DirichletEquivalentPfcImplantBC

construction:Undocumented Class

The DirichletEquivalentPfcImplantBC has not been documented. The content listed below should be used as a starting point for documenting the class, which includes the typical automatic documentation associated with a MooseObject; however, what is contained is ultimately determined by what is necessary to make the documentation clear for users.

Imposes the essential boundary condition $var element = document.getElementById("moose-equation-a65c054a-cf07-40ff-8cfe-5c8c81beff71");katex.render("u=g", element, {displayMode:false,throwOnError:false});$ , where $var element = document.getElementById("moose-equation-ee90b915-616b-459d-b699-f50206b85e72");katex.render("g", element, {displayMode:false,throwOnError:false});$ is a constant calculated assuming the recombination fluxquickly becomes equal to the incident flux. The recombination term is calculated using the simulation temperature and the pre-exponent and Energy values provided

Overview

Implements a dirichlet boundary condition where the value at the surface is calculated as the steady-state balance between a known incident flux of particles into the material and an opposing desorption flux back out of the material, which is based on a user-defined recombination condition.

This option is not necessarily intended to offer a good general physical representation but is used to replicate the numerical model of Delaporte-Mathurin et al. (2019).

This boundary condition aims to simplify Eq. (1) for the particular case of steady-state equilibrium, as shown in Eq. (3).

$(1)var element = document.getElementById("moose-equation-777b584e-c9fe-476d-b868-d8f5aec04c07");katex.render(" \\varphi_{net} = \\varphi_{incident} - K_{r}(T)C_{m}^2", element, {displayMode:true,throwOnError:false});$

Where the recombination coefficient, $var element = document.getElementById("moose-equation-b96d0580-ae7b-45da-a616-f5111a4c0841");katex.render("K_r", element, {displayMode:false,throwOnError:false});$ , is given by Eq. (2).

$(2)var element = document.getElementById("moose-equation-ee375cbd-9ec0-40a6-b410-0980ad894b5b");katex.render(" K_{r}(T) = K_0\\exp\\left(-E_r / k_B T\\right)", element, {displayMode:true,throwOnError:false});$

At equilibirum, the recombination flux is equal to the incident flux and the mobile concentration can be found from Eq. (3).

$(3)var element = document.getElementById("moose-equation-a505d951-96da-4889-a155-e09ca2728b9b");katex.render(" C_m = \\sqrt{\\frac{\\varphi}{K_r(T)}}", element, {displayMode:true,throwOnError:false});$

User inputs are required for $var element = document.getElementById("moose-equation-3416e4aa-1156-4249-9775-125f9a478793");katex.render("K_0", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-7ef22ae4-f81a-4940-917c-70c56e52d272");katex.render("E_r", element, {displayMode:false,throwOnError:false});$ , and $var element = document.getElementById("moose-equation-ce5a68f1-1d15-4d6c-8e9d-736420536e7b");katex.render("\\varphi", element, {displayMode:false,throwOnError:false});$ . The temperature is taken from a coupled variable. Note that again a scale factor is required for the conversion of the mobile concentration from $var element = document.getElementById("moose-equation-9e548cff-afb0-4b65-8349-0dfff889b706");katex.render("\\text{m}^{-3}", element, {displayMode:false,throwOnError:false});$ to atomic fraction.

Example Input File Syntax

Input Parameters

EEnergy Barrier in Arhhenious Expression
C++ Type:double
Options:
Description:Energy Barrier in Arhhenious Expression
TTemperature
C++ Type:std::vector<VariableName>
Options:
Description:Temperature
boundaryThe list of boundary IDs from the mesh where this boundary condition applies
C++ Type:std::vector<BoundaryName>
Options:
Description:The list of boundary IDs from the mesh where this boundary condition applies
k0pre-exponent factor
C++ Type:double
Options:
Description:pre-exponent factor
scale_factorscale factor
C++ Type:double
Options:
Description:scale factor
variableThe name of the variable that this residual object operates on
C++ Type:NonlinearVariableName
Options:
Description:The name of the variable that this residual object operates on

Required Parameters

diag_save_inThe name of auxiliary variables to save this BC's diagonal jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector<AuxVariableName>
Options:
Description:The name of auxiliary variables to save this BC's diagonal jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
displacementsThe displacements
C++ Type:std::vector<VariableName>
Options:
Description:The displacements
flux0The value of the implantation flux.
Default:0
C++ Type:double
Options:
Description:The value of the implantation flux.
presetTrueWhether or not to preset the BC (apply the value before the solve begins).
Default:True
C++ Type:bool
Options:
Description:Whether or not to preset the BC (apply the value before the solve begins).
save_inThe name of auxiliary variables to save this BC's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector<AuxVariableName>
Options:
Description:The name of auxiliary variables to save this BC's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
set_x_compTrueWhether to set the x-component of the variable
Default:True
C++ Type:bool
Options:
Description:Whether to set the x-component of the variable
set_y_compTrueWhether to set the y-component of the variable
Default:True
C++ Type:bool
Options:
Description:Whether to set the y-component of the variable
set_z_compTrueWhether to set the z-component of the variable
Default:True
C++ Type:bool
Options:
Description:Whether to set the z-component of the variable

Optional Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Options:
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Options:
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
Options:
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
Options:
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
Options:
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

extra_matrix_tagsThe extra tags for the matrices this Kernel should fill
C++ Type:std::vector<TagName>
Options:
Description:The extra tags for the matrices this Kernel should fill
extra_vector_tagsThe extra tags for the vectors this Kernel should fill
C++ Type:std::vector<TagName>
Options:
Description:The extra tags for the vectors this Kernel should fill
matrix_tagssystem timeThe tag for the matrices this Kernel should fill
Default:system time
C++ Type:MultiMooseEnum
Options:nontime, system, time
Description:The tag for the matrices this Kernel should fill
vector_tagsresidualThe tag for the vectors this Kernel should fill
Default:residual
C++ Type:MultiMooseEnum
Options:nontime, time, residual
Description:The tag for the vectors this Kernel should fill

Tagging Parameters

References

Rémi Delaporte-Mathurin, Etienne A. Hodille, Jonathan Mougenot, Yann Charles, and Christian Grisolia. Finite element analysis of hydrogen retention in iter plasma facing components using festim. Nuclear Materials and Energy, 21:100709, 2019. URL: https://www.sciencedirect.com/science/article/pii/S2352179119300547, doi:https://doi.org/10.1016/j.nme.2019.100709.

@article{DELAPORTE2019,
    author = "Delaporte-Mathurin, Rémi and Hodille, Etienne A. and Mougenot, Jonathan and Charles, Yann and Grisolia, Christian",
    title = "Finite element analysis of hydrogen retention in ITER plasma facing components using FESTIM",
    journal = "Nuclear Materials and Energy",
    volume = "21",
    pages = "100709",
    year = "2019",
    issn = "2352-1791",
    doi = "https://doi.org/10.1016/j.nme.2019.100709",
    url = "https://www.sciencedirect.com/science/article/pii/S2352179119300547",
    keywords = "Fusion, Tritium, Finite elements, Plasma facing components, Hydrogen isotopes",
    abstract = "The behaviour of hydrogen isotopes in ITER monoblocks was studied using the code FESTIM (Finite Element Simulation of Tritium In Materials) which is introduced in this publication. FESTIM has been validated by reproducing experimental data and the Method of Manufactured Solutions was used for analytical verification. Following relevant plasma scenarios, both transient heat transfer and hydrogen isotopes (HIs) diffusion have been simulated in order to assess HIs retention in monoblocks. Relevant materials properties have been used. Each plasma cycle is composed of a current ramp up, a current plateau, a current ramp down and a resting phase before the following shot. 100 cycles are simulated. The total HIs inventory in the tokamak during resting phases reaches 1.8×10−3mg whereas during the implantation phases it keeps increasing as a power law of time. Particle flux on the cooling channel of the monoblock is also computed. The breakthrough time is estimated to be t=1×105s which corresponds to 24 cycles. Relevance of 2D modelling has been demonstrated by comparing the total HIs inventory obtained by 2D and 1D simulations. Using 1D simulations, a relative error is observed compared to 2D simulations which can reach -25\% during the resting phase. The error during implantation phases keeps increasing."
}

Overview
Example Input File Syntax
Input Parameters
References

Module

Examples

Source Code

Comparison to Analytical Solution

Thermal Desorption Spectrum

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