Ver 1kb

doc/content/verification_and_validation/figures/comparison_ver-1kb.py

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+/Users/lee/projects/TMAP8/test/tests/ver-1kb/comparison_ver-1kb.py

doc/content/verification_and_validation/index.md

@@ -32,6 +32,7 @@ TMAP8 also contains [example cases](examples/tmap_index.md), which showcase how
 | ver-1ja | [Radioactive Decay of Mobile Tritium in a Slab](ver-1ja.md)                                       |
 | ver-1jb | [Radioactive Decay of Mobile Tritium in a Slab with a Distributed Trap Concentration](ver-1jb.md) |
 | ver-1ka | [Simple Volumetric Source](ver-1ka.md)                                                            |
+| ver-1kb | [Henry’s Law Boundaries with No Volumetric Source](ver-1kb.md)                                    |
 
 # List of benchmarking cases
 

doc/content/verification_and_validation/ver-1kb.md

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+# ver-1kb
+
+# Henry’s Law Boundaries with No Volumetric Source
+
+## General Case Description
+
+Two enclosures are separated by a membrane that allows diffusion according to Henry’s law, with no volumetric source present. Enclosure 2 has twice the volume of Enclosure 1.
+
+## Case Set Up
+
+This verification problem is taken from [!cite](ambrosek2008verification).
+
+Over time, the pressures of T$_2$, which diffuses across the membrane in accordance with Henry’s law, will gradually equilibrate between the two enclosures.
+
+The diffusion process in each of the two enclosures can be described by the following equations:
+
+\begin{equation}
+\frac{\partial C_1}{\partial t} = D \nabla^2 C_1
+\end{equation}
+
+\begin{equation}
+\frac{\partial C_1}{\partial t} = D \nabla^2 C_1
+\end{equation}
+
+where $C_1$, $C_2$ represent the concentration fields in enclosures 1 and 2 respectively, and $D$ denotes the diffusivity.
+
+The concentration in Enclosure 1 is related to the partial pressure and concentration in Enclosure 2 via the interface sorption law:
+
+\begin{equation}
+C_1 = K P_2^n = K \left( \frac{C_2 RT}{n} \right)
+\end{equation}
+
+where $R$ is the ideal gas constant in J/mol/K, $T$ is the temperature in K, $K$ is the solubility, and $n$ is the exponent of the sorption law. For the Henry’s law, $n=1$.
+
+## Results
+
+Two subcases are considered. In the first subcase, it is assumed that the pressures in the two enclosures are in equilibrium, implying $K = 1/RT$.
+Consistent with the results from TMAP7, the pressure evolution in both enclosures is shown in [ver-1kb_comparison_time] as a function of time, confirming the equilibrium between the pressures in enclosures 1 and 2. The linear regression in [ver-1kb_comparison_concentration] demonstrates that the concentration values at the interface comply with the sorption law, with a proportionality coefficient consistent with the solubility value $K = \approx 2.4 \times 10^{-4}$. As shown in [ver-1kb_mass_conservation], mass is conserved between the two enclosures over time.
+
+!media comparison_ver-1kb.py
+       image_name=ver-1kb_comparison_time.png
+       style=width:50%;margin-bottom:2%;margin-left:auto;margin-right:auto
+       id=ver-1kb_comparison_time
+       caption=Equilibration of species pressures under Henry’s law for $K=1/RT$.
+
+!media comparison_ver-1kb.py
+       image_name=ver-1kb_comparison_concentration.png
+       style=width:50%;margin-bottom:2%;margin-left:auto;margin-right:auto
+       id=ver-1kb_comparison_concentration
+       caption=Concentration in enclosure 1 as a function of pressure in enclosure 2 at the interface for $K=1/RT$. Validation of the sorption law across the interface.
+
+!media comparison_ver-1kb.py
+       image_name=ver-1kb_mass_conservation.png
+       style=width:50%;margin-bottom:2%;margin-left:auto;margin-right:auto
+       id=ver-1kb_mass_conservation
+       caption=Total mass conservation across both enclosures over time for $K=1/RT$.
+
+In the second subcase, the sorption law with $K = 10/RT$ prevents the pressures in the two enclosures from reaching equilibrium. As illustrated in [ver-1kb_comparison_time_k10], the pressure jump maintains a ratio of $C_1/C_2 \approx 10$, which is consistent with the relationship $C_1 = K *RT * C_2$ for $K=10/RT$. The linear regression in [ver-1kb_comparison_concentration_k10] confirms that the concentration values at the interface adhere to the sorption law, with a proportionality coefficient aligned with the solubility value $K = \approx 2.4 \times 10^{-5}$. Additionally, [ver-1kb_mass_conservation_k10] verifies that mass is conserved between the two enclosures over time.
+
+!media comparison_ver-1kb.py
+       image_name=ver-1kb_comparison_time_k10.png
+       style=width:50%;margin-bottom:2%;margin-left:auto;margin-right:auto
+       id=ver-1kb_comparison_time_k10
+       caption=Pressures jump of species pressures under Henry’s law for $K=10/RT$.
+
+!media comparison_ver-1kb.py
+       image_name=ver-1kb_comparison_concentration_k10.png
+       style=width:50%;margin-bottom:2%;margin-left:auto;margin-right:auto
+       id=ver-1kb_comparison_concentration_k10
+       caption=Concentration in enclosure 1 as a function of pressure in enclosure 2 at the interface for $K=10/RT$. Validation of the sorption law across the interface.
+
+!media comparison_ver-1kb.py
+       image_name=ver-1kb_mass_conservation_k10.png
+       style=width:50%;margin-bottom:2%;margin-left:auto;margin-right:auto
+       id=ver-1kb_mass_conservation_k10
+       caption=Total mass conservation across both enclosures over time for $K=10/RT$.
+
+## Input files
+
+!style halign=left
+The input file for this case can be found at [/ver-1kb.i], which is also used as tests in TMAP8 at [/ver-1kb/tests].
+
+!bibtex bibliography

test/tests/ver-1kb/comparison_ver-1kb.py

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+import numpy as np
+import pandas as pd
+import os
+from matplotlib import gridspec
+import matplotlib.pyplot as plt
+
+# Changes working directory to script directory (for consistent MooseDocs usage)
+script_folder = os.path.dirname(__file__)
+os.chdir(script_folder)
+
+# Extract columns for time, pressures, concentration_enclosure_1_at_interface, and concentration_enclosure_2_at_interface
+if "/TMAP8/doc/" in script_folder:     # if in documentation folder
+    csv_folder = "../../../../test/tests/ver-1kb/gold/ver-1kb_out.csv"
+else:                                  # if in test folder
+    csv_folder = "./gold/ver-1kb_out.csv"
+expt_data = pd.read_csv(csv_folder)
+TMAP8_time = expt_data['time']
+TMAP8_pressure_enclosure_1 = expt_data['pressure_enclosure_1']
+TMAP8_pressure_enclosure_2 = expt_data['pressure_enclosure_2']
+concentration_enclosure_1_at_interface = expt_data['concentration_enclosure_1_at_interface']
+pressure_enclosure_2_at_interface = expt_data['pressure_enclosure_2_at_interface']
+mass_conservation_sum_encl1_encl2 = expt_data['mass_conservation_sum_encl1_encl2'].values
+
+# Repeat the same for K=10/RT
+if "/TMAP8/doc/" in script_folder:     # if in documentation folder
+    csv_folder_k10 = "../../../../test/tests/ver-1kb/gold/ver-1kb_out_k10.csv"
+else:                                  # if in test folder
+    csv_folder_k10 = "./gold/ver-1kb_out_k10.csv"
+expt_data_k10 = pd.read_csv(csv_folder_k10)
+TMAP8_time_k10 = expt_data_k10['time']
+TMAP8_pressure_enclosure_1_k10 = expt_data_k10['pressure_enclosure_1']
+TMAP8_pressure_enclosure_2_k10 = expt_data_k10['pressure_enclosure_2']
+concentration_enclosure_1_at_interface_k10 = expt_data_k10['concentration_enclosure_1_at_interface']
+pressure_enclosure_2_at_interface_k10 = expt_data_k10['pressure_enclosure_2_at_interface']
+mass_conservation_sum_encl1_encl2_k10 = expt_data_k10['mass_conservation_sum_encl1_encl2'].values
+
+# Subplot 1: Time vs Pressure
+fig1 = plt.figure(figsize=[6, 5.5])
+ax1 = fig1.add_subplot(111)
+ax1.plot(TMAP8_time / 3600, TMAP8_pressure_enclosure_1, label=r"H2 Encl 1", c='tab:red', linestyle='dotted')
+ax1.plot(TMAP8_time / 3600, TMAP8_pressure_enclosure_2, label=r"H2 Encl 2", c='tab:blue', linestyle='dotted')
+ax1.yaxis.set_major_formatter(plt.FuncFormatter(lambda val, pos: '{:.1e}'.format(val)))
+ax1.set_xlabel('Time (hr)')
+ax1.set_ylabel('Pressure (Pa)')
+ax1.set_xlim(0, 3)
+ax1.set_ylim(bottom=0)
+ax1.legend(loc="best")
+ax1.grid(which='major', color='0.65', linestyle='--', alpha=0.3)
+fig1.savefig('ver-1kb_comparison_time.png', bbox_inches='tight')
+
+# Subplot 2: Pressure Encl 2 vs Concentration Encl 1 at interface
+k = np.sum(concentration_enclosure_1_at_interface * pressure_enclosure_2_at_interface) / np.sum(pressure_enclosure_2_at_interface ** 2)
+line_fit = k * pressure_enclosure_2_at_interface[1:]
+fig2 = plt.figure(figsize=[6, 5.5])
+ax2 = fig2.add_subplot(111)
+ax2.plot(pressure_enclosure_2_at_interface[1:], concentration_enclosure_1_at_interface[1:], marker='o', linestyle='None', c='tab:blue')
+ax2.plot(pressure_enclosure_2_at_interface[1:], line_fit, label=f'Fit: y = {k:.2e}x\n', c='tab:red', linestyle='--')
+ax2.set_xlabel(r"Pressure Encl 2 at interface (Pa)")
+ax2.set_ylabel(r"Concentration Encl 1 at interface (mol/m^3)")
+ax2.legend(loc="best")
+ax2.grid(which='major', color='0.65', linestyle='--', alpha=0.3)
+fig2.savefig('ver-1kb_comparison_concentration.png', bbox_inches='tight')
+
+# Subplot 3: Mass Conservation Sum Encl 1 and 2 vs Time
+fig3 = plt.figure(figsize=[6, 5.5])
+ax3 = fig3.add_subplot(111)
+ax3.plot(TMAP8_time / 3600, mass_conservation_sum_encl1_encl2, 'o', color='tab:blue', markersize=0.7)
+ax3.yaxis.set_major_formatter(plt.FuncFormatter(lambda val, pos: '{:.3e}'.format(val)))
+ax3.set_xlabel('Time (hr)')
+ax3.set_ylabel(r"Mass Conservation Sum Encl 1 and 2 (mol/m^3)")
+ax3.grid(which='major', color='0.65', linestyle='--', alpha=0.3)
+fig3.savefig('ver-1kb_mass_conservation.png', bbox_inches='tight')
+
+# Repeat the same for K=10/RT
+# Subplot 1 : Time vs Pressure
+fig1_k10 = plt.figure(figsize=[6, 5.5])
+ax1_k10 = fig1_k10.add_subplot(111)
+ax1_k10.plot(TMAP8_time_k10 / 3600, TMAP8_pressure_enclosure_1_k10, label=r"H2 Encl 1", c='tab:red', linestyle='-')
+ax1_k10.plot(TMAP8_time_k10 / 3600, TMAP8_pressure_enclosure_2_k10, label=r"H2 Encl 2", c='tab:blue', linestyle='-')
+ax1_k10.yaxis.set_major_formatter(plt.FuncFormatter(lambda val, pos: '{:.1e}'.format(val)))
+ax1_k10.set_xlabel('Time (hr)')
+ax1_k10.set_ylabel('Pressure (Pa)')
+ax1_k10.set_xlim(0, 3)
+ax1_k10.set_ylim(bottom=0)
+ax1_k10.legend(loc="best")
+ax1_k10.grid(which='major', color='0.65', linestyle='--', alpha=0.3)
+fig1_k10.savefig('ver-1kb_comparison_time_k10.png', bbox_inches='tight')
+
+# Subplot 2 : Pressure Encl 2 vs Concentration Encl 1 at interface
+k_k10 = np.sum(concentration_enclosure_1_at_interface_k10 * pressure_enclosure_2_at_interface_k10) / np.sum(pressure_enclosure_2_at_interface_k10 ** 2)
+line_fit_k10 = k_k10 * pressure_enclosure_2_at_interface_k10[1:]
+fig2_k10 = plt.figure(figsize=[6, 5.5])
+ax2_k10 = fig2_k10.add_subplot(111)
+ax2_k10.plot(pressure_enclosure_2_at_interface_k10[1:], concentration_enclosure_1_at_interface_k10[1:], marker='o', linestyle='None', c='tab:blue')
+ax2_k10.plot(pressure_enclosure_2_at_interface_k10[1:], line_fit_k10, label=f'Fit: y = {k_k10:.2e}x\n', c='tab:red', linestyle='--')
+ax2_k10.set_xlabel(r"Pressure Encl 2 at interface (Pa)")
+ax2_k10.set_ylabel(r"Concentration Encl 1 at interface (mol/m^3)")
+ax2_k10.legend(loc="best")
+ax2_k10.grid(which='major', color='0.65', linestyle='--', alpha=0.3)
+fig2_k10.savefig('ver-1kb_comparison_concentration_k10.png', bbox_inches='tight')
+
+# Subplot 3 : Mass Conservation Sum Encl 1 and 2 vs Time
+fig3_k10 = plt.figure(figsize=[6, 5.5])
+ax3_k10 = fig3_k10.add_subplot(111)
+ax3_k10.plot(TMAP8_time_k10 / 3600, mass_conservation_sum_encl1_encl2_k10, 'o', color='tab:blue', markersize=0.7)
+ax3.yaxis.set_major_formatter(plt.FuncFormatter(lambda val, pos: '{:.3e}'.format(val)))
+ax3_k10.set_xlabel('Time (hr)')
+ax3_k10.set_ylabel(r"Mass Conservation Sum Encl 1 and 2 (mol/m^3)")
+ax3_k10.grid(which='major', color='0.65', linestyle='--', alpha=0.3)
+fig3_k10.savefig('ver-1kb_mass_conservation_k10.png', bbox_inches='tight')
+