diff --git a/doc/content/verification_and_validation/figures/comparison_ver-1kc.py b/doc/content/verification_and_validation/figures/comparison_ver-1kc.py new file mode 120000 index 00000000..a8666ee5 --- /dev/null +++ b/doc/content/verification_and_validation/figures/comparison_ver-1kc.py @@ -0,0 +1 @@ +../../../../test/tests/ver-1kc/comparison_ver-1kc.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 aaddaa2e..28d1026f 100644 --- a/doc/content/verification_and_validation/index.md +++ b/doc/content/verification_and_validation/index.md @@ -33,6 +33,7 @@ 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) | # List of benchmarking cases diff --git a/doc/content/verification_and_validation/ver-1kc.md b/doc/content/verification_and_validation/ver-1kc.md new file mode 100644 index 00000000..864cfbfa --- /dev/null +++ b/doc/content/verification_and_validation/ver-1kc.md @@ -0,0 +1,64 @@ +# ver-1kc-1 + +# Sieverts’ Law Boundaries with No Volumetric Source + +## General Case Description + +Two enclosures are separated by a membrane that allows diffusion according to Sievert'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). + +This setup describes a diffusion system in which tritium T$_2$ is 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 pressures are specified as $10^{5}$ Pa for Enclosure 1 and $10^{-10}$ Pa for Enclosure 2. + +The diffusion process in each of the two enclosures can be described 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. + +This case is similar to the [ver-1kb](ver-1kb.md) case, with the key difference being that sorption here follows Sieverts' law instead of Henry's law. +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 $K = \frac{10}{\sqrt{RT}}$, 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. + +!media comparison_ver-1kc.py + image_name=ver-1kc_comparison_time_k10.png + style=width:50%;margin-bottom:2%;margin-left:auto;margin-right:auto + id=ver-1kc_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 + style=width:50%;margin-bottom:2%;margin-left:auto;margin-right:auto + id=ver-1kc_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 + style=width:50%;margin-bottom:2%;margin-left:auto;margin-right:auto + id=ver-1kc_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]. + +!bibtex bibliography diff --git a/test/tests/ver-1kc/comparison_ver-1kc.py b/test/tests/ver-1kc/comparison_ver-1kc.py new file mode 100644 index 00000000..e59e1c6d --- /dev/null +++ b/test/tests/ver-1kc/comparison_ver-1kc.py @@ -0,0 +1,78 @@ +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) + +# 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" +else: # if in test folder + csv_folder_k10 = "./gold/ver-1kc_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'] +concentration_ratio_k10 = expt_data_k10['concentration_ratio'] + +# Subplot 1 : Pressure vs time + +fig = plt.figure(figsize=[6.5,5.5]) +gs = gridspec.GridSpec(1,1) +ax = fig.add_subplot(gs[0]) + +ax.plot(TMAP8_time_k10, TMAP8_pressure_enclosure_1_k10, label=r"T$_2$ Enclosure 1", c='tab:red', linestyle='-') +ax.plot(TMAP8_time_k10, TMAP8_pressure_enclosure_2_k10, label=r"T$_2$ Enclosure 2", c='tab:blue', linestyle='-') +ax.yaxis.set_major_formatter(plt.FuncFormatter(lambda val, pos: '{:.1e}'.format(val))) +ax.set_xlabel('Time (s)') +ax.set_ylabel('Pressure (Pa)') +ax.set_xlim(0, TMAP8_time_k10.max()) +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) + +# Subplot 2: Solubility and concentration ratios vs time + +fig = plt.figure(figsize=[6.5,5.5]) +gs = gridspec.GridSpec(1,1) +ax = fig.add_subplot(gs[0]) + +solubility_ratio = [10] * len(TMAP8_time_k10[1:]) +ax.plot(TMAP8_time_k10[1:], concentration_ratio_k10[1:], label=r"Concentration Ratio (TMAP8)", color='tab:blue', linestyle='-') +ax.plot(TMAP8_time_k10[1:], solubility_ratio, label=r"Solubility Ratio (Analytical)", color='tab:red', linestyle='--') +ax.set_yticks(np.arange(0, 21, 10)) +ax.set_xlim(0,TMAP8_time_k10.max()) +ax.set_xlabel('Time (s)') +ax.set_ylabel(r"Concentrations ratio $C_{\text{encl1}} / \sqrt{C_{\text{encl2}}}$") +ax.legend(loc="best") +ax.grid(which='major', color='0.65', linestyle='--', alpha=0.3) +RMSE = np.sqrt(np.mean((concentration_ratio_k10[1:]-solubility_ratio)**2)) +RMSPE = RMSE*100/np.mean(solubility_ratio) +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) + +# Subplot 3 : Mass Conservation Sum Encl 1 and 2 vs Time + +fig = plt.figure(figsize=[6.5,5.5]) +gs = gridspec.GridSpec(1,1) +ax = fig.add_subplot(gs[0]) + +ax.plot(TMAP8_time_k10, mass_conservation_sum_encl1_encl2_k10, c='tab:blue') +ax.yaxis.set_major_formatter(plt.FuncFormatter(lambda val, pos: '{:.3e}'.format(val))) +ax.set_xlabel('Time (s)') +ax.set_ylabel(r"Mass Conservation Sum Encl 1 and 2 (mol/m$^3$)") +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) + diff --git a/test/tests/ver-1kc/gold/ver-1kc_out_k10.csv b/test/tests/ver-1kc/gold/ver-1kc_out_k10.csv new file mode 100644 index 00000000..fc46e2d0 --- /dev/null +++ b/test/tests/ver-1kc/gold/ver-1kc_out_k10.csv @@ -0,0 +1,3220 @@ +time,concentration_encl_1_inventory,concentration_encl_2_inventory,concentration_enclosure_1_at_interface,concentration_enclosure_2_at_interface,concentration_ratio,mass_conservation_sum_encl1_encl2,pressure_enclosure_1,pressure_enclosure_1_at_interface,pressure_enclosure_2,pressure_enclosure_2_at_interface,solubility +0,0.001984493858205,4.0291238939313e-18,24.054471008545,2.4054471008545e-14,155095038.63291,0.001984493858205,100000,100000,1e-10,1e-10,240544710085.45 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+4,0.001238621305494,0.00047111541718175,16.503307528597,2.7235911968057,10.00000072887,0.0017097367226758,68656.470283854,68628.490673681,11191.632928552,11301.435429126,0.0014602841941711 diff --git a/test/tests/ver-1kc/tests b/test/tests/ver-1kc/tests new file mode 100644 index 00000000..1f9008cb --- /dev/null +++ b/test/tests/ver-1kc/tests @@ -0,0 +1,39 @@ +[Tests] + design = 'InterfaceSorption.md MatDiffusion.md TimeDerivative.md' + issues = '#12' + verification = 'ver-1kc.md' + [ver-1kc_csv] + type = CSVDiff + input = ver-1kc.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 + 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] + type = CSVDiff + heavy = true + input = ver-1kc.i + csvdiff = ver-1kc_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] + 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 + 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] + 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.' + required_python_packages = 'matplotlib numpy pandas os git' + [] +[] diff --git a/test/tests/ver-1kc/ver-1kc.i b/test/tests/ver-1kc/ver-1kc.i new file mode 100644 index 00000000..8edddc43 --- /dev/null +++ b/test/tests/ver-1kc/ver-1kc.i @@ -0,0 +1,247 @@ +nb_segments_TMAP7 = 20 +node_size_TMAP7 = '${units 1.25e-5 m}' +long_total = '${units ${fparse nb_segments_TMAP7 * node_size_TMAP7} m}' +nb_segments_TMAP8 = 1e2 +simulation_time = '${units 10 s}' +temperature = '${units 500 K}' +R = '${units 8.31446261815324 J/mol/K}' # ideal gas constant from PhysicalConstants.h +initial_pressure_1 = '${units 1e5 Pa}' +initial_pressure_2 = '${units 1e-10 Pa}' +initial_concentration_1 = '${units ${fparse initial_pressure_1 / (R*temperature)} mol/m^3}' +initial_concentration_2 = '${units ${fparse initial_pressure_2 / (R*temperature)} mol/m^3}' +solubility = '${units ${fparse 10/sqrt(R*temperature)} mol/m^3/Pa^(1/2)}' # Sieverts' law solubility +diffusivity = '${units ${fparse 4.31e-6 * exp(-2818/temperature)} m^2/s}' +n_sorption = 0.5 # Sieverts' Law +unit_scale = 1 +unit_scale_neighbor = 1 + +[Mesh] + [generated] + type = GeneratedMeshGenerator + dim = 1 + nx = ${nb_segments_TMAP8} + xmax = ${long_total} + [] + [enclosure_1] + type = SubdomainBoundingBoxGenerator + input = generated + block_id = 1 + bottom_left = '0 0 0' + top_right = '${fparse 1/3 * long_total} 0 0' + [] + [enclosure_2] + type = SubdomainBoundingBoxGenerator + input = enclosure_1 + block_id = 2 + bottom_left = '${fparse 1/3 * long_total} 0 0' + top_right = '${fparse long_total} 0 0' + [] + [interface] + type = SideSetsBetweenSubdomainsGenerator + input = enclosure_2 + primary_block = 1 + paired_block = 2 + new_boundary = interface + [] + [interface2] + type = SideSetsBetweenSubdomainsGenerator + input = interface + primary_block = 2 + paired_block = 1 + new_boundary = interface2 + [] +[] + +[Variables] + [concentration_enclosure_1] + block = 1 + order = FIRST + family = LAGRANGE + initial_condition = '${initial_concentration_1}' + [] + [concentration_enclosure_2] + block = 2 + order = FIRST + family = LAGRANGE + initial_condition = '${initial_concentration_2}' + [] +[] + +[AuxVariables] + [pressure_enclosure_1] + order = CONSTANT + family = MONOMIAL + block = 1 + initial_condition = '${initial_pressure_1}' + [] + [pressure_enclosure_2] + order = CONSTANT + family = MONOMIAL + block = 2 + initial_condition = '${initial_pressure_2}' + [] +[] + +[Kernels] + [diffusion_enclosure_1] + type = MatDiffusion + variable = concentration_enclosure_1 + diffusivity = ${diffusivity} + block = '1' + [] + [time_enclosure_1] + type = TimeDerivative + variable = concentration_enclosure_1 + block = '1' + [] + [diffusion_enclosure_2] + type = MatDiffusion + variable = concentration_enclosure_2 + diffusivity = ${diffusivity} + block = '2' + [] + [time_enclosure_2] + type = TimeDerivative + variable = concentration_enclosure_2 + block = '2' + [] +[] + +[AuxKernels] + [pressure_enclosure_1] + type = ParsedAux + variable = pressure_enclosure_1 + coupled_variables = 'concentration_enclosure_1' + expression = '${fparse R*temperature}*concentration_enclosure_1' + block = 1 + execute_on = 'initial timestep_end' + [] + [pressure_enclosure_2] + type = ParsedAux + variable = pressure_enclosure_2 + coupled_variables = 'concentration_enclosure_2' + expression = '${fparse R*temperature}*concentration_enclosure_2' + block = 2 + execute_on = 'initial timestep_end' + [] +[] + +[InterfaceKernels] + [interface_sorption] + type = InterfaceSorption + K0 = ${solubility} + Ea = 0 + n_sorption = ${n_sorption} + diffusivity = ${diffusivity} + unit_scale = ${unit_scale} + unit_scale_neighbor = ${unit_scale_neighbor} + temperature = ${temperature} + variable = concentration_enclosure_1 + neighbor_var = concentration_enclosure_2 + sorption_penalty = 1e1 + boundary = interface + [] +[] + +[Postprocessors] + [pressure_enclosure_1] + type = ElementAverageValue + variable = pressure_enclosure_1 + block = 1 + execute_on = 'initial timestep_end' + [] + [pressure_enclosure_2] + type = ElementAverageValue + variable = pressure_enclosure_2 + block = 2 + execute_on = 'initial timestep_end' + [] + [concentration_enclosure_1_at_interface] + type = SideAverageValue + boundary = interface + variable = concentration_enclosure_1 + outputs = 'csv console' + execute_on = 'initial timestep_end' + [] + [concentration_enclosure_2_at_interface] + type = SideAverageValue + boundary = interface2 + variable = concentration_enclosure_2 + outputs = 'csv console' + execute_on = 'initial timestep_end' + [] + [concentration_ratio] + type = ParsedPostprocessor + expression = 'concentration_enclosure_1_at_interface / sqrt(concentration_enclosure_2_at_interface)' + pp_names = 'concentration_enclosure_1_at_interface concentration_enclosure_2_at_interface' + execute_on = 'initial timestep_end' + outputs = 'csv console' + [] + [solubility] + type = ParsedPostprocessor + expression = 'concentration_enclosure_1_at_interface / pressure_enclosure_2_at_interface' + pp_names = 'concentration_enclosure_1_at_interface pressure_enclosure_2_at_interface' + execute_on = 'initial timestep_end' + outputs = 'csv console' + [] + [pressure_enclosure_1_at_interface] + type = SideAverageValue + boundary = interface + variable = pressure_enclosure_1 + outputs = 'csv console' + execute_on = 'initial timestep_end' + [] + [pressure_enclosure_2_at_interface] + type = SideAverageValue + boundary = interface2 + variable = pressure_enclosure_2 + outputs = 'csv console' + execute_on = 'initial timestep_end' + [] + [concentration_encl_1_inventory] + type = ElementIntegralVariablePostprocessor + variable = concentration_enclosure_1 + block = 1 + execute_on = 'initial timestep_end' + [] + [concentration_encl_2_inventory] + type = ElementIntegralVariablePostprocessor + variable = concentration_enclosure_2 + block = 2 + execute_on = 'initial timestep_end' + [] + [mass_conservation_sum_encl1_encl2] + type = LinearCombinationPostprocessor + pp_names = 'concentration_encl_1_inventory concentration_encl_2_inventory' + pp_coefs = '1 1' + execute_on = 'initial timestep_end' + [] +[] + +[Executioner] + type = Transient + end_time = ${simulation_time} + dtmax = 10 + nl_abs_tol = 1e-8 + nl_rel_tol = 1e-6 + scheme = 'bdf2' + solve_type = NEWTON + petsc_options_iname = '-pc_type' + petsc_options_value = 'lu' + nl_max_its = 6 + [TimeStepper] + type = IterationAdaptiveDT + dt = 0.01 + optimal_iterations = 5 + iteration_window = 3 + growth_factor = 1.05 + cutback_factor_at_failure = 0.8 + [] +[] + +[Outputs] + file_base = 'ver-1kc_out_k10' + csv = true + exodus = true + execute_on = 'initial timestep_end' +[]