From 7f0a26f2a39109888ab6d23da5b2a51796f5b8c5 Mon Sep 17 00:00:00 2001 From: Guillaume Giudicelli Date: Thu, 22 Aug 2024 13:42:02 -0600 Subject: [PATCH 1/8] Add references for divertor monoblock --- doc/content/bib/vtb.bib | 32 ++++++++++++++++++++++++++++++++ 1 file changed, 32 insertions(+) diff --git a/doc/content/bib/vtb.bib b/doc/content/bib/vtb.bib index 36674d0d..4dac591f 100755 --- a/doc/content/bib/vtb.bib +++ b/doc/content/bib/vtb.bib @@ -1955,3 +1955,35 @@ @article{domain_overlap_huxford2023 year = {2023}, month = {4} } + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Divertor monoblock + +@article{Hodille2021126003, + author = {E. A. Hodille and R. Delaporte-Mathurin and J. Denis and M. Pecovnik and E. Bernard and Y. Ferro and R. Sakamoto and Y. Charles and J. Mougenot and A. De Backer and C. S. Becquart and S. Markelj and C. Grisolia}, + doi = {10.1088/1741-4326/AC2ABC}, + issn = {0029-5515}, + issue = {12}, + journal = {Nuclear Fusion}, + month = {10}, + pages = {126003}, + publisher = {IOP Publishing}, + title = {Modelling of hydrogen isotopes trapping, diffusion and permeation in divertor monoblocks under ITER-like conditions}, + volume = {61}, + url = {https://iopscience.iop.org/article/10.1088/1741-4326/ac2abc}, + year = {2021} +} + +@article{Shimada2024114438, + author = {Masashi Shimada and Pierre-Clément A. Simon and Casey T. Icenhour and Gyanender Singh}, + doi = {10.1016/J.FUSENGDES.2024.114438}, + issn = {0920-3796}, + journal = {Fusion Engineering and Design}, + month = {6}, + pages = {114438}, + publisher = {North-Holland}, + title = {Toward a high-fidelity tritium transport modeling for retention and permeation experiments}, + volume = {203}, + url = {https://linkinghub.elsevier.com/retrieve/pii/S0920379624002916}, + year = {2024} +} From 7acd49986d72dcda87c0219cc00d4c5b44dc5407 Mon Sep 17 00:00:00 2001 From: Guillaume Giudicelli Date: Thu, 22 Aug 2024 13:42:17 -0600 Subject: [PATCH 2/8] Add divertor monoblock documentation --- doc/content/fusion/index.md | 3 + .../fusion/mcf/divertor_monoblock/index.md | 312 ++++++++++++++++++ doc/content/resources/manual_indexing.md | 1 + 3 files changed, 316 insertions(+) create mode 100644 doc/content/fusion/index.md create mode 100644 doc/content/fusion/mcf/divertor_monoblock/index.md diff --git a/doc/content/fusion/index.md b/doc/content/fusion/index.md new file mode 100644 index 00000000..494a2f13 --- /dev/null +++ b/doc/content/fusion/index.md @@ -0,0 +1,3 @@ +# Fusion devices + +- [Tokamak divertor monoblock](fusion/mcf/divertor_monoblock/index.md) \ No newline at end of file diff --git a/doc/content/fusion/mcf/divertor_monoblock/index.md b/doc/content/fusion/mcf/divertor_monoblock/index.md new file mode 100644 index 00000000..bd5f55e4 --- /dev/null +++ b/doc/content/fusion/mcf/divertor_monoblock/index.md @@ -0,0 +1,312 @@ +# Divertor Monoblock During Pulsed Operation + +*Contact: Pierre Clement Simon (pierreclement.simon.at.inl.gov), Masashi Shimada (masashi.shimada.at.inl.gov)* + +*Model link: [Divertor Monoblock](https://github.com/idaholab/virtual_test_bed/tree/devel/fusion/mcf/divertor_monoblock)* + +!tag name=SAM Generic PBR Model pairs=reactor_type:fusion_mcf + reactor:ITER_like + geometry:divertor + simulation_type:tritium_migration + transient:pulse + codes_used:TMAP8 + computing_needs:Workstation + fiscal_year:2024 + sponsor:DOE_FES + institution:INL + +TMAP8 is used to model tritium transport in a divertor monoblock to elucidate the effects of pulsed operation (up to fifty 1600-second plasma discharge and cool-down cycles) on the tritium in-vessel inventory source term and ex-vessel release term (i.e., tritium retention and permeation) for safety analysis. This example reproduces the results presented in [!cite](Shimada2024114438). + +## General description of the simulation case and corresponding input file + +### Introduction + +!style halign=left +In a magnetic confinement fusion system, the divertor components will be subjected to intense particle and heat fluxes from plasma, +as well as 14-MeV neutrons stemming from deuterium-tritium (D-T) reactions, +thus creating extremely high temperature and hydrogen concentration gradients across tens of millimeters. +Furthermore, the thermomechanical properties of the divertor materials will evolve over time in response to displacement damage and gas/solid transmutations. +Thus, predictive modeling of tritium transport in the divertor poses enormous challenges, as it requires simulation capabilities capable of +(1) multi-material configurations, (2) high thermal cycles, (3) complex 2D and 3D geometries, (4) and microstructural evolution +resulting from displacement damage and gas/solid transmutations. +For example, the ITER divertor, which consists of tungsten (W) monoblocks bonded to cooling tubes made of copper-chromium-zirconium (CuCrZr) alloy, +is designed to withstand high heat fluxes (∼10 MW $m^{−2}$) during steady-state plasma operation from intense D-T plasma flux (∼1024 $m^{−2}s^{−1}$). +In this example, we simulate tritium retention and permeation as well as thermal transport in an ITER-like 2D W-Cu-CuCrZr monoblock and demonstrate +the first three (out of four) aforementioned required simulation capabilities for tritium transport in the divertor using TMAP8, as presented in [!cite](Shimada2024114438). +This simulation was also based on the cases published in [!cite](Hodille2021126003). + +The sections below describe the simulation details and explain how they translate into the example TMAP8 input file. +Not every part of the input file is explained here. +If the interested reader has more questions about this example case and how to modify this input file to adapt it to a different case, +feel free to reach out to the TMAP8 development team on the [TMAP8 GitHub discussion page](https://github.com/idaholab/TMAP8/discussions). + + +### Divertor monoblock geometry and mesh generation + +!style halign=left +[fig:mesh] shows the geometry, mesh, and temperature distribution of the 2D monoblock employed in [!cite](Shimada2024114438) and in the present example. +The 2D monoblock consisted of three materials: + +1. W monoblock ($r$ (mm) > 8.5), +2. Cu interlayer (7.5 < $r$ (mm) < 8.5), +3. CuCrZr tube (6.0 < $r$ (mm) < 7.5), and +4. H$_2$O cooling ($r$ (mm) < 6.0), + +where $r=\sqrt{x^2+y^2}$ in a Cartesian coordinate system, and the center point ($x$, $y$) = (0, 0) is defined at the center of the CuCrZr tube. + +!media media/fusion/mcf/divertor_monoblock/divertor_monoblock_mesh.png + id=fig:mesh + caption=2D monoblock: (left) geometry and mesh; (right) temperature distribution. This corresponds to Fig. 1 in Ref. [!cite](Shimada2024114438). + style=display:block;margin-left:auto;margin-right:auto;width:50% + +`MOOSE` is equipped with a set of user-friendly, built-in mesh generators for creating meshes based on simple geometries (e.g., a monoblock). +The built-in mesh generator [ConcentricCircleMeshGenerator](https://mooseframework.inl.gov/source/meshgenerators/ConcentricCircleMeshGenerator.html) is used to create meshes for the 2D monoblock geometry. +Only the left-hand (−14.0 < $x$ (mm) < 0 & −14.0 < $y$ (mm) < 14.0) portion of the monoblock is used, +such that the mesh size is halved by assuming symmetry at the $x = 0$ plane. +This example uses a total of 9,418 nodes, creating 28,402 degrees of freedom in the non-linear system. +The finer mesh size and time step are required to compute the trapping-limited diffusion regime, as described in TMAP8 verification case `ver-1d`. +However, a set of relatively low detrapping energies (< 0.85 eV) is used here to reduce the computing time via the relatively coarse mesh size. + +In the input file, the mesh is defined as: + +!listing fusion/mcf/divertor_monoblock/divertor_monoblock.i link=false block=Mesh + +### Nomenclature of variables and physical parameters + +!style halign=left +[tab:variables] lists the variables and physical parameters used in this example with their units. + +!table id=tab:variables caption=Nomenclature of variables and physical parameters used in this example. +| Symbol | Variable or Physical Property | Unit | +| --- | --- | --- | +| $C_s$ | Concentration of solute (mobile) species | m$^{−3}$ | +| $C_t$ | Concentration of trapped species | m$^{−3}$ | +| $T$ | Temperature | K | +| $D$ | Diffusivity of solute (mobile) species | m$^{2}$ s$^{-1}$ | +| $K_s$ | Solubility of solute (mobile) species | m$^{−3}$ Pa$^{-1/2}$ | +| $C_{total}$ | Total concentration of species $C_{total}=C_s + C_t$ | m$^{−3}$ | +| $C_t^e$ | Concentration of empty trapping sites | m$^{−3}$ | +| $C_t^0$ | Concentration of trapping sites $C_t^e=C_t^0-C_t$ | m$^{−3}$ | +| $\alpha_t$ | Trapping rate coefficient, $2.75 \times 10^{11}$ | s$^{−1}$ | +| $\alpha_r$ | Release rate coefficient $\alpha_r=\alpha_{r0} \exp⁡((-E_{dt})/(k_b T))$ | s$^{−1}$ | +| $\alpha_{r0}$ | Pre-exponential factor, $8.40 \times 10^{12}$ | s$^{−1}$ | +| $E_{dt}$ | Detrapping energy | eV | +| $N$ | Atomic number density | m$^{−3}$ | +| $\rho$ | Density | g m$^{-3}$ | +| $c_p$ | Specific heat | J kg$^{-1}$ K$^{-1}$ | +| $k_T$ | Thermal conductivity | W m$^{-1}$ K$^{-1}$ | + + +### Variables and governing equations + +!style halign=left +To simulate tritium and thermal transport, we define two sets of [!ac](PDEs). +First, the strong form of the mass conservation equation for solute (mobile) T atoms, $C_s$, is written as: + +\begin{equation} \label{eq:concentration} +\frac{\partial C_s}{\partial t} + \nabla \cdot (-D \nabla C_s) + \alpha_t \frac{C_t^e}{N} C_s - \alpha_r C_t = 0. +\end{equation} + +We use three sets of mass conservation equations to calculate the behaviors of solute T atoms in three different materials (i.e., W, Cu, CuCrZr). +Second, the strong form of the conservation of energy equation is written as: + +\begin{equation} \label{eq:temperature} +\rho c_p \frac{\partial T}{\partial t} - \nabla \cdot (k_T \nabla T) = 0. +\end{equation} + +[tab:variables] lists all the symbols and definitions used in [eq:concentration] and [eq:temperature]. + +The next step is to convert these two strong-form PDEs into their weak forms by multiplying with a test function, $\psi$, and integrating over a domain, $\Omega$ with surface $\delta \Omega$ and outward-facing normal vector $\hat{n}$. Using the divergence theorem, one can obtain the weak form of the mass conservation equation ([eq:concentration]) as follows: + +\begin{equation} \label{eq:concentration_weak} +\int_{\Omega}\psi \frac{\partial C_s}{\partial t} +-\int_{\delta \Omega} \psi D \nabla C_s \cdot \hat{n} ++\int_{\Omega} \nabla \psi \cdot D \nabla C_s ++\int_{\Omega} \psi \alpha_t \frac{C_t^e}{N} C_s +-\int_{\Omega} \psi \alpha_r C_t = 0. +\end{equation} + +Similarly, the weak form of the conservation of energy equation can be written by multiplying [eq:temperature] with a test function, $\psi$, and integrating over a domain, $\Omega$ with surface $\delta \Omega$ and outward-facing normal vector $\hat{n}$. Using the divergence theorem, one can obtain the weak form of the conservation of energy equation as follows: + +\begin{equation} \label{eq:temperature_weak} +\int_{\Omega}\psi c_p \frac{\partial T}{\partial t} +-\int_{\delta \Omega} \psi k_T \nabla T \cdot \hat{n} ++\int_{\Omega} \nabla \psi \cdot k_T \nabla T = 0. +\end{equation} + +Then, to solve for the [!ac](PDEs) and physical phenomena, we can select appropriate kernels and boundary conditions (BCs) from MOOSE’s extensive library. The following three subsections describe each kernel, BC, and numerical method utilized in the present work. + +In the input file, the variables are defined as: + +!listing fusion/mcf/divertor_monoblock/divertor_monoblock.i link=false block=Variables + +Note the usage of `initial_condition` and `block` parameters in order to set initial conditions and material block applicability for each variable. + + +### Kernels + +!style halign=left +For the mass conservation equation, we use [ADTimeDerivative](https://mooseframework.inl.gov/source/kernels/ADTimeDerivative.html) and [ADMatDiffusion](https://mooseframework.inl.gov/source/kernels/ADMatDiffusion.html) to represent the 1$^{\text{st}}$ and 3$^{\text{rd}}$ terms of [eq:concentration_weak]. +The TMAP8 kernels [TrappingNodalKernel](https://mooseframework.inl.gov/TMAP8/source/nodal_kernels/TrappingNodalKernel.html) and [ReleasingNodalKernel](https://mooseframework.inl.gov/TMAP8/source/nodal_kernels/ReleasingNodalKernel.html) represent the 4$^{\text{th}}$ and 5$^{\text{th}}$ terms of [eq:concentration_weak], +respectively, and simulate the trapping/release behavior of hydrogen isotopes in/from trap sites. +For the conservation of energy equation, [SpecificHeatConductionTimeDerivative](https://mooseframework.inl.gov/source/kernels/SpecificHeatConductionTimeDerivative.html) and [HeatConduction](https://mooseframework.inl.gov/source/kernels/HeatConduction.html) solve the 1$^{\text{st}}$ and 3$^{\text{rd}}$ terms of [eq:temperature_weak]. +`ADTimeDerivative` and `ADMatDiffusion` are kernels from the core MOOSE framework, and `SpecificHeatConductionTimeDerivative` and `HeatConduction` are kernels from the [MOOSE Heat Transfer Module](https://mooseframework.inl.gov/modules/heat_transfer/index.html). These pre-made kernels are commonly +re-used to represent time derivative, diffusion, and heat conduction terms in a given material within a variety of MOOSE-based simulations. + +!listing fusion/mcf/divertor_monoblock/divertor_monoblock.i link=false block=Kernels + +[NodalKernels](https://mooseframework.inl.gov/syntax/NodalKernels/index.html) are used for non-diffusive variables (trapped species). + +!listing fusion/mcf/divertor_monoblock/divertor_monoblock.i link=false block=NodalKernels + + +### AuxVariables and AuxKernels + +!style halign=left +[AuxVariables](https://mooseframework.inl.gov/syntax/AuxVariables/index.html) are used to track quantities that are not solved for by the [!ac](PDEs), +but are needed to compute materials properties, +or are desirable to obtain as outputs, such as the total concentration of tritium or flux values. +[AuxKernels](https://mooseframework.inl.gov/syntax/AuxKernels/index.html) provide the expressions that define the `AuxVariables`. + +!listing fusion/mcf/divertor_monoblock/divertor_monoblock.i link=false block=AuxVariables + +!listing fusion/mcf/divertor_monoblock/divertor_monoblock.i link=false block=AuxKernels + + +### Boundary conditions and history + +!style halign=left +For the mass conservation equation, we use [FunctionNeumannBC](https://mooseframework.inl.gov/source/bcs/FunctionNeumannBC.html) and [DirichletBC](https://mooseframework.inl.gov/source/bcs/DirichletBC.html) to solve the 2$^{\text{nd}}$ term of [eq:concentration_weak]. +`FunctionNeumannBC` is used to treat the time-dependent plasma exposure at the top (plasma-exposed) surface, +and `DirichletBC` is used to set the BC of the solute T atom concentration to zero at the inner CuCrZr tube (at $r = 6$ mm). +For the energy conservation equation, we use `FunctionNeumannBC` and `DirichletBC` to solve the 2$^{\text{nd}}$ term of [eq:temperature_weak]. +`FunctionNeumannBC` is used to treat the time-dependent heat flux at the top (plasma-exposed) surface, +and [FunctionDirichletBC](https://mooseframework.inl.gov/source/bcs/FunctionDirichletBC.html) is used to treat the temperature increase in the cooling tube. +`FunctionNeumannBC`, `FunctionDirichletBC`, `DirichletBC`, and `FunctionDirichletBC` are MOOSE objects commonly used to represent the BCs of the variables to be solved. + +We simulate a 20,000-second plasma discharge, with each 1,600-second cycle consisting of a 100-second plasma ramp-up, +a 400-second steady-state plasma discharge, a 100-second plasma ramp-down, and a 1,000-second waiting phase. +Up to 50 cycles are simulated to achieve the total discharge. +[fig:tritium_temperature_history] shows the integrated (solute, total and trapped) tritium concentration profiles in the monoblock. +It shows that implantation fluxes and temperatures vary linearly up to (from) their steady-state values from (up to) their initial values during ramp-up (ramp-down). + +!media media/fusion/mcf/divertor_monoblock/divertor_monoblock_history.png + id=fig:tritium_temperature_history + caption=Temperature profiles (orange) and integrated tritium concentration profiles (blue) during two 1,600-second-cycle plasma discharges. This corresponds to Fig. 2 in [!cite](Shimada2024114438). + style=display:block;margin-left:auto;margin-right:auto;width:60% + +During the steady-state plasma discharge, we set a heat flux of 10 MW$\cdot$m$^{-2}$ at the top of the 2D monoblock (at $y = 14.0$ mm) +and a cooling temperature of 552 K at the inner CuCrZr tube (at $r = 6.0$ mm). +We assume a 100% T plasma with a 5.0 $\times$ 10$^{23}$ m$^{-2}$$\cdot$s$^{-1}$ plasma particle flux +(which is half of the full 1.0 $\times$ 10$^{24}$ m$^{-2}$$\cdot$s$^{-1}$ DT plasma particle flux), +and only 0.1% of the incident plasma particle flux (5.0 $\times$ 10$^{20}$ m$^{-2}$$\cdot$s$^{-1}$) +entered the first layer of mesh at the exposed surface ($y = 14.0$ mm) as in [!cite](Shimada2024114438). +The solute T atom concentration is set to zero at the inner CuCrZr tube (at $r = 6.0$ mm). + +We treated this plasma exposure by setting the flux BC of the +solute T atom concentration at the exposed surface ($y = 14.0$ mm) +as a simplification of the complex plasma implantation and recombination phenomena, +which would require a very fine mesh and increase computational costs. + +!listing fusion/mcf/divertor_monoblock/divertor_monoblock.i link=false block=BCs + + +### Functions + +!style halign=left + +In this example, [Functions](https://mooseframework.inl.gov/syntax/Functions/index.html) are used to define the time-dependent tritium +and heat flux at the exposed surface, as well as the coolant temperature. +Functions can also be spatially-dependent. +The functions are then provided to BCs, as described above. + +!listing fusion/mcf/divertor_monoblock/divertor_monoblock.i link=false block=Functions + + +### Material properties + +!style halign=left +We use the tritium mass transport properties listed in [tab:material_properties_tritium] +to solve the mass conservation equation ([eq:concentration_weak]) for two variables: +$C_s$ and $C_t$ (i.e., solute and trapped T atom concentrations) in three materials +and the thermal properties (i.e., density, temperature-dependent specific heat, and thermal conductivity) listed in [tab:material_properties_thermal] +to solve the energy conservation equation ([eq:temperature_weak]) for one variable: the temperature $T$. +The diffusivity is defined as $D=D_0 \exp⁡(-E_D/k_B/T)$ and the solubility is defined as $K_s=K_{s,0} \exp⁡(-E_s/k_B/T)$. + +!table id=tab:material_properties_tritium + caption=Tritium mass transport and trapping properties used in the W, Cu, and CuCrZr layers. $^{**}$NOTE: Two-component solubility in W kept the maximum solubility ratio between W and Cu to 104 at low temperature. The references are provided in [!cite](Shimada2024114438). +| Material | $D_0$ (m$^2$/s) | $E_D$ (eV) | $K_{s,0}$ (Pa$^{1/2}$) | $E_s$ (eV) | Detrapping energy: $E_{dt}$ (eV) | Trap density: $n_{trap}$ (at.fr.) | +| --- | --- | --- | --- | --- | --- | --- | +| W | 2.4$\times$10$^{-7}$ | 0.39 | 1.87$\times$10$^{24}$ | 1.04 | 0.85 | 1.0$\times$10$^{-4}$ | +| W | | | 3.14$\times$10$^{20}$$^{**}$ | 0.57$^{**}$ | | | +| Cu | 6.6$\times$10$^{-7}$ | 0.39 | 3.14$\times$10$^{24}$ | 0.57 | 0.50 | 5.0$\times$10$^{-5}$ | +| CuCrZr | 3.9$\times$10$^{-7}$ | 0.42 | 4.28$\times$10$^{23}$ | 0.39 | 0.83 | 5.0$\times$10$^{-5}$ | + +!table id=tab:material_properties_thermal + caption=Thermal properties used in the W, Cu, and CuCrZr layers. The references are provided in [!cite](Shimada2024114438). +| Material | Density: $\rho$ (g m$^{-3}$) | Specific heat: $c_p$ (J kg$^{-1}$ K$^{-1}$) | Thermal conductivity: $k_T$ (W m$^{-1}$ K$^{-1}$) | +| --- | --- | --- | --- | +| W | 19,300 | 1.16$\times$10$^{2}$ +7.11$\times$10$^{-2}$ T –6.58$\times$10$^{-5}$ T$^{2}$ +3.24$\times$10$^{-8}$ T$^{3}$ –5.45$\times$10$^{-12}$ T$^{4}$ (293 < T (K) < 2500) | 2.41$\times$10$^{2}$ –2.90$\times$10$^{-1}$ T + 2.54$\times$10$^{-4}$ T$^{2}$ –1.03$\times$10$^{-7}$ T$^{3}$ +1.52$\times$10$^{-11}$ T$^{4}$ (293 < T (K) < 2500) | +| Cu | 8,960 | 4.21$\times$10$^{2}$ –6.85$\times$10$^{-2}$ T (293 < T (K) < 873) | 3.16$\times$10$^{2}$ +3.18$\times$10$^{-1}$ T –3.49$\times$10$^{-4}$ T$^{2}$ +1.66$\times$10$^{-7}$ T$^{3}$ (293 < T (K) < 873) | +| CuCrZr | 8,900 | 390 | 3.87$\times$10$^{2}$ –1.28$\times$10$^{-1}$ T (293 < T (K) < 927) | + +!listing fusion/mcf/divertor_monoblock/divertor_monoblock.i link=false block=Materials + + +### Interface Kernels + +!style halign=left +TMAP8 assumes equilibrium between the chemical potentials of the diffusing species similar to how +TMAP4 and TMAP7 treated the diffusing species across two different materials with different chemical potentials. +[SolubilityRatioMaterial`](https://mooseframework.inl.gov/TMAP8/source/materials/SolubilityRatioMaterial.html) is used to treat solute concentration differences stemming from a difference in T solubilities across the interface. +The solubility ratio jump is calculated via the following: +\begin{equation} \label{eq:solubility} +J = \frac{C_{s,1}}{K_{s,1}} - \frac{C_{s,2}}{K_{s,2}}. +\end{equation} + +[ADPenaltyInterfaceDiffusion](https://mooseframework.inl.gov/source/interfacekernels/PenaltyInterfaceDiffusion.html) is used to conserve the particle flux at this interface between two different solubilities. +The extremely low tritium solubility in W at low temperature leads to an extremely low solute concentration in W, +creating a large solute concentration difference between W and Cu. +Two-component solubility in W is used to keep the maximum solubility ratio between W and Cu to 104 at low temperature +to avoid the convergence issue associated with calculating two significantly different solute concentration in W and Cu. + +!listing fusion/mcf/divertor_monoblock/divertor_monoblock.i link=false block=InterfaceKernels + + +### Numerical method + +!style halign=left +We use a standard preconditioner: the [“single matrix preconditioner”](https://mooseframework.inl.gov/source/preconditioners/SingleMatrixPreconditioner.html). +The Newton method is used to model the [transient](https://mooseframework.inl.gov/source/executioners/Transient.html) tritium and thermal transport in a 2D monoblock. +It is important to note that MOOSE is equipped with the built-in Message Passing Interface (MPI) protocol, +as tritium and thermal transport analysis of fifty 1,600-second cycle plasma discharges in the 2D monoblock is +performed in under 2 hours using a single device/computer (3.5 GHz Apple M2 Pro, 10-Core CPU/16-Core GPU) with this MPI feature. + +!listing fusion/mcf/divertor_monoblock/divertor_monoblock.i link=false block=Executioner + + +## Results + +!style halign=left +The simulation results from this example are shown in [fig:results2D_a] and [fig:results2D_b]. +For more results, information, and discussion about the results for this example case and +their significance, the reader is referred to [!cite](Shimada2024114438). + +!media media/fusion/mcf/divertor_monoblock/divertor_monoblock_results_2D_a.png + id=fig:results2D_a + caption=Tritium concentration profile in W (left), Cu (center), and CuCrZr (right) after ten 1,600-second cycles ($t = 14912$ s). This corresponds to Fig. 4A in [!cite](Shimada2024114438). + style=display:block;margin-left:auto;margin-right:auto;width:40% + +!media media/fusion/mcf/divertor_monoblock/divertor_monoblock_results_2D_b.png + id=fig:results2D_b + caption=Tritium concentration profile in W (left), Cu (center), and CuCrZr (right) after fifty 1,600-second cycles ($t = 78912$ s). This corresponds to Fig. 4B in [!cite](Shimada2024114438). + style=display:block;margin-left:auto;margin-right:auto;width:40% + + +## Complete input file + +Below is the complete input file, which can be run reliably with approximately 4 processor cores. Note that this input file has not been optimized for computational costs. + +!listing fusion/mcf/divertor_monoblock/divertor_monoblock.i + +!bibtex bibliography diff --git a/doc/content/resources/manual_indexing.md b/doc/content/resources/manual_indexing.md index 92490a51..f19e2d2a 100644 --- a/doc/content/resources/manual_indexing.md +++ b/doc/content/resources/manual_indexing.md @@ -10,6 +10,7 @@ - [Lead-cooled Fast Reactor (LFR)](lfr/index.md) \\ - [Micro Reactors (MR)](microreactors/index.md) - [Seismic Analysis](seismic_analysis/index.md) +- [Fusion Devices](fusion/index.md) !alert note From 6e9231f6b00d5efb6e22eb0e32735901a0736d10 Mon Sep 17 00:00:00 2001 From: Guillaume Giudicelli Date: Thu, 22 Aug 2024 13:42:36 -0600 Subject: [PATCH 3/8] Add divertor monoblock media refs #423 --- .../divertor_monoblock_history.png | Bin 0 -> 219238 bytes .../divertor_monoblock_mesh.png | Bin 0 -> 2510890 bytes .../divertor_monoblock_results_2D_a.png | Bin 0 -> 863073 bytes 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