diff --git a/doc/content/bib/tmap8.bib b/doc/content/bib/tmap8.bib index f3e8dd35..b6c62ad4 100644 --- a/doc/content/bib/tmap8.bib +++ b/doc/content/bib/tmap8.bib @@ -287,3 +287,25 @@ @article{li2010analytical year={2010}, publisher={American Society of Civil Engineers} } + +@article{kizu2001co, + title={Co-permeation of deuterium and hydrogen through Pd}, + author={Kizu, Kaname and Pisarev, Alexander and Tanabe, Tetsuo}, + journal={Journal of nuclear materials}, + volume={289}, + number={3}, + pages={291--302}, + year={2001}, + publisher={Elsevier} +} + +@article{katz1960permeability, + title={Permeability and diffusivity of hydrogen through a palladium tube}, + author={Katz, OM and Gulbransen, EA}, + journal={Review of Scientific Instruments}, + volume={31}, + number={6}, + pages={615--617}, + year={1960}, + publisher={American Institute of Physics} +} diff --git a/doc/content/verification_and_validation/figures/comparison_val-2e.py b/doc/content/verification_and_validation/figures/comparison_val-2e.py new file mode 120000 index 00000000..656884ec --- /dev/null +++ b/doc/content/verification_and_validation/figures/comparison_val-2e.py @@ -0,0 +1 @@ +../../../../test/tests/val-2e/comparison_val-2e.py \ No newline at end of file diff --git a/doc/content/verification_and_validation/figures/val-2e_equipment_schematic.png b/doc/content/verification_and_validation/figures/val-2e_equipment_schematic.png new file mode 100644 index 00000000..88b693e3 Binary files /dev/null and b/doc/content/verification_and_validation/figures/val-2e_equipment_schematic.png differ diff --git a/doc/content/verification_and_validation/index.md b/doc/content/verification_and_validation/index.md index ffde74a3..482ddaee 100644 --- a/doc/content/verification_and_validation/index.md +++ b/doc/content/verification_and_validation/index.md @@ -51,3 +51,4 @@ TMAP8 also contains [example cases](examples/tmap_index.md), which showcase how | val-2b | [Diffusion Experiment in Beryllium](val-2b.md) | | val-2c | [Test Cell Release Experiment](val-2c.md) | | 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) | diff --git a/doc/content/verification_and_validation/val-2e.md b/doc/content/verification_and_validation/val-2e.md new file mode 100644 index 00000000..01ea549d --- /dev/null +++ b/doc/content/verification_and_validation/val-2e.md @@ -0,0 +1,269 @@ +# val-2e + +# Co-permeation of H$_2$ and D$_2$ through Pd + +## Case Description + +This validation problem is taken from [!cite](ambrosek2008verification), which utilized experimental data from [!cite](kizu2001co). +Kizu et al. describe permeation experiments in which H$_2$ and D$_2$ permeate through thin Pd membranes. +This case is part of the validation suite of TMAP7 as val-2e [!citep](ambrosek2008verification). + +The experimental equipment has two vacuum chambers separated by a Pd membrane. +The membrane area is 1.8 $\times 10^{-4}$ m$^2$ and has thicknesses of either 0.025 mm or 0.05 mm, depending on the test. +Copper gaskets hold the membrane in place and it is reasonably assumed that gas can only move from one chamber to another by diffusing through the membrane. +The membrane's temperature is controlled between 820 and 870 K using an electric heater and a thermocouple. +Gas is supplied to one chamber (the upstream chamber) from regulated bottles at different compositions and pressures. +The base pressure on both upstream and downstream chambers is maintained below 1 $\times 10^{-6}$ Pa using turbomolecular and rotary pumps. +Pressure is measured by an ion gage on each side, and downstream gas composition is measured with a quadrupole mass spectrometer. +Flow rates through the membrane are determined by pressure increases in the downstream chamber at a fixed pumping rate of 0.1 m$^3$/s. + +The structure of the system is shown in [val-2e_equipment_schematic]. +Enclosure 1 is the source of background pressure to the experimental system. +Enclosure 4 is the vacuum pumping system that provides a sink for all system flows. +Enclosure 5 is the gas feed to the upstream experimental chamber, enclosure 2. +The pressures in enclosures 1, 4, and 5 are held constant or as a functional value while the pressures in enclosures 2 and 3 evolve with the flow and diffusion. +Depending on the experiment, the feed pressure of H$_2$ is 0, 0.14, or 0.063 Pa. +Combined with the evacuation to enclosure 4, this provides the upstream H$_2$ pressure for permeation. +The D$_2$ pressure is a stepped function of time, one step corresponding to each of the data points from [!cite](kizu2001co). +Steps are arbitrarily set at 100 s, but equilibrium is achieved in times much shorter than that. Effectively no HD is fed into the upstream experimental chamber, in keeping with the experimental setup given by [!cite](kizu2001co). +Rather, with either solution-law or recombination limited-boundary conditions for diffusion, HD is formed in accordance with the laws of chemical equilibrium. +Likewise in the downstream chamber, enclosure 3, HD is formed together with H$_2$ and D$_2$ in chemical equilibrium from diffusing H and D. + +!media figures/val-2e_equipment_schematic.png + style=width:50%;margin-bottom:2%;margin-left:auto;margin-right:auto + id=val-2e_equipment_schematic + caption=Schematic of the modeled enclosures for val-2e. + +The first three test cases are permeation tests of D$_2$ alone through membranes of each thickness. +For the 0.025 membrane, tests are conducted at both 825 K and 865 K whereas the 0.05 mm membrane is tested only at 825 K. + +[tab:val-2e_cases] described the different cases subcases being modeled in this validation effort. + +!table id=tab:val-2e_cases caption=Different subcases being modeled in this validation effort and their specific conditions. +| case name | Temperature (K) | Membrane thickness (mm) | Inlet gas composition | Remark | +| ----------- | ---------------- | --------------------------- | ---------------------------- | --------- | +| val-2ea | 825 | 0.05 | D$_2$ | Assumes solubility equilibrium ([eq:seivert_concentration]) | +| val-2eb | 825 | 0.025 | D$_2$ | Assumes solubility equilibrium ([eq:seivert_concentration]) | +| val-2ec | 865 | 0.025 | D$_2$ | Assumes solubility equilibrium ([eq:seivert_concentration]) | +| val-2ed | 870 | 0.025 | D$_2$ + H$_2$ at 0.063 Pa | Assumes solubility equilibrium ([eq:seivert_concentration]) | +| val-2ee | 870 | 0.025 | D$_2$ + H$_2$ at 0.063 Pa | Accounts for recombination kinetics ([eq:recombination]) | + + + +## Model Description + +In the first three cases (val-2ea, val-2eb, and val-2ec), TMAP8 simulates a one-dimensional domain to represent the deuterium diffusion and gas flowing in the enclosures. +Note that this case can easily be extended to a two- or three-dimensional case. + +This model considers the diffusion of deuterium on both sides of the Pd membrane. +First, the diffusion of deuterium in the membrane is described as: + +\begin{equation} \label{eq:diffusion} +\frac{d C_i}{d t} = \nabla D_i \nabla C_i, +\end{equation} + +where $C_i$ is the concentration of hydrogen isotope $i$ in membrane, +$i$ represents hydrogen isotope H or D, +$t$ is the time, +$D_i$ is the diffusivity of hydrogen isotope $i$. + +The flow of gas into enclosures 2 and 3 can be given by + +\begin{equation} \label{eq:dt_P2} +\frac{P_{Ij}}{dt} = \frac{Q (P_{I,j-1}-P_{Ij})}{V_j}, +\end{equation} + +where $Q$ is the volumetric flow rate of always 0.1 m$^3$/s, +$V_j$ is the volume of current enclosure $j$, $P_{I,j-1}$ and $P_{I,j}$ are the pressure of gas molecules $I$ in the previous enclosure $j-1$ and current enclosure $j$, gas molecules $I$ represents H$_2$, or D$_2$, or HD. + +The hydrogen isotopes recombine into gas on both sides of the membrane, and there are several ways to model this process, two of which are used in this validation case: (1) Assuming steady state at the surface, also called lawdep boundary conditions in TMAP4 and TMAP7 [!citep](ambrosek2008verification), and (2) capturing the kinetics of dissociation and recombination, also called ratedep conditions in TMAP4 and TMAP7 [!citep](ambrosek2008verification). + +By assuming that the kinetics of the dissociation and recombination processes are faster than diffusion, surface reactions can be assumed to be at steady state. +The concentrations on both sides can then be described as + +\begin{equation} \label{eq:seivert_concentration} +C_i = K_s P_{Ij}^{n}, +\end{equation} + +where $K_s$ is the solubility of hydrogen isotope in the membrane, and $n$ is the exponent for the relation of pressure and concentration. + +However, for the kinetics of surface reactions to be captured, the boundary conditions is set as + +\begin{equation} \label{eq:recombination} +J_{ij} = 2 A (K_r C_i^2 - K_d P_{Ij}), +\end{equation} + +where $J_{ij}$ is the recombination flux of hydrogen isotope $i$ out of the sample sides in enclosure $j$, +$A$ is the area on either side of the membrane, +and $K_r$ and $K_d$ are the recombination and dissociation coefficients, respectively. +The coefficient of 2 accounts for the fact that 2 atoms (D and H) form one isotope molecule (HD). + +The two co-permeation simulations, i.e., val-2ed and val-2ec, also include the chemical reactions in the upstream and downstream enclosure. +The reaction rates for H$_2$, D$_2$, and HD are described by + +\begin{equation} \label{eq:chemical_reaction_lawdep} +\frac{- 2 d P_{H_2}}{dt} = \frac{- 2 d P_{D_2}}{dt} = \frac{d P_{HD}}{dt} = 2 P_{H_2}^{0.5} P_{D_2}^{0.5} - P_{HD} +\end{equation} + +for lawdep boundary condition and + +\begin{equation} \label{eq:chemical_reaction_ratedep} +\frac{- 2 d P_{H_2}}{dt} = \frac{- 2 d P_{D_2}}{dt} = \frac{d P_{HD}}{dt} = \frac{k_b T A}{V} (K_r C_H C_D - K_d P_{HD}), +\end{equation} + +for ratedep boundary condition, +where $k_b$ is the Boltzmann’s constant, +$A$ is the surface area of the membrane, +$T$ are the temperature. + +## Case and Model Parameters + +The pressure history of deuterium on the enclosure 5 for first three simulations (val-2ea, val-2eb, and val-2ec) is presented in [val-2e_abc_pressure_history], as shown in [val-2e_comparison_pressure_history]. The initial pressures on other enclosures are presented in [val-2e_abc_pressure_initial]. + +!table id=val-2e_abc_pressure_history caption=Values of deuterium pressure on enclosure 5 during simulations val-2ea, val-2eb, and val-2ec [!citep](ambrosek2008verification). +| time (s) | Pressure $P_{D_2,5}$ (Pa) | +| --------- | ---------------------------- | +| 0 - 150 | 1.2 $\times 10^{-4}$ | +| 150 - 250 | 2.41 $\times 10^{-4}$ | +| 250 - 350 | 6.06 $\times 10^{-4}$ | +| 350 - 450 | 1.3 $\times 10^{-3}$ | +| 450 - 550 | 2.53 $\times 10^{-3}$ | +| 550 - 650 | 7.08 $\times 10^{-3}$ | +| 650 - 750 | 1.45 $\times 10^{-2}$ | +| 750 - 850 | 2.63 $\times 10^{-2}$ | +| 850 - 950 | 6.51 $\times 10^{-2}$ | +| 950 - 1050 | 1.16 $\times 10^{-1}$ | +| 1050 - 1150 | 2.97 $\times 10^{-1}$ | +| 1150 - 1250 | 7.6 $\times 10^{-1}$ | +| 1250 - 1350 | 1.55 | +| 1350 - 1900 | 3.37 | + +!media comparison_val-2e.py + image_name=val-2e_comparison_pressure_history.png + style=width:50%;margin-bottom:2%;margin-left:auto;margin-right:auto + id=val-2e_comparison_pressure_history + caption= The pressure history of D$_2$ in enclosure 5 for simulations val-2ea, val-2eb, and val-2ec. + +!table id=val-2e_abc_pressure_initial caption=Values of deuterium pressure during simulations val-2ea, val-2eb, and val-2ec [!citep](ambrosek2008verification). +| Parameter | Description | Value | Units | +| --------- | ------------------------------------ | ----------------------------------------------------------- | --------------------- | +| $P_{D_2,1}$ | Deuterium pressure in enclosure 1 | 1 $\times 10^{-6}$ | Pa | +| $P_{D_2,2}$ | Deuterium pressure in enclosure 2 | 1 $\times 10^{-6}$ | Pa | +| $P_{D_2,3}$ | Deuterium pressure in enclosure 3 | 1 $\times 10^{-6}$ | Pa | +| $P_{D_2,4}$ | Deuterium pressure in enclosure 4 | 1 $\times 10^{-10}$ | Pa | + +The pressure history of D$_2$ on the enclosure 5 for next two simulations (val-2ed and val-2ee) is presented in [val-2e_de_pressure_history], as shown in [val-2e_comparison_mixture_pressure_history]. The initial pressures on other enclosures are presented in [val-2e_de_pressure_initial]. + +!table id=val-2e_de_pressure_history caption=Values of deuterium pressure on enclosure 5 during simulations val-2ed and val-2ee [!citep](ambrosek2008verification). +| time (s) | Pressure $P_{D_2,5}$ (Pa) | +| --------- | ---------------------------- | +| 0 - 150 | 1.8421 $\times 10^{-4}$ | +| 150 - 250 | 1 $\times 10^{-3}$ | +| 250 - 350 | 3 $\times 10^{-3}$ | +| 350 - 450 | 9 $\times 10^{-3}$ | +| 450 - 550 | 2.7 $\times 10^{-2}$ | +| 550 - 650 | 8.1 $\times 10^{-2}$ | +| 650 - 750 | 2.43 $\times 10^{-1}$ | +| 750 - 1000 | 7.29 $\times 10^{-1}$ | + +!media comparison_val-2e.py + image_name=val-2e_comparison_mixture_pressure_history.png + style=width:50%;margin-bottom:2%;margin-left:auto;margin-right:auto + id=val-2e_comparison_mixture_pressure_history + caption= The pressure history of D$_2$ in enclosure 5 for simulations val-2ed and val-2ee. + +!table id=val-2e_de_pressure_initial caption=Values of pressure of H$_2$, D$_2$, and HD during simulations val-2ed and val-2ee [!citep](ambrosek2008verification). +| Parameter | Description | Value | Units | +| ----------- | ------------------------------------ | -------------------------------------------------------- | --------------------- | +| $P_{D_2,1}$ | D$_2$ pressure in enclosure 1 | 1 $\times 10^{-7}$ | Pa | +| $P_{H_2,1}$ | H$_2$ pressure in enclosure 1 | 1 $\times 10^{-7}$ | Pa | +| $P_{HD,1}$ | HD pressure in enclosure 1 | 1 $\times 10^{-7}$ | Pa | +| $P_{D_2,2}$ | initial D$_2$ pressure in enclosure 2 | 1 $\times 10^{-7}$ | Pa | +| $P_{H_2,2}$ | initial H$_2$ pressure in enclosure 2 | 6.3 $\times 10^{-2}$ | Pa | +| $P_{HD,2}$ | initial HD pressure in enclosure 2 | 1 $\times 10^{-7}$ | Pa | +| $P_{D_2,3}$ | initial D$_2$ pressure in enclosure 3 | 1 $\times 10^{-20}$ | Pa | +| $P_{H_2,3}$ | initial H$_2$ pressure in enclosure 3 | 1 $\times 10^{-20}$ | Pa | +| $P_{HD,3}$ | initial HD pressure in enclosure 3 | 1 $\times 10^{-20}$ | Pa | +| $P_{D_2,4}$ | D$_2$ pressure in enclosure 4 | 1 $\times 10^{-10}$ | Pa | +| $P_{H_2,4}$ | H$_2$ pressure in enclosure 4 | 1 $\times 10^{-10}$ | Pa | +| $P_{HD,4}$ | HD pressure in enclosure 4 | 1 $\times 10^{-10}$ | Pa | +| $P_{H_2,5}$ | H$_2$ pressure in enclosure 4 | 6.3 $\times 10^{-2}$ | Pa | +| $P_{HD,5}$ | HD pressure in enclosure 4 | 1 $\times 10^{-10}$ | Pa | + + +!alert note title=Updates of times and initial pressures in val-2ee to be consistent with val-2ed. +In [!cite](ambrosek2008verification), the times and initial pressures in val-2ee are different from the values used in val-2ed. However, we use the same values from val-2ed in val-2ee for consistency. The trivial difference in times and initial pressures do not impact the final results. + +Other case and model parameters used in TMAP8 are listed in [val-2e_parameters]: + + +!table id=val-2e_parameters caption=Values of material properties. +| Parameter | Description | Value | Units | Reference | +| --------- | ------------------------------------ | ----------------------------------------------------------- | --------------------- | --------------------- | +| $k_b$ | Boltzmann constant | 1.380649 $\times 10^{-23}$ | J/K | [PhysicalConstants.h](https://physics.nist.gov/cgi-bin/cuu/Value?k) | +| $R$ | Gas constant | 8.31446261815324 | J/mol/K | [PhysicalConstants.h](https://physics.nist.gov/cgi-bin/cuu/Value?r) | +| $A$ | surface area | 1.8$\times 10^{-4}$ | m$^2$ | [!cite](kizu2001co) | +| $V$ | enclosure volume | 0.005 | m$^3$ | [!cite](kizu2001co) | +| $T_1$ | temperature in val-2ea and val-2eb | 825 | K | [!cite](kizu2001co) | +| $T_2$ | temperature in val-2ec | 865 | K | [!cite](kizu2001co) | +| $T_3$ | temperature in val-2ed and val-2ee | 870 | K | [!cite](kizu2001co) | +| $Q$ | flow rate in all enclosures | 0.1 | m$^3$/s | [!cite](ambrosek2008verification) | +| $L_1$ | thinckness of membrane in val-2ea | 5$\times 10^{-5}$ | m | [!cite](kizu2001co) | +| $L_2$ | thinckness of membrane in val-2eb, val-2ec, val-2ed, val-2ee | 2.5$\times 10^{-5}$ | m | [!cite](kizu2001co) | +| $D_H$ | hydrogen diffusivity in membrane | 3.728$\times 10^{-4} \exp(-1315.8/T)$ | m$^2$/s | [!cite](katz1960permeability) | +| $D_D$ | deuterium diffusivity in membrane | 2.636$\times 10^{-4} \exp(-1315.8/T)$ | m$^2$/s | [!cite](ambrosek2008verification) | +| $K_{s,1}$ | solubility of hydrogen isotope in val-2ea, val-2eb, val-2ec | 1.511$\times 10^{23} \exp(-5918/T)$ | atom/m$^3$/Pa$^{0.9297}$ | [!cite](ambrosek2008verification) | +| $K_{s,2}$ | solubility of hydrogen isotope in val-2ed, val-2ee | 9.355$\times 10^{22} \exp(-5918/T)$ | atom/m$^3$/Pa$^{0.9297}$ | [!cite](ambrosek2008verification) | +| $n$ | exponent for the relation of pressure and concentration | 0.9297 | - | [!cite](kizu2001co) | +| $K_{r,D_2}$ | D$_2$ recombination coefficient | 2.502$\times 10^{-24} / \sqrt{4T} \exp(11836/T)$ | m$^4$/s | [!cite](ambrosek2008verification) | +| $K_{r,H_2}$ | H$_2$ recombination coefficient | 2.502$\times 10^{-24} / \sqrt{2T} \exp(11836/T)$ | m$^4$/s | [!cite](ambrosek2008verification) | +| $K_{r,HD}$ | HD recombination coefficient | 2.502$\times 10^{-24} / \sqrt{3T} \exp(11836/T)$ | m$^4$/s | [!cite](ambrosek2008verification) | +| $K_{d,D_2}$ | D$_2$ dissociation coefficient | 2.1897$\times 10^{22} / \sqrt{4T}$ | molecular/m$^2$/Pa | [!cite](ambrosek2008verification) | +| $K_{d,H_2}$ | H$_2$ dissociation coefficient | 2.1897$\times 10^{22} / \sqrt{2T}$ | molecular/m$^2$/Pa | [!cite](ambrosek2008verification) | +| $K_{d,HD}$ | HD dissociation coefficient | 2.1897$\times 10^{22} / \sqrt{3T}$ | molecular/m$^2$/Pa | [!cite](ambrosek2008verification) | + +!alert warning title=Typo in [!cite](ambrosek2008verification) +There are typos on the equations for hydrogen diffusivity, recombination and dissociation coefficients in the input files from TMAP7 in val-2ed and val-2ee. The correct values are provided in [val-2e_parameters] and used in TMAP8. The pre-factor for hydrogen diffusivity used in TMAP8 is 3.728 $\times 10^{-4}$ m$^2$/s instead of 2.636 $\times 10^{-4}$ m$^2$/s as used in the input file published in [!cite](ambrosek2008verification). The activation energy for recombination coefficient used in TMAP8 is 11836 K instead of the -11836 K value shown in Eq. (71) in [!cite](ambrosek2008verification) - note that the input files in [!cite](ambrosek2008verification) use the proper value. The values of the species molecular weight in amu are also updated from the input files shown in [!cite](ambrosek2008verification). + +!alert warning title=Solubility values for val-2ea, val-2eb, val-2ec differ from those for val-2ed, val-2ee +To achieve a lower RMSPE in [val-2e_comparison_diffusion], the solubility values for val-2ea, val-2eb, and val-2ec were taken from the simulations in [!cite](ambrosek2008verification), rather than using the values provided in the documentation in [!cite](ambrosek2008verification). + +## Results + +[val-2e_comparison_diffusion] shows the comparison of the TMAP8 calculation and the experimental data from [!cite](kizu2001co), including simulations val-2ea, val-2eb, and val-2ec. There are reasonable agreements between the TMAP predictions and the experimental data with root mean square percentage errors (RMSPE) of RMSPE = 23.51 %, 30.80 %, and 47.70 % for val-2ea, val-2eb, and val-2ec, respectively. + +!media comparison_val-2e.py + image_name=val-2e_comparison_diffusion.png + style=width:50%;margin-bottom:2%;margin-left:auto;margin-right:auto + id=val-2e_comparison_diffusion + caption= Comparison of the D$_2$ flux versus D$_2$ pressure on the upstream side of the membrane from TMAP8 calculation and the experimental data. + +[val-2e_comparison_mixture_diffusion] shows the comparison of the D$_2$, H$_2$, and HD flux versus effective D$_2$ pressure on the upstream side of the membrane from val-2ed using TMAP8 assuming steady state for surface reactions (i.e., lawdep condition) and the experimental data. The effective D$_2$ pressure is calculated using $P_{D_2} + 0.5 P_{HD}$. Although the total gas release is well captured, the release of individual gases are not well predicted, except for H$_2$ at low pressure, and D$_2$ at high pressure. In this scenario, RMSPE = 76.26 %, 100.83 %, 115.79 %, 10.77 % for H$_2$, D$_2$, HD, and the summation of all gases, respectively. + +!media comparison_val-2e.py + image_name=val-2e_comparison_mixture_diffusion.png + style=width:50%;margin-bottom:2%;margin-left:auto;margin-right:auto + id=val-2e_comparison_mixture_diffusion + caption= Comparison of the D$_2$, H$_2$, and HD flux versus effective D$_2$ pressure on the upstream side of the membrane from TMAP8 calculation using steady state surface condition (i.e., lawdep) for case val-2ed and the experimental data. + +[val-2e_comparison_mixture_diffusion_recombination] shows the comparison of the D$_2$, H$_2$, and HD flux versus effective D$_2$ pressure on the upstream side of the membrane from val-2ee using TMAP8 accounting for dissociation and recombination at the membrane's surface (i.e., ratedep condition) and the experimental data. There is a reasonable agreement between the TMAP8 predictions and the experimental data, except for the high pressure conditions greater than 0.1 Pa and for HD, especially at higher pressures. In this scenario, RMSPE = 11.34 %, 30.70 %, 79.72 %, 43.99 % for H$_2$, D$_2$, HD, and the summation of all gases, respectively. +Note that the agreement could be improved by adjusting the model parameters. It is also possible to perform this optimization with [MOOSE's stochastic tools module](https://mooseframework.inl.gov/modules/stochastic_tools/index.html). + +!alert warning title=Typo in experimental data from [!cite](ambrosek2008verification) +The experimental data from [!cite](ambrosek2008verification) for all cases in val-2e is slightly lower than the experimental data from [!cite](kizu2001co). We have therefore extracted and used the original experimental data from [!cite](kizu2001co). + +!media comparison_val-2e.py + image_name=val-2e_comparison_mixture_diffusion_recombination.png + style=width:50%;margin-bottom:2%;margin-left:auto;margin-right:auto + id=val-2e_comparison_mixture_diffusion_recombination + caption= Comparison of the D$_2$, H$_2$, and HD flux versus effective D$_2$ pressure on the upstream side of the membrane from TMAP8 calculation capturing dissociation and recombination at the surface (i.e., ratedep condition) for case val-2ee and the experimental data. + +!alert note title=Difference between the simulation results from TMAP7 and TMAP8 +Due to the corrected typos in [val-2e_parameters], the simulation results in val-2ed and val-2ee from TMAP8 differ from the results from TMAP7. + +## Input files + +!style halign=left +For this case, the main input files are [/val-2ea.i], [/val-2ed.i], and [/val-2ee.i]. Note that [/val-2ed.i] and [/val-2ee.i] utilize a common base file [/val-2e_base_three_gases.i] with the line `!include val-2e_base_three_gases.i`, and [/val-2ea.i] and [/val-2e_base_three_gases.i] utilize a common base file [/val-2e_base.i] with the line `!include val-2e_base.i`. The base input files contain all the features and TMAP8 objects common to these cases, reducing duplication. These files are also used as tests in TMAP8 at [/val-2e/tests]. Sub-cases `ver-1eb` and `ver-1ec` are adapted from [/val-2ea.i], as it done in [/val-2e/tests]. + +!bibtex bibliography diff --git a/test/tests/val-2e/comparison_val-2e.py b/test/tests/val-2e/comparison_val-2e.py new file mode 100644 index 00000000..d9fc725e --- /dev/null +++ b/test/tests/val-2e/comparison_val-2e.py @@ -0,0 +1,516 @@ +import matplotlib.pyplot as plt +import numpy as np +from matplotlib import gridspec +import pandas as pd +import os + +# Changes working directory to script directory (for consistent MooseDocs usage) +script_folder = os.path.dirname(__file__) +os.chdir(script_folder) + +#=============================================================================== +# Define methods + +def numerical_solution_on_experiment_input(experiment_input, tmap_input, tmap_output): + """interpolate numerical solution to the experimental time step + + Args: + experiment_input (float, ndarray): experimental input data points + tmap_input (float, ndarray): numerical input data points + tmap_output (float, ndarray): numerical output data points + + Returns: + float, ndarray: updated tmap_output based on the data points in experiment_input + """ + new_tmap_output = np.zeros(len(experiment_input)) + for i in range(len(experiment_input)): + left_limit = np.argwhere((np.diff(tmap_input < experiment_input[i])))[0][0] + right_limit = left_limit + 1 + new_tmap_output[i] = (experiment_input[i] - tmap_input[left_limit]) / (tmap_input[right_limit] - tmap_input[left_limit]) * (tmap_output[right_limit] - tmap_output[left_limit]) + tmap_output[left_limit] + return new_tmap_output + +def read_csv_from_TMAP8(file_name, parameter_names): + """Read simulation data in csv files from TMAP8 + + Args: + file_name (string): the file name at simulation folder + parameter_names (list): the list of parameters extracted from csv files + + Returns: + float, ndarray: the matrix keep the simulation results, first axis depended on len(parameter_names) + """ + if "/tmap8/doc/" in script_folder.lower(): # if in documentation folder + csv_folder = f"../../../../test/tests/val-2e/gold/{file_name}" + else: # if in test folder + csv_folder = f"./gold/{file_name}" + simulation_data = pd.read_csv(csv_folder) + simulation_results = [] + for i in range(len(parameter_names)): + simulation_results.append(simulation_data[parameter_names[i]]) + return simulation_results + +#=============================================================================== +# Physical constants +kb = 1.380649e-23 # J/K Boltzmann constant +R = 8.31446261815324 # J/mol/K Gas constant +Na = 6.02214076e23 # atom/mol Avogadro's number + +# Model parameters for a/b/c +Q = 0.1 # m^3/s flow rate +T = [825, 825, 865] # K +Area = 1.8e-4 # m^2 area +time_history = np.array([150,250,350,450,550,650,750,850,950,1050,1150,1250,1350,1900]) # s +pressure_history = np.array([1.20e-4,2.41e-4,6.06e-4,1.30e-3,2.53e-3,7.08e-3,1.45e-2,2.63e-2,6.51e-2,0.116,0.297,0.760,1.550,3.370]) # Pa +pressure_enclosure1 = 1e-6 # Pa +dt_maximum = 5 # s - from the input file + +################################################################################ +################################# Val-2e a/b/c ################################# +################################################################################ +# Extract predictions in 1D model for val2e-abc +simulation_file_names = ["val-2ea_out.csv", "val-2eb_out.csv", "val-2ec_out.csv"] +parameter_names = ['time','flux_surface_right_D','pressure_upstream_D2','pressure_downstream_D2'] +simulation_results_list = [] +for i in range(len(simulation_file_names)): + file_name = simulation_file_names[i] + simulation_results = read_csv_from_TMAP8(file_name, parameter_names) # read csv file + simulation_results[parameter_names.index('flux_surface_right_D')] = -simulation_results[parameter_names.index('flux_surface_right_D')] * 1e12 / Na # D atoms/mum^2/s -> D2 mol/m^2/s + simulation_results_list.append(simulation_results) + +# find the pressure and flux +pressure_up_array = [] +pressure_down_array = [] +flux_array = [] +flux_calculated_array = [] +time_array = [] +for index in range(len(simulation_results_list)): + tmp_pressure_up_array = [] + tmp_pressure_down_array = [] + tmp_flux_array = [] + tmp_flux_calculated_array = [] + tmp_time_array = [] + time_history_copy = np.copy(time_history) + for i in range(len(simulation_results_list[index][parameter_names.index('time')])): + if len(time_history_copy) == 0: break + if (time_history_copy[0] - simulation_results_list[index][parameter_names.index('time')][i]) < dt_maximum: + tmp_pressure_up_array.append(simulation_results_list[index][parameter_names.index('pressure_upstream_D2')][i]) + tmp_pressure_down_array.append(simulation_results_list[index][parameter_names.index('pressure_downstream_D2')][i]) + tmp_flux_array.append(simulation_results_list[index][parameter_names.index('flux_surface_right_D')][i]) + tmp_time_array.append(simulation_results_list[index][parameter_names.index('time')]) + + tmp_flux_calculated = (tmp_pressure_down_array[-1] - pressure_enclosure1) * Q / R / T[index] / Area + tmp_flux_calculated_array.append(tmp_flux_calculated) + time_history_copy = time_history_copy[1:] + pressure_up_array.append(tmp_pressure_up_array) + pressure_down_array.append(tmp_pressure_down_array) + flux_array.append(tmp_flux_array) + flux_calculated_array.append(tmp_flux_calculated_array) + time_array.append(tmp_time_array) + if len(tmp_time_array) < len(time_history): + print(f"Some data missing: \n{time_array} \nand \n{time_history}") + +# ============================================================================ # +# Extract data from experiments +experiment_results_list = [] +experiment_file_names = ["experiment_thick_825K.csv", "experiment_thin_825K.csv", "experiment_thin_865K.csv"] + +experiment_parameter_names = ['Pressure [Pa]','Flux [mol/m^2/s]'] +for i in range(len(experiment_file_names)): + file_name = experiment_file_names[i] + experiment_results = read_csv_from_TMAP8(file_name, experiment_parameter_names) # read csv file + experiment_results_list.append(experiment_results) + +# ============================================================================ # +# Plot pressure history +fig = plt.figure(figsize=[6.5,5.5]) +gs = gridspec.GridSpec(1,1) +ax = fig.add_subplot(gs[0]) + +time_history_plot = np.array([0,150,150,250,250,350,350,450,450,550,550, + 650,650,750,750,850,850,950,950,1050,1050, + 1150,1150,1250,1250,1350,1350,1900]) # s +pressure_history_plot = np.array([1.20e-4,1.20e-4,2.41e-4,2.41e-4,6.06e-4,6.06e-4, + 1.30e-3,1.30e-3,2.53e-3,2.53e-3,7.08e-3,7.08e-3, + 1.45e-2,1.45e-2,2.63e-2,2.63e-2,6.51e-2,6.51e-2, + 0.116,0.116,0.297,0.297,0.760,0.760,1.550,1.550, + 3.370,3.370]) # Pa +time_history_plot_mixture = np.array([0,150,150,250,250,350,350,450,450,550,550, + 650,650,750,750,1900]) # s +pressure_history_plot_mixture_D2 = np.array([1.8421-4,1.8421-4,1e-3,1e-3,3e-3,3e-3, + 0.009,0.009,0.027,0.027,0.081,0.081,0.243,0.243, + 0.729,0.729]) # Pa +plt.plot(time_history_plot, pressure_history_plot, label = r'D$_2$') +ax.set_xlabel(u'Time (s)') +ax.set_ylabel(r"Pressure (Pa)") +ax.set_xlim([0,1900]) +ax.legend(loc="best") +plt.grid(which='major', color='0.65', linestyle='--', alpha=0.3) +ax.minorticks_on() +plt.savefig('val-2e_comparison_pressure_history.png', bbox_inches='tight', dpi=300) +plt.close(fig) + +# ============================================================================ # +# Plot figure for pressure and flux for 2e-abc +fig = plt.figure(figsize=[6.5,5.5]) +gs = gridspec.GridSpec(1,1) +ax = fig.add_subplot(gs[0]) + +label_name = ["0.05mm, 825K", "0.025mm, 825K", "0.025mm, 865K"] +label_name_postfix = ["val-2ea", "val-2eb", "val-2ec"] +signal_list = ['o','s','^'] +for index in [2,1,0]: + ax.plot(pressure_up_array[index], flux_calculated_array[index], label=f'{label_name[index]} in {label_name_postfix[index]} (TMAP8)', c=f'C{index}') +for index in [2,1,0]: + ax.plot(experiment_results_list[index][experiment_parameter_names.index('Pressure [Pa]')], + experiment_results_list[index][experiment_parameter_names.index('Flux [mol/m^2/s]')], + signal_list[index], label=f'{label_name[index]} (experiment)', c=f'C{index}') +ax.set_xlabel(u'Pressure (Pa)') +ax.set_ylabel(r"Flux (mol/m$^2$/s)") +ax.legend(loc="best") +ax.set_xlim([1e-4,1e1]) +ax.set_xscale('log') +ax.set_yscale('log') +plt.grid(which='major', color='0.65', linestyle='--', alpha=0.3) +text_loc = [[5e-3,5e-7], [2.5e-4,1.8e-6], [8e-4,8e-6]] +for index in range(len(simulation_results_list)): + experiment_input = experiment_results_list[index][experiment_parameter_names.index('Pressure [Pa]')] + experiment_output = experiment_results_list[index][experiment_parameter_names.index('Flux [mol/m^2/s]')] + tmap_flux_for_rmspe = numerical_solution_on_experiment_input(experiment_input, + pressure_up_array[index], + flux_calculated_array[index]) + RMSPE = np.sqrt(np.mean(((tmap_flux_for_rmspe-experiment_output)/experiment_output)**2) )*100 + ax.text(text_loc[index][0],text_loc[index][1], 'RMSPE = %.2f '%RMSPE+'%',fontweight='bold',color=f'C{index}') +ax.minorticks_on() +plt.savefig('val-2e_comparison_diffusion.png', bbox_inches='tight', dpi=300) +plt.close(fig) + + +################################################################################ +################################## Val-2e d/e ################################## +################################################################################ +# Modeling data for d/e +T = 870 # K +time_history = np.array([150,250,350,450,550,650,750,1000]) +pressure_history_D = np.array([1.8421e-4,1e-3,3e-3,0.009,0.027,0.081,0.243,0.729]) +pressure_history_H = 0.063 +pressure_enclosure1 = 1e-7 + +# Extract predictions in 1D model for val2e-de +simulation_results_list = [] +simulation_file_names = ["val-2ed_out.csv"] +parameter_names = ['time','pressure_downstream_H2','pressure_downstream_D2','pressure_downstream_HD','pressure_upstream_H2','pressure_upstream_D2','pressure_upstream_HD','flux_surface_right_D','flux_surface_right_H'] +for i in range(len(simulation_file_names)): + file_name = simulation_file_names[i] + simulation_results = read_csv_from_TMAP8(file_name, parameter_names) # read csv file + simulation_results[parameter_names.index('flux_surface_right_D')] = -simulation_results[parameter_names.index('flux_surface_right_D')] * 1e12 / Na # D atoms/mum^2/s -> D mol/m^2/s + simulation_results[parameter_names.index('flux_surface_right_H')] = -simulation_results[parameter_names.index('flux_surface_right_H')] * 1e12 / Na # D atoms/mum^2/s -> D mol/m^2/s + simulation_results_list.append(simulation_results) + +# find the pressure and flux +pressure_array_H2 = [] +pressure_array_D2 = [] +pressure_array_HD = [] +pressure_down_array_H2 = [] +pressure_down_array_D2 = [] +pressure_down_array_HD = [] +flux_array_H2 = [] +flux_array_D2 = [] +flux_array_HD = [] +flux_array_sum = [] +for index in range(len(simulation_results_list)): + tmp_pressure_array_H2 = [] + tmp_pressure_array_D2 = [] + tmp_pressure_array_HD = [] + tmp_pressure_down_array_H2 = [] + tmp_pressure_down_array_D2 = [] + tmp_pressure_down_array_HD = [] + tmp_flux_array_H2 = [] + tmp_flux_array_D2 = [] + tmp_flux_array_HD = [] + tmp_flux_array_sum = [] + time_history_copy = np.copy(time_history) + for i in range(len(simulation_results_list[index][parameter_names.index('time')])): + if len(time_history_copy) == 0: break + if (time_history_copy[0] - simulation_results_list[index][parameter_names.index('time')][i]) < dt_maximum: + # Get pressure + tmp_pressure_array_H2.append(simulation_results_list[index][parameter_names.index('pressure_upstream_H2')][i]) + tmp_pressure_array_D2.append(simulation_results_list[index][parameter_names.index('pressure_upstream_D2')][i]) + tmp_pressure_array_HD.append(simulation_results_list[index][parameter_names.index('pressure_upstream_HD')][i]) + tmp_pressure_down_array_H2.append(simulation_results_list[index][parameter_names.index('pressure_downstream_H2')][i]) + tmp_pressure_down_array_D2.append(simulation_results_list[index][parameter_names.index('pressure_downstream_D2')][i]) + tmp_pressure_down_array_HD.append(simulation_results_list[index][parameter_names.index('pressure_downstream_HD')][i]) + # Get flux + tmp_flux_H2 = (tmp_pressure_down_array_H2[-1] - pressure_enclosure1) * Q / R / T / Area + tmp_flux_D2 = (tmp_pressure_down_array_D2[-1] - pressure_enclosure1) * Q / R / T / Area + tmp_flux_HD = (tmp_pressure_down_array_HD[-1] - pressure_enclosure1) * Q / R / T / Area + tmp_flux_array_H2.append(tmp_flux_H2) + tmp_flux_array_D2.append(tmp_flux_D2) + tmp_flux_array_HD.append(tmp_flux_HD) + tmp_flux_array_sum.append(tmp_flux_H2+tmp_flux_D2+tmp_flux_HD) + time_history_copy = time_history_copy[1:] + pressure_array_H2.append(tmp_pressure_array_H2) + pressure_array_D2.append(tmp_pressure_array_D2) + pressure_array_HD.append(tmp_pressure_array_HD) + pressure_down_array_H2.append(tmp_pressure_down_array_H2) + pressure_down_array_D2.append(tmp_pressure_down_array_D2) + pressure_down_array_HD.append(tmp_pressure_down_array_HD) + flux_array_H2.append(tmp_flux_array_H2) + flux_array_D2.append(tmp_flux_array_D2) + flux_array_HD.append(tmp_flux_array_HD) + flux_array_sum.append(tmp_flux_array_sum) + + if len(tmp_pressure_array_D2) < len(time_history): + print(f"Some data missing: \n{tmp_pressure_array_D2} \nand \n{pressure_history_D}") +pressure_array_H2 = np.array(pressure_array_H2) +pressure_array_D2 = np.array(pressure_array_D2) +pressure_array_HD = np.array(pressure_array_HD) +flux_array_H2 = np.array(flux_array_H2) +flux_array_D2 = np.array(flux_array_D2) +flux_array_HD = np.array(flux_array_HD) +flux_array_sum = np.array(flux_array_sum) + +# ============================================================================ # +# Extract data from experiments +experiment_results_list = [] +experiment_file_names = ["experiment_mixture_H2.csv", "experiment_mixture_D2.csv", "experiment_mixture_HD.csv"] + +experiment_parameter_names = ['Pressure [Pa]','Flux [mol/m^2/s]'] +for i in range(len(experiment_file_names)): + file_name = experiment_file_names[i] + experiment_results = read_csv_from_TMAP8(file_name, experiment_parameter_names) # read csv file + experiment_results_list.append(experiment_results) + +# get sum results +experiment_results_pressure_sum = (experiment_results_list[0][experiment_parameter_names.index('Pressure [Pa]')] + + experiment_results_list[1][experiment_parameter_names.index('Pressure [Pa]')] + + experiment_results_list[2][experiment_parameter_names.index('Pressure [Pa]')]) / 3 +experiment_results_flux_sum = (experiment_results_list[0][experiment_parameter_names.index('Flux [mol/m^2/s]')] + + experiment_results_list[1][experiment_parameter_names.index('Flux [mol/m^2/s]')] + + experiment_results_list[2][experiment_parameter_names.index('Flux [mol/m^2/s]')]) + +# ============================================================================ # +# Plot pressure history +fig = plt.figure(figsize=[6.5,5.5]) +gs = gridspec.GridSpec(1,1) +ax = fig.add_subplot(gs[0]) + +time_history_plot_mixture = np.array([0,150,150,250,250,350,350,450,450,550,550, + 650,650,750,750,1000]) # s +pressure_history_plot_mixture_D2 = np.array([1.8421e-4,1.8421e-4,1e-3,1e-3,3e-3,3e-3, + 0.009,0.009,0.027,0.027,0.081,0.081,0.243,0.243, + 0.729,0.729]) # Pa +pressure_history_plot_mixture_H2 = np.ones(len(pressure_history_plot_mixture_D2)) * pressure_history_H +plt.plot(time_history_plot_mixture, pressure_history_plot_mixture_D2, label = r"D$_2$", color='C0') +plt.plot(time_history_plot_mixture, pressure_history_plot_mixture_H2, label = r"H$_2$", color='C1') +ax.set_xlabel(u'Time (s)') +ax.set_ylabel(r"Pressure (Pa)") +ax.legend(loc="best") +ax.set_xlim([0,1000]) +plt.grid(which='major', color='0.65', linestyle='--', alpha=0.3) +ax.minorticks_on() +plt.savefig('val-2e_comparison_mixture_pressure_history.png', bbox_inches='tight', dpi=300) +plt.close(fig) + +# ============================================================================ # +# Plot figure for pressure and flux for 2ed +fig = plt.figure(figsize=[6.5,5.5]) +gs = gridspec.GridSpec(1,1) +ax = fig.add_subplot(gs[0]) + +label_name = [r"H$_2$", r"D$_2$", r"HD", r"sum"] +signal_list = ['o','s','^','+'] + + +ax.plot(pressure_array_D2[0] + pressure_array_HD[0] / 2, + flux_array_sum[0], label=f'{label_name[3]} in val-2ed (TMAP8)', c=f'C{3}') +ax.plot(pressure_array_D2[0] + pressure_array_HD[0] / 2, + flux_array_D2[0], label=f'{label_name[1]} in val-2ed (TMAP8)', c=f'C{1}') +ax.plot(pressure_array_D2[0] + pressure_array_HD[0] / 2, + flux_array_H2[0], label=f'{label_name[0]} in val-2ed (TMAP8)', c=f'C{0}') +ax.plot(pressure_array_D2[0] + pressure_array_HD[0] / 2, + flux_array_HD[0], label=f'{label_name[2]} in val-2ed (TMAP8)', c=f'C{2}') + +ax.plot(experiment_results_pressure_sum, + experiment_results_flux_sum, + signal_list[3], label=f'{label_name[3]} (experiment)', c=f'C{3}') +ax.plot(experiment_results_list[1][experiment_parameter_names.index('Pressure [Pa]')], + experiment_results_list[1][experiment_parameter_names.index('Flux [mol/m^2/s]')], + signal_list[1], label=f'{label_name[1]} (experiment)', c=f'C{1}') +ax.plot(experiment_results_list[0][experiment_parameter_names.index('Pressure [Pa]')], + experiment_results_list[0][experiment_parameter_names.index('Flux [mol/m^2/s]')], + signal_list[0], label=f'{label_name[0]} (experiment)', c=f'C{0}') +ax.plot(experiment_results_list[2][experiment_parameter_names.index('Pressure [Pa]')], + experiment_results_list[2][experiment_parameter_names.index('Flux [mol/m^2/s]')], + signal_list[2], label=f'{label_name[2]} (experiment)', c=f'C{2}') + +ax.set_xlabel(u'Effective deuterium pressure (Pa)') +ax.set_ylabel(r"Partial release rates (mol/m$^2$/s)") +ax.legend(loc="best") +ax.set_xlim([1e-3, 1e0]) +ax.set_ylim([2e-8,4e-4]) +ax.set_xscale('log') +ax.set_yscale('log') +plt.grid(which='major', color='0.65', linestyle='--', alpha=0.3) +# error +simulation_output_list = [flux_array_H2[0], flux_array_D2[0], flux_array_HD[0], flux_array_sum[0]] +text_loc = [[1.0e-3,1.0e-5], [1.0e-3,1.9e-6], [1.0e-3,1.5e-7], [1.0e-3,3e-5]] +for index in range(len(simulation_output_list)): + simulation_input = pressure_array_D2[0] + pressure_array_HD[0] / 2 + simulation_output = simulation_output_list[index] + if index == 3: + experiment_input = experiment_results_pressure_sum[:-1] + experiment_output = experiment_results_flux_sum[:-1] + else: + experiment_input = experiment_results_list[index][experiment_parameter_names.index('Pressure [Pa]')][:-1] + experiment_output = experiment_results_list[index][experiment_parameter_names.index('Flux [mol/m^2/s]')][:-1] + tmap_flux_for_rmspe = numerical_solution_on_experiment_input(experiment_input, + simulation_input, + simulation_output) + RMSE = np.sqrt(np.mean((tmap_flux_for_rmspe-experiment_output)**2) ) + RMSPE = RMSE*100/np.mean(experiment_output) + ax.text(text_loc[index][0],text_loc[index][1], 'RMSPE = %.2f '%RMSPE+'%',fontweight='bold',color=f'C{index}') +ax.minorticks_on() +plt.savefig('val-2e_comparison_mixture_diffusion.png', bbox_inches='tight', dpi=300) +plt.close(fig) + +# ============================================================================ # +# Extract predictions in 1D model for val2ee +simulation_results_list = [] +simulation_file_names = ["val-2ee_out.csv"] +parameter_names = ['time','pressure_downstream_H2','pressure_downstream_D2','pressure_downstream_HD','pressure_upstream_H2','pressure_upstream_D2','pressure_upstream_HD','flux_surface_right_D','flux_surface_right_H','flux_on_left_D2','flux_on_left_H2','flux_on_left_HD'] +for i in range(len(simulation_file_names)): + file_name = simulation_file_names[i] + simulation_results = read_csv_from_TMAP8(file_name, parameter_names) # read csv file + simulation_results[parameter_names.index('flux_surface_right_D')] = -simulation_results[parameter_names.index('flux_surface_right_D')] * 1e12 / Na # D atoms/mum^2/s -> D mol/m^2/s + simulation_results[parameter_names.index('flux_surface_right_H')] = -simulation_results[parameter_names.index('flux_surface_right_H')] * 1e12 / Na # D atoms/mum^2/s -> D mol/m^2/s + simulation_results[parameter_names.index('flux_on_left_D2')] = -simulation_results[parameter_names.index('flux_on_left_D2')] * 1e12 / Na # D atoms/mum^2/s -> D mol/m^2/s + simulation_results[parameter_names.index('flux_on_left_H2')] = -simulation_results[parameter_names.index('flux_on_left_H2')] * 1e12 / Na # D atoms/mum^2/s -> D mol/m^2/s + simulation_results[parameter_names.index('flux_on_left_HD')] = -simulation_results[parameter_names.index('flux_on_left_HD')] * 1e12 / Na # D atoms/mum^2/s -> D mol/m^2/s + simulation_results_list.append(simulation_results) + +# find the pressure and flux +pressure_array_H2 = [] +pressure_array_D2 = [] +pressure_array_HD = [] +pressure_down_array_H2 = [] +pressure_down_array_D2 = [] +pressure_down_array_HD = [] +flux_array_H2 = [] +flux_array_D2 = [] +flux_array_HD = [] +flux_array_sum = [] +for index in range(len(simulation_results_list)): + tmp_pressure_array_H2 = [] + tmp_pressure_array_D2 = [] + tmp_pressure_array_HD = [] + tmp_pressure_down_array_H2 = [] + tmp_pressure_down_array_D2 = [] + tmp_pressure_down_array_HD = [] + tmp_flux_array_H2 = [] + tmp_flux_array_D2 = [] + tmp_flux_array_HD = [] + tmp_flux_array_sum = [] + time_history_copy = np.copy(time_history) + for i in range(len(simulation_results_list[index][parameter_names.index('time')])): + if len(time_history_copy) == 0: break + if (time_history_copy[0] - simulation_results_list[index][parameter_names.index('time')][i]) < dt_maximum: + # Get pressure + tmp_pressure_array_H2.append(simulation_results_list[index][parameter_names.index('pressure_upstream_H2')][i]) + tmp_pressure_array_D2.append(simulation_results_list[index][parameter_names.index('pressure_upstream_D2')][i]) + tmp_pressure_array_HD.append(simulation_results_list[index][parameter_names.index('pressure_upstream_HD')][i]) + tmp_pressure_down_array_H2.append(simulation_results_list[index][parameter_names.index('pressure_downstream_H2')][i]) + tmp_pressure_down_array_D2.append(simulation_results_list[index][parameter_names.index('pressure_downstream_D2')][i]) + tmp_pressure_down_array_HD.append(simulation_results_list[index][parameter_names.index('pressure_downstream_HD')][i]) + # Get flux + tmp_flux_H2 = (tmp_pressure_down_array_H2[-1] - pressure_enclosure1) * Q / R / T / Area + tmp_flux_D2 = (tmp_pressure_down_array_D2[-1] - pressure_enclosure1) * Q / R / T / Area + tmp_flux_HD = (tmp_pressure_down_array_HD[-1] - pressure_enclosure1) * Q / R / T / Area + tmp_flux_array_H2.append(tmp_flux_H2) + tmp_flux_array_D2.append(tmp_flux_D2) + tmp_flux_array_HD.append(tmp_flux_HD) + tmp_flux_array_sum.append(tmp_flux_H2+tmp_flux_D2+tmp_flux_HD) + time_history_copy = time_history_copy[1:] + pressure_array_H2.append(tmp_pressure_array_H2) + pressure_array_D2.append(tmp_pressure_array_D2) + pressure_array_HD.append(tmp_pressure_array_HD) + pressure_down_array_H2.append(tmp_pressure_down_array_H2) + pressure_down_array_D2.append(tmp_pressure_down_array_D2) + pressure_down_array_HD.append(tmp_pressure_down_array_HD) + flux_array_H2.append(tmp_flux_array_H2) + flux_array_D2.append(tmp_flux_array_D2) + flux_array_HD.append(tmp_flux_array_HD) + flux_array_sum.append(tmp_flux_array_sum) + + if len(tmp_pressure_array_D2) < len(time_history): + print(f"Some data missing: \n{tmp_pressure_array_D2} \nand \n{pressure_history_D}") +pressure_array_H2 = np.array(pressure_array_H2) +pressure_array_D2 = np.array(pressure_array_D2) +pressure_array_HD = np.array(pressure_array_HD) +flux_array_H2 = np.array(flux_array_H2) +flux_array_D2 = np.array(flux_array_D2) +flux_array_HD = np.array(flux_array_HD) +flux_array_sum = np.array(flux_array_sum) + + +# ============================================================================ # +# Plot figure for pressure and flux for 2ee +fig = plt.figure(figsize=[6.5,5.5]) +gs = gridspec.GridSpec(1,1) +ax = fig.add_subplot(gs[0]) + +label_name = [r"H$_2$", r"D$_2$", r"HD", r"sum"] +signal_list = ['o','s','^','+'] + +layer = 0 +ax.plot(pressure_array_D2[layer] + pressure_array_HD[layer] / 2, + flux_array_sum[layer], label=f'{label_name[3]} in val-2ee (TMAP8)', c=f'C{3}') +ax.plot(pressure_array_D2[layer] + pressure_array_HD[layer] / 2, + flux_array_D2[layer], label=f'{label_name[1]} in val-2ee (TMAP8)', c=f'C{1}') +ax.plot(pressure_array_D2[layer] + pressure_array_HD[layer] / 2, + flux_array_HD[layer], label=f'{label_name[2]} in val-2ee (TMAP8)', c=f'C{2}') +ax.plot(pressure_array_D2[layer] + pressure_array_HD[layer] / 2, + flux_array_H2[layer], label=f'{label_name[0]} in val-2ee (TMAP8)', c=f'C{0}') +ax.plot(experiment_results_pressure_sum, + experiment_results_flux_sum, + signal_list[3], label=f'{label_name[3]} (experiment)', c=f'C{3}') +ax.plot(experiment_results_list[1][experiment_parameter_names.index('Pressure [Pa]')], + experiment_results_list[1][experiment_parameter_names.index('Flux [mol/m^2/s]')], + signal_list[1], label=f'{label_name[1]} (experiment)', c=f'C{1}') +ax.plot(experiment_results_list[2][experiment_parameter_names.index('Pressure [Pa]')], + experiment_results_list[2][experiment_parameter_names.index('Flux [mol/m^2/s]')], + signal_list[2], label=f'{label_name[2]} (experiment)', c=f'C{2}') +ax.plot(experiment_results_list[0][experiment_parameter_names.index('Pressure [Pa]')], + experiment_results_list[0][experiment_parameter_names.index('Flux [mol/m^2/s]')], + signal_list[0], label=f'{label_name[0]} (experiment)', c=f'C{0}') + + +ax.set_xlabel(u'Effective deuterium pressure (Pa)') +ax.set_ylabel(r"Partial release rates (mol/m$^2$/s)") +ax.legend(loc="best") +ax.set_xlim([1e-3, 1e0]) +ax.set_ylim([2e-8,4e-4]) +ax.set_xscale('log') +ax.set_yscale('log') +plt.grid(which='major', color='0.65', linestyle='--', alpha=0.3) +# error +simulation_output_list = [flux_array_H2[0], flux_array_D2[0], flux_array_HD[0], flux_array_sum[0]] +text_loc = [[1e-3,1.0e-5], [2.5e-3,4e-8 ], [1.0e-3,3.0e-7], [1.0e-3,2.5e-5]] +for index in range(len(simulation_output_list)): + simulation_input = pressure_array_D2[0] + pressure_array_HD[0] / 2 + simulation_output = simulation_output_list[index] + if index == 3: + experiment_input = experiment_results_pressure_sum[:-1] + experiment_output = experiment_results_flux_sum[:-1] + else: + experiment_input = experiment_results_list[index][experiment_parameter_names.index('Pressure [Pa]')][:-1] + experiment_output = experiment_results_list[index][experiment_parameter_names.index('Flux [mol/m^2/s]')][:-1] + tmap_flux_for_rmspe = numerical_solution_on_experiment_input(experiment_input, + simulation_input, + simulation_output) + RMSE = np.sqrt(np.mean((tmap_flux_for_rmspe-experiment_output)**2) ) + RMSPE = RMSE*100/np.mean(experiment_output) + ax.text(text_loc[index][0],text_loc[index][1], 'RMSPE = %.2f '%RMSPE+'%',fontweight='bold',color=f'C{index}') +ax.minorticks_on() +plt.savefig('val-2e_comparison_mixture_diffusion_recombination.png', bbox_inches='tight', dpi=300) +plt.close(fig) + diff --git a/test/tests/val-2e/gold/experiment_mixture_D2.csv b/test/tests/val-2e/gold/experiment_mixture_D2.csv new file mode 100644 index 00000000..0654d5ca --- /dev/null +++ b/test/tests/val-2e/gold/experiment_mixture_D2.csv @@ -0,0 +1,9 @@ +Pressure [Pa],Flux [mol/m^2/s] +0.004524216780801966, 1.0021452340650378e-7 +0.009543936007219683, 3.024744477072597e-7 +0.020181302822182397, 0.0000013152516076740708 +0.05063429662262204, 0.000005530298399072939 +0.10148666410400967, 0.00001580286558514525 +0.20064074399563508, 0.000030048247009339013 +0.5065570349826607, 0.00006243221125096368 +0.9685644277381521, 0.00010229385426517369 \ No newline at end of file diff --git a/test/tests/val-2e/gold/experiment_mixture_H2.csv b/test/tests/val-2e/gold/experiment_mixture_H2.csv new file mode 100644 index 00000000..6aedbc21 --- /dev/null +++ b/test/tests/val-2e/gold/experiment_mixture_H2.csv @@ -0,0 +1,9 @@ +Pressure [Pa],Flux [mol/m^2/s] +0.004524216780801966, 0.000016166803744912416 +0.009543936007219683, 0.00001511692005263664 +0.020181302822182397, 0.00001335726025542993 +0.05063429662262204, 0.00001146281130068396 +0.10148666410400967, 0.000010206576599745438 +0.20064074399563508, 0.000008518344580100988 +0.5065570349826607, 0.00000818067037762332 +0.9685644277381521, 0.000007885899693103643 \ No newline at end of file diff --git a/test/tests/val-2e/gold/experiment_mixture_HD.csv b/test/tests/val-2e/gold/experiment_mixture_HD.csv new file mode 100644 index 00000000..f7296f0f --- /dev/null +++ b/test/tests/val-2e/gold/experiment_mixture_HD.csv @@ -0,0 +1,9 @@ +Pressure [Pa],Flux [mol/m^2/s] +0.004524216780801966, 0.000002818483593315244 +0.009543936007219683, 0.000005106005498112279 +0.020181302822182397, 0.000010042054016459564 +0.05063429662262204, 0.00001422257161865392 +0.10148666410400967, 0.00002414424958172987 +0.20064074399563508, 0.00003499241701722998 +0.5065570349826607, 0.00004774417882543832 +0.9685644277381521, 0.00005610373559038218 \ No newline at end of file diff --git a/test/tests/val-2e/gold/experiment_thick_825K.csv b/test/tests/val-2e/gold/experiment_thick_825K.csv new file mode 100644 index 00000000..05f782b3 --- /dev/null +++ b/test/tests/val-2e/gold/experiment_thick_825K.csv @@ -0,0 +1,14 @@ +Pressure [Pa],Flux [mol/m^2/s] +0.00025187096604994995, 4.1669071191580695e-8 +0.0006024670878789285, 1.0076403360649629e-7 +0.0013000864451623367, 2.2048939031166577e-7 +0.0026600460054627072, 4.4690988889173473e-7 +0.007205366617339495, 0.0000012608080007769607 +0.014432095191314873, 0.000002358452741876647 +0.026904699060306493, 0.00000391242350655847 +0.06523592779765103, 0.00000902350274837349 +0.12125980505922447, 0.000015105368429667453 +0.30287960219682436, 0.00003058623999675382 +0.786652200915388, 0.00006728861195174498 +1.6308796662254377, 0.00010944721752538247 +3.346249117973162, 0.00019943803510445436 \ No newline at end of file diff --git a/test/tests/val-2e/gold/experiment_thin_825K.csv b/test/tests/val-2e/gold/experiment_thin_825K.csv new file mode 100644 index 00000000..decdcbde --- /dev/null +++ b/test/tests/val-2e/gold/experiment_thin_825K.csv @@ -0,0 +1,14 @@ +Pressure [Pa],Flux [mol/m^2/s] +0.0002416910178739083, 1.2200612799523452e-7 +0.0005540899625183756, 2.2697495080063419e-7 +0.002558628599014938, 8.547185968699137e-7 +0.007158267277180123, 0.000002426195242477441 +0.01334145188049612, 0.000004412188025353658 +0.027154478917097786, 0.000008404409530476977 +0.06450496803903671, 0.000017856843040052643 +0.06450496803903671, 0.000017856843040052643 +0.122356383049439, 0.000032141100248366645 +0.305636827730252, 0.00005569775468853237 +0.7920170027376378, 0.00011852656979112164 +1.6094362804002411, 0.00020815045604912088 +3.3550520753894255, 0.0003639512294750235 \ No newline at end of file diff --git a/test/tests/val-2e/gold/experiment_thin_865K.csv b/test/tests/val-2e/gold/experiment_thin_865K.csv new file mode 100644 index 00000000..239339a8 --- /dev/null +++ b/test/tests/val-2e/gold/experiment_thin_865K.csv @@ -0,0 +1,12 @@ +Pressure [Pa],Flux [mol/m^2/s] +0.0012373183982408427, 5.005117047364166e-7 +0.0025759243252609612, 0.0000013257916186586545 +0.007221709215138166, 0.0000028169085231215905 +0.01323134639087021, 0.00000520072015970521 +0.027012385245199815, 0.000011037605079022432 +0.06521648398262139, 0.00002194307189507736 +0.12112974446851635, 0.000038144812206228325 +0.30389251627486413, 0.00006694304551247713 +0.7867460063528895, 0.00015552294551086454 +1.609820142228338, 0.00026025843121689355 +3.351487053249286, 0.0004598238033786746 \ No newline at end of file diff --git a/test/tests/val-2e/gold/val-2ea_out.csv b/test/tests/val-2e/gold/val-2ea_out.csv new file mode 100644 index 00000000..8b7b6904 --- /dev/null +++ b/test/tests/val-2e/gold/val-2ea_out.csv @@ -0,0 +1,438 @@ +time,flux_surface_left_D,flux_surface_right_D,pressure_downstream_D2,pressure_upstream_D2 +0,0,0,0,0 +0.01,5218.0362931943,-5231.0790344456,1e-06,2.1e-05 +0.021,9822.8229354477,-9830.1607827209,1.0067485500276e-06,4.0217702085732e-05 +0.0331,13832.287503964,-13838.651491729,1.0218260247434e-06,5.7545724019906e-05 +0.04641,17229.107353137,-17233.912984101,1.0445210736781e-06,7.2538943222223e-05 +0.061051,20028.485478837,-20032.013406885,1.0730124044879e-06,8.5077319292293e-05 +0.0771561,22269.634127473,-22272.144947918,1.1049925158438e-06,9.5223588398349e-05 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a/test/tests/val-2e/parameters_deuterium_gas.params b/test/tests/val-2e/parameters_deuterium_gas.params new file mode 100644 index 00000000..755198c5 --- /dev/null +++ b/test/tests/val-2e/parameters_deuterium_gas.params @@ -0,0 +1,8 @@ +# Physical Constants +# Note that we do NOT use the same number of digits as in TMAP7. +# This is to be consistent with PhysicalConstant.h +kb = '${units 1.380649e-23 J/K}' # Boltzmann constant +R = '${units 8.31446261815324 J/mol/K}' # Gas constant + +# Model data used in TMAP7 case +temperature = '${units 825 K}' \ No newline at end of file diff --git a/test/tests/val-2e/parameters_three_gases.params b/test/tests/val-2e/parameters_three_gases.params new file mode 100644 index 00000000..260cd166 --- /dev/null +++ b/test/tests/val-2e/parameters_three_gases.params @@ -0,0 +1,8 @@ +# Physical Constants +# Note that we do NOT use the same number of digits as in TMAP7. +# This is to be consistent with PhysicalConstant.h +kb = '${units 1.380649e-23 J/K}' # Boltzmann constant +R = '${units 8.31446261815324 J/mol/K}' # Gas constant + +# Model data used in TMAP7 case +temperature = '${units 870 K}' \ No newline at end of file diff --git a/test/tests/val-2e/tests b/test/tests/val-2e/tests new file mode 100644 index 00000000..136ac390 --- /dev/null +++ b/test/tests/val-2e/tests @@ -0,0 +1,80 @@ +[Tests] + design = 'MatReaction.md MatBodyForce.md EquilibriumBC.md MatNeumannBC.md' + verification = 'val-2e.md' + issues = '#12' + [val-2ea_csvdiff] + type = CSVDiff + input = val-2ea.i + csvdiff = val-2ea_out.csv + requirement = 'The system shall be able to model permeation of Deuterium from a 0.05 mm thick membrane at 825 K to generate CSV data for use in comparisons with the experimental data.' + [] + [val-2ea] + type = Exodiff + input = val-2ea.i + should_execute = False # this test relies on the output files from val-2ea_csvdiff, so it shouldn't be run twice + exodiff = val-2ea_out.e + requirement = 'The system shall be able to model permeation of Deuterium from a 0.05 mm thick membrane at 825 K.' + [] + [val-2eb_csvdiff] + type = CSVDiff + input = val-2ea.i + csvdiff = val-2eb_out.csv + cli_args = 'slab_thickness="${units 2.5e-5 m -> mum}" file_name="val-2eb_out"' + requirement = 'The system shall be able to model permeation of Deuterium from a 0.025 mm thin membrane at 825 K to generate CSV data for use in comparisons with the experimental data.' + [] + [val-2eb] + type = Exodiff + input = val-2ea.i + should_execute = False # this test relies on the output files from val-2eb_csvdiff, so it shouldn't be run twice + exodiff = val-2eb_out.e + cli_args = 'slab_thickness="${units 2.5e-5 m -> mum}" file_name="val-2eb_out"' + requirement = 'The system shall be able to model permeation of Deuterium from a 0.025 mm thin membrane at 825 K.' + [] + [val-2ec_csvdiff] + type = CSVDiff + input = val-2ea.i + csvdiff = val-2ec_out.csv + cli_args = 'temperature="${units 865 K}" slab_thickness="${units 2.5e-5 m -> mum}" file_name="val-2ec_out"' + requirement = 'The system shall be able to model permeation of Deuterium from a 0.025 mm thin membrane at 865 K to generate CSV data for use in comparisons with the experimental data.' + [] + [val-2ec] + type = Exodiff + input = val-2ea.i + should_execute = False # this test relies on the output files from val-2ec_csvdiff, so it shouldn't be run twice + exodiff = val-2ec_out.e + cli_args = 'temperature="${units 865 K}" slab_thickness="${units 2.5e-5 m -> mum}" file_name="val-2ec_out"' + requirement = 'The system shall be able to model permeation of Deuterium from a 0.025 mm thin membrane at 865 K and generate an exodus file.' + [] + [val-2ed_csvdiff] + type = CSVDiff + input = val-2ed.i + csvdiff = val-2ed_out.csv + requirement = 'The system shall be able to model permeation of mixture gas from a 0.025 mm thin membrane at 870 K using lawdep boundary conditions to generate CSV data for use in comparisons with the experimental data.' + [] + [val-2ed] + type = Exodiff + input = val-2ed.i + should_execute = False # this test relies on the output files from val-2ed_csvdiff, so it shouldn't be run twice + exodiff = val-2ed_out.e + requirement = 'The system shall be able to model permeation of mixture gas with chemical reaction from a 0.025 mm thin membrane at 870 K using lawdep boundary conditions and generate an exodus file.' + [] + [val-2ee_csvdiff] + type = CSVDiff + input = val-2ee.i + csvdiff = val-2ee_out.csv + requirement = 'The system shall be able to model permeation of mixture gas from a 0.025 mm thin membrane at 870 K using ratedep boundary conditions to generate CSV data for use in comparisons with the experimental data.' + [] + [val-2ee] + type = Exodiff + input = val-2ee.i + should_execute = False # this test relies on the output files from val-2ee_csvdiff, so it shouldn't be run twice + exodiff = val-2ee_out.e + requirement = 'The system shall be able to model permeation of mixture gas with chemical reaction from a 0.025 mm thin membrane at 870 K using ratedep boundary conditions and generate an exodus file.' + [] + [ver-2e_comparison] + type = RunCommand + command = 'python3 comparison_val-2e.py' + requirement = 'The system shall be able to generate comparison plots between the analytical solution and experimental data of validation case 2e, modeling the permeation of Deuterium from a membrane.' + required_python_packages = 'matplotlib numpy pandas os' + [] +[] diff --git a/test/tests/val-2e/val-2e_base.i b/test/tests/val-2e/val-2e_base.i new file mode 100644 index 00000000..49dd2c11 --- /dev/null +++ b/test/tests/val-2e/val-2e_base.i @@ -0,0 +1,185 @@ +# Base input file for Validation Problem #2ea #2eb #2ec #2ed #2ee +# Include [Mesh], [Problem], [Kernels] for D2 and D, [Materials] for D, +# [Postprocessors] for D2 and D, [Debug], [Preconditioning], +# [Executioner] and [Outputs] blocks + +# This input file is not meant to run on its own and is included in case-specific input files. + +# Enclosure data used in TMAP7 case +surface_area = '${units 1.8e-4 m^2 -> mum^2}' +pressure_enclosure4 = '${units 1e-10 Pa}' +volume_enclosure = '${units 0.005 m^3 -> mum^3}' +flow_rate = '${units 0.1 m^3/s -> mum^3/s}' +flow_rate_by_V = '${fparse flow_rate / volume_enclosure}' + +# Diffusion data used in TMAP7 case +diffusivity_pre_D = '${units 2.636e-4 m^2/s -> mum^2/s}' +diffusivity_energy_D = '${units ${fparse 1315.8 * R} J/mol}' + +# Modeling data used in current case +num_node = 20 # - +concentration_to_pressure_conversion_factor = '${units ${fparse kb*temperature} Pa*m^3 -> Pa*mum^3}' + +[Mesh] + [generated] + type = GeneratedMeshGenerator + dim = 1 + nx = '${num_node}' + xmax = '${slab_thickness}' + [] +[] + +[Problem] + type = ReferenceResidualProblem + reference_vector = 'ref' + extra_tag_vectors = 'ref' +[] + +[Kernels] + # Gas flow kernels + # Equation for D2 in enclosure upstream + [timeDerivative_upstream_D2] + type = ADTimeDerivative + variable = D2_pressure_upstream + extra_vector_tags = 'ref' + [] + [MatReaction_upstream_D2_influx_5] + type = ADMatReaction + variable = D2_pressure_upstream + v = 'D2_pressure_enclosure5' + reaction_rate = ${flow_rate_by_V} + extra_vector_tags = 'ref' + [] + [MatReaction_upstream_D2_influx_1] + type = ADMatReaction + variable = D2_pressure_upstream + v = 'D2_pressure_enclosure1' + reaction_rate = ${flow_rate_by_V} + extra_vector_tags = 'ref' + [] + [MatReaction_upstream_D2_outflux_4] + type = ADMatReaction + variable = D2_pressure_upstream + v = 'D2_pressure_upstream' + reaction_rate = -${flow_rate_by_V} + extra_vector_tags = 'ref' + [] + # Equation for enclosure downstream + [timeDerivative_D2_downstream] + type = ADTimeDerivative + variable = D2_pressure_downstream + extra_vector_tags = 'ref' + [] + [MatReaction_downstream_D2_influx_1] + type = ADMatReaction + variable = D2_pressure_downstream + v = 'D2_pressure_enclosure1' + reaction_rate = ${flow_rate_by_V} + extra_vector_tags = 'ref' + [] + [MatReaction_downstream_D2_outflux_4] + type = ADMatReaction + variable = D2_pressure_downstream + v = 'D2_pressure_downstream' + reaction_rate = -${flow_rate_by_V} + extra_vector_tags = 'ref' + [] + + # Diffusion kernels + [timeDerivative_diffusion_D] + type = ADTimeDerivative + variable = D_concentration + extra_vector_tags = 'ref' + [] + [MatDiffusion_diffusion_D] + type = ADMatDiffusion + variable = D_concentration + diffusivity = diffusivity_D + extra_vector_tags = 'ref' + [] +[] + +[Materials] + [diffusivity_D] + type = ADParsedMaterial + property_name = 'diffusivity_D' + expression = '${diffusivity_pre_D} * exp( - ${diffusivity_energy_D} / ${R} / ${temperature})' + [] +[] + +[Postprocessors] + # Pressure + [pressure_upstream_D2] + type = SideAverageValue + variable = D2_pressure_upstream + boundary = right + [] + [pressure_downstream_D2] + type = SideAverageValue + variable = D2_pressure_downstream + boundary = left + [] + # Flux + [flux_surface_right_D] + type = SideDiffusiveFluxIntegral + variable = D_concentration + diffusivity = diffusivity_D_nonAD + boundary = 'right' + execute_on = 'initial timestep_end' + outputs = 'console csv exodus' + [] + [flux_surface_left_D] + type = SideDiffusiveFluxIntegral + variable = D_concentration + diffusivity = diffusivity_D_nonAD + boundary = 'left' + execute_on = 'initial timestep_end' + outputs = 'console csv exodus' + [] +[] + +[Debug] + show_var_residual_norms = true +[] + +[Preconditioning] + [smp] + type = SMP + full = true + [] +[] + +[Executioner] + type = Transient + scheme = bdf2 + solve_type = 'NEWTON' + petsc_options_iname = '-pc_type' + petsc_options_value = 'lu' + automatic_scaling = true + compute_scaling_once = true + line_search = none + nl_rel_tol = 1e-10 + nl_abs_tol = 1e-10 + dtmax = 5 + end_time = ${simulation_time} + nl_max_its = 15 + [TimeStepper] + type = IterationAdaptiveDT + dt = 0.01 + optimal_iterations = 12 + iteration_window = 1 + growth_factor = 1.1 + cutback_factor = 0.9 + cutback_factor_at_failure = 0.9 + [] +[] + +[Outputs] + file_base = ${file_name} + exodus = true + perf_graph = true + [csv] + type = CSV + execute_on = 'initial timestep_end' + [] +[] diff --git a/test/tests/val-2e/val-2e_base_three_gases.i b/test/tests/val-2e/val-2e_base_three_gases.i new file mode 100644 index 00000000..e90107e4 --- /dev/null +++ b/test/tests/val-2e/val-2e_base_three_gases.i @@ -0,0 +1,366 @@ +# Base input file for Validation Problem #2ed 2ee +# Except for the blocks in val-2e_base.i +# Include [Variables], [AuxVariables], [AuxKernels], [Functions], +# [Kernels] for H2, HD, and H, [Materials] for H, +# [Postprocessors] for H2, HD, and H blocks + +# This input file is not meant to run on its own and is included in case-specific input files. + +# Enclosure data used in TMAP7 case +pressure_enclosure1 = '${units 1e-7 Pa}' +pressure_initial_enclosure2 = '${units 1e-7 Pa}' +pressure_initial_enclosure2_H2 = '${units 0.063 Pa}' +pressure_initial_enclosure3 = '${units 1e-20 Pa}' + +# Modeling data used in current case +slab_thickness = '${units 2.5e-5 m -> mum}' +simulation_time = '${units 1000 s}' + +# Diffusion data used in TMAP7 case +diffusivity_pre_H = '${units 3.728e-4 m^2/s -> mum^2/s}' +diffusivity_energy_H = '${units ${fparse 1315.8 * R} J/mol}' + +!include val-2e_base.i + +[Variables] + [D2_pressure_upstream] + initial_condition = '${pressure_initial_enclosure2}' + [] + [H2_pressure_upstream] + initial_condition = '${pressure_initial_enclosure2_H2}' + [] + [HD_pressure_upstream] + initial_condition = '${pressure_initial_enclosure2}' + [] + + [D2_pressure_downstream] + initial_condition = '${pressure_initial_enclosure3}' + [] + [H2_pressure_downstream] + initial_condition = '${pressure_initial_enclosure3}' + [] + [HD_pressure_downstream] + initial_condition = '${pressure_initial_enclosure3}' + [] + + [D_concentration] + initial_condition = 0 + [] + [H_concentration] + initial_condition = 0 + [] +[] + +[AuxVariables] + [D2_pressure_enclosure1] + initial_condition = '${pressure_enclosure1}' + [] + [H2_pressure_enclosure1] + initial_condition = '${pressure_enclosure1}' + [] + [HD_pressure_enclosure1] + initial_condition = '${pressure_enclosure1}' + [] + [D2_pressure_enclosure4] + initial_condition = '${pressure_enclosure4}' + [] + [H2_pressure_enclosure4] + initial_condition = '${pressure_enclosure4}' + [] + [HD_pressure_enclosure4] + initial_condition = '${pressure_enclosure4}' + [] + [D2_pressure_enclosure5] + initial_condition = 1.8421e-4 + [] + [H2_pressure_enclosure5] + initial_condition = '${pressure_initial_enclosure2_H2}' + [] + [HD_pressure_enclosure5] + initial_condition = '${pressure_enclosure4}' + [] + + [D2_partial_pressure_upstream] + initial_condition = '${fparse pressure_initial_enclosure2 + pressure_initial_enclosure2/2}' + [] + [D2_partial_pressure_downstream] + initial_condition = '${fparse pressure_initial_enclosure3 + pressure_initial_enclosure3/2}' + [] + [H2_partial_pressure_upstream] + initial_condition = '${fparse pressure_initial_enclosure2_H2 + pressure_initial_enclosure2/2}' + [] + [H2_partial_pressure_downstream] + initial_condition = '${fparse pressure_initial_enclosure3 + pressure_initial_enclosure3/2}' + [] + + [sqrt_PH2_sqrt_PD2_upstream] + [] + [sqrt_PH2_sqrt_PD2_downstream] + [] + + [HD_pressure_upstream_reference] + [] + [HD_pressure_downstream_reference] + [] +[] + +[AuxKernels] + [D2_pressure_enclosure5_kernel] + type = FunctionAux + variable = D2_pressure_enclosure5 + function = D2_pressure_enclosure5_function + [] + [H2_pressure_enclosure5_kernel] + type = FunctionAux + variable = H2_pressure_enclosure5 + function = H2_pressure_enclosure5_function + [] + + [sqrt_PH2_sqrt_PD2_upstream_kernel] + type = ParsedAux + variable = sqrt_PH2_sqrt_PD2_upstream + coupled_variables = 'D2_pressure_upstream H2_pressure_upstream' + expression = 'sqrt(D2_pressure_upstream) * sqrt(H2_pressure_upstream)' + [] + [sqrt_PH2_sqrt_PD2_downstream_kernel] + type = ParsedAux + variable = sqrt_PH2_sqrt_PD2_downstream + coupled_variables = 'D2_pressure_downstream H2_pressure_downstream' + expression = 'sqrt(D2_pressure_downstream) * sqrt(H2_pressure_downstream)' + [] + + [D2_partial_pressure_upstream_kernel] + type = ParsedAux + variable = D2_partial_pressure_upstream + coupled_variables = 'D2_pressure_upstream HD_pressure_upstream' + expression = 'D2_pressure_upstream + HD_pressure_upstream / 2' + [] + [D2_partial_pressure_downstream_kernel] + type = ParsedAux + variable = D2_partial_pressure_downstream + coupled_variables = 'D2_pressure_downstream HD_pressure_downstream' + expression = 'D2_pressure_downstream + HD_pressure_downstream / 2' + [] + [H2_partial_pressure_upstream_kernel] + type = ParsedAux + variable = H2_partial_pressure_upstream + coupled_variables = 'H2_pressure_upstream HD_pressure_upstream' + expression = 'H2_pressure_upstream + HD_pressure_upstream / 2' + [] + [H2_partial_pressure_downstream_kernel] + type = ParsedAux + variable = H2_partial_pressure_downstream + coupled_variables = 'H2_pressure_downstream HD_pressure_downstream' + expression = 'H2_pressure_downstream + HD_pressure_downstream / 2' + [] + + [HD_pressure_upstream_reference_kernel] + type = ParsedAux + variable = HD_pressure_upstream_reference + coupled_variables = 'D2_pressure_upstream H2_pressure_upstream' + expression = '2 * sqrt(D2_pressure_upstream) * sqrt(H2_pressure_upstream)' + [] + [HD_pressure_downstream_reference_kernel] + type = ParsedAux + variable = HD_pressure_downstream_reference + coupled_variables = 'D2_pressure_downstream H2_pressure_downstream' + expression = '2 * sqrt(D2_pressure_downstream) * sqrt(H2_pressure_downstream)' + [] +[] + +[Functions] + [D2_pressure_enclosure5_function] + type = ParsedFunction + expression = 'if(t < 150, 1.8421e-4, + if(t < 250, 1e-3, + if(t < 350, 3e-3, + if(t < 450, 0.009, + if(t < 550, 0.027, + if(t < 650, 0.081, + if(t < 750, 0.243, + if(t < ${simulation_time}, 0.729, 0.729))))))))' + [] + [H2_pressure_enclosure5_function] + type = ParsedFunction + expression = '${pressure_initial_enclosure2_H2}' # Pa + [] +[] + +[Kernels] + # Gas flow kernels + # Equation for D2 in enclosure upstream in val-2e_base.i + # Equation for H2 in enclosure upstream + [timeDerivative_upstream_H2] + type = ADTimeDerivative + variable = H2_pressure_upstream + extra_vector_tags = 'ref' + [] + [MatReaction_upstream_H2_influx_5] + type = ADMatReaction + variable = H2_pressure_upstream + v = 'H2_pressure_enclosure5' + reaction_rate = ${flow_rate_by_V} + extra_vector_tags = 'ref' + [] + [MatReaction_upstream_H2_influx_1] + type = ADMatReaction + variable = H2_pressure_upstream + v = 'H2_pressure_enclosure1' + reaction_rate = ${flow_rate_by_V} + extra_vector_tags = 'ref' + [] + [MatReaction_upstream_H2_outflux_4] + type = ADMatReaction + variable = H2_pressure_upstream + v = 'H2_pressure_upstream' + reaction_rate = -${flow_rate_by_V} + extra_vector_tags = 'ref' + [] + # Equation for HD in enclosure upstream + [timeDerivative_upstream_HD] + type = ADTimeDerivative + variable = HD_pressure_upstream + extra_vector_tags = 'ref' + [] + [MatReaction_upstream_HD_influx_5] + type = ADMatReaction + variable = HD_pressure_upstream + v = 'HD_pressure_enclosure5' + reaction_rate = ${flow_rate_by_V} + extra_vector_tags = 'ref' + [] + [MatReaction_upstream_HD_influx_1] + type = ADMatReaction + variable = HD_pressure_upstream + v = 'HD_pressure_enclosure1' + reaction_rate = ${flow_rate_by_V} + extra_vector_tags = 'ref' + [] + [MatReaction_upstream_HD_outflux_4] + type = ADMatReaction + variable = HD_pressure_upstream + v = 'HD_pressure_upstream' + reaction_rate = -${flow_rate_by_V} + extra_vector_tags = 'ref' + [] + + # Equation for D2 enclosure downstream in val-2e_base.i + # Equation for H2 enclosure downstream + [timeDerivative_downstream_H2] + type = ADTimeDerivative + variable = H2_pressure_downstream + extra_vector_tags = 'ref' + [] + [MatReaction_downstream_H2_influx_1] + type = ADMatReaction + variable = H2_pressure_downstream + v = 'H2_pressure_enclosure1' + reaction_rate = ${flow_rate_by_V} + extra_vector_tags = 'ref' + [] + [MatReaction_downstream_H2_outflux_4] + type = ADMatReaction + variable = H2_pressure_downstream + v = 'H2_pressure_downstream' + reaction_rate = -${flow_rate_by_V} + extra_vector_tags = 'ref' + [] + # Equation for HD enclosure downstream + [timeDerivative_downstream_HD] + type = ADTimeDerivative + variable = HD_pressure_downstream + extra_vector_tags = 'ref' + [] + [MatReaction_downstream_HD_influx_1] + type = ADMatReaction + variable = HD_pressure_downstream + v = 'HD_pressure_enclosure1' + reaction_rate = ${flow_rate_by_V} + extra_vector_tags = 'ref' + [] + [MatReaction_downstream_HD_outflux_4] + type = ADMatReaction + variable = HD_pressure_downstream + v = 'HD_pressure_downstream' + reaction_rate = -${flow_rate_by_V} + extra_vector_tags = 'ref' + [] + + # Diffusion kernels + [timeDerivative_diffusion_H] + type = ADTimeDerivative + variable = H_concentration + extra_vector_tags = 'ref' + [] + [MatDiffusion_diffusion_H] + type = ADMatDiffusion + variable = H_concentration + diffusivity = diffusivity_H + extra_vector_tags = 'ref' + [] +[] + +[Materials] + [diffusivity_H] + type = ADParsedMaterial + property_name = 'diffusivity_H' + expression = '${diffusivity_pre_H} * exp( - ${diffusivity_energy_H} / ${R} / ${temperature})' + [] + [converter_to_regular] + type = MaterialADConverter + ad_props_in = 'diffusivity_D diffusivity_H' + reg_props_out = 'diffusivity_D_nonAD diffusivity_H_nonAD' + outputs = none + [] +[] + +[Postprocessors] + # Pressure + [pressure_upstream_H2] + type = SideAverageValue + variable = H2_pressure_upstream + boundary = right + [] + [pressure_downstream_H2] + type = SideAverageValue + variable = H2_pressure_downstream + boundary = left + [] + [pressure_upstream_HD] + type = SideAverageValue + variable = HD_pressure_upstream + boundary = right + [] + [pressure_upstream_HD_reference] + type = SideAverageValue + variable = HD_pressure_upstream_reference + boundary = right + [] + [pressure_downstream_HD] + type = SideAverageValue + variable = HD_pressure_downstream + boundary = left + [] + [pressure_downstream_HD_reference] + type = SideAverageValue + variable = HD_pressure_downstream_reference + boundary = left + [] + # Flux + [flux_surface_right_H] + type = SideDiffusiveFluxIntegral + variable = H_concentration + diffusivity = diffusivity_H_nonAD + boundary = 'right' + execute_on = 'initial timestep_end' + outputs = 'console csv exodus' + [] + [flux_surface_left_H] + type = SideDiffusiveFluxIntegral + variable = H_concentration + diffusivity = diffusivity_H_nonAD + boundary = 'left' + execute_on = 'initial timestep_end' + outputs = 'console csv exodus' + [] +[] diff --git a/test/tests/val-2e/val-2ea.i b/test/tests/val-2e/val-2ea.i new file mode 100644 index 00000000..bb6bbd9f --- /dev/null +++ b/test/tests/val-2e/val-2ea.i @@ -0,0 +1,138 @@ +# Validation Problem #2ea from TMAP7's V&V document +# Deuterium permeation through 0.05-mm Pd at 825 K. +# No Soret effect, or trapping included. + +# Necessary physical and model parameters (kb, R, temperature) +!include parameters_deuterium_gas.params + +# Enclosure data used in TMAP7 case +pressure_enclosure1 = '${units 1e-6 Pa}' +pressure_initial = '${units 1e-6 Pa}' + +# Modeling data used in current case +slab_thickness = '${units 5e-5 m -> mum}' +file_name = 'val-2ea_out' +simulation_time = '${units 1900 s}' + +!include val-2e_base.i + +# Diffusion data used in TMAP7 case +solubility_exponent = 0.9297 # - +solubility_pre = '${units ${fparse 1.511e23 / 1e18} at/mum^3/Pa^0.9297}' +solubility_energy = '${units ${fparse 5918 * R} J/mol}' + +[Variables] + [D2_pressure_upstream] + initial_condition = '${pressure_initial}' + [] + [D2_pressure_downstream] + initial_condition = '${pressure_initial}' + [] + [D_concentration] + initial_condition = 0 + [] +[] + +[AuxVariables] + [D2_pressure_enclosure1] + initial_condition = '${pressure_enclosure1}' + [] + [D2_pressure_enclosure4] + initial_condition = '${pressure_enclosure4}' + [] + [D2_pressure_enclosure5] + [] +[] + +[AuxKernels] + [D2_pressure_enclosure5_kernel] + type = FunctionAux + variable = D2_pressure_enclosure5 + function = D2_pressure_enclosure5_function + [] +[] + +[Functions] + [D2_pressure_enclosure5_function] + type = ParsedFunction + expression = 'if(t < 150, 1.20e-4, + if(t < 250, 2.41e-4, + if(t < 350, 6.06e-4, + if(t < 450, 1.30e-3, + if(t < 550, 2.53e-3, + if(t < 650, 7.08e-3, + if(t < 750, 1.45e-2, + if(t < 850, 2.63e-2, + if(t < 950, 6.51e-2, + if(t < 1050, 0.116, + if(t < 1150, 0.297, + if(t < 1250, 0.760, + if(t < 1350, 1.550, + if(t < 1900, 3.370, 3.370))))))))))))))' + [] +[] + +[Kernels] + # Gas flow kernels + # Equation for enclosure upstream + [MatReaction_upstream_D2_outflux_membrane] + type = ADMatBodyForce + variable = D2_pressure_upstream + material_property = 'membrane_reaction_rate_right' + extra_vector_tags = 'ref' + [] + # Equation for enclosure downstream + [MatReaction_downstream_D2_influx_membrane] + type = ADMatBodyForce + variable = D2_pressure_downstream + material_property = 'membrane_reaction_rate_left' + extra_vector_tags = 'ref' + [] +[] + +[Materials] + [membrane_reaction_rate_right] + type = ADParsedMaterial + property_name = 'membrane_reaction_rate_right' + postprocessor_names = flux_surface_right_D + expression = 'flux_surface_right_D * ${surface_area} / ${volume_enclosure} * ${concentration_to_pressure_conversion_factor} / 2' + outputs = 'exodus' + [] + [membrane_reaction_rate_left] + type = ADParsedMaterial + property_name = 'membrane_reaction_rate_left' + postprocessor_names = flux_surface_left_D + expression = 'flux_surface_left_D * ${surface_area} / ${volume_enclosure} * ${concentration_to_pressure_conversion_factor} / 2' + outputs = 'exodus' + [] + [converter_to_regular] + type = MaterialADConverter + ad_props_in = 'diffusivity_D' + reg_props_out = 'diffusivity_D_nonAD' + outputs = none + [] +[] + +[BCs] + # The surface of the slab in contact with the source is assumed to be in equilibrium with the source enclosure + [right_diffusion] + type = EquilibriumBC + variable = D_concentration + enclosure_var = D2_pressure_upstream + boundary = 'right' + Ko = '${solubility_pre}' + activation_energy = '${solubility_energy}' + p = '${solubility_exponent}' + temperature = ${temperature} + [] + [left_diffusion] + type = EquilibriumBC + variable = D_concentration + enclosure_var = D2_pressure_downstream + boundary = 'left' + Ko = '${solubility_pre}' + activation_energy = '${solubility_energy}' + p = '${solubility_exponent}' + temperature = ${temperature} + [] +[] diff --git a/test/tests/val-2e/val-2ed.i b/test/tests/val-2e/val-2ed.i new file mode 100644 index 00000000..b0349284 --- /dev/null +++ b/test/tests/val-2e/val-2ed.i @@ -0,0 +1,208 @@ +# Validation Problem #2ed from TMAP7's V&V document +# Deuterium permeation through 0.05-mm Pd at 825 K. +# No Soret effect, or trapping included. + +# Necessary physical and model parameters (kb, R, temperature) +!include parameters_three_gases.params + +# Solubility data used in TMAP7 case +solubility_exponent = 0.9297 # - +solubility_pre = '${units ${fparse 9.355e22 / 1e18} at/mum^3/Pa^0.9297}' +solubility_energy = '${units ${fparse 5918 * R} J/mol}' + +# Modeling data used in current case +file_name = 'val-2ed_out' + +!include val-2e_base_three_gases.i + +[Kernels] + # Gas flow kernels + # Equation for D2 in enclosure upstream + [MatReaction_upstream_D2_reaction] + type = ADMatReaction + variable = D2_pressure_upstream + v = 'sqrt_PH2_sqrt_PD2_upstream' + reaction_rate = -1 + extra_vector_tags = 'ref' + [] + [MatReaction_upstream_D2_re_reaction] + type = ADMatReaction + variable = D2_pressure_upstream + v = 'HD_pressure_upstream' + reaction_rate = 0.5 + extra_vector_tags = 'ref' + [] + # Equation for H2 in enclosure upstream + [MatReaction_upstream_H2_reaction] + type = ADMatReaction + variable = H2_pressure_upstream + v = 'sqrt_PH2_sqrt_PD2_upstream' + reaction_rate = -1 + extra_vector_tags = 'ref' + [] + [MatReaction_upstream_H2_re_reaction] + type = ADMatReaction + variable = H2_pressure_upstream + v = 'HD_pressure_upstream' + reaction_rate = 0.5 + extra_vector_tags = 'ref' + [] + # Equation for HD in enclosure upstream + [MatReaction_upstream_HD_reaction] + type = ADMatReaction + variable = HD_pressure_upstream + v = 'sqrt_PH2_sqrt_PD2_upstream' + reaction_rate = 2 + extra_vector_tags = 'ref' + [] + [MatReaction_upstream_HD_re_reaction] + type = ADMatReaction + variable = HD_pressure_upstream + v = 'HD_pressure_upstream' + reaction_rate = -1 + extra_vector_tags = 'ref' + [] + # Membrane upstream + [MatReaction_upstream_outflux_membrane_D] + type = ADMatBodyForce + variable = D2_pressure_upstream + material_property = 'membrane_reaction_rate_right_D' + extra_vector_tags = 'ref' + [] + [MatReaction_upstream_outflux_membrane_H] + type = ADMatBodyForce + variable = H2_pressure_upstream + material_property = 'membrane_reaction_rate_right_H' + extra_vector_tags = 'ref' + [] + + # Equation for D2 enclosure downstream + [MatReaction_downstream_D2_reaction] + type = ADMatReaction + variable = D2_pressure_downstream + v = 'sqrt_PH2_sqrt_PD2_downstream' + reaction_rate = -1 + extra_vector_tags = 'ref' + [] + [MatReaction_downstream_D2_re_reaction] + type = ADMatReaction + variable = D2_pressure_downstream + v = 'HD_pressure_downstream' + reaction_rate = 0.5 + extra_vector_tags = 'ref' + [] + # Equation for H2 enclosure downstream + [MatReaction_downstream_H2_reaction] + type = ADMatReaction + variable = H2_pressure_downstream + v = 'sqrt_PH2_sqrt_PD2_downstream' + reaction_rate = -1 + extra_vector_tags = 'ref' + [] + [MatReaction_downstream_H2_re_reaction] + type = ADMatReaction + variable = H2_pressure_downstream + v = 'HD_pressure_downstream' + reaction_rate = 0.5 + extra_vector_tags = 'ref' + [] + # Equation for HD enclosure downstream + [MatReaction_downstream_HD_reaction] + type = ADMatReaction + variable = HD_pressure_downstream + v = 'sqrt_PH2_sqrt_PD2_downstream' + reaction_rate = 2 + extra_vector_tags = 'ref' + [] + [MatReaction_downstream_HD_re_reaction] + type = ADMatReaction + variable = HD_pressure_downstream + v = 'HD_pressure_downstream' + reaction_rate = -1 + extra_vector_tags = 'ref' + [] + # Membrane downstream + [MatReaction_downstream_influx_membrane_D] + type = ADMatBodyForce + variable = D2_pressure_downstream + material_property = 'membrane_reaction_rate_left_D' + extra_vector_tags = 'ref' + [] + [MatReaction_downstream_influx_membrane_H] + type = ADMatBodyForce + variable = H2_pressure_downstream + material_property = 'membrane_reaction_rate_left_H' + extra_vector_tags = 'ref' + [] +[] + +[Materials] + [membrane_reaction_rate_right_D] + type = ADParsedMaterial + property_name = 'membrane_reaction_rate_right_D' + postprocessor_names = flux_surface_right_D + expression = 'flux_surface_right_D * ${surface_area} / ${volume_enclosure} * ${concentration_to_pressure_conversion_factor}/2' + [] + [membrane_reaction_rate_left_D] + type = ADParsedMaterial + property_name = 'membrane_reaction_rate_left_D' + postprocessor_names = flux_surface_left_D + expression = 'flux_surface_left_D * ${surface_area} / ${volume_enclosure} * ${concentration_to_pressure_conversion_factor}/2' + [] + [membrane_reaction_rate_right_H] + type = ADParsedMaterial + property_name = 'membrane_reaction_rate_right_H' + postprocessor_names = flux_surface_right_H + expression = 'flux_surface_right_H * ${surface_area} / ${volume_enclosure} * ${concentration_to_pressure_conversion_factor}/2' + [] + [membrane_reaction_rate_left_H] + type = ADParsedMaterial + property_name = 'membrane_reaction_rate_left_H' + postprocessor_names = flux_surface_left_H + expression = 'flux_surface_left_H * ${surface_area} / ${volume_enclosure} * ${concentration_to_pressure_conversion_factor}/2' + [] +[] + +[BCs] + # The surface of the slab in contact with the source is assumed to be in equilibrium with the source enclosure + [right_diffusion_D] + type = EquilibriumBC + variable = D_concentration + enclosure_var = D2_partial_pressure_upstream + boundary = 'right' + Ko = '${solubility_pre}' + activation_energy = '${solubility_energy}' + p = '${solubility_exponent}' + temperature = ${temperature} + [] + [left_diffusion_D] + type = EquilibriumBC + variable = D_concentration + enclosure_var = D2_partial_pressure_downstream + boundary = 'left' + Ko = '${solubility_pre}' + activation_energy = '${solubility_energy}' + p = '${solubility_exponent}' + temperature = ${temperature} + [] + [right_diffusion_H] + type = EquilibriumBC + variable = H_concentration + enclosure_var = H2_partial_pressure_upstream + boundary = 'right' + Ko = '${solubility_pre}' + activation_energy = '${solubility_energy}' + p = '${solubility_exponent}' + temperature = ${temperature} + [] + [left_diffusion_H] + type = EquilibriumBC + variable = H_concentration + enclosure_var = H2_partial_pressure_downstream + boundary = 'left' + Ko = '${solubility_pre}' + activation_energy = '${solubility_energy}' + p = '${solubility_exponent}' + temperature = ${temperature} + [] +[] diff --git a/test/tests/val-2e/val-2ee.i b/test/tests/val-2e/val-2ee.i new file mode 100644 index 00000000..98470244 --- /dev/null +++ b/test/tests/val-2e/val-2ee.i @@ -0,0 +1,389 @@ +# Validation Problem #2ee from TMAP7's V&V document +# Deuterium permeation through 0.05-mm Pd at 825 K. +# No Soret effect, or trapping included. + +# Necessary physical and model parameters (kb, R, temperature) +!include parameters_three_gases.params + +# Surface reaction data used in TMAP7 case +K_r_pre_D2 = '${units ${fparse 2.502e-24 / sqrt(4 * temperature)} m^4/s -> mum^4/s}' +K_r_pre_H2 = '${units ${fparse 2.502e-24 / sqrt(2 * temperature)} m^4/s -> mum^4/s}' +K_r_pre_HD = '${units ${fparse 2.502e-24 / sqrt(3 * temperature)} m^4/s -> mum^4/s}' +K_r_energy = '${units ${fparse -11836 * R} J/mol}' +K_d_D2 = '${units ${fparse 2.1897e22 / sqrt(4 * temperature)} at/m^2/Pa -> at/mum^2/Pa}' +K_d_H2 = '${units ${fparse 2.1897e22 / sqrt(2 * temperature)} at/m^2/Pa -> at/mum^2/Pa}' +K_d_HD = '${units ${fparse 2.1897e22 / sqrt(3 * temperature)} at/m^2/Pa -> at/mum^2/Pa}' + +# Modeling data used in current case +file_name = 'val-2ee_out' + +!include val-2e_base_three_gases.i + +[Kernels] + # Gas flow kernels + # Equation for D2 in enclosure upstream + [MatReaction_upstream_D2_reaction] + type = ADMatReactionFlexible + variable = D2_pressure_upstream + vs = 'D_concentration H_concentration' + reaction_rate_name = 'K_r_HD' + coeff = '${fparse -0.5 * kb * temperature * surface_area / volume_enclosure}' + extra_vector_tags = 'ref' + [] + [MatReaction_upstream_D2_re_reaction] + type = ADMatReaction + variable = D2_pressure_upstream + v = 'HD_pressure_upstream' + reaction_rate = '${fparse 0.5 * K_d_HD * kb * temperature * surface_area / volume_enclosure}' + extra_vector_tags = 'ref' + [] + # Equation for H2 in enclosure upstream + [MatReaction_upstream_H2_reaction] + type = ADMatReactionFlexible + variable = H2_pressure_upstream + vs = 'D_concentration H_concentration' + reaction_rate_name = 'K_r_HD' + coeff = '${fparse -0.5 * kb * temperature * surface_area / volume_enclosure}' + extra_vector_tags = 'ref' + [] + [MatReaction_upstream_H2_re_reaction] + type = ADMatReaction + variable = H2_pressure_upstream + v = 'HD_pressure_upstream' + reaction_rate = '${fparse 0.5 * K_d_HD * kb * temperature * surface_area / volume_enclosure}' + extra_vector_tags = 'ref' + [] + # Equation for HD in enclosure upstream + [MatReaction_upstream_HD_reaction] + type = ADMatReactionFlexible + variable = HD_pressure_upstream + vs = 'D_concentration H_concentration' + reaction_rate_name = 'K_r_HD' + coeff = '${fparse kb * temperature * surface_area / volume_enclosure}' + extra_vector_tags = 'ref' + [] + [MatReaction_upstream_HD_re_reaction] + type = ADMatReaction + variable = HD_pressure_upstream + v = 'HD_pressure_upstream' + reaction_rate = '${fparse - K_d_HD * kb * temperature * surface_area / volume_enclosure}' + extra_vector_tags = 'ref' + [] + # Membrane upstream + [MatReaction_upstream_outflux_membrane_D2] + type = ADMatBodyForce + variable = D2_pressure_upstream + material_property = 'membrane_reaction_rate_right_D2' + extra_vector_tags = 'ref' + [] + [MatReaction_upstream_outflux_membrane_H2] + type = ADMatBodyForce + variable = H2_pressure_upstream + material_property = 'membrane_reaction_rate_right_H2' + extra_vector_tags = 'ref' + [] + [MatReaction_upstream_outflux_membrane_HD] + type = ADMatBodyForce + variable = HD_pressure_upstream + material_property = 'membrane_reaction_rate_right_HD' + extra_vector_tags = 'ref' + [] + + # Equation for D2 enclosure downstream + [MatReaction_downstream_D2_reaction] + type = ADMatReactionFlexible + variable = D2_pressure_downstream + vs = 'D_concentration H_concentration' + reaction_rate_name = 'K_r_HD' + coeff = '${fparse -0.5 * kb * temperature * surface_area / volume_enclosure}' + extra_vector_tags = 'ref' + [] + [MatReaction_downstream_D2_re_reaction] + type = ADMatReaction + variable = D2_pressure_downstream + v = 'HD_pressure_downstream' + reaction_rate = '${fparse 0.5 * K_d_HD * kb * temperature * surface_area / volume_enclosure}' + extra_vector_tags = 'ref' + [] + # Equation for H2 enclosure downstream + [MatReaction_downstream_H2_reaction] + type = ADMatReactionFlexible + variable = H2_pressure_downstream + vs = 'D_concentration H_concentration' + reaction_rate_name = 'K_r_HD' + coeff = '${fparse -0.5 * kb * temperature * surface_area / volume_enclosure}' + extra_vector_tags = 'ref' + [] + [MatReaction_downstream_H2_re_reaction] + type = ADMatReaction + variable = H2_pressure_downstream + v = 'HD_pressure_downstream' + reaction_rate = '${fparse 0.5 * K_d_HD * kb * temperature * surface_area / volume_enclosure}' + extra_vector_tags = 'ref' + [] + # Equation for HD enclosure downstream + [MatReaction_downstream_HD_reaction] + type = ADMatReactionFlexible + variable = HD_pressure_downstream + vs = 'D_concentration H_concentration' + reaction_rate_name = 'K_r_HD' + coeff = '${fparse kb * temperature * surface_area / volume_enclosure}' + extra_vector_tags = 'ref' + [] + [MatReaction_downstream_HD_re_reaction] + type = ADMatReaction + variable = HD_pressure_downstream + v = 'HD_pressure_downstream' + reaction_rate = '${fparse - K_d_HD * kb * temperature * surface_area / volume_enclosure}' + extra_vector_tags = 'ref' + [] + # Membrane downstream + [MatReaction_downstream_influx_membrane_D2] + type = ADMatBodyForce + variable = D2_pressure_downstream + material_property = 'membrane_reaction_rate_left_D2' + extra_vector_tags = 'ref' + [] + [MatReaction_downstream_influx_membrane_H2] + type = ADMatBodyForce + variable = H2_pressure_downstream + material_property = 'membrane_reaction_rate_left_H2' + extra_vector_tags = 'ref' + [] + [MatReaction_downstream_influx_membrane_HD] + type = ADMatBodyForce + variable = HD_pressure_downstream + material_property = 'membrane_reaction_rate_left_HD' + extra_vector_tags = 'ref' + [] +[] + +[Materials] + [K_r_D2] + type = ADParsedMaterial + property_name = 'K_r_D2' + expression = '${K_r_pre_D2} * exp( - ${K_r_energy} / ${R} / ${temperature})' + [] + [K_r_H2] + type = ADParsedMaterial + property_name = 'K_r_H2' + expression = '${K_r_pre_H2} * exp( - ${K_r_energy} / ${R} / ${temperature})' + [] + [K_r_HD] + type = ADParsedMaterial + property_name = 'K_r_HD' + expression = '${K_r_pre_HD} * exp( - ${K_r_energy} / ${R} / ${temperature})' + [] + [membrane_reaction_rate_right_D2] + type = ADParsedMaterial + property_name = 'membrane_reaction_rate_right_D2' + material_property_names = flux_on_right_D2 + expression = '-flux_on_right_D2 * ${surface_area} / ${volume_enclosure} * ${concentration_to_pressure_conversion_factor}' + [] + [membrane_reaction_rate_left_D2] + type = ADParsedMaterial + property_name = 'membrane_reaction_rate_left_D2' + material_property_names = flux_on_left_D2 + expression = '-flux_on_left_D2 * ${surface_area} / ${volume_enclosure} * ${concentration_to_pressure_conversion_factor}' + [] + [membrane_reaction_rate_right_H2] + type = ADParsedMaterial + property_name = 'membrane_reaction_rate_right_H2' + material_property_names = flux_on_right_H2 + expression = '-flux_on_right_H2 * ${surface_area} / ${volume_enclosure} * ${concentration_to_pressure_conversion_factor}' + [] + [membrane_reaction_rate_left_H2] + type = ADParsedMaterial + property_name = 'membrane_reaction_rate_left_H2' + material_property_names = flux_on_left_H2 + expression = '-flux_on_left_H2 * ${surface_area} / ${volume_enclosure} * ${concentration_to_pressure_conversion_factor}' + [] + [membrane_reaction_rate_right_HD] + type = ADParsedMaterial + property_name = 'membrane_reaction_rate_right_HD' + material_property_names = flux_on_right_HD + expression = '-flux_on_right_HD * ${surface_area} / ${volume_enclosure} * ${concentration_to_pressure_conversion_factor}' + [] + [membrane_reaction_rate_left_HD] + type = ADParsedMaterial + property_name = 'membrane_reaction_rate_left_HD' + material_property_names = flux_on_left_HD + expression = '-flux_on_left_HD * ${surface_area} / ${volume_enclosure} * ${concentration_to_pressure_conversion_factor}' + [] + [flux_on_left_D] + type = ADParsedMaterial + coupled_variables = 'D_concentration H_concentration D2_pressure_downstream HD_pressure_downstream' + property_name = 'flux_on_left_D' + material_property_names = 'K_r_D2 K_r_HD' + expression = '- 2 * K_r_D2 * D_concentration ^ 2 + 2 * ${K_d_D2} * D2_pressure_downstream - K_r_HD * D_concentration * H_concentration + ${K_d_HD} * HD_pressure_downstream' + outputs = 'exodus' + [] + [flux_on_right_D] + type = ADParsedMaterial + coupled_variables = 'D_concentration H_concentration D2_pressure_upstream HD_pressure_upstream' + property_name = 'flux_on_right_D' + material_property_names = 'K_r_D2 K_r_HD' + expression = '- 2 * K_r_D2 * D_concentration ^ 2 + 2 * ${K_d_D2} * D2_pressure_upstream - K_r_HD * D_concentration * H_concentration + ${K_d_HD} * HD_pressure_upstream' + outputs = 'exodus' + [] + [flux_on_left_H] + type = ADParsedMaterial + coupled_variables = 'D_concentration H_concentration H2_pressure_downstream HD_pressure_downstream' + property_name = 'flux_on_left_H' + material_property_names = 'K_r_H2 K_r_HD' + expression = '- 2 * K_r_H2 * H_concentration ^ 2 + 2 * ${K_d_H2} * H2_pressure_downstream - K_r_HD * D_concentration * H_concentration + ${K_d_HD} * HD_pressure_downstream' + outputs = 'exodus' + [] + [flux_on_right_H] + type = ADParsedMaterial + coupled_variables = 'D_concentration H_concentration H2_pressure_upstream HD_pressure_upstream' + property_name = 'flux_on_right_H' + material_property_names = 'K_r_H2 K_r_HD' + expression = '- 2 * K_r_H2 * H_concentration ^ 2 + 2 * ${K_d_H2} * H2_pressure_upstream - K_r_HD * D_concentration * H_concentration + ${K_d_HD} * HD_pressure_upstream' + outputs = 'exodus' + [] + [flux_on_left_D2] + type = ADParsedMaterial + coupled_variables = 'D_concentration D2_pressure_downstream' + property_name = 'flux_on_left_D2' + material_property_names = 'K_r_D2' + expression = '- K_r_D2 * D_concentration ^ 2 + ${K_d_D2} * D2_pressure_downstream' + outputs = 'exodus' + [] + [flux_on_left_HD] + type = ADParsedMaterial + coupled_variables = 'D_concentration H_concentration HD_pressure_downstream' + property_name = 'flux_on_left_HD' + material_property_names = 'K_r_HD' + expression = '- K_r_HD * D_concentration * H_concentration + ${K_d_HD} * HD_pressure_downstream' + outputs = 'exodus' + [] + [flux_on_left_H2] + type = ADParsedMaterial + coupled_variables = 'H_concentration H2_pressure_downstream' + property_name = 'flux_on_left_H2' + material_property_names = 'K_r_H2' + expression = '- K_r_H2 * H_concentration ^ 2 + ${K_d_H2} * H2_pressure_downstream' + outputs = 'exodus' + [] + [flux_on_right_D2] + type = ADParsedMaterial + coupled_variables = 'D_concentration D2_pressure_upstream' + property_name = 'flux_on_right_D2' + material_property_names = 'K_r_D2' + expression = '- K_r_D2 * D_concentration ^ 2 + ${K_d_D2} * D2_pressure_upstream' + outputs = 'exodus' + [] + [flux_on_right_HD] + type = ADParsedMaterial + coupled_variables = 'D_concentration H_concentration HD_pressure_upstream' + property_name = 'flux_on_right_HD' + material_property_names = 'K_r_HD' + expression = '- K_r_HD * D_concentration * H_concentration + ${K_d_HD} * HD_pressure_upstream' + outputs = 'exodus' + [] + [flux_on_right_H2] + type = ADParsedMaterial + coupled_variables = 'H_concentration H2_pressure_upstream' + property_name = 'flux_on_right_H2' + material_property_names = 'K_r_H2' + expression = '- K_r_H2 * H_concentration ^ 2 + ${K_d_H2} * H2_pressure_upstream' + outputs = 'exodus' + [] +[] + +[BCs] + # recombination BCs + [left_diffusion_D] + type = ADMatNeumannBC + variable = D_concentration + boundary = left + value = 1 + boundary_material = flux_on_left_D + [] + [right_diffusion_D] + type = ADMatNeumannBC + variable = D_concentration + boundary = right + value = 1 + boundary_material = flux_on_right_D + [] + [left_diffusion_H] + type = ADMatNeumannBC + variable = H_concentration + boundary = left + value = 1 + boundary_material = flux_on_left_H + [] + [right_diffusion_H] + type = ADMatNeumannBC + variable = H_concentration + boundary = right + value = 1 + boundary_material = flux_on_right_H + [] +[] + +[Postprocessors] + # Flux + [dcdx_right_D] + type = ADSideAverageMaterialProperty + boundary = right + property = flux_on_right_D + outputs = 'console csv exodus' + [] + [dcdx_left_D] + type = ADSideAverageMaterialProperty + boundary = left + property = flux_on_left_D + outputs = 'console csv exodus' + [] + [dcdx_right_H] + type = ADSideAverageMaterialProperty + boundary = right + property = flux_on_right_H + outputs = 'console csv exodus' + [] + [dcdx_left_H] + type = ADSideAverageMaterialProperty + boundary = left + property = flux_on_left_H + outputs = 'console csv exodus' + [] + [flux_on_left_H2] + type = ADSideAverageMaterialProperty + boundary = left + property = flux_on_left_H2 + outputs = 'console csv exodus' + [] + [flux_on_left_D2] + type = ADSideAverageMaterialProperty + boundary = left + property = flux_on_left_D2 + outputs = 'console csv exodus' + [] + [flux_on_left_HD] + type = ADSideAverageMaterialProperty + boundary = left + property = flux_on_left_HD + outputs = 'console csv exodus' + [] + [flux_on_right_H2] + type = ADSideAverageMaterialProperty + boundary = right + property = flux_on_right_H2 + outputs = 'console csv exodus' + [] + [flux_on_right_D2] + type = ADSideAverageMaterialProperty + boundary = right + property = flux_on_right_D2 + outputs = 'console csv exodus' + [] + [flux_on_right_HD] + type = ADSideAverageMaterialProperty + boundary = right + property = flux_on_right_HD + outputs = 'console csv exodus' + [] +[]