From b66905306f4cf267530f29c97326443dc0256dcb Mon Sep 17 00:00:00 2001 From: Lee Date: Fri, 4 Oct 2024 11:14:44 +0200 Subject: [PATCH] (Ref. #12) --- .../verification_and_validation/index.md | 2 +- .../verification_and_validation/ver-1ka.md | 33 + test/tests/ver-1ka/comparison_ver-1ka.py | 27 + test/tests/ver-1ka/gold/ver-1ka_out.csv | 108002 +++++++++++++++ test/tests/ver-1ka/tests | 11 + test/tests/ver-1ka/ver-1ka.i | 46 + 6 files changed, 108120 insertions(+), 1 deletion(-) create mode 100644 doc/content/verification_and_validation/ver-1ka.md create mode 100644 test/tests/ver-1ka/comparison_ver-1ka.py create mode 100644 test/tests/ver-1ka/gold/ver-1ka_out.csv create mode 100644 test/tests/ver-1ka/tests create mode 100644 test/tests/ver-1ka/ver-1ka.i diff --git a/doc/content/verification_and_validation/index.md b/doc/content/verification_and_validation/index.md index 68fbdd3f..7d25a2a6 100644 --- a/doc/content/verification_and_validation/index.md +++ b/doc/content/verification_and_validation/index.md @@ -24,7 +24,7 @@ TMAP8 also contains [example cases](examples/tmap_index.md), which showcase how | ver-1ha | [Convective Gas Outflow Problem](ver-1ha.md) | | 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) # List of benchmarking cases diff --git a/doc/content/verification_and_validation/ver-1ka.md b/doc/content/verification_and_validation/ver-1ka.md new file mode 100644 index 00000000..ac712ca5 --- /dev/null +++ b/doc/content/verification_and_validation/ver-1ka.md @@ -0,0 +1,33 @@ +# ver-1ka + +# Simple Volumetric Source + +## General Case Description + +This problem involves two enclosures connected by a diffusive membrane that follows Sieverts law for diffusion. Both enclosures contain hydrogen (H$_2$), deuterium (T$_2$), and hydrogen deuteride (HT). In the first enclosure, there is an initial inventory of only hydrogen (H$_2$) along with a constant volumetric source rate of deuterium (T$_2$). The second enclosure starts out empty. + +## Case Set up + +This verification problem is taken from [!cite](longhurst1992verification). +The rise in pressure of T$_2$ molecules in the first enclosure can be monitored by using a non-flow type membrane between the two enclosures. Consequently, the rate of pressure increase can be expressed as: + +\begin{equation} +\frac{dP_{T_2}}{dt} = \frac{S}{V} kT +\end{equation} + +where $S$ represents the volumetric source rate, $V$ is the volume of the enclosure, $k$ is the Boltzmann constant, and $T$ is the temperature of the enclosure. + +Comparison of the TMAP8 results and the analytical solution is shown in +[ver-1ka_comparison_time] as a function of time. The TMAP8 code predictions match very well with the analytical solution. + +!media figures/ver-1ka_comparison_time.png + style=width:50%;margin-bottom:2% + id=ver-1ka_comparison_time + caption=Comparison of T$_2$ partial pressure in an enclosure with no loss pathways as function of time calculated through TMAP8 and analytically + +## Input files + +!style halign=left +The input file for this case can be found at [/ver-1ka.i], which is also used as tests in TMAP8 at [/ver-1ka/tests]. + +!bibtex bibliography \ No newline at end of file diff --git a/test/tests/ver-1ka/comparison_ver-1ka.py b/test/tests/ver-1ka/comparison_ver-1ka.py new file mode 100644 index 00000000..cdfe04e9 --- /dev/null +++ b/test/tests/ver-1ka/comparison_ver-1ka.py @@ -0,0 +1,27 @@ +import numpy as np +import pandas as pd +import matplotlib.pyplot as plt + +df = pd.read_csv('./gold/ver-1ka_out.csv') + +S = 1e20 # m^-3 * s^-1 +V = 1 # m^3 +kb = 1.380649e-23 # Boltzmann constant (J/K) +T = 500 # K + +t_csv = df['time'] +v = df['v'] +t = np.arange(0, 10801, 540) + +expression = (S / V) * kb * T * t + +plt.plot(t_csv/3600, v, linestyle='-', color='magenta', label='TMAP8', linewidth=3) +plt.plot(t/3600, expression, marker='+', linestyle='', color='black', label=r"theory", markersize=10) + +plt.gca().yaxis.set_major_formatter(plt.FuncFormatter(lambda val, pos: '{:.1e}'.format(val))) + +plt.xlabel('Time (hr)') +plt.ylabel('Pressure (Pa)') +plt.legend() +plt.grid(True) +plt.savefig('ver-1ka_comparison_time.png', bbox_inches='tight') diff --git a/test/tests/ver-1ka/gold/ver-1ka_out.csv b/test/tests/ver-1ka/gold/ver-1ka_out.csv new file mode 100644 index 00000000..eccad12a --- /dev/null +++ b/test/tests/ver-1ka/gold/ver-1ka_out.csv @@ -0,0 +1,108002 @@ +time,v +0,0 +0.1,0.06903245 +0.2,0.1380648999941 +0.3,0.20709735003798 +0.4,0.27612979991202 +0.5,0.34516224981324 +0.6,0.41419469985019 +0.7,0.48322714985579 +0.8,0.55225959992453 +0.9,0.62129204984545 +1,0.69032449986581 +1.1,0.75935694973833 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ver-1ka_out.csv + requirement = 'The system shall be able to model the tritium volumetric source in one enclosure' + [] +[] \ No newline at end of file diff --git a/test/tests/ver-1ka/ver-1ka.i b/test/tests/ver-1ka/ver-1ka.i new file mode 100644 index 00000000..3d143c75 --- /dev/null +++ b/test/tests/ver-1ka/ver-1ka.i @@ -0,0 +1,46 @@ +initial_pressure = 0 # Pa +kb = 1.380649e-23 # Boltzmann constant J/K +T = 500 # K +S = 1e20 # 1/m^3/s +V = 1 # m^3 +end_time = 10800 # s + +[Mesh] + type = GeneratedMesh + dim = 2 + nx = 10 + ny = 10 + xmax = 1 + ymax = 1 +[] + +[Variables] + [v] + family = SCALAR + order = FIRST + initial_condition = '${fparse initial_pressure}' + [] +[] + +[ScalarKernels] + [time] + type = ODETimeDerivative + variable = v + [] + [source] + type = ParsedODEKernel + variable = v + expression = '${fparse - S/V * kb * T}' + [] +[] + +[Executioner] + type = Transient + dt = .1 + end_time = ${end_time} + scheme = 'bdf2' +[] + +[Outputs] + csv = true +[] \ No newline at end of file