Merge pull request #231 from lkadz/ver-1kc-2

Add ver-1kc-2

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

@@ -0,0 +1 @@
+../../../../test/tests/ver-1kc-1/comparison_ver-1kc-1.py

doc/content/verification_and_validation/figures/comparison_ver-1kc-2.py

@@ -0,0 +1 @@
+../../../../test/tests/ver-1kc-2/comparison_ver-1kc-2.py

doc/content/verification_and_validation/index.md

@@ -33,7 +33,8 @@ TMAP8 also contains [example cases](examples/tmap_index.md), which showcase how
 | 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)                                    |
-| ver-1kc | [Sieverts’ Law Boundaries with No Volumetric Source](ver-1kc.md)                                  |
+| ver-1kc-1 | [Sieverts’ Law Boundaries with No Volumetric Source](ver-1kc-1.md)                              |
+| ver-1kc-2 | [Sieverts’ Law Boundaries with Chemical Reaction and No Volumetric Source](ver-1kc-2.md)        |
 
 # List of benchmarking cases
 

doc/content/verification_and_validation/ver-1kc.md → doc/content/verification_and_validation/ver-1kc-1.md

@@ -36,29 +36,29 @@ where $R$ is the ideal gas constant in J/mol/K, $T$ is the temperature in K, $K$
 ## Results
 
 We assume that $K = \frac{10}{\sqrt{RT}}$, which is expected to lead to $C_1 = 10 \sqrt{C_2}$ at equilibrium.
-As illustrated in [ver-1kc_comparison_time_k10], the pressure jump maintains a ratio of $\frac{C_1}{\sqrt{C_2}} \approx 10$, which is consistent with the relationship $C_1 = K (RT C_2)^n$ for $K = \frac{10}{\sqrt{RT}}$ and $n=0.5$ The concentration ratio between enclosures 1 and 2 in [ver-1kc_concentration_ratio_k10] shows that the results obtained with TMAP8 are consistent with the analytical results derived from the sorption law for $K \sqrt{RT}=10$. As shown in [ver-1kc_mass_conservation_k10], mass is conserved between the two enclosures over time, with a variation in mass of only $0.4$ %. This variation in mass can be further minimized by refining the mesh, i.e., increasing the number of segments in the domain.
+As illustrated in [ver-1kc-1_comparison_time_k10], the pressure jump maintains a ratio of $\frac{C_1}{\sqrt{C_2}} \approx 10$, which is consistent with the relationship $C_1 = K (RT C_2)^n$ for $K = \frac{10}{\sqrt{RT}}$ and $n=0.5$ The concentration ratio between enclosures 1 and 2 in [ver-1kc-1_concentration_ratio_k10] shows that the results obtained with TMAP8 are consistent with the analytical results derived from the sorption law for $K \sqrt{RT}=10$. As shown in [ver-1kc-1_mass_conservation_k10], mass is conserved between the two enclosures over time, with a variation in mass of only $0.4$ %. This variation in mass can be further minimized by refining the mesh, i.e., increasing the number of segments in the domain.
 
-!media comparison_ver-1kc.py
-       image_name=ver-1kc_comparison_time_k10.png
+!media comparison_ver-1kc-1.py
+       image_name=ver-1kc-1_comparison_time_k10.png
        style=width:50%;margin-bottom:2%;margin-left:auto;margin-right:auto
-       id=ver-1kc_comparison_time_k10
+       id=ver-1kc-1_comparison_time_k10
        caption=Evolution of species concentration over time governed by Sieverts' law with $K = \frac{10}{\sqrt{RT}}$.
 
-!media comparison_ver-1kc.py
-       image_name=ver-1kc_concentration_ratio_k10.png
+!media comparison_ver-1kc-1.py
+       image_name=ver-1kc-1_concentration_ratio_k10.png
        style=width:50%;margin-bottom:2%;margin-left:auto;margin-right:auto
-       id=ver-1kc_concentration_ratio_k10
+       id=ver-1kc-1_concentration_ratio_k10
        caption=Concentrations ratio between enclosures 1 and 2 at the interface for $K = \frac{10}{\sqrt{RT}}$. This verifies TMAP8's ability to apply Sieverts' law across the interface.
 
-!media comparison_ver-1kc.py
-       image_name=ver-1kc_mass_conservation_k10.png
+!media comparison_ver-1kc-1.py
+       image_name=ver-1kc-1_mass_conservation_k10.png
        style=width:50%;margin-bottom:2%;margin-left:auto;margin-right:auto
-       id=ver-1kc_mass_conservation_k10
+       id=ver-1kc-1_mass_conservation_k10
        caption=Total mass conservation across both enclosures over time for $K = \frac{10}{\sqrt{RT}}$.
 
 ## Input files
 
 !style halign=left
-The input file for this case can be found at [/ver-1kc.i]. To limit the computational costs of the test cases, the tests run a version of the file with a coarser mesh and less number of time steps. More information about the changes can be found in the test specification file for this case [/ver-1kc/tests].
+The input file for this case can be found at [/ver-1kc-1.i]. To limit the computational costs of the test cases, the tests run a version of the file with a coarser mesh and less number of time steps. More information about the changes can be found in the test specification file for this case [/ver-1kc-1/tests].
 
 !bibtex bibliography

doc/content/verification_and_validation/ver-1kc-2.md

@@ -0,0 +1,131 @@
+# ver-1kc-2
+
+# Sieverts’ Law Boundaries with Chemical Reactions and No Volumetric Source
+
+## General Case Description
+
+Two enclosures are separated by a membrane that allows diffusion according to Sieverts' law and chemical reactions, 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).
+
+Unlike the [ver-1kc-1](ver-1kc-1.md) case, which only considers tritium T$_2$, this setup describes a diffusion system in which tritium T$_2$, dihydrogen H$_2$ and HT are modeled across a one-dimensional domain split into two enclosures. The total system length is $2.5 \times 10^{-4}$ m, divided into 100 segments. The system operates at a constant temperature of 500 Kelvin. Initial tritium T$_2$ and dihydrogen H$_2$ pressures are specified as $10^{5}$ Pa for Enclosure 1 and $10^{-10}$ Pa for Enclosure 2. Initially, there is no HT in either enclosure.
+
+The reaction between the species is described as follows
+
+\begin{equation}
+\text{H}_2 + \text{T}_2 \leftrightarrow 2\text{HT}
+\end{equation}
+
+The kinematic evolutions of the species are given by the following equations
+
+\begin{equation}
+\frac{d C_{\text{HT}}}{dt} = 2K_1 C_{\text{H}_2} C_{\text{T}_2} - K_2 C_{\text{HT}}^2
+\end{equation}
+
+\begin{equation}
+\frac{d C_{\text{H}_2}}{dt} = -K_1 C_{\text{H}_2} C_{\text{T}_2} + \frac{1}{2} K_2 C_{\text{HT}}^2
+\end{equation}
+
+\begin{equation}
+\frac{d C_{\text{T}_2}}{dt} = -K_1 c_{\text{H}_2} C_{\text{T}_2} + \frac{1}{2} K_2 C_{\text{HT}}^2
+\end{equation}
+
+where $K_1$ and $K_2$ represent the reaction rates for the forward and reverse reactions, respectively.
+
+At equilibrium, the time derivatives are zero
+
+\begin{equation}
+2K_1 C_{\text{H}_2} C_{\text{T}_2} - K_2 C_{\text{HT}}^2 = 0
+\end{equation}
+
+From this, we can derive the same equilibrium condition as used in TMAP7:
+
+\begin{equation}
+P_{\text{HT}} = \eta \sqrt{P_{\text{H}_2} P_{\text{T}_2}}
+\end{equation}
+
+where the equilibrium constant $\eta$ is defined as
+
+\begin{equation} \label{eq:eta}
+\eta = \sqrt{\frac{2K_1}{K_2}}
+\end{equation}
+
+Similarly to TMAP7, the equilibrium constant $\eta$ has been set to a fixed value of $\eta = 2$.
+
+The diffusion process for each species in the two enclosures can be expressed by
+
+\begin{equation}
+\frac{\partial C_1}{\partial t} = \nabla D \nabla C_1,
+\end{equation}
+and
+\begin{equation}
+\frac{\partial C_2}{\partial t} = \nabla D \nabla C_2,
+\end{equation}
+
+where $C_1$ and $C_2$ represent the concentration fields in enclosures 1 and 2 respectively, $t$ is the time, and $D$ denotes the diffusivity.
+Note that the diffusivity may vary across different species and enclosures. However, in this case, it is assumed to be identical for all.
+
+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( C_2 RT \right)^n
+\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 Sieverts' law, $n=0.5$.
+
+## Results
+
+We assume that $K = 10/\sqrt{RT}$, which is expected to result in $C_1 = 10 \sqrt{C_2}$ at equilibrium.
+As illustrated in [ver-1kc-2_comparison_time_k10], similarly to ver-1kc-1, T$_2$ and H$_2$ pressures reach equilibrium in both enclosures. What is new, however, is that HT is produced in both enclosures following the sorption law.
+
+Thus, it is crucial to ensure that the chemical equilibrium between HT, T$_2$ and H$_2$ is achieved. This can be verified in both enclosures by examining the ratio between $P_{\text{HT}}$ and $\sqrt{P_{\text{H}_2} P_{\text{T}_2}}$, which must equal $\eta=2$.
+As shown in [ver-1kc-2_equilibrium_constant_k10], this ratio approaches $\eta=2$ for both enclosures, as observed in TMAP7. However, achieving this balance involves a compromise to reproduce TMAP7's results. The ratio of $K_1$ and $K_2$ must respect [eq:eta]. The values of $K_1$ and $K_2$ must also be large enough to ensure that the kinetics of chemical reactions are faster than diffusion or surface permeation to be closer to the equilibrium assumption used in TMAP7. Here, the equilibrium in enclosure 1 is achieved rapidly. Increasing $K_1$ and $K_2$ would also enable a quicker attainment of equilibrium in enclosure 2. However, using very high values for $K_1$ and $K_2$ would lead to an unnecessary increase in computational costs.
+
+The concentration ratios for T$_2$, H$_2$, and HT between enclosures 1 and 2, shown in [ver-1kc-2_concentration_ratio_T2_k10], [ver-1kc-2_concentration_ratio_H2_k10], and [ver-1kc-2_concentration_ratio_HT_k10], demonstrate that the results obtained with TMAP8 are consistent with the analytical results derived from the sorption law for $K \sqrt{RT} = 10$.
+
+As shown in [ver-1kc-2_mass_conservation_k10], mass is conserved between the two enclosures over time. The variation in mass is only $0.6$ %. This variation in mass can be further minimized by refining the mesh, i.e., increasing the number of segments in the domain.
+
+!media comparison_ver-1kc-2.py
+       image_name=ver-1kc-2_comparison_time_k10.png
+       style=width:50%;margin-bottom:2%;margin-left:auto;margin-right:auto
+       id=ver-1kc-2_comparison_time_k10
+       caption=Evolution of species concentration over time governed by Sieverts' law with $K = 10/\sqrt{RT}$ and $\eta = \sqrt{2K_1/K_2}$.
+
+!media comparison_ver-1kc-2.py
+       image_name=ver-1kc-2_equilibrium_constant_k10.png
+       style=width:50%;margin-bottom:2%;margin-left:auto;margin-right:auto
+       id=ver-1kc-2_equilibrium_constant_k10
+       caption=Equilibrium constant as a function of time for $\eta = \sqrt{2K_1/K_2}=2$.
+
+!media comparison_ver-1kc-2.py
+       image_name=ver-1kc-2_concentration_ratio_T2_k10.png
+       style=width:50%;margin-bottom:2%;margin-left:auto;margin-right:auto
+       id=ver-1kc-2_concentration_ratio_T2_k10
+       caption=T$_2$ concentration ratio between enclosures 1 and 2 at the interface for $K = 10/\sqrt{RT}$ and $\eta = \sqrt{2K_1/K_2}$. This verifies TMAP8's ability to apply Sieverts' law across the interface.
+
+!media comparison_ver-1kc-2.py
+       image_name=ver-1kc-2_concentration_ratio_H2_k10.png
+       style=width:50%;margin-bottom:2%;margin-left:auto;margin-right:auto
+       id=ver-1kc-2_concentration_ratio_H2_k10
+       caption=H$_2$ concentration ratio between enclosures 1 and 2 at the interface for $K = 10/\sqrt{RT}$ and $\eta = \sqrt{2K_1/K_2}$. This verifies TMAP8's ability to apply Sieverts' law across the interface.
+
+!media comparison_ver-1kc-2.py
+       image_name=ver-1kc-2_concentration_ratio_HT_k10.png
+       style=width:50%;margin-bottom:2%;margin-left:auto;margin-right:auto
+       id=ver-1kc-2_concentration_ratio_HT_k10
+       caption=HT concentration ratio between enclosures 1 and 2 at the interface for $K = 10/\sqrt{RT}$ and $\eta = \sqrt{2K_1/K_2}$. This verifies TMAP8's ability to apply Sieverts' law across the interface.
+
+!media comparison_ver-1kc-2.py
+       image_name=ver-1kc-2_mass_conservation_k10.png
+       style=width:50%;margin-bottom:2%;margin-left:auto;margin-right:auto
+       id=ver-1kc-2_mass_conservation_k10
+       caption=Total mass conservation across both enclosures over time for $K = 10/\sqrt{RT}$ and $\eta = \sqrt{2K_1/K_2}$.
+
+## Input files
+
+!style halign=left
+The input file for this case can be found at [/ver-1kc-2.i].
+
+!bibtex bibliography

test/tests/ver-1kc/comparison_ver-1kc.py → test/tests/ver-1kc-1/comparison_ver-1kc-1.py

@@ -10,9 +10,9 @@
 
 # Load experimental data
 if "/TMAP8/doc/" in script_folder:     # if in documentation folder
-    csv_folder_k10 = "../../../../test/tests/ver-1kc/gold/ver-1kc_out_k10.csv"
+    csv_folder_k10 = "../../../../test/tests/ver-1kc-1/gold/ver-1kc-1_out_k10.csv"
 else:                                  # if in test folder
-    csv_folder_k10 = "./gold/ver-1kc_out_k10.csv"
+    csv_folder_k10 = "./gold/ver-1kc-1_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']
@@ -37,7 +37,7 @@
 ax.set_ylim(bottom=0)
 ax.legend(loc="best")
 ax.grid(which='major', color='0.65', linestyle='--', alpha=0.3)
-fig.savefig('ver-1kc_comparison_time_k10.png', bbox_inches='tight', dpi=300)
+fig.savefig('ver-1kc-1_comparison_time_k10.png', bbox_inches='tight', dpi=300)
 
 # Subplot 2: Solubility and concentration ratios vs time
 
@@ -59,7 +59,7 @@
 x_pos = TMAP8_time_k10.max() / 7200
 y_pos = 0.9 * ax.get_ylim()[1]
 ax.text(x_pos, y_pos, 'RMSPE = %.3f ' % RMSPE + '%', fontweight='bold')
-fig.savefig('ver-1kc_concentration_ratio_k10.png', bbox_inches='tight', dpi=300)
+fig.savefig('ver-1kc-1_concentration_ratio_k10.png', bbox_inches='tight', dpi=300)
 
 # Subplot 3 : Mass Conservation Sum Encl 1 and 2 vs Time
 
@@ -74,5 +74,5 @@
 ax.grid(which='major', color='0.65', linestyle='--', alpha=0.3)
 mass_variation_percentage = (np.max(mass_conservation_sum_encl1_encl2_k10)-np.min(mass_conservation_sum_encl1_encl2_k10))/np.min(mass_conservation_sum_encl1_encl2_k10)*100
 print("Percentage of mass variation: ", mass_variation_percentage)
-fig.savefig('ver-1kc_mass_conservation_k10.png', bbox_inches='tight', dpi=300)
+fig.savefig('ver-1kc-1_mass_conservation_k10.png', bbox_inches='tight', dpi=300)
 

test/tests/ver-1kc/tests → test/tests/ver-1kc-1/tests

@@ -1,39 +1,39 @@
 [Tests]
   design = 'InterfaceSorption.md MatDiffusion.md TimeDerivative.md'
   issues = '#12'
-  verification = 'ver-1kc.md'
-  [ver-1kc_csv]
+  verification = 'ver-1kc-1.md'
+  [ver-1kc-1_csv]
     type = CSVDiff
-    input = ver-1kc.i
+    input = ver-1kc-1.i
     cli_args = "nb_segments_TMAP8=1e1
                 simulation_time=4
                 Executioner/nl_abs_tol=1e-5
                 Executioner/nl_rel_tol=1e-4
                 Outputs/exodus=false
-                Outputs/file_base=ver-1kc_out_k10_light"
-    csvdiff = ver-1kc_out_k10_light.csv
+                Outputs/file_base=ver-1kc-1_out_k10_light"
+    csvdiff = ver-1kc-1_out_k10_light.csv
     requirement = 'The system shall be able to model the diffusion of T2 across a membrane separating two enclosures in accordance with Sieverts’ law with a concentration jump at the interface.'
   []
-  [ver-1kc_csv_heavy]
+  [ver-1kc-1_csv_heavy]
     type = CSVDiff
     heavy = true
-    input = ver-1kc.i
-    csvdiff = ver-1kc_out_k10.csv
+    input = ver-1kc-1.i
+    csvdiff = ver-1kc-1_out_k10.csv
     requirement = 'The system shall be able to model the diffusion of T2 across a membrane separating two enclosures in accordance with Sieverts’ law with a concentration jump at the interface with a fine mesh and tight tolerances for higher accuracy.'
   []
-  [ver-1kc_exodus_heavy]
+  [ver-1kc-1_exodus_heavy]
     type = Exodiff
     heavy = true
-    input = ver-1kc.i
-    exodiff = ver-1kc_out_k10.e
-    prereq = ver-1kc_csv_heavy
-    should_execute = false # this test relies on the output files from ver-1kc_csv_concentration_jump, so it shouldn't be run twice
+    input = ver-1kc-1.i
+    exodiff = ver-1kc-1_out_k10.e
+    prereq = ver-1kc-1_csv_heavy
+    should_execute = false # this test relies on the output files from ver-1kc-1_csv_concentration_jump, so it shouldn't be run twice
     requirement = 'The system shall be able to model the diffusion of T2 across a membrane separating two enclosures in accordance with Sieverts’ law with a concentration jump at the interface with a fine mesh and tight tolerances for higher accuracy and generate an exodus file.'
   []
-  [ver-1kc_comparison]
+  [ver-1kc-1_comparison]
     type = RunCommand
-    command = 'python3 comparison_ver-1kc.py'
-    requirement = 'The system shall be able to generate comparison plots between the analytical solution and simulated solution of verification case 1kc, modeling a diffusion across a membrane separating two enclosures in accordance with Sieverts’ law.'
+    command = 'python3 comparison_ver-1kc-1.py'
+    requirement = 'The system shall be able to generate comparison plots between the analytical solution and simulated solution of verification case 1kc-1, modeling a diffusion across a membrane separating two enclosures in accordance with Sieverts’ law.'
     required_python_packages = 'matplotlib numpy pandas os git'
   []
 []

test/tests/ver-1kc/ver-1kc.i → test/tests/ver-1kc-1/ver-1kc-1.i

@@ -240,7 +240,7 @@ unit_scale_neighbor = 1
 []
 
 [Outputs]
-  file_base = 'ver-1kc_out_k10'
+  file_base = 'ver-1kc-1_out_k10'
   csv = true
   exodus = true
   execute_on = 'initial timestep_end'