diff --git a/doc/content/bib/tmap8.bib b/doc/content/bib/tmap8.bib index 60cbe210b..6b2739e88 100644 --- a/doc/content/bib/tmap8.bib +++ b/doc/content/bib/tmap8.bib @@ -390,3 +390,44 @@ @article{MAJER2002438 url = {https://www.sciencedirect.com/science/article/pii/S0925838801014529}, author = {G. Majer and J. Gottwald and D. T. Peterson and R. G. Barnes} } + +@article{calderoni2008measurement, + title={{Measurement of tritium permeation in FLiBe (2LiF--BeF2)}}, + author={Calderoni, P and Sharpe, P and Hara, M and Oya, Y}, + journal={Fusion Engineering and Design}, + volume={83}, + number={7-9}, + pages={1331--1334}, + year={2008}, + publisher={Elsevier} +} + +@article{causey2012tritium, + title={Tritium barriers and tritium diffusion in fusion reactors}, + author={Causey, Rion A and Karnesky, Richard A and San Marchi, Chris}, + journal={Comprehensive Nuclear Materials}, + volume={4}, + pages={511--549}, + year={2012}, + publisher={Elsevier} +} + +@article{hattab2024openfoam, + title={{An OpenFOAM multi-region solver for tritium transport modeling in fusion systems}}, + author={Hattab, Federico and Siriano, Simone and Giannetti, Fabio}, + journal={Fusion Engineering and Design}, + volume={202}, + pages={114362}, + year={2024}, + publisher={Elsevier} +} + +@article{altunoglu1991permeation, + title={Permeation of hydrogen through nickel foils: surface reaction rates at low temperatures}, + author={Altunoglu, AK and Blackburn, DA and Braithwaite, N St J and Grant, DM}, + journal={Journal of the Less Common Metals}, + volume={172}, + pages={718--726}, + year={1991}, + publisher={Elsevier} +} diff --git a/doc/content/verification_and_validation/figures/comparison_val-2g.py b/doc/content/verification_and_validation/figures/comparison_val-2g.py new file mode 120000 index 000000000..076b7a77e --- /dev/null +++ b/doc/content/verification_and_validation/figures/comparison_val-2g.py @@ -0,0 +1 @@ +../../../../test/tests/val-2g/comparison_val-2g.py \ No newline at end of file diff --git a/doc/content/verification_and_validation/index.md b/doc/content/verification_and_validation/index.md index 1382522a5..927d598aa 100644 --- a/doc/content/verification_and_validation/index.md +++ b/doc/content/verification_and_validation/index.md @@ -56,3 +56,4 @@ TMAP8 also contains [example cases](examples/tmap_index.md), which showcase how | val-2d | [Thermal Desorption Spectroscopy on Tungsten](val-2d.md) | | val-2e | [Co-permeation of H$_2$ and D$_2$ through Pd](val-2e.md) | | val-2f | [Modelling self-damaged tungsten effects on deuterium transport](val-2f.md) | +| val-2g | [Permeation experiment with FLiBe](val-2g.md) | diff --git a/doc/content/verification_and_validation/val-2g.md b/doc/content/verification_and_validation/val-2g.md new file mode 100644 index 000000000..07122733f --- /dev/null +++ b/doc/content/verification_and_validation/val-2g.md @@ -0,0 +1,225 @@ +# val-2g + +# Permeation experiment with FLiBe + +## Case Description + +In this experiment from [!cite](calderoni2008measurement), tritium permeation through molten FLiBe (2LiF–BeF$_2$) is measured using a stainless steel permeation cell composed of two internal volumes separated by a 2 mm thick nickel membrane. The bottom side of the membrane is exposed to a T$_2$/argon gas mixture at controlled partial pressures ranging from 1 to 1250 Pa, while the top side is in contact with molten FLiBe. Temperatures are varied between 500°C and 700°C (773–973 K). As tritium permeated through the membrane and dissolved in the FLiBe, it is carried away from the liquid surface by an argon sweep gas containing 5$\%$ H$_2$. + +## Model Description + +To model this case and understand the physics step by step in order to match the experimental data, we propose two approaches: + +- A 1D case with a Ni membrane in contact with FLiBe, +- A 2D case with both a Ni membrane and FLiBe, including an additional Ni layer to investigate tritium losses at the sides. + +### 1D case: Nickel Membrane with FLiBe + +We model this experimental study in TMAP8 using a 1D simulation that includes three interfaces: enclosure-nickel membrane, nickel membrane-FLiBe, and FLiBe-air. The full domain spans 2 mm of membrane length and 8.1 mm of FLiBe length. The governing equations and modeling assumptions are detailed below. + +The diffusion for tritium in the nickel membrane and FLiBe can be expressed by + +\begin{equation} +\frac{\partial C_{T_2, \, \text{Ni}}}{\partial t} = \nabla D_{\text{Ni}} \nabla C_{T_2, \, \text{Ni}}, +\end{equation} +and +\begin{equation} +\frac{\partial C_{T_2, \, \text{FLiBe}}}{\partial t} = \nabla D_{\text{FLiBe}} \nabla C_{T_2, \, \text{FLiBe}}, +\end{equation} + +where $C_{T_2, \, \text{Ni}}$ and $C_{T_2, \, \text{FLiBe}}$ represent the concentration fields in the nickel membrane and FLiBe, respectively, $t$ is the time, and $D_{\text{Ni}}$ and $D_{\text{FLiBe}}$ denotes the diffusivity coefficients. + +The concentration in FLiBe is related to the concentration in the nickel membrane via the interface sorption law: + +\begin{equation} +C_{T_2, \, \text{FLiBe}} = \frac{K_{s, \, \text{FLiBe}}}{K_{s, \, \text{Ni}}^2} C_{T_2, \, \text{Ni}}^2, +\end{equation} + +where $K_{s, \, \text{FLiBe}}$ and $K_{s, \, \text{Ni}}$ are the solubilities for tritium in FLiBe and nickel respectively. + +At the top of the experimental setup, a Dirichlet boundary condition with a tritium concentration set to zero is imposed, reflecting the assumption that tritium is continuously swept away from the surface: + +\begin{equation} +C_{T_2, \, \text{FLiBe}} = 0. +\end{equation} + +On the left boundary, which interfaces with the tritium gas, a Dirichlet condition is imposed based on Sieverts’ law: + +\begin{equation} +C_{\text{Ni}} = K_{s,\,\text{Ni}}(T) \cdot \sqrt{P_0} +\end{equation} + +where $K_{s,\,\text{Ni}}(T)$ is the temperature-dependent solubility of tritium in Ni, and $P_0$ is the applied tritium partial pressure. + +These sorption law interfaces assume that the kinetics of the surface reactions are much faster than the other kinetics of the problem. + +### 2D Simulation: Nickel Membrane without FLiBe + +This simulation models a 2D domain composed solely of a nickel membrane, without any adjacent FLiBe region. The geometry is rectangular, with a length of 2 mm and a width of 25 mm. Tritium transport in the Ni membrane is governed by Fick’s law, given by: + +\begin{equation} +\frac{\partial C_{T_2, \, \text{Ni}}}{\partial t} = \nabla D_{\text{Ni}} \nabla C_{T_2, \, \text{Ni}}, +\end{equation} + +where $C_{\text{Ni}}$ is the tritium concentration in the nickel membrane, and $D_{\text{Ni}}$ is the diffusivity of tritium in Ni. + +On the left boundary, which interfaces with the tritium gas, a Dirichlet condition is imposed based on Sieverts’ law: + +\begin{equation} +C_{\text{Ni}} = K_{s,\,\text{Ni}}(T) \cdot \sqrt{P_0} +\end{equation} + +where $K_{s,\,\text{Ni}}(T)$ is the temperature-dependent solubility of tritium in Ni, and $P_0$ is the applied tritium partial pressure. + +On the top and bottom boundaries, Neumann conditions are applied to enforce zero flux: + +\begin{equation} +\frac{\partial C_{\text{Ni}}}{\partial y} = 0. +\end{equation} + +On the right boundary, which is exposed to the surrounding air, a Dirichlet condition sets the tritium concentration to zero: + +\begin{equation} +C_{\text{Ni}} = 0. +\end{equation} + +### 2D Simulation: Ni Membrane with FLiBe and Side Ni Layer + +This case models a 2D domain composed of three regions: a Ni membrane, a Ni layer at the top, and a block of FLiBe on the right. The geometry enables investigation of tritium side losses through the additional Ni layer. The full domain spans 2 mm of membrane length, 8.1 mm of FLiBe length, and 25 mm in width, with a side layer of width 2 mm. + +Tritium diffusion in both the Ni regions and the FLiBe block is governed by Fick's law. The time evolution of the tritium concentration $C_{T_2, \, \text{Ni}}$ in the Ni membrane is given by: + +\begin{equation} +\frac{\partial C_{T_2, \, \text{Ni}}}{\partial t} = \nabla D_{\text{Ni}} \nabla C_{T_2, \, \text{Ni}}, +\end{equation} + +while in the FLiBe region, the concentration $C_{T_2, \, \text{FLiBe}}$ evolves according to: + +\begin{equation} +\frac{\partial C_{T_2, \, \text{FLiBe}}}{\partial t} = \nabla D_{\text{FLiBe}} \nabla C_{T_2, \, \text{FLiBe}}. +\end{equation} + +At the left boundary of the Ni membrane, a Dirichlet boundary condition is imposed based on Sieverts' law with a spatially varying pressure profile: + +\begin{equation} +C_{\text{Ni}}(y) = K_{s,\,\text{Ni}}(T) \cdot \sqrt{P(y)}, +\end{equation} + +where $K_{s,\,\text{Ni}}(T)$ is the temperature-dependent solubility of tritium in Ni, and $P(y)$ is the applied pressure defined as: + +\begin{equation} +P(y) = +\begin{cases} +P_0, & y < 25\, \text{mm} \\ +P_0 \cdot \left[ 1 - 3 \left( \frac{y - 25\text{e-3}}{1\text{e-3}} \right)^2 + 2 \left( \frac{y - 25\text{e-3}}{1\text{e-3}} \right)^3 \right], & 25\, \text{mm} \leq y \leq 27\, \text{mm} +\end{cases} +\end{equation} + +This pressure profile ensures a smooth transition toward zero tritium concentration near the top of the system, reflecting sweep-out conditions. + +Neumann boundary conditions are applied at the bottom of the Ni membrane and the FLiBe region, and at the top of the Ni layer to enforce zero normal flux: + +\begin{equation} +\frac{\partial C}{\partial n} = 0. +\end{equation} + +A the rightmost boundaries of both the Ni and FLiBe regions, Dirichlet conditions set the tritium concentration to zero: + +\begin{equation} +C_{\text{FLiBe}} = 0, +\end{equation} + +\begin{equation} +C_{\text{Ni}} = 0, +\end{equation} + +indicating that tritium is assumed to be continuously and perfectly removed by a sweep gas. + +At the interface between the Ni membrane and the top Ni side layer, continuity conditions are applied to ensure smooth transport of tritium across the materials. Both the concentration and the flux are required to match: + +\begin{equation} +C_{\text{Ni, membrane}} = C_{\text{Ni, layer}}, +\end{equation} + +\begin{equation} +\frac{\partial C_{\text{Ni, membrane}}}{\partial n} = \frac{\partial C_{\text{Ni, layer}}}{\partial n}. +\end{equation} + +Finally, at the interface between the Ni membrane and FLiBe, the concentration in FLiBe is related to the concentration in the nickel membrane via the interface sorption law: + +\begin{equation} +C_{\text{FLiBe}} = \frac{K_{s,\,\text{FLiBe}}}{K_{s,\,\text{Ni}}^2} C_{\text{Ni}}^2, +\end{equation} + +where $K_{s,\,\text{FLiBe}}$ is the solubility of tritium in FLiBe. + +## Model Parameters + +[val-2g_set_up_values] summarizes the physical parameters used in the simulation, including material properties, boundary conditions, and geometric dimensions derived from experimental data: + +!table id=val-2g_set_up_values caption=Physical parameters and geometry used in the simulation. +| Parameter | Description | Value | Units | Reference | +|---------- |------------ |------ |------- |---------- | +| $D_{\text{FLiBe}}$ | FLiBe diffusion | $9.3 \times 10^{-7} \cdot \exp(-42 \times 10^3 / RT)$ | m²/s | [!cite](calderoni2008measurement) | +| $K_{s,\,\text{FLiBe}}$ | FLiBe solubility | $7.9 \times 10^{-2} \cdot \exp(-35 \times 10^3 / RT)$ | mol/m³/Pa | [!cite](calderoni2008measurement) | +| $D_{\text{Ni}}$ | Ni diffusion | $7 \times 10^{-7} \cdot \exp(-39.5 \times 10^3 / RT)$ | m²/s | [!cite](hattab2024openfoam) / [!cite](causey2012tritium) | +| $K_{s,\,\text{Ni}}$ | Ni solubility | $564 \times 10^{-3} \cdot \exp(-15.8 \times 10^3 / RT)$ | mol/m³/Pa$^{0.5}$ | [!cite](hattab2024openfoam) / [!cite](causey2012tritium) | +| $P_0$ | Initial pressure | $170$, $316$, $538$, $1210$ | Pa | [!cite](calderoni2008measurement) | +| $C_0$ | Initial concentrations in Ni and FLiBe | $10^{-12}$ | mol/m³ | - | +| $L$ | Lengths of Ni and FLiBe regions | Ni membrane: $2$, FLiBe: $8.1$ | mm | [!cite](calderoni2008measurement) | +| $W$ | Widths of the domain | Ni membrane $25$, Ni layer: $2$ | mm | [!cite](calderoni2008measurement) | + +## Results and discussion + +We first analyze the TMAP8 simulation results using the 1D case without any additional layer, in order to compare them with experimental data. As shown in [val-2g_tritium_flux_1D], the simulation captures the correct order of magnitude for the tritium flux as a function of the T$_2$ partial pressure. At low pressures, the TMAP8 results show good agreement with the experimental measurements. However, at higher pressures, the model deviates significantly, and the fit deteriorates. Specifically, we observe a linear relationship between the tritium flux and pressure, whereas the expected behavior should follow a square-root dependence. + +!media comparison_val-2g.py + image_name=val-2g_tritium_flux_1D.png + style=width:50%;margin-bottom:2%;margin-left:auto;margin-right:auto + id=val-2g_tritium_flux_1D + caption= Steady state permeation flux for the 1D case, through Ni and FLiBe at different temperatures and input pressures. The TMAP8 results are compared against experimental results from [!cite](calderoni2008measurement). + +We now aim to test the hypothesis that tritium transport through the Ni membrane is the limiting factor. To do so, we removed the FLiBe region and focused solely on simulating tritium diffusion within the nickel membrane. As shown in [val-2g_tritium_flux_2D_no_FLiBe], the resulting tritium flux is significantly overestimated compared to the experimental data, as expected from the removal of additional transport resistance. This result confirms that the presence of FLiBe plays a critical role and must be included in subsequent simulations to more accurately capture the physical behavior of the system at the interface. + +!media comparison_val-2g.py + image_name=val-2g_tritium_flux_2D_no_FLiBe.png + style=width:50%;margin-bottom:2%;margin-left:auto;margin-right:auto + id=val-2g_tritium_flux_2D_no_FLiBe + caption= Steady state permeation flux for the 2D case without FLiBe, through Ni and FLiBe at different temperatures and input pressures. The TMAP8 results are compared against experimental results from [!cite](calderoni2008measurement). + +To better match the experimental data, we next tested the hypothesis that permeation losses through the side walls could potentially lead to the expected square-root dependence at high pressure. This motivated the implementation of the 2D case with an additional Ni layer. + +As shown in [mass_conservation_2D_with_layer], we first verified that mass conservation is respected in the simulation, with a root mean square percentage error (RMSPE) of 4.57 % for the case at 1210 Pa and 823 K. Then, in [val-2g_tritium_flux_2D], we observe that while the tritium flux is reduced compared to the 1D case without a side layer, the flux decreases uniformly across all pressures. Importantly, the relationship between flux and pressure remains linear, rather than exhibiting the expected square root behavior. + +!media comparison_val-2g.py + image_name=val-2g_mass_conservation_2D_with_layer.png + style=width:50%;margin-bottom:2%;margin-left:auto;margin-right:auto + id=mass_conservation_2D_with_layer + caption= Mass conservation verification for the 1210 Pa, 823K case: time evolution of $dn/dt$ compared to the net flux. + +!media comparison_val-2g.py + image_name=val-2g_tritium_flux_2D.png + style=width:50%;margin-bottom:2%;margin-left:auto;margin-right:auto + id=val-2g_tritium_flux_2D + caption= Steady state permeation flux for the 2D case, through Ni and FLiBe at different temperatures and input pressures. The TMAP8 results are compared against experimental results from [!cite](calderoni2008measurement). For comparison, the 1D results are shown with shading. + +This analysis suggests that the additional Ni layer alone does not explain the deviation from experimental data. Other possible mechanisms that may need to be considered to improve agreement with the experimental data include: + +- Temperature heterogeneity within the system +- Convective transport within the FLiBe +- Effects related to corrosion, impurities, or surface chemistry +- The presence of hydrogen affecting tritium transport +- Limitations or assumptions in the experimental setup (e.g., the current model tracks the flux exiting the FLiBe) + +## Input files + +!style halign=left +All the input files for this case can be found at: + +- [/val-2g_1D.i]: This file contains the 1D simulation of the nickel membrane and FLiBe +- [/val-2g_2D_no_FLiBe.i]: This file contains the 2D simulation of the nickel membrane without FLiBe +- [/val-2g.i]: This file contains the 2D simulation of the nickel membrane and FLiBe, including an additional Ni layer + +[/val-2g/tests] uses `cli_args` to modify [/val-2g.i] and impose the desired temperatures and initial pressures to reproduce the experimental conditions. + +To limit the computational costs of the test case, the test runs a version of the file with a smaller simulation time. More information about the changes can be found in the test specification file for this case, namely [/val-2g/tests]. diff --git a/test/tests/val-2g/comparison_val-2g.py b/test/tests/val-2g/comparison_val-2g.py new file mode 100644 index 000000000..d76f3c451 --- /dev/null +++ b/test/tests/val-2g/comparison_val-2g.py @@ -0,0 +1,348 @@ +import numpy as np +import pandas as pd +import os +from matplotlib import gridspec +import matplotlib.pyplot as plt +from matplotlib.ticker import ScalarFormatter + +# Changes working directory to script directory (for consistent MooseDocs usage) +script_folder = os.path.dirname(__file__) +os.chdir(script_folder) + +#=============================================================================== +# Load experimental data + +if "/tmap8/doc/" in script_folder.lower(): # if in documentation folder + data_folder = "../../../../test/tests/val-2g/gold/" +else: # if in test folder + data_folder = "./gold/" +data_by_temperature = {} + +#=============================================================================== +# General parameters + +R = 8.31446261815324 # J/mol/K ideal gas constant from PhysicalConstants.h +temperature = 973 # 823 # K +n_sieverts = 0.5 # Sieverts' law + +#=============================================================================== +# 1D case without any layer: Tritium permeation flux as a function of tritium partial pressure +# for a range of temperatures and initial pressures + +fig = plt.figure(figsize=[6.5, 5.5]) +gs = gridspec.GridSpec(1, 1) +ax = fig.add_subplot(gs[0]) + +for filename in os.listdir(data_folder): + if filename.endswith(".csv") and filename.startswith("val-2g_1D_"): + parts = filename.replace(".csv", "").split("_") + try: + T = int(parts[2][:-1]) # Remove 'K' + P = int(parts[3][:-2]) # Remove 'Pa' + df = pd.read_csv(os.path.join(data_folder, filename)) + average_flux = df["right_flux_membrane"].iloc[-1] + data_by_temperature.setdefault(T, []).append((P, average_flux)) + except Exception as e: + print(f"Skipping {filename}: {e}") + +# Define consistent color and marker maps based on temperature in Celsius +temperatures_C = [550, 600, 650, 700] +temperature_color_map = {T: f"C{i}" for i, T in enumerate(temperatures_C)} +temperature_marker_map = {550: 'o', 600: 's', 650: 'D', 700: '^'} + +# Experimental data +exp_data = pd.DataFrame({ + "pressure": [170, 316, 316, 538, 538, 538, 1210, 1210, 1210, 1210], + "flux": np.array([ + 1.0684039087947879, + 1.0423452768729637, + 2.0325732899022793, + 1.1465798045602602, + 1.745928338762214, + 2.866449511400651, + 3.6351791530944624, + 2.5146579804560254, + 1.7068403908794778, + 1.1596091205211714 + ]) * 1e-7, + "temperature": [700, 650, 700, 600, 650, 700, 700, 650, 600, 550] +}) + +for T_C in reversed(sorted(exp_data["temperature"].unique())): + subset = exp_data[exp_data["temperature"] == T_C] + ax.scatter( + subset["pressure"], + subset["flux"], + marker=temperature_marker_map[T_C], + facecolors='none', + edgecolors=temperature_color_map[T_C], + label=f"{T_C} °C exp" + ) + +# Plot TMAP8 data +for T in reversed(sorted(data_by_temperature.keys())): + T_C = T - 273 + values = sorted(data_by_temperature[T]) + pressures, fluxes = zip(*values) + ax.scatter( + pressures, + fluxes, + marker=temperature_marker_map.get(T_C, 'x'), + color=temperature_color_map.get(T_C, 'k'), + label=f"{T_C} °C (TMAP8)" + ) + +# Styling +ax.set_xlabel(r"$T_2$ partial pressure (Pa)") +ax.set_ylabel(r"Tritium molar flux (mol/m$^2$/s)") +ax.legend(loc="best") +ax.grid(which='major', color='0.65', linestyle='--', alpha=0.3) +fig.savefig('val-2g_tritium_flux_1D.png', bbox_inches='tight', dpi=300) + +#=============================================================================== +# 2D case with a Ni layer: Tritium permeation flux as a function of tritium partial pressure +# for a range of temperatures and initial pressures + +data_density = {} # from _out.csv +data_total = {} # from _1D_*.csv + +fig = plt.figure(figsize=[6.5, 5.5]) +gs = gridspec.GridSpec(1, 1) +ax = fig.add_subplot(gs[0]) + +# Loop through files +for filename in os.listdir(data_folder): + if filename.endswith(".csv") and filename.startswith("val-2g_"): + try: + parts = filename.replace(".csv", "").split("_") + + # Extract temperature and pressure from parts + T = next(int(p[:-1]) for p in parts if p.endswith("K")) + P = next(int(p[:-2]) for p in parts if p.endswith("Pa")) + + df = pd.read_csv(os.path.join(data_folder, filename)) + + if "_1D_" in filename: + flux = df["right_flux_membrane"].iloc[-1] + data_total.setdefault(T, []).append((P, flux)) + + elif filename.endswith("_out.csv"): + flux = df["right_flux_density_membrane"].iloc[-1] + data_density.setdefault(T, []).append((P, flux)) + + except Exception as e: + print(f"Skipping {filename}: {e}") + +# Color and marker maps +temperatures_C = [550, 600, 650, 700] +temperature_color_map = {T: f"C{i}" for i, T in enumerate(temperatures_C)} +temperature_marker_map = {550: 'o', 600: 's', 650: 'D', 700: '^'} + +# Experimental data +exp_data = pd.DataFrame({ + "pressure": [170, 316, 316, 538, 538, 538, 1210, 1210, 1210, 1210], + "flux": np.array([ + 1.0684039087947879, + 1.0423452768729637, + 2.0325732899022793, + 1.1465798045602602, + 1.745928338762214, + 2.866449511400651, + 3.6351791530944624, + 2.5146579804560254, + 1.7068403908794778, + 1.1596091205211714 + ]) * 1e-7, + "temperature": [700, 650, 700, 600, 650, 700, 700, 650, 600, 550] +}) + +# Plot experimental +for T_C in reversed(sorted(exp_data["temperature"].unique())): + subset = exp_data[exp_data["temperature"] == T_C] + ax.scatter( + subset["pressure"], + subset["flux"], + marker=temperature_marker_map[T_C], + facecolors='none', + edgecolors=temperature_color_map[T_C], + label=f"{T_C} °C exp" + ) + +# Plot _1D_ data (total flux) +for T in sorted(data_total.keys(), reverse=True): + T_C = T - 273 + values = sorted(data_total[T]) + pressures, fluxes = zip(*values) + ax.scatter( + pressures, + fluxes, + marker=temperature_marker_map.get(T_C, 'x'), + color=temperature_color_map.get(T_C, 'k'), + alpha=0.5 + ) + +# Plot _out data (flux density) +for T in sorted(data_density.keys(), reverse=True): + T_C = T - 273 + values = sorted(data_density[T]) + pressures, fluxes = zip(*values) + ax.scatter( + pressures, + fluxes, + marker=temperature_marker_map.get(T_C, 'x'), + color=temperature_color_map.get(T_C, 'k'), + label=f"{T_C} °C (TMAP8)" + ) + +# Styling +ax.set_xlabel(r"$T_2$ partial pressure (Pa)") +ax.set_ylabel(r"Tritium molar flux (mol/m$^2$/s)") +ax.legend(loc="best") +ax.grid(which='major', color='0.65', linestyle='--', alpha=0.3) +fig.savefig('val-2g_tritium_flux_2D.png', bbox_inches='tight', dpi=300) + +#=============================================================================== +# 2D case without FLiBe: Tritium permeation flux as a function of tritium partial pressure +# for a range of temperatures and initial pressures + +fig = plt.figure(figsize=[6.5, 5.5]) +gs = gridspec.GridSpec(1, 1) +ax = fig.add_subplot(gs[0]) +data_by_temperature_no_FLiBe = {} +for filename in os.listdir(data_folder): + if filename.endswith(".csv") and "no_FLiBe" in filename and filename.startswith("val-2g_"): + parts = filename.replace(".csv", "").split("_") + try: + # Extract temperature and pressure from parts ending with 'K' and 'Pa' + T = next(int(p[:-1]) for p in parts if p.endswith("K")) + P = next(int(p[:-2]) for p in parts if p.endswith("Pa")) + + df = pd.read_csv(os.path.join(data_folder, filename)) + average_flux = df["flux_density_right"].iloc[-1] + data_by_temperature_no_FLiBe.setdefault(T, []).append((P, average_flux)) + + except Exception as e: + print(f"Skipping {filename}: {e}") + +# Define consistent color and marker maps based on temperature in Celsius +temperatures_C = [550, 600, 650, 700] +temperature_color_map = {T: f"C{i}" for i, T in enumerate(temperatures_C)} +temperature_marker_map = {550: 'o', 600: 's', 650: 'D', 700: '^'} + +# Experimental data +exp_data = pd.DataFrame({ + "pressure": [170, 316, 316, 538, 538, 538, 1210, 1210, 1210, 1210], + "flux": np.array([ + 1.0684039087947879, + 1.0423452768729637, + 2.0325732899022793, + 1.1465798045602602, + 1.745928338762214, + 2.866449511400651, + 3.6351791530944624, + 2.5146579804560254, + 1.7068403908794778, + 1.1596091205211714 + ]) * 1e-7, + "temperature": [700, 650, 700, 600, 650, 700, 700, 650, 600, 550] +}) + +for T_C in reversed(sorted(exp_data["temperature"].unique())): + subset = exp_data[exp_data["temperature"] == T_C] + ax.scatter( + subset["pressure"], + subset["flux"], + marker=temperature_marker_map[T_C], + facecolors='none', + edgecolors=temperature_color_map[T_C], + label=f"{T_C} °C exp" + ) + +# Plot TMAP8 data +for T in reversed(sorted(data_by_temperature_no_FLiBe.keys())): + T_C = T - 273 + values = sorted(data_by_temperature_no_FLiBe[T]) + pressures, fluxes = zip(*values) + ax.scatter( + pressures, + fluxes, + marker=temperature_marker_map.get(T_C, 'x'), + color=temperature_color_map.get(T_C, 'k'), + label=f"{T_C} °C (TMAP8)" + ) + +# Styling +ax.set_xlabel(r"$T_2$ partial pressure (Pa)") +ax.set_ylabel(r"Tritium molar flux (mol/m$^2$/s)") +ax.legend(loc="best") +ax.grid(which='major', color='0.65', linestyle='--', alpha=0.3) +fig.savefig('val-2g_tritium_flux_2D_no_FLiBe.png', bbox_inches='tight', dpi=300) + +#=============================================================================== +# Mass conservation check + +if "/tmap8/doc/" in script_folder.lower(): # if in documentation folder + data_folder = "../../../../test/tests/val-2g/gold/val-2g_823K_1210Pa_out.csv" +else: # if in test folder + data_folder = "./gold/val-2g_823K_1210Pa_out.csv" +data_by_temperature = {} +# Load data +df = pd.read_csv(data_folder) + +# Define start time to skip early points +start_time = 1000 # Adjust this as needed + +# Extract relevant columns +time = df['time'].values +n = df['tritium_amount'].values +phi_in = - df['left_flux'].values +phi_right = df['right_flux'].values +phi_top = df['top_flux'].values +phi_out = phi_right + phi_top + +# Compute dn/dt and time midpoints +dt = np.diff(time) +dn = np.diff(n) +dndt = dn / dt +time_mid = 0.5 * (time[1:] + time[:-1]) + +# Compute phi_in - phi_out and interpolate to time_mid +phi_balance = phi_in - phi_out +phi_balance_mid = 0.5 * (phi_balance[1:] + phi_balance[:-1]) +phi_top_mid = 0.5 * (phi_top[1:] + phi_top[:-1]) +phi_right_mid = 0.5 * (phi_right[1:] + phi_right[:-1]) + +# Filter based on start_time +mask = time_mid >= start_time +time_mid = time_mid[mask] +dndt = dndt[mask] +phi_balance_mid = phi_balance_mid[mask] +phi_top_mid = phi_top_mid[mask] +phi_right_mid = phi_right_mid[mask] + +# Compute RMSE and RMSPE +rmse = np.sqrt(np.mean((dndt - phi_balance_mid) ** 2)) +rmspe = rmse * 100 / np.mean(np.abs(dndt)) + +# Plotting +fig = plt.figure(figsize=[6.5, 5.5]) +gs = gridspec.GridSpec(1, 1) +ax = fig.add_subplot(gs[0]) + +ax.plot(time_mid, dndt, label='dn/dt (mol/s)') +ax.plot(time_mid, phi_balance_mid, '--', label='flux_in - flux_out (mol/s)') +ax.plot(time_mid, phi_top_mid, ':', label='top_flux (mol/s)') +ax.plot(time_mid, phi_right_mid, ':', label='right_flux (mol/s)') + + +ax.set_xlabel('Time (s)') +ax.set_ylabel('Rate (mol/s)') +ax.legend() +ax.grid(which='major', color='0.65', linestyle='--', alpha=0.3) + +# Add RMSPE annotation at right-middle +ax.text(0.95, 0.5, f'RMSPE = {rmspe:.2f} %', transform=ax.transAxes, + fontsize=10, verticalalignment='center', horizontalalignment='right', fontweight='bold') + +plt.tight_layout() +plt.savefig("val-2g_mass_conservation_2D_with_layer.png", dpi=300) diff --git a/test/tests/val-2g/gold/val-2g_1D_823K_1210Pa.csv b/test/tests/val-2g/gold/val-2g_1D_823K_1210Pa.csv new file mode 100644 index 000000000..dabd43813 --- /dev/null +++ b/test/tests/val-2g/gold/val-2g_1D_823K_1210Pa.csv @@ -0,0 +1,8068 @@ 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+1e-05,9.9930243151633e-13,0.020323795339963,0.0025696112747318,-2.9582840798455e-06,-0.00011258082608666,-7.1881713839439e-05,-2.8145206521666e-06,-1.4376342767888e-07,3.4091436525322e-18,1.2553797797497e-16,1.3534710157904e-16,3.1384494493741e-18,2.7069420315809e-19,7.6453468459347e-11,1.0680959149501e-06 diff --git a/test/tests/val-2g/gold/val-2g_out_light.e b/test/tests/val-2g/gold/val-2g_out_light.e new file mode 100644 index 000000000..837c93b83 Binary files /dev/null and b/test/tests/val-2g/gold/val-2g_out_light.e differ diff --git a/test/tests/val-2g/tests b/test/tests/val-2g/tests new file mode 100644 index 000000000..8c65ea1f4 --- /dev/null +++ b/test/tests/val-2g/tests @@ -0,0 +1,112 @@ +[Tests] + design = 'SideSetsBetweenSubdomainsGenerator.md InterfaceSorption.md' + issues = '#193' + [val-2g] + type = CSVDiff + input = val-2g.i + cli_args = "simulation_time=1e-5 + Outputs/file_base=val-2g_out_light" + csvdiff = val-2g_out_light.csv + requirement = 'The system shall be able to model the light test for the transient diffusion through a crucible containing molten salt with a constant concentration boundary condition as the species source, for 823 K and 1210 Pa.' + [] + [val-2g_823K_1210Pa] + type = CSVDiff + heavy = true + input = val-2g.i + csvdiff = val-2g_823K_1210Pa_out.csv + cli_args = 'temperature_exp="${units 823 K}" initial_pressure="${units 1210 Pa}" Outputs/file_base="val-2g_823K_1210Pa_out"' + requirement = 'The system shall be able to model transient diffusion through a crucible containing molten salt with a constant concentration boundary condition as the species source, for 823 K and 1210 Pa.' + max_time = 3600 + min_parallel = 10 + [] + [val-2g_873K_1210Pa] + type = CSVDiff + heavy = true + input = val-2g.i + csvdiff = val-2g_873K_1210Pa_out.csv + cli_args = 'temperature_exp="${units 873 K}" initial_pressure="${units 1210 Pa}" Outputs/file_base="val-2g_873K_1210Pa_out"' + requirement = 'The system shall be able to model transient diffusion through a crucible containing molten salt with a constant concentration boundary condition as the species source, for 873 K and 1210 Pa.' + max_time = 3600 + min_parallel = 10 + [] + [val-2g_923K_1210Pa] + type = CSVDiff + heavy = true + input = val-2g.i + csvdiff = val-2g_923K_1210Pa_out.csv + cli_args = 'temperature_exp="${units 923 K}" initial_pressure="${units 1210 Pa}" Outputs/file_base="val-2g_923K_1210Pa_out"' + requirement = 'The system shall be able to model transient diffusion through a crucible containing molten salt with a constant concentration boundary condition as the species source, for 923 K and 1210 Pa.' + max_time = 3600 + min_parallel = 10 + [] + [val-2g_973K_1210Pa] + type = CSVDiff + heavy = true + input = val-2g.i + csvdiff = val-2g_973K_1210Pa_out.csv + cli_args = 'temperature_exp="${units 973 K}" initial_pressure="${units 1210 Pa}" Outputs/file_base="val-2g_973K_1210Pa_out"' + requirement = 'The system shall be able to model transient diffusion through a crucible containing molten salt with a constant concentration boundary condition as the species source, for 973 K and 1210 Pa.' + max_time = 3600 + min_parallel = 10 + [] + [val-2g_873K_538Pa] + type = CSVDiff + heavy = true + input = val-2g.i + csvdiff = val-2g_873K_538Pa_out.csv + cli_args = 'temperature_exp="${units 873 K}" initial_pressure="${units 538 Pa}" Outputs/file_base="val-2g_873K_538Pa_out"' + requirement = 'The system shall be able to model transient diffusion through a crucible containing molten salt with a constant concentration boundary condition as the species source, for 873 K and 538 Pa.' + max_time = 3600 + min_parallel = 10 + [] + [val-2g_923K_538Pa] + type = CSVDiff + heavy = true + input = val-2g.i + csvdiff = val-2g_923K_538Pa_out.csv + cli_args = 'temperature_exp="${units 923 K}" initial_pressure="${units 538 Pa}" Outputs/file_base="val-2g_923K_538Pa_out"' + requirement = 'The system shall be able to model transient diffusion through a crucible containing molten salt with a constant concentration boundary condition as the species source, for 923 K and 538 Pa.' + max_time = 3600 + min_parallel = 10 + [] + [val-2g_973K_538Pa] + type = CSVDiff + heavy = true + input = val-2g.i + csvdiff = val-2g_973K_538Pa_out.csv + cli_args = 'temperature_exp="${units 973 K}" initial_pressure="${units 538 Pa}" Outputs/file_base="val-2g_973K_538Pa_out"' + requirement = 'The system shall be able to model transient diffusion through a crucible containing molten salt with a constant concentration boundary condition as the species source, for 973 K and 538 Pa.' + max_time = 3600 + min_parallel = 10 + [] + [val-2g_923K_316Pa] + type = CSVDiff + heavy = true + input = val-2g.i + csvdiff = val-2g_923K_316Pa_out.csv + cli_args = 'temperature_exp="${units 923 K}" initial_pressure="${units 316 Pa}" Outputs/file_base="val-2g_923K_316Pa_out"' + requirement = 'The system shall be able to model transient diffusion through a crucible containing molten salt with a constant concentration boundary condition as the species source, for 923 K and 316 Pa.' + max_time = 3600 + min_parallel = 10 + [] + [val-2g_973K_316Pa] + type = CSVDiff + heavy = true + input = val-2g.i + csvdiff = val-2g_973K_316Pa_out.csv + cli_args = 'temperature_exp="${units 973 K}" initial_pressure="${units 316 Pa}" Outputs/file_base="val-2g_973K_316Pa_out"' + requirement = 'The system shall be able to model transient diffusion through a crucible containing molten salt with a constant concentration boundary condition as the species source, for 973 K and 316 Pa.' + max_time = 3600 + min_parallel = 10 + [] + [val-2g_973K_170Pa] + type = CSVDiff + heavy = true + input = val-2g.i + csvdiff = val-2g_973K_170Pa_out.csv + cli_args = 'temperature_exp="${units 973 K}" initial_pressure="${units 170 Pa}" Outputs/file_base="val-2g_973K_170Pa_out"' + requirement = 'The system shall be able to model transient diffusion through a crucible containing molten salt with a constant concentration boundary condition as the species source, for 973 K and 170 Pa.' + max_time = 3600 + min_parallel = 10 + [] +[] diff --git a/test/tests/val-2g/val-2g.i b/test/tests/val-2g/val-2g.i new file mode 100644 index 000000000..d7103a2ec --- /dev/null +++ b/test/tests/val-2g/val-2g.i @@ -0,0 +1,532 @@ +!include val-2g_parameters.params + +# Materials properties +## diffusivity of tritium in FLiBe +D_FLiBe_prefactor = '${units 9.3e-7 m^2/s}' +D_FLiBe_energy = '${units 42e3 J/mol}' +D_FLiBe = '${units ${fparse D_FLiBe_prefactor * exp(- D_FLiBe_energy / (R*temperature_exp))} m^2/s}' +## Henry's law solubility for tritium in FLiBe +K_s_FLiBe_prefactor = '${units 7.9e-2 mol/m^3/Pa}' +K_s_FLiBe_energy = '${units 35e3 J/mol}' +# K_s_FLiBe = '${fparse K_s_FLiBe_prefactor * exp(- K_s_FLiBe_energy / (R*temperature_exp))}' + +# Initial conditions +initial_pressure = '${units 1210 Pa}' # input pressure +initial_concentration_FLiBe = '${units 1e-12 mol/m^3}' + +# Geometry and mesh +length_Ni = '${units 2 mm -> m}' # Ni membrane thickness +num_nodes_Ni = 5 +length_FLiBe = '${units 8.1 mm -> m}' # FLiBe membrane thickness +num_nodes_FLiBe = 20 +width_inner = '${units 25 mm -> m}' +num_nodes_inner = 50 +width_wall = '${units 2 mm -> m}' +num_nodes_wall = 10 +thickness = '${units 1 m}' + +[Mesh] + [cmg] + type = CartesianMeshGenerator + dim = 2 + dx = '0.00032 ${fparse length_Ni-0.0004-0.00032} 0.0004 0.000405 ${fparse length_FLiBe-0.000405-0.000405} 0.000405' + dy = '${fparse width_inner-0.0005} 0.0005 0.0002 ${fparse width_wall-0.0002-0.00018} 0.00018' + ix = '10 ${num_nodes_Ni} 15 15 ${num_nodes_FLiBe} 20' + iy = '${num_nodes_inner} 15 15 ${fparse num_nodes_wall} 10' + subdomain_id = '1 1 1 2 2 2 + 1 1 1 2 2 2 + 3 3 3 3 3 3 + 3 3 3 3 3 3 + 3 3 3 3 3 3' + [] + [interface_Ni_FLiBe] + type = SideSetsBetweenSubdomainsGenerator + input = cmg + primary_block = '1' + paired_block = '2' + new_boundary = 'interface_Ni_FLiBe' + [] + [interface_Ni_membrane_FLiBe_other_direction] + type = SideSetsBetweenSubdomainsGenerator + input = 'interface_Ni_FLiBe' + primary_block = '2' + paired_block = '1' + new_boundary = 'interface_Ni_membrane_FLiBe_other_direction' + [] + [interface_Ni_wall_FLiBe] + type = SideSetsBetweenSubdomainsGenerator + input = 'interface_Ni_membrane_FLiBe_other_direction' + primary_block = '3' + paired_block = '2' + new_boundary = 'interface_Ni_FLiBe' + [] + [interface_Ni_wall_FLiBe_other_direction] + type = SideSetsBetweenSubdomainsGenerator + input = 'interface_Ni_wall_FLiBe' + primary_block = '2' + paired_block = '3' + new_boundary = 'interface_Ni_wall_FLiBe_other_direction' + [] + [restrict_bottom_Ni] + type = ParsedGenerateSideset + combinatorial_geometry = '1' + input = 'interface_Ni_wall_FLiBe_other_direction' + new_sideset_name = 'bottom_Ni' + included_boundaries = 'bottom' + included_subdomains = '1' + [] + [restrict_bottom_FLiBe] + type = ParsedGenerateSideset + combinatorial_geometry = '1' + input = 'restrict_bottom_Ni' + new_sideset_name = 'bottom_FLiBe' + included_boundaries = 'bottom' + included_subdomains = '2' + [] + [restrict_right_FLiBe] + type = ParsedGenerateSideset + combinatorial_geometry = '1' + input = 'restrict_bottom_FLiBe' + new_sideset_name = 'right_FLiBe' + included_boundaries = 'right' + included_subdomains = '2' + [] + [restrict_right_Ni] + type = ParsedGenerateSideset + combinatorial_geometry = '1' + input = 'restrict_right_FLiBe' + new_sideset_name = 'right_Ni' + included_boundaries = 'right' + included_subdomains = '3' + [] + [left_null_pressure] + type = ParsedGenerateSideset + combinatorial_geometry = 'y > 25e-3' + included_boundaries = 'left' + new_sideset_name = 'left_null_pressure' + input = 'restrict_right_Ni' + [] + [left_normal_pressure] + type = ParsedGenerateSideset + combinatorial_geometry = 'y < 25e-3' + included_boundaries = 'left' + new_sideset_name = 'left_normal_pressure' + input = 'left_null_pressure' + [] + [interface_Ni_wall_Ni_membrane] + type = SideSetsBetweenSubdomainsGenerator + input = 'left_normal_pressure' + primary_block = '1' + paired_block = '3' + new_boundary = 'interface_Ni_wall_Ni_membrane' + [] + [interface_Ni_wall_Ni_membrane_FLiBe_other_direction] + type = SideSetsBetweenSubdomainsGenerator + input = 'interface_Ni_wall_Ni_membrane' + primary_block = '3' + paired_block = '1' + new_boundary = 'interface_Ni_wall_Ni_membrane_FLiBe_other_direction' + [] + [restrict_left] + type = ParsedGenerateSideset + combinatorial_geometry = 'y < 10e-3' + input = 'interface_Ni_wall_Ni_membrane_FLiBe_other_direction' + new_sideset_name = 'restrict_left' + included_boundaries = 'left' + included_subdomains = '1' + [] +[] + +[Variables] + [tritium_concentration_Ni_membrane] + initial_condition = ${initial_concentration_Ni} # mol/m^3 + block = 1 + [] + [tritium_concentration_Ni_wall] + initial_condition = ${initial_concentration_Ni} # mol/m^3 + block = 3 + [] + [tritium_concentration_FLiBe] + initial_condition = ${initial_concentration_FLiBe} # mol/m^3 + block = 2 + [] +[] + +[AuxVariables] + [enclosure_pressure] + [] + [enclosure_pressure_null] + [] + [tritium_concentration_Ni_membrane_squared] + block = 1 + [] + [tritium_concentration_Ni_wall_squared] + block = 3 + [] + [bounds_dummy_Ni_membrane] + order = FIRST + family = LAGRANGE + [] + [bounds_dummy_Ni_wall] + order = FIRST + family = LAGRANGE + [] + [bounds_dummy_FLiBe] + order = FIRST + family = LAGRANGE + [] +[] + +[Bounds] + [tritium_concentration_Ni_membrane_lower_bound] + type = ConstantBounds + variable = bounds_dummy_Ni_membrane + bounded_variable = tritium_concentration_Ni_membrane + bound_type = lower + bound_value = '${fparse -1e-30}' + [] + [tritium_concentration_Ni_wall_lower_bound] + type = ConstantBounds + variable = bounds_dummy_Ni_wall + bounded_variable = tritium_concentration_Ni_wall + bound_type = lower + bound_value = '${fparse -1e-30}' + [] + [tritium_concentration_FLiBe_lower_bound] + type = ConstantBounds + variable = bounds_dummy_FLiBe + bounded_variable = tritium_concentration_FLiBe + bound_type = lower + bound_value = '${fparse -1e-30}' + [] +[] + +[Kernels] + # Diffusion in Ni membrane + [diffusion_Ni_membrane] + type = ADMatDiffusion + variable = 'tritium_concentration_Ni_membrane' + diffusivity = ${D_Ni} + block = 1 + [] + [time_diff_Ni_membrane] + type = TimeDerivative + variable = 'tritium_concentration_Ni_membrane' + block = 1 + [] + # Diffusion in Ni wall + [diffusion_Ni_wall] + type = ADMatDiffusion + variable = 'tritium_concentration_Ni_wall' + diffusivity = ${D_Ni} + block = 3 + [] + [time_diff_Ni_wall] + type = TimeDerivative + variable = 'tritium_concentration_Ni_wall' + block = 3 + [] + # Diffusion in FLiBe + [diffusion_FLiBe] + type = ADMatDiffusion + variable = 'tritium_concentration_FLiBe' + diffusivity = ${D_FLiBe} + block = 2 + [] + [time_diff_FLiBe] + type = TimeDerivative + variable = 'tritium_concentration_FLiBe' + block = 2 + [] +[] + +[AuxKernels] + [enclosure_pressure_null] + type = FunctionAux + function = 'pressure_value' + variable = 'enclosure_pressure_null' + execute_on = 'INITIAL TIMESTEP_END' + [] + [enclosure_pressure] + type = FunctionAux + function = 'pressure_value' + variable = 'enclosure_pressure' + execute_on = 'INITIAL TIMESTEP_END' + [] +[] + +[BCs] + [left_concentration] + type = EquilibriumBC + Ko = ${K_s_Ni_prefactor} + activation_energy = ${K_s_Ni_energy} + boundary = 'left_normal_pressure' + enclosure_var = 'enclosure_pressure' + temperature = ${temperature_exp} + variable = 'tritium_concentration_Ni_membrane' + p = ${n_Sieverts} + [] + [left_concentration_null] + type = EquilibriumBC + Ko = ${K_s_Ni_prefactor} + activation_energy = ${K_s_Ni_energy} + boundary = 'left_null_pressure' + enclosure_var = 'enclosure_pressure_null' + temperature = ${temperature_exp} + variable = 'tritium_concentration_Ni_wall' + p = ${n_Sieverts} + [] + [right_concentration_FLiBe] + type = ADDirichletBC + boundary = 'right_FLiBe' + variable = 'tritium_concentration_FLiBe' + value = 0.0 + [] + [right_concentration_Ni] + type = ADDirichletBC + boundary = 'right_Ni' + variable = 'tritium_concentration_Ni_wall' + value = 0.0 + [] + [bottom_flux_Ni] + type = ADNeumannBC + boundary = 'bottom_Ni' + variable = 'tritium_concentration_Ni_membrane' + value = 0.0 + [] + [bottom_flux_FLiBe] + type = ADNeumannBC + boundary = 'bottom_FLiBe' + variable = 'tritium_concentration_FLiBe' + value = 0.0 + [] + [top_concentration] + type = ADDirichletBC + boundary = 'top' + variable = 'tritium_concentration_Ni_wall' + value = 0.0 + [] + [equates_concentration_Ni_wall_Ni_membrane] + type = MatchedValueBC + variable = 'tritium_concentration_Ni_membrane' + boundary = 'interface_Ni_wall_Ni_membrane' + v = 'tritium_concentration_Ni_wall' + [] +[] + +[InterfaceKernels] + [interface_sorption_Ni_membrane_FLiBe] + type = InterfaceSorption + K0 = '${fparse K_s_FLiBe_prefactor / (K_s_Ni_prefactor^2) / (R*temperature_exp)^2}' + Ea = '${fparse K_s_FLiBe_energy - (2*K_s_Ni_energy)}' + n_sorption = 2 + diffusivity = ${D_Ni} + unit_scale = ${unit_scale} + unit_scale_neighbor = ${unit_scale_neighbor} + temperature = ${temperature_exp} + variable = 'tritium_concentration_FLiBe' + neighbor_var = 'tritium_concentration_Ni_membrane' + sorption_penalty = 1e1 + boundary = 'interface_Ni_membrane_FLiBe_other_direction' + [] + [interface_sorption_Ni_wall_FLiBe] + type = InterfaceSorption + K0 = '${fparse K_s_FLiBe_prefactor / (K_s_Ni_prefactor^2) / (R*temperature_exp)^2}' + Ea = '${fparse K_s_FLiBe_energy - (2*K_s_Ni_energy)}' + n_sorption = 2 + diffusivity = ${D_Ni} + unit_scale = ${unit_scale} + unit_scale_neighbor = ${unit_scale_neighbor} + temperature = ${temperature_exp} + variable = 'tritium_concentration_FLiBe' + neighbor_var = 'tritium_concentration_Ni_wall' + sorption_penalty = 1e1 + boundary = 'interface_Ni_wall_FLiBe_other_direction' + [] + [interface_Ni_wall_Ni_membrane] + type = InterfaceDiffusion + variable = 'tritium_concentration_Ni_wall' + neighbor_var = 'tritium_concentration_Ni_membrane' + boundary = 'interface_Ni_wall_Ni_membrane_FLiBe_other_direction' + D = '${D_Ni}' + D_neighbor = '${D_Ni}' + [] +[] + +[Functions] + [pressure_value] + type = ParsedFunction + expression = 'if(y<25e-3, ${initial_pressure}, ${initial_pressure}*(1-3*((y-25e-3)/2e-3)^2+2*((y-25e-3)/2e-3)^3))' + [] +[] + +[Postprocessors] + [left_flux_density_membrane] # mol/m^2/s + type = SideDiffusiveFluxAverage + boundary = 'left_normal_pressure' + variable = 'tritium_concentration_Ni_membrane' + diffusivity = ${D_Ni} + # outputs = none + [] + [left_flux_density_wall] # mol/m^2/s + type = SideDiffusiveFluxAverage + boundary = 'left_null_pressure' + variable = 'tritium_concentration_Ni_wall' + diffusivity = ${D_Ni} + # outputs = none + [] + [right_flux_density_membrane] # mol/m^2/s + type = SideDiffusiveFluxAverage + boundary = 'right_FLiBe' + variable = 'tritium_concentration_FLiBe' + diffusivity = ${D_FLiBe} + # outputs = none + [] + [right_flux_density_wall] # mol/m^2/s + type = SideDiffusiveFluxAverage + boundary = 'right_Ni' + variable = 'tritium_concentration_Ni_wall' + diffusivity = ${D_Ni} + # outputs = none + [] + + # Mass conservation + + ## left boundary + [left_flux_membrane] # mol/s + type = ParsedPostprocessor + expression = 'left_flux_density_membrane*${thickness}*${width_inner}' + pp_names = 'left_flux_density_membrane' + # outputs = none + [] + [left_flux_wall] # mol/s + type = ParsedPostprocessor + expression = 'left_flux_density_wall*${thickness}*${width_wall}' + pp_names = 'left_flux_density_wall' + # outputs = none + [] + [left_flux] # mol/s + type = ParsedPostprocessor + expression = 'left_flux_membrane+left_flux_wall' + pp_names = 'left_flux_membrane left_flux_wall' + # outputs = none + [] + # right boundary + [right_flux_membrane] # mol/s + type = ParsedPostprocessor + expression = 'right_flux_density_membrane*${thickness}*${width_inner}' + pp_names = 'right_flux_density_membrane' + # outputs = none + [] + [right_flux_wall] # mol/s + type = ParsedPostprocessor + expression = 'right_flux_density_wall*${thickness}*${width_wall}' + pp_names = 'right_flux_density_wall' + # outputs = none + [] + [right_flux] # mol/s + type = ParsedPostprocessor + expression = 'right_flux_membrane+right_flux_wall' + pp_names = 'right_flux_membrane right_flux_wall' + # outputs = none + [] + + ## in cell + # [] + [Ni_membrane_concentration] # mol/m^3 + type = ElementAverageValue + variable = 'tritium_concentration_Ni_membrane' + block = 1 + # outputs = none + [] + [Ni_membrane_amount] # mol + type = ParsedPostprocessor + expression = 'Ni_membrane_concentration*${thickness}*${length_Ni}*${width_inner}' + pp_names = 'Ni_membrane_concentration' + outputs = none + [] + [FLiBe_concentration] # mol/m^3 + type = ElementAverageValue + variable = 'tritium_concentration_FLiBe' + block = 2 + #outputs = none + [] + [FLiBe_amount] # mol + type = ParsedPostprocessor + expression = 'FLiBe_concentration*${thickness}*${length_FLiBe}*${width_inner}' + pp_names = 'FLiBe_concentration' + outputs = none + [] + [Ni_wall_concentration] # mol/m^3 + type = ElementAverageValue + variable = 'tritium_concentration_Ni_wall' + block = 3 + #outputs = none + [] + [Ni_wall_amount] # mol + type = ParsedPostprocessor + expression = 'Ni_wall_concentration*${thickness}*${fparse length_Ni+length_FLiBe}*${width_wall}' + pp_names = 'Ni_wall_concentration' + outputs = none + [] + [tritium_amount] # mol + type = ParsedPostprocessor + expression = 'Ni_membrane_amount+FLiBe_amount+Ni_wall_amount' + pp_names = 'Ni_membrane_amount FLiBe_amount Ni_wall_amount' + # outputs = none + [] + + # top boundary + [top_flux_density] # mol/m^2/s + type = SideDiffusiveFluxAverage + boundary = 'top' + variable = 'tritium_concentration_Ni_wall' + diffusivity = ${D_Ni} + outputs = none + [] + [top_flux] # mol/s + type = ParsedPostprocessor + expression = 'top_flux_density*${thickness}*${fparse length_Ni+length_FLiBe}' + pp_names = 'top_flux_density' + # outputs = none + [] +[] + +[Preconditioning] + [SMP] + type = SMP + full = true + [] +[] + +[Executioner] + type = Transient + end_time = ${simulation_time} + nl_max_its = 9 + l_max_its = 30 + scheme = 'bdf2' + solve_type = 'Newton' + petsc_options_iname = '-pc_type -sub_pc_type -snes_type' + petsc_options_value = 'asm lu vinewtonrsls' # This petsc option helps prevent negative concentrations with bounds' + nl_abs_tol = 1e-11 + [TimeStepper] + type = IterationAdaptiveDT + dt = 1e-6 + optimal_iterations = 7 + iteration_window = 1 + growth_factor = 1.1 + cutback_factor = 0.9 + cutback_factor_at_failure = 0.9 + [] +[] + +[Outputs] + file_base = 'val-2g_823K_1210Pa_out' + [csv] + type = CSV + [] + [exodus] + type = Exodus + time_step_interval = 20 + [] +[] diff --git a/test/tests/val-2g/val-2g_1D.i b/test/tests/val-2g/val-2g_1D.i new file mode 100644 index 000000000..b829cd172 --- /dev/null +++ b/test/tests/val-2g/val-2g_1D.i @@ -0,0 +1,248 @@ +!include val-2g_parameters.params + +# Materials properties +## diffusivity of tritium in FLiBe +D_FLiBe_prefactor = '${units 9.3e-7 m^2/s}' +D_FLiBe_energy = '${units 42e3 J/mol}' +D_FLiBe = '${units ${fparse D_FLiBe_prefactor * exp(- D_FLiBe_energy / (R*temperature_exp))} m^2/s}' +## Henry's law solubility for tritium in FLiBe +K_s_FLiBe_prefactor = '${units 7.9e-2 mol/m^3/Pa}' +K_s_FLiBe_energy = '${units 35e3 J/mol}' + +# Initial conditions +initial_pressure = '${units 1210 Pa}' # input pressure +initial_concentration_FLiBe = '${units 1e-12 mol/m^3}' + +# Geometry and mesh +length_Ni = '${units 2 mm -> m}' # Ni membrane thickness +num_nodes_Ni = 10 +length_FLiBe = '${units 8.1 mm -> m}' # FLiBe membrane thickness +num_nodes_FLiBe = 100 +thickness = '${units 1 m}' +width_inner = '${units 25 mm -> m}' + +[Mesh] + [cmg] + type = CartesianMeshGenerator + dim = 1 + dx = '${length_Ni} ${length_FLiBe}' + ix = '${num_nodes_Ni} ${num_nodes_FLiBe}' + subdomain_id = '1 2' + [] + [interface_Ni_FLiBe] + type = SideSetsBetweenSubdomainsGenerator + input = cmg + primary_block = '1' + paired_block = '2' + new_boundary = 'interface_Ni_FLiBe' + [] + [interface_Ni_FLiBe_other_direction] + type = SideSetsBetweenSubdomainsGenerator + input = interface_Ni_FLiBe + primary_block = '2' + paired_block = '1' + new_boundary = 'interface_Ni_FLiBe_other_direction' + [] +[] + +[Variables] + [tritium_concentration_Ni_membrane] + initial_condition = ${initial_concentration_Ni} # mol/m^3 + block = 1 + [] + [tritium_concentration_FLiBe] + initial_condition = ${initial_concentration_FLiBe} # mol/m^3 + block = 2 + [] +[] + +[AuxVariables] + [enclosure_pressure] + family = SCALAR + initial_condition = ${initial_pressure} + [] +[] + +[Kernels] + # Diffusion in Ni membrane + [diffusion_Ni] + type = ADMatDiffusion + variable = 'tritium_concentration_Ni_membrane' + diffusivity = ${D_Ni} + block = 1 + [] + [time_diff_Ni] + type = TimeDerivative + variable = 'tritium_concentration_Ni_membrane' + block = 1 + [] + # Diffusion in FLiBe + [diffusion_FLiBe] + type = ADMatDiffusion + variable = 'tritium_concentration_FLiBe' + diffusivity = ${D_FLiBe} + block = 2 + [] + [time_diff_FLiBe] + type = TimeDerivative + variable = 'tritium_concentration_FLiBe' + block = 2 + [] +[] + +[BCs] + [left_concentration] + type = EquilibriumBC + Ko = ${K_s_Ni_prefactor} + activation_energy = ${K_s_Ni_energy} + boundary = 'left' + enclosure_var = 'enclosure_pressure' + temperature = ${temperature_exp} + variable = 'tritium_concentration_Ni_membrane' + p = ${n_Sieverts} + [] + [right_concentration] + type = ADDirichletBC + boundary = 'right' + variable = 'tritium_concentration_FLiBe' + value = 0.0 + [] +[] + +[InterfaceKernels] + [interface_sorption_Ni_FLiBe] + type = InterfaceSorption + K0 = '${fparse K_s_FLiBe_prefactor / (K_s_Ni_prefactor^2) / (R*temperature_exp)^2}' + Ea = '${fparse K_s_FLiBe_energy - (2*K_s_Ni_energy)}' + n_sorption = 2 + diffusivity = ${D_Ni} + unit_scale = ${unit_scale} + unit_scale_neighbor = ${unit_scale_neighbor} + temperature = ${temperature_exp} + variable = 'tritium_concentration_FLiBe' + neighbor_var = 'tritium_concentration_Ni_membrane' + sorption_penalty = 1e1 + boundary = 'interface_Ni_FLiBe_other_direction' + [] +[] + +[Functions] + [max_dt_size_function] + type = ParsedFunction + expression = 'if(t<${fparse 8500}, ${fparse 1e2}, + if(t<${fparse 37000}, ${fparse 1e1}, + if(t<${fparse 38500}, ${fparse 1e0}, ${fparse 1e1})))' + [] +[] + +[Postprocessors] + # left and right flux + [left_flux_membrane] # mol/m^2/s + type = SideDiffusiveFluxAverage + boundary = 'left' + variable = 'tritium_concentration_Ni_membrane' + diffusivity = ${D_Ni} + # outputs = none + [] + [right_flux_membrane] # mol/m^2/s + type = SideDiffusiveFluxAverage + boundary = 'right' + variable = 'tritium_concentration_FLiBe' + diffusivity = ${D_FLiBe} + # outputs = none + [] + + # Mass conservation + ## left boundary + [left_inventory] # mol/s + type = ParsedPostprocessor + expression = 'left_flux_membrane*${thickness}*${width_inner}' + pp_names = 'left_flux_membrane' + # outputs = none + [] + ## right boundary + [right_inventory] # mol/s + type = ParsedPostprocessor + expression = 'right_flux_membrane*${thickness}*${width_inner}' + pp_names = 'right_flux_membrane' + # outputs = none + [] + ## in cell + # [] + [Ni_membrane_inventory1] # mol/m^3 + type = ElementAverageValue + variable = 'tritium_concentration_Ni_membrane' + block = 1 + outputs = none + [] + [Ni_membrane_inventory] # mol + type = ParsedPostprocessor + expression = 'Ni_membrane_inventory1*${thickness}*${length_Ni}*${width_inner}' + pp_names = 'Ni_membrane_inventory1' + outputs = none + [] + [FLiBe_inventory1] # mol/m^3 + type = ElementAverageValue + variable = 'tritium_concentration_FLiBe' + block = 2 + outputs = none + [] + [FLiBe_inventory] # mol + type = ParsedPostprocessor + expression = 'FLiBe_inventory1*${thickness}*${length_FLiBe}*${width_inner}' + pp_names = 'FLiBe_inventory1' + outputs = none + [] + [tritium_inventory] # mol + type = ParsedPostprocessor + expression = 'Ni_membrane_inventory+FLiBe_inventory' + pp_names = 'Ni_membrane_inventory FLiBe_inventory' + # outputs = none + [] + [max_time_step_size] + type = FunctionValuePostprocessor + function = 'max_dt_size_function' + execute_on = 'initial nonlinear linear timestep_end' + outputs = none + [] +[] + +[Preconditioning] + [SMP] + type = SMP + full = true + [] +[] + +[Executioner] + type = Transient + end_time = ${simulation_time} + nl_max_its = 9 + l_max_its = 30 + scheme = 'bdf2' + solve_type = 'PJFNK' + petsc_options_iname = '-pc_type' + petsc_options_value = 'lu' + nl_abs_tol = 1e-11 + [TimeStepper] + type = IterationAdaptiveDT + dt = 1e-6 + optimal_iterations = 7 + iteration_window = 1 + growth_factor = 1.1 + cutback_factor = 0.9 + cutback_factor_at_failure = 0.9 + timestep_limiting_postprocessor = max_time_step_size + [] +[] + +[Outputs] + file_base = 'val-2g_1D_823K_1210Pa' + [csv] + type = CSV + [] + [exodus] + type = Exodus + time_step_interval = 200 + [] +[] diff --git a/test/tests/val-2g/val-2g_2D_no_FLiBe.i b/test/tests/val-2g/val-2g_2D_no_FLiBe.i new file mode 100644 index 000000000..38b1e2a5a --- /dev/null +++ b/test/tests/val-2g/val-2g_2D_no_FLiBe.i @@ -0,0 +1,221 @@ +!include val-2g_parameters.params + +# Materials properties +## diffusivity of tritium in air +D_air = '${units 1e-5 m^2/s}' + +# Initial conditions +initial_pressure = '${units 1210 Pa}' # input pressure +initial_concentration_air = '${units 1e-12 mol/m^3}' + +# Geometry and mesh +length_Ni = '${units 2 mm -> m}' # Ni membrane thickness +num_nodes_Ni = 10 +length_air = '${units 8.1 mm -> m}' # air membrane thickness +num_nodes_air = 50 + +[Mesh] + [cmg] + type = CartesianMeshGenerator + dim = 1 + dx = '${length_Ni} ${length_air}' + ix = '${num_nodes_Ni} ${num_nodes_air}' + subdomain_id = '1 2' + [] + [interface_Ni_air] + type = SideSetsBetweenSubdomainsGenerator + input = cmg + primary_block = '1' + paired_block = '2' + new_boundary = 'interface_Ni_air' + [] + [interface_Ni_air_other_direction] + type = SideSetsBetweenSubdomainsGenerator + input = interface_Ni_air + primary_block = '2' + paired_block = '1' + new_boundary = 'interface_Ni_air_other_direction' + [] +[] + +[Variables] + [tritium_concentration_Ni] + initial_condition = ${initial_concentration_Ni} # mol/m^3 + block = 1 + [] + [tritium_concentration_air] + initial_condition = ${initial_concentration_air} # mol/m^3 + block = 2 + [] +[] + +[AuxVariables] + [enclosure_pressure] + family = SCALAR + initial_condition = ${initial_pressure} + [] + [bounds_dummy_Ni] + order = FIRST + family = LAGRANGE + [] + [bounds_dummy_air] + order = FIRST + family = LAGRANGE + [] +[] + +[Bounds] + [tritium_concentration_Ni_membrane_lower_bound] + type = ConstantBounds + variable = bounds_dummy_Ni + bounded_variable = tritium_concentration_Ni + bound_type = lower + bound_value = '${fparse -1e-30}' + [] + [tritium_concentration_Ni_wall_lower_bound] + type = ConstantBounds + variable = bounds_dummy_air + bounded_variable = tritium_concentration_air + bound_type = lower + bound_value = '${fparse -1e-30}' + [] +[] + +[Kernels] + # Diffusion in Ni membrane + [diffusion_Ni] + type = ADMatDiffusion + variable = 'tritium_concentration_Ni' + diffusivity = ${D_Ni} + block = 1 + [] + [time_diff_Ni] + type = TimeDerivative + variable = 'tritium_concentration_Ni' + block = 1 + [] + # Diffusion in air + [diffusion_air] + type = ADMatDiffusion + variable = 'tritium_concentration_air' + diffusivity = ${D_air} + block = 2 + [] + [time_diff_air] + type = TimeDerivative + variable = 'tritium_concentration_air' + block = 2 + [] +[] + +[BCs] + [left_concentration] + type = EquilibriumBC + Ko = ${K_s_Ni_prefactor} + activation_energy = ${K_s_Ni_energy} + boundary = 'left' + enclosure_var = 'enclosure_pressure' + temperature = ${temperature_exp} + variable = 'tritium_concentration_Ni' + p = ${n_Sieverts} + [] + [right_concentration] + type = ADDirichletBC + boundary = 'right' + variable = 'tritium_concentration_air' + value = 0.0 + [] +[] + +[InterfaceKernels] + [interface_sorption_Ni_air] + type = InterfaceSorption + K0 = ${K_s_Ni_prefactor} + Ea = ${K_s_Ni_energy} + n_sorption = ${n_Sieverts} + diffusivity = ${D_Ni} + unit_scale = ${unit_scale} + unit_scale_neighbor = ${unit_scale_neighbor} + temperature = ${temperature_exp} + variable = 'tritium_concentration_Ni' + neighbor_var = 'tritium_concentration_air' + sorption_penalty = 1e1 + boundary = 'interface_Ni_air' + [] +[] + +[Functions] + [max_dt_size_function] + type = ParsedFunction + expression = 'if(t<${fparse 8500}, ${fparse 1e2}, + if(t<${fparse 37000}, ${fparse 1e1}, + if(t<${fparse 38500}, ${fparse 1e0}, ${fparse 1e1})))' + [] +[] + +[Postprocessors] + [average_flux_left] # mol/m^2/s + type = SideDiffusiveFluxAverage + variable = 'tritium_concentration_Ni' + boundary = 'left' + diffusivity = ${D_Ni} + [] + [average_flux_Ni_air_interface] # mol/m^2/s + type = SideDiffusiveFluxAverage + variable = 'tritium_concentration_Ni' + boundary = 'interface_Ni_air' + diffusivity = ${D_Ni} + [] + [average_flux_right] # mol/m^2/s + type = SideDiffusiveFluxAverage + variable = 'tritium_concentration_air' + boundary = 'right' + diffusivity = ${D_air} + [] + [max_time_step_size] + type = FunctionValuePostprocessor + function = 'max_dt_size_function' + execute_on = 'initial nonlinear linear timestep_end' + outputs = none + [] +[] + +[Preconditioning] + [SMP] + type = SMP + full = true + [] +[] + +[Executioner] + type = Transient + end_time = ${simulation_time} + nl_max_its = 9 + l_max_its = 30 + scheme = 'bdf2' + solve_type = 'Newton' + petsc_options_iname = '-pc_type -sub_pc_type -snes_type' + petsc_options_value = 'asm lu vinewtonrsls' # This petsc option helps prevent negative concentrations with bounds' + nl_abs_tol = 1e-11 + [TimeStepper] + type = IterationAdaptiveDT + dt = 1e-6 + optimal_iterations = 7 + iteration_window = 1 + growth_factor = 1.1 + cutback_factor = 0.9 + cutback_factor_at_failure = 0.9 + timestep_limiting_postprocessor = max_time_step_size + [] +[] + +[Outputs] + file_base = 'val-2g_823K_1210Pa_out' + [csv] + type = CSV + [] + [exodus] + type = Exodus + time_step_interval = 200 + [] +[] diff --git a/test/tests/val-2g/val-2g_2D_no_layer.i b/test/tests/val-2g/val-2g_2D_no_layer.i new file mode 100644 index 000000000..8a3d01b34 --- /dev/null +++ b/test/tests/val-2g/val-2g_2D_no_layer.i @@ -0,0 +1,368 @@ +!include val-2g_parameters.params + +# Materials properties +## diffusivity of tritium in FLiBe +D_FLiBe_prefactor = '${units 9.3e-7 m^2/s}' +D_FLiBe_energy = '${units 42e3 J/mol}' +D_FLiBe = '${units ${fparse D_FLiBe_prefactor * exp(- D_FLiBe_energy / (R*temperature_exp))} m^2/s}' +## Henry's law solubility for tritium in FLiBe +K_s_FLiBe_prefactor = '${units 7.9e-2 mol/m^3/Pa}' +K_s_FLiBe_energy = '${units 35e3 J/mol}' +# K_s_FLiBe = '${fparse K_s_FLiBe_prefactor * exp(- K_s_FLiBe_energy / (R*temperature_exp))}' + +# Initial conditions +initial_pressure = '${units 1210 Pa}' # input pressure +initial_concentration_FLiBe = '${units 1e-12 mol/m^3}' + +# Geometry and mesh +length_Ni = '${units 2 mm -> m}' # Ni membrane thickness +num_nodes_Ni = 5 # 10 +length_FLiBe = '${units 8.1 mm -> m}' # FLiBe membrane thickness +num_nodes_FLiBe = 20 # 30 +width_inner = '${units 25 mm -> m}' +num_nodes_inner = 25 # 50 +thickness = '${units 1 m}' + +[Mesh] + [cmg] + type = CartesianMeshGenerator + dim = 2 + dx = '${fparse length_Ni} ${fparse length_FLiBe}' + dy = '${fparse width_inner}' + ix = '${num_nodes_Ni} ${num_nodes_FLiBe}' + iy = '${num_nodes_inner}' + subdomain_id = '1 2' + [] + [interface_Ni_FLiBe] + type = SideSetsBetweenSubdomainsGenerator + input = cmg + primary_block = '1' + paired_block = '2' + new_boundary = 'interface_Ni_FLiBe' + [] + [interface_Ni_membrane_FLiBe_other_direction] + type = SideSetsBetweenSubdomainsGenerator + input = 'interface_Ni_FLiBe' + primary_block = '2' + paired_block = '1' + new_boundary = 'interface_Ni_membrane_FLiBe_other_direction' + [] + [restrict_bottom_Ni] + type = ParsedGenerateSideset + combinatorial_geometry = '1' + input = 'interface_Ni_membrane_FLiBe_other_direction' + new_sideset_name = 'bottom_Ni' + included_boundaries = 'bottom' + included_subdomains = '1' + [] + [restrict_bottom_FLiBe] + type = ParsedGenerateSideset + combinatorial_geometry = '1' + input = 'restrict_bottom_Ni' + new_sideset_name = 'bottom_FLiBe' + included_boundaries = 'bottom' + included_subdomains = '2' + [] + [restrict_top_Ni] + type = ParsedGenerateSideset + combinatorial_geometry = '1' + input = 'restrict_bottom_FLiBe' + new_sideset_name = 'top_Ni' + included_boundaries = 'top' + included_subdomains = '1' + [] + [restrict_top_FLiBe] + type = ParsedGenerateSideset + combinatorial_geometry = '1' + input = 'restrict_top_Ni' + new_sideset_name = 'top_FLiBe' + included_boundaries = 'top' + included_subdomains = '2' + [] +[] + +[Variables] + [tritium_concentration_Ni_membrane] + initial_condition = ${initial_concentration_Ni} # mol/m^3 + block = 1 + [] + [tritium_concentration_FLiBe] + initial_condition = ${initial_concentration_FLiBe} # mol/m^3 + block = 2 + [] +[] + +[AuxVariables] + [enclosure_pressure] + initial_condition = ${initial_pressure} + [] + [tritium_concentration_Ni_membrane_squared] + block = 1 + [] + [bounds_dummy_Ni_membrane] + order = FIRST + family = LAGRANGE + [] + [bounds_dummy_FLiBe] + order = FIRST + family = LAGRANGE + [] +[] + +[Bounds] + [tritium_concentration_Ni_membrane_lower_bound] + type = ConstantBounds + variable = bounds_dummy_Ni_membrane + bounded_variable = tritium_concentration_Ni_membrane + bound_type = lower + bound_value = '${fparse -1e-20}' + [] + [tritium_concentration_FLiBe_lower_bound] + type = ConstantBounds + variable = bounds_dummy_FLiBe + bounded_variable = tritium_concentration_FLiBe + bound_type = lower + bound_value = '${fparse -1e-20}' + [] +[] + +[Kernels] + # Diffusion in Ni membrane + [diffusion_Ni_membrane] + type = ADMatDiffusion + variable = 'tritium_concentration_Ni_membrane' + diffusivity = ${D_Ni} + block = 1 + [] + [time_diff_Ni_membrane] + type = TimeDerivative + variable = 'tritium_concentration_Ni_membrane' + block = 1 + [] + # Diffusion in FLiBe + [diffusion_FLiBe] + type = ADMatDiffusion + variable = 'tritium_concentration_FLiBe' + diffusivity = ${D_FLiBe} + block = 2 + [] + [time_diff_FLiBe] + type = TimeDerivative + variable = 'tritium_concentration_FLiBe' + block = 2 + [] +[] + +[AuxKernels] + [tritium_concentration_Ni_membrane_squared] + type = ParsedAux + variable = 'tritium_concentration_Ni_membrane_squared' + coupled_variables = 'tritium_concentration_Ni_membrane' + expression = 'tritium_concentration_Ni_membrane^2' + [] +[] + +[BCs] + [left_concentration] + type = EquilibriumBC + Ko = ${K_s_Ni_prefactor} + activation_energy = ${K_s_Ni_energy} + boundary = 'left' + enclosure_var = 'enclosure_pressure' + temperature = ${temperature_exp} + variable = 'tritium_concentration_Ni_membrane' + p = ${n_Sieverts} + [] + [right_concentration_FLiBe] + type = ADDirichletBC + boundary = 'right' + variable = 'tritium_concentration_FLiBe' + value = 0.0 + [] + [bottom_flux_Ni] + type = ADNeumannBC + boundary = 'bottom_Ni' + variable = 'tritium_concentration_Ni_membrane' + value = 0.0 + [] + [bottom_flux_FLiBe] + type = ADNeumannBC + boundary = 'bottom_FLiBe' + variable = 'tritium_concentration_FLiBe' + value = 0.0 + [] + [top_flux_Ni] + type = ADNeumannBC + boundary = 'top_Ni' + variable = 'tritium_concentration_Ni_membrane' + value = 0.0 + [] + [top_flux_FLiBe] + type = ADNeumannBC + boundary = 'top_FLiBe' + variable = 'tritium_concentration_FLiBe' + value = 0.0 + [] +[] + +[InterfaceKernels] + [interface_sorption_Ni_membrane_FLiBe] + type = InterfaceSorption + K0 = '${fparse K_s_FLiBe_prefactor / (K_s_Ni_prefactor^2) / (R*temperature_exp)^2}' + Ea = '${fparse K_s_FLiBe_energy - (2*K_s_Ni_energy)}' + n_sorption = 2 + diffusivity = ${D_Ni} + unit_scale = ${unit_scale} + unit_scale_neighbor = ${unit_scale_neighbor} + temperature = ${temperature_exp} + variable = 'tritium_concentration_FLiBe' + neighbor_var = 'tritium_concentration_Ni_membrane' + sorption_penalty = 1e2 + boundary = 'interface_Ni_membrane_FLiBe_other_direction' + [] +[] + +[Postprocessors] + [left_flux_density_membrane] # mol/m^2/s + type = SideDiffusiveFluxAverage + boundary = 'left' + variable = 'tritium_concentration_Ni_membrane' + diffusivity = ${D_Ni} + # outputs = none + [] + [right_flux_density_membrane] # mol/m^2/s + type = SideDiffusiveFluxAverage + boundary = 'right' + variable = 'tritium_concentration_FLiBe' + diffusivity = ${D_FLiBe} + # outputs = none + [] + + # Mass conservation + + ## left boundary + [left_flux] # mol/s + type = ParsedPostprocessor + expression = 'left_flux_density_membrane*${thickness}*${width_inner}' + pp_names = 'left_flux_density_membrane' + # outputs = none + [] + # right boundary + [right_flux] # mol/s + type = ParsedPostprocessor + expression = 'right_flux_density_membrane*${thickness}*${width_inner}' + pp_names = 'right_flux_density_membrane' + # outputs = none + [] + + ## in cell + # [] + [Ni_membrane_concentration] # mol/m^3 + type = ElementAverageValue + variable = 'tritium_concentration_Ni_membrane' + block = 1 + outputs = none + [] + [Ni_membrane_amount] # mol + type = ParsedPostprocessor + expression = 'Ni_membrane_concentration*${thickness}*${length_Ni}*${width_inner}' + pp_names = 'Ni_membrane_concentration' + outputs = none + [] + [FLiBe_concentration] # mol/m^3 + type = ElementAverageValue + variable = 'tritium_concentration_FLiBe' + block = 2 + outputs = none + [] + [FLiBe_amount] # mol + type = ParsedPostprocessor + expression = 'FLiBe_concentration*${thickness}*${length_FLiBe}*${width_inner}' + pp_names = 'FLiBe_concentration' + outputs = none + [] + [tritium_amount] # mol + type = ParsedPostprocessor + expression = 'Ni_membrane_amount+FLiBe_amount' + pp_names = 'Ni_membrane_amount FLiBe_amount' + # outputs = none + [] + + # top boundary + [top_flux_density_Ni_membrane] # mol/m^2/s + type = SideDiffusiveFluxAverage + boundary = 'top_Ni' + variable = 'tritium_concentration_Ni_membrane' + diffusivity = ${D_Ni} + outputs = none + [] + [top_flux_Ni_membrane] # mol/s + type = ParsedPostprocessor + expression = 'top_flux_density_Ni_membrane*${thickness}*${length_Ni}' + pp_names = 'top_flux_density_Ni_membrane' + outputs = none + [] + [top_flux_density_FLiBe] # mol/m^2/s + type = SideDiffusiveFluxAverage + boundary = 'top_FLiBe' + variable = 'tritium_concentration_FLiBe' + diffusivity = ${D_FLiBe} + outputs = none + [] + [top_flux_FLiBe] # mol/s + type = ParsedPostprocessor + expression = 'top_flux_density_FLiBe*${thickness}*${length_FLiBe}' + pp_names = 'top_flux_density_FLiBe' + outputs = none + [] + [top_flux] # mol/s + type = ParsedPostprocessor + expression = 'top_flux_Ni_membrane + top_flux_FLiBe' + pp_names = 'top_flux_Ni_membrane top_flux_FLiBe' + # outputs = none + [] +[] + +[Preconditioning] + [SMP] + type = SMP + full = true + [] +[] + +[Executioner] + type = Transient + end_time = ${simulation_time} + nl_max_its = 9 + l_max_its = 30 + scheme = 'bdf2' + solve_type = 'Newton' + petsc_options_iname = '-pc_type -sub_pc_type -snes_type' + petsc_options_value = 'asm lu vinewtonrsls' # This petsc option helps prevent negative concentrations with bounds' + nl_abs_tol = 1e-11 + [TimeStepper] + type = IterationAdaptiveDT + dt = 1e-6 + optimal_iterations = 7 + iteration_window = 1 + growth_factor = 1.1 + cutback_factor = 0.9 + cutback_factor_at_failure = 0.9 + [] +[] + +[Debug] + show_var_residual_norms = true +[] + +[Outputs] + file_base = 'val-2g_823K_1210Pa_out' + [csv] + type = CSV + [] + [exodus] + type = Exodus + time_step_interval = 20 + [] +[] + diff --git a/test/tests/val-2g/val-2g_parameters.params b/test/tests/val-2g/val-2g_parameters.params new file mode 100644 index 000000000..4fe38dc4c --- /dev/null +++ b/test/tests/val-2g/val-2g_parameters.params @@ -0,0 +1,26 @@ +# This file provides the common parameters used in all 4 tritium transport cases +# ============================================================================== + +# Physical constants +R = '${units 8.31446261815324 J/mol/K}' # Ideal gas constant + +# Simulation +simulation_time = '${units 50000 s}' +temperature_exp = '${units 823 K}' + +# Sorption law +n_Sieverts = 0.5 +unit_scale = 1 +unit_scale_neighbor = 1 + +# Nickel properties +D_Ni_prefactor = '${units 7e-7 m^2/s}' +D_Ni_energy = '${units 39.5e3 J/mol}' +D_Ni = '${units ${fparse D_Ni_prefactor * exp(- D_Ni_energy / (R*temperature_exp))} m^2/s}' + +K_s_Ni_prefactor = '${units 564e-3 mol/m^3/Pa^0.5}' +K_s_Ni_energy = '${units 15.8e3 J/mol}' + +# Initial condition +initial_concentration_Ni = '${units 1e-12 mol/m^3}' +