1x1cube.e
  []
[]

[Variables]
  [T]
    order = FIRST
    family = LAGRANGE
    initial_condition = 300
  []
[]

[AuxVariables]
  [th_cond]
    order = CONSTANT
    family = MONOMIAL
  []
  [cp]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = T
  []
  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = T
  []
[]

[AuxKernels]
  [th_cond]
    type = MaterialRealAux
    variable = th_cond
    property = thermal_conductivity
    block = 1
    execute_on = 'initial linear'
  []

  [cp]
    type = MaterialRealAux
    variable = cp
    property = specific_heat
    block = 1
    execute_on = 'initial linear'
  []

[]

[Functions]
  [temp_ramp]
    type = PiecewiseLinear
    x = '0.0 100.e6'
    y = '300 1200'
  []
[]

[BCs]
  [VariableT]
    type = FunctionDirichletBC
    boundary = 2      # All cube faces
    variable = T
    function = temp_ramp
  []
[]


[Materials]
  [fuel_thermalU3Si2]
    type = SilicideFuelThermal
    block = 1
    temperature = T
    specific_heat_model = HANDBOOK
    thermal_conductivity_model = HANDBOOK
  []

  [density]
    type = ParsedMaterial
    block = 1
    property_name = density
    expression = 1.0
  []
[]

[Executioner]
   type = Transient
   solve_type = PJFNK

   petsc_options = '-snes_ksp_ew'
   petsc_options_iname = '-ksp_gmres_restart'
   petsc_options_value = '101'

   line_search = 'none'

   l_max_its = 100
   nl_max_its = 100
   nl_rel_tol = 1e-4
   nl_abs_tol = 1e-6
   l_tol = 1e-5
   start_time = 0.0
   num_steps = 100
   dt = 1.0e6
[]

[Postprocessors]
   [ave_temp_interior]
     # average temperature of the cladding interior and all pellet exteriors
     type = SideAverageValue
     boundary = 2
     variable = T
     execute_on = 'initial linear'
   []
   [avg_th_cond]
     type = ElementAverageValue
     block = 1
     variable = th_cond
     execute_on = 'initial linear'
   []
   [avg_cp]
     type = ElementAverageValue
     block = 1
     variable = cp
     execute_on = 'initial linear'
   []
   [average_fuel_T]
     type = ElementAverageValue
     block = 1
     variable = T
     execute_on = 'initial linear'
   []
 []

[Outputs]
  exodus = true
[]

(examples/accident_tolerant_fuel/u3si2_sic/u3si2_outer_monolith_1.5D.i)

# Model is of a 10 pellet fuel rodlet modeled in 1.5D.  The rodlet contains
# U3Si2 fuel and a multilayer silicon carbide cladding (an inner composite
# winding layer) and an outer monolithic layer. The inner composite layer is
# 0.75 mm thick and the outer monolithic layer is 0.25 mm thick. The internal
# layered1D mesh generator can model a clad an arbitrary number of additional blocks.
# Therefore, to create the multilayer SiC clad the composite layer is assigned to the
# clad block and the monolithic_layer is assigned to the monolithic_layer block
# as specified in the additional_block_names parameter in the Mesh block.


initial_fuel_density = 11590.0

[GlobalParams]
  density = ${initial_fuel_density}
  initial_porosity = 0.05
  order = SECOND
  family = LAGRANGE
  energy_per_fission = 3.2e-11 # J/fission
  displacements = disp_x
  temperature = temperature
[]

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

[Mesh]
  coord_type = RZ
  [layered1D_mesh]
    type = Layered1DMeshGenerator
    slices_per_block = 10
    clad_gap_width = 8.0e-5
    clad_mesh_density = customize
    clad_thickness = 0.00075
    nx_c = 5
    additional_block_names = 'monolithic_layer'
    additional_elements_per_ring = '3'
    additional_ring_thicknesses = '0.00025'
    fuel_height = 0.1186
    plenum_height = 0.027
  []
  patch_update_strategy = auto
  partitioner = centroid
  centroid_partitioner_direction = y
[]

[UserObjects]
  [pin_geometry]
    type = Layered1DFuelPinGeometry
    mesh_generator = layered1D_mesh
  []
[]

[Variables]
  [temperature]
    initial_condition = 580.0 # set initial temperature to coolant inlet
  []
[]

[AuxVariables]
  [disp_y] ## Required for easier visualization in Paraview
  []
  [disp_z] ## Required for easier visualization in Paraview
  []
  [fast_neutron_flux]
    block = 'clad monolithic_layer'
    order = CONSTANT
    family = MONOMIAL
  []
  [fast_neutron_fluence]
    block = 'clad monolithic_layer'
    order = CONSTANT
    family = MONOMIAL
  []
  [grain_radius]
    block = fuel
    initial_condition = 10e-6
  []
  [solid_swell]
    order = CONSTANT
    family = MONOMIAL
    block = fuel
  []
  [gaseous_swelling]
    order = CONSTANT
    family = MONOMIAL
    block = fuel
  []
  [densification]
    order = CONSTANT
    family = MONOMIAL
    block = fuel
  []
  [volumetric_swelling_strain]
    order = CONSTANT
    family = MONOMIAL
    block = fuel
  []
  [relocation]
    order = CONSTANT
    family = MONOMIAL
    block = fuel
  []
[]

[Functions]
  [power_history]
    type = PiecewiseLinear
    x = '0 1e4 1e8'
    y = '0 25000 25000'
    scale_factor = 1
  []
  [axial_peaking_factors]
    type = ParsedFunction
    expression = 1
  []
  [pressure_ramp]
    type = PiecewiseLinear
    x = '-200 0 1e8'
    y = '6.537e-3 1 1'
  []
  [q]
    type = CompositeFunction
    functions = 'power_history axial_peaking_factors'
  []
  [clad_axial_pressure]
    type = CladdingAxialPressureFunction
    plenum_pressure = plenum_pressure
    coolant_pressure = pressure_ramp
    coolant_pressure_scaling_factor = 15.5e6
    fuel_pin_geometry = pin_geometry
  []
  [fuel_axial_pressure]
    type = ParsedFunction
    expression = plenum_pressure
    symbol_names = plenum_pressure
    symbol_values = plenum_pressure
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = temperature
    extra_vector_tags = 'ref'
  []
  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temperature
    extra_vector_tags = 'ref'
  []
  [heat_source]
    type = NeutronHeatSource
    variable = temperature
    block = fuel
    burnup_function = burnup
    extra_vector_tags = 'ref'
  []
[]

[Physics]
  [SolidMechanics]
    [Layered1D]
      [fuel]
        block = fuel
        add_variables = true
        strain = SMALL
        incremental = true
        add_scalar_variables = true
        out_of_plane_strain_name = strain_yy
        fuel_pin_geometry = pin_geometry
        out_of_plane_pressure_function = fuel_axial_pressure
        eigenstrain_names = 'fuel_thermal_strain fuel_swelling_strain'
        generate_output = 'stress_xx stress_yy stress_zz vonmises_stress strain_xx'
        extra_vector_tags = 'ref'
        group_scalar_vars_in_reference_residual = true
        mesh_generator = layered1D_mesh
      []
      [composite]
        block = clad
        add_variables = true
        strain = SMALL
        incremental = true
        add_scalar_variables = true
        out_of_plane_strain_name = strain_yy
        fuel_pin_geometry = pin_geometry
        out_of_plane_pressure_function = clad_axial_pressure
        eigenstrain_names = 'composite_thermal_strain composite_swelling_strain'
        generate_output = 'stress_xx stress_yy stress_zz vonmises_stress strain_xx'
        extra_vector_tags = 'ref'
        group_scalar_vars_in_reference_residual = true
        mesh_generator = layered1D_mesh
      []
      [monolith]
        block = monolithic_layer
        add_variables = true
        strain = SMALL
        incremental = true
        add_scalar_variables = true
        out_of_plane_strain_name = strain_yy
        fuel_pin_geometry = pin_geometry
        out_of_plane_pressure_function = clad_axial_pressure
        eigenstrain_names = 'monolith_thermal_strain monolith_swelling_strain'
        generate_output = 'stress_xx stress_yy stress_zz vonmises_stress strain_xx'
        extra_vector_tags = 'ref'
        group_scalar_vars_in_reference_residual = true
        mesh_generator = layered1D_mesh
      []
    []
  []
[]

[Burnup]
  [burnup]
    block = fuel
    rod_ave_lin_pow = power_history
    axial_power_profile = axial_peaking_factors
    num_radial = 80
    num_axial = 11
    order = CONSTANT
    family = MONOMIAL
    fuel_pin_geometry = pin_geometry
    fuel_volume_ratio = 1.0
    RPF = RPF
    fuel_type = U3Si2
  []
[]

[AuxKernels]
  [fast_neutron_flux]
    type = MaterialRealAux
    variable = fast_neutron_flux
    property = fast_neutron_flux
    block = 'clad monolithic_layer'
    execute_on = timestep_begin
  []
  [fast_neutron_fluence]
    type = MaterialRealAux
    variable = fast_neutron_fluence
    property = fast_neutron_fluence
    block = 'clad monolithic_layer'
    execute_on = timestep_begin
  []
  [grain_radius]
    type = GrainRadiusAux
    block = fuel
    variable = grain_radius
    temperature = temperature
    execute_on = linear
  []
  [solid_swell]
    type = MaterialRealAux
    variable = solid_swell
    property = solid_swelling
    execute_on = timestep_end
    block = fuel
  []
  [gas_swell]
    type = MaterialRealAux
    variable = gaseous_swelling
    property = gaseous_swelling
    execute_on = timestep_end
    block = fuel
  []
  [densification]
    type = MaterialRealAux
    variable = densification
    property = densification
    execute_on = timestep_end
    block = fuel
  []
  [volumetric_swelling_strain]
    type = MaterialRealAux
    variable = volumetric_swelling_strain
    property = volumetric_swelling_strain
    execute_on = timestep_end
    block = fuel
  []
[]

[Contact]
  [pellet_clad_mechanical]
    primary = 5
    secondary = 10
    formulation = kinematic
    model = frictionless
    penalty = 1e7
  []
[]

[ThermalContact]
  [thermal_contact]
    type = GasGapHeatTransfer
    variable = temperature
    primary = 5
    secondary = 10
    initial_moles = initial_moles # coupling to a postprocessor which supplies the initial plenum/gap gas mass
    gas_released = fis_gas_released # coupling to a postprocessor which supplies the fission gas addition
    contact_pressure = contact_pressure
  []
[]

[BCs]
  [no_x_all] # pin pellets and clad along axis of symmetry (y)
    type = DirichletBC
    variable = disp_x
    boundary = 12
    value = 0.0
  []
  [Pressure] # apply coolant pressure on clad outer walls
    [coolantPressure]
      use_displaced_mesh = false
      boundary = 2
      function = pressure_ramp # use the pressure_ramp function defined above
      factor = 15.5e6
    []
  []
  [PlenumPressure] # apply plenum pressure on clad inner walls and pellet surfaces
    [plenumPressure]
      use_displaced_mesh = false
      boundary = 9
      initial_pressure = 2.0e6
      startup_time = 0
      R = 8.314
      output_initial_moles = initial_moles # coupling to post processor to get initial fill gas mass
      temperature = ave_temp_interior # coupling to post processor to get gas temperature approximation
      volume = gas_volume # coupling to post processor to get gas volume
      material_input = fis_gas_released # coupling to post processor to get fission gas added
      output = plenum_pressure # coupling to post processor to output plenum/gap pressure
    []
  []
[]

[CoolantChannel]
  [convective_clad_surface] # apply convective boundary to clad outer surface
    variable = temperature
    boundary = 2
    inlet_temperature = 580 # K
    inlet_pressure = 15.5e6 # Pa
    inlet_massflux = 3800 # kg/m^2-sec
    rod_diameter = 10.368e-3 # m
    rod_pitch = 1.26e-2 # m
    linear_heat_rate = power_history
    axial_power_profile = axial_peaking_factors
  []
[]

[Materials]
  [flux]
    type = FastNeutronFlux
    calculate_fluence = true
    block = 'clad monolithic_layer'
    rod_ave_lin_pow = power_history
    axial_power_profile = axial_peaking_factors
    factor = 3e13
  []
  ### U3Si2 Fuel
  [fuel_thermal]
    type = SilicideFuelThermal
    block = fuel
    thermal_conductivity_model = WHITE
    temperature = temperature
  []
  [fuel_elasticity_tensor]
    type = U3Si2ElasticityTensor
    block = fuel
  []
  [fuel_stress]
    type = ComputeMultipleInelasticStress
    block = fuel
    tangent_operator = elastic
    inelastic_models = 'fuel_creep'
  []
  [fuel_creep]
    type = U3Si2CreepUpdate
    block = fuel
    temperature = temperature
  []
  [fuel_thermal_expansion]
    type = U3Si2ThermalExpansionEigenstrain
    block = fuel
    temperature = temperature
    stress_free_temperature = 295.0
    eigenstrain_name = fuel_thermal_strain
  []
  [fuel_volumetric_swelling]
    type = U3Si2VolumetricSwellingEigenstrain
    block = fuel
    gaseous_swelling_type = FINLAY
    temperature = temperature
    burnup_function = burnup
    eigenstrain_name = fuel_swelling_strain
  []
  [fission_gas_release]
    type = U3Si2Sifgrs
    block = fuel
    temperature = temperature
    burnup_function = burnup
    grain_radius_const = 2.5e-05
  []

  [fuel_density]
    type = StrainAdjustedDensity
    block = fuel
    strain_free_density = ${initial_fuel_density}
  []

  ### Composite SiC
  [composite_thermal]
    type = CompositeSiCThermal
    thermal_conductivity_model = STONE
    temperature = temperature
    block = clad
  []
  [composite_density]
    type = StrainAdjustedDensity
    block = clad
    strain_free_density = 2700.0
  []
  [composite_elasticity_tensor]
    type = CompositeSiCElasticityTensor
    block = clad
  []
  [composite_stress]
    type = ComputeStrainIncrementBasedStress
    block = clad
  []
  [composite_thermal_expansion]
    type = CompositeSiCThermalExpansionEigenstrain
    block = clad
    stress_free_temperature = 295.0
    temperature = temperature
    eigenstrain_name = composite_thermal_strain
  []
  [composite_irradiation_swelling]
    type = CompositeSiCVolumetricSwellingEigenstrain
    block = clad
    temperature = temperature
    fast_neutron_fluence = fast_neutron_fluence
    swelling_model = KATOH
    number_of_substeps = 1000
    eigenstrain_name = composite_swelling_strain
  []

  ### Monolithic SiC
  [monolith_thermal]
    type = MonolithicSiCThermal
    temperature = temperature
    thermal_conductivity_model = STONE
    block = monolithic_layer
  []
  [monolith_density]
    type = StrainAdjustedDensity
    block = monolithic_layer
    strain_free_density = 3120.0
  []
  [monolith_elasticity_tensor]
    type = MonolithicSiCElasticityTensor
    block = monolithic_layer
  []
  [monolith_stress]
    type = ComputeMultipleInelasticStress
    block = monolithic_layer
    tangent_operator = elastic
    inelastic_models = 'monolith_creep'
  []
  [monolith_creep]
    type = MonolithicSiCCreepUpdate
    block = monolithic_layer
    fast_neutron_flux = fast_neutron_flux
    temperature = temperature
    k_function = 2e-37
  []
  [monolith_thermal_expansion]
    type = MonolithicSiCThermalExpansionEigenstrain
    block = monolithic_layer
    stress_free_temperature = 295.0
    temperature = temperature
    eigenstrain_name = monolith_thermal_strain
  []
  [monolith_irradiation_swelling]
    type = CompositeSiCVolumetricSwellingEigenstrain
    block = monolithic_layer
    temperature = temperature
    fast_neutron_fluence = fast_neutron_fluence
    swelling_model = KATOH
    number_of_substeps = 1000
    eigenstrain_name = monolith_swelling_strain
  []
[]

[Dampers]
  [limitT]
    type = MaxIncrement
    max_increment = 100.0
    variable = temperature
  []
  [limitX]
    type = MaxIncrement
    max_increment = 1e-5
    variable = disp_x
  []
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'

  line_search = 'none'

  l_max_its = 50
  l_tol = 8e-3
  nl_max_its = 50
  nl_rel_tol = 1e-4
  nl_abs_tol = 1e-7

  start_time = -200
  n_startup_steps = 1
  end_time = 8.0e7
  dtmax = 1e6
  dtmin = 1

  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 2e2
    optimal_iterations = 25
    iteration_window = 5
    growth_factor = 2
    cutback_factor = .5
  []
[]

[Postprocessors]
  [ave_temp_interior] # average temperature of the cladding interior and all pellet exteriors
    type = LayeredSideAverageValuePostprocessor
    boundary = 9
    variable = temperature
    execute_on = 'initial linear'
    fuel_pin_geometry = pin_geometry
  []
  [clad_inner_vol] # volume inside of cladding
    type = LayeredInternalVolumePostprocessor
    boundary = 7
    component = 0
    fuel_pin_geometry = pin_geometry
    out_of_plane_strain = strain_yy
    execute_on = 'initial linear'
  []
  [pellet_volume] # fuel pellet total volume
    type = LayeredInternalVolumePostprocessor
    boundary = 8
    component = 0
    fuel_pin_geometry = pin_geometry
    out_of_plane_strain = strain_yy
    execute_on = 'initial linear'
  []
  [avg_clad_temp] # average temperature of cladding interior
    type = LayeredSideAverageValuePostprocessor
    boundary = 7
    variable = temperature
    fuel_pin_geometry = pin_geometry
    execute_on = 'initial linear'
  []
  [fis_gas_produced] # fission gas produced (moles)
    type = LayeredElementIntegralFisGasGeneratedSifgrsPostprocessor
    block = fuel
    fuel_pin_geometry = pin_geometry
  []
  [fis_gas_released] # fission gas released to plenum (moles)
    type = LayeredElementIntegralFisGasReleasedSifgrsPostprocessor
    block = fuel
    fuel_pin_geometry = pin_geometry
  []
  [fis_gas_grain]
    type = LayeredElementIntegralFisGasGrainSifgrsPostprocessor
    block = fuel
    outputs = exodus
    fuel_pin_geometry = pin_geometry
  []
  [fis_gas_boundary]
    type = LayeredElementIntegralFisGasBoundarySifgrsPostprocessor
    block = fuel
    outputs = exodus
    fuel_pin_geometry = pin_geometry
  []
  [fission_gas_release]
    type = FGRPercent
    fission_gas_released = fis_gas_released
    fission_gas_generated = fis_gas_produced
  []

  [gas_volume]
    type = LayeredInternalVolumePostprocessor
    boundary = 9
    execute_on = 'initial linear'
    component = 0
    out_of_plane_strain = strain_yy
    fuel_pin_geometry = pin_geometry
  []
  [flux_from_clad] # area integrated heat flux from the cladding
    type = LayeredSideFluxIntegralPostprocessor
    variable = temperature
    boundary = 5
    diffusivity = thermal_conductivity
    fuel_pin_geometry = pin_geometry
  []
  [flux_from_fuel] # area integrated heat flux from the fuel
    type = LayeredSideFluxIntegralPostprocessor
    variable = temperature
    boundary = 10
    diffusivity = thermal_conductivity
    fuel_pin_geometry = pin_geometry
  []
  [_dt] # time step
    type = TimestepSize
  []
  [num_lin_it]
    type = NumLinearIterations
  []
  [num_nonlin_it]
    type = NumNonlinearIterations
  []
  [tot_lin_it]
    type = CumulativeValuePostprocessor
    postprocessor = num_lin_it
  []
  [tot_nonlin_it]
    type = CumulativeValuePostprocessor
    postprocessor = num_nonlin_it
  []
  [alive_time]
    type = PerfGraphData
    section_name = Root
    data_type = TOTAL
  []

  [rod_total_power]
    type = LayeredElementIntegralPowerPostprocessor
    variable = temperature
    burnup_function = burnup
    block = fuel
    fuel_pin_geometry = pin_geometry
  []
  [rod_input_power]
    type = FunctionValuePostprocessor
    function = power_history
    scale_factor = 0.1186 # rod height
  []

  [solid_swelling]
    type = ElementAverageValue
    variable = solid_swell
    block = fuel
  []
  [gaseous_swelling]
    type = ElementAverageValue
    variable = gaseous_swelling
    block = fuel
  []
  [densification]
    type = ElementAverageValue
    variable = densification
    block = fuel
  []
  [volumetric_swelling]
    type = ElementAverageValue
    variable = volumetric_swelling_strain
    block = fuel
  []
[]

[Outputs]
  perf_graph = true
  exodus = true
  csv = true
  color = false
[]

(test/tests/thermalSilicideFuel/thermalU3Si_zhang.i)

# The mesh is a 1x1x1 cube (single element).
# The temperature is ramped on all faces of the cube from 300 K to 1800K
#       over 800 seconds.
#
# Thermal conductivity is computed using the Zhang model.
#
#
# The thermal conductivity calculated by BISON is compared against the analytical
# thermal conductivity.
#
# The results are as follows:
#                  Thermal Conductivity
#               -------------------------
#               BISON           Analytical
# Temp(K)      (W/m-K)          (W/m-K)
#  300         13.6943          13.6943
#  500         18.5503          18.5503
#  700         23.0355          23.0355
#  900         27.1482          27.1482
# 1100         31.1175          31.1175
# 1300         34.9871          34.9871
# 1500         38.6189          38.6189
# 1700         41.9211          41.9211
# 1800         43.5370          43.5370

[Mesh]
  [mesh]
    type = FileMeshGenerator
    file = 1x1x1cube.e
  []
[]


[Variables]
  [T]
    order = FIRST
    family = LAGRANGE
    initial_condition = 300     # set initial T to 300 K
  []
[]


[AuxVariables]
  [th_cond]
    order = CONSTANT
    family = MONOMIAL
  []
  [cp]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = T
  []

  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = T
  []
[]


[AuxKernels]
  [th_cond]
    type = MaterialRealAux
    variable = th_cond
    property = thermal_conductivity
    block = 1
    execute_on = 'initial linear'
  []

  [cp]
    type = MaterialRealAux
    variable = cp
    property = specific_heat
    block = 1
    execute_on = 'initial linear'
  []
[]

[Functions]
  [temp_ramp]
    type = PiecewiseLinear
    x = '0.0 100 200 300 400 500 600 700 800'
    y = '300 500 700 900 1100 1300 1500 1700 1800'
  []
[]

[BCs]
  [VariableT]
    type = FunctionDirichletBC
    boundary = 2      # All cube faces
    variable = T
    function = temp_ramp
  []
[]


[Materials]
  [fuel_thermalU3Si]
    type = SilicideFuelThermal
    block = 1
    temperature = T
    silicon_mole_fraction = 0.25
    specific_heat_model = WHITE   # This is the default
    thermal_conductivity_model = ZHANG
  []

  [density]
    type = ParsedMaterial
    block = 1
    property_name = density
    expression = 1200.0
  []
[]

[Executioner]

  type = Transient

  solve_type = PJFNK

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-ksp_gmres_restart'
  petsc_options_value = '101'

  line_search = 'none'


  l_max_its = 100
  nl_max_its = 100
  nl_rel_tol = 1e-4
  nl_abs_tol = 1e-6
  l_tol = 1e-5
  start_time = 0.0
  num_steps = 8
  dt = 100
[]

[Postprocessors]
  [ave_temp_interior]
    # average temperature of the cladding interior and all pellet exteriors
    type = SideAverageValue
    boundary = 2
    variable = T
    execute_on = 'initial linear'
  []
  [avg_th_cond]
    type = ElementAverageValue
    block = 1
    variable = th_cond
    execute_on = 'initial linear'
  []
  [average_fuel_T]
    type = ElementAverageValue
    block = 1
    variable = T
    execute_on = 'initial linear'
  []
[]

[Outputs]
  exodus = true
[]

Description
Thermal Conductivity Models
Specific Heat Capacity
Example Input Syntax
Input Parameters
Input Files
References