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TMAP8 divertor example tritium flux update #425

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2b0d737
Update divertor monoblock case - tritium flux value
simopier May 25, 2026
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Update documentation
simopier May 25, 2026
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regold tests
simopier May 26, 2026
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simopier Jun 24, 2026
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86 changes: 46 additions & 40 deletions doc/content/examples/divertor_monoblock/index.md
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Original file line number Diff line number Diff line change
Expand Up @@ -189,14 +189,19 @@ During the steady-state plasma discharge, we set a heat flux of 10 MW$\cdot$m$^{
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}$$\cdot$s$^{-1}$)
entered the first layer of mesh at the exposed surface ($y = 14.0$ mm) as in [!cite](Shimada2024114438).
and only 0.1% of the incident plasma particle flux is treated as a retained tritium surface flux at
the exposed surface ($y = 14.0$ mm), corresponding to 5.0 $\times$ 10$^{20}$ m$^{-2}$$\cdot$s$^{-1}$.
For the normalized atomic-fraction variable used in the input file, this boundary condition is written as a
Neumann flux of 7.89 $\times$ 10$^{-9}$ m$\cdot$s$^{-1}$.
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.
which would otherwise require a more detailed near-surface implantation model and increase computational costs.

!alert warning title=Updated tritium retained surface flux value from [!cite](Shimada2024114438)
Since publication, the input file has been updated to fix a typo in [!cite](Shimada2024114438), where the retained tritium surface flux was divided by the thickness of the first mesh layer ($dx = 1 \times 10^{-4}$ m), leading to a flux of 7.89 $\times$ 10$^{-13}$ $\cdot$s$^{-1}$ instead of 7.89 $\times$ 10$^{-9}$ m$\cdot$s$^{-1}$. The updated input files now use the corrected value of 7.89 $\times$ 10$^{-9}$ m$\cdot$s$^{-1}$.
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!alert warning title=Small typo fixed for the heat flux from [!cite](Shimada2024114438)
Since publication, the input file has been updated to fix a small typo that has a minor, almost insignificant effect on the results. The typo set the heat flux to be equal to 300 W/m$^2$ while the pulse was off, as opposed to being equal to 0 W/m$^2$. This was likely due to a mistake in using the off-pulse temperature of the cooling channel (300 K) rather than the zero flux. The change from 300 W/m$^2$ to 0 W/m$^2$ was observed to be negligible, which is attributed to the fact that 300 W/m$^2$ is a small value in this scenario. For context, the maximum heat flux value is 1 $\times 10^{7}$ W/m$^2$. The current version of the input file uses 0 W/m$^2$.
Expand Down Expand Up @@ -246,7 +251,7 @@ The diffusivity is defined as $D=D_0 \exp⁡(-E_D/k_B/T)$ and the solubility is
!listing test/tests/divertor_monoblock/divertor_monoblock.i link=false block=Materials


# Interface Kernels
### Interface Kernels

!style halign=left
TMAP8 assumes equilibrium between the chemical potentials of the diffusing species similar to how
Expand All @@ -265,45 +270,10 @@ to avoid the convergence issue associated with calculating two significantly dif

!listing test/tests/divertor_monoblock/divertor_monoblock.i link=false block=InterfaceKernels


### Numerical method

!style halign=left
We use a standard preconditioner: the [“single matrix preconditioner”](SingleMatrixPreconditioner.md).
The Newton method is used to model the [transient](Transient.md) 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 test/tests/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 examples/figures/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 examples/figures/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%

!alert warning title=The exodus file in `gold` is a smaller version of the output
The input file [/divertor_monoblock.i] returns the outputs that were used in [!cite](Shimada2024114438). However, a slightly modified version of this input is run in [/divertor_monoblock/tests] as part of TMAP8's [Software Quality Assurance](sqa/index.md exact=True) process: It simulates only one pulse cycle, has a coarser mesh, and outputs the results less regularly to limit the file size. As a result, the exodus file in the test `gold` directory is a smaller version of the output generated when running the full input file.

Note that the current model has been utilized in a follow up study to perform a sensitivity study on material properties and operation conditions, for which the documentation is available [here](examples/divertor_monoblock/sensitivity.md exact=True).

## Postprocessors
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!style halign=left
Relevant postprocessors have been added to characterize temperatures, fluxes and concentrations of tritium at various points in the model.
Relevant postprocessors have been added to characterize temperatures, fluxes and concentrations of tritium at various points in the model.

First, we add a postprocessor to track the flux across the CuCrZr boundary, and scale it to obtain a total flux

Expand Down Expand Up @@ -347,6 +317,42 @@ And the total area (2D volume) each material occupies

!listing test/tests/divertor_monoblock/divertor_monoblock.i block=Postprocessors/total_retention link=false

### Numerical method

!style halign=left
We use a standard preconditioner: the [“single matrix preconditioner”](SingleMatrixPreconditioner.md).
The Newton method is used to model the [transient](Transient.md) 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 test/tests/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 examples/figures/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). The input files have been updated since publication and will provide different results (see warning below).
style=display:block;margin-left:auto;margin-right:auto;width:40%

!media examples/figures/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). The input files have been updated since publication and will provide different results (see warning below).
style=display:block;margin-left:auto;margin-right:auto;width:40%

!alert warning title=Updated results since publication of [!cite](Shimada2024114438).
As detailed in the `Boundary conditions and history` section above, the BCs for tritium influx and heat flux have been updated since publication of [!cite](Shimada2024114438) to fix typos. While the heat flux correction only has very minor effects, the new tritium flux is 4 orders of magnitude larger than in [!cite](Shimada2024114438), leading to higher tritium concentrations, overall retention, and losses to the coolant side.

@lin-yang-ly lin-yang-ly Jun 24, 2026

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The sentence mentioned "the BCs for tritium influx and heat flux have been updated". In the input file, the heat flux is still 1e7 W/m^2, which is same with the published paper. Maybe we should remove the heat flux here.

@simopier simopier Jun 25, 2026

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The minimum value of the heat flux was updated. Not the maximum value. I'll make it more specific.


!alert warning title=The exodus file in `gold` is a smaller version of the output
The input file [/divertor_monoblock.i] returns the outputs updated from [!cite](Shimada2024114438). However, a slightly modified version of this input is run in [/divertor_monoblock/tests] as part of TMAP8's [Software Quality Assurance](sqa/index.md exact=True) process: It simulates only one pulse cycle, has a coarser mesh, and outputs the results less regularly to limit the file size. As a result, the exodus file in the test `gold` directory is a smaller version of the output generated when running the full input file.

Note that the current model has been utilized in a follow up study to perform a sensitivity study on material properties and operation conditions, for which the documentation is available [here](examples/divertor_monoblock/sensitivity.md exact=True).

## Complete input file

Expand Down
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