From f8fb539e42c22ee2d7835edc58084f09a1e2dac8 Mon Sep 17 00:00:00 2001 From: Lin Yang <132409718+lin-yang-ly@users.noreply.github.com> Date: Tue, 7 Jul 2026 15:35:20 -0600 Subject: [PATCH 1/2] Add val-2l PCC voltage validation case Add the val-2l validation case for BCY20 PCC membrane hydrogen permeation under applied voltage, including no-Joule and Joule-heating model inputs, Bayesian optimization coverage, compact gold data, and documentation figures. Refs #429 AI-assisted: true AI-model: GPT-5 AI-version: Codex Co-Authored-By: GPT-5 --- doc/content/bib/tmap8.bib | 84 +++ .../figures/comparison_val-2l.py | 223 ++++++ ...val-2l_pcc_voltage_transport_schematic.png | Bin 0 -> 46932 bytes .../verification_and_validation/index.md | 1 + .../verification_and_validation/val-2l.md | 150 ++++ test/tests/val-2l/bayesian_main_val2l.i | 226 ++++++ test/tests/val-2l/comparison_val-2l.py | 223 ++++++ test/tests/val-2l/gold/Lee2005_500C_FI.csv | 10 + test/tests/val-2l/gold/Lee2005_500C_VI.csv | 10 + test/tests/val-2l/gold/Lee2005_700C_FI.csv | 10 + test/tests/val-2l/gold/Lee2005_700C_VI.csv | 10 + .../val-2l/gold/val-2l_bayesian_history.csv | 21 + .../val-2l/gold/val-2l_initial_summary.csv | 11 + .../val-2l/gold/val-2l_joule_heating_out.csv | 3 + .../val-2l/gold/val-2l_joule_summary.csv | 11 + .../val-2l/gold/val-2l_optimized_summary.csv | 11 + test/tests/val-2l/gold/val-2l_out.csv | 3 + .../val-2l/gold/val-2l_parameter_sets.csv | 15 + test/tests/val-2l/parameters_initial.params | 16 + test/tests/val-2l/parameters_optimized.params | 16 + ...rameters_optimized_manuscript_table.params | 16 + test/tests/val-2l/tests | 45 ++ test/tests/val-2l/val-2l.i | 139 ++++ test/tests/val-2l/val-2l_joule_heating.i | 680 ++++++++++++++++++ .../val-2l/val-2l_joule_heating_aggregator.i | 159 ++++ test/tests/val-2l/val-2l_membrane.i | 574 +++++++++++++++ 26 files changed, 2667 insertions(+) create mode 100644 doc/content/verification_and_validation/figures/comparison_val-2l.py create mode 100644 doc/content/verification_and_validation/figures/val-2l_pcc_voltage_transport_schematic.png create mode 100644 doc/content/verification_and_validation/val-2l.md create mode 100644 test/tests/val-2l/bayesian_main_val2l.i create mode 100644 test/tests/val-2l/comparison_val-2l.py create mode 100644 test/tests/val-2l/gold/Lee2005_500C_FI.csv create mode 100644 test/tests/val-2l/gold/Lee2005_500C_VI.csv create mode 100644 test/tests/val-2l/gold/Lee2005_700C_FI.csv create mode 100644 test/tests/val-2l/gold/Lee2005_700C_VI.csv create mode 100644 test/tests/val-2l/gold/val-2l_bayesian_history.csv create mode 100644 test/tests/val-2l/gold/val-2l_initial_summary.csv create mode 100644 test/tests/val-2l/gold/val-2l_joule_heating_out.csv create mode 100644 test/tests/val-2l/gold/val-2l_joule_summary.csv create mode 100644 test/tests/val-2l/gold/val-2l_optimized_summary.csv create mode 100644 test/tests/val-2l/gold/val-2l_out.csv create mode 100644 test/tests/val-2l/gold/val-2l_parameter_sets.csv create mode 100644 test/tests/val-2l/parameters_initial.params create mode 100644 test/tests/val-2l/parameters_optimized.params create mode 100644 test/tests/val-2l/parameters_optimized_manuscript_table.params create mode 100644 test/tests/val-2l/tests create mode 100644 test/tests/val-2l/val-2l.i create mode 100644 test/tests/val-2l/val-2l_joule_heating.i create mode 100644 test/tests/val-2l/val-2l_joule_heating_aggregator.i create mode 100644 test/tests/val-2l/val-2l_membrane.i diff --git a/doc/content/bib/tmap8.bib b/doc/content/bib/tmap8.bib index 333fc918c..3f1970df1 100644 --- a/doc/content/bib/tmap8.bib +++ b/doc/content/bib/tmap8.bib @@ -799,3 +799,87 @@ @book{incropera2007fundamentals year={2007}, publisher={John Wiley \& Sons} } + +% References added for val-2l PCC membrane voltage validation. + +@article{yang2026elucidating, + title={{Elucidating hydrogen isotope transport mechanisms in proton-conducting ceramics with trapping effects using TMAP8}}, + author={Yang, Lin and Simon, Pierre-Cl{\'e}ment A and Tang, Wei and Li, Meng and Zhao, Zeyu and Ding, Dong and Fuerst, Thomas}, + journal={International Journal of Hydrogen Energy}, + volume={210}, + pages={153551}, + year={2026}, + publisher={Elsevier} +} + +@article{lee2005thin, + title={{Thin film preparation and hydrogen pumping characteristics of BaCe0. 8Y0. 2O3- $\delta$}}, + author={Lee, TH and Dorris, SE and Balachandran, U}, + journal={Solid State Ionics}, + volume={176}, + number={15-16}, + pages={1479--1484}, + year={2005}, + publisher={Elsevier} +} + +@article{lee1986protonic, + title={Protonic conduction in acceptor-doped KTaO3 crystals}, + author={Lee, Wing-Kit and Nowick, AS and Boatner, LA}, + journal={Solid State Ionics}, + volume={18}, + pages={989--993}, + year={1986}, + publisher={Elsevier} +} + +@article{mukundan1999tritium, + title={Tritium Conductivity and Isotope Effect in Proton-Conducting Perovskites}, + author={Mukundan, R and Brosha, Eric L and Birdsell, Stephen A and Costello, Alison L and Garzon, Fernando H and Willms, R Scott}, + journal={Journal of The Electrochemical Society}, + volume={146}, + number={6}, + pages={2184--2187}, + year={1999}, + publisher={The Electrochemical Society, Inc.} +} + +@article{iwahara1988proton, + title={{Proton Conduction in Sintered Oxides Based on BaCeO3}}, + author={Iwahara, H and Uchida, H and Ono, K and Ogaki, K}, + journal={Journal of the Electrochemical Society}, + volume={135}, + number={2}, + pages={529--533}, + year={1988}, + publisher={The Electrochemical Society} +} + +@incollection{holz2020analysis, + title={{Analysis of the Electrochemical Transport Properties of Doped Barium Cerate for Proton Conductivity in Low Humidity Conditions: A Review}}, + author={Holz, Laura I V and Gra{\c{c}}a, Vanessa C D and Loureiro, Francisco J A and Fagg, Duncan P}, + booktitle={Analytical Chemistry - Advancement, Perspectives and Applications}, + editor={Srivastva, Abhay Nanda}, + publisher={IntechOpen}, + year={2020}, + doi={10.5772/intechopen.93970} +} + +@article{slaughter2023moose, + title={{MOOSE Stochastic Tools: A module for performing parallel, memory-efficient in situ stochastic simulations}}, + author={Slaughter, Andrew E and Prince, Zachary M and German, Peter and Halvic, Ian and Jiang, Wen and Spencer, Benjamin W and Dhulipala, Somayajulu LN and Gaston, Derek R}, + journal={SoftwareX}, + volume={22}, + pages={101345}, + year={2023}, + publisher={Elsevier} +} + +@article{dhulipala2025moose, + title={{MOOSE ProbML: Parallelized probabilistic machine learning and uncertainty quantification for computational energy applications}}, + author={Dhulipala, Somayajulu LN and German, Peter and Che, Yifeng and Prince, Zachary M and Xie, Xianjian and Simon, Pierre-Cl{\'e}ment A and Labour{\'e}, Vincent M and Yan, Hao}, + journal={Journal of Computational Science}, + pages={102776}, + year={2025}, + publisher={Elsevier} +} diff --git a/doc/content/verification_and_validation/figures/comparison_val-2l.py b/doc/content/verification_and_validation/figures/comparison_val-2l.py new file mode 100644 index 000000000..58fdfe8b0 --- /dev/null +++ b/doc/content/verification_and_validation/figures/comparison_val-2l.py @@ -0,0 +1,223 @@ +#!/usr/bin/env python3 +"""Generate figures for val-2l from compact gold CSV files.""" + +from pathlib import Path +import csv +import math + +import matplotlib + +matplotlib.use("Agg") +import matplotlib.pyplot as plt + +EXP_CONV = 1.0 / 2.24e4 * 6.022e23 * 2 / 60 * 1e4 +R = 8.31446261815324 +N_A = 6.02214076e23 + + +def _paths(): + script_dir = Path(__file__).resolve().parent + if (script_dir / "gold").is_dir(): + return script_dir / "gold", script_dir + repo_root = script_dir.parents[3] + return repo_root / "test/tests/val-2l/gold", script_dir + + +GOLD_DIR, OUTPUT_DIR = _paths() + + +def read_csv(path): + with path.open(newline="") as stream: + return list(csv.DictReader(stream)) + + +def load_experiment(temp_label): + vi = read_csv(GOLD_DIR / f"Lee2005_{temp_label}_VI.csv") + fi = read_csv(GOLD_DIR / f"Lee2005_{temp_label}_FI.csv") + return [ + (float(v["Voltage(V)"]), float(f["Flux(cm^3/min/cm^2)"]) * EXP_CONV) + for v, f in zip(vi, fi) + ] + + +def load_summary(filename, temp_key="temperature_K"): + rows = [] + for row in read_csv(GOLD_DIR / filename): + rows.append( + { + "temperature": float(row[temp_key]), + "voltage": float(row["voltage_V"]), + "flux": float(row["flux_atoms_m2_s"]), + **row, + } + ) + return rows + + +def rmspe(sim_rows, exp_rows, temperature): + refs = exp_rows[::2] + vals = [] + for voltage, ref_flux in refs: + candidates = [ + row for row in sim_rows + if abs(row["temperature"] - temperature) < 2.0 and abs(row["voltage"] - voltage) < 0.03 + ] + if candidates: + vals.append((candidates[0]["flux"], ref_flux)) + if not vals: + return float("nan") + mean_ref = sum(ref for _, ref in vals) / len(vals) + return math.sqrt(sum((sim - ref) ** 2 for sim, ref in vals) / len(vals)) / mean_ref * 100.0 + + +def split_by_temp(rows, temp): + return sorted([row for row in rows if abs(row["temperature"] - temp) < 2.0], key=lambda row: row["voltage"]) + + +def plot_flux(summary_name, output_name, title, overlay=None, temp_key="temperature_K"): + rows = load_summary(summary_name, temp_key=temp_key) + exp_773 = load_experiment("500C") + exp_973 = load_experiment("700C") + fig, ax = plt.subplots(figsize=(6.5, 5.0)) + + for temp, color, label, exp_rows in [ + (973.0, "C1", "973 K", exp_973), + (773.0, "C0", "773 K", exp_773), + ]: + sim = split_by_temp(rows, temp) + ax.plot([r["voltage"] for r in sim], [r["flux"] for r in sim], ".-", color=color, label=f"TMAP8 {label}") + ax.plot([v for v, _ in exp_rows], [f for _, f in exp_rows], "s", color=color, fillstyle="none", label=f"Lee et al. {label}") + err = rmspe(rows, exp_rows, temp) + xpos = 0.58 if temp == 973.0 else 0.08 + ypos = 0.88 if temp == 973.0 else 0.78 + if math.isfinite(err): + ax.text(xpos, ypos, f"RMSPE {label}: {err:.2f}%", color=color, transform=ax.transAxes) + + if overlay: + over_rows = load_summary(overlay["summary"]) + sim = split_by_temp(over_rows, overlay["temperature"]) + ax.plot([r["voltage"] for r in sim], [r["flux"] for r in sim], "--", color=overlay.get("color", "C0"), label=overlay["label"]) + + ax.set_xlabel("Voltage (V)") + ax.set_ylabel(r"Hydrogen flux (atoms m$^{-2}$ s$^{-1}$)") + ax.set_title(title) + ax.grid(True, linestyle="--", color="0.75", alpha=0.5) + ax.legend(fontsize=8) + fig.tight_layout() + fig.savefig(OUTPUT_DIR / output_name, dpi=300) + plt.close(fig) + + +def plot_temperature(): + rows = load_summary("val-2l_joule_summary.csv", temp_key="temperature_nominal_K") + fig, ax = plt.subplots(figsize=(6.5, 5.0)) + for temp, color, label in [(773.0, "C0", "773 K"), (973.0, "C1", "973 K")]: + sim = split_by_temp(rows, temp) + ax.plot([r["voltage"] for r in sim], [float(r["delta_T_K"]) for r in sim], ".-", color=color, label=f"Delta T {label}") + ax.plot([r["voltage"] for r in sim], [float(r["temperature_max_K"]) - temp for r in sim], "--", color=color, label=f"Peak rise {label}") + ax.set_xlabel("Voltage (V)") + ax.set_ylabel("Temperature rise (K)") + ax.set_title("Joule-heating temperature response") + ax.grid(True, linestyle="--", color="0.75", alpha=0.5) + ax.legend(fontsize=8) + fig.tight_layout() + fig.savefig(OUTPUT_DIR / "val-2l_joule_temperature.png", dpi=300) + plt.close(fig) + + +def plot_bayesian_history(): + rows = read_csv(GOLD_DIR / "val-2l_bayesian_history.csv") + if not rows: + return + fig, ax = plt.subplots(figsize=(6.5, 4.5)) + iteration = [int(r["iteration"]) for r in rows] + best = [float(r["best_objective"]) for r in rows] + step = [float(r["best_step_objective"]) for r in rows] + ax.plot(iteration, step, ".", color="C2", label="step best") + ax.plot(iteration, best, "-", color="C0", label="best so far") + ax.set_xlabel("Bayesian optimization iteration") + ax.set_ylabel("Objective, log inverse RMSPE") + ax.grid(True, linestyle="--", color="0.75", alpha=0.5) + ax.legend() + fig.tight_layout() + fig.savefig(OUTPUT_DIR / "val-2l_bayesian_optimization.png", dpi=300) + plt.close(fig) + + +def _params(which): + data = {r["parameter"]: float(r[which]) for r in read_csv(GOLD_DIR / "val-2l_parameter_sets.csv")} + return data + + +def d_ot(params, temp): + return 2.03 * 10 ** params["diffusivity_OT_prefactor_exponent"] * math.exp(-params["diffusivity_OT_energy"] / R / temp) + + +def d_vo(params, temp): + return 1.1 * 10 ** params["diffusivity_V_O_prefactor_exponent"] * math.exp(-params["diffusivity_V_O_energy"] / R / temp) + + +def k_eq(params, temp, species): + if species == "H2": + dh, ds = params["delta_H_T2"], params["delta_S_T2"] + else: + dh, ds = params["delta_H_T2O"], params["delta_S_T2O"] + return math.exp((dh - temp * ds) / R / temp) + + +def k_forward(params, temp, species): + if species == "H2": + exponent = params["T2_reaction_forward_mol_exponent"] + energy = params["T2_reaction_forward_energy"] + else: + exponent = params["T2O_reaction_forward_mol_exponent"] + energy = params["T2O_reaction_forward_energy"] + return 8.0 * 10 ** exponent / N_A * math.exp(-energy / R / temp) + + +def plot_parameters(): + initial = _params("initial") + optimized = _params("optimized") + temps = [700.0 + i * 10.0 for i in range(41)] + xvals = [1000.0 / t for t in temps] + panels = [ + ("OH diffusivity", lambda p, t: d_ot(p, t), r"m$^2$/s"), + ("O vacancy diffusivity", lambda p, t: d_vo(p, t), r"m$^2$/s"), + ("H2 equilibrium", lambda p, t: k_eq(p, t, "H2"), "-"), + ("H2O equilibrium", lambda p, t: k_eq(p, t, "H2O"), "-"), + ("H2 forward rate", lambda p, t: k_forward(p, t, "H2"), r"m$^4$/atom/s"), + ("H2O forward rate", lambda p, t: k_forward(p, t, "H2O"), r"m$^4$/atom/s"), + ] + fig, axes = plt.subplots(2, 3, figsize=(10.5, 6.4)) + for ax, (title, func, units) in zip([a for row in axes for a in row], panels): + ax.plot(xvals, [func(initial, t) for t in temps], color="C0", label="initial") + ax.plot(xvals, [func(optimized, t) for t in temps], color="C1", label="optimized") + ax.set_yscale("log") + ax.invert_xaxis() + ax.set_title(title, fontsize=10) + ax.set_xlabel(r"1000/T (K$^{-1}$)") + ax.set_ylabel(units) + ax.grid(True, linestyle="--", color="0.8", alpha=0.5) + axes[0][0].legend(fontsize=8) + fig.tight_layout() + fig.savefig(OUTPUT_DIR / "val-2l_parameter_comparison.png", dpi=300) + plt.close(fig) + + +def main(): + plot_flux("val-2l_initial_summary.csv", "val-2l_initial_flux.png", "Initial parameter set") + plot_flux("val-2l_optimized_summary.csv", "val-2l_optimized_flux.png", "Bayesian-optimized parameter set") + plot_flux( + "val-2l_joule_summary.csv", + "val-2l_joule_flux.png", + "Optimized parameter set with Joule heating", + overlay={"summary": "val-2l_optimized_summary.csv", "temperature": 773.0, "label": "No Joule heat, 773 K", "color": "C0"}, + temp_key="temperature_nominal_K", + ) + plot_temperature() + plot_bayesian_history() + plot_parameters() + + +if __name__ == "__main__": + main() diff --git a/doc/content/verification_and_validation/figures/val-2l_pcc_voltage_transport_schematic.png b/doc/content/verification_and_validation/figures/val-2l_pcc_voltage_transport_schematic.png new file mode 100644 index 0000000000000000000000000000000000000000..2f73ec51d6f742b1eb671c449a215a014aed497e GIT binary patch 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also contains [example cases](examples/tmap_index.md), which showcase how | val-2e | [Co-permeation of H$_2$ and D$_2$ through Pd](val-2e.md) | | val-2f | [Modelling self-damaged tungsten effects on deuterium transport](val-2f.md) | | val-2g | [Deuterium Transport in Proton-Conducting Ceramics](val-2g.md) | +| val-2l | [Hydrogen Permeation Through a BCY20 Proton-Conducting Ceramic Membrane Under Applied Voltage](val-2l.md) | | val-2k | [Oxide effects on deuterium release from self-irradiated tungsten](val-2k.md) | | val-2j | [Tritium TDS from Li$_2$TiO$_3$ Solid Breeder](val-2j.md) | diff --git a/doc/content/verification_and_validation/val-2l.md b/doc/content/verification_and_validation/val-2l.md new file mode 100644 index 000000000..233d48c71 --- /dev/null +++ b/doc/content/verification_and_validation/val-2l.md @@ -0,0 +1,150 @@ +# val-2l + +# Hydrogen Permeation Through a BCY20 Proton-Conducting Ceramic Membrane Under Applied Voltage + +## Case Description + +This validation case compares a TMAP8 component-scale proton-conducting ceramic (PCC) membrane model against hydrogen permeation measurements from Lee et al. [!citep](lee2005thin). The experiments measured hydrogen flux through a BaCe$_{0.8}$Y$_{0.2}$O$_{3-\delta}$ (BCY20) membrane under applied voltages at 773 K and 973 K. Because hydrogen and tritium share similar transport mechanisms in PCC membranes, these data provide a suitable validation benchmark. Hydrogen diffusivity exceeds tritium diffusivity by a factor of $\sqrt{3}$ due to isotope mass scaling [!citep](lee1986protonic,mukundan1999tritium). + +The validation includes the voltage-driven transport model, a Bayesian optimization driver using MOOSE Stochastic Tools, and a Joule-heating extension of the membrane model. + +!media figures/val-2l_pcc_voltage_transport_schematic.png + style=width:40%;margin-bottom:2%;margin-left:auto;margin-right:auto + id=val-2l_transport_schematic + caption=Schematic for hydrogen-isotope transport in a PCC membrane. $Q$ represents hydrogen isotopes, and $O$ represents oxygen. + +## Model Description + +The hydrogen transport model is based on the PCC model from [!cite](yang2026elucidating), extended to include Nernst-Planck migration under an applied voltage and Joule heating. Hydrogen transport depends on diffusion in the material and on surface dissociation and recombination reactions. + +The surface chemical reactions using Kroger-Vink notation are + +\begin{equation} +H_2O + V_O^{\cdot\cdot} + O_O^x \rightleftharpoons 2OH_O^{\cdot}, +\end{equation} + +and + +\begin{equation} +H_2 + 2 O_O^x \rightleftharpoons 2OH_O^{\cdot} + 2 e^{\prime}. +\end{equation} + +The hydrogen transport in the PCC membrane is governed by + +\begin{equation} +\frac{\partial C^H}{\partial t} = \nabla \cdot D^H \nabla C^H + \frac{\partial}{\partial x}\left( \frac{C^H D^H F}{RT} \frac{\partial \phi}{\partial x} \right), +\end{equation} + +where $C^H$ is the concentration of mobile hydrogen, $D^H$ is the hydrogen diffusivity, and $\phi$ is the electric potential. Oxygen vacancies are also affected by the applied voltage, + +\begin{equation} +\frac{\partial C^{V_O}}{\partial t} = \nabla \cdot D^{V_O} \nabla C^{V_O} + \frac{\partial}{\partial x} \left(\frac{2 C^{V_O} D^{V_O} F}{RT} \frac{\partial \phi}{\partial x} \right), +\end{equation} + +where the factor of 2 represents the charge number of $V_O^{\cdot\cdot}$. Since ionic transport is the dominant contribution to the current density in BaCeO$_3$-based proton conductors under hydrogen environments [!citep](iwahara1988proton,holz2020analysis), electron diffusion is neglected. The electron concentration is treated as a temperature-dependent constant that affects the surface reaction balance. + +To account for Joule heating caused by ionic current through the membrane under applied voltage, the Joule-heating model couples the heat equation to the species transport equations: + +\begin{equation} +\rho c_p \frac{\partial T}{\partial t} = \nabla \cdot (\kappa \nabla T) + \dot{q}_J, +\end{equation} + +with the volumetric heating source + +\begin{equation} +\dot{q}_J = \sigma_{\mathrm{ion}} |\nabla \phi|^2. +\end{equation} + +The ionic conductivity is computed from the Nernst-Einstein relation, + +\begin{equation} +\sigma_{\mathrm{ion}} = \frac{F^2}{RT} \sum_i z_i^2 D_i C_i, +\end{equation} + +where the sum includes the hydroxyl group and oxygen vacancy contributions. Fixed-temperature boundary conditions are applied at both membrane surfaces, consistent with furnace-controlled experimental conditions. + +## Case and Model Parameters + +The simulations use a one-dimensional 10 $\mu$m membrane with 300 elements. The upstream hydrogen pressure is $8.11 \times 10^4$ Pa, and the water partial pressure is $3.04 \times 10^3$ Pa, matching Lee et al. [!citep](lee2005thin). The membrane density is 6.154 g/cm$^3$. For the Joule-heating model, the thermal conductivity is 1.05 W/(m K), based on dense BaCeO$_3$ measurements [!citep](tenevich2023mechanical), and the specific heat capacity is 120 J/(mol K), based on high-temperature calorimetry for BaCeO$_3$ [!citep](yamanaka2003thermophysical). + +!table id=val-2l_parameters caption=Experimental conditions and selected model parameters for the BCY20 membrane validation model. +| Parameter | Description | Value | Units | Reference | +| --------- | ----------- | ----- | ----- | --------- | +| $T$ | temperature | 773 and 973 | K | [!cite](lee2005thin) | +| $l$ | membrane thickness | 10 | $\mu$m | [!cite](lee2005thin) | +| $\rho$ | membrane density | 6.154 | g/cm$^3$ | [!cite](lee2005thin) | +| $P_{H_2}$ | upstream H$_2$ pressure | $8.11 \times 10^4$ | Pa | [!cite](lee2005thin) | +| $P_{H_2O}$ | H$_2$O partial pressure | $3.04 \times 10^3$ | Pa | [!cite](lee2005thin) | +| $\kappa$ | thermal conductivity | 1.05 | W/(m K) | [!cite](tenevich2023mechanical) | +| $c_p$ | specific heat capacity | 120 | J/(mol K) | [!cite](yamanaka2003thermophysical) | +| $D_0^{OH}$ | hydroxyl diffusivity base pre-exponential | 2.03 | m$^2$/s multiplier | [!cite](kreuer1999aspects) | +| $D_0^{V_O}$ | oxygen vacancy diffusivity base pre-exponential | 1.1 | m$^2$/s multiplier | [!cite](kreuer1999aspects) | + +## Bayesian Optimization + +Due to the large uncertainty in the experimental data and material parameters, this validation case includes a Bayesian optimization driver using the MOOSE Stochastic Tools Module [!citep](slaughter2023moose,dhulipala2025moose). The optimization uses a Gaussian process surrogate model with an Expected Improvement acquisition function. During optimization, the surrogate model is iteratively trained using accumulated simulation results and used to select promising parameter sets for evaluation. + +The objective function uses the RMSPE of the hydrogen flux-voltage curves at 773 K and 973 K. The two temperature conditions are evaluated simultaneously because the experiments were performed on the same BCY20 sample: + +\begin{equation} +f(x) = \log\left( \frac{1}{\mathrm{RMSPE}^{773 K}(x) + \mathrm{RMSPE}^{973 K}(x)} \right), +\end{equation} + +where $x$ is the candidate parameter set. A higher value indicates better agreement between simulation and experiment. + +The 14 optimized parameters span reaction thermodynamics, reaction kinetics, transport properties, and electron concentration. The ranges are specified in [/bayesian_main_val2l.i], and the optimized parameter include files are [/parameters_optimized.params] and [/parameters_optimized_manuscript_table.params]. + +!media comparison_val-2l.py + image_name=val-2l_bayesian_optimization.png + style=width:50%;margin-bottom:2%;margin-left:auto;margin-right:auto + id=val-2l_bayesian_optimization + caption=Evolution of the Bayesian optimization objective function for the BCY20 membrane model. + +## Results + +Initial simulations using literature-based parameter estimates reproduce the parabolic trend of flux with applied voltage at 773 K but overpredict the flux, especially at 973 K. This discrepancy reflects the large uncertainty in empirical material properties and surface reaction parameters adopted from the literature. + +!media comparison_val-2l.py + image_name=val-2l_initial_flux.png + style=width:50%;margin-bottom:2%;margin-left:auto;margin-right:auto + id=val-2l_initial_flux + caption=Hydrogen flux comparison with Lee et al. experimental data under applied voltage at 773 K and 973 K before Bayesian optimization. + +After optimization, the simulations without Joule heating align better with the experimental measurements. The remaining discrepancy at high applied voltage under 773 K may be caused by missing voltage-dependent surface kinetics or by near-surface concentration effects not captured in the simplified electron treatment. + +!media comparison_val-2l.py + image_name=val-2l_optimized_flux.png + style=width:50%;margin-bottom:2%;margin-left:auto;margin-right:auto + id=val-2l_optimized_flux + caption=Hydrogen flux comparison with Lee et al. experimental data under applied voltage at 773 K and 973 K after Bayesian optimization. + +Including Joule heating slightly increases the predicted hydrogen flux at high voltage under 773 K. This effect is modest and does not fully explain the remaining discrepancy between simulation and experiment. The temperature response is much stronger at 773 K than at 973 K because the membrane is more resistive at lower temperature. + +!media comparison_val-2l.py + image_name=val-2l_joule_flux.png + style=width:50%;margin-bottom:2%;margin-left:auto;margin-right:auto + id=val-2l_joule_flux + caption=Hydrogen flux comparison with Lee et al. experimental data using optimized parameters with Joule heating. The 773 K no-Joule-heating optimized result is included as a dashed reference. + +!media comparison_val-2l.py + image_name=val-2l_joule_temperature.png + style=width:50%;margin-bottom:2%;margin-left:auto;margin-right:auto + id=val-2l_joule_temperature + caption=Steady-state temperature rise from Joule heating as a function of applied voltage. + +The optimized material parameters change the hydrogen diffusivity, oxygen vacancy diffusivity, reaction equilibrium constants, and forward reaction rates relative to the literature-based values. These differences indicate parameter uncertainty, possible model inadequacy, or experimental uncertainty. Future work will validate the model against a broader collection of experimental data and use Bayesian inference to identify the dominant uncertainty sources [!citep](dhulipala2025moose,DHULIPALA2025155795). + +!media comparison_val-2l.py + image_name=val-2l_parameter_comparison.png + style=width:80%;margin-bottom:2%;margin-left:auto;margin-right:auto + id=val-2l_parameter_comparison + caption=Comparison of initial and optimized transport parameters as functions of inverse temperature. + +## Input Files + +The no-Joule-heating validation model is defined by [/val-2l_membrane.i] and aggregated over the ten voltage-temperature setpoints by [/val-2l.i]. The Joule-heating membrane model is defined by [/val-2l_joule_heating.i] and aggregated by [/val-2l_joule_heating_aggregator.i]. The Bayesian optimization driver is [/bayesian_main_val2l.i]. The regression tests are listed in [/tests]. The figure-generation script is [/comparison_val-2l.py] and mirrored in [comparison_val-2l.py](figures/comparison_val-2l.py) for MooseDocs figure generation. + +!alert note title=V&V versus regression cost +The full validation calculations use a 300-element membrane mesh and ten voltage-temperature setpoints, so the primary model and Bayesian optimization tests are marked as heavy. The documentation figures use compact gold CSV summaries to avoid storing large Exodus output files for this validation case. + +!bibtex bibliography diff --git a/test/tests/val-2l/bayesian_main_val2l.i b/test/tests/val-2l/bayesian_main_val2l.i new file mode 100644 index 000000000..6d5d21e93 --- /dev/null +++ b/test/tests/val-2l/bayesian_main_val2l.i @@ -0,0 +1,226 @@ +# val-2l: BCY20 hydrogen permeation under applied voltage. +# Unit system: length is converted to nm for the spatial solve, time is s, +# temperature is K, pressure is Pa, concentrations are atoms/nm^3, +# and fluxes reported by the membrane model are atoms/nm^2/s. + +# Phase 7 - 14-parameter joint Bayesian optimization (500 C + 700 C). +# RMSPE uses global normalization: sqrt(sum_sq / 10) / mean_target_flux. +# Warm-started from Phase 2 R4 optimal (5 params) + Phase 1 optimal (2 params) +# + Phase 1/2 defaults (6 fixed params) + 0 for new electron_concentration_initial_energy. +# Both 500 C and 700 C simultaneously (10 voltage points). +# 5-core run (num_parallel_proposals=5, mpiexec -n 5), 40 steps per autorun round. +# max_procs_per_app=1 enables 5-way parallel execution with mpiexec -n 5. +# Target: RMSPE < 0.20 (score > log(5) approximately 1.609). + +[StochasticTools] +[] + +# Uniform distributions for 14 parameters (warm-start +/- physically motivated bounds) +[Distributions] + [delta_H_T2O_dist] + type = Uniform + lower_bound = -165000 + upper_bound = -115000 + [] + [delta_S_T2O_dist] + type = Uniform + lower_bound = -168 + upper_bound = -100 + [] + [delta_H_T2_dist] + type = Uniform + lower_bound = -115000 + upper_bound = -50000 + [] + [delta_S_T2_dist] + type = Uniform + lower_bound = -38 + upper_bound = -30 + [] + [T2O_reaction_forward_energy_dist] + type = Uniform + lower_bound = -10000 + upper_bound = 15000 + [] + [T2O_reaction_forward_mol_exponent_dist] + type = Uniform + lower_bound = -13 + upper_bound = -6.5 + [] + [T2_reaction_forward_energy_dist] + type = Uniform + lower_bound = 5000 + upper_bound = 12000 + [] + [T2_reaction_forward_mol_exponent_dist] + type = Uniform + lower_bound = -4.5 + upper_bound = -2 + [] + [diffusivity_OT_energy_dist] + type = Uniform + lower_bound = -5000 + upper_bound = 70000 + [] + [diffusivity_OT_prefactor_exponent_dist] + type = Uniform + lower_bound = -14 + upper_bound = -5 + [] + [diffusivity_V_O_energy_dist] + type = Uniform + lower_bound = 50000 + upper_bound = 120000 + [] + [diffusivity_V_O_prefactor_exponent_dist] + type = Uniform + lower_bound = -6.5 + upper_bound = 0.6 + [] + [electron_concentration_initial_expo_dist] + type = Uniform + lower_bound = -4.5 + upper_bound = 0.5 + [] + [electron_concentration_initial_energy_dist] + type = Uniform + lower_bound = -20000 + upper_bound = 65000 + [] +[] + +# Acquisition function: Expected Improvement for optimization +[ParallelAcquisition] + [expectedimprovement] + type = ExpectedImprovement + tuning = 1.0 + [] +[] + +[Samplers] + [sample] + type = GenericActiveLearningSampler + distributions = 'delta_H_T2O_dist + delta_S_T2O_dist + delta_H_T2_dist + delta_S_T2_dist + T2O_reaction_forward_energy_dist + T2O_reaction_forward_mol_exponent_dist + T2_reaction_forward_energy_dist + T2_reaction_forward_mol_exponent_dist + diffusivity_OT_energy_dist + diffusivity_OT_prefactor_exponent_dist + diffusivity_V_O_energy_dist + diffusivity_V_O_prefactor_exponent_dist + electron_concentration_initial_expo_dist + electron_concentration_initial_energy_dist' + sorted_indices = 'conditional/sorted_indices' + num_parallel_proposals = 5 # must be >= MPI ranks to avoid GenericActiveLearner MPI deadlock + num_tries = 50000 + seed = 2403 + # initial_values = '-163837 -156.4 -59289 -36.4 10620 -10.5945 14331 -3.56 9569.299999999999 -12.4266 76832.3 -2.3516 -2.5919 0' + initial_values = '-162200.0 -166.7 -112177.032 -36.9926058 10000.0 -7 10000.0 -4 68480.23 -6 52083.55 -6 -4.1 0' + max_procs_per_row = 1 + execute_on = PRE_MULTIAPP_SETUP + [] +[] + +[MultiApps] + [sub] + type = SamplerFullSolveMultiApp + input_files = 'val-2l.i' + sampler = sample + mode = batch-reset + max_procs_per_app = 1 + ignore_solve_not_converge = true + [] +[] + +[Transfers] + [reporter_transfer] + type = SamplerReporterTransfer + from_reporter = 'pp_log_inverse_error/value' + stochastic_reporter = 'constant' + from_multi_app = sub + sampler = sample + [] +[] + +[Controls] + [cmdline] + type = MultiAppSamplerControl + multi_app = sub + sampler = sample + param_names = 'delta_H_T2O + delta_S_T2O + delta_H_T2 + delta_S_T2 + T2O_reaction_forward_energy + T2O_reaction_forward_mol_exponent + T2_reaction_forward_energy + T2_reaction_forward_mol_exponent + diffusivity_OT_energy + diffusivity_OT_prefactor_exponent + diffusivity_V_O_energy + diffusivity_V_O_prefactor_exponent + electron_concentration_initial_expo + electron_concentration_initial_energy' + [] +[] + +[Reporters] + [constant] + type = StochasticReporter + [] + [conditional] + type = GenericActiveLearner + output_value = constant/reporter_transfer:pp_log_inverse_error:value + sampler = sample + al_gp = GP_al_trainer + gp_evaluator = GP_eval + acquisition = 'expectedimprovement' + [] +[] + +[Trainers] + [GP_al_trainer] + type = ActiveLearningGaussianProcess + covariance_function = 'covar' + standardize_params = 'true' + standardize_data = 'true' + tune_parameters = 'covar:signal_variance covar:length_factor' + num_iters = 1000 + learning_rate = 0.025 + show_every_nth_iteration = 10 + batch_size = 100 + [] +[] + +[Surrogates] + [GP_eval] + type = GaussianProcessSurrogate + trainer = GP_al_trainer + [] +[] + +[Covariance] + [covar] + type = SquaredExponentialCovariance + signal_variance = 1.0 + noise_variance = 1e-2 # 4.0 + length_factor = '10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 0.1 1.0 10.0 10.0 10.0' # '0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5' + [] +[] + +[Executioner] + type = Transient + num_steps = 20 +[] + +[Outputs] + file_base = 'bayesian_val2l_results/val-2l_bayesian_out' + [out] + type = JSON + execute_system_information_on = NONE + [] +[] diff --git a/test/tests/val-2l/comparison_val-2l.py b/test/tests/val-2l/comparison_val-2l.py new file mode 100644 index 000000000..58fdfe8b0 --- /dev/null +++ b/test/tests/val-2l/comparison_val-2l.py @@ -0,0 +1,223 @@ +#!/usr/bin/env python3 +"""Generate figures for val-2l from compact gold CSV files.""" + +from pathlib import Path +import csv +import math + +import matplotlib + +matplotlib.use("Agg") +import matplotlib.pyplot as plt + +EXP_CONV = 1.0 / 2.24e4 * 6.022e23 * 2 / 60 * 1e4 +R = 8.31446261815324 +N_A = 6.02214076e23 + + +def _paths(): + script_dir = Path(__file__).resolve().parent + if (script_dir / "gold").is_dir(): + return script_dir / "gold", script_dir + repo_root = script_dir.parents[3] + return repo_root / "test/tests/val-2l/gold", script_dir + + +GOLD_DIR, OUTPUT_DIR = _paths() + + +def read_csv(path): + with path.open(newline="") as stream: + return list(csv.DictReader(stream)) + + +def load_experiment(temp_label): + vi = read_csv(GOLD_DIR / f"Lee2005_{temp_label}_VI.csv") + fi = read_csv(GOLD_DIR / f"Lee2005_{temp_label}_FI.csv") + return [ + (float(v["Voltage(V)"]), float(f["Flux(cm^3/min/cm^2)"]) * EXP_CONV) + for v, f in zip(vi, fi) + ] + + +def load_summary(filename, temp_key="temperature_K"): + rows = [] + for row in read_csv(GOLD_DIR / filename): + rows.append( + { + "temperature": float(row[temp_key]), + "voltage": float(row["voltage_V"]), + "flux": float(row["flux_atoms_m2_s"]), + **row, + } + ) + return rows + + +def rmspe(sim_rows, exp_rows, temperature): + refs = exp_rows[::2] + vals = [] + for voltage, ref_flux in refs: + candidates = [ + row for row in sim_rows + if abs(row["temperature"] - temperature) < 2.0 and abs(row["voltage"] - voltage) < 0.03 + ] + if candidates: + vals.append((candidates[0]["flux"], ref_flux)) + if not vals: + return float("nan") + mean_ref = sum(ref for _, ref in vals) / len(vals) + return math.sqrt(sum((sim - ref) ** 2 for sim, ref in vals) / len(vals)) / mean_ref * 100.0 + + +def split_by_temp(rows, temp): + return sorted([row for row in rows if abs(row["temperature"] - temp) < 2.0], key=lambda row: row["voltage"]) + + +def plot_flux(summary_name, output_name, title, overlay=None, temp_key="temperature_K"): + rows = load_summary(summary_name, temp_key=temp_key) + exp_773 = load_experiment("500C") + exp_973 = load_experiment("700C") + fig, ax = plt.subplots(figsize=(6.5, 5.0)) + + for temp, color, label, exp_rows in [ + (973.0, "C1", "973 K", exp_973), + (773.0, "C0", "773 K", exp_773), + ]: + sim = split_by_temp(rows, temp) + ax.plot([r["voltage"] for r in sim], [r["flux"] for r in sim], ".-", color=color, label=f"TMAP8 {label}") + ax.plot([v for v, _ in exp_rows], [f for _, f in exp_rows], "s", color=color, fillstyle="none", label=f"Lee et al. {label}") + err = rmspe(rows, exp_rows, temp) + xpos = 0.58 if temp == 973.0 else 0.08 + ypos = 0.88 if temp == 973.0 else 0.78 + if math.isfinite(err): + ax.text(xpos, ypos, f"RMSPE {label}: {err:.2f}%", color=color, transform=ax.transAxes) + + if overlay: + over_rows = load_summary(overlay["summary"]) + sim = split_by_temp(over_rows, overlay["temperature"]) + ax.plot([r["voltage"] for r in sim], [r["flux"] for r in sim], "--", color=overlay.get("color", "C0"), label=overlay["label"]) + + ax.set_xlabel("Voltage (V)") + ax.set_ylabel(r"Hydrogen flux (atoms m$^{-2}$ s$^{-1}$)") + ax.set_title(title) + ax.grid(True, linestyle="--", color="0.75", alpha=0.5) + ax.legend(fontsize=8) + fig.tight_layout() + fig.savefig(OUTPUT_DIR / output_name, dpi=300) + plt.close(fig) + + +def plot_temperature(): + rows = load_summary("val-2l_joule_summary.csv", temp_key="temperature_nominal_K") + fig, ax = plt.subplots(figsize=(6.5, 5.0)) + for temp, color, label in [(773.0, "C0", "773 K"), (973.0, "C1", "973 K")]: + sim = split_by_temp(rows, temp) + ax.plot([r["voltage"] for r in sim], [float(r["delta_T_K"]) for r in sim], ".-", color=color, label=f"Delta T {label}") + ax.plot([r["voltage"] for r in sim], [float(r["temperature_max_K"]) - temp for r in sim], "--", color=color, label=f"Peak rise {label}") + ax.set_xlabel("Voltage (V)") + ax.set_ylabel("Temperature rise (K)") + ax.set_title("Joule-heating temperature response") + ax.grid(True, linestyle="--", color="0.75", alpha=0.5) + ax.legend(fontsize=8) + fig.tight_layout() + fig.savefig(OUTPUT_DIR / "val-2l_joule_temperature.png", dpi=300) + plt.close(fig) + + +def plot_bayesian_history(): + rows = read_csv(GOLD_DIR / "val-2l_bayesian_history.csv") + if not rows: + return + fig, ax = plt.subplots(figsize=(6.5, 4.5)) + iteration = [int(r["iteration"]) for r in rows] + best = [float(r["best_objective"]) for r in rows] + step = [float(r["best_step_objective"]) for r in rows] + ax.plot(iteration, step, ".", color="C2", label="step best") + ax.plot(iteration, best, "-", color="C0", label="best so far") + ax.set_xlabel("Bayesian optimization iteration") + ax.set_ylabel("Objective, log inverse RMSPE") + ax.grid(True, linestyle="--", color="0.75", alpha=0.5) + ax.legend() + fig.tight_layout() + fig.savefig(OUTPUT_DIR / "val-2l_bayesian_optimization.png", dpi=300) + plt.close(fig) + + +def _params(which): + data = {r["parameter"]: float(r[which]) for r in read_csv(GOLD_DIR / "val-2l_parameter_sets.csv")} + return data + + +def d_ot(params, temp): + return 2.03 * 10 ** params["diffusivity_OT_prefactor_exponent"] * math.exp(-params["diffusivity_OT_energy"] / R / temp) + + +def d_vo(params, temp): + return 1.1 * 10 ** params["diffusivity_V_O_prefactor_exponent"] * math.exp(-params["diffusivity_V_O_energy"] / R / temp) + + +def k_eq(params, temp, species): + if species == "H2": + dh, ds = params["delta_H_T2"], params["delta_S_T2"] + else: + dh, ds = params["delta_H_T2O"], params["delta_S_T2O"] + return math.exp((dh - temp * ds) / R / temp) + + +def k_forward(params, temp, species): + if species == "H2": + exponent = params["T2_reaction_forward_mol_exponent"] + energy = params["T2_reaction_forward_energy"] + else: + exponent = params["T2O_reaction_forward_mol_exponent"] + energy = params["T2O_reaction_forward_energy"] + return 8.0 * 10 ** exponent / N_A * math.exp(-energy / R / temp) + + +def plot_parameters(): + initial = _params("initial") + optimized = _params("optimized") + temps = [700.0 + i * 10.0 for i in range(41)] + xvals = [1000.0 / t for t in temps] + panels = [ + ("OH diffusivity", lambda p, t: d_ot(p, t), r"m$^2$/s"), + ("O vacancy diffusivity", lambda p, t: d_vo(p, t), r"m$^2$/s"), + ("H2 equilibrium", lambda p, t: k_eq(p, t, "H2"), "-"), + ("H2O equilibrium", lambda p, t: k_eq(p, t, "H2O"), "-"), + ("H2 forward rate", lambda p, t: k_forward(p, t, "H2"), r"m$^4$/atom/s"), + ("H2O forward rate", lambda p, t: k_forward(p, t, "H2O"), r"m$^4$/atom/s"), + ] + fig, axes = plt.subplots(2, 3, figsize=(10.5, 6.4)) + for ax, (title, func, units) in zip([a for row in axes for a in row], panels): + ax.plot(xvals, [func(initial, t) for t in temps], color="C0", label="initial") + ax.plot(xvals, [func(optimized, t) for t in temps], color="C1", label="optimized") + ax.set_yscale("log") + ax.invert_xaxis() + ax.set_title(title, fontsize=10) + ax.set_xlabel(r"1000/T (K$^{-1}$)") + ax.set_ylabel(units) + ax.grid(True, linestyle="--", color="0.8", alpha=0.5) + axes[0][0].legend(fontsize=8) + fig.tight_layout() + fig.savefig(OUTPUT_DIR / "val-2l_parameter_comparison.png", dpi=300) + plt.close(fig) + + +def main(): + plot_flux("val-2l_initial_summary.csv", "val-2l_initial_flux.png", "Initial parameter set") + plot_flux("val-2l_optimized_summary.csv", "val-2l_optimized_flux.png", "Bayesian-optimized parameter set") + plot_flux( + "val-2l_joule_summary.csv", + "val-2l_joule_flux.png", + "Optimized parameter set with Joule heating", + overlay={"summary": "val-2l_optimized_summary.csv", "temperature": 773.0, "label": "No Joule heat, 773 K", "color": "C0"}, + temp_key="temperature_nominal_K", + ) + plot_temperature() + plot_bayesian_history() + plot_parameters() + + +if __name__ == "__main__": + main() diff --git a/test/tests/val-2l/gold/Lee2005_500C_FI.csv b/test/tests/val-2l/gold/Lee2005_500C_FI.csv new file mode 100644 index 000000000..3a4ad54d6 --- /dev/null +++ b/test/tests/val-2l/gold/Lee2005_500C_FI.csv @@ -0,0 +1,10 @@ +Current(A/cm^2),Flux(cm^3/min/cm^2) +0.09141735041024615, 0.6218274111675122 +0.1813838302981789, 1.2369488820603363 +0.36396838102861717, 2.5568307216949897 +0.7273113868320993, 5.3385650985518565 +0.9087077246347809, 6.716508497020525 +1.0908169901941165, 8.154805357961393 +1.2720757454472684, 9.532621428450163 +1.5469406643986392, 11.52046585063579 +1.818616169701821, 13.414087567696043 \ No newline at end of file diff --git a/test/tests/val-2l/gold/Lee2005_500C_VI.csv b/test/tests/val-2l/gold/Lee2005_500C_VI.csv new file mode 100644 index 000000000..4b0511445 --- /dev/null +++ b/test/tests/val-2l/gold/Lee2005_500C_VI.csv @@ -0,0 +1,10 @@ +Current(A/cm^2),Voltage(V) +0.09195056529041638, 0.2528561064472667 +0.18180792659998496, 0.5518045490421181 +0.3627635306209421, 0.88369488093245 +0.7277832092451931, 1.228388860985546 +0.909227645333534, 1.3639034384890738 +1.0910606402446668, 1.519380864684732 +1.2735328770900705, 1.6671250787272887 +1.5474041763806372, 1.8229692345714446 +1.8187811787119903, 1.963346966109397 \ No newline at end of file diff --git a/test/tests/val-2l/gold/Lee2005_700C_FI.csv b/test/tests/val-2l/gold/Lee2005_700C_FI.csv new file mode 100644 index 000000000..3a8108ff1 --- /dev/null +++ b/test/tests/val-2l/gold/Lee2005_700C_FI.csv @@ -0,0 +1,10 @@ +Current(A/cm^2),Flux(cm^3/min/cm^2) +0.10208393762690164, 0.8159052568221696 +0.20724352113943928, 1.607989081136986 +0.4129742245871633, 3.1612566865319893 +0.6178172416207404, 4.716940344690194 +0.824560657738125, 6.284704266664406 +1.0329419178027386, 7.812794059053417 +1.3411816481461107, 10.201125795813871 +1.6512717670710848, 12.575215537338611 +2.064983646565779, 15.544671543984876 \ No newline at end of file diff --git a/test/tests/val-2l/gold/Lee2005_700C_VI.csv b/test/tests/val-2l/gold/Lee2005_700C_VI.csv new file mode 100644 index 000000000..61b4e67e9 --- /dev/null +++ b/test/tests/val-2l/gold/Lee2005_700C_VI.csv @@ -0,0 +1,10 @@ +Current(A/cm^2),Voltage(V) +0.10354651512418064, 0.03332748850295297 +0.20666706757271433, 0.10156853993480358 +0.4122942850842905, 0.20215275729873194 +0.62010142923006, 0.3336136195174827 +0.8265429871509612, 0.4807120597447935 +1.0331348848397377, 0.5953557509145831 +1.3420580511957023, 0.7303394518080452 +1.6507932928418225, 0.8402169494767548 +2.0632379176939883, 1.0092335036304367 \ No newline at end of file diff --git a/test/tests/val-2l/gold/val-2l_bayesian_history.csv b/test/tests/val-2l/gold/val-2l_bayesian_history.csv new file mode 100644 index 000000000..e20ce094d --- /dev/null +++ b/test/tests/val-2l/gold/val-2l_bayesian_history.csv @@ -0,0 +1,21 @@ +iteration,best_step_objective,best_objective +1,-4.316250558387e+00,-4.316250558387e+00 +2,-3.095862552764e-02,-3.095862552764e-02 +3,-6.045265262499e-01,-3.095862552764e-02 +4,-1.776226854705e-01,-3.095862552764e-02 +5,-2.078811255613e-01,-3.095862552764e-02 +6,-2.029379666800e-01,-3.095862552764e-02 +7,-3.270231381510e-02,-3.095862552764e-02 +8,-2.073219746140e-01,-3.095862552764e-02 +9,-1.976802368833e-01,-3.095862552764e-02 +10,-2.077031121510e-01,-3.095862552764e-02 +11,2.118004316510e-01,2.118004316510e-01 +12,-2.080904185965e-01,2.118004316510e-01 +13,-2.080342319987e-01,2.118004316510e-01 +14,-1.443282460440e+00,2.118004316510e-01 +15,2.111226001064e-01,2.118004316510e-01 +16,-2.076687861796e-01,2.118004316510e-01 +17,-2.074749930210e-01,2.118004316510e-01 +18,-1.615918270406e-01,2.118004316510e-01 +19,-2.072116035859e-01,2.118004316510e-01 +20,-5.690857212113e-02,2.118004316510e-01 diff --git a/test/tests/val-2l/gold/val-2l_initial_summary.csv b/test/tests/val-2l/gold/val-2l_initial_summary.csv new file mode 100644 index 000000000..944aa9816 --- /dev/null +++ b/test/tests/val-2l/gold/val-2l_initial_summary.csv @@ -0,0 +1,11 @@ +case,source_file,temperature_K,voltage_V,flux_atoms_m2_s +initial,compare_initial_sub0.csv,773,0.25285610644727,8.264088704272101e+21 +initial,compare_initial_sub1.csv,773,0.88369488093245,5.253673696240700e+22 +initial,compare_initial_sub2.csv,773,1.3639034384891,1.005355282608500e+23 +initial,compare_initial_sub3.csv,773,1.6671250787273,1.357217560017700e+23 +initial,compare_initial_sub4.csv,773,1.9633469661094,1.733025364592800e+23 +initial,compare_initial_sub5.csv,973,0.033327488502953,1.881303584084300e+23 +initial,compare_initial_sub6.csv,973,0.20215275729873,1.042150352754700e+24 +initial,compare_initial_sub7.csv,973,0.48071205974479,3.486156730430300e+24 +initial,compare_initial_sub8.csv,973,0.73033945180805,6.485710668604799e+24 +initial,compare_initial_sub9.csv,973,1.0092335036304,1.049947737831300e+25 diff --git a/test/tests/val-2l/gold/val-2l_joule_heating_out.csv b/test/tests/val-2l/gold/val-2l_joule_heating_out.csv new file mode 100644 index 000000000..eb89023ab --- /dev/null +++ b/test/tests/val-2l/gold/val-2l_joule_heating_out.csv @@ -0,0 +1,3 @@ +time,combined_relative_error_sq,pp_RMSPE,pp_log_inverse_error +0,0.22481272817032,0,0 +1,0.22481272817032,0.1499375630622,1.8975363177924 diff --git a/test/tests/val-2l/gold/val-2l_joule_summary.csv b/test/tests/val-2l/gold/val-2l_joule_summary.csv new file mode 100644 index 000000000..34332c45b --- /dev/null +++ b/test/tests/val-2l/gold/val-2l_joule_summary.csv @@ -0,0 +1,11 @@ +case,source_file,temperature_nominal_K,temperature_average_K,temperature_min_K,temperature_max_K,delta_T_K,voltage_V,flux_atoms_m2_s +optimized_joule_heat,jh_500C_V0.csv,773,774.013603418,773.004252231,774.519914813,1.51566258269,0.25285610644727,4.357891982749000e+21 +optimized_joule_heat,jh_500C_V1.csv,773,785.082496784,773.050413796,791.122047047,18.0716332505,0.88369488093245,2.758198446799900e+22 +optimized_joule_heat,jh_500C_V2.csv,773,801.548872008,773.118576923,815.820103495,42.7015265719,1.3639034384891,5.274495746909100e+22 +optimized_joule_heat,jh_500C_V3.csv,773,815.507630332,773.176066808,836.756099439,63.5800326315,1.6671250787273,7.120539594539899e+22 +optimized_joule_heat,jh_500C_V4.csv,773,831.805601767,773.24294453,861.199203339,87.9562588087,1.9633469661094,9.093687151485799e+22 +optimized_joule_heat,jh_700C_V5.csv,973,973.068385886,973.000258694,973.102671418,0.1024127246,0.033327488502953,6.819193956169400e+21 +optimized_joule_heat,jh_700C_V6.csv,973,973.745194802,973.002147566,974.123637524,1.12148995863,0.20215275729873,2.839547497931400e+22 +optimized_joule_heat,jh_700C_V7.csv,973,974.358960666,973.003894675,974.979641024,1.97574634847,0.48071205974479,6.460613809120000e+22 +optimized_joule_heat,jh_700C_V8.csv,973,974.771564118,973.005385244,975.497098777,2.49171353333,0.73033945180805,9.890346653931899e+22 +optimized_joule_heat,jh_700C_V9.csv,973,975.20006603,973.007055396,976.061038776,3.05398337992,1.0092335036304,1.374327992190900e+23 diff --git a/test/tests/val-2l/gold/val-2l_optimized_summary.csv b/test/tests/val-2l/gold/val-2l_optimized_summary.csv new file mode 100644 index 000000000..4f9b47486 --- /dev/null +++ b/test/tests/val-2l/gold/val-2l_optimized_summary.csv @@ -0,0 +1,11 @@ +case,source_file,temperature_K,voltage_V,flux_atoms_m2_s +optimized_no_joule,nojoule_773K_flux.csv,773,0.252856106447267,4.342616798621200e+21 +optimized_no_joule,nojoule_773K_flux.csv,773,0.88369488093245,2.718614991862900e+22 +optimized_no_joule,nojoule_773K_flux.csv,773,1.36390343848907,5.158106473350300e+22 +optimized_no_joule,nojoule_773K_flux.csv,773,1.66712507872729,6.930280916286200e+22 +optimized_no_joule,nojoule_773K_flux.csv,773,1.9633469661094,8.810597967999700e+22 +optimized_no_joule,compare_phase2_sub5.csv,973,0.033327488502953,7.255889511278300e+21 +optimized_no_joule,compare_phase2_sub6.csv,973,0.20215275729873,2.898145318454500e+22 +optimized_no_joule,compare_phase2_sub7.csv,973,0.48071205974479,6.389884327129200e+22 +optimized_no_joule,compare_phase2_sub8.csv,973,0.73033945180805,9.694986917216500e+22 +optimized_no_joule,compare_phase2_sub9.csv,973,1.0092335036304,1.340913599769100e+23 diff --git a/test/tests/val-2l/gold/val-2l_out.csv b/test/tests/val-2l/gold/val-2l_out.csv new file mode 100644 index 000000000..8fabb894a --- /dev/null +++ b/test/tests/val-2l/gold/val-2l_out.csv @@ -0,0 +1,3 @@ +time,combined_relative_error_sq,pp_RMSPE,pp_log_inverse_error +0,1.5125031325949e+45,0,0 +1,1.5125031325949e+45,0.19933135799107,1.6127867234925 diff --git a/test/tests/val-2l/gold/val-2l_parameter_sets.csv b/test/tests/val-2l/gold/val-2l_parameter_sets.csv new file mode 100644 index 000000000..0fd1dfbc3 --- /dev/null +++ b/test/tests/val-2l/gold/val-2l_parameter_sets.csv @@ -0,0 +1,15 @@ +parameter,group,description,initial,optimized,manuscript_table_optimized,units +delta_H_T2O,Reaction thermodynamics,enthalpy for H2O reaction,-1.622000000000e+05,-1.544152110000e+05,-1.253430390000e+05,J/mol +delta_S_T2O,Reaction thermodynamics,entropy for H2O reaction,-1.667000000000e+02,-1.671875850000e+02,-1.010439380000e+02,J/mol/K +delta_H_T2,Reaction thermodynamics,enthalpy for H2 reaction,-1.121770320000e+05,-5.460376630000e+04,-5.121752170000e+04,J/mol +delta_S_T2,Reaction thermodynamics,entropy for H2 reaction,-3.699260580000e+01,-3.369294060000e+01,-3.332022110000e+01,J/mol/K +T2O_reaction_forward_energy,Reaction kinetics,activation energy for H2O forward reaction,1.000000000000e+04,-7.315954740000e+03,1.159394500000e+04,J/mol +T2O_reaction_forward_mol_exponent,Reaction kinetics,exponent for H2O forward pre-exponential,-7.000000000000e+00,-1.197925920000e+01,-1.289195690000e+01,- +T2_reaction_forward_energy,Reaction kinetics,activation energy for H2 forward reaction,1.000000000000e+04,5.133854780000e+03,5.293511290000e+03,J/mol +T2_reaction_forward_mol_exponent,Reaction kinetics,exponent for H2 forward pre-exponential,-4.000000000000e+00,-4.059982970000e+00,-2.575016120000e+00,- +diffusivity_OT_energy,Transport properties,activation energy for hydroxyl diffusivity,6.848023000000e+04,8.658800790000e+03,2.450201750000e+04,J/mol +diffusivity_OT_prefactor_exponent,Transport properties,exponent for hydroxyl diffusivity pre-exponential,-6.000000000000e+00,-1.260001190000e+01,-1.211547210000e+01,- +diffusivity_V_O_energy,Transport properties,activation energy for oxygen vacancy diffusivity,5.208355000000e+04,5.876589260000e+04,8.195202040000e+04,J/mol +diffusivity_V_O_prefactor_exponent,Transport properties,exponent for oxygen vacancy diffusivity pre-exponential,-6.000000000000e+00,-5.330843750000e+00,-4.008936870000e+00,- +electron_concentration_initial_expo,Electron concentration,initial electron concentration exponent,-4.100000000000e+00,4.940966860000e-01,-3.167926130000e+00,- +electron_concentration_initial_energy,Electron concentration,electron concentration activation energy,0.000000000000e+00,5.908461060000e+04,-9.448531390000e+03,J/mol diff --git a/test/tests/val-2l/parameters_initial.params b/test/tests/val-2l/parameters_initial.params new file mode 100644 index 000000000..ea7e0bc77 --- /dev/null +++ b/test/tests/val-2l/parameters_initial.params @@ -0,0 +1,16 @@ +# Initial literature-based parameters for val-2l +# Values are in the units used by val-2l_membrane.i and val-2l_joule_heating.i. +delta_H_T2O = '${units -1.62200000e+05 J/mol}' +delta_S_T2O = '${units -1.66700000e+02 J/mol/K}' +delta_H_T2 = '${units -1.12177032e+05 J/mol}' +delta_S_T2 = '${units -3.69926058e+01 J/mol/K}' +T2O_reaction_forward_energy = '${units 1.00000000e+04 J/mol}' +T2O_reaction_forward_mol_exponent = -7.00000000e+00 +T2_reaction_forward_energy = '${units 1.00000000e+04 J/mol}' +T2_reaction_forward_mol_exponent = -4.00000000e+00 +diffusivity_OT_energy = '${units 6.84802300e+04 J/mol}' +diffusivity_OT_prefactor_exponent = -6.00000000e+00 +diffusivity_V_O_energy = '${units 5.20835500e+04 J/mol}' +diffusivity_V_O_prefactor_exponent = -6.00000000e+00 +electron_concentration_initial_expo = -4.10000000e+00 +electron_concentration_initial_energy = '${units 0.00000000e+00 J/mol}' diff --git a/test/tests/val-2l/parameters_optimized.params b/test/tests/val-2l/parameters_optimized.params new file mode 100644 index 000000000..47bdaf076 --- /dev/null +++ b/test/tests/val-2l/parameters_optimized.params @@ -0,0 +1,16 @@ +# Optimized parameters used by the val-2l comparison runs +# Values are in the units used by val-2l_membrane.i and val-2l_joule_heating.i. +delta_H_T2O = '${units -1.54415211e+05 J/mol}' +delta_S_T2O = '${units -1.67187585e+02 J/mol/K}' +delta_H_T2 = '${units -5.46037663e+04 J/mol}' +delta_S_T2 = '${units -3.36929406e+01 J/mol/K}' +T2O_reaction_forward_energy = '${units -7.31595474e+03 J/mol}' +T2O_reaction_forward_mol_exponent = -1.19792592e+01 +T2_reaction_forward_energy = '${units 5.13385478e+03 J/mol}' +T2_reaction_forward_mol_exponent = -4.05998297e+00 +diffusivity_OT_energy = '${units 8.65880079e+03 J/mol}' +diffusivity_OT_prefactor_exponent = -1.26000119e+01 +diffusivity_V_O_energy = '${units 5.87658926e+04 J/mol}' +diffusivity_V_O_prefactor_exponent = -5.33084375e+00 +electron_concentration_initial_expo = 4.94096686e-01 +electron_concentration_initial_energy = '${units 5.90846106e+04 J/mol}' diff --git a/test/tests/val-2l/parameters_optimized_manuscript_table.params b/test/tests/val-2l/parameters_optimized_manuscript_table.params new file mode 100644 index 000000000..8bec94880 --- /dev/null +++ b/test/tests/val-2l/parameters_optimized_manuscript_table.params @@ -0,0 +1,16 @@ +# Optimized parameters listed in the manuscript table +# Values are in the units used by val-2l_membrane.i and val-2l_joule_heating.i. +delta_H_T2O = '${units -1.25343039e+05 J/mol}' +delta_S_T2O = '${units -1.01043938e+02 J/mol/K}' +delta_H_T2 = '${units -5.12175217e+04 J/mol}' +delta_S_T2 = '${units -3.33202211e+01 J/mol/K}' +T2O_reaction_forward_energy = '${units 1.15939450e+04 J/mol}' +T2O_reaction_forward_mol_exponent = -1.28919569e+01 +T2_reaction_forward_energy = '${units 5.29351129e+03 J/mol}' +T2_reaction_forward_mol_exponent = -2.57501612e+00 +diffusivity_OT_energy = '${units 2.45020175e+04 J/mol}' +diffusivity_OT_prefactor_exponent = -1.21154721e+01 +diffusivity_V_O_energy = '${units 8.19520204e+04 J/mol}' +diffusivity_V_O_prefactor_exponent = -4.00893687e+00 +electron_concentration_initial_expo = -3.16792613e+00 +electron_concentration_initial_energy = '${units -9.44853139e+03 J/mol}' diff --git a/test/tests/val-2l/tests b/test/tests/val-2l/tests new file mode 100644 index 000000000..f6b2dc1ad --- /dev/null +++ b/test/tests/val-2l/tests @@ -0,0 +1,45 @@ +[Tests] + design = 'EquilibriumBC.md MatDiffusion.md MatNeumannBC.md ADHeatConduction.md ADHeatConductionTimeDerivative.md ADJouleHeatingSource.md' + issues = '#429' + validation = 'val-2l.md' + [val-2l_optimized_csvdiff] + type = CSVDiff + input = 'val-2l.i' + cli_args = 'Outputs/file_base=val-2l_out' + csvdiff = val-2l_out.csv + heavy = true + requirement = 'The system shall be able to model hydrogen permeation through a BCY20 proton-conducting ceramic membrane under applied voltage using Bayesian-optimized parameters without Joule heating.' + [] + [val-2l_joule_heating_csvdiff] + type = CSVDiff + input = 'val-2l_joule_heating_aggregator.i' + cli_args = 'Outputs/file_base=val-2l_joule_heating_out' + csvdiff = val-2l_joule_heating_out.csv + heavy = true + requirement = 'The system shall be able to model hydrogen permeation through a BCY20 proton-conducting ceramic membrane under applied voltage with Joule heating enabled.' + [] + [val-2l_bayesian_json] + type = JSONDiff + input = bayesian_main_val2l.i + cli_args = "Executioner/num_steps=1 + Samplers/sample/num_parallel_proposals=2 + Samplers/sample/num_tries=100 + Trainers/GP_al_trainer/num_iters=10 + Trainers/GP_al_trainer/batch_size=20 + Outputs/file_base=bayesian_val2l_results/val-2l_bayesian_short_out" + jsondiff = bayesian_val2l_results/val-2l_bayesian_short_out.json + abs_zero = 1e-8 + rel_err = 1e-5 + skip_keys = 'acquisition_function' + max_parallel = 1 + recover = false + heavy = true + requirement = 'The system shall be able to perform a shortened Bayesian optimization study for hydrogen permeation through a BCY20 proton-conducting ceramic membrane under applied voltage.' + [] + [val-2l_comparison] + type = RunCommand + command = 'python comparison_val-2l.py' + requirement = 'The system shall be able to generate comparison plots between simulated and experimental hydrogen flux data for the val-2l BCY20 membrane validation case.' + required_python_packages = 'matplotlib' + [] +[] diff --git a/test/tests/val-2l/val-2l.i b/test/tests/val-2l/val-2l.i new file mode 100644 index 000000000..0af2a41a2 --- /dev/null +++ b/test/tests/val-2l/val-2l.i @@ -0,0 +1,139 @@ +# val-2l: BCY20 hydrogen permeation under applied voltage. +# Unit system: length is converted to nm for the spatial solve, time is s, +# temperature is K, pressure is Pa, concentrations are atoms/nm^3, +# and fluxes reported by the membrane model are atoms/nm^2/s. + +# Level 2: voltage aggregator for the val-2l no-Joule membrane model. +# Level 2: Voltage aggregator for the val-2l real (H2+H2O) LEE2005 case +# Uses the optimized parameter set for the val-2l voltage validation. +# Runs Level 3 sub-apps at 10 voltage points (5@500C + 5@700C), +# collects recombination_flux_OT_dry_right from each, +# computes combined RMSPE. + +# --- 14 optimized parameters used by the val-2l validation runs --- +delta_H_T2O = -1.54415211e+05 +delta_S_T2O = -1.67187585e+02 +delta_H_T2 = -5.46037663e+04 +delta_S_T2 = -3.36929406e+01 +T2O_reaction_forward_energy = -7.31595474e+03 +T2O_reaction_forward_mol_exponent = -1.19792592e+01 +T2_reaction_forward_energy = 5.13385478e+03 +T2_reaction_forward_mol_exponent = -4.05998297e+00 +diffusivity_OT_energy = 8.65880079e+03 +diffusivity_OT_prefactor_exponent = -1.26000119e+01 +diffusivity_V_O_energy = 5.87658926e+04 +diffusivity_V_O_prefactor_exponent = -5.33084375e+00 +electron_concentration_initial_expo = 4.94096686e-01 +electron_concentration_initial_energy = 5.90846106e+04 + +# Experimental target flux values for recombination_flux_OT_dry_right +# NOTE: These must be in the same units as the simulation output. + +# Physics parameters +molar_volume = '${units 2.24e4 cm^3/mol}' +N_A = '${units 6.022e23 at/mol}' # H2/mol + +# 500C target data (rows 1,3,5,7,9 from Lee2005_500C gold files) +target_voltage_V0 = '${units 0.2528561064472667 V}' +target_voltage_V1 = '${units 0.88369488093245 V}' +target_voltage_V2 = '${units 1.3639034384890738 V}' +target_voltage_V3 = '${units 1.6671250787272887 V}' +target_voltage_V4 = '${units 1.963346966109397 V}' + +target_flux_V0 = '${units ${fparse 0.6218274111675122 / molar_volume * N_A * 2 / 60 * 1e4} at/m^2/s}' # cm^3/min/cm^2 -> atoms/m^2/s +target_flux_V1 = '${units ${fparse 2.5568307216949897 / molar_volume * N_A * 2 / 60 * 1e4} at/m^2/s}' # cm^3/min/cm^2 -> atoms/m^2/s +target_flux_V2 = '${units ${fparse 6.716508497020525 / molar_volume * N_A * 2 / 60 * 1e4} at/m^2/s}' # cm^3/min/cm^2 -> atoms/m^2/s +target_flux_V3 = '${units ${fparse 9.532621428450163 / molar_volume * N_A * 2 / 60 * 1e4} at/m^2/s}' # cm^3/min/cm^2 -> atoms/m^2/s +target_flux_V4 = '${units ${fparse 13.414087567696043 / molar_volume * N_A * 2 / 60 * 1e4} at/m^2/s}' # cm^3/min/cm^2 -> atoms/m^2/s + +# 700C target data (rows 1,3,5,7,9 from Lee2005_700C gold files) +target_voltage_V5 = '${units 0.03332748850295297 V}' +target_voltage_V6 = '${units 0.20215275729873194 V}' +target_voltage_V7 = '${units 0.4807120597447935 V}' +target_voltage_V8 = '${units 0.7303394518080452 V}' +target_voltage_V9 = '${units 1.0092335036304367 V}' + +target_flux_V5 = '${units ${fparse 0.8159052568221696 / molar_volume * N_A * 2 / 60 * 1e4} at/m^2/s}' +target_flux_V6 = '${units ${fparse 3.1612566865319893 / molar_volume * N_A * 2 / 60 * 1e4} at/m^2/s}' +target_flux_V7 = '${units ${fparse 6.284704266664406 / molar_volume * N_A * 2 / 60 * 1e4} at/m^2/s}' +target_flux_V8 = '${units ${fparse 10.201125795813871 / molar_volume * N_A * 2 / 60 * 1e4} at/m^2/s}' +target_flux_V9 = '${units ${fparse 15.544671543984876 / molar_volume * N_A * 2 / 60 * 1e4} at/m^2/s}' + +mean_target_flux = '${fparse (target_flux_V0 + target_flux_V1 + target_flux_V2 + target_flux_V3 + target_flux_V4 + target_flux_V5 + target_flux_V6 + target_flux_V7 + target_flux_V8 + target_flux_V9) / 10}' + +[Mesh] + [gmg] + type = GeneratedMeshGenerator + dim = 1 + nx = 1 + [] +[] + +[Problem] + solve = false + kernel_coverage_check = false +[] + +[Executioner] + type = Steady +[] + +[MultiApps] + [sub] + type = FullSolveMultiApp + input_files = 'val-2l_membrane.i' + positions = '0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0' + cli_args = 'V_current=${target_voltage_V0};target_flux=${target_flux_V0};delta_H_T2O=${delta_H_T2O};delta_S_T2O=${delta_S_T2O};delta_H_T2=${delta_H_T2};delta_S_T2=${delta_S_T2};T2O_reaction_forward_mol_exponent=${T2O_reaction_forward_mol_exponent};T2O_reaction_forward_energy=${T2O_reaction_forward_energy};T2_reaction_forward_mol_exponent=${T2_reaction_forward_mol_exponent};T2_reaction_forward_energy=${T2_reaction_forward_energy};diffusivity_OT_prefactor_exponent=${diffusivity_OT_prefactor_exponent};diffusivity_OT_energy=${diffusivity_OT_energy};diffusivity_V_O_prefactor_exponent=${diffusivity_V_O_prefactor_exponent};diffusivity_V_O_energy=${diffusivity_V_O_energy};electron_concentration_initial_expo=${electron_concentration_initial_expo};electron_concentration_initial_energy=${electron_concentration_initial_energy};Outputs/csv/enable=false + V_current=${target_voltage_V1};target_flux=${target_flux_V1};delta_H_T2O=${delta_H_T2O};delta_S_T2O=${delta_S_T2O};delta_H_T2=${delta_H_T2};delta_S_T2=${delta_S_T2};T2O_reaction_forward_mol_exponent=${T2O_reaction_forward_mol_exponent};T2O_reaction_forward_energy=${T2O_reaction_forward_energy};T2_reaction_forward_mol_exponent=${T2_reaction_forward_mol_exponent};T2_reaction_forward_energy=${T2_reaction_forward_energy};diffusivity_OT_prefactor_exponent=${diffusivity_OT_prefactor_exponent};diffusivity_OT_energy=${diffusivity_OT_energy};diffusivity_V_O_prefactor_exponent=${diffusivity_V_O_prefactor_exponent};diffusivity_V_O_energy=${diffusivity_V_O_energy};electron_concentration_initial_expo=${electron_concentration_initial_expo};electron_concentration_initial_energy=${electron_concentration_initial_energy};Outputs/csv/enable=false + V_current=${target_voltage_V2};target_flux=${target_flux_V2};delta_H_T2O=${delta_H_T2O};delta_S_T2O=${delta_S_T2O};delta_H_T2=${delta_H_T2};delta_S_T2=${delta_S_T2};T2O_reaction_forward_mol_exponent=${T2O_reaction_forward_mol_exponent};T2O_reaction_forward_energy=${T2O_reaction_forward_energy};T2_reaction_forward_mol_exponent=${T2_reaction_forward_mol_exponent};T2_reaction_forward_energy=${T2_reaction_forward_energy};diffusivity_OT_prefactor_exponent=${diffusivity_OT_prefactor_exponent};diffusivity_OT_energy=${diffusivity_OT_energy};diffusivity_V_O_prefactor_exponent=${diffusivity_V_O_prefactor_exponent};diffusivity_V_O_energy=${diffusivity_V_O_energy};electron_concentration_initial_expo=${electron_concentration_initial_expo};electron_concentration_initial_energy=${electron_concentration_initial_energy};Outputs/csv/enable=false + V_current=${target_voltage_V3};target_flux=${target_flux_V3};delta_H_T2O=${delta_H_T2O};delta_S_T2O=${delta_S_T2O};delta_H_T2=${delta_H_T2};delta_S_T2=${delta_S_T2};T2O_reaction_forward_mol_exponent=${T2O_reaction_forward_mol_exponent};T2O_reaction_forward_energy=${T2O_reaction_forward_energy};T2_reaction_forward_mol_exponent=${T2_reaction_forward_mol_exponent};T2_reaction_forward_energy=${T2_reaction_forward_energy};diffusivity_OT_prefactor_exponent=${diffusivity_OT_prefactor_exponent};diffusivity_OT_energy=${diffusivity_OT_energy};diffusivity_V_O_prefactor_exponent=${diffusivity_V_O_prefactor_exponent};diffusivity_V_O_energy=${diffusivity_V_O_energy};electron_concentration_initial_expo=${electron_concentration_initial_expo};electron_concentration_initial_energy=${electron_concentration_initial_energy};Outputs/csv/enable=false + V_current=${target_voltage_V4};target_flux=${target_flux_V4};delta_H_T2O=${delta_H_T2O};delta_S_T2O=${delta_S_T2O};delta_H_T2=${delta_H_T2};delta_S_T2=${delta_S_T2};T2O_reaction_forward_mol_exponent=${T2O_reaction_forward_mol_exponent};T2O_reaction_forward_energy=${T2O_reaction_forward_energy};T2_reaction_forward_mol_exponent=${T2_reaction_forward_mol_exponent};T2_reaction_forward_energy=${T2_reaction_forward_energy};diffusivity_OT_prefactor_exponent=${diffusivity_OT_prefactor_exponent};diffusivity_OT_energy=${diffusivity_OT_energy};diffusivity_V_O_prefactor_exponent=${diffusivity_V_O_prefactor_exponent};diffusivity_V_O_energy=${diffusivity_V_O_energy};electron_concentration_initial_expo=${electron_concentration_initial_expo};electron_concentration_initial_energy=${electron_concentration_initial_energy};Outputs/csv/enable=false + V_current=${target_voltage_V5};target_flux=${target_flux_V5};temperature_initial=973;delta_H_T2O=${delta_H_T2O};delta_S_T2O=${delta_S_T2O};delta_H_T2=${delta_H_T2};delta_S_T2=${delta_S_T2};T2O_reaction_forward_mol_exponent=${T2O_reaction_forward_mol_exponent};T2O_reaction_forward_energy=${T2O_reaction_forward_energy};T2_reaction_forward_mol_exponent=${T2_reaction_forward_mol_exponent};T2_reaction_forward_energy=${T2_reaction_forward_energy};diffusivity_OT_prefactor_exponent=${diffusivity_OT_prefactor_exponent};diffusivity_OT_energy=${diffusivity_OT_energy};diffusivity_V_O_prefactor_exponent=${diffusivity_V_O_prefactor_exponent};diffusivity_V_O_energy=${diffusivity_V_O_energy};electron_concentration_initial_expo=${electron_concentration_initial_expo};electron_concentration_initial_energy=${electron_concentration_initial_energy};Outputs/csv/enable=false + V_current=${target_voltage_V6};target_flux=${target_flux_V6};temperature_initial=973;delta_H_T2O=${delta_H_T2O};delta_S_T2O=${delta_S_T2O};delta_H_T2=${delta_H_T2};delta_S_T2=${delta_S_T2};T2O_reaction_forward_mol_exponent=${T2O_reaction_forward_mol_exponent};T2O_reaction_forward_energy=${T2O_reaction_forward_energy};T2_reaction_forward_mol_exponent=${T2_reaction_forward_mol_exponent};T2_reaction_forward_energy=${T2_reaction_forward_energy};diffusivity_OT_prefactor_exponent=${diffusivity_OT_prefactor_exponent};diffusivity_OT_energy=${diffusivity_OT_energy};diffusivity_V_O_prefactor_exponent=${diffusivity_V_O_prefactor_exponent};diffusivity_V_O_energy=${diffusivity_V_O_energy};electron_concentration_initial_expo=${electron_concentration_initial_expo};electron_concentration_initial_energy=${electron_concentration_initial_energy};Outputs/csv/enable=false + V_current=${target_voltage_V7};target_flux=${target_flux_V7};temperature_initial=973;delta_H_T2O=${delta_H_T2O};delta_S_T2O=${delta_S_T2O};delta_H_T2=${delta_H_T2};delta_S_T2=${delta_S_T2};T2O_reaction_forward_mol_exponent=${T2O_reaction_forward_mol_exponent};T2O_reaction_forward_energy=${T2O_reaction_forward_energy};T2_reaction_forward_mol_exponent=${T2_reaction_forward_mol_exponent};T2_reaction_forward_energy=${T2_reaction_forward_energy};diffusivity_OT_prefactor_exponent=${diffusivity_OT_prefactor_exponent};diffusivity_OT_energy=${diffusivity_OT_energy};diffusivity_V_O_prefactor_exponent=${diffusivity_V_O_prefactor_exponent};diffusivity_V_O_energy=${diffusivity_V_O_energy};electron_concentration_initial_expo=${electron_concentration_initial_expo};electron_concentration_initial_energy=${electron_concentration_initial_energy};Outputs/csv/enable=false + V_current=${target_voltage_V8};target_flux=${target_flux_V8};temperature_initial=973;delta_H_T2O=${delta_H_T2O};delta_S_T2O=${delta_S_T2O};delta_H_T2=${delta_H_T2};delta_S_T2=${delta_S_T2};T2O_reaction_forward_mol_exponent=${T2O_reaction_forward_mol_exponent};T2O_reaction_forward_energy=${T2O_reaction_forward_energy};T2_reaction_forward_mol_exponent=${T2_reaction_forward_mol_exponent};T2_reaction_forward_energy=${T2_reaction_forward_energy};diffusivity_OT_prefactor_exponent=${diffusivity_OT_prefactor_exponent};diffusivity_OT_energy=${diffusivity_OT_energy};diffusivity_V_O_prefactor_exponent=${diffusivity_V_O_prefactor_exponent};diffusivity_V_O_energy=${diffusivity_V_O_energy};electron_concentration_initial_expo=${electron_concentration_initial_expo};electron_concentration_initial_energy=${electron_concentration_initial_energy};Outputs/csv/enable=false + V_current=${target_voltage_V9};target_flux=${target_flux_V9};temperature_initial=973;delta_H_T2O=${delta_H_T2O};delta_S_T2O=${delta_S_T2O};delta_H_T2=${delta_H_T2};delta_S_T2=${delta_S_T2};T2O_reaction_forward_mol_exponent=${T2O_reaction_forward_mol_exponent};T2O_reaction_forward_energy=${T2O_reaction_forward_energy};T2_reaction_forward_mol_exponent=${T2_reaction_forward_mol_exponent};T2_reaction_forward_energy=${T2_reaction_forward_energy};diffusivity_OT_prefactor_exponent=${diffusivity_OT_prefactor_exponent};diffusivity_OT_energy=${diffusivity_OT_energy};diffusivity_V_O_prefactor_exponent=${diffusivity_V_O_prefactor_exponent};diffusivity_V_O_energy=${diffusivity_V_O_energy};electron_concentration_initial_expo=${electron_concentration_initial_expo};electron_concentration_initial_energy=${electron_concentration_initial_energy};Outputs/csv/enable=false' + execute_on = 'INITIAL' + max_procs_per_app = 1 + ignore_solve_not_converge = true + [] +[] + +[Transfers] + [get_error_sum] + type = MultiAppPostprocessorTransfer + from_multi_app = sub + from_postprocessor = relative_error_sq + to_postprocessor = combined_relative_error_sq + reduction_type = sum + [] +[] + +[Postprocessors] + [combined_relative_error_sq] + type = Receiver + [] + [pp_RMSPE] + type = ParsedPostprocessor + pp_names = 'combined_relative_error_sq' + expression = 'sqrt(combined_relative_error_sq / 10) / ${mean_target_flux}' + execute_on = 'TIMESTEP_END' + [] + [pp_log_inverse_error] + type = ParsedPostprocessor + pp_names = 'pp_RMSPE' + expression = 'if(pp_RMSPE > 0, log(1 / pp_RMSPE), -5)' + execute_on = 'TIMESTEP_END' + [] +[] + +[Controls] + [stochastic] + type = SamplerReceiver + [] +[] + +[Outputs] + console = true + csv = true +[] diff --git a/test/tests/val-2l/val-2l_joule_heating.i b/test/tests/val-2l/val-2l_joule_heating.i new file mode 100644 index 000000000..aa8097525 --- /dev/null +++ b/test/tests/val-2l/val-2l_joule_heating.i @@ -0,0 +1,680 @@ +# val-2l: BCY20 hydrogen permeation under applied voltage. +# Unit system: length is converted to nm for the spatial solve, time is s, +# temperature is K, pressure is Pa, concentrations are atoms/nm^3, +# and fluxes reported by the membrane model are atoms/nm^2/s. + +# Level 3: Real (H2+H2O) BCY voltage simulation with Joule heating (standard RMSPE) +# Based on jouleheating_Voltage_BCY_real_LEE2005.i +# Uses standard RMSPE: sqrt(mean(((sim-ref)/ref)^2)) with per-point normalization + +# Physical constants +R = '${units 8.31446261815324 J/mol/K}' # ideal gas constant based on number used in include/utils/PhysicalConstants.h +N_a = '${units 6.02214076e23 at/mol}' # ideal gas constant based on number used in include/utils/PhysicalConstants.h +q = '${units 1.602176634e-19 C}' # quantity of charge +F = '${fparse N_a * q}' + +# Thermal properties of BCY20 +# thermal conductivity: 1.05 W/(m*K) for dense BaCeO3 +# Ref: Tenevich et al. 2023, Ceramics International, Vol. 49, 31087-31095 +thermal_conductivity_BCY20 = '${units 1.05 W/m/K -> W/nm/K}' + +# thermal parameters +temperature_initial = '${units 773 K}' # 500C + +# Model parameters +endtime = '1e5' +dt_max = '2e3' +dt_start_charging = '${units 1e-5 s}' +bound_value_min = '${units -1e-20 at/nm^3}' + +# Geometry and mesh +length = '${units 10 mum -> nm}' # BCY20 +num_nodes = 300 + +# Material properties +density_BCY20 = '${units ${fparse 1.0 * 6.154} g/cm^3 -> g/m^3}' +molar_mass_BCY20 = '${units 283.42 g/mol}' +N = '${units ${fparse density_BCY20 / molar_mass_BCY20 * N_a} at/m^3 -> at/nm^3}' +# density in g/nm^3 for pairing with specific_heat in J/(g*K) +density_BCY20_thermal = '${fparse density_BCY20 * 1e-27}' # g/m^3 -> g/nm^3 +# specific heat: ~120 J/(mol*K) for BaCeO3 at high temperature +# Ref: Yamanaka et al. 2003, J. Alloys and Compounds, Vol. 359, 109-113 +specific_heat_BCY20_molar = '${units 120 J/mol/K}' +specific_heat_BCY20 = '${fparse specific_heat_BCY20_molar / molar_mass_BCY20}' # 120/283.42 = 0.4233 J/(g*K) + +# Initial concentrations +OT_concentration_initial = 1e-5 +hydration_limit_S = 0.2 +oxygen_vacancy_concentration_initial = '${units ${fparse hydration_limit_S / 2 * N} at/nm^3}' +oxygen_concentration_initial = '${units ${fparse 3 * N - oxygen_vacancy_concentration_initial - OT_concentration_initial} at/nm^3}' + +##### Dry Pressure conditions +pressure_atm = '${units 101315 Pa}' +pressure_T2_low = '${units 0 Pa}' # pure N2 and 3% H2O +pressure_T2_high = '${units ${fparse 0.8 * pressure_atm} Pa}' # 80% H2 in N2 and 3% H2O +pressure_T2O_constant = '${units ${fparse 0.03 * pressure_atm} Pa}' # 80% H2 in N2 and 3% H2O + +# chemical_reaction - optimized parameters used for val-2l Joule-heating validation +delta_H_T2O = '${units -1.54415211e+05 J/mol}' +delta_S_T2O = '${units -1.67187585e+02 J/mol/K}' +delta_H_T2 = '${units -5.46037663e+04 J/mol}' +delta_S_T2 = '${units -3.36929406e+01 J/mol/K}' +T2O_reaction_forward_mol_exponent = -1.19792592e+01 +ramp_time = 1 +T2O_reaction_forward_mol = '${units ${fparse 8.0 * 10 ^ T2O_reaction_forward_mol_exponent} m^4/mol/s}' +T2O_reaction_forward_value = '${units ${fparse T2O_reaction_forward_mol / N_a} m^4/at/s -> nm^4/at/s}' +T2O_reaction_forward_energy = '${units -7.31595474e+03 J/mol}' +T2_reaction_forward_mol_exponent = -4.05998297e+00 +T2_reaction_forward_mol = '${units ${fparse 8.0 * 10 ^ T2_reaction_forward_mol_exponent} m^4/mol/s}' +T2_reaction_forward_value = '${units ${fparse T2_reaction_forward_mol / N_a} m^4/at/s -> nm^4/at/s}' +T2_reaction_forward_energy = '${units 5.13385478e+03 J/mol}' +diffusivity_OT_prefactor_exponent = -1.26000119e+01 +diffusivity_OT_prefactor = '${units ${fparse 2.03 * 10 ^ diffusivity_OT_prefactor_exponent} m^2/s -> nm^2/s}' +diffusivity_OT_energy = '${units 8.65880079e+03 J/mol}' +diffusivity_V_O_prefactor_exponent = -5.33084375e+00 +diffusivity_V_O_prefactor = '${units ${fparse 1.1 * 10 ^ diffusivity_V_O_prefactor_exponent} m^2/s -> nm^2/s}' +diffusivity_V_O_energy = '${units 5.87658926e+04 J/mol}' +diffusivity_e_prefactor = '${units 2.06292148e-02 m^2/s -> nm^2/s}' # data from Yang 2026 +diffusivity_e_energy = '${units 9.53470966e+04 J/mol}' +# ELECTRON +electron_concentration_initial_expo = 4.94096686e-01 +electron_concentration_initial_energy = '${units 5.90846106e+04 J/mol}' +electron_concentration_initial = '${units ${fparse 10 ^ electron_concentration_initial_expo * N} at/nm^3}' + +# voltage +V_current = 2.0 # CONSTANT_VOLTAGE - no ${units} wrapper so CLI override works + +# target flux for error computation (overridden by parent via cli_args) +target_flux = 1e20 + +[Mesh] + [cmg] + type = CartesianMeshGenerator + dim = 1 + dx = '${fparse length}' + ix = '${fparse num_nodes}' + subdomain_id = '0' + [] +[] + +[Variables] + #### Dry variable + [OT_concentration_dry] # (atoms/nm^3) + initial_condition = ${OT_concentration_initial} + [] + [Oxygen_vacancy_concentration_dry] + initial_condition = ${oxygen_vacancy_concentration_initial} + [] + # Temperature as nonlinear variable (promoted from AuxVariable for Joule heating coupling) + [temperature] + initial_condition = ${temperature_initial} + [] +[] + +[Bounds] + [concentration_dry_lower_bound] + type = ConstantBounds + variable = bounds_dummy + bounded_variable = OT_concentration_dry + bound_type = lower + bound_value = ${bound_value_min} + [] + [concentration_dry_V_O_lower_bound] + type = ConstantBounds + variable = bounds_dummy + bounded_variable = Oxygen_vacancy_concentration_dry + bound_type = lower + bound_value = ${bound_value_min} + [] + [concentration_dry_V_O_upper_bound] + type = ConstantBounds + variable = bounds_dummy + bounded_variable = Oxygen_vacancy_concentration_dry + bound_type = upper + bound_value = ${fparse 3 * N} + [] + [temperature_lower_bound] + type = ConstantBounds + variable = bounds_dummy + bounded_variable = temperature + bound_type = lower + bound_value = 300 + [] + [temperature_upper_bound] + type = ConstantBounds + variable = bounds_dummy + bounded_variable = temperature + bound_type = upper + bound_value = 2000 + [] +[] + +[AuxVariables] + [bounds_dummy] + order = FIRST + family = LAGRANGE + [] + #### Dry auxvariable + [pressure_T2_dry] + [] + [pressure_T2O_dry] + [] + [Oxygen_concentration_dry] + initial_condition = ${oxygen_concentration_initial} + [] + [electron_concentration_dry] + [] + + # CONSTANT_VOLTAGE + [voltage_phi] + [] +[] + + +[AuxKernels] + #### Dry auxkernels + [pressure_T2_dry_Aux] + type = FunctionAux + variable = pressure_T2_dry + function = Pressure_T2_dry_function + [] + [pressure_T2O_dry_Aux] + type = FunctionAux + variable = pressure_T2O_dry + function = Pressure_T2O_dry_function + [] + [Oxygen_concentration_dry_Aux] # at/nm^3 + type = ParsedAux + variable = Oxygen_concentration_dry + coupled_variables = 'Oxygen_vacancy_concentration_dry' + expression = '3 * ${N} - Oxygen_vacancy_concentration_dry' + [] + + # ELECTRON + [electron_concentration_dry_Aux] + type = ParsedAux + variable = electron_concentration_dry + coupled_variables = 'temperature' + expression = '${electron_concentration_initial} * 0.5 * exp(-${electron_concentration_initial_energy} / ${R} / temperature)' + execute_on = 'INITIAL TIMESTEP_END' + [] + + # CONSTANT_VOLTAGE + [phi_auxkernel] + type = FunctionAux + variable = voltage_phi + function = '${V_current} * (${length} - x) / ${length}' + execute_on = 'INITIAL TIMESTEP_END' + [] + +[] + +[Problem] + type = ReferenceResidualProblem + extra_tag_vectors = 'ref' + reference_vector = 'ref' +[] + +[Kernels] + #### Dry kernels + [time_OT_dry] + type = ADTimeDerivative + variable = OT_concentration_dry + extra_vector_tags = ref + [] + [diffusion_OT_dry] + type = ADMatDiffusion + variable = OT_concentration_dry + diffusivity = diffusivity_OT + extra_vector_tags = ref + [] + [time_V_O_dry] + type = ADTimeDerivative + variable = Oxygen_vacancy_concentration_dry + extra_vector_tags = ref + [] + [diffusion_V_O_dry] + type = ADMatDiffusion + variable = Oxygen_vacancy_concentration_dry + diffusivity = diffusivity_V_O + extra_vector_tags = ref + [] + # voltage for OH + [diffusion_phi_PCC_OH] + type = ADMatDiffusion + variable = OT_concentration_dry + v = voltage_phi + diffusivity = conductivity_OH + extra_vector_tags = ref + [] + # voltage for V_O + [diffusion_phi_PCC_V_O] + type = ADMatDiffusion + variable = Oxygen_vacancy_concentration_dry + v = voltage_phi + diffusivity = conductivity_V_O + extra_vector_tags = ref + [] + + # --- Heat equation --- + [heat_time] + type = ADHeatConductionTimeDerivative + variable = temperature + specific_heat = specific_heat_BCY20 + density_name = density_BCY20_thermal + extra_vector_tags = ref + [] + [heat_conduction] + type = ADHeatConduction + variable = temperature + thermal_conductivity = thermal_conductivity_BCY20 + extra_vector_tags = ref + [] + [joule_heating] + type = ADJouleHeatingSource + variable = temperature + heating_term = joule_heating_Q + extra_vector_tags = ref + [] +[] + +[BCs] + #### Dry BCs + [left_OT_dry] + type = ADMatNeumannBC + variable = OT_concentration_dry + boundary = left + value = 1 + boundary_material = flux_on_OT_dry + [] + [left_V_O_dry] + type = ADMatNeumannBC + variable = Oxygen_vacancy_concentration_dry + boundary = left + value = 1 + boundary_material = flux_on_V_O_dry + [] + [right_OT_dry] + type = ADMatNeumannBC + variable = OT_concentration_dry + boundary = right + value = 1 + boundary_material = flux_on_OT_dry + [] + [right_V_O_dry] + type = ADMatNeumannBC + variable = Oxygen_vacancy_concentration_dry + boundary = right + value = 1 + boundary_material = flux_on_V_O_dry + [] + + # Thermal BCs: fixed temperature at both surfaces (furnace-controlled) + [left_temperature] + type = ADDirichletBC + variable = temperature + boundary = left + value = ${temperature_initial} + [] + [right_temperature] + type = ADDirichletBC + variable = temperature + boundary = right + value = ${temperature_initial} + [] +[] + +[Functions] + [Pressure_T2_dry_function] + type = ParsedFunction + expression = 'min(t / ${ramp_time}, 1.0) * (${pressure_T2_high} * (${length} - x) / ${length} + ${pressure_T2_low}) / ${pressure_atm}' + [] + [Pressure_T2O_dry_function] + type = ParsedFunction + expression = 'min(t / ${ramp_time}, 1.0) * (${pressure_T2O_constant}) / ${pressure_atm}' + [] +[] + +[Materials] + [diffusivity_OT] + type = ADParsedMaterial + property_name = 'diffusivity_OT' + coupled_variables = 'temperature' + expression = '${diffusivity_OT_prefactor} * exp(-${diffusivity_OT_energy} / ${R} / temperature)' + [] + [diffusivity_V_O] + type = ADParsedMaterial + property_name = 'diffusivity_V_O' + coupled_variables = 'temperature' + expression = '${diffusivity_V_O_prefactor} * exp(-${diffusivity_V_O_energy} / ${R} / temperature)' + [] + [diffusivity_e] + type = ADParsedMaterial + property_name = 'diffusivity_e' + coupled_variables = 'temperature' + expression = '${diffusivity_e_prefactor} * exp(-${diffusivity_e_energy} / ${R} / temperature)' + [] + [converter_to_nonAD] + type = MaterialADConverter + ad_props_in = 'diffusivity_OT diffusivity_V_O diffusivity_e conductivity_OH conductivity_e' + reg_props_out = 'diffusivity_OT_nonAD diffusivity_V_O_nonAD diffusivity_e_nonAD conductivity_OH_nonAD conductivity_e_nonAD' + outputs = 'none' + [] + [conductivity_OH] + type = ADParsedMaterial + property_name = 'conductivity_OH' + coupled_variables = 'OT_concentration_dry temperature' + material_property_names = 'diffusivity_OT' + expression = 'diffusivity_OT * ${F} * OT_concentration_dry / ${R} / temperature' + [] + [conductivity_V_O] + type = ADParsedMaterial + property_name = 'conductivity_V_O' + coupled_variables = 'Oxygen_vacancy_concentration_dry temperature' + material_property_names = 'diffusivity_V_O' + expression = '2 * diffusivity_V_O * ${F} * Oxygen_vacancy_concentration_dry / ${R} / temperature' + [] + [conductivity_e] + type = ADParsedMaterial + property_name = 'conductivity_e' + coupled_variables = 'electron_concentration_dry temperature' + material_property_names = 'diffusivity_e' + expression = '- diffusivity_e * ${F} * electron_concentration_dry / ${R} / temperature' + [] + [reaction_equilibrium_constant_T2] + type = ADParsedMaterial + property_name = 'T2_K_eq' + coupled_variables = 'temperature' + expression = 'exp( ( ${delta_H_T2} - temperature * ${delta_S_T2}) / ${R} / temperature )' + [] + [reaction_forward_T2] + type = ADParsedMaterial + property_name = 'T2_K_forward' + coupled_variables = 'temperature' + expression = '${T2_reaction_forward_value} * exp(-${T2_reaction_forward_energy} / ${R} / temperature)' + [] + [reaction_reverse_T2] + type = ADParsedMaterial + property_name = 'T2_K_reverse' + material_property_names = 'T2_K_forward T2_K_eq' + expression = 'T2_K_forward / T2_K_eq' + [] + + [reaction_equilibrium_constant_T2O] + type = ADParsedMaterial + property_name = 'T2O_K_eq' + coupled_variables = 'temperature' + expression = 'exp( ( ${delta_H_T2O} - temperature * ${delta_S_T2O}) / ${R} / temperature )' + [] + [reaction_forward_T2O] + type = ADParsedMaterial + property_name = 'T2O_K_forward' + coupled_variables = 'temperature' + expression = '${T2O_reaction_forward_value} * exp(-${T2O_reaction_forward_energy} / ${R} / temperature)' + [] + [reaction_reverse_T2O] + type = ADParsedMaterial + property_name = 'T2O_K_reverse' + material_property_names = 'T2O_K_forward T2O_K_eq' + expression = 'T2O_K_forward / T2O_K_eq' + [] + + #### Reaction for dry + [flux_base_on_T2_dry] # T2 + 2 O -> 2 OT + 2 e + type = ADDerivativeParsedMaterial + coupled_variables = 'OT_concentration_dry pressure_T2_dry Oxygen_vacancy_concentration_dry electron_concentration_dry' + property_name = 'flux_base_on_T2_dry' + material_property_names = 'T2_K_forward T2_K_reverse' + expression = '(T2_K_forward * pressure_T2_dry * (3 * ${N} - Oxygen_vacancy_concentration_dry)^2 - T2_K_reverse * OT_concentration_dry^2 * electron_concentration_dry^2)' + [] + [flux_base_on_T2O_dry] # T2O + V_O + O -> 2 OT + type = ADDerivativeParsedMaterial + coupled_variables = 'OT_concentration_dry pressure_T2O_dry Oxygen_vacancy_concentration_dry' + property_name = 'flux_base_on_T2O_dry' + material_property_names = 'T2O_K_forward T2O_K_reverse' + expression = '(T2O_K_forward * pressure_T2O_dry * (3 * ${N} - Oxygen_vacancy_concentration_dry) * Oxygen_vacancy_concentration_dry - T2O_K_reverse * OT_concentration_dry^2)' + [] + + + #### Flux for dry + [flux_on_e_dry] # electron + type = ADDerivativeParsedMaterial + property_name = 'flux_on_e_dry' + material_property_names = 'flux_base_on_T2_dry' + expression = '2 * flux_base_on_T2_dry' + [] + [flux_on_OT_dry] # OT + type = ADDerivativeParsedMaterial + property_name = 'flux_on_OT_dry' + material_property_names = 'flux_base_on_T2_dry flux_base_on_T2O_dry' + expression = '2 * flux_base_on_T2_dry + 2 * flux_base_on_T2O_dry' + [] + [flux_on_T2_dry] # T2 + type = ADDerivativeParsedMaterial + property_name = 'flux_on_T2_dry' + material_property_names = 'flux_base_on_T2_dry' + expression = '-1 * flux_base_on_T2_dry' + [] + [flux_on_V_O_dry] # V_O + type = ADDerivativeParsedMaterial + property_name = 'flux_on_V_O_dry' + material_property_names = 'flux_base_on_T2O_dry' + expression = '-1 * flux_base_on_T2O_dry' + [] + [flux_on_T2O_dry] # T2O + type = ADDerivativeParsedMaterial + property_name = 'flux_on_T2O_dry' + material_property_names = 'flux_base_on_T2O_dry' + expression = '-1 * flux_base_on_T2O_dry' + [] + + # --- Thermal material properties for BCY20 --- + [thermal_conductivity_mat] + type = ADGenericConstantMaterial + prop_names = 'thermal_conductivity_BCY20' + prop_values = '${thermal_conductivity_BCY20}' + [] + [specific_heat_mat] + type = ADGenericConstantMaterial + prop_names = 'specific_heat_BCY20' + prop_values = '${specific_heat_BCY20}' + [] + [density_thermal_mat] + type = ADGenericConstantMaterial + prop_names = 'density_BCY20_thermal' + prop_values = '${density_BCY20_thermal}' + [] + + # --- Joule heating --- + # Total ionic electrical conductivity from Nernst-Einstein relation (excluding electrons) + # sigma = q*F/(R*T) * (z_OH^2 * D_OT * c_OT + z_VO^2 * D_VO * c_VO) + # z_OH = 1, z_VO = 2, so z^2 = 1 and 4 + [total_electrical_conductivity] + type = ADParsedMaterial + property_name = 'sigma_total' + coupled_variables = 'OT_concentration_dry Oxygen_vacancy_concentration_dry temperature' + material_property_names = 'diffusivity_OT diffusivity_V_O' + expression = '${q} * ${F} / (${R} * temperature) * (diffusivity_OT * OT_concentration_dry + 4.0 * diffusivity_V_O * Oxygen_vacancy_concentration_dry)' + [] + # Joule heating volumetric source: Q = sigma_total * |grad(phi)|^2 + # |grad(phi)|^2 = (V_current / length)^2 = constant (voltage_phi is linear AuxVariable) + [joule_heating_material] + type = ADParsedMaterial + property_name = 'joule_heating_Q' + material_property_names = 'sigma_total' + expression = 'sigma_total * (${V_current} / ${length})^2' + [] +[] + +[Postprocessors] + #### Postprocessors for flux under dry + [recombination_flux_T2_dry_left] + type = ADSideAverageMaterialProperty + boundary = left + property = flux_on_T2_dry + execute_on = 'INITIAL TIMESTEP_END' + outputs = 'console csv' + [] + [recombination_flux_T2O_dry_left] + type = ADSideAverageMaterialProperty + boundary = left + property = flux_on_T2O_dry + execute_on = 'INITIAL TIMESTEP_END' + outputs = 'console csv' + [] + [recombination_flux_OT_dry_left] + type = ADSideAverageMaterialProperty + boundary = left + property = flux_on_OT_dry + execute_on = 'INITIAL TIMESTEP_END' + outputs = 'console csv' + [] + [recombination_flux_OT_dry_right] + type = ADSideAverageMaterialProperty + boundary = right + property = flux_on_OT_dry + execute_on = 'INITIAL TIMESTEP_END' + outputs = 'console csv' + [] + [recombination_flux_T2O_dry_right] + type = ADSideAverageMaterialProperty + boundary = right + property = flux_on_T2O_dry + execute_on = 'INITIAL TIMESTEP_END' + outputs = 'console csv' + [] + [recombination_flux_T2_dry_right] + type = ADSideAverageMaterialProperty + boundary = right + property = flux_on_T2_dry + execute_on = 'INITIAL TIMESTEP_END' + outputs = 'console csv' + [] + + # necessary parameters + [T2_K_eq_average] + type = ADElementAverageMaterialProperty + mat_prop = T2_K_eq + [] + [T2_K_forward_average] + type = ADElementAverageMaterialProperty + mat_prop = T2_K_forward + [] + [T2_K_reverse_average] + type = ADElementAverageMaterialProperty + mat_prop = T2_K_reverse + [] + [T2O_K_eq_average] + type = ADElementAverageMaterialProperty + mat_prop = T2O_K_eq + [] + [T2O_K_forward_average] + type = ADElementAverageMaterialProperty + mat_prop = T2O_K_forward + [] + [T2O_K_reverse_average] + type = ADElementAverageMaterialProperty + mat_prop = T2O_K_reverse + [] + [diffusivity_OT_average] + type = ADElementAverageMaterialProperty + mat_prop = diffusivity_OT + execute_on = 'INITIAL TIMESTEP_END' + [] + [diffusivity_V_O_average] + type = ADElementAverageMaterialProperty + mat_prop = diffusivity_V_O + execute_on = 'INITIAL TIMESTEP_END' + [] + [temperature_average] + type = ElementAverageValue + variable = temperature + execute_on = 'INITIAL TIMESTEP_END' + [] + [voltage_value] + type = ParsedPostprocessor + expression = ${V_current} + execute_on = 'INITIAL TIMESTEP_END' + [] + [pressure_T2_average] + type = ElementAverageValue + variable = pressure_T2_dry + execute_on = 'INITIAL TIMESTEP_END' + [] + [log_error_sq] + type = ParsedPostprocessor + pp_names = 'recombination_flux_OT_dry_right' + expression = '(log(abs(recombination_flux_OT_dry_right * 1e18)) - log(${target_flux}))^2' + execute_on = 'INITIAL TIMESTEP_END' + [] + [relative_error_sq] + type = ParsedPostprocessor + pp_names = 'recombination_flux_OT_dry_right' + expression = '((abs(recombination_flux_OT_dry_right * 1e18) - ${target_flux}) / ${target_flux})^2' + execute_on = 'INITIAL TIMESTEP_END' + [] + + # Joule heating diagnostics + [temperature_max] + type = ElementExtremeValue + variable = temperature + value_type = max + execute_on = 'INITIAL TIMESTEP_END' + [] + [temperature_min] + type = ElementExtremeValue + variable = temperature + value_type = min + execute_on = 'INITIAL TIMESTEP_END' + [] + [delta_T] + type = ParsedPostprocessor + pp_names = 'temperature_max temperature_min' + expression = 'temperature_max - temperature_min' + execute_on = 'TIMESTEP_END' + [] +[] + +[Controls] + [stochastic] + type = SamplerReceiver + [] +[] + +[Executioner] + type = Transient + scheme = implicit-euler + solve_type = NEWTON + petsc_options_iname = '-pc_type -snes_type' + petsc_options_value = 'lu vinewtonrsls' + nl_rel_tol = 5e-6 + nl_abs_tol = 5e-7 + end_time = ${endtime} + automatic_scaling = true + compute_scaling_once = true + line_search = none + error_on_dtmin = false # must stay false for ignore_solve_not_converge to work in Level 2 + abort_on_solve_fail = true # fast-fail on first NL divergence; prevents stutter at dtmin + dtmin = 1e-10 + nl_max_its = 40 + dtmax = ${dt_max} + [TimeStepper] + type = IterationAdaptiveDT + dt = ${dt_start_charging} + optimal_iterations = 20 + growth_factor = 1.5 + cutback_factor = 0.5 + cutback_factor_at_failure = 0.5 + [] +[] + +[Debug] + show_var_residual_norms = true +[] + +[Outputs] + exodus = false + [csv] + type = CSV + [] +[] diff --git a/test/tests/val-2l/val-2l_joule_heating_aggregator.i b/test/tests/val-2l/val-2l_joule_heating_aggregator.i new file mode 100644 index 000000000..a20d573a0 --- /dev/null +++ b/test/tests/val-2l/val-2l_joule_heating_aggregator.i @@ -0,0 +1,159 @@ +# val-2l: BCY20 hydrogen permeation under applied voltage. +# Unit system: length is converted to nm for the spatial solve, time is s, +# temperature is K, pressure is Pa, concentrations are atoms/nm^3, +# and fluxes reported by the membrane model are atoms/nm^2/s. + +# Level 2: voltage aggregator for the val-2l Joule-heating membrane model. +# Uses n20_faster optimized parameters (71 steps, ~20.2% RMSPE). +# Runs Level 3 sub-apps at 10 voltage points (5@500C + 5@700C), +# collects recombination_flux_OT_dry_right from each, +# computes combined RMSPE. + +# --- 14 local n5 optimized parameters --- +delta_H_T2O = -1.54415211e+05 +delta_S_T2O = -1.67187585e+02 +delta_H_T2 = -5.46037663e+04 +delta_S_T2 = -3.36929406e+01 +T2O_reaction_forward_energy = -7.31595474e+03 +T2O_reaction_forward_mol_exponent = -1.19792592e+01 +T2_reaction_forward_energy = 5.13385478e+03 +T2_reaction_forward_mol_exponent = -4.05998297e+00 +diffusivity_OT_energy = 8.65880079e+03 +diffusivity_OT_prefactor_exponent = -1.26000119e+01 +diffusivity_V_O_energy = 5.87658926e+04 +diffusivity_V_O_prefactor_exponent = -5.33084375e+00 +electron_concentration_initial_expo = 4.94096686e-01 +electron_concentration_initial_energy = 5.90846106e+04 + +# Experimental target flux values for recombination_flux_OT_dry_right +# NOTE: These must be in the same units as the simulation output. + +# Physics parameters +molar_volume = '${units 2.24e4 cm^3/mol}' +N_A = '${units 6.022e23 at/mol}' # H2/mol + +# 500C target data (rows 1,3,5,7,9 from Lee2005_500C gold files) +target_voltage_V0 = '${units 0.2528561064472667 V}' +target_voltage_V1 = '${units 0.88369488093245 V}' +target_voltage_V2 = '${units 1.3639034384890738 V}' +target_voltage_V3 = '${units 1.6671250787272887 V}' +target_voltage_V4 = '${units 1.963346966109397 V}' + +target_flux_V0 = '${units ${fparse 0.6218274111675122 / molar_volume * N_A * 2 / 60 * 1e4} at/m^2/s}' # cm^3/min/cm^2 -> atoms/m^2/s +target_flux_V1 = '${units ${fparse 2.5568307216949897 / molar_volume * N_A * 2 / 60 * 1e4} at/m^2/s}' # cm^3/min/cm^2 -> atoms/m^2/s +target_flux_V2 = '${units ${fparse 6.716508497020525 / molar_volume * N_A * 2 / 60 * 1e4} at/m^2/s}' # cm^3/min/cm^2 -> atoms/m^2/s +target_flux_V3 = '${units ${fparse 9.532621428450163 / molar_volume * N_A * 2 / 60 * 1e4} at/m^2/s}' # cm^3/min/cm^2 -> atoms/m^2/s +target_flux_V4 = '${units ${fparse 13.414087567696043 / molar_volume * N_A * 2 / 60 * 1e4} at/m^2/s}' # cm^3/min/cm^2 -> atoms/m^2/s + +# 700C target data (rows 1,3,5,7,9 from Lee2005_700C gold files) +target_voltage_V5 = '${units 0.03332748850295297 V}' +target_voltage_V6 = '${units 0.20215275729873194 V}' +target_voltage_V7 = '${units 0.4807120597447935 V}' +target_voltage_V8 = '${units 0.7303394518080452 V}' +target_voltage_V9 = '${units 1.0092335036304367 V}' + +target_flux_V5 = '${units ${fparse 0.8159052568221696 / molar_volume * N_A * 2 / 60 * 1e4} at/m^2/s}' +target_flux_V6 = '${units ${fparse 3.1612566865319893 / molar_volume * N_A * 2 / 60 * 1e4} at/m^2/s}' +target_flux_V7 = '${units ${fparse 6.284704266664406 / molar_volume * N_A * 2 / 60 * 1e4} at/m^2/s}' +target_flux_V8 = '${units ${fparse 10.201125795813871 / molar_volume * N_A * 2 / 60 * 1e4} at/m^2/s}' +target_flux_V9 = '${units ${fparse 15.544671543984876 / molar_volume * N_A * 2 / 60 * 1e4} at/m^2/s}' + +[Mesh] + [gmg] + type = GeneratedMeshGenerator + dim = 1 + nx = 1 + [] +[] + +[Problem] + solve = false + kernel_coverage_check = false +[] + +[Executioner] + type = Steady +[] + +[MultiApps] + active = 'sub' + [sub] + type = FullSolveMultiApp + input_files = 'val-2l_joule_heating.i' + positions = '0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0' + # # without csv + # cli_args = 'V_current=${target_voltage_V0};target_flux=${target_flux_V0};delta_H_T2O=${delta_H_T2O};delta_S_T2O=${delta_S_T2O};delta_H_T2=${delta_H_T2};delta_S_T2=${delta_S_T2};T2O_reaction_forward_mol_exponent=${T2O_reaction_forward_mol_exponent};T2O_reaction_forward_energy=${T2O_reaction_forward_energy};T2_reaction_forward_mol_exponent=${T2_reaction_forward_mol_exponent};T2_reaction_forward_energy=${T2_reaction_forward_energy};diffusivity_OT_prefactor_exponent=${diffusivity_OT_prefactor_exponent};diffusivity_OT_energy=${diffusivity_OT_energy};diffusivity_V_O_prefactor_exponent=${diffusivity_V_O_prefactor_exponent};diffusivity_V_O_energy=${diffusivity_V_O_energy};electron_concentration_initial_expo=${electron_concentration_initial_expo};electron_concentration_initial_energy=${electron_concentration_initial_energy};Outputs/csv/enable=false + # V_current=${target_voltage_V1};target_flux=${target_flux_V1};delta_H_T2O=${delta_H_T2O};delta_S_T2O=${delta_S_T2O};delta_H_T2=${delta_H_T2};delta_S_T2=${delta_S_T2};T2O_reaction_forward_mol_exponent=${T2O_reaction_forward_mol_exponent};T2O_reaction_forward_energy=${T2O_reaction_forward_energy};T2_reaction_forward_mol_exponent=${T2_reaction_forward_mol_exponent};T2_reaction_forward_energy=${T2_reaction_forward_energy};diffusivity_OT_prefactor_exponent=${diffusivity_OT_prefactor_exponent};diffusivity_OT_energy=${diffusivity_OT_energy};diffusivity_V_O_prefactor_exponent=${diffusivity_V_O_prefactor_exponent};diffusivity_V_O_energy=${diffusivity_V_O_energy};electron_concentration_initial_expo=${electron_concentration_initial_expo};electron_concentration_initial_energy=${electron_concentration_initial_energy};Outputs/csv/enable=false + # V_current=${target_voltage_V2};target_flux=${target_flux_V2};delta_H_T2O=${delta_H_T2O};delta_S_T2O=${delta_S_T2O};delta_H_T2=${delta_H_T2};delta_S_T2=${delta_S_T2};T2O_reaction_forward_mol_exponent=${T2O_reaction_forward_mol_exponent};T2O_reaction_forward_energy=${T2O_reaction_forward_energy};T2_reaction_forward_mol_exponent=${T2_reaction_forward_mol_exponent};T2_reaction_forward_energy=${T2_reaction_forward_energy};diffusivity_OT_prefactor_exponent=${diffusivity_OT_prefactor_exponent};diffusivity_OT_energy=${diffusivity_OT_energy};diffusivity_V_O_prefactor_exponent=${diffusivity_V_O_prefactor_exponent};diffusivity_V_O_energy=${diffusivity_V_O_energy};electron_concentration_initial_expo=${electron_concentration_initial_expo};electron_concentration_initial_energy=${electron_concentration_initial_energy};Outputs/csv/enable=false + # V_current=${target_voltage_V3};target_flux=${target_flux_V3};delta_H_T2O=${delta_H_T2O};delta_S_T2O=${delta_S_T2O};delta_H_T2=${delta_H_T2};delta_S_T2=${delta_S_T2};T2O_reaction_forward_mol_exponent=${T2O_reaction_forward_mol_exponent};T2O_reaction_forward_energy=${T2O_reaction_forward_energy};T2_reaction_forward_mol_exponent=${T2_reaction_forward_mol_exponent};T2_reaction_forward_energy=${T2_reaction_forward_energy};diffusivity_OT_prefactor_exponent=${diffusivity_OT_prefactor_exponent};diffusivity_OT_energy=${diffusivity_OT_energy};diffusivity_V_O_prefactor_exponent=${diffusivity_V_O_prefactor_exponent};diffusivity_V_O_energy=${diffusivity_V_O_energy};electron_concentration_initial_expo=${electron_concentration_initial_expo};electron_concentration_initial_energy=${electron_concentration_initial_energy};Outputs/csv/enable=false + # V_current=${target_voltage_V4};target_flux=${target_flux_V4};delta_H_T2O=${delta_H_T2O};delta_S_T2O=${delta_S_T2O};delta_H_T2=${delta_H_T2};delta_S_T2=${delta_S_T2};T2O_reaction_forward_mol_exponent=${T2O_reaction_forward_mol_exponent};T2O_reaction_forward_energy=${T2O_reaction_forward_energy};T2_reaction_forward_mol_exponent=${T2_reaction_forward_mol_exponent};T2_reaction_forward_energy=${T2_reaction_forward_energy};diffusivity_OT_prefactor_exponent=${diffusivity_OT_prefactor_exponent};diffusivity_OT_energy=${diffusivity_OT_energy};diffusivity_V_O_prefactor_exponent=${diffusivity_V_O_prefactor_exponent};diffusivity_V_O_energy=${diffusivity_V_O_energy};electron_concentration_initial_expo=${electron_concentration_initial_expo};electron_concentration_initial_energy=${electron_concentration_initial_energy};Outputs/csv/enable=false + # V_current=${target_voltage_V5};target_flux=${target_flux_V5};temperature_initial=973;delta_H_T2O=${delta_H_T2O};delta_S_T2O=${delta_S_T2O};delta_H_T2=${delta_H_T2};delta_S_T2=${delta_S_T2};T2O_reaction_forward_mol_exponent=${T2O_reaction_forward_mol_exponent};T2O_reaction_forward_energy=${T2O_reaction_forward_energy};T2_reaction_forward_mol_exponent=${T2_reaction_forward_mol_exponent};T2_reaction_forward_energy=${T2_reaction_forward_energy};diffusivity_OT_prefactor_exponent=${diffusivity_OT_prefactor_exponent};diffusivity_OT_energy=${diffusivity_OT_energy};diffusivity_V_O_prefactor_exponent=${diffusivity_V_O_prefactor_exponent};diffusivity_V_O_energy=${diffusivity_V_O_energy};electron_concentration_initial_expo=${electron_concentration_initial_expo};electron_concentration_initial_energy=${electron_concentration_initial_energy};Outputs/csv/enable=false + # V_current=${target_voltage_V6};target_flux=${target_flux_V6};temperature_initial=973;delta_H_T2O=${delta_H_T2O};delta_S_T2O=${delta_S_T2O};delta_H_T2=${delta_H_T2};delta_S_T2=${delta_S_T2};T2O_reaction_forward_mol_exponent=${T2O_reaction_forward_mol_exponent};T2O_reaction_forward_energy=${T2O_reaction_forward_energy};T2_reaction_forward_mol_exponent=${T2_reaction_forward_mol_exponent};T2_reaction_forward_energy=${T2_reaction_forward_energy};diffusivity_OT_prefactor_exponent=${diffusivity_OT_prefactor_exponent};diffusivity_OT_energy=${diffusivity_OT_energy};diffusivity_V_O_prefactor_exponent=${diffusivity_V_O_prefactor_exponent};diffusivity_V_O_energy=${diffusivity_V_O_energy};electron_concentration_initial_expo=${electron_concentration_initial_expo};electron_concentration_initial_energy=${electron_concentration_initial_energy};Outputs/csv/enable=false + # V_current=${target_voltage_V7};target_flux=${target_flux_V7};temperature_initial=973;delta_H_T2O=${delta_H_T2O};delta_S_T2O=${delta_S_T2O};delta_H_T2=${delta_H_T2};delta_S_T2=${delta_S_T2};T2O_reaction_forward_mol_exponent=${T2O_reaction_forward_mol_exponent};T2O_reaction_forward_energy=${T2O_reaction_forward_energy};T2_reaction_forward_mol_exponent=${T2_reaction_forward_mol_exponent};T2_reaction_forward_energy=${T2_reaction_forward_energy};diffusivity_OT_prefactor_exponent=${diffusivity_OT_prefactor_exponent};diffusivity_OT_energy=${diffusivity_OT_energy};diffusivity_V_O_prefactor_exponent=${diffusivity_V_O_prefactor_exponent};diffusivity_V_O_energy=${diffusivity_V_O_energy};electron_concentration_initial_expo=${electron_concentration_initial_expo};electron_concentration_initial_energy=${electron_concentration_initial_energy};Outputs/csv/enable=false + # V_current=${target_voltage_V8};target_flux=${target_flux_V8};temperature_initial=973;delta_H_T2O=${delta_H_T2O};delta_S_T2O=${delta_S_T2O};delta_H_T2=${delta_H_T2};delta_S_T2=${delta_S_T2};T2O_reaction_forward_mol_exponent=${T2O_reaction_forward_mol_exponent};T2O_reaction_forward_energy=${T2O_reaction_forward_energy};T2_reaction_forward_mol_exponent=${T2_reaction_forward_mol_exponent};T2_reaction_forward_energy=${T2_reaction_forward_energy};diffusivity_OT_prefactor_exponent=${diffusivity_OT_prefactor_exponent};diffusivity_OT_energy=${diffusivity_OT_energy};diffusivity_V_O_prefactor_exponent=${diffusivity_V_O_prefactor_exponent};diffusivity_V_O_energy=${diffusivity_V_O_energy};electron_concentration_initial_expo=${electron_concentration_initial_expo};electron_concentration_initial_energy=${electron_concentration_initial_energy};Outputs/csv/enable=false + # V_current=${target_voltage_V9};target_flux=${target_flux_V9};temperature_initial=973;delta_H_T2O=${delta_H_T2O};delta_S_T2O=${delta_S_T2O};delta_H_T2=${delta_H_T2};delta_S_T2=${delta_S_T2};T2O_reaction_forward_mol_exponent=${T2O_reaction_forward_mol_exponent};T2O_reaction_forward_energy=${T2O_reaction_forward_energy};T2_reaction_forward_mol_exponent=${T2_reaction_forward_mol_exponent};T2_reaction_forward_energy=${T2_reaction_forward_energy};diffusivity_OT_prefactor_exponent=${diffusivity_OT_prefactor_exponent};diffusivity_OT_energy=${diffusivity_OT_energy};diffusivity_V_O_prefactor_exponent=${diffusivity_V_O_prefactor_exponent};diffusivity_V_O_energy=${diffusivity_V_O_energy};electron_concentration_initial_expo=${electron_concentration_initial_expo};electron_concentration_initial_energy=${electron_concentration_initial_energy};Outputs/csv/enable=false' + # with csv + cli_args = 'V_current=${target_voltage_V0};target_flux=${target_flux_V0};delta_H_T2O=${delta_H_T2O};delta_S_T2O=${delta_S_T2O};delta_H_T2=${delta_H_T2};delta_S_T2=${delta_S_T2};T2O_reaction_forward_mol_exponent=${T2O_reaction_forward_mol_exponent};T2O_reaction_forward_energy=${T2O_reaction_forward_energy};T2_reaction_forward_mol_exponent=${T2_reaction_forward_mol_exponent};T2_reaction_forward_energy=${T2_reaction_forward_energy};diffusivity_OT_prefactor_exponent=${diffusivity_OT_prefactor_exponent};diffusivity_OT_energy=${diffusivity_OT_energy};diffusivity_V_O_prefactor_exponent=${diffusivity_V_O_prefactor_exponent};diffusivity_V_O_energy=${diffusivity_V_O_energy};electron_concentration_initial_expo=${electron_concentration_initial_expo};electron_concentration_initial_energy=${electron_concentration_initial_energy};Outputs/csv/enable=true + V_current=${target_voltage_V1};target_flux=${target_flux_V1};delta_H_T2O=${delta_H_T2O};delta_S_T2O=${delta_S_T2O};delta_H_T2=${delta_H_T2};delta_S_T2=${delta_S_T2};T2O_reaction_forward_mol_exponent=${T2O_reaction_forward_mol_exponent};T2O_reaction_forward_energy=${T2O_reaction_forward_energy};T2_reaction_forward_mol_exponent=${T2_reaction_forward_mol_exponent};T2_reaction_forward_energy=${T2_reaction_forward_energy};diffusivity_OT_prefactor_exponent=${diffusivity_OT_prefactor_exponent};diffusivity_OT_energy=${diffusivity_OT_energy};diffusivity_V_O_prefactor_exponent=${diffusivity_V_O_prefactor_exponent};diffusivity_V_O_energy=${diffusivity_V_O_energy};electron_concentration_initial_expo=${electron_concentration_initial_expo};electron_concentration_initial_energy=${electron_concentration_initial_energy};Outputs/csv/enable=true + V_current=${target_voltage_V2};target_flux=${target_flux_V2};delta_H_T2O=${delta_H_T2O};delta_S_T2O=${delta_S_T2O};delta_H_T2=${delta_H_T2};delta_S_T2=${delta_S_T2};T2O_reaction_forward_mol_exponent=${T2O_reaction_forward_mol_exponent};T2O_reaction_forward_energy=${T2O_reaction_forward_energy};T2_reaction_forward_mol_exponent=${T2_reaction_forward_mol_exponent};T2_reaction_forward_energy=${T2_reaction_forward_energy};diffusivity_OT_prefactor_exponent=${diffusivity_OT_prefactor_exponent};diffusivity_OT_energy=${diffusivity_OT_energy};diffusivity_V_O_prefactor_exponent=${diffusivity_V_O_prefactor_exponent};diffusivity_V_O_energy=${diffusivity_V_O_energy};electron_concentration_initial_expo=${electron_concentration_initial_expo};electron_concentration_initial_energy=${electron_concentration_initial_energy};Outputs/csv/enable=true + V_current=${target_voltage_V3};target_flux=${target_flux_V3};delta_H_T2O=${delta_H_T2O};delta_S_T2O=${delta_S_T2O};delta_H_T2=${delta_H_T2};delta_S_T2=${delta_S_T2};T2O_reaction_forward_mol_exponent=${T2O_reaction_forward_mol_exponent};T2O_reaction_forward_energy=${T2O_reaction_forward_energy};T2_reaction_forward_mol_exponent=${T2_reaction_forward_mol_exponent};T2_reaction_forward_energy=${T2_reaction_forward_energy};diffusivity_OT_prefactor_exponent=${diffusivity_OT_prefactor_exponent};diffusivity_OT_energy=${diffusivity_OT_energy};diffusivity_V_O_prefactor_exponent=${diffusivity_V_O_prefactor_exponent};diffusivity_V_O_energy=${diffusivity_V_O_energy};electron_concentration_initial_expo=${electron_concentration_initial_expo};electron_concentration_initial_energy=${electron_concentration_initial_energy};Outputs/csv/enable=true + V_current=${target_voltage_V4};target_flux=${target_flux_V4};delta_H_T2O=${delta_H_T2O};delta_S_T2O=${delta_S_T2O};delta_H_T2=${delta_H_T2};delta_S_T2=${delta_S_T2};T2O_reaction_forward_mol_exponent=${T2O_reaction_forward_mol_exponent};T2O_reaction_forward_energy=${T2O_reaction_forward_energy};T2_reaction_forward_mol_exponent=${T2_reaction_forward_mol_exponent};T2_reaction_forward_energy=${T2_reaction_forward_energy};diffusivity_OT_prefactor_exponent=${diffusivity_OT_prefactor_exponent};diffusivity_OT_energy=${diffusivity_OT_energy};diffusivity_V_O_prefactor_exponent=${diffusivity_V_O_prefactor_exponent};diffusivity_V_O_energy=${diffusivity_V_O_energy};electron_concentration_initial_expo=${electron_concentration_initial_expo};electron_concentration_initial_energy=${electron_concentration_initial_energy};Outputs/csv/enable=true + V_current=${target_voltage_V5};target_flux=${target_flux_V5};temperature_initial=973;delta_H_T2O=${delta_H_T2O};delta_S_T2O=${delta_S_T2O};delta_H_T2=${delta_H_T2};delta_S_T2=${delta_S_T2};T2O_reaction_forward_mol_exponent=${T2O_reaction_forward_mol_exponent};T2O_reaction_forward_energy=${T2O_reaction_forward_energy};T2_reaction_forward_mol_exponent=${T2_reaction_forward_mol_exponent};T2_reaction_forward_energy=${T2_reaction_forward_energy};diffusivity_OT_prefactor_exponent=${diffusivity_OT_prefactor_exponent};diffusivity_OT_energy=${diffusivity_OT_energy};diffusivity_V_O_prefactor_exponent=${diffusivity_V_O_prefactor_exponent};diffusivity_V_O_energy=${diffusivity_V_O_energy};electron_concentration_initial_expo=${electron_concentration_initial_expo};electron_concentration_initial_energy=${electron_concentration_initial_energy};Outputs/csv/enable=true + V_current=${target_voltage_V6};target_flux=${target_flux_V6};temperature_initial=973;delta_H_T2O=${delta_H_T2O};delta_S_T2O=${delta_S_T2O};delta_H_T2=${delta_H_T2};delta_S_T2=${delta_S_T2};T2O_reaction_forward_mol_exponent=${T2O_reaction_forward_mol_exponent};T2O_reaction_forward_energy=${T2O_reaction_forward_energy};T2_reaction_forward_mol_exponent=${T2_reaction_forward_mol_exponent};T2_reaction_forward_energy=${T2_reaction_forward_energy};diffusivity_OT_prefactor_exponent=${diffusivity_OT_prefactor_exponent};diffusivity_OT_energy=${diffusivity_OT_energy};diffusivity_V_O_prefactor_exponent=${diffusivity_V_O_prefactor_exponent};diffusivity_V_O_energy=${diffusivity_V_O_energy};electron_concentration_initial_expo=${electron_concentration_initial_expo};electron_concentration_initial_energy=${electron_concentration_initial_energy};Outputs/csv/enable=true + V_current=${target_voltage_V7};target_flux=${target_flux_V7};temperature_initial=973;delta_H_T2O=${delta_H_T2O};delta_S_T2O=${delta_S_T2O};delta_H_T2=${delta_H_T2};delta_S_T2=${delta_S_T2};T2O_reaction_forward_mol_exponent=${T2O_reaction_forward_mol_exponent};T2O_reaction_forward_energy=${T2O_reaction_forward_energy};T2_reaction_forward_mol_exponent=${T2_reaction_forward_mol_exponent};T2_reaction_forward_energy=${T2_reaction_forward_energy};diffusivity_OT_prefactor_exponent=${diffusivity_OT_prefactor_exponent};diffusivity_OT_energy=${diffusivity_OT_energy};diffusivity_V_O_prefactor_exponent=${diffusivity_V_O_prefactor_exponent};diffusivity_V_O_energy=${diffusivity_V_O_energy};electron_concentration_initial_expo=${electron_concentration_initial_expo};electron_concentration_initial_energy=${electron_concentration_initial_energy};Outputs/csv/enable=true + V_current=${target_voltage_V8};target_flux=${target_flux_V8};temperature_initial=973;delta_H_T2O=${delta_H_T2O};delta_S_T2O=${delta_S_T2O};delta_H_T2=${delta_H_T2};delta_S_T2=${delta_S_T2};T2O_reaction_forward_mol_exponent=${T2O_reaction_forward_mol_exponent};T2O_reaction_forward_energy=${T2O_reaction_forward_energy};T2_reaction_forward_mol_exponent=${T2_reaction_forward_mol_exponent};T2_reaction_forward_energy=${T2_reaction_forward_energy};diffusivity_OT_prefactor_exponent=${diffusivity_OT_prefactor_exponent};diffusivity_OT_energy=${diffusivity_OT_energy};diffusivity_V_O_prefactor_exponent=${diffusivity_V_O_prefactor_exponent};diffusivity_V_O_energy=${diffusivity_V_O_energy};electron_concentration_initial_expo=${electron_concentration_initial_expo};electron_concentration_initial_energy=${electron_concentration_initial_energy};Outputs/csv/enable=true + V_current=${target_voltage_V9};target_flux=${target_flux_V9};temperature_initial=973;delta_H_T2O=${delta_H_T2O};delta_S_T2O=${delta_S_T2O};delta_H_T2=${delta_H_T2};delta_S_T2=${delta_S_T2};T2O_reaction_forward_mol_exponent=${T2O_reaction_forward_mol_exponent};T2O_reaction_forward_energy=${T2O_reaction_forward_energy};T2_reaction_forward_mol_exponent=${T2_reaction_forward_mol_exponent};T2_reaction_forward_energy=${T2_reaction_forward_energy};diffusivity_OT_prefactor_exponent=${diffusivity_OT_prefactor_exponent};diffusivity_OT_energy=${diffusivity_OT_energy};diffusivity_V_O_prefactor_exponent=${diffusivity_V_O_prefactor_exponent};diffusivity_V_O_energy=${diffusivity_V_O_energy};electron_concentration_initial_expo=${electron_concentration_initial_expo};electron_concentration_initial_energy=${electron_concentration_initial_energy};Outputs/csv/enable=true' + execute_on = 'INITIAL' + max_procs_per_app = 1 + ignore_solve_not_converge = true + [] + [sub_small] + type = FullSolveMultiApp + input_files = 'val-2l_joule_heating.i' + positions = '0 0 0' + # with csv + cli_args = 'V_current=${target_voltage_V0};target_flux=${target_flux_V0};delta_H_T2O=${delta_H_T2O};delta_S_T2O=${delta_S_T2O};delta_H_T2=${delta_H_T2};delta_S_T2=${delta_S_T2};T2O_reaction_forward_mol_exponent=${T2O_reaction_forward_mol_exponent};T2O_reaction_forward_energy=${T2O_reaction_forward_energy};T2_reaction_forward_mol_exponent=${T2_reaction_forward_mol_exponent};T2_reaction_forward_energy=${T2_reaction_forward_energy};diffusivity_OT_prefactor_exponent=${diffusivity_OT_prefactor_exponent};diffusivity_OT_energy=${diffusivity_OT_energy};diffusivity_V_O_prefactor_exponent=${diffusivity_V_O_prefactor_exponent};diffusivity_V_O_energy=${diffusivity_V_O_energy};electron_concentration_initial_expo=${electron_concentration_initial_expo};electron_concentration_initial_energy=${electron_concentration_initial_energy};Outputs/csv/enable=true' + execute_on = 'INITIAL' + max_procs_per_app = 1 + ignore_solve_not_converge = true + [] +[] + +[Transfers] + [get_error_sum] + type = MultiAppPostprocessorTransfer + from_multi_app = sub + from_postprocessor = relative_error_sq + to_postprocessor = combined_relative_error_sq + reduction_type = sum + [] +[] + +[Postprocessors] + [combined_relative_error_sq] + type = Receiver + [] + [pp_RMSPE] + type = ParsedPostprocessor + pp_names = 'combined_relative_error_sq' + expression = 'sqrt(combined_relative_error_sq / 10)' + execute_on = 'TIMESTEP_END' + [] + [pp_log_inverse_error] + type = ParsedPostprocessor + pp_names = 'pp_RMSPE' + expression = 'log(1 / pp_RMSPE)' + execute_on = 'TIMESTEP_END' + [] +[] + +[Controls] + [stochastic] + type = SamplerReceiver + [] +[] + +[Outputs] + console = true + csv = true +[] diff --git a/test/tests/val-2l/val-2l_membrane.i b/test/tests/val-2l/val-2l_membrane.i new file mode 100644 index 000000000..9d6948554 --- /dev/null +++ b/test/tests/val-2l/val-2l_membrane.i @@ -0,0 +1,574 @@ +# val-2l: BCY20 hydrogen permeation under applied voltage. +# Unit system: length is converted to nm for the spatial solve, time is s, +# temperature is K, pressure is Pa, concentrations are atoms/nm^3, +# and fluxes reported by the membrane model are atoms/nm^2/s. + +# 14 optimized parameters used by the val-2l validation runs +# Polycrystalline, Porous NiO-BCY base assumed having no impact on hydrogen diffusion + +# Physical constants +R = '${units 8.31446261815324 J/mol/K}' # ideal gas constant based on number used in include/utils/PhysicalConstants.h +N_a = '${units 6.02214076e23 at/mol}' # ideal gas constant based on number used in include/utils/PhysicalConstants.h +q = '${units 1.602176634e-19 C}' # quantity of charge +F = '${fparse N_a * q}' + +# thermal parameters +temperature_initial = '${units 773 K}' # 500C + +# Model parameters +endtime = '1e5' +dt_max = '2e3' +dt_start_charging = '${units 1e-5 s}' +bound_value_min = '${units -1e-20 at/nm^3}' + +# Geometry and mesh +length = '${units 10 mum -> nm}' # BCY20 +num_nodes = 300 + +# Material properties +density_BCY20 = '${units ${fparse 1.0 * 6.154} g/cm^3 -> g/m^3}' +molar_mass_BCY20 = '${units 283.42 g/mol}' +N = '${units ${fparse density_BCY20 / molar_mass_BCY20 * N_a} at/m^3 -> at/nm^3}' # 1.3076089986e10 + +# Initial concentrations +OT_concentration_initial = 1e-5 +hydration_limit_S = 0.2 +oxygen_vacancy_concentration_initial = '${units ${fparse hydration_limit_S / 2 * N} at/nm^3}' +oxygen_concentration_initial = '${units ${fparse 3 * N - oxygen_vacancy_concentration_initial - OT_concentration_initial} at/nm^3}' + +##### Dry Pressure conditions +pressure_atm = '${units 101315 Pa}' +pressure_T2_low = '${units 0 Pa}' # pure N2 and 3% H2O +pressure_T2_high = '${units ${fparse 0.8 * pressure_atm} Pa}' # 80% H2 in N2 and 3% H2O +pressure_T2O_constant = '${units ${fparse 0.03 * pressure_atm} Pa}' # 80% H2 in N2 and 3% H2O + +# chemical_reaction - optimized parameters used for val-2l no-Joule validation +delta_H_T2O = '${units -1.54415211e+05 J/mol}' +delta_S_T2O = '${units -1.67187585e+02 J/mol/K}' +delta_H_T2 = '${units -5.46037663e+04 J/mol}' +delta_S_T2 = '${units -3.36929406e+01 J/mol/K}' +T2O_reaction_forward_mol_exponent = -1.19792592e+01 +ramp_time = 1 +T2O_reaction_forward_mol = '${units ${fparse 8.0 * 10 ^ T2O_reaction_forward_mol_exponent} m^4/mol/s}' +T2O_reaction_forward_value = '${units ${fparse T2O_reaction_forward_mol / N_a} m^4/at/s -> nm^4/at/s}' +T2O_reaction_forward_energy = '${units -7.31595474e+03 J/mol}' +T2_reaction_forward_mol_exponent = -4.05998297e+00 +T2_reaction_forward_mol = '${units ${fparse 8.0 * 10 ^ T2_reaction_forward_mol_exponent} m^4/mol/s}' +T2_reaction_forward_value = '${units ${fparse T2_reaction_forward_mol / N_a} m^4/at/s -> nm^4/at/s}' +T2_reaction_forward_energy = '${units 5.13385478e+03 J/mol}' +diffusivity_OT_prefactor_exponent = -1.26000119e+01 +diffusivity_OT_prefactor = '${units ${fparse 2.03 * 10 ^ diffusivity_OT_prefactor_exponent} m^2/s -> nm^2/s}' +diffusivity_OT_energy = '${units 8.65880079e+03 J/mol}' +diffusivity_V_O_prefactor_exponent = -5.33084375e+00 +diffusivity_V_O_prefactor = '${units ${fparse 1.1 * 10 ^ diffusivity_V_O_prefactor_exponent} m^2/s -> nm^2/s}' +diffusivity_V_O_energy = '${units 5.87658926e+04 J/mol}' +diffusivity_e_prefactor = '${units 2.06292148e-02 m^2/s -> nm^2/s}' # data from Yang 2026 +diffusivity_e_energy = '${units 9.53470966e+04 J/mol}' +# ELECTRON +electron_concentration_initial_expo = 4.94096686e-01 +electron_concentration_initial_energy = '${units 5.90846106e+04 J/mol}' +electron_concentration_initial = '${units ${fparse 10 ^ electron_concentration_initial_expo * N} at/nm^3}' + +# voltage +V_current = 2.0 # CONSTANT_VOLTAGE - no ${units} wrapper so CLI override works + +# target flux for error computation (overridden by parent via cli_args) +target_flux = 1e20 + +[Mesh] + [cmg] + type = CartesianMeshGenerator + dim = 1 + dx = '${fparse length}' + ix = '${fparse num_nodes}' + subdomain_id = '0' + [] +[] + +[Variables] + #### Dry variable + [OT_concentration_dry] # (atoms/nm^3) + initial_condition = ${OT_concentration_initial} + [] + [Oxygen_vacancy_concentration_dry] + initial_condition = ${oxygen_vacancy_concentration_initial} + [] +[] + +[Bounds] + [concentration_dry_lower_bound] + type = ConstantBounds + variable = bounds_dummy + bounded_variable = OT_concentration_dry + bound_type = lower + bound_value = ${bound_value_min} + [] + [concentration_dry_V_O_lower_bound] + type = ConstantBounds + variable = bounds_dummy + bounded_variable = Oxygen_vacancy_concentration_dry + bound_type = lower + bound_value = ${bound_value_min} + [] + [concentration_dry_V_O_upper_bound] + type = ConstantBounds + variable = bounds_dummy + bounded_variable = Oxygen_vacancy_concentration_dry + bound_type = upper + bound_value = ${fparse 3 * N} + [] +[] + +[AuxVariables] + [bounds_dummy] + order = FIRST + family = LAGRANGE + [] + [temperature] + initial_condition = ${temperature_initial} + [] + #### Dry auxvariable + [pressure_T2_dry] + [] + [pressure_T2O_dry] + [] + [Oxygen_concentration_dry] + initial_condition = ${oxygen_concentration_initial} + [] + [electron_concentration_dry] + [] + + # CONSTANT_VOLTAGE + [voltage_phi] + [] +[] + + +[AuxKernels] + [temperature_Aux] + type = FunctionAux + variable = temperature + function = Temperature_function + [] + + #### Dry auxkernels + [pressure_T2_dry_Aux] + type = FunctionAux + variable = pressure_T2_dry + function = Pressure_T2_dry_function + [] + [pressure_T2O_dry_Aux] + type = FunctionAux + variable = pressure_T2O_dry + function = Pressure_T2O_dry_function + [] + [Oxygen_concentration_dry_Aux] # at/nm^3 + type = ParsedAux + variable = Oxygen_concentration_dry + coupled_variables = 'Oxygen_vacancy_concentration_dry' + expression = '3 * ${N} - Oxygen_vacancy_concentration_dry' + [] + + # ELECTRON + [electron_concentration_dry_Aux] + type = ParsedAux + variable = electron_concentration_dry + coupled_variables = 'temperature' + expression = '${electron_concentration_initial} * 0.5 * exp(-${electron_concentration_initial_energy} / ${R} / temperature)' + execute_on = 'INITIAL TIMESTEP_END' + [] + + # CONSTANT_VOLTAGE + [phi_auxkernel] + type = FunctionAux + variable = voltage_phi + function = '${V_current} * (${length} - x) / ${length}' + execute_on = 'INITIAL TIMESTEP_END' + [] + +[] + +[Problem] + type = ReferenceResidualProblem + extra_tag_vectors = 'ref' + reference_vector = 'ref' +[] + +[Kernels] + #### Dry kernels + [time_OT_dry] + type = ADTimeDerivative + variable = OT_concentration_dry + extra_vector_tags = ref + [] + [diffusion_OT_dry] + type = ADMatDiffusion + variable = OT_concentration_dry + diffusivity = diffusivity_OT + extra_vector_tags = ref + [] + [time_V_O_dry] + type = ADTimeDerivative + variable = Oxygen_vacancy_concentration_dry + extra_vector_tags = ref + [] + [diffusion_V_O_dry] + type = ADMatDiffusion + variable = Oxygen_vacancy_concentration_dry + diffusivity = diffusivity_V_O + extra_vector_tags = ref + [] + # voltage for OH + [diffusion_phi_PCC_OH] + type = ADMatDiffusion + variable = OT_concentration_dry + v = voltage_phi + diffusivity = conductivity_OH + extra_vector_tags = ref + [] + # voltage for V_O + [diffusion_phi_PCC_V_O] + type = ADMatDiffusion + variable = Oxygen_vacancy_concentration_dry + v = voltage_phi + diffusivity = conductivity_V_O + extra_vector_tags = ref + [] +[] + +[BCs] + #### Dry BCs + [left_OT_dry] + type = ADMatNeumannBC + variable = OT_concentration_dry + boundary = left + value = 1 + boundary_material = flux_on_OT_dry + [] + [left_V_O_dry] + type = ADMatNeumannBC + variable = Oxygen_vacancy_concentration_dry + boundary = left + value = 1 + boundary_material = flux_on_V_O_dry + [] + [right_OT_dry] + type = ADMatNeumannBC + variable = OT_concentration_dry + boundary = right + value = 1 + boundary_material = flux_on_OT_dry + [] + [right_V_O_dry] + type = ADMatNeumannBC + variable = Oxygen_vacancy_concentration_dry + boundary = right + value = 1 + boundary_material = flux_on_V_O_dry + [] +[] + +[Functions] + [Temperature_function] + type = ParsedFunction + expression = '${temperature_initial}' + [] + [Pressure_T2_dry_function] + type = ParsedFunction + expression = 'min(t / ${ramp_time}, 1.0) * (${pressure_T2_high} * (${length} - x) / ${length} + ${pressure_T2_low}) / ${pressure_atm}' + [] + [Pressure_T2O_dry_function] + type = ParsedFunction + expression = 'min(t / ${ramp_time}, 1.0) * (${pressure_T2O_constant}) / ${pressure_atm}' + [] +[] + +[Materials] + [diffusivity_OT] + type = ADParsedMaterial + property_name = 'diffusivity_OT' + coupled_variables = 'temperature' + expression = '${diffusivity_OT_prefactor} * exp(-${diffusivity_OT_energy} / ${R} / temperature)' + [] + [diffusivity_V_O] + type = ADParsedMaterial + property_name = 'diffusivity_V_O' + coupled_variables = 'temperature' + expression = '${diffusivity_V_O_prefactor} * exp(-${diffusivity_V_O_energy} / ${R} / temperature)' + [] + [diffusivity_e] + type = ADParsedMaterial + property_name = 'diffusivity_e' + coupled_variables = 'temperature' + expression = '${diffusivity_e_prefactor} * exp(-${diffusivity_e_energy} / ${R} / temperature)' + [] + [converter_to_nonAD] + type = MaterialADConverter + ad_props_in = 'diffusivity_OT diffusivity_V_O diffusivity_e conductivity_OH conductivity_e' + reg_props_out = 'diffusivity_OT_nonAD diffusivity_V_O_nonAD diffusivity_e_nonAD conductivity_OH_nonAD conductivity_e_nonAD' + outputs = 'none' + [] + [conductivity_OH] + type = ADParsedMaterial + property_name = 'conductivity_OH' + coupled_variables = 'OT_concentration_dry temperature' + material_property_names = 'diffusivity_OT' + expression = 'diffusivity_OT * ${F} * OT_concentration_dry / ${R} / temperature' + [] + [conductivity_V_O] + type = ADParsedMaterial + property_name = 'conductivity_V_O' + coupled_variables = 'Oxygen_vacancy_concentration_dry temperature' + material_property_names = 'diffusivity_V_O' + expression = '2 * diffusivity_V_O * ${F} * Oxygen_vacancy_concentration_dry / ${R} / temperature' + [] + [conductivity_e] + type = ADParsedMaterial + property_name = 'conductivity_e' + coupled_variables = 'electron_concentration_dry temperature' + material_property_names = 'diffusivity_e' + expression = '- diffusivity_e * ${F} * electron_concentration_dry / ${R} / temperature' + [] + [reaction_equilibrium_constant_T2] + type = ADParsedMaterial + property_name = 'T2_K_eq' + coupled_variables = 'temperature' + expression = 'exp( ( ${delta_H_T2} - temperature * ${delta_S_T2}) / ${R} / temperature )' + [] + [reaction_forward_T2] + type = ADParsedMaterial + property_name = 'T2_K_forward' + coupled_variables = 'temperature' + expression = '${T2_reaction_forward_value} * exp(-${T2_reaction_forward_energy} / ${R} / temperature)' + [] + [reaction_reverse_T2] + type = ADParsedMaterial + property_name = 'T2_K_reverse' + material_property_names = 'T2_K_forward T2_K_eq' + expression = 'T2_K_forward / T2_K_eq' + [] + + [reaction_equilibrium_constant_T2O] + type = ADParsedMaterial + property_name = 'T2O_K_eq' + coupled_variables = 'temperature' + expression = 'exp( ( ${delta_H_T2O} - temperature * ${delta_S_T2O}) / ${R} / temperature )' + [] + [reaction_forward_T2O] + type = ADParsedMaterial + property_name = 'T2O_K_forward' + coupled_variables = 'temperature' + expression = '${T2O_reaction_forward_value} * exp(-${T2O_reaction_forward_energy} / ${R} / temperature)' + [] + [reaction_reverse_T2O] + type = ADParsedMaterial + property_name = 'T2O_K_reverse' + material_property_names = 'T2O_K_forward T2O_K_eq' + expression = 'T2O_K_forward / T2O_K_eq' + [] + + #### Reaction for dry + [flux_base_on_T2_dry] # T2 + 2 O -> 2 OT + 2 e + type = ADDerivativeParsedMaterial + coupled_variables = 'OT_concentration_dry pressure_T2_dry Oxygen_vacancy_concentration_dry electron_concentration_dry' + property_name = 'flux_base_on_T2_dry' + material_property_names = 'T2_K_forward T2_K_reverse' + expression = '(T2_K_forward * pressure_T2_dry * (3 * ${N} - Oxygen_vacancy_concentration_dry)^2 - T2_K_reverse * OT_concentration_dry^2 * electron_concentration_dry^2)' + [] + [flux_base_on_T2O_dry] # T2O + V_O + O -> 2 OT + type = ADDerivativeParsedMaterial + coupled_variables = 'OT_concentration_dry pressure_T2O_dry Oxygen_vacancy_concentration_dry' + property_name = 'flux_base_on_T2O_dry' + material_property_names = 'T2O_K_forward T2O_K_reverse' + expression = '(T2O_K_forward * pressure_T2O_dry * (3 * ${N} - Oxygen_vacancy_concentration_dry) * Oxygen_vacancy_concentration_dry - T2O_K_reverse * OT_concentration_dry^2)' + [] + + + #### Flux for dry + [flux_on_e_dry] # electron + type = ADDerivativeParsedMaterial + property_name = 'flux_on_e_dry' + material_property_names = 'flux_base_on_T2_dry' + expression = '2 * flux_base_on_T2_dry' + [] + [flux_on_OT_dry] # OT + type = ADDerivativeParsedMaterial + property_name = 'flux_on_OT_dry' + material_property_names = 'flux_base_on_T2_dry flux_base_on_T2O_dry' + expression = '2 * flux_base_on_T2_dry + 2 * flux_base_on_T2O_dry' + [] + [flux_on_T2_dry] # T2 + type = ADDerivativeParsedMaterial + property_name = 'flux_on_T2_dry' + material_property_names = 'flux_base_on_T2_dry' + expression = '-1 * flux_base_on_T2_dry' + [] + [flux_on_V_O_dry] # V_O + type = ADDerivativeParsedMaterial + property_name = 'flux_on_V_O_dry' + material_property_names = 'flux_base_on_T2O_dry' + expression = '-1 * flux_base_on_T2O_dry' + [] + [flux_on_T2O_dry] # T2O + type = ADDerivativeParsedMaterial + property_name = 'flux_on_T2O_dry' + material_property_names = 'flux_base_on_T2O_dry' + expression = '-1 * flux_base_on_T2O_dry' + [] +[] + +[Postprocessors] + #### Postprocessors for flux under dry + [recombination_flux_T2_dry_left] + type = ADSideAverageMaterialProperty + boundary = left + property = flux_on_T2_dry + execute_on = 'INITIAL TIMESTEP_END' + outputs = 'console csv' + [] + [recombination_flux_T2O_dry_left] + type = ADSideAverageMaterialProperty + boundary = left + property = flux_on_T2O_dry + execute_on = 'INITIAL TIMESTEP_END' + outputs = 'console csv' + [] + [recombination_flux_OT_dry_left] + type = ADSideAverageMaterialProperty + boundary = left + property = flux_on_OT_dry + execute_on = 'INITIAL TIMESTEP_END' + outputs = 'console csv' + [] + [recombination_flux_OT_dry_right] + type = ADSideAverageMaterialProperty + boundary = right + property = flux_on_OT_dry + execute_on = 'INITIAL TIMESTEP_END' + outputs = 'console csv' + [] + [recombination_flux_T2O_dry_right] + type = ADSideAverageMaterialProperty + boundary = right + property = flux_on_T2O_dry + execute_on = 'INITIAL TIMESTEP_END' + outputs = 'console csv' + [] + [recombination_flux_T2_dry_right] + type = ADSideAverageMaterialProperty + boundary = right + property = flux_on_T2_dry + execute_on = 'INITIAL TIMESTEP_END' + outputs = 'console csv' + [] + + # necessary parameters + [T2_K_eq_average] + type = ADElementAverageMaterialProperty + mat_prop = T2_K_eq + [] + [T2_K_forward_average] + type = ADElementAverageMaterialProperty + mat_prop = T2_K_forward + [] + [T2_K_reverse_average] + type = ADElementAverageMaterialProperty + mat_prop = T2_K_reverse + [] + [T2O_K_eq_average] + type = ADElementAverageMaterialProperty + mat_prop = T2O_K_eq + [] + [T2O_K_forward_average] + type = ADElementAverageMaterialProperty + mat_prop = T2O_K_forward + [] + [T2O_K_reverse_average] + type = ADElementAverageMaterialProperty + mat_prop = T2O_K_reverse + [] + [diffusivity_OT_average] + type = ADElementAverageMaterialProperty + mat_prop = diffusivity_OT + execute_on = 'INITIAL TIMESTEP_END' + [] + [diffusivity_V_O_average] + type = ADElementAverageMaterialProperty + mat_prop = diffusivity_V_O + execute_on = 'INITIAL TIMESTEP_END' + [] + [temperature_average] + type = ElementAverageValue + variable = temperature + execute_on = 'INITIAL TIMESTEP_END' + [] + [voltage_value] + type = ParsedPostprocessor + expression = ${V_current} + execute_on = 'INITIAL TIMESTEP_END' + [] + [pressure_T2_average] + type = ElementAverageValue + variable = pressure_T2_dry + execute_on = 'INITIAL TIMESTEP_END' + [] + [log_error_sq] + type = ParsedPostprocessor + pp_names = 'recombination_flux_OT_dry_right' + expression = '(log(abs(recombination_flux_OT_dry_right * 1e18)) - log(${target_flux}))^2' + execute_on = 'TIMESTEP_END' + [] + [relative_error_sq] + type = ParsedPostprocessor + pp_names = 'recombination_flux_OT_dry_right' + expression = '(abs(recombination_flux_OT_dry_right * 1e18) - ${target_flux})^2' + execute_on = 'TIMESTEP_END' + [] +[] + +[Controls] + [stochastic] + type = SamplerReceiver + [] +[] + +[Executioner] + type = Transient + scheme = implicit-euler + solve_type = NEWTON + petsc_options_iname = '-pc_type -snes_type' + petsc_options_value = 'lu vinewtonrsls' + nl_rel_tol = 5e-6 + nl_abs_tol = 5e-7 + end_time = ${endtime} + automatic_scaling = true + compute_scaling_once = true + line_search = none + error_on_dtmin = false # must stay false for ignore_solve_not_converge to work in Level 2 + abort_on_solve_fail = true # fast-fail on first NL divergence; prevents stutter at dtmin + dtmin = 1e-10 + nl_max_its = 20 + dtmax = ${dt_max} + [TimeStepper] + type = IterationAdaptiveDT + dt = ${dt_start_charging} + optimal_iterations = 15 + growth_factor = 2.0 + cutback_factor = 0.5 + cutback_factor_at_failure = 0.5 + [] +[] + +[Debug] + show_var_residual_norms = true +[] + +[Outputs] + exodus = false + [csv] + type = CSV + [] + # [exodus] + # type = Exodus + # [] +[] From b6b26c1f6a1f2605e5ca48fd9c11b6e947fa56b0 Mon Sep 17 00:00:00 2001 From: Lin Yang <132409718+lin-yang-ly@users.noreply.github.com> Date: Wed, 8 Jul 2026 08:26:47 -0600 Subject: [PATCH 2/2] Add PCC multiscale fuel-cycle example Refs #429 AI-assisted: true AI-model: GPT-5 AI-version: Codex Co-Authored-By: GPT-5 --- doc/content/bib/tmap8.bib | 66 + .../examples/PCC_multiscale_example/index.md | 152 + doc/content/examples/index.md | 3 +- test/tests/PCC_multiscale_example/analysis.md | 139 + .../comparison_PCC_membrane.py | 112 + .../dir_pcc_fuel_cycle.i | 708 ++++ .../dir_pcc_membrane_sub.i | 715 ++++ .../fit_residence_time.py | 102 + .../fuel_cycle_PCC_membrane.i | 748 +++++ ...pcc_fuel_cycle_2rt_10Pa_out2_reference.csv | 2681 +++++++++++++++ ..._pcc_fuel_cycle_2rt_10Pa_out_reference.csv | 2880 +++++++++++++++++ .../gold/fuel_cycle_PCC_membrane_out.csv | 42 + .../gold/fuel_cycle_base_out_reference.csv | 2880 +++++++++++++++++ .../gold/membrane_10_Pa_flux.csv | 42 + .../gold/membrane_5_Pa_flux.csv | 101 + .../gold/membrane_5_Pa_flux_tmp.csv | 98 + .../PCC_multiscale_example/pcc_membrane_sub.i | 726 +++++ .../PCC_multiscale_example/plot_dir_flux.py | 61 + .../plot_dir_fraction_pressure.py | 133 + .../plot_inventory_comparison.py | 188 ++ .../split_membrane_steps.py | 87 + .../steady_pcc_membrane_sub.i | 715 ++++ test/tests/PCC_multiscale_example/tests | 40 + 23 files changed, 13418 insertions(+), 1 deletion(-) create mode 100644 doc/content/examples/PCC_multiscale_example/index.md create mode 100644 test/tests/PCC_multiscale_example/analysis.md create mode 100644 test/tests/PCC_multiscale_example/comparison_PCC_membrane.py create mode 100644 test/tests/PCC_multiscale_example/dir_pcc_fuel_cycle.i create mode 100644 test/tests/PCC_multiscale_example/dir_pcc_membrane_sub.i create mode 100644 test/tests/PCC_multiscale_example/fit_residence_time.py create mode 100644 test/tests/PCC_multiscale_example/fuel_cycle_PCC_membrane.i create mode 100644 test/tests/PCC_multiscale_example/gold/dir_pcc_fuel_cycle_2rt_10Pa_out2_reference.csv create mode 100644 test/tests/PCC_multiscale_example/gold/dir_pcc_fuel_cycle_2rt_10Pa_out_reference.csv create mode 100644 test/tests/PCC_multiscale_example/gold/fuel_cycle_PCC_membrane_out.csv create mode 100644 test/tests/PCC_multiscale_example/gold/fuel_cycle_base_out_reference.csv create mode 100644 test/tests/PCC_multiscale_example/gold/membrane_10_Pa_flux.csv create mode 100644 test/tests/PCC_multiscale_example/gold/membrane_5_Pa_flux.csv create mode 100644 test/tests/PCC_multiscale_example/gold/membrane_5_Pa_flux_tmp.csv create mode 100644 test/tests/PCC_multiscale_example/pcc_membrane_sub.i create mode 100644 test/tests/PCC_multiscale_example/plot_dir_flux.py create mode 100644 test/tests/PCC_multiscale_example/plot_dir_fraction_pressure.py create mode 100644 test/tests/PCC_multiscale_example/plot_inventory_comparison.py create mode 100644 test/tests/PCC_multiscale_example/split_membrane_steps.py create mode 100644 test/tests/PCC_multiscale_example/steady_pcc_membrane_sub.i create mode 100644 test/tests/PCC_multiscale_example/tests diff --git a/doc/content/bib/tmap8.bib b/doc/content/bib/tmap8.bib index 3f1970df1..0f794ed1f 100644 --- a/doc/content/bib/tmap8.bib +++ b/doc/content/bib/tmap8.bib @@ -883,3 +883,69 @@ @article{dhulipala2025moose year={2025}, publisher={Elsevier} } + +@article{simon2026, + title={{Advanced tritium transport modeling and verification, validation, and benchmarking from component level to fuel cycle scale using TMAP8}}, + author={Simon, Pierre-Cl{\'e}ment A and Icenhour, Casey T and Yang, Lin and Kadz, Lee and Bhave, Chaitanya and Singh, Gyanender and Giudicelli, Guillaume and Lindsay, Alexander D and Humrickhouse, Paul and Calderoni, Pattrick and Shimada, Masashi}, + journal={Fusion Engineering and Design}, + year={2026}, + note={(submitted)} +} + +@article{gaston2015physics, + title={Physics-based multiscale coupling for full core nuclear reactor simulation}, + author={Gaston, Derek R and Permann, Cody J and Peterson, John W and Slaughter, Andrew E and Andr{\v{s}}, David and Wang, Yaqi and Short, Michael P and Perez, Danielle M and Tonks, Michael R and Ortensi, Javier and others}, + journal={Annals of Nuclear Energy}, + volume={84}, + pages={45--54}, + year={2015}, + publisher={Elsevier} +} + +@article{permann2020moose, + title={MOOSE: Enabling massively parallel multiphysics simulation}, + author={Permann, Cody J and Gaston, Derek R and Andr{\v{s}}, David and Carlsen, Robert W and Kong, Fande and Lindsay, Alexander D and Miller, Jason M and Peterson, John W and Slaughter, Andrew E and Stogner, Roy H and others}, + journal={SoftwareX}, + volume={11}, + pages={100430}, + year={2020}, + publisher={Elsevier} +} + +@article{li2024direct, + title={Direct internal recycling fractions approaching unity}, + author={Li, Chao and Way, J Douglas and Fuerst, Thomas F and Wolden, Colin A}, + journal={Fusion Engineering and Design}, + volume={209}, + pages={114705}, + year={2024}, + publisher={Elsevier} +} + +@article{abdou2020physics, + title={{Physics and technology considerations for the deuterium--tritium fuel cycle and conditions for tritium fuel self sufficiency}}, + author={Abdou, Mohamed and Riva, Marco and Ying, Alice and Day, Christian and Loarte, Alberto and Baylor, LR and Humrickhouse, Paul and Fuerst, Thomas F and Cho, Seungyon}, + journal={Nuclear fusion}, + volume={61}, + number={1}, + pages={013001}, + year={2020}, + publisher={IOP Publishing} +} + +@article{yang2026multiscale, + title={Multiscale Assessment of Tritium Behavior in Preliminary Fusion Pilot Plant Design Using Surrogate Models in TMAP8}, + author={Yang, Lin and Simon, Pierre-Cl{\'e}ment A and Yildirim, Emre and Trueba, Jos{\'e} and Robinson, Matthew and Shimada, Masashi}, + journal={arXiv preprint arXiv:2604.19647}, + year={2026} +} + +@article{bonanos2015h, + title={H/D isotope effects in high temperature proton conductors}, + author={Bonanos, Nikolaos and Huijser, A and Poulsen, Finn Willy}, + journal={Solid State Ionics}, + volume={275}, + pages={9--13}, + year={2015}, + publisher={Elsevier} +} diff --git a/doc/content/examples/PCC_multiscale_example/index.md b/doc/content/examples/PCC_multiscale_example/index.md new file mode 100644 index 000000000..3a6860f69 --- /dev/null +++ b/doc/content/examples/PCC_multiscale_example/index.md @@ -0,0 +1,152 @@ +# PCC Multiscale Fuel-Cycle Example + +## General Case Description + +This example integrates a component-level proton-conducting-ceramic (PCC) membrane model into a +system-level tritium fuel-cycle model to examine the potential of PCC membranes as a tritium +extraction technology and as direct internal recycling (DIR) pathways. The two scales are coupled +directly using the MOOSE MultiApp system, with the fuel-cycle model serving as the main application +and the PCC membrane model serving as a sub-application. This coupling evaluates the impact of the +voltage-driven membrane performance predictions from the validated PCC membrane model +[!cite](yang2026elucidating) on fuel-cycle components, rather than treating membrane performance as +a fixed efficiency. + +The tritium fuel-cycle configuration includes 11 subsystems based on the fuel-cycle example from +Meschini et al. reproduced in TMAP8 [!cite](meschini2023modeling,simon2026): the Breeding Blanket, +Tritium Extraction System, First Wall, Divertor, Heat Exchanger, Detritiation System, Vacuum Pump, +Fuel Clean-up, Isotope Separation System, Storage and Management, and the Tritium Permeation +Membrane. The baseline model represents each major component as a zero-dimensional inventory with +input and output flows, source terms, non-radioactive losses, and radioactive decay. + +## Model Description + +The time-dependent tritium retention in each component $i$ is represented by an ordinary +differential equation based on residence time [!cite](abdou2020physics,meschini2023modeling): + +\begin{equation} +\label{eqn:pcc_multiscale_fuel_cycle} +\frac{dI_i}{dt} = \sum_{j\neq i}{\frac{I_j}{\tau_j}} - \left(1+\epsilon_i\right)\frac{I_i}{\tau_i} - \lambda I_i + S_i, +\end{equation} + +where $I_i$ and $\tau_i$ are the tritium inventory and residence time of component $i$, $\epsilon_i$ +represents non-radioactive tritium losses, $\lambda$ is the radioactive decay constant, and $S_i$ is +the tritium source term. + +The PCC membrane is incorporated into the two DIR loops, corresponding to the Vacuum Pump and Fuel +Clean-up systems, and into the Tritium Permeation Membrane. For the two DIR loops, component-scale +PCC membrane simulations are automatically performed during the fuel-cycle calculation. The +fuel-cycle model provides the upstream tritium partial pressure, and each component model returns the +recovered downstream tritium flow. + +At each time step, the fuel cycle converts the tritium inventory stored as T$_2$ gas in the Vacuum +Pump and Fuel Clean-up components into an upstream partial pressure using the ideal-gas law, + +\begin{equation} +\label{eqn:pcc_multiscale_pressure} +P_i = \frac{I_i}{M_{T_2}} \frac{R\,T_\text{feed}}{V_i}, +\end{equation} + +where $M_{T_2}$ is the molar mass of T$_2$, $T_\text{feed} = 773$ K is the assumed feed-gas +temperature, and $V_{VP} = 1600$ m$^3$ and $V_{FCU} = 100$ m$^3$ are the assumed upstream volumes +of the two DIR membrane modules. These volumes maintain upstream pressures on the order of 10 Pa due +to the low tritium partial pressure [!cite](li2024direct). The pressure is passed to the +component-level membrane model as its upstream boundary condition. Each membrane model solves the +voltage-driven transport problem at an applied voltage of 2 V and 773 K, and returns the recovered +steady tritium flux $J_i$ to storage. The membrane sub-applications reuse the hydrogen-calibrated +parameter set with isotope rescaling for tritium, with the tritium diffusivity scaled as +$D_T = D_H / \sqrt{3}$ [!cite](bonanos2015h). + +The DIR fraction is computed from the membrane response rather than prescribed: + +\begin{equation} +\label{eqn:pcc_multiscale_dir} +f_{\mathrm{DIR},i} = \frac{J_i}{I_i/\tau_i}. +\end{equation} + +The active membrane areas are $4\times10^{-1}$ m$^2$ for the Vacuum Pump DIR loop and 1 m$^2$ for +the Fuel Clean-up DIR loop. + +For the Tritium Permeation Membrane, the residence-time representation is updated from a +component-level PCC membrane release calculation rather than running another on-the-fly sub-app. A +standalone membrane calculation at an upstream T$_2$ pressure of 5 Pa gives the downstream tritium +release curve. The two-parameter residence time proposed by Yang et al. [!cite](yang2026multiscale) +is then used to fit the delay time $\tau_{11,0}$ and the release time constant $\tau_{11,1}$. With +an applied voltage of 2 V, the fitted values are $\tau_{11,0} = 14.88$ s and $\tau_{11,1} = 10.68$ +s, which are significantly lower than the baseline residence time of 100 s. + +!media fit_residence_time.py + image_name=fit_residence_time.png + style=width:50%;margin-bottom:2%;margin-left:auto;margin-right:auto + id=pcc_multiscale_residence_time + caption=Two-parameter residence-time fit to downstream tritium release from the PCC membrane at 5 Pa upstream T$_2$ pressure. + +## Multiscale Coupling + +The coupling is implemented using the MultiApp and Transfer systems in MOOSE +[!cite](gaston2015physics,permann2020moose). The fuel-cycle model is the main application, while +each DIR loop is represented by an independent instance of the 1D PCC membrane model. The membrane +sub-applications are solved to steady state at each fuel-cycle time step and coupled back through +postprocessor transfers. + +!listing test/tests/PCC_multiscale_example/dir_pcc_fuel_cycle.i link=false block=MultiApps + +!listing test/tests/PCC_multiscale_example/dir_pcc_fuel_cycle.i link=false block=Transfers + +The model is evaluated on a single-point mesh because all system-level fuel-cycle components are +treated as zero-dimensional inventories. Adaptive time stepping is used to resolve the pulsed +fueling cycle, and BDF2 is used for time integration. The full system-level calculation can be run +for two or more years, but the automated tests use input validation and compact reference data for +the documentation figures to avoid committing large generated output files. + +## Results + +The coupled model computes the upstream T$_2$ partial pressures feeding the two DIR membranes and +the resulting DIR recovery fractions. As tritium accumulates in the Vacuum Pump and Fuel Clean-up +components, the upstream pressure rises to the order of 10 Pa, with fluctuations from periodic +pulsing during the fuel cycle. Once the inventories build up, the voltage-driven membranes recover +nearly all tritium routed through both loops: the Vacuum Pump DIR fraction remains near 1.0, while +the Fuel Clean-up DIR fraction fluctuates between approximately 0.8 and 1.0. + +!media plot_dir_fraction_pressure.py + image_name=dir_pcc_dir_fraction_pressure.png + style=width:50%;margin-bottom:2%;margin-left:auto;margin-right:auto + id=pcc_multiscale_dir_fraction_pressure + caption=Upstream T$_2$ partial pressure and computed DIR recovery fraction for the PCC-enhanced Vacuum Pump and Fuel Clean-up membrane loops. + +The PCC-enhanced fuel cycle reduces inventories in components connected to the DIR loops. In the +manuscript calculation, the Isotope Separation System inventory decreases by six orders of magnitude +relative to the baseline case, while the Fuel Clean-up system and Tritium Permeation Membrane +inventories are reduced by about one order of magnitude. The PCC-enhanced fuel cycle remains +self-sufficient with a startup inventory of 0.79 kg, approximately 30% lower than the 1.14 kg +required by the baseline configuration. + +!media plot_inventory_comparison.py + image_name=dir_pcc_inventory_comparison.png + style=width:50%;margin-bottom:2%;margin-left:auto;margin-right:auto + id=pcc_multiscale_inventory_comparison + caption=Inventory comparison between the baseline fuel-cycle model and the PCC-enhanced multiscale fuel-cycle model. + +## Input Files + +The main fuel-cycle input for the manuscript-style multiscale example is +[/PCC_multiscale_example/dir_pcc_fuel_cycle.i]. The component-level PCC membrane sub-application is +[/PCC_multiscale_example/dir_pcc_membrane_sub.i]. + +!listing test/tests/PCC_multiscale_example/dir_pcc_fuel_cycle.i link=false block=Variables + +!listing test/tests/PCC_multiscale_example/dir_pcc_fuel_cycle.i link=false block=ScalarKernels + +!listing test/tests/PCC_multiscale_example/dir_pcc_fuel_cycle.i link=false block=Postprocessors + +!listing test/tests/PCC_multiscale_example/dir_pcc_fuel_cycle.i link=false block=Executioner + +The shorter `fuel_cycle_PCC_membrane.i` and `pcc_membrane_sub.i` inputs in the same directory retain +a compact lock-step membrane-container coupling demonstration that is useful for checking the basic +pressure-to-flux bridge. + +!alert note title=Full multiscale runs are intentionally manual +The full coupled fuel-cycle calculation solves two component-level PCC membrane sub-applications +during the system-level transient and can produce large CSV outputs. The automated tests validate +the input and regenerate the documentation figures from compact committed reference data. + +!bibtex bibliography diff --git a/doc/content/examples/index.md b/doc/content/examples/index.md index 1c25d81a6..fc82c3de2 100644 --- a/doc/content/examples/index.md +++ b/doc/content/examples/index.md @@ -10,9 +10,10 @@ Because TMAP8 is built on MOOSE, it brings MOOSE's capacity to solve ordinary di equations using [ScalarKernels](syntax/ScalarKernels/index.md). These can be quite useful to model parts of the system at high levels of abstraction while working with detailed models of specific components. -As examples, we propose two fuel cycle models. +As examples, we propose three fuel cycle models. [The first model](examples/fuel_cycle_Abdou/index.md) re-creates the fuel cycle model described in [!cite](Abdou2021) as a high-level abstraction of a fuel cycle in a potential fusion power plant. [The second model](examples/fuel_cycle_Meschini/index.md) re-creates the fuel cycle model described in [!cite](meschini2023modeling), which models the tritium fuel cycle for ARC-and STEP-class DT fusion power plants. +[The PCC multiscale model](examples/PCC_multiscale_example/index.md) couples voltage-driven PCC membrane sub-applications to a system-level fuel-cycle model to compute DIR recovery fractions and inventory impacts from component-scale transport. !content location=fuel_cycle diff --git a/test/tests/PCC_multiscale_example/analysis.md b/test/tests/PCC_multiscale_example/analysis.md new file mode 100644 index 000000000..1844dd363 --- /dev/null +++ b/test/tests/PCC_multiscale_example/analysis.md @@ -0,0 +1,139 @@ +# PCC Membrane ↔ Fuel-Cycle MultiApp Coupling — Analysis Record + +Record of the analysis, design, and verification for coupling the component-level +proton-conducting-ceramic (PCC) tritium-separation membrane into the system-level Meschini-2023 +fuel cycle via a MOOSE MultiApp. + +## 1. Objective + +Replace the lumped tritium-separation-membrane term in the fuel cycle (fixed extraction efficiency +`eta_2 = 0.85`, recovery residence time `residence11`) with a detailed 1D BCY membrane component +model, so the recovery emerges from physics. The membrane upstream is modeled as a **container** +(gas plenum) whose pressure drives the component model, co-evolved in time with the fuel cycle. + +## 2. The two models + +| | Parent (system level) | Sub-app (component level) | +|---|---|---| +| File | `fuel_cycle_PCC_membrane.i` | `pcc_membrane_sub.i` | +| Physics | 11 coupled scalar ODE inventories (Meschini 2023) | 1D BCY membrane: reaction-limited sorption + voltage drift + Joule heating | +| Units | kg of tritium, seconds | nm, Pa, at/nm³, flux at/nm²/s | +| Interface | container pressure (Pa) out, permeation rate (kg/s) in | upstream pressure (Pa) in, fluxes out | + +## 3. Container model and flow topology + +The membrane inventory `I11` (`T_11_membrane`) is a **container** (gas plenum, initial **0 Pa**): + +- IN: the full TES output `T_02_TES/residence2`. +- OUT (permeate): the membrane permeation rate `J` (from the component model) → **heat exchanger + (I5)**. +- OUT (retentate): `T_11_membrane/residence11` (un-permeated) → **recycled to the TES (I2)**. +- decay retained. + +Mass balance (ParsedODEKernel residuals are negated/LHS): +- `[I11]` container: `dN/dt = T_02_TES/residence2 − J − T_11_membrane/residence11 − N·λ`. +- `[I2]` TES: `+ T_11_membrane/residence11` recycle added. +- `[I5]` HX: source is the permeate `J` (`membrane_permeation_rate`). +- `[I10]` storage: membrane term **removed** (permeate goes to the HX, not storage). + +Tritium path: TES → container → {HX (permeate), TES (retentate recycle), decay}. Conserved (minus +decay). Diagnostics: `eta_2_calculated = J/feed` (instantaneous) and `eta_2_cumulative = +∫J dt / ∫feed dt` (smooth; the instantaneous ratio is noisy early when the feed ≈ 0). + +## 4. Pressure ↔ flux bridge (ideal gas) + +- **Down:** `membrane_upstream_pressure = max(T_11_membrane, 0)/M_T2_molar · R · T_feed / V_feed` + [Pa]. `max(.,0)` guards a transient negative holdup (the scalar ODE is not positivity-bounded) + from producing a nonphysical negative pressure. **No upper cap** — the holdup is bounded by the + system inventory, so the pressure cannot run away (an earlier `min(.,1.5e5)` cap was a + never-triggered magic number and was removed). +- **Up:** `permeation_rate_kg_per_s = max(-flux_right, 0) · 1e18 · A_membrane · M_T_atomic / N_a` + [kg/s] (downstream OT flux is negative when tritium permeates out; `1e18`: at/nm²/s → at/m²/s; + one T per OT → atomic-T molar mass). The upstream/downstream fluxes are also pulled up + (`membrane_flux_upstream/downstream`) so the parent CSV carries them too. + +## 5. Lock-step TransientMultiApp coupling (mirrors TE_models/1d_pressure_bakeout...) + +- `TransientMultiApp`, `execute_on = TIMESTEP_END`, `positions = '0 0 0'`. The membrane co-evolves + on the **same global clock** as the fuel cycle (no steady-state self-termination, warm + continuation). The sub `endtime` is large; the parent drives the stop time. +- `sub_cycling = true`: the membrane takes its own (smaller, adaptive) timesteps to reach the + parent's time within each fuel-cycle step — required because the parent `dt` (≥ ~1e3 s, up to + 1e6 s) far exceeds the membrane's stable step from a cold start. `output_sub_cycles = false` keeps + the sub CSV to one row per fuel-cycle step. +- Transfers (all `TIMESTEP_END`, `MultiAppPostprocessorTransfer`): down `membrane_upstream_pressure + → received_pressure`; up `permeation_rate_kg_per_s → membrane_permeation_rate`, and the + left/right fluxes. Within `TIMESTEP_END`, `execute(TIMESTEP_END)` computes the pressure before + `execMultiApps`, so the fresh end-of-step pressure is sent down. +- **Fixed-point (Picard) iteration with under-relaxation** on the parent (`fixed_point_max_its`, + `relaxation_factor`, `transformed_postprocessors = 'membrane_permeation_rate'`). The membrane + permeates steeply at low container pressure, so an explicit one-step-lagged coupling oscillates + and drives the holdup negative; Picard makes `J` and the holdup mutually consistent each step. + (`TransientMultiApp` supports fixed-point iteration natively; `FullSolveMultiApp` does not unless + `auto_advance = true`.) + +## 6. Membrane area is the key calibration knob + +The membrane is a voltage-driven pump: at large area it permeates faster than the fuel cycle feeds +it, so the container cannot pressurize. Verified directly: at `A_membrane = 1 m²` the membrane +permeates ~1.5e-8 kg/s even at ~1e-5 Pa, exceeding the TES feed (~2e-9 kg/s early), so the +container pressure stays ~0 (sub-µPa) and the holdup hovers at ~0. The area is therefore sized so +the membrane permeates ~the feed only at a meaningful pressure: + +| Param | File | Value | Role | +|---|---|---|---| +| `A_membrane` | sub | 2.0e-3 m² (≈20 cm²) | flux → kg/s scale; sets the operating pressure | +| `V_feed` | parent | 10 m³ | holdup → pressure; lowers gain / slows dynamics (steady P is area-set) | +| `T_feed` | parent | 773 K | container gas temperature (matches the membrane) | +| `residence11` | parent | 100 s | retentate recycle time to the TES | + +Steady container pressure is set by the membrane (flux = feed) and is largely independent of +`V_feed`; `V_feed` and `A_membrane` are documented placeholders to calibrate to a real device. + +## 7. Verification (this machine: macOS arm64; `export SDKROOT=/Users/$(whoami)/sdks/MacOSX26.2.sdk`) + +Coupled run (`simulation_time = 20000`, ~75 s with Picard + sub_cycling), exit 0, no solver +failures, all values finite: +- Container pressure rises **smoothly 0 → 0.37 Pa** (continues toward ~Pa-scale as the TES fills) — + the key verification curve. +- `membrane_permeation_rate` and `T_05_HX` (HX, fed by permeate) grow smoothly. +- Container holdup `T_11_membrane` positive and smooth (a negligible −4e-8 numerical blip at the + very start; `max(.,0)` clamps the pressure there). +- `eta_2_cumulative` is smooth, settling ~0.38 by t=20000 (vs the lumped 0.85 → RMSPE ≈ 41%): with + this area the physics-based recovery is well below the assumed value, and it declines as the feed + grows (the fixed-area membrane saturates). +- `total_tritium` conserved (0.8030 → 0.8033, breeding gain). +- Both CSVs carry the interface quantities — parent: `membrane_upstream_pressure`, + `membrane_permeation_rate`, `membrane_flux_upstream/downstream`; sub + (`fuel_cycle_PCC_membrane_out_pcc_membrane0_csv.csv`): `received_pressure`, + `recombination_flux_OT_dry_left/right`, `permeation_rate_kg_per_s`. + +## 8. How to run + +```bash +cd test/tests/PCC_multiscale_example +../../../tmap8-opt -i fuel_cycle_PCC_membrane.i --check-input +../../../tmap8-opt -i fuel_cycle_PCC_membrane.i simulation_time=20000 # coupled run (manual/heavy) +python3 comparison_PCC_membrane.py # plots incl. container pressure +../../../../run_tests --re PCC_multiscale_example # CI tests (filter is --re, NOT -i) +``` +If an arm64/JIT error appears, first `export SDKROOT=/Users/$(whoami)/sdks/MacOSX26.2.sdk`. + +**Testing structure.** The CI `tests` cover only `check_input` (input validity) and `comparison` +(the verification plot, which reads the committed gold). The full coupled run is **not** a CI +CSVDiff: the warm-continued, sub-cycled bounded membrane solver intermittently emits a non-fatal +"failed to converge" warning, and the harness's `--error` flag would turn that fatal. The coupled +run is therefore exercised manually (above) and its gold is committed for the plot. + +## 9. Notes / future work + +- `A_membrane`/`V_feed` are placeholders; calibrate to a real device and target recovery. To raise + the recovery toward 0.85, increase the area (but not so far the container stops pressurizing) or + lengthen `residence11`. +- The full 3-year run is expensive (membrane PDE sub-cycled + Picard-iterated every fuel-cycle + step) — heavy. +- Coupled CSVDiff is environment-sensitive (nonlinear PDE sub-app); gold on macOS arm64, relaxed + tolerances. +- A `steady_*` `FullSolveMultiApp` variant of these inputs exists in the directory as a + single-pass comparison; this case is the lock-step `TransientMultiApp` version. +- `tests` uses issue `#429`. diff --git a/test/tests/PCC_multiscale_example/comparison_PCC_membrane.py b/test/tests/PCC_multiscale_example/comparison_PCC_membrane.py new file mode 100644 index 000000000..f998d9573 --- /dev/null +++ b/test/tests/PCC_multiscale_example/comparison_PCC_membrane.py @@ -0,0 +1,112 @@ +#!/usr/bin/env python3 +"""Comparison / verification plots for the PCC membrane <-> fuel-cycle MultiApp coupling. + +The tritium-separation membrane is modeled as an upstream CONTAINER (gas plenum, initially 0 Pa) +fed by the TES (T_02_TES/residence2). A 1D proton-conducting-ceramic (BCY) membrane sub-app, +co-evolved in lock-step (TransientMultiApp), permeates tritium from the container to the heat +exchanger; the un-permeated retentate (T_11_membrane/residence11) is recycled to the TES. This +script plots the container pressure history (the key verification curve), the physics-based +extraction efficiency (instantaneous and cumulative, vs the lumped 0.85 assumption with RMSPE), the +flow split, and the global tritium conservation. + +Run as part of the test suite (RunCommand) or standalone for documentation figures. +""" + +import os + +import numpy as np +import pandas as pd +import matplotlib.pyplot as plt + +# Resolve data/figure paths for both the test tree and the documentation build. +script_folder = os.path.dirname(os.path.abspath(__file__)) +if "/TMAP8/doc/" in script_folder: + path = "../../../../test/tests/PCC_multiscale_example" +else: + path = script_folder + +# Prefer a freshly produced output; fall back to the committed gold. +candidates = [ + os.path.join(path, "fuel_cycle_PCC_membrane_out.csv"), + os.path.join(path, "gold", "fuel_cycle_PCC_membrane_out.csv"), +] +csv_file = next((c for c in candidates if os.path.isfile(c)), None) +if csv_file is None: + raise FileNotFoundError("Could not find fuel_cycle_PCC_membrane_out.csv in {}".format(candidates)) + +data = pd.read_csv(csv_file) + +eta_2_lumped = 0.85 # the fixed extraction efficiency used by the lumped fuel_cycle_PCC.i +residence11 = 100.0 # membrane container retentate residence time [s] (fuel cycle) + +time = data["time"].to_numpy() +pressure = data["membrane_upstream_pressure"].to_numpy() +holdup = data["T_11_membrane"].to_numpy() +eta_inst = data["eta_2_calculated"].to_numpy() +eta_cum = data["eta_2_cumulative"].to_numpy() +feed = data["feed_rate"].to_numpy() +permeation = data["membrane_permeation_rate"].to_numpy() +retentate = holdup / residence11 # recycled to the TES +total = data["total_tritium"].to_numpy() + +# RMSPE of the cumulative (smooth) recovery vs the lumped 0.85, over the filled-system window. +mask = feed > 1.0e-9 +if np.any(mask): + rmspe = 100.0 * np.sqrt(np.mean(((eta_cum[mask] - eta_2_lumped) / eta_2_lumped) ** 2)) +else: + rmspe = float("nan") + +fig, axes = plt.subplots(2, 2, figsize=(12, 8)) + +# (a) Container pressure history -- the key verification curve. +ax = axes[0, 0] +ax.plot(time, pressure, "-o", ms=3, color="tab:purple") +ax.set_xlabel("Time (s)") +ax.set_ylabel("Container T2 pressure (Pa)") +ax.set_title("Membrane upstream container pressure") + +# (b) Extraction efficiency: instantaneous and cumulative vs the lumped assumption. +ax = axes[0, 1] +ax.plot(time, eta_inst, "-", color="tab:blue", alpha=0.6, label="instantaneous") +ax.plot(time, eta_cum, "-o", ms=3, color="tab:green", label="cumulative") +ax.axhline(eta_2_lumped, ls="--", color="tab:red", label="lumped eta_2 = 0.85") +ax.set_xlabel("Time (s)") +ax.set_ylabel("Membrane extraction efficiency (-)") +ax.set_title("Tritium recovery efficiency (physics-based)") +ax.set_ylim(0, 1.5) +ax.legend() +ax.text( + 0.04, + 0.06, + "cumulative RMSPE vs lumped = {:.1f}%".format(rmspe), + transform=ax.transAxes, + bbox=dict(boxstyle="round", fc="white", ec="0.7"), +) + +# (c) Container flow split: feed in, permeate (-> HX), retentate (-> TES). +ax = axes[1, 0] +ax.plot(time, feed, "-", color="black", label="TES feed in") +ax.plot(time, permeation, "-o", ms=3, color="tab:blue", label="permeate -> HX") +ax.plot(time, retentate, "-s", ms=3, color="tab:orange", label="retentate -> TES") +ax.set_xlabel("Time (s)") +ax.set_ylabel("Tritium flow rate (kg/s)") +ax.set_title("Container flow split") +ax.legend() + +# (d) Global tritium conservation. +ax = axes[1, 1] +ax.plot(time, total, "-o", ms=3, color="tab:orange") +ax.set_xlabel("Time (s)") +ax.set_ylabel("Total system tritium (kg)") +ax.set_title("Total tritium inventory (conservation check)") + +fig.suptitle("PCC membrane container coupled into the tritium fuel cycle", fontsize=13) +fig.tight_layout(rect=(0, 0, 1, 0.97)) + +os.makedirs(os.path.join(path, "figures"), exist_ok=True) +out_fig = os.path.join(path, "figures", "comparison_PCC_membrane.png") +fig.savefig(out_fig, dpi=150) +print("Saved figure to {}".format(out_fig)) +print("Final container pressure: {:.4g} Pa".format(pressure[-1])) +print("Final cumulative recovery efficiency: {:.4g}".format(eta_cum[-1])) +print("Cumulative recovery vs lumped 0.85: RMSPE = {:.2f}%".format(rmspe)) diff --git a/test/tests/PCC_multiscale_example/dir_pcc_fuel_cycle.i b/test/tests/PCC_multiscale_example/dir_pcc_fuel_cycle.i new file mode 100644 index 000000000..ba0691436 --- /dev/null +++ b/test/tests/PCC_multiscale_example/dir_pcc_fuel_cycle.i @@ -0,0 +1,708 @@ +# This input file re-creates the deuterium-tritium fuel cycle model +# described by Meschini et al (2023). +# "Modeling and analysis of the tritium fuel cycle for ARC- and STEP-class D-T +# fusion power plants." S Meschini & S E Ferry & R Delaporte-Mathurin +# & D G Whyte Nucl. Fusion 63 (2023) https://doi.org/10.1088/1741-4326/acf3fc +# +# Unit system: fuel-cycle inventories are kg of tritium and time is seconds. PCC DIR coupling +# converts kg of T2 holdup to Pa using the MOOSE units system and SI gas constants. + +# The mesh is completely ignored, but TMAP/MOOSE will complain without it. If high-fidelity +# models of specific components are required, the scalar variables can be coupled to +# "Field" variables which can vary spatially across the mesh, or could be co-ordinated +# with sub-apps. + +pulse_time = '${units 1800 s}' +initial_inventory = '${units 0.803 kg}' # 1.14 kg} +accuracy_time = '${units 94608000 s}' # 864000 s} +time_interval_middle = '${units 1e6 s}' +simulation_time = '${units 94608000 s}' # 3 years + +# Modeling parameters +resident_time_1 = '${units 4500 s}' +resident_time_2 = '${units 86400 s}' +resident_time_3 = '${units 1000 s}' +resident_time_4 = '${units 1000 s}' +resident_time_5 = '${units 1000 s}' +resident_time_6 = '${units 3600 s}' +resident_time_7 = '${units 600 s}' +resident_time_8 = '${units 360 s}' +resident_time_9 = '${units 14040 s}' +# TPM (I11) two-parameter residence time, fitted from a standalone permeation run at 5 Pa upstream +# (membrane_5_Pa_flux.csv) to the DELAYED first-order form +# J_back = J_inf*(1 - exp(-(t-tau0)/tau1)) for t > tau0 (see fit_residence_time.py): the membrane +# releases nothing for the transport delay tau0 = 11.69 s, then rises first-order with tau1 = 18.08 s +# (R^2 = 0.9998). Implemented like fuel_cycle_two_parameter_TEdata.i: a logistic time-gate +# residence_time_smooth_factor_11 (0 -> 1 around tau0) multiplies the membrane release term, while the +# residence constant (residence11) is tau1. The PCC enhancement of the TPM acts ONLY through this +# residence time (eta_2 is unchanged). Only tau1 sets the steady-state inventory; tau0 delays the +# early release (g -> 1 at steady state, recovering the tau1-only behavior). +resident_time_11_tau0 = '${units 14.8844 s}' # PCC-fitted TPM transport delay tau0 +resident_time_11_tau1 = '${units 10.6776 s}' # PCC-fitted TPM first-order rise time tau1 (was 100 s) +Delta_time_unit = '${units 0.01 s}' # logistic-gate sharpness (matches the TE-data example) +epsilon_low = 0 # - +epsilon = 1e-4 # - +f_5to1 = 0.33 # - +f_5to3 = 0.33 # - +f_5to6 = 1e-4 # - +f_9to6 = 0.1 # - +f_Pto3 = 1e-4 # - +f_Pto4 = 1e-4 # - +# f_DIR_VP / f_DIR_FCU removed: the DIR fractions are now CALCULATED from the membrane permeation +# (DIR_fraction_VP/FCU = flux_to_storage / DIR feed flux), not fixed inputs. +eta_2 = 0.95 # - # in-p +TBR_value = 1.067 # - +AF_value = 0.7 # - # in-p +- 0.3 +t_decay = '${units 1.73e-9 1/s}' +TBE_value = 0.02 # - # in-p +tritium_burn_rate_value = 8.99e-7 # - + +# --- PCC-enhanced DIR coupling: upstream-pressure bridge parameters (parent side) --- +# The two DIR systems (VP = I7, FCU = I8) are PCC-membrane-enhanced. Their inventories +# (T_07_vacuum, T_08_FCU, kg of tritium held as T2 gas) set the upstream T2 partial pressure of a +# membrane component sub-app (ideal gas, P = N/M_T2 * R*T_feed / V). Each sub-app returns the steady +# permeation rate (kg/s) recovered to storage; the DIR fraction = flux_to_storage / input_flux. +# V_VP / V_FCU are documented placeholder plenum volumes -- calibrate to the device. +M_T2_molar = '${units 6.032e-3 kg/mol}' # T2 molar mass (plenum holdup is T2 gas) +T_feed = '${units 773 K}' # plenum gas temperature (matches the membrane) +V_VP = '${units 1600.0 m^3}' # VP DIR membrane plenum volume (TUNING PARAMETER) +V_FCU = '${units 100.0 m^3}' # FCU DIR membrane plenum volume (TUNING PARAMETER) +R_gas = '${units 8.31446261815324 J/mol/K}' # ideal gas constant +FCU_membrane_area = '${units 4e-1 m^2}' +VP_membrane_area = '${units 1e0 m^2}' + +[Mesh] + type = GeneratedMesh + dim = 1 + xmin = 0 + xmax = 1 + nx = 1 +[] + +# One variable for each inventory of tritium is generated. All variables +# are defined as "SCALAR", meaning that they are a single value and are +# disconnected from any specific geometry + +[Variables] + [T_01_BZ] + family = SCALAR + [] + [T_02_TES] + family = SCALAR + [] + [T_03_FW] + family = SCALAR + [] + [T_04_DIV] + family = SCALAR + [] + [T_05_HX] + family = SCALAR + [] + [T_06_DS] # Detritiation system + family = SCALAR + [] + [T_07_vacuum] + family = SCALAR + [] + [T_08_FCU] + family = SCALAR + [] + [T_09_ISS] + family = SCALAR + [] + [T_10_storage] + family = SCALAR + initial_condition = ${initial_inventory} + [] + [T_11_membrane] # Tritium separation membrane + family = SCALAR + [] +[] + +# Tritium burn fraction is going to be small. Much +# will be lost to the scrape-off-layer (SOL) and +# recycled. + +# TES - tritium extraction system pulls tritium from +# the blanket + +# CPS - Coolant purification system pulls tritium from +# the coolant (CPS is signored in ARC reactor) +# Ignored in ARC due to liquid FLiBe + +# An ODE is defined in TMAP8 such that all of the terms must +# be on the left hand side. The terms can be split +# across multiple "ScalarKernels", which are additive, +# so that we have one ODETimeDerivative for each tritium +# inventory and a ParsedODEKernel for the rest of the +# terms. These equations should reflect those described +# in Appendix A of the paper (A.1-A.13), with negation +# on the ParsedODEKernels due to moving the terms to the +# left hand side. + +[ScalarKernels] + [I1t] + type = ODETimeDerivative + variable = T_01_BZ + [] + [I2t] + type = ODETimeDerivative + variable = T_02_TES + [] + [I3t] + type = ODETimeDerivative + variable = T_03_FW + [] + [I4t] + type = ODETimeDerivative + variable = T_04_DIV + [] + [I5t] + type = ODETimeDerivative + variable = T_05_HX + [] + [I6t] + type = ODETimeDerivative + variable = T_06_DS + [] + [I7t] + type = ODETimeDerivative + variable = T_07_vacuum + [] + [I8t] + type = ODETimeDerivative + variable = T_08_FCU + [] + [I9t] + type = ODETimeDerivative + variable = T_09_ISS + [] + [I10t] + type = ODETimeDerivative + variable = T_10_storage + [] + [I11t] + type = ODETimeDerivative + variable = T_11_membrane + [] + [I1] # Breeding Zone + type = ParsedODEKernel + expression = '-(breeder_pulse + T_03_FW / residence3 + T_04_DIV / residence4 + HX_BZ_leak_fraction * T_05_HX / residence5 - T_01_BZ / residence1 - T_01_BZ * epsilon1 / residence1 - T_01_BZ * tdecay)' + variable = 'T_01_BZ' + coupled_variables = 'T_03_FW T_04_DIV T_05_HX' + postprocessors = 'breeder_pulse HX_BZ_leak_fraction residence1 residence3 residence4 residence5 tdecay epsilon1' + [] + [I2] #Tritium Extraction System + type = ParsedODEKernel + expression = '-(T_01_BZ / residence1 - T_02_TES / residence2 - T_02_TES * epsilon2 / residence2 - T_02_TES * tdecay)' + variable = 'T_02_TES' + coupled_variables = 'T_01_BZ' + postprocessors = 'residence1 residence2 tdecay epsilon2' + [] + [I3] #First Wall + type = ParsedODEKernel + expression = '-(P_FW_leak_fraction * burn_pulse + HX_FW_leak_fraction * T_05_HX / residence5 + - T_03_FW / residence3 - T_03_FW * epsilon3 / residence3 - T_03_FW * tdecay)' + variable = 'T_03_FW' + coupled_variables = 'T_05_HX' + postprocessors = 'P_FW_leak_fraction HX_FW_leak_fraction burn_pulse residence5 residence3 tdecay epsilon3' + [] + # TBE = tritium_burn_fraction * tritium_fueling_efficiency + [I4] #Divertor + type = ParsedODEKernel + expression = '-(P_DIV_leak_fraction * burn_pulse + (1 - HX_BZ_leak_fraction - HX_DS_leak_fraction - HX_FW_leak_fraction) * T_05_HX / residence5 + - T_04_DIV * epsilon4 / residence4 - T_04_DIV / residence4 - T_04_DIV * tdecay)' + variable = 'T_04_DIV' + coupled_variables = 'T_05_HX' + postprocessors = 'P_DIV_leak_fraction HX_BZ_leak_fraction HX_DS_leak_fraction HX_FW_leak_fraction burn_pulse residence5 residence4 tdecay epsilon4' + [] + [I5] #Heat eXchanger + type = ParsedODEKernel + expression = '-((1 - TES_efficiency) * T_02_TES / residence2 - T_05_HX / residence5 - T_05_HX * epsilon5 / residence5 - T_05_HX * tdecay)' + variable = 'T_05_HX' + coupled_variables = 'T_02_TES' + postprocessors = 'TES_efficiency residence2 residence5 tdecay epsilon5' + [] + [I6] #Detritiation system + type = ParsedODEKernel + expression = '-(HX_DS_leak_fraction * T_05_HX / residence5 + ISS_DS_leak_fraction * T_09_ISS / residence9 - T_06_DS / residence6 - T_06_DS * epsilon6 / residence6 - T_06_DS * tdecay)' + variable = 'T_06_DS' + coupled_variables = 'T_05_HX T_09_ISS' + postprocessors = 'HX_DS_leak_fraction ISS_DS_leak_fraction residence5 residence9 residence6 tdecay epsilon6' + [] + [I7] #Vacuum Pump + type = ParsedODEKernel + expression = '-((1 - TBE - P_FW_leak_fraction - P_DIV_leak_fraction) * burn_pulse + - T_07_vacuum / residence7 - T_07_vacuum * epsilon7 / residence7 - T_07_vacuum * tdecay)' + variable = 'T_07_vacuum' + postprocessors = 'TBE burn_pulse P_FW_leak_fraction P_DIV_leak_fraction residence7 tdecay epsilon7' + [] + [I8] #Fuel clean-up + type = ParsedODEKernel + expression = '-((1 - DIR_fraction_VP) * T_07_vacuum / residence7 - T_08_FCU / residence8 - T_08_FCU * epsilon8 / residence8 - T_08_FCU * tdecay)' + variable = 'T_08_FCU' + coupled_variables = 'T_07_vacuum' + postprocessors = 'DIR_fraction_VP residence7 residence8 tdecay epsilon8' + [] + [I9] #Isotope Separation System + type = ParsedODEKernel + expression = '-(T_06_DS / residence6 + (1 - DIR_fraction_FCU) * T_08_FCU / residence8 - T_09_ISS / residence9 - T_09_ISS * epsilon9 / residence9 - T_09_ISS*tdecay)' + variable = 'T_09_ISS' + coupled_variables = 'T_06_DS T_08_FCU' + postprocessors = 'DIR_fraction_FCU residence6 residence8 residence9 tdecay epsilon9' + [] + [I10] #Storage and Management (STO) + type = ParsedODEKernel + expression = '-((1 - ISS_DS_leak_fraction) * T_09_ISS / residence9 + DIR_fraction_VP * T_07_vacuum / residence7 + DIR_fraction_FCU * T_08_FCU / residence8 + T_11_membrane / residence11 * residence_time_smooth_factor_11 - burn_pulse - T_10_storage * tdecay)' + variable = 'T_10_storage' + coupled_variables = 'T_09_ISS T_07_vacuum T_08_FCU T_11_membrane' + postprocessors = 'ISS_DS_leak_fraction DIR_fraction_VP DIR_fraction_FCU burn_pulse residence9 residence8 residence7 residence11 residence_time_smooth_factor_11 tdecay AF' + [] + [I11] #Tritium Separation Membrane (TSM) + type = ParsedODEKernel + expression = '-(TES_efficiency * T_02_TES/residence2 - T_11_membrane / residence11 * residence_time_smooth_factor_11 - T_11_membrane * epsilon11 / residence11 - T_11_membrane * tdecay)' + variable = 'T_11_membrane' + coupled_variables = 'T_02_TES' + postprocessors = 'TES_efficiency residence2 residence11 residence_time_smooth_factor_11 tdecay epsilon11' + [] +[] + +[Functions] + [breeder_pulse_function] + type = ParsedFunction + symbol_names = 'AF tritium_burn_rate TBR' + symbol_values = 'AF tritium_burn_rate TBR' + # expression = 'if(t % ${pulse_time} < AF * ${pulse_time}, tritium_burn_rate * TBR, 0)' + # expression = 'AF * tritium_burn_rate * TBR' + expression = 'if(t > ${accuracy_time}, AF * tritium_burn_rate * TBR, + if(t % ${pulse_time} < AF * ${pulse_time}, tritium_burn_rate * TBR, 0))' + [] + [burn_pulse_function] + type = ParsedFunction + symbol_names = 'AF tritium_burn_rate TBE' + symbol_values = 'AF tritium_burn_rate TBE' + # expression = 'if(t % ${pulse_time} < AF * ${pulse_time}, tritium_burn_rate / TBE, 0)' + # expression = 'AF * tritium_burn_rate / TBE' + expression = 'if(t > ${accuracy_time}, AF * tritium_burn_rate / TBE, + if(t % ${pulse_time} < AF * ${pulse_time}, tritium_burn_rate / TBE, 0))' + [] + [dt_function] + type = ParsedFunction + symbol_names = 'AF' + symbol_values = 'AF' + # expression = 'if(t % ${pulse_time} < 1, 1, + # if(t % ${pulse_time} < AF * ${pulse_time} - 1, AF * ${pulse_time} - t % ${pulse_time} - 1, + # if(t % ${pulse_time} < AF * ${pulse_time}, 2, + # if(t % ${pulse_time} < ${pulse_time} - 1, ${pulse_time} - t % ${pulse_time} - 1, + # if(t % ${pulse_time} < ${pulse_time}, 2, 2)))))' + # expression = 'if(t % ${pulse_time} < AF * ${pulse_time}, AF * ${pulse_time} - t % ${pulse_time} + 0.1, + # if(t % ${pulse_time} < ${pulse_time}, ${pulse_time} - t % ${pulse_time} + 0.1, 2))' + expression = 'if(t > ${accuracy_time}, ${time_interval_middle}, + if(t % ${pulse_time} < AF * ${pulse_time}, AF * ${pulse_time} - t % ${pulse_time} + 0.1, + if(t % ${pulse_time} < ${pulse_time}, ${pulse_time} - t % ${pulse_time} + 0.1, 2)))' + [] +[] + +# These postprocessors define the constants referenced in +# the equations above. The value of any of these constants +# could be informed by more detailed models (using sub-apps +# and transfers), but it is important that the postprocessor +# is evaluated before the executioner attempts to solve the +# ODE, which is not the default behavior. +[Postprocessors] + [burn_pulse] + type = FunctionValuePostprocessor + function = burn_pulse_function + execute_on = 'initial timestep_end' + [] + [breeder_pulse] + type = FunctionValuePostprocessor + function = breeder_pulse_function + execute_on = 'initial timestep_end' + [] + [HX_BZ_leak_fraction] #f_{5-1} + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${f_5to1} + [] + [HX_FW_leak_fraction] #f_{5-3} + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${f_5to3} + [] + [HX_DS_leak_fraction] #f_{5-6} + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${f_5to6} + [] + [ISS_DS_leak_fraction] #f_{9-6} + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${f_9to6} + [] + [P_DIV_leak_fraction] #f_{P-4} + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${f_Pto4} + [] + [P_FW_leak_fraction] #f_{P-3} + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${f_Pto3} + [] + [TES_efficiency] #eta_2 from Abdou et al. 2020 + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${eta_2} + [] + [TBR] + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${TBR_value} # for t_d = 2 yrs + [] + # --- PCC-enhanced DIR fractions: now CALCULATED from the membrane permeation, not fixed --- + # DIR_fraction = membrane flux to storage / DIR feed flow, clamped to [0,1] (computed at + # TIMESTEP_BEGIN from the start-of-step inventory and the freshly transferred sub-app flux, then + # held constant through the ODE solve like the original constant fraction). + [DIR_fraction_VP] + type = ParsedPostprocessor + pp_names = 'flux_to_storage_VP T_07_now' + expression = 'if(T_07_now > 1e-30, min(max(flux_to_storage_VP / (T_07_now / ${resident_time_7}), 0), 1), 0)' + execute_on = 'INITIAL TIMESTEP_BEGIN' + [] + [DIR_fraction_FCU] + type = ParsedPostprocessor + pp_names = 'flux_to_storage_FCU T_08_now' + expression = 'if(T_08_now > 1e-30, min(max(flux_to_storage_FCU / (T_08_now / ${resident_time_8}), 0), 1), 0)' + execute_on = 'INITIAL TIMESTEP_BEGIN' + [] + # --- PCC DIR coupling postprocessors (VP and FCU membranes) --- + # T_*_now read on TIMESTEP_END so the down-transfer at the next step's TIMESTEP_BEGIN (inside + # execMultiApps, before execute(TIMESTEP_BEGIN)) sees the start-of-step inventory; also on + # TIMESTEP_BEGIN so the DIR_fraction can use the same value. + [T_07_now] # VP (vacuum pump) inventory [kg] + type = ScalarVariable + variable = T_07_vacuum + execute_on = 'INITIAL TIMESTEP_BEGIN TIMESTEP_END' + [] + [T_08_now] # FCU (fuel clean-up) inventory [kg] + type = ScalarVariable + variable = T_08_FCU + execute_on = 'INITIAL TIMESTEP_BEGIN TIMESTEP_END' + [] + [pressure_VP] # VP membrane upstream T2 partial pressure [Pa] from the VP inventory via ideal gas + type = ParsedPostprocessor + pp_names = 'T_07_now' + expression = 'max(T_07_now, 0) / ${M_T2_molar} * ${R_gas} * ${T_feed} / ${V_VP}' + execute_on = 'INITIAL TIMESTEP_END' + [] + [pressure_FCU] # FCU membrane upstream T2 partial pressure [Pa] + type = ParsedPostprocessor + pp_names = 'T_08_now' + expression = 'max(T_08_now, 0) / ${M_T2_molar} * ${R_gas} * ${T_feed} / ${V_FCU}' + execute_on = 'INITIAL TIMESTEP_END' + [] + [flux_to_storage_VP] # tritium permeated to storage by the VP membrane [kg/s] (from the sub-app) + type = Receiver + default = 0 + execute_on = 'INITIAL TIMESTEP_BEGIN' + [] + [flux_to_storage_FCU] # tritium permeated to storage by the FCU membrane [kg/s] (from the sub-app) + type = Receiver + default = 0 + execute_on = 'INITIAL TIMESTEP_BEGIN' + [] + [AF] + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${AF_value} # (0.75 from Meschini) + [] + [tdecay] + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${t_decay} # (from Meschini) 1.7828336471961835e-9 (from Abdou) + [] + [TBE] + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${TBE_value} # (0.005 - 0.1) Meschini + [] + [tritium_burn_rate] + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${tritium_burn_rate_value} # (5.3125e-6 from Abdou) (9.3e-7 Kg/s from Meschini paper) (8.99e-7 Kg/s from Meschini matlab) + [] + [epsilon1] #BZ + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${epsilon} + [] + [epsilon2] #TES + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${epsilon} + [] + [epsilon3] #FW + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${epsilon_low} + [] + [epsilon4] #DIV + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${epsilon_low} + [] + [epsilon5] #HX + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${epsilon} + [] + [epsilon6] #DS + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${epsilon} + [] + [epsilon7] #Vac + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${epsilon} + [] + [epsilon8] #FCU + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${epsilon} + [] + [epsilon9] #ISS + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${epsilon} + [] + [epsilon11] #TSM + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${epsilon} + [] + [residence1] #BZ + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${resident_time_1} # s 1.25 h, (Meschini) and (Ferrero et al) T_BZ = 3 g, 864000 # s 10 days + # value = 1 h - 240 h + [] + [residence2] #TES + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${resident_time_2} # s Meschini + #value = 1 h - 240 h Riva + [] + [residence3] #FW + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${resident_time_3} # s Riva + [] + [residence4] #DIV + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${resident_time_4} # s Riva + [] + [residence5] #HX + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${resident_time_5} # s Abdou 2021 paper chosen for analysis + [] + [residence6] #DS + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${resident_time_6} # s Meschini + [] + [residence7] #Vac + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${resident_time_7} # s + [] + [residence8] #FCU + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${resident_time_8} # 0.1625 h 3600 # s 1 h Meschini + # value = 0.1 - 1 h Meschini + #value = 5 h Coleman + #value = 8640 Abdou + #value = 86400 Abdou + [] + [residence9] #ISS + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${resident_time_9} # s 6.3375 h Meschini + #value = 0.9 - 11 h # (for four hour overall residence time in inner loop) + [] + [residence11] #TSM (first-order rise constant tau1) + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${resident_time_11_tau1} # PCC-fitted tau1 + [] + # Logistic time-gate for the TPM two-parameter residence time: ~0 for t < tau0, ~1 for t > tau0, + # so the membrane release to storage is delayed by the transport delay tau0 (see I10/I11). + [residence_time_smooth_factor_11] + type = ParsedPostprocessor + use_t = true + expression = '1 / (1 + exp(- (t - ${resident_time_11_tau0}) / (${Delta_time_unit} * ${resident_time_11_tau0})))' + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + [] + # These postprocessors exist to sum up the tritium inventory + # across the entirety of the system + [T_BZ] + type = ScalarVariable + variable = T_01_BZ + execute_on = TIMESTEP_END + [] + [T_TES] + type = ScalarVariable + variable = T_02_TES + execute_on = TIMESTEP_END + [] + [T_FW] + type = ScalarVariable + variable = T_03_FW + execute_on = TIMESTEP_END + [] + [T_DIV] + type = ScalarVariable + variable = T_04_DIV + execute_on = TIMESTEP_END + [] + [T_HX] + type = ScalarVariable + variable = T_05_HX + execute_on = TIMESTEP_END + [] + [T_DS] + type = ScalarVariable + variable = T_06_DS + execute_on = TIMESTEP_END + [] + [T_VAC] + type = ScalarVariable + variable = T_07_vacuum + execute_on = TIMESTEP_END + [] + [T_FCU] + type = ScalarVariable + variable = T_08_FCU + execute_on = TIMESTEP_END + [] + [T_ISS] + type = ScalarVariable + variable = T_09_ISS + execute_on = TIMESTEP_END + [] + [T_STO] + type = ScalarVariable + variable = T_10_storage + execute_on = TIMESTEP_END + [] + [T_TSM] + type = ScalarVariable + variable = T_11_membrane + execute_on = TIMESTEP_END + [] + [total_tritium] + type = SumPostprocessor + values = 'T_BZ T_TES T_FW T_DIV T_HX T_DS T_VAC T_FCU T_ISS T_STO T_TSM' + [] +[] +[UserObjects] + [terminator] + type = Terminator + expression = 'T_STO < 0' + fail_mode = 'HARD' + message = 'Tritium in storage has been depleted' + [] + [terminator2] + type = Terminator + expression = 'total_tritium < 0' + fail_mode = 'HARD' + message = 'Tritium in system has been depleted' + [] +[] + +[MultiApps] + # Two PCC membrane component sub-apps, one per DIR stream (re-solved to steady each fuel-cycle + # step). Driven by the VP / FCU upstream pressures; return the permeated flow to storage. + [vp_membrane] # vacuum-pump DIR membrane (active area 6e-2 m^2) + type = FullSolveMultiApp + input_files = 'dir_pcc_membrane_sub.i' + execute_on = 'TIMESTEP_BEGIN' + max_procs_per_app = 1 + ignore_solve_not_converge = true + cli_args = 'A_membrane=${VP_membrane_area};Outputs/csv/enable=false' + [] + [fcu_membrane] # fuel-clean-up DIR membrane (active area 3e-2 m^2) + type = FullSolveMultiApp + input_files = 'dir_pcc_membrane_sub.i' + execute_on = 'TIMESTEP_BEGIN' + max_procs_per_app = 1 + ignore_solve_not_converge = true + cli_args = 'A_membrane=${FCU_membrane_area};Outputs/csv/enable=false' + [] +[] + +[Transfers] + # VP membrane: upstream pressure down, permeation-to-storage up + [push_pressure_VP] + type = MultiAppPostprocessorTransfer + to_multi_app = vp_membrane + from_postprocessor = pressure_VP + to_postprocessor = received_pressure + execute_on = 'TIMESTEP_BEGIN' + [] + [pull_flux_VP] + type = MultiAppPostprocessorTransfer + from_multi_app = vp_membrane + from_postprocessor = permeation_rate_kg_per_s + to_postprocessor = flux_to_storage_VP + reduction_type = average + execute_on = 'TIMESTEP_BEGIN' + [] + # FCU membrane: upstream pressure down, permeation-to-storage up + [push_pressure_FCU] + type = MultiAppPostprocessorTransfer + to_multi_app = fcu_membrane + from_postprocessor = pressure_FCU + to_postprocessor = received_pressure + execute_on = 'TIMESTEP_BEGIN' + [] + [pull_flux_FCU] + type = MultiAppPostprocessorTransfer + from_multi_app = fcu_membrane + from_postprocessor = permeation_rate_kg_per_s + to_postprocessor = flux_to_storage_FCU + reduction_type = average + execute_on = 'TIMESTEP_BEGIN' + [] +[] + +[Executioner] + type = Transient + start_time = 0 + dtmin = 1 + end_time = ${simulation_time} # 30 years - 946080000, 2 years - 31536000, 3 years - 94608000 + [TimeStepper] + type = FunctionDT + function = dt_function + [] + solve_type = 'PJFNK' + nl_rel_tol = 1e-08 + nl_abs_tol = 1e-14 +[] + +[Outputs] + hide = "AF breeder_pulse burn_pulse HX_BZ_leak_fraction HX_FW_leak_fraction HX_DS_leak_fraction " + "ISS_DS_leak_fraction P_DIV_leak_fraction P_FW_leak_fraction TES_efficiency TBR " + "T_BZ T_DS T_DIV T_TSM T_FCU T_FW T_HX T_ISS T_STO T_TES " + "T_VAC epsilon1 epsilon11 epsilon2 epsilon3 epsilon4 epsilon5 epsilon6 epsilon7 epsilon8 " + "epsilon9 residence1 residence11 residence2 residence3 residence4 residence5 residence6 " + "residence7 residence8 residence9 tdecay TBE tritium_burn_rate T_07_now T_08_now" + file_base = 'dir_pcc_fuel_cycle_2rt_10Pa_out2' + csv = true + console = false +[] diff --git a/test/tests/PCC_multiscale_example/dir_pcc_membrane_sub.i b/test/tests/PCC_multiscale_example/dir_pcc_membrane_sub.i new file mode 100644 index 000000000..e2bbfe541 --- /dev/null +++ b/test/tests/PCC_multiscale_example/dir_pcc_membrane_sub.i @@ -0,0 +1,715 @@ +# Sub-app (component level) for the PCC membrane <-> fuel-cycle MultiApp coupling. +# Derived from tritium_transport_PCC/jouleheating_Voltage_BCY_real_LEE2005.i. +# Real (H2+H2O) BCY proton-conducting-ceramic membrane with applied voltage and Joule heating. +# Temperature is a nonlinear Variable coupled to the Joule heating source. +# +# Unit system: the membrane model uses nm for length, Pa for gas pressure, at/nm^3 for +# concentrations, at/nm^2/s for surface fluxes, and kg/s for transferred tritium flow. +# +# Coupling interface: +# IN (from parent): received_pressure -- upstream T2 partial pressure [Pa] set from the +# fuel-cycle membrane feed-plenum holdup (T_11_membrane) via ideal gas. +# OUT (to parent): permeation_rate_kg_per_s -- tritium mass flow permeated to the downstream +# side [kg/s], obtained from the steady permeation flux at the right boundary. +# The sub-app is run to (pseudo-)steady state each parent timestep (see steady_state_detection). + +# Physical constants +R = '${units 8.31446261815324 J/mol/K}' # ideal gas constant based on number used in include/utils/PhysicalConstants.h +N_a = '${units 6.02214076e23 at/mol}' # ideal gas constant based on number used in include/utils/PhysicalConstants.h +q = '${units 1.602176634e-19 C}' # quantity of charge +F = '${fparse N_a * q}' + +# Thermal properties of BCY20 +# thermal conductivity: 1.05 W/(m*K) for dense BaCeO3 +# Ref: Tenevich et al. 2023, Ceramics International, Vol. 49, 31087-31095 +thermal_conductivity_BCY20 = '${units 1.05 W/m/K -> W/nm/K}' + +# thermal parameters +temperature_initial = '${units 773 K}' # 500C + +# Model parameters +endtime = '1e5' +dt_max = '2e3' +dt_start_charging = '${units 1e-5 s}' +bound_value_min = '${units -1e-20 at/nm^3}' + +# Geometry and mesh +length = '${units 10 mum -> nm}' # BCY20 +num_nodes = 300 + +# Material properties +density_BCY20 = '${units ${fparse 1.0 * 6.154} g/cm^3 -> g/m^3}' +molar_mass_BCY20 = '${units 283.42 g/mol}' +N = '${units ${fparse density_BCY20 / molar_mass_BCY20 * N_a} at/m^3 -> at/nm^3}' +# density in g/nm^3 for pairing with specific_heat in J/(g*K) +density_BCY20_thermal = '${fparse density_BCY20 * 1e-27}' # g/m^3 -> g/nm^3 +# specific heat: ~120 J/(mol*K) for BaCeO3 at high temperature +# Ref: Yamanaka et al. 2003, J. Alloys and Compounds, Vol. 359, 109-113 +specific_heat_BCY20_molar = '${units 120 J/mol/K}' +specific_heat_BCY20 = '${fparse specific_heat_BCY20_molar / molar_mass_BCY20}' # 120/283.42 = 0.4233 J/(g*K) + +# Initial concentrations +OT_concentration_initial = 1e-5 +hydration_limit_S = 0.2 +oxygen_vacancy_concentration_initial = '${units ${fparse hydration_limit_S / 2 * N} at/nm^3}' +oxygen_concentration_initial = '${units ${fparse 3 * N - oxygen_vacancy_concentration_initial - OT_concentration_initial} at/nm^3}' + +##### Dry Pressure conditions +pressure_atm = '${units 101315 Pa}' +pressure_T2_low = '${units 0 Pa}' # downstream (permeate) T2 partial pressure +pressure_T2_high = '${units ${fparse 1e-10 * pressure_atm} Pa}' # default standalone upstream T2 pressure +# In the fuel-cycle coupling the membrane separates tritium (T2): permeation must be driven only by +# the tritium partial pressure supplied by the parent. The independent water (T2O) source of the +# "real" model is therefore disabled (set to 0) so it does not inject a tritium-independent, +# voltage-pumped baseline flux. Set non-zero only for standalone wet-gas studies. +pressure_T2O_constant = '${units 0 Pa}' + +# chemical_reaction — optimized BCY parameters (n20_faster, 72 steps), identical to OPTIMIZED_PARAMS +# in tritium_transport_PCC/scripts/compare_original_optimized_results_flux.py (the published +# validation set used for the "after optimization" flux-vs-voltage figure). +delta_H_T2O = '${units -1.54415211e+05 J/mol}' +delta_S_T2O = '${units -1.67187585e+02 J/mol/K}' +delta_H_T2 = '${units -5.46037663e+04 J/mol}' +delta_S_T2 = '${units -3.36929406e+01 J/mol/K}' +T2O_reaction_forward_mol_exponent = -1.19792592e+01 +ramp_time = 1 +T2O_reaction_forward_mol = '${units ${fparse 8.0 * 10 ^ T2O_reaction_forward_mol_exponent} m^4/mol/s}' +T2O_reaction_forward_value = '${units ${fparse T2O_reaction_forward_mol / N_a} m^4/at/s -> nm^4/at/s}' +T2O_reaction_forward_energy = '${units -7.31595474e+03 J/mol}' +T2_reaction_forward_mol_exponent = -4.05998297e+00 +T2_reaction_forward_mol = '${units ${fparse 8.0 * 10 ^ T2_reaction_forward_mol_exponent} m^4/mol/s}' +T2_reaction_forward_value = '${units ${fparse T2_reaction_forward_mol / N_a} m^4/at/s -> nm^4/at/s}' +T2_reaction_forward_energy = '${units 5.13385478e+03 J/mol}' +diffusivity_OT_prefactor_exponent = -1.26000119e+01 +diffusivity_OT_prefactor = '${units ${fparse 2.03 * 10 ^ diffusivity_OT_prefactor_exponent / sqrt(3)} m^2/s -> nm^2/s}' +diffusivity_OT_energy = '${units 8.65880079e+03 J/mol}' +diffusivity_V_O_prefactor_exponent = -5.33084375e+00 +diffusivity_V_O_prefactor = '${units ${fparse 1.1 * 10 ^ diffusivity_V_O_prefactor_exponent} m^2/s -> nm^2/s}' +diffusivity_V_O_energy = '${units 5.87658926e+04 J/mol}' +diffusivity_e_prefactor = '${units 2.06292148e-02 m^2/s -> nm^2/s}' # data from Yang 2026 +diffusivity_e_energy = '${units 9.53470966e+04 J/mol}' +# ELECTRON +electron_concentration_initial_expo = 4.94096686e-01 +electron_concentration_initial_energy = '${units 5.90846106e+04 J/mol}' +electron_concentration_initial = '${units ${fparse 10 ^ electron_concentration_initial_expo * N} at/nm^3}' + +# voltage +V_current = 2.0 # CONSTANT_VOLTAGE - no ${units} wrapper so CLI override works + +# --- MultiApp coupling: feed-plenum bridge parameters (sub-app side) --- +# The membrane active area scales the permeation flux [at/m^2/s] to a tritium mass flow [kg/s]. +# In the DIR coupling the parent (dir_pcc_fuel_cycle.i) sets A_membrane per instance via cli_args: +# VP (vacuum-pump) membrane = 6e-2 m^2, FCU (fuel-clean-up) membrane = 3e-2 m^2. The value below is +# only the standalone fallback used when this sub-app is run on its own. +A_membrane = '${units 3e-2 m^2}' # membrane active area [m^2] (parent overrides per DIR stream) +M_T_atomic = '${units 3.016e-3 kg/mol}' # atomic tritium molar mass (each OT carries one T atom) + +[Mesh] + [cmg] + type = CartesianMeshGenerator + dim = 1 + dx = '${fparse length}' + ix = '${fparse num_nodes}' + subdomain_id = '0' + [] +[] + +[Variables] + #### Dry variable + [OT_concentration_dry] # (atoms/nm^3) + initial_condition = ${OT_concentration_initial} + [] + [Oxygen_vacancy_concentration_dry] + initial_condition = ${oxygen_vacancy_concentration_initial} + [] + # Temperature as nonlinear variable (promoted from AuxVariable for Joule heating coupling) + [temperature] + initial_condition = ${temperature_initial} + [] +[] + +[Bounds] + [concentration_dry_lower_bound] + type = ConstantBounds + variable = bounds_dummy + bounded_variable = OT_concentration_dry + bound_type = lower + bound_value = ${bound_value_min} + [] + [concentration_dry_V_O_lower_bound] + type = ConstantBounds + variable = bounds_dummy + bounded_variable = Oxygen_vacancy_concentration_dry + bound_type = lower + bound_value = ${bound_value_min} + [] + [concentration_dry_V_O_upper_bound] + type = ConstantBounds + variable = bounds_dummy + bounded_variable = Oxygen_vacancy_concentration_dry + bound_type = upper + bound_value = ${fparse 3 * N} + [] + [temperature_lower_bound] + type = ConstantBounds + variable = bounds_dummy + bounded_variable = temperature + bound_type = lower + bound_value = 300 + [] + [temperature_upper_bound] + type = ConstantBounds + variable = bounds_dummy + bounded_variable = temperature + bound_type = upper + bound_value = 2000 + [] +[] + +[AuxVariables] + [bounds_dummy] + order = FIRST + family = LAGRANGE + [] + #### Dry auxvariable + [pressure_T2_dry] + [] + [pressure_T2O_dry] + [] + [Oxygen_concentration_dry] + initial_condition = ${oxygen_concentration_initial} + [] + [electron_concentration_dry] + [] + + # CONSTANT_VOLTAGE + [voltage_phi] + [] +[] + + +[AuxKernels] + #### Dry auxkernels + [pressure_T2_dry_Aux] + type = FunctionAux + variable = pressure_T2_dry + function = Pressure_T2_dry_function + [] + [pressure_T2O_dry_Aux] + type = FunctionAux + variable = pressure_T2O_dry + function = Pressure_T2O_dry_function + [] + [Oxygen_concentration_dry_Aux] # at/nm^3 + type = ParsedAux + variable = Oxygen_concentration_dry + coupled_variables = 'Oxygen_vacancy_concentration_dry' + expression = '3 * ${N} - Oxygen_vacancy_concentration_dry' + [] + + # ELECTRON + [electron_concentration_dry_Aux] + type = ParsedAux + variable = electron_concentration_dry + coupled_variables = 'temperature' + expression = '${electron_concentration_initial} * 0.5 * exp(-${electron_concentration_initial_energy} / ${R} / temperature)' + execute_on = 'INITIAL TIMESTEP_END' + [] + + # CONSTANT_VOLTAGE + [phi_auxkernel] + type = FunctionAux + variable = voltage_phi + function = '${V_current} * (${length} - x) / ${length}' + execute_on = 'INITIAL TIMESTEP_END' + [] + +[] + +[Problem] + type = ReferenceResidualProblem + extra_tag_vectors = 'ref' + reference_vector = 'ref' +[] + +[Kernels] + #### Dry kernels + [time_OT_dry] + type = ADTimeDerivative + variable = OT_concentration_dry + extra_vector_tags = ref + [] + [diffusion_OT_dry] + type = ADMatDiffusion + variable = OT_concentration_dry + diffusivity = diffusivity_OT + extra_vector_tags = ref + [] + [time_V_O_dry] + type = ADTimeDerivative + variable = Oxygen_vacancy_concentration_dry + extra_vector_tags = ref + [] + [diffusion_V_O_dry] + type = ADMatDiffusion + variable = Oxygen_vacancy_concentration_dry + diffusivity = diffusivity_V_O + extra_vector_tags = ref + [] + # voltage for OH + [diffusion_phi_PCC_OH] + type = ADMatDiffusion + variable = OT_concentration_dry + v = voltage_phi + diffusivity = conductivity_OH + extra_vector_tags = ref + [] + # voltage for V_O + [diffusion_phi_PCC_V_O] + type = ADMatDiffusion + variable = Oxygen_vacancy_concentration_dry + v = voltage_phi + diffusivity = conductivity_V_O + extra_vector_tags = ref + [] + + # --- Heat equation --- + [heat_time] + type = ADHeatConductionTimeDerivative + variable = temperature + specific_heat = specific_heat_BCY20 + density_name = density_BCY20_thermal + extra_vector_tags = ref + [] + [heat_conduction] + type = ADHeatConduction + variable = temperature + thermal_conductivity = thermal_conductivity_BCY20 + extra_vector_tags = ref + [] + [joule_heating] + type = ADJouleHeatingSource + variable = temperature + heating_term = joule_heating_Q + extra_vector_tags = ref + [] +[] + +[BCs] + #### Dry BCs + [left_OT_dry] + type = ADMatNeumannBC + variable = OT_concentration_dry + boundary = left + value = 1 + boundary_material = flux_on_OT_dry + [] + [left_V_O_dry] + type = ADMatNeumannBC + variable = Oxygen_vacancy_concentration_dry + boundary = left + value = 1 + boundary_material = flux_on_V_O_dry + [] + [right_OT_dry] + type = ADMatNeumannBC + variable = OT_concentration_dry + boundary = right + value = 1 + boundary_material = flux_on_OT_dry + [] + [right_V_O_dry] + type = ADMatNeumannBC + variable = Oxygen_vacancy_concentration_dry + boundary = right + value = 1 + boundary_material = flux_on_V_O_dry + [] + + # Thermal BCs: fixed temperature at both surfaces (furnace-controlled) + [left_temperature] + type = ADDirichletBC + variable = temperature + boundary = left + value = ${temperature_initial} + [] + [right_temperature] + type = ADDirichletBC + variable = temperature + boundary = right + value = ${temperature_initial} + [] +[] + +[Functions] + [Pressure_T2_dry_function] + # P_up (upstream T2 partial pressure, Pa) is supplied by the parent via the received_pressure + # postprocessor. The time ramp of the standalone model is removed here: FullSolveMultiApp + # warm-starts the sub-app (keeps the solution between invocations) while resetting sub-time to 0, + # so a time ramp would re-impose a zero-pressure shock onto an already-equilibrated field and + # stall the solve. The pressure is therefore applied as a constant with the same spatial + # (upstream->permeate) profile and /pressure_atm normalization. + type = ParsedFunction + symbol_names = 'P_up' + symbol_values = 'received_pressure' + expression = '(P_up * (${length} - x) / ${length} + ${pressure_T2_low}) / ${pressure_atm}' + [] + [Pressure_T2O_dry_function] + type = ParsedFunction + expression = 'min(t / ${ramp_time}, 1.0) * (${pressure_T2O_constant}) / ${pressure_atm}' + [] +[] + +[Materials] + [diffusivity_OT] + type = ADParsedMaterial + property_name = 'diffusivity_OT' + coupled_variables = 'temperature' + expression = '${diffusivity_OT_prefactor} * exp(-${diffusivity_OT_energy} / ${R} / temperature)' + [] + [diffusivity_V_O] + type = ADParsedMaterial + property_name = 'diffusivity_V_O' + coupled_variables = 'temperature' + expression = '${diffusivity_V_O_prefactor} * exp(-${diffusivity_V_O_energy} / ${R} / temperature)' + [] + [diffusivity_e] + type = ADParsedMaterial + property_name = 'diffusivity_e' + coupled_variables = 'temperature' + expression = '${diffusivity_e_prefactor} * exp(-${diffusivity_e_energy} / ${R} / temperature)' + [] + [converter_to_nonAD] + type = MaterialADConverter + ad_props_in = 'diffusivity_OT diffusivity_V_O diffusivity_e conductivity_OH conductivity_e' + reg_props_out = 'diffusivity_OT_nonAD diffusivity_V_O_nonAD diffusivity_e_nonAD conductivity_OH_nonAD conductivity_e_nonAD' + outputs = 'none' + [] + [conductivity_OH] + type = ADParsedMaterial + property_name = 'conductivity_OH' + coupled_variables = 'OT_concentration_dry temperature' + material_property_names = 'diffusivity_OT' + expression = 'diffusivity_OT * ${F} * OT_concentration_dry / ${R} / temperature' + [] + [conductivity_V_O] + type = ADParsedMaterial + property_name = 'conductivity_V_O' + coupled_variables = 'Oxygen_vacancy_concentration_dry temperature' + material_property_names = 'diffusivity_V_O' + expression = '2 * diffusivity_V_O * ${F} * Oxygen_vacancy_concentration_dry / ${R} / temperature' + [] + [conductivity_e] + type = ADParsedMaterial + property_name = 'conductivity_e' + coupled_variables = 'electron_concentration_dry temperature' + material_property_names = 'diffusivity_e' + expression = '- diffusivity_e * ${F} * electron_concentration_dry / ${R} / temperature' + [] + [reaction_equilibrium_constant_T2] + type = ADParsedMaterial + property_name = 'T2_K_eq' + coupled_variables = 'temperature' + expression = 'exp( ( ${delta_H_T2} - temperature * ${delta_S_T2}) / ${R} / temperature )' + [] + [reaction_forward_T2] + type = ADParsedMaterial + property_name = 'T2_K_forward' + coupled_variables = 'temperature' + expression = '${T2_reaction_forward_value} * exp(-${T2_reaction_forward_energy} / ${R} / temperature)' + [] + [reaction_reverse_T2] + type = ADParsedMaterial + property_name = 'T2_K_reverse' + material_property_names = 'T2_K_forward T2_K_eq' + expression = 'T2_K_forward / T2_K_eq' + [] + + [reaction_equilibrium_constant_T2O] + type = ADParsedMaterial + property_name = 'T2O_K_eq' + coupled_variables = 'temperature' + expression = 'exp( ( ${delta_H_T2O} - temperature * ${delta_S_T2O}) / ${R} / temperature )' + [] + [reaction_forward_T2O] + type = ADParsedMaterial + property_name = 'T2O_K_forward' + coupled_variables = 'temperature' + expression = '${T2O_reaction_forward_value} * exp(-${T2O_reaction_forward_energy} / ${R} / temperature)' + [] + [reaction_reverse_T2O] + type = ADParsedMaterial + property_name = 'T2O_K_reverse' + material_property_names = 'T2O_K_forward T2O_K_eq' + expression = 'T2O_K_forward / T2O_K_eq' + [] + + #### Reaction for dry + [flux_base_on_T2_dry] # T2 + 2 O -> 2 OT + 2 e + type = ADDerivativeParsedMaterial + coupled_variables = 'OT_concentration_dry pressure_T2_dry Oxygen_vacancy_concentration_dry electron_concentration_dry' + property_name = 'flux_base_on_T2_dry' + material_property_names = 'T2_K_forward T2_K_reverse' + expression = '(T2_K_forward * pressure_T2_dry * (3 * ${N} - Oxygen_vacancy_concentration_dry)^2 - T2_K_reverse * OT_concentration_dry^2 * electron_concentration_dry^2)' + [] + [flux_base_on_T2O_dry] # T2O + V_O + O -> 2 OT + type = ADDerivativeParsedMaterial + coupled_variables = 'OT_concentration_dry pressure_T2O_dry Oxygen_vacancy_concentration_dry' + property_name = 'flux_base_on_T2O_dry' + material_property_names = 'T2O_K_forward T2O_K_reverse' + expression = '(T2O_K_forward * pressure_T2O_dry * (3 * ${N} - Oxygen_vacancy_concentration_dry) * Oxygen_vacancy_concentration_dry - T2O_K_reverse * OT_concentration_dry^2)' + [] + + + #### Flux for dry + [flux_on_e_dry] # electron + type = ADDerivativeParsedMaterial + property_name = 'flux_on_e_dry' + material_property_names = 'flux_base_on_T2_dry' + expression = '2 * flux_base_on_T2_dry' + [] + [flux_on_OT_dry] # OT + type = ADDerivativeParsedMaterial + property_name = 'flux_on_OT_dry' + material_property_names = 'flux_base_on_T2_dry flux_base_on_T2O_dry' + expression = '2 * flux_base_on_T2_dry + 2 * flux_base_on_T2O_dry' + [] + [flux_on_T2_dry] # T2 + type = ADDerivativeParsedMaterial + property_name = 'flux_on_T2_dry' + material_property_names = 'flux_base_on_T2_dry' + expression = '-1 * flux_base_on_T2_dry' + [] + [flux_on_V_O_dry] # V_O + type = ADDerivativeParsedMaterial + property_name = 'flux_on_V_O_dry' + material_property_names = 'flux_base_on_T2O_dry' + expression = '-1 * flux_base_on_T2O_dry' + [] + [flux_on_T2O_dry] # T2O + type = ADDerivativeParsedMaterial + property_name = 'flux_on_T2O_dry' + material_property_names = 'flux_base_on_T2O_dry' + expression = '-1 * flux_base_on_T2O_dry' + [] + + # --- Thermal material properties for BCY20 --- + [thermal_conductivity_mat] + type = ADGenericConstantMaterial + prop_names = 'thermal_conductivity_BCY20' + prop_values = '${thermal_conductivity_BCY20}' + [] + [specific_heat_mat] + type = ADGenericConstantMaterial + prop_names = 'specific_heat_BCY20' + prop_values = '${specific_heat_BCY20}' + [] + [density_thermal_mat] + type = ADGenericConstantMaterial + prop_names = 'density_BCY20_thermal' + prop_values = '${density_BCY20_thermal}' + [] + + # --- Joule heating --- + # Total ionic electrical conductivity from Nernst-Einstein relation (excluding electrons) + # sigma = q*F/(R*T) * (z_OH^2 * D_OT * c_OT + z_VO^2 * D_VO * c_VO) + # z_OH = 1, z_VO = 2, so z^2 = 1 and 4 + [total_electrical_conductivity] + type = ADParsedMaterial + property_name = 'sigma_total' + coupled_variables = 'OT_concentration_dry Oxygen_vacancy_concentration_dry temperature' + material_property_names = 'diffusivity_OT diffusivity_V_O' + expression = '${q} * ${F} / (${R} * temperature) * (diffusivity_OT * OT_concentration_dry + 4.0 * diffusivity_V_O * Oxygen_vacancy_concentration_dry)' + [] + # Joule heating volumetric source: Q = sigma_total * |grad(phi)|^2 + # |grad(phi)|^2 = (V_current / length)^2 = constant (voltage_phi is linear AuxVariable) + [joule_heating_material] + type = ADParsedMaterial + property_name = 'joule_heating_Q' + material_property_names = 'sigma_total' + expression = 'sigma_total * (${V_current} / ${length})^2' + [] +[] + +[Postprocessors] + #### Postprocessors for flux under dry + [recombination_flux_T2_dry_left] + type = ADSideAverageMaterialProperty + boundary = left + property = flux_on_T2_dry + execute_on = 'INITIAL TIMESTEP_END' + outputs = 'csv' + [] + [recombination_flux_T2O_dry_left] + type = ADSideAverageMaterialProperty + boundary = left + property = flux_on_T2O_dry + execute_on = 'INITIAL TIMESTEP_END' + outputs = 'csv' + [] + [recombination_flux_OT_dry_left] + type = ADSideAverageMaterialProperty + boundary = left + property = flux_on_OT_dry + execute_on = 'INITIAL TIMESTEP_END' + outputs = 'csv' + [] + [recombination_flux_OT_dry_right] + type = ADSideAverageMaterialProperty + boundary = right + property = flux_on_OT_dry + execute_on = 'INITIAL TIMESTEP_END' + outputs = 'csv' + [] + [recombination_flux_T2O_dry_right] + type = ADSideAverageMaterialProperty + boundary = right + property = flux_on_T2O_dry + execute_on = 'INITIAL TIMESTEP_END' + outputs = 'csv' + [] + [recombination_flux_T2_dry_right] + type = ADSideAverageMaterialProperty + boundary = right + property = flux_on_T2_dry + execute_on = 'INITIAL TIMESTEP_END' + outputs = 'csv' + [] + + # necessary parameters + [T2_K_eq_average] + type = ADElementAverageMaterialProperty + mat_prop = T2_K_eq + [] + [T2_K_forward_average] + type = ADElementAverageMaterialProperty + mat_prop = T2_K_forward + [] + [T2_K_reverse_average] + type = ADElementAverageMaterialProperty + mat_prop = T2_K_reverse + [] + [T2O_K_eq_average] + type = ADElementAverageMaterialProperty + mat_prop = T2O_K_eq + [] + [T2O_K_forward_average] + type = ADElementAverageMaterialProperty + mat_prop = T2O_K_forward + [] + [T2O_K_reverse_average] + type = ADElementAverageMaterialProperty + mat_prop = T2O_K_reverse + [] + [diffusivity_OT_average] + type = ADElementAverageMaterialProperty + mat_prop = diffusivity_OT + execute_on = 'INITIAL TIMESTEP_END' + [] + [diffusivity_V_O_average] + type = ADElementAverageMaterialProperty + mat_prop = diffusivity_V_O + execute_on = 'INITIAL TIMESTEP_END' + [] + [temperature_average] + type = ElementAverageValue + variable = temperature + execute_on = 'INITIAL TIMESTEP_END' + [] + [voltage_value] + type = ParsedPostprocessor + expression = ${V_current} + execute_on = 'INITIAL TIMESTEP_END' + [] + [pressure_T2_average] + type = ElementAverageValue + variable = pressure_T2_dry + execute_on = 'INITIAL TIMESTEP_END' + [] + + # --- MultiApp coupling postprocessors --- + [received_pressure] # upstream T2 partial pressure [Pa] received from the parent fuel-cycle model + type = Receiver + default = ${pressure_T2_high} # fallback so standalone runs reproduce the base feed pressure + execute_on = 'INITIAL TIMESTEP_BEGIN' + [] + [permeation_rate_kg_per_s] # tritium mass flow permeated to the downstream side [kg/s] + # The downstream-boundary OT flux is negative when tritium permeates OUT to the permeate side, + # so the forward permeation rate is max(-flux, 0): only net downstream transport is recovered. + # flux[at/nm^2/s] * 1e18 -> at/m^2/s ; * A_membrane[m^2] -> at/s ; * M_T_atomic/N_a -> kg/s + type = ParsedPostprocessor + pp_names = 'recombination_flux_OT_dry_right' + expression = 'max(-recombination_flux_OT_dry_right, 0) * 1e18 * ${A_membrane} * ${M_T_atomic} / ${N_a}' + execute_on = 'INITIAL TIMESTEP_END' + [] + + # Joule heating diagnostics + [temperature_max] + type = ElementExtremeValue + variable = temperature + value_type = max + execute_on = 'INITIAL TIMESTEP_END' + [] + [temperature_min] + type = ElementExtremeValue + variable = temperature + value_type = min + execute_on = 'INITIAL TIMESTEP_END' + [] + [delta_T] + type = ParsedPostprocessor + pp_names = 'temperature_max temperature_min' + expression = 'temperature_max - temperature_min' + execute_on = 'TIMESTEP_END' + [] +[] + +[Executioner] + type = Transient + scheme = implicit-euler + solve_type = NEWTON + petsc_options_iname = '-pc_type -snes_type' + petsc_options_value = 'lu vinewtonrsls' + nl_rel_tol = 5e-6 + # Slightly looser absolute tolerance than the standalone model: when driven across the full range + # of upstream pressures by the fuel cycle, the residual can stall just above 5e-7 in some states. + # 1e-6 (still 3+ orders below the initial residual) converges reliably without affecting the flux. + nl_abs_tol = 1e-6 + end_time = ${endtime} + # Run to (pseudo-)steady permeation each time the parent invokes this sub-app, then terminate + # early. end_time is a hard cap; steady_state_start_time avoids declaring steady state during + # the upstream-pressure ramp (ramp_time). + steady_state_detection = true + steady_state_tolerance = 1e-6 + steady_state_start_time = '${fparse 10 * ramp_time}' + automatic_scaling = true + compute_scaling_once = true + line_search = none + error_on_dtmin = false # must stay false for ignore_solve_not_converge to work in Level 2 + abort_on_solve_fail = true # fast-fail on first NL divergence; prevents stutter at dtmin + dtmin = 1e-10 + nl_max_its = 60 + dtmax = ${dt_max} + [TimeStepper] + type = IterationAdaptiveDT + dt = ${dt_start_charging} + optimal_iterations = 20 + growth_factor = 1.5 + cutback_factor = 0.5 + cutback_factor_at_failure = 0.5 + [] +[] + +[Debug] + show_var_residual_norms = true +[] + +[Outputs] + exodus = false + console = false + # CSV suppressed by the parent (Outputs/csv/enable=false via cli_args) since two DIR membrane + # instances share this file; the DIR fluxes are recorded in the parent fuel-cycle output instead. + [csv] + type = CSV + [] +[] diff --git a/test/tests/PCC_multiscale_example/fit_residence_time.py b/test/tests/PCC_multiscale_example/fit_residence_time.py new file mode 100644 index 000000000..354972e4f --- /dev/null +++ b/test/tests/PCC_multiscale_example/fit_residence_time.py @@ -0,0 +1,102 @@ +#!/usr/bin/env python3 +"""Fit the PCC membrane transient permeation to a first-order residence-time response. + +The PCC-enhanced tritium-permeation membrane (TPM) is represented in the fuel cycle by a single +residence time. We obtain it from a standalone membrane permeation run at a fixed upstream tritium +partial pressure (5 Pa), saved as ``membrane_5_Pa_flux.csv``. The downstream permeation flux +``J_back = recombination_flux_OT_dry_right`` rises from ~0 toward a plateau ``J_inf`` with a +characteristic time ``tau``: + + J_back(t) = J_inf * (1 - exp(-t / tau)) + +``tau`` (the fitted membrane response time) is used as the TPM residence time ``resident_time_11`` in +the fuel cycle. This script fits ``J_inf`` and ``tau`` and plots the tritium-release data against the +fitted curve. +""" + +import os + +import numpy as np +import pandas as pd +import matplotlib.pyplot as plt +from scipy.optimize import curve_fit + +# Resolve data/figure paths for both the test tree and the documentation build. +script_folder = os.path.dirname(os.path.abspath(__file__)) +if "/TMAP8/doc/" in script_folder: + test_dir = "../../../../test/tests/PCC_multiscale_example" +else: + test_dir = script_folder +path = os.path.join(test_dir, "gold") + +csv_file = os.path.join(path, "membrane_5_Pa_flux.csv") +if not os.path.isfile(csv_file): + raise FileNotFoundError("Membrane permeation data not found: {}".format(csv_file)) + +data = pd.read_csv(csv_file) +t = data["time"].to_numpy() +j_back = data["recombination_flux_OT_dry_right"].to_numpy() + + +def residence_response(time, j_inf, tau0, tau1): + """Delayed first-order response. + + J_back = 0 for t <= tau0 (transport delay) + = J_inf * (1 - exp(-(t-tau0)/tau1)) for t > tau0 (rise toward the plateau) + + The system has a delay tau0 before tritium appears downstream, then the flux rises with time + constant tau1. Implemented with max(t - tau0, 0) so it is 0 for t <= tau0. + """ + return j_inf * (1.0 - np.exp(-np.maximum(time - tau0, 0.0) / tau1)) + + +# Initial guess: plateau from the last value; small delay tau0; rise tau1 ~ tens of seconds. +# Bounds keep the delay and rise time non-negative. +p0 = [j_back[-1], 1.0, 30.0] +popt, _ = curve_fit( + residence_response, + t, + j_back, + p0=p0, + bounds=([-np.inf, 0.0, 1e-6], [np.inf, np.inf, np.inf]), + maxfev=20000, +) +j_inf, tau0, tau1 = popt + +fit = residence_response(t, *popt) +ss_res = np.sum((j_back - fit) ** 2) +ss_tot = np.sum((j_back - j_back.mean()) ** 2) +r2 = 1.0 - ss_res / ss_tot + +print("Fitted J_back = J_inf*(1 - exp(-(t-tau0)/tau1)) for t > tau0, else 0:") +print(" J_inf = {:.6g} (at/nm^2/s)".format(j_inf)) +print(" tau0 = {:.6g} s (transport delay -- shifts timing only)".format(tau0)) +print(" tau1 = {:.6g} s <-- use as resident_time_11 (only tau1 sets the steady-state inventory)".format(tau1)) +print(" R^2 = {:.5f}".format(r2)) + +# Plot the tritium-release data and the fitted curve: absolute flux, linear time axis, at/m^2/s. +unit = 1e18 # at/nm^2/s -> at/m^2/s +t_fit = np.concatenate([np.linspace(0.0, 500.0, 300), np.linspace(500.0, t.max(), 400)]) +plt.rcParams.update({"font.size": 1.5 * plt.rcParamsDefault["font.size"]}) # scale all fonts 1.5x +fig, ax = plt.subplots(figsize=[6.5, 5.5]) +ax.plot(t, np.abs(j_back) * unit, "-", ms=4, color="C0", label="membrane simulation (5 Pa)") +ax.plot(t_fit, np.abs(residence_response(t_fit, *popt)) * unit, "-", color="C1", + label=r"fitting") +ax.set_xlabel("Time (s)") +ax.set_ylabel(r"Tritium release (at/m$^2$/s)") +ax.set_xlim([0,100]) +ax.set_ylim(bottom=0) +ax.legend(loc="lower right") +ax.text( + 0.40, + 0.65, + r"$\tau_0$ = {:.2f} s".format(tau0) + "\n" + r"$\tau_1$ = {:.2f} s".format(tau1) + + "\n" + + r"$R^2$ = {:.4f}".format(r2), + transform=ax.transAxes, +) + +os.makedirs(os.path.join(path, "../figures"), exist_ok=True) +out_fig = os.path.join(path, "../figures", "fit_residence_time.png") +fig.savefig(out_fig, dpi=150, bbox_inches="tight") +print("Saved figure to {}".format(out_fig)) diff --git a/test/tests/PCC_multiscale_example/fuel_cycle_PCC_membrane.i b/test/tests/PCC_multiscale_example/fuel_cycle_PCC_membrane.i new file mode 100644 index 000000000..efb11bfae --- /dev/null +++ b/test/tests/PCC_multiscale_example/fuel_cycle_PCC_membrane.i @@ -0,0 +1,748 @@ +# Parent (system level) for the PCC membrane <-> fuel-cycle MultiApp coupling. +# Derived from fuel_cycle_2023/fuel_cycle_PCC.i. +# +# Unit system: fuel-cycle inventories are kg of tritium and time is seconds. The membrane feed +# plenum pressure is computed in Pa through MOOSE units and SI gas constants. +# +# The tritium-separation membrane (inventory I11, T_11_membrane) is no longer the lumped eta_2 / +# residence11 box. It is now a CONTAINER (gas plenum, initial 0 Pa) coupled to a 1D +# proton-conducting-ceramic (BCY) membrane component sub-app (pcc_membrane_sub.i) via a lock-step +# TransientMultiApp: +# * ALL of the TES output (T_02_TES/residence2) feeds the container (I11). +# * The container holdup T_11_membrane (kg) is converted to an upstream T2 partial pressure +# (membrane_upstream_pressure, ideal gas) and pushed to the sub-app each step. +# * The sub-app co-evolves in time and returns the permeated tritium flow (membrane_permeation_ +# rate, kg/s), which goes to the heat exchanger (I5). +# * The un-permeated retentate (T_11_membrane/residence11) is recycled back to the TES (I2). +# * Storage (I10) no longer receives a membrane term. +# * eta_2 is now a calculated diagnostic (eta_2_calculated = permeated / TES feed; ~0.85 expected). +# +# This input file re-creates the deuterium-tritium fuel cycle model +# described by Meschini et al (2023). +# "Modeling and analysis of the tritium fuel cycle for ARC- and STEP-class D-T +# fusion power plants." S Meschini & S E Ferry & R Delaporte-Mathurin +# & D G Whyte Nucl. Fusion 63 (2023) https://doi.org/10.1088/1741-4326/acf3fc + +# The mesh is completely ignored, but TMAP/MOOSE will complain without it. If high-fidelity +# models of specific components are required, the scalar variables can be coupled to +# "Field" variables which can vary spatially across the mesh, or could be co-ordinated +# with sub-apps. + +pulse_time = '${units 1800 s}' +initial_inventory = '${units 0.803 kg}' # 1.14 kg} +accuracy_time = '${units 864000 s}' # 864000 s} +time_interval_middle = '${units 1e6 s}' +simulation_time = '${units 94608000 s}' # 3 years + +# Modeling parameters +resident_time_1 = '${units 4500 s}' +resident_time_2 = '${units 86400 s}' +resident_time_3 = '${units 1000 s}' +resident_time_4 = '${units 1000 s}' +resident_time_5 = '${units 1000 s}' +resident_time_6 = '${units 3600 s}' +resident_time_7 = '${units 600 s}' +resident_time_8 = '${units 360 s}' +resident_time_9 = '${units 14040 s}' +resident_time_11 = '${units 100 s}' # in-p +epsilon_low = 0 # - +epsilon = 1e-4 # - +f_5to1 = 0.33 # - +f_5to3 = 0.33 # - +f_5to6 = 1e-4 # - +f_9to6 = 0.1 # - +f_Pto3 = 1e-4 # - +f_Pto4 = 1e-4 # - +f_DIR_VP = 0.85 # - # in-p +f_DIR_FCU = 0.85 # - # in-p +eta_2 = 0.85 # - # in-p +TBR_value = 1.067 # - +AF_value = 0.7 # - # in-p +- 0.3 +t_decay = '${units 1.73e-9 1/s}' +TBE_value = 0.02 # - # in-p +tritium_burn_rate_value = 8.99e-7 # - + +# --- MultiApp coupling: feed-plenum bridge parameters (parent side) --- +# Convert the membrane feed-plenum holdup T_11_membrane (kg of tritium, held as T2 gas) to an +# upstream T2 partial pressure via the ideal gas law. V_feed must be physically paired with the +# sub-app A_membrane: together they set the coupling gain. Documented placeholder values; +# calibrate against a target steady membrane inventory. +M_T2_molar = '${units 6.032e-3 kg/mol}' # T2 molar mass (plenum holdup is T2 gas) +T_feed = '${units 773 K}' # feed-plenum gas temperature (matches sub-app) +# Container volume. Larger V_feed lowers the coupling gain (gain ~ 1/V_feed) and slows the holdup +# dynamics. Documented placeholder; the steady container pressure is set by the membrane +# (flux = feed) and is largely independent of V_feed. +V_feed = '${units 10.0 m^3}' # container volume (TUNING PARAMETER) +R_gas = '${units 8.31446261815324 J/mol/K}' # ideal gas constant + +[Mesh] + type = GeneratedMesh + dim = 1 + xmin = 0 + xmax = 1 + nx = 1 +[] + +# One variable for each inventory of tritium is generated. All variables +# are defined as "SCALAR", meaning that they are a single value and are +# disconnected from any specific geometry + +[Variables] + [T_01_BZ] + family = SCALAR + [] + [T_02_TES] + family = SCALAR + [] + [T_03_FW] + family = SCALAR + [] + [T_04_DIV] + family = SCALAR + [] + [T_05_HX] + family = SCALAR + [] + [T_06_DS] # Detritiation system + family = SCALAR + [] + [T_07_vacuum] + family = SCALAR + [] + [T_08_FCU] + family = SCALAR + [] + [T_09_ISS] + family = SCALAR + [] + [T_10_storage] + family = SCALAR + initial_condition = ${initial_inventory} + [] + [T_11_membrane] # Tritium separation membrane + family = SCALAR + [] +[] + +# Tritium burn fraction is going to be small. Much +# will be lost to the scrape-off-layer (SOL) and +# recycled. + +# TES - tritium extraction system pulls tritium from +# the blanket + +# CPS - Coolant purification system pulls tritium from +# the coolant (CPS is signored in ARC reactor) +# Ignored in ARC due to liquid FLiBe + +# An ODE is defined in TMAP8 such that all of the terms must +# be on the left hand side. The terms can be split +# across multiple "ScalarKernels", which are additive, +# so that we have one ODETimeDerivative for each tritium +# inventory and a ParsedODEKernel for the rest of the +# terms. These equations should reflect those described +# in Appendix A of the paper (A.1-A.13), with negation +# on the ParsedODEKernels due to moving the terms to the +# left hand side. + +[ScalarKernels] + [I1t] + type = ODETimeDerivative + variable = T_01_BZ + [] + [I2t] + type = ODETimeDerivative + variable = T_02_TES + [] + [I3t] + type = ODETimeDerivative + variable = T_03_FW + [] + [I4t] + type = ODETimeDerivative + variable = T_04_DIV + [] + [I5t] + type = ODETimeDerivative + variable = T_05_HX + [] + [I6t] + type = ODETimeDerivative + variable = T_06_DS + [] + [I7t] + type = ODETimeDerivative + variable = T_07_vacuum + [] + [I8t] + type = ODETimeDerivative + variable = T_08_FCU + [] + [I9t] + type = ODETimeDerivative + variable = T_09_ISS + [] + [I10t] + type = ODETimeDerivative + variable = T_10_storage + [] + [I11t] + type = ODETimeDerivative + variable = T_11_membrane + [] + [I1] # Breeding Zone + type = ParsedODEKernel + expression = '-(breeder_pulse + T_03_FW / residence3 + T_04_DIV / residence4 + HX_BZ_leak_fraction * T_05_HX / residence5 - T_01_BZ / residence1 - T_01_BZ * epsilon1 / residence1 - T_01_BZ * tdecay)' + variable = 'T_01_BZ' + coupled_variables = 'T_03_FW T_04_DIV T_05_HX' + postprocessors = 'breeder_pulse HX_BZ_leak_fraction residence1 residence3 residence4 residence5 tdecay epsilon1' + [] + [I2] #Tritium Extraction System + # Receives back the un-permeated membrane retentate (T_11_membrane/residence11) recycled from + # the container, in addition to the breeding-zone feed. + type = ParsedODEKernel + expression = '-(T_01_BZ / residence1 + T_11_membrane / residence11 - T_02_TES / residence2 - T_02_TES * epsilon2 / residence2 - T_02_TES * tdecay)' + variable = 'T_02_TES' + coupled_variables = 'T_01_BZ T_11_membrane' + postprocessors = 'residence1 residence2 residence11 tdecay epsilon2' + [] + [I3] #First Wall + type = ParsedODEKernel + expression = '-(P_FW_leak_fraction * burn_pulse + HX_FW_leak_fraction * T_05_HX / residence5 + - T_03_FW / residence3 - T_03_FW * epsilon3 / residence3 - T_03_FW * tdecay)' + variable = 'T_03_FW' + coupled_variables = 'T_05_HX' + postprocessors = 'P_FW_leak_fraction HX_FW_leak_fraction burn_pulse residence5 residence3 tdecay epsilon3' + [] + # TBE = tritium_burn_fraction * tritium_fueling_efficiency + [I4] #Divertor + type = ParsedODEKernel + expression = '-(P_DIV_leak_fraction * burn_pulse + (1 - HX_BZ_leak_fraction - HX_DS_leak_fraction - HX_FW_leak_fraction) * T_05_HX / residence5 + - T_04_DIV * epsilon4 / residence4 - T_04_DIV / residence4 - T_04_DIV * tdecay)' + variable = 'T_04_DIV' + coupled_variables = 'T_05_HX' + postprocessors = 'P_DIV_leak_fraction HX_BZ_leak_fraction HX_DS_leak_fraction HX_FW_leak_fraction burn_pulse residence5 residence4 tdecay epsilon4' + [] + [I5] #Heat eXchanger + # Now fed by the membrane PERMEATE (downstream flux, membrane_permeation_rate): the tritium that + # permeated through the membrane is routed to the HX, replacing the old (1 - eta_2) split. + type = ParsedODEKernel + expression = '-(membrane_permeation_rate - T_05_HX / residence5 - T_05_HX * epsilon5 / residence5 - T_05_HX * tdecay)' + variable = 'T_05_HX' + postprocessors = 'membrane_permeation_rate residence5 tdecay epsilon5' + [] + [I6] #Detritiation system + type = ParsedODEKernel + expression = '-(HX_DS_leak_fraction * T_05_HX / residence5 + ISS_DS_leak_fraction * T_09_ISS / residence9 - T_06_DS / residence6 - T_06_DS * epsilon6 / residence6 - T_06_DS * tdecay)' + variable = 'T_06_DS' + coupled_variables = 'T_05_HX T_09_ISS' + postprocessors = 'HX_DS_leak_fraction ISS_DS_leak_fraction residence5 residence9 residence6 tdecay epsilon6' + [] + [I7] #Vacuum Pump + type = ParsedODEKernel + expression = '-((1 - TBE - P_FW_leak_fraction - P_DIV_leak_fraction) * burn_pulse + - T_07_vacuum / residence7 - T_07_vacuum * epsilon7 / residence7 - T_07_vacuum * tdecay)' + variable = 'T_07_vacuum' + postprocessors = 'TBE burn_pulse P_FW_leak_fraction P_DIV_leak_fraction residence7 tdecay epsilon7' + [] + [I8] #Fuel clean-up + type = ParsedODEKernel + expression = '-((1 - DIR_fraction_VP) * T_07_vacuum / residence7 - T_08_FCU / residence8 - T_08_FCU * epsilon8 / residence8 - T_08_FCU * tdecay)' + variable = 'T_08_FCU' + coupled_variables = 'T_07_vacuum' + postprocessors = 'DIR_fraction_VP residence7 residence8 tdecay epsilon8' + [] + [I9] #Isotope Separation System + type = ParsedODEKernel + expression = '-(T_06_DS / residence6 + (1 - DIR_fraction_FCU) * T_08_FCU / residence8 - T_09_ISS / residence9 - T_09_ISS * epsilon9 / residence9 - T_09_ISS*tdecay)' + variable = 'T_09_ISS' + coupled_variables = 'T_06_DS T_08_FCU' + postprocessors = 'DIR_fraction_FCU residence6 residence8 residence9 tdecay epsilon9' + [] + [I10] #Storage and Management (STO) + # Storage no longer receives a membrane term: the membrane permeate now goes to the HX (I5), not + # to storage. Reverts to the base Meschini storage balance (ISS + vacuum + FCU - burn - decay). + type = ParsedODEKernel + expression = '-((1 - ISS_DS_leak_fraction) * T_09_ISS / residence9 + DIR_fraction_VP * T_07_vacuum / residence7 + DIR_fraction_FCU * T_08_FCU / residence8 - burn_pulse - T_10_storage * tdecay)' + variable = 'T_10_storage' + coupled_variables = 'T_09_ISS T_07_vacuum T_08_FCU' + postprocessors = 'ISS_DS_leak_fraction DIR_fraction_VP DIR_fraction_FCU burn_pulse residence9 residence8 residence7 tdecay AF' + [] + [I11] #Tritium Separation Membrane (TSM) -- upstream container / gas plenum + # Simplified container (initial 0 Pa). Fed the full TES output (T_02_TES/residence2); its holdup + # T_11_membrane sets the upstream pressure driving the PCC sub-app, which returns the permeated + # flow (membrane_permeation_rate -> HX via I5). The un-permeated retentate (T_11_membrane / + # residence11) is recycled back to the TES (I2). Radioactive decay retained. + type = ParsedODEKernel + expression = '-(T_02_TES / residence2 - membrane_permeation_rate - T_11_membrane / residence11 - T_11_membrane * tdecay)' + variable = 'T_11_membrane' + coupled_variables = 'T_02_TES' + postprocessors = 'residence2 residence11 tdecay membrane_permeation_rate' + [] +[] + +[Functions] + [breeder_pulse_function] + type = ParsedFunction + symbol_names = 'AF tritium_burn_rate TBR' + symbol_values = 'AF tritium_burn_rate TBR' + # expression = 'if(t % ${pulse_time} < AF * ${pulse_time}, tritium_burn_rate * TBR, 0)' + # expression = 'AF * tritium_burn_rate * TBR' + expression = 'if(t > ${accuracy_time}, AF * tritium_burn_rate * TBR, + if(t % ${pulse_time} < AF * ${pulse_time}, tritium_burn_rate * TBR, 0))' + [] + [burn_pulse_function] + type = ParsedFunction + symbol_names = 'AF tritium_burn_rate TBE' + symbol_values = 'AF tritium_burn_rate TBE' + # expression = 'if(t % ${pulse_time} < AF * ${pulse_time}, tritium_burn_rate / TBE, 0)' + # expression = 'AF * tritium_burn_rate / TBE' + expression = 'if(t > ${accuracy_time}, AF * tritium_burn_rate / TBE, + if(t % ${pulse_time} < AF * ${pulse_time}, tritium_burn_rate / TBE, 0))' + [] + [dt_function] + type = ParsedFunction + symbol_names = 'AF' + symbol_values = 'AF' + # expression = 'if(t % ${pulse_time} < 1, 1, + # if(t % ${pulse_time} < AF * ${pulse_time} - 1, AF * ${pulse_time} - t % ${pulse_time} - 1, + # if(t % ${pulse_time} < AF * ${pulse_time}, 2, + # if(t % ${pulse_time} < ${pulse_time} - 1, ${pulse_time} - t % ${pulse_time} - 1, + # if(t % ${pulse_time} < ${pulse_time}, 2, 2)))))' + # expression = 'if(t % ${pulse_time} < AF * ${pulse_time}, AF * ${pulse_time} - t % ${pulse_time} + 0.1, + # if(t % ${pulse_time} < ${pulse_time}, ${pulse_time} - t % ${pulse_time} + 0.1, 2))' + expression = 'if(t > ${accuracy_time}, ${time_interval_middle}, + if(t % ${pulse_time} < AF * ${pulse_time}, AF * ${pulse_time} - t % ${pulse_time} + 0.1, + if(t % ${pulse_time} < ${pulse_time}, ${pulse_time} - t % ${pulse_time} + 0.1, 2)))' + [] +[] + +# These postprocessors define the constants referenced in +# the equations above. The value of any of these constants +# could be informed by more detailed models (using sub-apps +# and transfers), but it is important that the postprocessor +# is evaluated before the executioner attempts to solve the +# ODE, which is not the default behavior. +[Postprocessors] + [burn_pulse] + type = FunctionValuePostprocessor + function = burn_pulse_function + execute_on = 'initial timestep_end' + [] + [breeder_pulse] + type = FunctionValuePostprocessor + function = breeder_pulse_function + execute_on = 'initial timestep_end' + [] + [HX_BZ_leak_fraction] #f_{5-1} + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${f_5to1} + [] + [HX_FW_leak_fraction] #f_{5-3} + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${f_5to3} + [] + [HX_DS_leak_fraction] #f_{5-6} + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${f_5to6} + [] + [ISS_DS_leak_fraction] #f_{9-6} + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${f_9to6} + [] + [P_DIV_leak_fraction] #f_{P-4} + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${f_Pto4} + [] + [P_FW_leak_fraction] #f_{P-3} + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${f_Pto3} + [] + [TES_efficiency] #eta_2 from Abdou et al. 2020 + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${eta_2} + [] + [TBR] + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${TBR_value} # for t_d = 2 yrs + [] + [DIR_fraction_VP] #f_DIR + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${f_DIR_VP} # (0.1 - 0.9) + [] + [DIR_fraction_FCU] #f_DIR + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${f_DIR_FCU} # (0.1 - 0.9) + [] + [AF] + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${AF_value} # (0.75 from Meschini) + [] + [tdecay] + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${t_decay} # (from Meschini) 1.7828336471961835e-9 (from Abdou) + [] + [TBE] + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${TBE_value} # (0.005 - 0.1) Meschini + [] + [tritium_burn_rate] + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${tritium_burn_rate_value} # (5.3125e-6 from Abdou) (9.3e-7 Kg/s from Meschini paper) (8.99e-7 Kg/s from Meschini matlab) + [] + [epsilon1] #BZ + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${epsilon} + [] + [epsilon2] #TES + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${epsilon} + [] + [epsilon3] #FW + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${epsilon_low} + [] + [epsilon4] #DIV + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${epsilon_low} + [] + [epsilon5] #HX + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${epsilon} + [] + [epsilon6] #DS + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${epsilon} + [] + [epsilon7] #Vac + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${epsilon} + [] + [epsilon8] #FCU + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${epsilon} + [] + [epsilon9] #ISS + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${epsilon} + [] + [epsilon11] #TSM + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${epsilon} + [] + [residence1] #BZ + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${resident_time_1} # s 1.25 h, (Meschini) and (Ferrero et al) T_BZ = 3 g, 864000 # s 10 days + # value = 1 h - 240 h + [] + [residence2] #TES + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${resident_time_2} # s Meschini + #value = 1 h - 240 h Riva + [] + [residence3] #FW + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${resident_time_3} # s Riva + [] + [residence4] #DIV + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${resident_time_4} # s Riva + [] + [residence5] #HX + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${resident_time_5} # s Abdou 2021 paper chosen for analysis + [] + [residence6] #DS + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${resident_time_6} # s Meschini + [] + [residence7] #Vac + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${resident_time_7} # s + [] + [residence8] #FCU + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${resident_time_8} # 0.1625 h 3600 # s 1 h Meschini + # value = 0.1 - 1 h Meschini + #value = 5 h Coleman + #value = 8640 Abdou + #value = 86400 Abdou + [] + [residence9] #ISS + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${resident_time_9} # s 6.3375 h Meschini + #value = 0.9 - 11 h # (for four hour overall residence time in inner loop) + [] + [residence11] #TSM + type = ConstantPostprocessor + execute_on = 'TIMESTEP_BEGIN INITIAL LINEAR NONLINEAR' + value = ${resident_time_11} # (from Meschini) 1958.25 # s (1899.50 m / 0.97 m/s = 1958.25) (from Papa et al. 2021) + [] + # These postprocessors exist to sum up the tritium inventory + # across the entirety of the system + [T_BZ] + type = ScalarVariable + variable = T_01_BZ + execute_on = TIMESTEP_END + [] + [T_TES] + type = ScalarVariable + variable = T_02_TES + execute_on = TIMESTEP_END + [] + [T_FW] + type = ScalarVariable + variable = T_03_FW + execute_on = TIMESTEP_END + [] + [T_DIV] + type = ScalarVariable + variable = T_04_DIV + execute_on = TIMESTEP_END + [] + [T_HX] + type = ScalarVariable + variable = T_05_HX + execute_on = TIMESTEP_END + [] + [T_DS] + type = ScalarVariable + variable = T_06_DS + execute_on = TIMESTEP_END + [] + [T_VAC] + type = ScalarVariable + variable = T_07_vacuum + execute_on = TIMESTEP_END + [] + [T_FCU] + type = ScalarVariable + variable = T_08_FCU + execute_on = TIMESTEP_END + [] + [T_ISS] + type = ScalarVariable + variable = T_09_ISS + execute_on = TIMESTEP_END + [] + [T_STO] + type = ScalarVariable + variable = T_10_storage + execute_on = TIMESTEP_END + [] + [T_TSM] + type = ScalarVariable + variable = T_11_membrane + execute_on = TIMESTEP_END + [] + [total_tritium] + type = SumPostprocessor + values = 'T_BZ T_TES T_FW T_DIV T_HX T_DS T_VAC T_FCU T_ISS T_STO T_TSM' + [] + + # --- MultiApp coupling postprocessors (membrane container <-> PCC sub-app) --- + # All coupling transfers fire on TIMESTEP_END (lock-step TransientMultiApp). Within a timestep_end, + # execute(TIMESTEP_END) computes these postprocessors BEFORE execMultiApps, so the fresh + # end-of-step container pressure is sent down; the sub-app advances on the shared clock and its + # permeation flux is pulled up for use in the next step's fuel-cycle solve. + [T_TSM_now] # membrane feed-plenum holdup [kg], drives the upstream pressure + type = ScalarVariable + variable = T_11_membrane + execute_on = 'INITIAL TIMESTEP_END' + [] + [T_TES_now] # TES inventory [kg], used to report the calculated extraction efficiency + type = ScalarVariable + variable = T_02_TES + execute_on = 'INITIAL TIMESTEP_END' + [] + [membrane_upstream_pressure] # container T2 partial pressure from holdup via ideal gas [Pa] + # max(.,0) guards against a transient negative holdup (the scalar ODE is not positivity-bounded) + # producing a nonphysical negative pressure that would break the sub-app reaction kinetics. No + # upper cap is needed: the holdup is bounded by the total system inventory, so P cannot run away. + type = ParsedPostprocessor + pp_names = 'T_TSM_now' + expression = 'max(T_TSM_now, 0) / ${M_T2_molar} * ${R_gas} * ${T_feed} / ${V_feed}' + execute_on = 'INITIAL TIMESTEP_END' + [] + [membrane_permeation_rate] # tritium permeate (downstream) -> HX [kg/s], received from the sub-app + type = Receiver + default = 0 + execute_on = 'INITIAL TIMESTEP_END' + [] + [membrane_flux_upstream] # upstream (left-boundary) OT flux from the sub-app [at/nm^2/s] + type = Receiver + default = 0 + execute_on = 'INITIAL TIMESTEP_END' + [] + [membrane_flux_downstream] # downstream (right-boundary) OT flux from the sub-app [at/nm^2/s] + type = Receiver + default = 0 + execute_on = 'INITIAL TIMESTEP_END' + [] + [feed_rate] # TES feed rate into the container [kg/s] + type = ParsedPostprocessor + pp_names = 'T_TES_now' + expression = 'T_TES_now / ${resident_time_2}' + execute_on = 'INITIAL TIMESTEP_END' + [] + [eta_2_calculated] # instantaneous physics-based extraction efficiency = permeated / TES feed [-] + type = ParsedPostprocessor + pp_names = 'membrane_permeation_rate feed_rate' + expression = 'if(feed_rate > 1e-12, membrane_permeation_rate / feed_rate, 0)' + execute_on = 'TIMESTEP_END' + [] + # Cumulative (time-integrated) extraction efficiency: a smooth, robust diagnostic that avoids the + # large early swings of the instantaneous ratio (which divides by a near-zero feed while the TES + # is still filling). eta_2_cumulative = (integral of permeation) / (integral of feed). + [cumulative_permeation] # time-integrated permeate to HX [kg] + type = TimeIntegratedPostprocessor + value = membrane_permeation_rate + execute_on = 'INITIAL TIMESTEP_END' + [] + [cumulative_feed] # time-integrated TES feed into the container [kg] + type = TimeIntegratedPostprocessor + value = feed_rate + execute_on = 'INITIAL TIMESTEP_END' + [] + [eta_2_cumulative] # cumulative extraction efficiency [-] + type = ParsedPostprocessor + pp_names = 'cumulative_permeation cumulative_feed' + expression = 'if(cumulative_feed > 1e-12, cumulative_permeation / cumulative_feed, 0)' + execute_on = 'TIMESTEP_END' + [] +[] +[UserObjects] + [terminator] + type = Terminator + expression = 'T_STO < 0' + fail_mode = 'HARD' + message = 'Tritium in storage has been depleted' + [] + [terminator2] + type = Terminator + expression = 'total_tritium < 0' + fail_mode = 'HARD' + message = 'Tritium in system has been depleted' + [] +[] + +[MultiApps] + [pcc_membrane] + # 1D PCC membrane component, co-evolved with the fuel cycle on a shared clock. sub_cycling lets + # the membrane take its own (smaller, adaptive) timesteps to reach the parent's time within each + # fuel-cycle step -- needed because the parent dt (>= ~1e3 s, up to 1e6 s) is far larger than the + # membrane's stable timestep from a cold start. output_sub_cycles=false keeps the sub CSV to one + # row per fuel-cycle step (a clean fuel-cycle-time series of the membrane state). + type = TransientMultiApp + input_files = 'pcc_membrane_sub.i' + execute_on = 'TIMESTEP_END' + positions = '0 0 0' + max_procs_per_app = 1 + sub_cycling = true + output_sub_cycles = false + [] +[] + +[Transfers] + [push_pressure] # parent -> sub: container T2 partial pressure [Pa] (no reduction_type for to_multiapp) + type = MultiAppPostprocessorTransfer + to_multi_app = pcc_membrane + from_postprocessor = membrane_upstream_pressure + to_postprocessor = received_pressure + execute_on = 'TIMESTEP_END' + [] + [pull_permeation] # sub -> parent: permeated tritium flow [kg/s] (reduction_type required for from_multiapp) + type = MultiAppPostprocessorTransfer + from_multi_app = pcc_membrane + from_postprocessor = permeation_rate_kg_per_s + to_postprocessor = membrane_permeation_rate + reduction_type = average + execute_on = 'TIMESTEP_END' + [] + [pull_flux_upstream] # sub -> parent: upstream (left-boundary) OT flux [at/nm^2/s] + type = MultiAppPostprocessorTransfer + from_multi_app = pcc_membrane + from_postprocessor = recombination_flux_OT_dry_left + to_postprocessor = membrane_flux_upstream + reduction_type = average + execute_on = 'TIMESTEP_END' + [] + [pull_flux_downstream] # sub -> parent: downstream (right-boundary) OT flux [at/nm^2/s] + type = MultiAppPostprocessorTransfer + from_multi_app = pcc_membrane + from_postprocessor = recombination_flux_OT_dry_right + to_postprocessor = membrane_flux_downstream + reduction_type = average + execute_on = 'TIMESTEP_END' + [] +[] + +[Executioner] + type = Transient + start_time = 0 + dtmin = 1 + end_time = ${simulation_time} # 30 years - 946080000, 2 years - 31536000, 3 years - 94608000 + [TimeStepper] + type = FunctionDT + function = dt_function + [] + solve_type = 'PJFNK' + nl_rel_tol = 1e-08 + nl_abs_tol = 1e-14 + # Lock-step TransientMultiApp coupling with fixed-point (Picard) iteration. The large membrane + # area (A = 1 m^2) plus the applied voltage makes the membrane permeate steeply at very low + # pressure, so an explicit one-step-lagged coupling oscillates and drives the container holdup + # negative. Iterating the container-pressure <-> permeation loop each step with under-relaxation + # of the fed-back permeation makes it consistent and stable (TransientMultiApp supports this). + fixed_point_max_its = 30 + fixed_point_rel_tol = 1e-5 + fixed_point_abs_tol = 1e-16 + accept_on_max_fixed_point_iteration = true + relaxation_factor = 0.3 + transformed_postprocessors = 'membrane_permeation_rate' +[] + +[Outputs] + hide = "AF breeder_pulse burn_pulse HX_BZ_leak_fraction HX_FW_leak_fraction HX_DS_leak_fraction " + "ISS_DS_leak_fraction P_DIV_leak_fraction P_FW_leak_fraction TES_efficiency TBR " + "DIR_fraction_VP DIR_fraction_FCU T_BZ T_DS T_DIV T_TSM T_FCU T_FW T_HX T_ISS T_STO T_TES " + "T_VAC epsilon1 epsilon11 epsilon2 epsilon3 epsilon4 epsilon5 epsilon6 epsilon7 epsilon8 " + "epsilon9 residence1 residence11 residence2 residence3 residence4 residence5 residence6 " + "residence7 residence8 residence9 tdecay TBE tritium_burn_rate T_TSM_now T_TES_now" + file_base = 'fuel_cycle_PCC_membrane_out' + csv = true + console = false +[] diff --git a/test/tests/PCC_multiscale_example/gold/dir_pcc_fuel_cycle_2rt_10Pa_out2_reference.csv b/test/tests/PCC_multiscale_example/gold/dir_pcc_fuel_cycle_2rt_10Pa_out2_reference.csv new file mode 100644 index 000000000..78165986b --- /dev/null +++ b/test/tests/PCC_multiscale_example/gold/dir_pcc_fuel_cycle_2rt_10Pa_out2_reference.csv @@ -0,0 +1,2681 @@ +time,DIR_fraction_FCU,DIR_fraction_VP,flux_to_storage_FCU,flux_to_storage_VP,pressure_FCU,pressure_VP,residence_time_smooth_factor_11,total_tritium,T_01_BZ,T_02_TES,T_03_FW,T_04_DIV,T_05_HX,T_06_DS,T_07_vacuum,T_08_FCU,T_09_ISS,T_10_storage,T_11_membrane +0,0,0,0,0,0,0,3.7200759760209e-44,0,0,0,0,0,0,0,0,0,0,0.803,0 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+99667.746648569,0.020094346802835,43.473539646665,2163.5049419123,0.011797113633886,520712080.07112,44139013636.811,0.45831163601463,132629.01065756,551183196.19404,16.310991848588,2.467551695e-05,5677.8156685699,-5675.1772909955,445120.45649379,32.174328551471,-447959.36432808,2805.4143169463,3.1082601826032e+43,773.33318210208,773.45942483887,773.00111320286,2 +100000,0.020094346802835,43.473539646665,2163.5049419123,0.011797113633886,520712080.07112,44139013636.811,0.45831163601463,132629.01065756,551183196.19404,16.310991848588,2.467551695e-05,5677.8156685699,-5675.1772909955,445120.45649379,32.174328551471,-447959.36432808,2805.4143169463,3.1082601826032e+43,773.33318210208,773.45942483887,773.00111320286,2 diff --git a/test/tests/PCC_multiscale_example/pcc_membrane_sub.i b/test/tests/PCC_multiscale_example/pcc_membrane_sub.i new file mode 100644 index 000000000..ecf6f4fdc --- /dev/null +++ b/test/tests/PCC_multiscale_example/pcc_membrane_sub.i @@ -0,0 +1,726 @@ +# Sub-app (component level) for the PCC membrane <-> fuel-cycle MultiApp coupling. +# Derived from tritium_transport_PCC/jouleheating_Voltage_BCY_real_LEE2005.i. +# Real (H2+H2O) BCY proton-conducting-ceramic membrane with applied voltage and Joule heating. +# Temperature is a nonlinear Variable coupled to the Joule heating source. +# +# Unit system: the membrane model uses nm for length, Pa for gas pressure, at/nm^3 for +# concentrations, at/nm^2/s for surface fluxes, and kg/s for transferred tritium flow. +# +# Coupling interface (lock-step TransientMultiApp: the sub co-evolves in time with the fuel cycle): +# IN (from parent): received_pressure -- upstream T2 partial pressure [Pa] of the fuel-cycle +# container (T_11_membrane holdup via ideal gas). +# OUT (to parent): permeation_rate_kg_per_s -- tritium permeated to the downstream side [kg/s]; +# also recombination_flux_OT_dry_left/right (upstream/downstream flux). +# The sub-app advances on the same global clock as the parent (no steady-state self-termination). + +# Physical constants +R = '${units 8.31446261815324 J/mol/K}' # ideal gas constant based on number used in include/utils/PhysicalConstants.h +N_a = '${units 6.02214076e23 at/mol}' # ideal gas constant based on number used in include/utils/PhysicalConstants.h +q = '${units 1.602176634e-19 C}' # quantity of charge +F = '${fparse N_a * q}' + +# Thermal properties of BCY20 +# thermal conductivity: 1.05 W/(m*K) for dense BaCeO3 +# Ref: Tenevich et al. 2023, Ceramics International, Vol. 49, 31087-31095 +thermal_conductivity_BCY20 = '${units 1.05 W/m/K -> W/nm/K}' + +# thermal parameters +temperature_initial = '${units 773 K}' # 500C + +# Model parameters +# end_time is set large so the parent (TransientMultiApp, lock-step) drives the actual stop time; +# the sub-app co-evolves on the same global clock as the fuel cycle. +endtime = '1e8' +dt_max = '2e3' +dt_start_charging = '${units 1e-5 s}' +bound_value_min = '${units -1e-20 at/nm^3}' + +# Geometry and mesh +length = '${units 10 mum -> nm}' # BCY20 +num_nodes = 300 + +# Material properties +density_BCY20 = '${units ${fparse 1.0 * 6.154} g/cm^3 -> g/m^3}' +molar_mass_BCY20 = '${units 283.42 g/mol}' +N = '${units ${fparse density_BCY20 / molar_mass_BCY20 * N_a} at/m^3 -> at/nm^3}' +# density in g/nm^3 for pairing with specific_heat in J/(g*K) +density_BCY20_thermal = '${fparse density_BCY20 * 1e-27}' # g/m^3 -> g/nm^3 +# specific heat: ~120 J/(mol*K) for BaCeO3 at high temperature +# Ref: Yamanaka et al. 2003, J. Alloys and Compounds, Vol. 359, 109-113 +specific_heat_BCY20_molar = '${units 120 J/mol/K}' +specific_heat_BCY20 = '${fparse specific_heat_BCY20_molar / molar_mass_BCY20}' # 120/283.42 = 0.4233 J/(g*K) + +# Initial concentrations +OT_concentration_initial = 1e-5 +hydration_limit_S = 0.2 +oxygen_vacancy_concentration_initial = '${units ${fparse hydration_limit_S / 2 * N} at/nm^3}' +oxygen_concentration_initial = '${units ${fparse 3 * N - oxygen_vacancy_concentration_initial - OT_concentration_initial} at/nm^3}' + +##### Dry Pressure conditions +pressure_atm = '${units 101315 Pa}' +pressure_T2_low = '${units 0 Pa}' # downstream (permeate) T2 partial pressure +# In the fuel-cycle coupling the membrane separates tritium (T2): permeation must be driven only by +# the tritium partial pressure supplied by the parent. The independent water (T2O) source of the +# "real" model is therefore disabled (set to 0) so it does not inject a tritium-independent, +# voltage-pumped baseline flux. Set non-zero only for standalone wet-gas studies. +pressure_T2O_constant = '${units 0 Pa}' + +# chemical_reaction — n20_faster optimized parameters (71 steps) +delta_H_T2O = '${units -1.54415211e+05 J/mol}' +delta_S_T2O = '${units -1.67187585e+02 J/mol/K}' +delta_H_T2 = '${units -5.46037663e+04 J/mol}' +delta_S_T2 = '${units -3.36929406e+01 J/mol/K}' +T2O_reaction_forward_mol_exponent = -1.19792592e+01 +ramp_time = 1 +T2O_reaction_forward_mol = '${units ${fparse 8.0 * 10 ^ T2O_reaction_forward_mol_exponent} m^4/mol/s}' +T2O_reaction_forward_value = '${units ${fparse T2O_reaction_forward_mol / N_a} m^4/at/s -> nm^4/at/s}' +T2O_reaction_forward_energy = '${units -7.31595474e+03 J/mol}' +T2_reaction_forward_mol_exponent = -4.05998297e+00 +T2_reaction_forward_mol = '${units ${fparse 8.0 * 10 ^ T2_reaction_forward_mol_exponent} m^4/mol/s}' +T2_reaction_forward_value = '${units ${fparse T2_reaction_forward_mol / N_a} m^4/at/s -> nm^4/at/s}' +T2_reaction_forward_energy = '${units 5.13385478e+03 J/mol}' +diffusivity_OT_prefactor_exponent = -1.26000119e+01 +diffusivity_OT_prefactor = '${units ${fparse 2.03 * 10 ^ diffusivity_OT_prefactor_exponent} m^2/s -> nm^2/s}' +diffusivity_OT_energy = '${units 8.65880079e+03 J/mol}' +diffusivity_V_O_prefactor_exponent = -5.33084375e+00 +diffusivity_V_O_prefactor = '${units ${fparse 1.1 * 10 ^ diffusivity_V_O_prefactor_exponent} m^2/s -> nm^2/s}' +diffusivity_V_O_energy = '${units 5.87658926e+04 J/mol}' +diffusivity_e_prefactor = '${units 2.06292148e-02 m^2/s -> nm^2/s}' # data from Yang 2026 +diffusivity_e_energy = '${units 9.53470966e+04 J/mol}' +# ELECTRON +electron_concentration_initial_expo = 4.94096686e-01 +electron_concentration_initial_energy = '${units 5.90846106e+04 J/mol}' +electron_concentration_initial = '${units ${fparse 10 ^ electron_concentration_initial_expo * N} at/nm^3}' + +# voltage +V_current = 2.0 # CONSTANT_VOLTAGE - no ${units} wrapper so CLI override works + +# target flux for error computation (overridden by parent via cli_args) +target_flux = 1e20 + +# --- MultiApp coupling: bridge parameters (sub-app side) --- +# The membrane active area scales the permeation flux [at/m^2/s] to a tritium mass flow [kg/s]. +# Sized so the membrane permeates ~the TES feed only at a meaningful (~Pa-scale) container pressure: +# a much larger area makes the voltage-driven membrane pump faster than the fuel cycle feeds it, so +# the container cannot pressurize. ~20 cm^2 is a realistic lab-membrane area. TUNING PARAMETER. +A_membrane = '${units 2.0e-3 m^2}' # membrane active area +M_T_atomic = '${units 3.016e-3 kg/mol}' # atomic tritium molar mass (each OT carries one T atom) + +[Mesh] + [cmg] + type = CartesianMeshGenerator + dim = 1 + dx = '${fparse length}' + ix = '${fparse num_nodes}' + subdomain_id = '0' + [] +[] + +[Variables] + #### Dry variable + [OT_concentration_dry] # (atoms/nm^3) + initial_condition = ${OT_concentration_initial} + [] + [Oxygen_vacancy_concentration_dry] + initial_condition = ${oxygen_vacancy_concentration_initial} + [] + # Temperature as nonlinear variable (promoted from AuxVariable for Joule heating coupling) + [temperature] + initial_condition = ${temperature_initial} + [] +[] + +[Bounds] + [concentration_dry_lower_bound] + type = ConstantBounds + variable = bounds_dummy + bounded_variable = OT_concentration_dry + bound_type = lower + bound_value = ${bound_value_min} + [] + [concentration_dry_V_O_lower_bound] + type = ConstantBounds + variable = bounds_dummy + bounded_variable = Oxygen_vacancy_concentration_dry + bound_type = lower + bound_value = ${bound_value_min} + [] + [concentration_dry_V_O_upper_bound] + type = ConstantBounds + variable = bounds_dummy + bounded_variable = Oxygen_vacancy_concentration_dry + bound_type = upper + bound_value = ${fparse 3 * N} + [] + [temperature_lower_bound] + type = ConstantBounds + variable = bounds_dummy + bounded_variable = temperature + bound_type = lower + bound_value = 300 + [] + [temperature_upper_bound] + type = ConstantBounds + variable = bounds_dummy + bounded_variable = temperature + bound_type = upper + bound_value = 2000 + [] +[] + +[AuxVariables] + [bounds_dummy] + order = FIRST + family = LAGRANGE + [] + #### Dry auxvariable + [pressure_T2_dry] + [] + [pressure_T2O_dry] + [] + [Oxygen_concentration_dry] + initial_condition = ${oxygen_concentration_initial} + [] + [electron_concentration_dry] + [] + + # CONSTANT_VOLTAGE + [voltage_phi] + [] +[] + + +[AuxKernels] + #### Dry auxkernels + [pressure_T2_dry_Aux] + type = FunctionAux + variable = pressure_T2_dry + function = Pressure_T2_dry_function + [] + [pressure_T2O_dry_Aux] + type = FunctionAux + variable = pressure_T2O_dry + function = Pressure_T2O_dry_function + [] + [Oxygen_concentration_dry_Aux] # at/nm^3 + type = ParsedAux + variable = Oxygen_concentration_dry + coupled_variables = 'Oxygen_vacancy_concentration_dry' + expression = '3 * ${N} - Oxygen_vacancy_concentration_dry' + [] + + # ELECTRON + [electron_concentration_dry_Aux] + type = ParsedAux + variable = electron_concentration_dry + coupled_variables = 'temperature' + expression = '${electron_concentration_initial} * 0.5 * exp(-${electron_concentration_initial_energy} / ${R} / temperature)' + execute_on = 'INITIAL TIMESTEP_END' + [] + + # CONSTANT_VOLTAGE + [phi_auxkernel] + type = FunctionAux + variable = voltage_phi + function = '${V_current} * (${length} - x) / ${length}' + execute_on = 'INITIAL TIMESTEP_END' + [] + +[] + +[Problem] + type = ReferenceResidualProblem + extra_tag_vectors = 'ref' + reference_vector = 'ref' +[] + +[Kernels] + #### Dry kernels + [time_OT_dry] + type = ADTimeDerivative + variable = OT_concentration_dry + extra_vector_tags = ref + [] + [diffusion_OT_dry] + type = ADMatDiffusion + variable = OT_concentration_dry + diffusivity = diffusivity_OT + extra_vector_tags = ref + [] + [time_V_O_dry] + type = ADTimeDerivative + variable = Oxygen_vacancy_concentration_dry + extra_vector_tags = ref + [] + [diffusion_V_O_dry] + type = ADMatDiffusion + variable = Oxygen_vacancy_concentration_dry + diffusivity = diffusivity_V_O + extra_vector_tags = ref + [] + # voltage for OH + [diffusion_phi_PCC_OH] + type = ADMatDiffusion + variable = OT_concentration_dry + v = voltage_phi + diffusivity = conductivity_OH + extra_vector_tags = ref + [] + # voltage for V_O + [diffusion_phi_PCC_V_O] + type = ADMatDiffusion + variable = Oxygen_vacancy_concentration_dry + v = voltage_phi + diffusivity = conductivity_V_O + extra_vector_tags = ref + [] + + # --- Heat equation --- + [heat_time] + type = ADHeatConductionTimeDerivative + variable = temperature + specific_heat = specific_heat_BCY20 + density_name = density_BCY20_thermal + extra_vector_tags = ref + [] + [heat_conduction] + type = ADHeatConduction + variable = temperature + thermal_conductivity = thermal_conductivity_BCY20 + extra_vector_tags = ref + [] + [joule_heating] + type = ADJouleHeatingSource + variable = temperature + heating_term = joule_heating_Q + extra_vector_tags = ref + [] +[] + +[BCs] + #### Dry BCs + [left_OT_dry] + type = ADMatNeumannBC + variable = OT_concentration_dry + boundary = left + value = 1 + boundary_material = flux_on_OT_dry + [] + [left_V_O_dry] + type = ADMatNeumannBC + variable = Oxygen_vacancy_concentration_dry + boundary = left + value = 1 + boundary_material = flux_on_V_O_dry + [] + [right_OT_dry] + type = ADMatNeumannBC + variable = OT_concentration_dry + boundary = right + value = 1 + boundary_material = flux_on_OT_dry + [] + [right_V_O_dry] + type = ADMatNeumannBC + variable = Oxygen_vacancy_concentration_dry + boundary = right + value = 1 + boundary_material = flux_on_V_O_dry + [] + + # Thermal BCs: fixed temperature at both surfaces (furnace-controlled) + [left_temperature] + type = ADDirichletBC + variable = temperature + boundary = left + value = ${temperature_initial} + [] + [right_temperature] + type = ADDirichletBC + variable = temperature + boundary = right + value = ${temperature_initial} + [] +[] + +[Functions] + [Pressure_T2_dry_function] + # P_up (upstream T2 partial pressure, Pa) is supplied by the parent via the received_pressure + # postprocessor. The time ramp of the standalone model is removed here: FullSolveMultiApp + # warm-starts the sub-app (keeps the solution between invocations) while resetting sub-time to 0, + # so a time ramp would re-impose a zero-pressure shock onto an already-equilibrated field and + # stall the solve. The pressure is therefore applied as a constant with the same spatial + # (upstream->permeate) profile and /pressure_atm normalization. + type = ParsedFunction + symbol_names = 'P_up' + symbol_values = 'received_pressure' + expression = '(P_up * (${length} - x) / ${length} + ${pressure_T2_low}) / ${pressure_atm}' + [] + [Pressure_T2O_dry_function] + type = ParsedFunction + expression = 'min(t / ${ramp_time}, 1.0) * (${pressure_T2O_constant}) / ${pressure_atm}' + [] +[] + +[Materials] + [diffusivity_OT] + type = ADParsedMaterial + property_name = 'diffusivity_OT' + coupled_variables = 'temperature' + expression = '${diffusivity_OT_prefactor} * exp(-${diffusivity_OT_energy} / ${R} / temperature)' + [] + [diffusivity_V_O] + type = ADParsedMaterial + property_name = 'diffusivity_V_O' + coupled_variables = 'temperature' + expression = '${diffusivity_V_O_prefactor} * exp(-${diffusivity_V_O_energy} / ${R} / temperature)' + [] + [diffusivity_e] + type = ADParsedMaterial + property_name = 'diffusivity_e' + coupled_variables = 'temperature' + expression = '${diffusivity_e_prefactor} * exp(-${diffusivity_e_energy} / ${R} / temperature)' + [] + [converter_to_nonAD] + type = MaterialADConverter + ad_props_in = 'diffusivity_OT diffusivity_V_O diffusivity_e conductivity_OH conductivity_e' + reg_props_out = 'diffusivity_OT_nonAD diffusivity_V_O_nonAD diffusivity_e_nonAD conductivity_OH_nonAD conductivity_e_nonAD' + outputs = 'none' + [] + [conductivity_OH] + type = ADParsedMaterial + property_name = 'conductivity_OH' + coupled_variables = 'OT_concentration_dry temperature' + material_property_names = 'diffusivity_OT' + expression = 'diffusivity_OT * ${F} * OT_concentration_dry / ${R} / temperature' + [] + [conductivity_V_O] + type = ADParsedMaterial + property_name = 'conductivity_V_O' + coupled_variables = 'Oxygen_vacancy_concentration_dry temperature' + material_property_names = 'diffusivity_V_O' + expression = '2 * diffusivity_V_O * ${F} * Oxygen_vacancy_concentration_dry / ${R} / temperature' + [] + [conductivity_e] + type = ADParsedMaterial + property_name = 'conductivity_e' + coupled_variables = 'electron_concentration_dry temperature' + material_property_names = 'diffusivity_e' + expression = '- diffusivity_e * ${F} * electron_concentration_dry / ${R} / temperature' + [] + [reaction_equilibrium_constant_T2] + type = ADParsedMaterial + property_name = 'T2_K_eq' + coupled_variables = 'temperature' + expression = 'exp( ( ${delta_H_T2} - temperature * ${delta_S_T2}) / ${R} / temperature )' + [] + [reaction_forward_T2] + type = ADParsedMaterial + property_name = 'T2_K_forward' + coupled_variables = 'temperature' + expression = '${T2_reaction_forward_value} * exp(-${T2_reaction_forward_energy} / ${R} / temperature)' + [] + [reaction_reverse_T2] + type = ADParsedMaterial + property_name = 'T2_K_reverse' + material_property_names = 'T2_K_forward T2_K_eq' + expression = 'T2_K_forward / T2_K_eq' + [] + + [reaction_equilibrium_constant_T2O] + type = ADParsedMaterial + property_name = 'T2O_K_eq' + coupled_variables = 'temperature' + expression = 'exp( ( ${delta_H_T2O} - temperature * ${delta_S_T2O}) / ${R} / temperature )' + [] + [reaction_forward_T2O] + type = ADParsedMaterial + property_name = 'T2O_K_forward' + coupled_variables = 'temperature' + expression = '${T2O_reaction_forward_value} * exp(-${T2O_reaction_forward_energy} / ${R} / temperature)' + [] + [reaction_reverse_T2O] + type = ADParsedMaterial + property_name = 'T2O_K_reverse' + material_property_names = 'T2O_K_forward T2O_K_eq' + expression = 'T2O_K_forward / T2O_K_eq' + [] + + #### Reaction for dry + [flux_base_on_T2_dry] # T2 + 2 O -> 2 OT + 2 e + type = ADDerivativeParsedMaterial + coupled_variables = 'OT_concentration_dry pressure_T2_dry Oxygen_vacancy_concentration_dry electron_concentration_dry' + property_name = 'flux_base_on_T2_dry' + material_property_names = 'T2_K_forward T2_K_reverse' + expression = '(T2_K_forward * pressure_T2_dry * (3 * ${N} - Oxygen_vacancy_concentration_dry)^2 - T2_K_reverse * OT_concentration_dry^2 * electron_concentration_dry^2)' + [] + [flux_base_on_T2O_dry] # T2O + V_O + O -> 2 OT + type = ADDerivativeParsedMaterial + coupled_variables = 'OT_concentration_dry pressure_T2O_dry Oxygen_vacancy_concentration_dry' + property_name = 'flux_base_on_T2O_dry' + material_property_names = 'T2O_K_forward T2O_K_reverse' + expression = '(T2O_K_forward * pressure_T2O_dry * (3 * ${N} - Oxygen_vacancy_concentration_dry) * Oxygen_vacancy_concentration_dry - T2O_K_reverse * OT_concentration_dry^2)' + [] + + + #### Flux for dry + [flux_on_e_dry] # electron + type = ADDerivativeParsedMaterial + property_name = 'flux_on_e_dry' + material_property_names = 'flux_base_on_T2_dry' + expression = '2 * flux_base_on_T2_dry' + [] + [flux_on_OT_dry] # OT + type = ADDerivativeParsedMaterial + property_name = 'flux_on_OT_dry' + material_property_names = 'flux_base_on_T2_dry flux_base_on_T2O_dry' + expression = '2 * flux_base_on_T2_dry + 2 * flux_base_on_T2O_dry' + [] + [flux_on_T2_dry] # T2 + type = ADDerivativeParsedMaterial + property_name = 'flux_on_T2_dry' + material_property_names = 'flux_base_on_T2_dry' + expression = '-1 * flux_base_on_T2_dry' + [] + [flux_on_V_O_dry] # V_O + type = ADDerivativeParsedMaterial + property_name = 'flux_on_V_O_dry' + material_property_names = 'flux_base_on_T2O_dry' + expression = '-1 * flux_base_on_T2O_dry' + [] + [flux_on_T2O_dry] # T2O + type = ADDerivativeParsedMaterial + property_name = 'flux_on_T2O_dry' + material_property_names = 'flux_base_on_T2O_dry' + expression = '-1 * flux_base_on_T2O_dry' + [] + + # --- Thermal material properties for BCY20 --- + [thermal_conductivity_mat] + type = ADGenericConstantMaterial + prop_names = 'thermal_conductivity_BCY20' + prop_values = '${thermal_conductivity_BCY20}' + [] + [specific_heat_mat] + type = ADGenericConstantMaterial + prop_names = 'specific_heat_BCY20' + prop_values = '${specific_heat_BCY20}' + [] + [density_thermal_mat] + type = ADGenericConstantMaterial + prop_names = 'density_BCY20_thermal' + prop_values = '${density_BCY20_thermal}' + [] + + # --- Joule heating --- + # Total ionic electrical conductivity from Nernst-Einstein relation (excluding electrons) + # sigma = q*F/(R*T) * (z_OH^2 * D_OT * c_OT + z_VO^2 * D_VO * c_VO) + # z_OH = 1, z_VO = 2, so z^2 = 1 and 4 + [total_electrical_conductivity] + type = ADParsedMaterial + property_name = 'sigma_total' + coupled_variables = 'OT_concentration_dry Oxygen_vacancy_concentration_dry temperature' + material_property_names = 'diffusivity_OT diffusivity_V_O' + expression = '${q} * ${F} / (${R} * temperature) * (diffusivity_OT * OT_concentration_dry + 4.0 * diffusivity_V_O * Oxygen_vacancy_concentration_dry)' + [] + # Joule heating volumetric source: Q = sigma_total * |grad(phi)|^2 + # |grad(phi)|^2 = (V_current / length)^2 = constant (voltage_phi is linear AuxVariable) + [joule_heating_material] + type = ADParsedMaterial + property_name = 'joule_heating_Q' + material_property_names = 'sigma_total' + expression = 'sigma_total * (${V_current} / ${length})^2' + [] +[] + +[Postprocessors] + #### Postprocessors for flux under dry + [recombination_flux_T2_dry_left] + type = ADSideAverageMaterialProperty + boundary = left + property = flux_on_T2_dry + execute_on = 'INITIAL TIMESTEP_END' + outputs = 'console csv' + [] + [recombination_flux_T2O_dry_left] + type = ADSideAverageMaterialProperty + boundary = left + property = flux_on_T2O_dry + execute_on = 'INITIAL TIMESTEP_END' + outputs = 'console csv' + [] + [recombination_flux_OT_dry_left] + type = ADSideAverageMaterialProperty + boundary = left + property = flux_on_OT_dry + execute_on = 'INITIAL TIMESTEP_END' + outputs = 'console csv' + [] + [recombination_flux_OT_dry_right] + type = ADSideAverageMaterialProperty + boundary = right + property = flux_on_OT_dry + execute_on = 'INITIAL TIMESTEP_END' + outputs = 'console csv' + [] + [recombination_flux_T2O_dry_right] + type = ADSideAverageMaterialProperty + boundary = right + property = flux_on_T2O_dry + execute_on = 'INITIAL TIMESTEP_END' + outputs = 'console csv' + [] + [recombination_flux_T2_dry_right] + type = ADSideAverageMaterialProperty + boundary = right + property = flux_on_T2_dry + execute_on = 'INITIAL TIMESTEP_END' + outputs = 'console csv' + [] + + # necessary parameters + [T2_K_eq_average] + type = ADElementAverageMaterialProperty + mat_prop = T2_K_eq + [] + [T2_K_forward_average] + type = ADElementAverageMaterialProperty + mat_prop = T2_K_forward + [] + [T2_K_reverse_average] + type = ADElementAverageMaterialProperty + mat_prop = T2_K_reverse + [] + [T2O_K_eq_average] + type = ADElementAverageMaterialProperty + mat_prop = T2O_K_eq + [] + [T2O_K_forward_average] + type = ADElementAverageMaterialProperty + mat_prop = T2O_K_forward + [] + [T2O_K_reverse_average] + type = ADElementAverageMaterialProperty + mat_prop = T2O_K_reverse + [] + [diffusivity_OT_average] + type = ADElementAverageMaterialProperty + mat_prop = diffusivity_OT + execute_on = 'INITIAL TIMESTEP_END' + [] + [diffusivity_V_O_average] + type = ADElementAverageMaterialProperty + mat_prop = diffusivity_V_O + execute_on = 'INITIAL TIMESTEP_END' + [] + [temperature_average] + type = ElementAverageValue + variable = temperature + execute_on = 'INITIAL TIMESTEP_END' + [] + [voltage_value] + type = ParsedPostprocessor + expression = ${V_current} + execute_on = 'INITIAL TIMESTEP_END' + [] + [pressure_T2_average] + type = ElementAverageValue + variable = pressure_T2_dry + execute_on = 'INITIAL TIMESTEP_END' + [] + [log_error_sq] + type = ParsedPostprocessor + pp_names = 'recombination_flux_OT_dry_right' + expression = '(log(abs(recombination_flux_OT_dry_right * 1e18)) - log(${target_flux}))^2' + execute_on = 'INITIAL TIMESTEP_END' + [] + [relative_error_sq] + type = ParsedPostprocessor + pp_names = 'recombination_flux_OT_dry_right' + expression = '(abs(recombination_flux_OT_dry_right * 1e18) - ${target_flux})^2' + execute_on = 'INITIAL TIMESTEP_END' + [] + + # --- MultiApp coupling postprocessors --- + [received_pressure] # upstream T2 partial pressure [Pa] received from the parent fuel-cycle model + type = Receiver + default = 0 # start uncharged, consistent with the parent container's 0 Pa initial condition + execute_on = 'INITIAL TIMESTEP_BEGIN TIMESTEP_END' + [] + [permeation_rate_kg_per_s] # tritium mass flow permeated to the downstream side [kg/s] + # The downstream-boundary OT flux is negative when tritium permeates OUT to the permeate side, + # so the forward permeation rate is max(-flux, 0): only net downstream transport is recovered. + # flux[at/nm^2/s] * 1e18 -> at/m^2/s ; * A_membrane[m^2] -> at/s ; * M_T_atomic/N_a -> kg/s + type = ParsedPostprocessor + pp_names = 'recombination_flux_OT_dry_right' + expression = 'max(-recombination_flux_OT_dry_right, 0) * 1e18 * ${A_membrane} * ${M_T_atomic} / ${N_a}' + execute_on = 'INITIAL TIMESTEP_END' + [] + + # Joule heating diagnostics + [temperature_max] + type = ElementExtremeValue + variable = temperature + value_type = max + execute_on = 'INITIAL TIMESTEP_END' + [] + [temperature_min] + type = ElementExtremeValue + variable = temperature + value_type = min + execute_on = 'INITIAL TIMESTEP_END' + [] + [delta_T] + type = ParsedPostprocessor + pp_names = 'temperature_max temperature_min' + expression = 'temperature_max - temperature_min' + execute_on = 'TIMESTEP_END' + [] +[] + +[Executioner] + type = Transient + scheme = implicit-euler + solve_type = NEWTON + petsc_options_iname = '-pc_type -snes_type' + petsc_options_value = 'lu vinewtonrsls' + nl_rel_tol = 5e-6 + # Absolute tolerance. When the membrane is warm-continued and sub-cycled by the lock-step + # TransientMultiApp, the bounded (vinewtonrsls) Newton residual occasionally stalls (~1e-5, + # scaled) at low container pressure; that emits a non-fatal "failed to converge" warning and the + # accepted solution is used. (This is why the full coupled run is a manual/heavy run, not a CI + # CSVDiff: the harness's --error flag would turn that warning fatal.) + nl_abs_tol = 1e-6 + # end_time is large; the parent (TransientMultiApp, lock-step) drives the actual stop time. No + # steady-state detection: the sub co-evolves with the fuel cycle and must not self-terminate. + end_time = ${endtime} + automatic_scaling = true + compute_scaling_once = true + line_search = none + error_on_dtmin = false + # Allow the sub to cut back dt and retry on a failed solve (rather than aborting) so it can + # robustly sub-cycle to the parent's time across the full range of container pressures. + abort_on_solve_fail = false + dtmin = 1e-10 + nl_max_its = 60 + dtmax = ${dt_max} + [TimeStepper] + type = IterationAdaptiveDT + dt = ${dt_start_charging} + optimal_iterations = 20 + growth_factor = 1.5 + cutback_factor = 0.5 + cutback_factor_at_failure = 0.5 + [] +[] + +[Debug] + show_var_residual_norms = true +[] + +[Outputs] + exodus = false + [csv] + type = CSV + [] +[] diff --git a/test/tests/PCC_multiscale_example/plot_dir_flux.py b/test/tests/PCC_multiscale_example/plot_dir_flux.py new file mode 100644 index 000000000..ed3f466bc --- /dev/null +++ b/test/tests/PCC_multiscale_example/plot_dir_flux.py @@ -0,0 +1,61 @@ +"""Tritium flux recovered to storage by each PCC DIR membrane (VP, FCU) vs time. + +``flux_to_storage_VP`` / ``flux_to_storage_FCU`` (from ``dir_pcc_fuel_cycle_out.csv``) are +the steady permeation rates [kg/s] the VP and FCU membrane sub-apps return to the storage +inventory each fuel-cycle step -- i.e. the tritium each DIR loop diverts directly back to +storage. Plotted log-log vs time (days), matching the figure style of the companion scripts. +""" + +import os + +import matplotlib.pyplot as plt +import pandas as pd + +plt.rcParams.update({"font.size": 18}) + +script_folder = os.path.dirname(os.path.abspath(__file__)) +if "/TMAP8/doc/" in script_folder: # documentation build + test_dir = "../../../../test/tests/PCC_multiscale_example" +else: # test folder + test_dir = script_folder +csv_candidates = [ + os.path.join(test_dir, "dir_pcc_fuel_cycle_out.csv"), + os.path.join(test_dir, "dir_pcc_fuel_cycle_2rt_10Pa_out.csv"), + os.path.join(test_dir, "gold", "dir_pcc_fuel_cycle_2rt_10Pa_out_reference.csv"), +] +dir_csv = next((candidate for candidate in csv_candidates if os.path.isfile(candidate)), None) +if dir_csv is None: + raise FileNotFoundError("Could not find a PCC DIR flux CSV in {}".format(csv_candidates)) +figures_dir = os.path.join(test_dir, "figures") +os.makedirs(figures_dir, exist_ok=True) + +time_unit = 3600 * 24 # seconds per day +pcc = pd.read_csv(dir_csv) +t = pcc["time"].values / time_unit + +fig, ax = plt.subplots(figsize=[6.5, 5.5]) +ax.plot( + t, pcc["flux_to_storage_VP"].values, "-", color="C0", label="VP DIR flux to storage" +) +ax.plot( + t, + pcc["flux_to_storage_FCU"].values, + "-", + color="C1", + label="FCU DIR flux to storage", +) + +ax.set_xlabel("Time (days)") +ax.set_ylabel("Flux to storage (kg/s)") +ax.set_xscale("log") +ax.set_yscale("log") +ax.set_xlim(left=0.1) +ax.set_ylim(bottom=1e-9) +ax.legend(loc="lower right", fontsize=16) +ax.grid(visible=True, which="major", color="0.65", linestyle="--", alpha=0.3) +ax.minorticks_on() + +fig_path = os.path.join(figures_dir, "dir_pcc_dir_flux.png") +plt.savefig(fig_path, bbox_inches="tight", dpi=300) +plt.close(fig) +print(f"Saved {fig_path}") diff --git a/test/tests/PCC_multiscale_example/plot_dir_fraction_pressure.py b/test/tests/PCC_multiscale_example/plot_dir_fraction_pressure.py new file mode 100644 index 000000000..55e2c24a1 --- /dev/null +++ b/test/tests/PCC_multiscale_example/plot_dir_fraction_pressure.py @@ -0,0 +1,133 @@ +"""DIR recovery fractions and upstream T2 pressures for the two PCC DIR membranes. + +Both quantities come from the multiscale result ``dir_pcc_fuel_cycle_2rt_10Pa_out2.csv``: + +- Left axis (blue) : upstream T2 partial pressure feeding each DIR membrane (VP, FCU) + [Pa], drawn at full resolution (VP solid, FCU dashed). +- Right axis (orange): the resulting DIR recovery fraction (flux_to_storage / DIR feed + flux) [-], linear 0-1. + +Quantities are colored by axis (pressure = blue/C0, DIR fraction = orange/C1) and the +axis labels/ticks/spines are colored to match. The result CSV holds tens of thousands of +rows, so the DIR-fraction curves are drawn at log-spaced sample points with open markers +(VP circles, FCU squares); otherwise the dashed lines merge into a solid block on the log +time axis. The pressure curves keep full resolution so the early per-pulse oscillation +envelope stays visible. A dotted horizontal line marks the baseline (fixed) VP DIR +fraction = 0.3 from ``fuel_cycle_2023/fuel_cycle_base.i`` (the base model has no separate +FCU DIR, i.e. 0). +""" + +import os + +import matplotlib.pyplot as plt +import numpy as np +import pandas as pd + +plt.rcParams.update({"font.size": 18}) + +script_folder = os.path.dirname(os.path.abspath(__file__)) +if "/TMAP8/doc/" in script_folder: # documentation build + test_dir = "../../../../test/tests/PCC_multiscale_example" +else: # test folder + test_dir = script_folder +csv_candidates = [ + os.path.join(test_dir, "dir_pcc_fuel_cycle_2rt_10Pa_out2.csv"), + os.path.join(test_dir, "gold", "dir_pcc_fuel_cycle_2rt_10Pa_out2_reference.csv"), +] +dir_csv = next((candidate for candidate in csv_candidates if os.path.isfile(candidate)), None) +if dir_csv is None: + raise FileNotFoundError( + "Could not find a PCC DIR pressure/fraction CSV in {}".format(csv_candidates) + ) +figures_dir = os.path.join(test_dir, "figures") +os.makedirs(figures_dir, exist_ok=True) + +time_unit = 3600 * 24 # seconds per day +baseline_dir_vp = 0.3 # fuel_cycle_base.i f_DIR (VP only; FCU baseline = 0) + +pcc = pd.read_csv(dir_csv) +t = pcc["time"].values / time_unit + +fig, ax = plt.subplots(figsize=[6.5, 5.5]) +ax2 = ax.twinx() + +# Left axis: upstream pressures (solid). Thin lines so the early per-pulse oscillation +# envelope (bang-bang transient before the coupling reaches steady state) stays legible. +sample_times = np.logspace(np.log10(0.1), np.log10(t.max()), 30000) +sample_idx = np.unique(np.searchsorted(t, sample_times).clip(0, len(t) - 1)) +ts = t[sample_idx] +(p_vp,) = ax.plot( + t, pcc["pressure_VP"].values, "-", color="C0", lw=1.5, alpha=0.6, label="VP pressure" +) +(p_fcu,) = ax.plot( + ts, pcc["pressure_FCU"].values[sample_idx], "--", color="C0", lw=1.5, label="FCU pressure" +) + +# Right axis: computed DIR fractions. Sample at log-spaced times so the dashed lines stay +# legible (the raw CSV has tens of thousands of rows, which renders as a solid block). +sample_times = np.logspace(np.log10(0.1), np.log10(t.max()), 1000) +sample_idx = np.unique(np.searchsorted(t, sample_times).clip(0, len(t) - 1)) +ts = t[sample_idx] +(f_vp,) = ax2.plot( + t, + pcc["DIR_fraction_VP"].values, + linestyle="-", + color="C1", + lw=1.5, + alpha=0.6, + label="VP DIR fraction", +) +(f_fcu,) = ax2.plot( + ts, + pcc["DIR_fraction_FCU"].values[sample_idx], + linestyle="--", + color="C1", + lw=1.5, + label="FCU DIR fraction", +) +base_line = ax2.axhline( + baseline_dir_vp, ls=":", color="C1", lw=3, label="baseline DIR" +) + +ax.set_xlabel("Time (days)") +# Left axis (pressure) in blue, right axis (DIR fraction) in orange. +ax.set_ylabel("Upstream T$_2$ pressure (Pa)", color="C0") +ax2.set_ylabel("DIR fraction (-)", color="C1") +ax.tick_params(axis="y", colors="C0") +ax2.tick_params(axis="y", colors="C1") +ax.spines["left"].set_color("C0") +ax.spines["right"].set_color("C1") +ax2.spines["left"].set_color("C0") +ax2.spines["right"].set_color("C1") +ax.set_xscale("log") +ax.set_xlim(left=0.1, right=1) +ax.set_ylim(bottom=-5, top=2e1) +ax.set_xticks([0.1, 1]) +# ax.set_xticklabels([r"10^{-1}", "10^0"]) +ax2.set_ylim(0, 1.05) +ax.xaxis.set_minor_formatter("") +# Scientific notation on the left (pressure) axis, with the 1e4 offset colored to match. +# ax.ticklabel_format(axis="y", style="sci", scilimits=(0, 0)) +ax.yaxis.get_offset_text().set_color("C0") +# Legend drawn on the twin (top) axes with a high z-order so its text/handles stay above +# every curve. The frame is transparent so the curves behind it remain visible. +# Matplotlib packs legend columns as contiguous slices with the extra entry in the FIRST +# column, so 5 handles give 3/2. Pad with an invisible spacer at the bottom of column 1 so +# the split becomes 2 (pressures) / 3 (DIR fractions). +blank = plt.Line2D([], [], linestyle="none", marker="", label=" ") +legend = ax2.legend( + handles=[p_vp, p_fcu, blank, f_fcu, f_vp, base_line], + loc="lower center", + bbox_to_anchor=(0.49, 0.03), + ncol=2, + fontsize=14, + framealpha=0.8, +) +legend.set_zorder(10) +ax.grid(visible=True, which="major", color="0.65", linestyle="--", alpha=0.3) +ax.minorticks_on() + +fig_path = os.path.join(figures_dir, "dir_pcc_dir_fraction_pressure.png") +plt.savefig(fig_path, bbox_inches="tight", dpi=300) +plt.close(fig) +print(f"Saved {fig_path}") diff --git a/test/tests/PCC_multiscale_example/plot_inventory_comparison.py b/test/tests/PCC_multiscale_example/plot_inventory_comparison.py new file mode 100644 index 000000000..0d3eae4f0 --- /dev/null +++ b/test/tests/PCC_multiscale_example/plot_inventory_comparison.py @@ -0,0 +1,188 @@ +"""Compare PCC-enhanced two-DIR fuel-cycle inventories with the Meschini baseline. + +Reads the multiscale result (``dir_pcc_fuel_cycle_out.csv``) and the baseline Meschini +fuel cycle and overlays the critical +component inventories (TES, VP, FCU, ISS, membrane, storage) on a log-log plot, matching +the style of ``fuel_cycle_2023/fuel_cycle_PCC_plot.py``. + +Baseline is drawn solid and PCC dashed with sparse open markers so near-overlapping +curves stay distinguishable, plus an inset that zooms into the late-time storage +divergence. The storage curve is shifted so its minimum sits at the required reserve +(minimum allowed) inventory: + storage_plot = T_10_storage - min(T_10_storage) + reserve_inventory +(the same transform used in ``fuel_cycle_PCC_plot.py``). +""" + +import io +import os +import time + +import matplotlib.pyplot as plt +import numpy as np +import pandas as pd +from matplotlib import gridspec + +plt.rcParams.update({"font.size": 18}) + +# Resolve paths relative to this script (scripts/ lives one level below the test dir) +script_folder = os.path.dirname(os.path.abspath(__file__)) +if "/TMAP8/doc/" in script_folder: # documentation build + test_dir = "../../../../test/tests/PCC_multiscale_example" +else: # test folder + test_dir = script_folder +pcc_candidates = [ + os.path.join(test_dir, "dir_pcc_fuel_cycle_2rt_10Pa_out.csv"), + os.path.join(test_dir, "gold", "dir_pcc_fuel_cycle_2rt_10Pa_out_reference.csv"), +] +base_candidates = [ + os.path.join(test_dir, "gold", "fuel_cycle_base_out_reference.csv"), + os.path.join(test_dir, "..", "fuel_cycle_2023", "fuel_cycle_base_out.csv"), +] +dir_csv = next((candidate for candidate in pcc_candidates if os.path.isfile(candidate)), None) +base_csv = next((candidate for candidate in base_candidates if os.path.isfile(candidate)), None) +if dir_csv is None: + raise FileNotFoundError( + "Could not find a PCC-enhanced fuel-cycle CSV in {}".format(pcc_candidates) + ) +if base_csv is None: + raise FileNotFoundError( + "Could not find a baseline fuel-cycle CSV in {}".format(base_candidates) + ) +figures_dir = os.path.join(test_dir, "figures") +os.makedirs(figures_dir, exist_ok=True) + +time_unit = 3600 * 24 # seconds per day +two_year = 3600 * 24 * 365 * 2 # s + + +def interpolation_on_expected_input(data_x, data_y, expected_input): + """Linearly interpolate ``data_y`` at ``expected_input`` along ``data_x``.""" + left_limit = np.argwhere(np.diff(data_x < expected_input))[0][0] + right_limit = left_limit + 1 + return (expected_input - data_x[left_limit]) / ( + data_x[right_limit] - data_x[left_limit] + ) * (data_y[right_limit] - data_y[left_limit]) + data_y[left_limit] + + +def read_csv_live(path, retries=5, delay=0.5): + """Read a CSV that may be concurrently written by a running MOOSE simulation. + + MOOSE appends rows and flushes/closes the file each output step, so the only + inconsistency a reader can catch is an incomplete trailing line. Read a snapshot, + drop a trailing line that is truncated (file does not end in a newline) or has the + wrong column count, and retry briefly if the file is missing or has no complete + data row yet. + """ + last_err = None + for _ in range(retries): + if os.path.isfile(path): + with open(path, "r") as f: + text = f.read() + lines = text.splitlines() + if len(lines) >= 2: + ncol = len(lines[0].split(",")) + if not text.endswith("\n") or len(lines[-1].split(",")) != ncol: + lines = lines[:-1] # drop incomplete trailing row + if len(lines) >= 2: # header + >=1 complete data row + try: + return pd.read_csv(io.StringIO("\n".join(lines) + "\n")) + except Exception as e: # rare parse race + last_err = e + time.sleep(delay) + raise RuntimeError( + f"Could not read a complete data row from {path} after {retries} attempts: {last_err}" + ) + + +# Required reserve (minimum allowed) storage inventory, kg +tritium_burn_rate = 8.99e-7 # kg/s +TBE = 0.02 +q = 0.25 +t_res = 24 * 3600 # s +AF = 0.7 +reserve_inventory = tritium_burn_rate / TBE * q * t_res * AF +print(f"Required reserve inventory = {round(reserve_inventory, 3)} kg") + +base = pd.read_csv(base_csv) +pcc = read_csv_live(dir_csv) + +# initial inventories differ between the two models +init_base = base["T_10_storage"].values[0] +init_pcc = pcc["T_10_storage"].values[0] + + +def storage_refined(df): + """Shift the storage so its minimum sits at the reserve (minimum allowed).""" + s = df["T_10_storage"].values + return s - np.min(s) + reserve_inventory + + +# Diagnostics on the RAW storage inventory (the plotted storage is the shifted curve) +for name, df, init in [("Baseline", base, init_base), ("PCC", pcc, init_pcc)]: + t_days = df["time"].values / time_unit + s = df["T_10_storage"].values + imin = int(np.argmin(s)) + print( + f"{name}: storage min = {round(s[imin], 3)} kg at {round(t_days[imin], 3)} days" + ) + try: + end_inv = interpolation_on_expected_input(t_days, s, two_year / time_unit) + print( + f"{name}: end (2 yr) inventory = {round(end_inv, 3)} kg " + f"({round(end_inv / init, 2)} I_startup)" + ) + except IndexError: + print(f"{name}: end (2 yr) inventory = not reached within the simulation") + try: + doubling = interpolation_on_expected_input(s, t_days, init * 2) + print(f"{name}: doubling time = {round(doubling, 3)} days") + except IndexError: + print(f"{name}: doubling time = not reached within the simulation") + +# Critical components: (column, label, color) +components = [ + ("T_10_storage", "Storage", "C5"), + ("T_09_ISS", "ISS", "C3"), + ("T_02_TES", "TES", "C0"), + ("T_07_vacuum", "VP", "C1"), + ("T_08_FCU", "FCU", "C2"), + ("T_11_membrane", "Membrane", "C4"), +] + +t_base = base["time"].values / time_unit +t_pcc = pcc["time"].values / time_unit + +fig = plt.figure(figsize=[6.5, 5.5]) +gs = gridspec.GridSpec(1, 1) +ax = fig.add_subplot(gs[0]) + +# Style legend (baseline = transparent line, PCC = solid line) +(hand_base,) = ax.plot([], [], '--', color="k", lw=2, alpha=0.35, label="baseline") +(hand_pcc,) = ax.plot([], [], color="k", lw=2, label="PCC") + +component_handles = [] +for col, label, color in components: + y_base = storage_refined(base) if col == "T_10_storage" else base[col].values + y_pcc = storage_refined(pcc) if col == "T_10_storage" else pcc[col].values + # Baseline drawn as a transparent line; PCC drawn as a solid opaque line on top, so the + # PCC result stands out against the faded baseline without dashes or markers. + ax.plot(t_base, y_base, "--", color=color, lw=1.5, alpha=0.35) + (curve,) = ax.plot(t_pcc, y_pcc, "-", color=color, lw=1.8, label=label) + component_handles.append(curve) + +ax.set_xlabel("Time (days)") +ax.set_ylabel("Tritium Inventory (kg)") +legend1 = ax.legend(handles=[hand_base, hand_pcc], loc="upper left", fontsize=16) +ax.add_artist(legend1) +ax.legend(handles=component_handles, loc="lower right", ncols=2, fontsize=16) +ax.set_xlim(left=0.1, right=650) +ax.set_ylim(1e-8, 1e2) +plt.xscale("log") +plt.yscale("log") +plt.grid(visible=True, which="major", color="0.65", linestyle="--", alpha=0.3) +ax.minorticks_on() + +fig_path = os.path.join(figures_dir, "dir_pcc_inventory_comparison.png") +plt.savefig(fig_path, bbox_inches="tight", dpi=300) +plt.close(fig) +print(f"Saved {fig_path}") diff --git a/test/tests/PCC_multiscale_example/split_membrane_steps.py b/test/tests/PCC_multiscale_example/split_membrane_steps.py new file mode 100644 index 000000000..19139c78e --- /dev/null +++ b/test/tests/PCC_multiscale_example/split_membrane_steps.py @@ -0,0 +1,87 @@ +#!/usr/bin/env python3 +"""Split the accumulated membrane sub-app CSV into one CSV per fuel-cycle timestep. + +The steady coupling runs the 1D membrane sub-app once per fuel-cycle timestep with +``keep_full_output_history = true``, so every step's membrane solve is appended into a single file +``membrane_steps/pcc_membrane_step.csv``. MOOSE cannot natively write a separate CSV per parent +timestep, so this post-processing script divides that accumulated file into per-step files. + +Each FullSolveMultiApp invocation restarts the sub-app from its internal time ~0, so a *decrease* in +the sub-app ``time`` column marks the boundary between fuel-cycle steps. Each segment (one +invocation) is written to its own file, named by step index and the fuel-cycle time taken from the +parent output ``steady_fuel_cycle_PCC_membrane_out.csv``. +""" + +import glob +import os + +import numpy as np +import pandas as pd + +# Resolve paths for both the test tree and the documentation build. +script_folder = os.path.dirname(os.path.abspath(__file__)) +if "/TMAP8/doc/" in script_folder: + path = "../../../../test/tests/PCC_multiscale_example" +else: + path = script_folder + +membrane_dir = os.path.join(path, "membrane_steps") +accumulated_csv = os.path.join(membrane_dir, "pcc_membrane_step.csv") +parent_csv = os.path.join(path, "steady_fuel_cycle_PCC_membrane_out.csv") + +if not os.path.isfile(accumulated_csv): + raise FileNotFoundError( + "Accumulated membrane CSV not found: {}. Run the coupled simulation first.".format( + accumulated_csv + ) + ) + +membrane = pd.read_csv(accumulated_csv) + +# Segment the accumulated file at each sub-app time reset (start of a new fuel-cycle step). +time = membrane["time"].to_numpy() +boundaries = [0] + list(np.where(np.diff(time) < 0.0)[0] + 1) + [len(membrane)] +segments = [membrane.iloc[boundaries[i]:boundaries[i + 1]] for i in range(len(boundaries) - 1)] +n_steps = len(segments) + +# Fuel-cycle time for each step, from the parent output (one solve per step; single-pass coupling). +fuel_cycle_times = None +if os.path.isfile(parent_csv): + parent = pd.read_csv(parent_csv) + ptimes = parent["time"].to_numpy() + if len(ptimes) == n_steps + 1: # parent has an extra t=0 (initial) row + fuel_cycle_times = ptimes[1:] + elif len(ptimes) >= n_steps: + fuel_cycle_times = ptimes[-n_steps:] # align the trailing N, warn below + if len(ptimes) != n_steps: + print( + "Note: parent has {} rows for {} membrane steps; aligned the trailing {}.".format( + len(ptimes), n_steps, n_steps + ) + ) +if fuel_cycle_times is None: + print("Note: parent output not found/aligned; naming per-step files by index only.") + fuel_cycle_times = [np.nan] * n_steps + +# Remove any previous per-step files so reruns start clean. +for old in glob.glob(os.path.join(membrane_dir, "step_*.csv")): + os.remove(old) + +for k, segment in enumerate(segments): + t_fc = fuel_cycle_times[k] + if np.isfinite(t_fc): + fname = "step_{:04d}_t{:.4g}.csv".format(k + 1, t_fc) + else: + fname = "step_{:04d}.csv".format(k + 1) + segment.to_csv(os.path.join(membrane_dir, fname), index=False) + +print( + "Split {} into {} per-step files in {}/ (e.g. {}).".format( + os.path.basename(accumulated_csv), + n_steps, + membrane_dir, + "step_0001_t{:.4g}.csv".format(fuel_cycle_times[0]) + if n_steps and np.isfinite(fuel_cycle_times[0]) + else "step_0001.csv", + ) +) diff --git a/test/tests/PCC_multiscale_example/steady_pcc_membrane_sub.i b/test/tests/PCC_multiscale_example/steady_pcc_membrane_sub.i new file mode 100644 index 000000000..399c40040 --- /dev/null +++ b/test/tests/PCC_multiscale_example/steady_pcc_membrane_sub.i @@ -0,0 +1,715 @@ +# Sub-app (component level) for the PCC membrane <-> fuel-cycle MultiApp coupling. +# Derived from tritium_transport_PCC/jouleheating_Voltage_BCY_real_LEE2005.i. +# Real (H2+H2O) BCY proton-conducting-ceramic membrane with applied voltage and Joule heating. +# Temperature is a nonlinear Variable coupled to the Joule heating source. +# +# Unit system: the membrane model uses nm for length, Pa for gas pressure, at/nm^3 for +# concentrations, at/nm^2/s for surface fluxes, and kg/s for transferred tritium flow. +# +# Coupling interface: +# IN (from parent): received_pressure -- upstream T2 partial pressure [Pa] set from the +# fuel-cycle membrane feed-plenum holdup (T_11_membrane) via ideal gas. +# OUT (to parent): permeation_rate_kg_per_s -- tritium mass flow permeated to the downstream +# side [kg/s], obtained from the steady permeation flux at the right boundary. +# The sub-app is run to (pseudo-)steady state each parent timestep (see steady_state_detection). + +# Physical constants +R = '${units 8.31446261815324 J/mol/K}' # ideal gas constant based on number used in include/utils/PhysicalConstants.h +N_a = '${units 6.02214076e23 at/mol}' # ideal gas constant based on number used in include/utils/PhysicalConstants.h +q = '${units 1.602176634e-19 C}' # quantity of charge +F = '${fparse N_a * q}' + +# Thermal properties of BCY20 +# thermal conductivity: 1.05 W/(m*K) for dense BaCeO3 +# Ref: Tenevich et al. 2023, Ceramics International, Vol. 49, 31087-31095 +thermal_conductivity_BCY20 = '${units 1.05 W/m/K -> W/nm/K}' + +# thermal parameters +temperature_initial = '${units 773 K}' # 500C + +# Model parameters +endtime = '140' +dt_max = '2e0' +dt_start_charging = '${units 1e-5 s}' +bound_value_min = '${units -1e-20 at/nm^3}' + +# Geometry and mesh +length = '${units 10 mum -> nm}' # BCY20 +num_nodes = 300 + +# Material properties +density_BCY20 = '${units ${fparse 1.0 * 6.154} g/cm^3 -> g/m^3}' +molar_mass_BCY20 = '${units 283.42 g/mol}' +N = '${units ${fparse density_BCY20 / molar_mass_BCY20 * N_a} at/m^3 -> at/nm^3}' +# density in g/nm^3 for pairing with specific_heat in J/(g*K) +density_BCY20_thermal = '${fparse density_BCY20 * 1e-27}' # g/m^3 -> g/nm^3 +# specific heat: ~120 J/(mol*K) for BaCeO3 at high temperature +# Ref: Yamanaka et al. 2003, J. Alloys and Compounds, Vol. 359, 109-113 +specific_heat_BCY20_molar = '${units 120 J/mol/K}' +specific_heat_BCY20 = '${fparse specific_heat_BCY20_molar / molar_mass_BCY20}' # 120/283.42 = 0.4233 J/(g*K) + +# Initial concentrations +OT_concentration_initial = 1e-5 +hydration_limit_S = 0.2 +oxygen_vacancy_concentration_initial = '${units ${fparse hydration_limit_S / 2 * N} at/nm^3}' +oxygen_concentration_initial = '${units ${fparse 3 * N - oxygen_vacancy_concentration_initial - OT_concentration_initial} at/nm^3}' + +##### Dry Pressure conditions +pressure_atm = '${units 101315 Pa}' +pressure_T2_low = '${units 0 Pa}' # downstream (permeate) T2 partial pressure +pressure_T2_high = '${units ${fparse 5 / 101315 * pressure_atm} Pa}' # default standalone upstream T2 pressure +# In the fuel-cycle coupling the membrane separates tritium (T2): permeation must be driven only by +# the tritium partial pressure supplied by the parent. The independent water (T2O) source of the +# "real" model is therefore disabled (set to 0) so it does not inject a tritium-independent, +# voltage-pumped baseline flux. Set non-zero only for standalone wet-gas studies. +pressure_T2O_constant = '${units 0 Pa}' + +# chemical_reaction — n20_faster optimized parameters (71 steps) +delta_H_T2O = '${units -1.54415211e+05 J/mol}' +delta_S_T2O = '${units -1.67187585e+02 J/mol/K}' +delta_H_T2 = '${units -5.46037663e+04 J/mol}' +delta_S_T2 = '${units -3.36929406e+01 J/mol/K}' +T2O_reaction_forward_mol_exponent = -1.19792592e+01 +ramp_time = 1 +T2O_reaction_forward_mol = '${units ${fparse 8.0 * 10 ^ T2O_reaction_forward_mol_exponent} m^4/mol/s}' +T2O_reaction_forward_value = '${units ${fparse T2O_reaction_forward_mol / N_a} m^4/at/s -> nm^4/at/s}' +T2O_reaction_forward_energy = '${units -7.31595474e+03 J/mol}' +T2_reaction_forward_mol_exponent = -4.05998297e+00 +T2_reaction_forward_mol = '${units ${fparse 8.0 * 10 ^ T2_reaction_forward_mol_exponent} m^4/mol/s}' +T2_reaction_forward_value = '${units ${fparse T2_reaction_forward_mol / N_a} m^4/at/s -> nm^4/at/s}' +T2_reaction_forward_energy = '${units 5.13385478e+03 J/mol}' +diffusivity_OT_prefactor_exponent = -1.26000119e+01 +diffusivity_OT_prefactor = '${units ${fparse 2.03 * 10 ^ diffusivity_OT_prefactor_exponent} m^2/s -> nm^2/s}' +diffusivity_OT_energy = '${units 8.65880079e+03 J/mol}' +diffusivity_V_O_prefactor_exponent = -5.33084375e+00 +diffusivity_V_O_prefactor = '${units ${fparse 1.1 * 10 ^ diffusivity_V_O_prefactor_exponent} m^2/s -> nm^2/s}' +diffusivity_V_O_energy = '${units 5.87658926e+04 J/mol}' +diffusivity_e_prefactor = '${units 2.06292148e-02 m^2/s -> nm^2/s}' # data from Yang 2026 +diffusivity_e_energy = '${units 9.53470966e+04 J/mol}' +# ELECTRON +electron_concentration_initial_expo = 4.94096686e-01 +electron_concentration_initial_energy = '${units 5.90846106e+04 J/mol}' +electron_concentration_initial = '${units ${fparse 10 ^ electron_concentration_initial_expo * N} at/nm^3}' + +# voltage +V_current = 2.0 # CONSTANT_VOLTAGE - no ${units} wrapper so CLI override works + +# --- MultiApp coupling: feed-plenum bridge parameters (sub-app side) --- +# The membrane active area scales the permeation flux [at/m^2/s] to a tritium mass flow [kg/s]. +# A_membrane must be physically paired with the parent feed-plenum volume V_feed: together they +# set the coupling gain. Documented placeholder; calibrate against a target membrane inventory. +# A_membrane is calibrated so the steady operating pressure sits in the well-behaved 10-80 kPa +# range given the fuel-cycle TES feed (~7e-7 kg/s). ~20 cm^2 is a realistic lab-membrane area. +A_membrane = '${units 2e-2 m^2}' # 2.0e-3 membrane active area (TUNING PARAMETER; pair with V_feed) +M_T_atomic = '${units 3.016e-3 kg/mol}' # atomic tritium molar mass (each OT carries one T atom) + +[Mesh] + [cmg] + type = CartesianMeshGenerator + dim = 1 + dx = '${fparse length}' + ix = '${fparse num_nodes}' + subdomain_id = '0' + [] +[] + +[Variables] + #### Dry variable + [OT_concentration_dry] # (atoms/nm^3) + initial_condition = ${OT_concentration_initial} + [] + [Oxygen_vacancy_concentration_dry] + initial_condition = ${oxygen_vacancy_concentration_initial} + [] + # Temperature as nonlinear variable (promoted from AuxVariable for Joule heating coupling) + [temperature] + initial_condition = ${temperature_initial} + [] +[] + +[Bounds] + [concentration_dry_lower_bound] + type = ConstantBounds + variable = bounds_dummy + bounded_variable = OT_concentration_dry + bound_type = lower + bound_value = ${bound_value_min} + [] + [concentration_dry_V_O_lower_bound] + type = ConstantBounds + variable = bounds_dummy + bounded_variable = Oxygen_vacancy_concentration_dry + bound_type = lower + bound_value = ${bound_value_min} + [] + [concentration_dry_V_O_upper_bound] + type = ConstantBounds + variable = bounds_dummy + bounded_variable = Oxygen_vacancy_concentration_dry + bound_type = upper + bound_value = ${fparse 3 * N} + [] + [temperature_lower_bound] + type = ConstantBounds + variable = bounds_dummy + bounded_variable = temperature + bound_type = lower + bound_value = 300 + [] + [temperature_upper_bound] + type = ConstantBounds + variable = bounds_dummy + bounded_variable = temperature + bound_type = upper + bound_value = 2000 + [] +[] + +[AuxVariables] + [bounds_dummy] + order = FIRST + family = LAGRANGE + [] + #### Dry auxvariable + [pressure_T2_dry] + [] + [pressure_T2O_dry] + [] + [Oxygen_concentration_dry] + initial_condition = ${oxygen_concentration_initial} + [] + [electron_concentration_dry] + [] + + # CONSTANT_VOLTAGE + [voltage_phi] + [] +[] + + +[AuxKernels] + #### Dry auxkernels + [pressure_T2_dry_Aux] + type = FunctionAux + variable = pressure_T2_dry + function = Pressure_T2_dry_function + [] + [pressure_T2O_dry_Aux] + type = FunctionAux + variable = pressure_T2O_dry + function = Pressure_T2O_dry_function + [] + [Oxygen_concentration_dry_Aux] # at/nm^3 + type = ParsedAux + variable = Oxygen_concentration_dry + coupled_variables = 'Oxygen_vacancy_concentration_dry' + expression = '3 * ${N} - Oxygen_vacancy_concentration_dry' + [] + + # ELECTRON + [electron_concentration_dry_Aux] + type = ParsedAux + variable = electron_concentration_dry + coupled_variables = 'temperature' + expression = '${electron_concentration_initial} * 0.5 * exp(-${electron_concentration_initial_energy} / ${R} / temperature)' + execute_on = 'INITIAL TIMESTEP_END' + [] + + # CONSTANT_VOLTAGE + [phi_auxkernel] + type = FunctionAux + variable = voltage_phi + function = '${V_current} * (${length} - x) / ${length}' + execute_on = 'INITIAL TIMESTEP_END' + [] + +[] + +[Problem] + type = ReferenceResidualProblem + extra_tag_vectors = 'ref' + reference_vector = 'ref' +[] + +[Kernels] + #### Dry kernels + [time_OT_dry] + type = ADTimeDerivative + variable = OT_concentration_dry + extra_vector_tags = ref + [] + [diffusion_OT_dry] + type = ADMatDiffusion + variable = OT_concentration_dry + diffusivity = diffusivity_OT + extra_vector_tags = ref + [] + [time_V_O_dry] + type = ADTimeDerivative + variable = Oxygen_vacancy_concentration_dry + extra_vector_tags = ref + [] + [diffusion_V_O_dry] + type = ADMatDiffusion + variable = Oxygen_vacancy_concentration_dry + diffusivity = diffusivity_V_O + extra_vector_tags = ref + [] + # voltage for OH + [diffusion_phi_PCC_OH] + type = ADMatDiffusion + variable = OT_concentration_dry + v = voltage_phi + diffusivity = conductivity_OH + extra_vector_tags = ref + [] + # voltage for V_O + [diffusion_phi_PCC_V_O] + type = ADMatDiffusion + variable = Oxygen_vacancy_concentration_dry + v = voltage_phi + diffusivity = conductivity_V_O + extra_vector_tags = ref + [] + + # --- Heat equation --- + [heat_time] + type = ADHeatConductionTimeDerivative + variable = temperature + specific_heat = specific_heat_BCY20 + density_name = density_BCY20_thermal + extra_vector_tags = ref + [] + [heat_conduction] + type = ADHeatConduction + variable = temperature + thermal_conductivity = thermal_conductivity_BCY20 + extra_vector_tags = ref + [] + [joule_heating] + type = ADJouleHeatingSource + variable = temperature + heating_term = joule_heating_Q + extra_vector_tags = ref + [] +[] + +[BCs] + #### Dry BCs + [left_OT_dry] + type = ADMatNeumannBC + variable = OT_concentration_dry + boundary = left + value = 1 + boundary_material = flux_on_OT_dry + [] + [left_V_O_dry] + type = ADMatNeumannBC + variable = Oxygen_vacancy_concentration_dry + boundary = left + value = 1 + boundary_material = flux_on_V_O_dry + [] + [right_OT_dry] + type = ADMatNeumannBC + variable = OT_concentration_dry + boundary = right + value = 1 + boundary_material = flux_on_OT_dry + [] + [right_V_O_dry] + type = ADMatNeumannBC + variable = Oxygen_vacancy_concentration_dry + boundary = right + value = 1 + boundary_material = flux_on_V_O_dry + [] + + # Thermal BCs: fixed temperature at both surfaces (furnace-controlled) + [left_temperature] + type = ADDirichletBC + variable = temperature + boundary = left + value = ${temperature_initial} + [] + [right_temperature] + type = ADDirichletBC + variable = temperature + boundary = right + value = ${temperature_initial} + [] +[] + +[Functions] + [Pressure_T2_dry_function] + # P_up (upstream T2 partial pressure, Pa) is supplied by the parent via the received_pressure + # postprocessor. The time ramp of the standalone model is removed here: FullSolveMultiApp + # warm-starts the sub-app (keeps the solution between invocations) while resetting sub-time to 0, + # so a time ramp would re-impose a zero-pressure shock onto an already-equilibrated field and + # stall the solve. The pressure is therefore applied as a constant with the same spatial + # (upstream->permeate) profile and /pressure_atm normalization. + type = ParsedFunction + symbol_names = 'P_up' + symbol_values = 'received_pressure' + expression = '(P_up * (${length} - x) / ${length} + ${pressure_T2_low}) / ${pressure_atm}' + [] + [Pressure_T2O_dry_function] + type = ParsedFunction + expression = 'min(t / ${ramp_time}, 1.0) * (${pressure_T2O_constant}) / ${pressure_atm}' + [] +[] + +[Materials] + [diffusivity_OT] + type = ADParsedMaterial + property_name = 'diffusivity_OT' + coupled_variables = 'temperature' + expression = '${diffusivity_OT_prefactor} * exp(-${diffusivity_OT_energy} / ${R} / temperature)' + [] + [diffusivity_V_O] + type = ADParsedMaterial + property_name = 'diffusivity_V_O' + coupled_variables = 'temperature' + expression = '${diffusivity_V_O_prefactor} * exp(-${diffusivity_V_O_energy} / ${R} / temperature)' + [] + [diffusivity_e] + type = ADParsedMaterial + property_name = 'diffusivity_e' + coupled_variables = 'temperature' + expression = '${diffusivity_e_prefactor} * exp(-${diffusivity_e_energy} / ${R} / temperature)' + [] + [converter_to_nonAD] + type = MaterialADConverter + ad_props_in = 'diffusivity_OT diffusivity_V_O diffusivity_e conductivity_OH conductivity_e' + reg_props_out = 'diffusivity_OT_nonAD diffusivity_V_O_nonAD diffusivity_e_nonAD conductivity_OH_nonAD conductivity_e_nonAD' + outputs = 'none' + [] + [conductivity_OH] + type = ADParsedMaterial + property_name = 'conductivity_OH' + coupled_variables = 'OT_concentration_dry temperature' + material_property_names = 'diffusivity_OT' + expression = 'diffusivity_OT * ${F} * OT_concentration_dry / ${R} / temperature' + [] + [conductivity_V_O] + type = ADParsedMaterial + property_name = 'conductivity_V_O' + coupled_variables = 'Oxygen_vacancy_concentration_dry temperature' + material_property_names = 'diffusivity_V_O' + expression = '2 * diffusivity_V_O * ${F} * Oxygen_vacancy_concentration_dry / ${R} / temperature' + [] + [conductivity_e] + type = ADParsedMaterial + property_name = 'conductivity_e' + coupled_variables = 'electron_concentration_dry temperature' + material_property_names = 'diffusivity_e' + expression = '- diffusivity_e * ${F} * electron_concentration_dry / ${R} / temperature' + [] + [reaction_equilibrium_constant_T2] + type = ADParsedMaterial + property_name = 'T2_K_eq' + coupled_variables = 'temperature' + expression = 'exp( ( ${delta_H_T2} - temperature * ${delta_S_T2}) / ${R} / temperature )' + [] + [reaction_forward_T2] + type = ADParsedMaterial + property_name = 'T2_K_forward' + coupled_variables = 'temperature' + expression = '${T2_reaction_forward_value} * exp(-${T2_reaction_forward_energy} / ${R} / temperature)' + [] + [reaction_reverse_T2] + type = ADParsedMaterial + property_name = 'T2_K_reverse' + material_property_names = 'T2_K_forward T2_K_eq' + expression = 'T2_K_forward / T2_K_eq' + [] + + [reaction_equilibrium_constant_T2O] + type = ADParsedMaterial + property_name = 'T2O_K_eq' + coupled_variables = 'temperature' + expression = 'exp( ( ${delta_H_T2O} - temperature * ${delta_S_T2O}) / ${R} / temperature )' + [] + [reaction_forward_T2O] + type = ADParsedMaterial + property_name = 'T2O_K_forward' + coupled_variables = 'temperature' + expression = '${T2O_reaction_forward_value} * exp(-${T2O_reaction_forward_energy} / ${R} / temperature)' + [] + [reaction_reverse_T2O] + type = ADParsedMaterial + property_name = 'T2O_K_reverse' + material_property_names = 'T2O_K_forward T2O_K_eq' + expression = 'T2O_K_forward / T2O_K_eq' + [] + + #### Reaction for dry + [flux_base_on_T2_dry] # T2 + 2 O -> 2 OT + 2 e + type = ADDerivativeParsedMaterial + coupled_variables = 'OT_concentration_dry pressure_T2_dry Oxygen_vacancy_concentration_dry electron_concentration_dry' + property_name = 'flux_base_on_T2_dry' + material_property_names = 'T2_K_forward T2_K_reverse' + expression = '(T2_K_forward * pressure_T2_dry * (3 * ${N} - Oxygen_vacancy_concentration_dry)^2 - T2_K_reverse * OT_concentration_dry^2 * electron_concentration_dry^2)' + [] + [flux_base_on_T2O_dry] # T2O + V_O + O -> 2 OT + type = ADDerivativeParsedMaterial + coupled_variables = 'OT_concentration_dry pressure_T2O_dry Oxygen_vacancy_concentration_dry' + property_name = 'flux_base_on_T2O_dry' + material_property_names = 'T2O_K_forward T2O_K_reverse' + expression = '(T2O_K_forward * pressure_T2O_dry * (3 * ${N} - Oxygen_vacancy_concentration_dry) * Oxygen_vacancy_concentration_dry - T2O_K_reverse * OT_concentration_dry^2)' + [] + + + #### Flux for dry + [flux_on_e_dry] # electron + type = ADDerivativeParsedMaterial + property_name = 'flux_on_e_dry' + material_property_names = 'flux_base_on_T2_dry' + expression = '2 * flux_base_on_T2_dry' + [] + [flux_on_OT_dry] # OT + type = ADDerivativeParsedMaterial + property_name = 'flux_on_OT_dry' + material_property_names = 'flux_base_on_T2_dry flux_base_on_T2O_dry' + expression = '2 * flux_base_on_T2_dry + 2 * flux_base_on_T2O_dry' + [] + [flux_on_T2_dry] # T2 + type = ADDerivativeParsedMaterial + property_name = 'flux_on_T2_dry' + material_property_names = 'flux_base_on_T2_dry' + expression = '-1 * flux_base_on_T2_dry' + [] + [flux_on_V_O_dry] # V_O + type = ADDerivativeParsedMaterial + property_name = 'flux_on_V_O_dry' + material_property_names = 'flux_base_on_T2O_dry' + expression = '-1 * flux_base_on_T2O_dry' + [] + [flux_on_T2O_dry] # T2O + type = ADDerivativeParsedMaterial + property_name = 'flux_on_T2O_dry' + material_property_names = 'flux_base_on_T2O_dry' + expression = '-1 * flux_base_on_T2O_dry' + [] + + # --- Thermal material properties for BCY20 --- + [thermal_conductivity_mat] + type = ADGenericConstantMaterial + prop_names = 'thermal_conductivity_BCY20' + prop_values = '${thermal_conductivity_BCY20}' + [] + [specific_heat_mat] + type = ADGenericConstantMaterial + prop_names = 'specific_heat_BCY20' + prop_values = '${specific_heat_BCY20}' + [] + [density_thermal_mat] + type = ADGenericConstantMaterial + prop_names = 'density_BCY20_thermal' + prop_values = '${density_BCY20_thermal}' + [] + + # --- Joule heating --- + # Total ionic electrical conductivity from Nernst-Einstein relation (excluding electrons) + # sigma = q*F/(R*T) * (z_OH^2 * D_OT * c_OT + z_VO^2 * D_VO * c_VO) + # z_OH = 1, z_VO = 2, so z^2 = 1 and 4 + [total_electrical_conductivity] + type = ADParsedMaterial + property_name = 'sigma_total' + coupled_variables = 'OT_concentration_dry Oxygen_vacancy_concentration_dry temperature' + material_property_names = 'diffusivity_OT diffusivity_V_O' + expression = '${q} * ${F} / (${R} * temperature) * (diffusivity_OT * OT_concentration_dry + 4.0 * diffusivity_V_O * Oxygen_vacancy_concentration_dry)' + [] + # Joule heating volumetric source: Q = sigma_total * |grad(phi)|^2 + # |grad(phi)|^2 = (V_current / length)^2 = constant (voltage_phi is linear AuxVariable) + [joule_heating_material] + type = ADParsedMaterial + property_name = 'joule_heating_Q' + material_property_names = 'sigma_total' + expression = 'sigma_total * (${V_current} / ${length})^2' + [] +[] + +[Postprocessors] + #### Postprocessors for flux under dry + [recombination_flux_T2_dry_left] + type = ADSideAverageMaterialProperty + boundary = left + property = flux_on_T2_dry + execute_on = 'INITIAL TIMESTEP_END' + outputs = 'console csv' + [] + [recombination_flux_T2O_dry_left] + type = ADSideAverageMaterialProperty + boundary = left + property = flux_on_T2O_dry + execute_on = 'INITIAL TIMESTEP_END' + outputs = 'console csv' + [] + [recombination_flux_OT_dry_left] + type = ADSideAverageMaterialProperty + boundary = left + property = flux_on_OT_dry + execute_on = 'INITIAL TIMESTEP_END' + outputs = 'console csv' + [] + [recombination_flux_OT_dry_right] + type = ADSideAverageMaterialProperty + boundary = right + property = flux_on_OT_dry + execute_on = 'INITIAL TIMESTEP_END' + outputs = 'console csv' + [] + [recombination_flux_T2O_dry_right] + type = ADSideAverageMaterialProperty + boundary = right + property = flux_on_T2O_dry + execute_on = 'INITIAL TIMESTEP_END' + outputs = 'console csv' + [] + [recombination_flux_T2_dry_right] + type = ADSideAverageMaterialProperty + boundary = right + property = flux_on_T2_dry + execute_on = 'INITIAL TIMESTEP_END' + outputs = 'console csv' + [] + + # necessary parameters + [T2_K_eq_average] + type = ADElementAverageMaterialProperty + mat_prop = T2_K_eq + [] + [T2_K_forward_average] + type = ADElementAverageMaterialProperty + mat_prop = T2_K_forward + [] + [T2_K_reverse_average] + type = ADElementAverageMaterialProperty + mat_prop = T2_K_reverse + [] + [T2O_K_eq_average] + type = ADElementAverageMaterialProperty + mat_prop = T2O_K_eq + [] + [T2O_K_forward_average] + type = ADElementAverageMaterialProperty + mat_prop = T2O_K_forward + [] + [T2O_K_reverse_average] + type = ADElementAverageMaterialProperty + mat_prop = T2O_K_reverse + [] + [diffusivity_OT_average] + type = ADElementAverageMaterialProperty + mat_prop = diffusivity_OT + execute_on = 'INITIAL TIMESTEP_END' + [] + [diffusivity_V_O_average] + type = ADElementAverageMaterialProperty + mat_prop = diffusivity_V_O + execute_on = 'INITIAL TIMESTEP_END' + [] + [temperature_average] + type = ElementAverageValue + variable = temperature + execute_on = 'INITIAL TIMESTEP_END' + [] + [voltage_value] + type = ParsedPostprocessor + expression = ${V_current} + execute_on = 'INITIAL TIMESTEP_END' + [] + [pressure_T2_average] + type = ElementAverageValue + variable = pressure_T2_dry + execute_on = 'INITIAL TIMESTEP_END' + [] + + # --- MultiApp coupling postprocessors --- + [received_pressure] # upstream T2 partial pressure [Pa] received from the parent fuel-cycle model + type = Receiver + default = ${pressure_T2_high} # fallback so standalone runs reproduce the base feed pressure + execute_on = 'INITIAL TIMESTEP_BEGIN' + [] + [permeation_rate_kg_per_s] # tritium mass flow permeated to the downstream side [kg/s] + # The downstream-boundary OT flux is negative when tritium permeates OUT to the permeate side, + # so the forward permeation rate is max(-flux, 0): only net downstream transport is recovered. + # flux[at/nm^2/s] * 1e18 -> at/m^2/s ; * A_membrane[m^2] -> at/s ; * M_T_atomic/N_a -> kg/s + type = ParsedPostprocessor + pp_names = 'recombination_flux_OT_dry_right' + expression = 'max(-recombination_flux_OT_dry_right, 0) * 1e18 * ${A_membrane} * ${M_T_atomic} / ${N_a}' + execute_on = 'INITIAL TIMESTEP_END' + [] + + # Joule heating diagnostics + [temperature_max] + type = ElementExtremeValue + variable = temperature + value_type = max + execute_on = 'INITIAL TIMESTEP_END' + [] + [temperature_min] + type = ElementExtremeValue + variable = temperature + value_type = min + execute_on = 'INITIAL TIMESTEP_END' + [] + [delta_T] + type = ParsedPostprocessor + pp_names = 'temperature_max temperature_min' + expression = 'temperature_max - temperature_min' + execute_on = 'TIMESTEP_END' + [] +[] + +[Executioner] + type = Transient + scheme = implicit-euler + solve_type = NEWTON + petsc_options_iname = '-pc_type -snes_type' + petsc_options_value = 'lu vinewtonrsls' + nl_rel_tol = 5e-6 + # Slightly looser absolute tolerance than the standalone model: when driven across the full range + # of upstream pressures by the fuel cycle, the residual can stall just above 5e-7 in some states. + # 1e-6 (still 3+ orders below the initial residual) converges reliably without affecting the flux. + nl_abs_tol = 1e-6 + end_time = ${endtime} + # Run to (pseudo-)steady permeation each time the parent invokes this sub-app, then terminate + # early. end_time is a hard cap; steady_state_start_time avoids declaring steady state during + # the upstream-pressure ramp (ramp_time). + # steady_state_detection = true + # steady_state_tolerance = 1e-6 + # steady_state_start_time = '${fparse 10 * ramp_time}' + automatic_scaling = true + compute_scaling_once = true + line_search = none + error_on_dtmin = false # must stay false for ignore_solve_not_converge to work in Level 2 + abort_on_solve_fail = true # fast-fail on first NL divergence; prevents stutter at dtmin + dtmin = 1e-10 + nl_max_its = 60 + dtmax = ${dt_max} + [TimeStepper] + type = IterationAdaptiveDT + dt = ${dt_start_charging} + optimal_iterations = 20 + growth_factor = 1.5 + cutback_factor = 0.5 + cutback_factor_at_failure = 0.5 + [] +[] + +[Debug] + show_var_residual_norms = true +[] + +[Outputs] + exodus = false + # Save the membrane result for every fuel-cycle step into the membrane_steps/ subfolder. The parent + # MultiApp sets keep_full_output_history = true so this CSV is accumulated (not overwritten) across + # all steps, letting the membrane solution be inspected for correctness. + file_base = 'membrane_steps/membrane_5_Pa_flux' + [csv] + type = CSV + [] +[] diff --git a/test/tests/PCC_multiscale_example/tests b/test/tests/PCC_multiscale_example/tests new file mode 100644 index 000000000..6e08df41b --- /dev/null +++ b/test/tests/PCC_multiscale_example/tests @@ -0,0 +1,40 @@ +# NOTE on testing the coupled run: +# The full multiscale fuel-cycle run (dir_pcc_fuel_cycle.i) solves one fuel-cycle model with two +# PCC membrane sub-applications at each fuel-cycle time step. It is intentionally not a CSVDiff +# test because the production run is expensive and creates large output files. CI covers input +# validity and the documentation figure scripts, which read compact committed reference CSVs. + +[Tests] + design = 'FullSolveMultiApp.md MultiAppPostprocessorTransfer.md ParsedODEKernel.md' + issues = '#429' + [check_input] + type = RunApp + input = 'dir_pcc_fuel_cycle.i' + check_input = True + capabilities = 'method=opt' + requirement = "The system shall provide a valid input coupling the system-level tritium fuel " + "cycle to component-level proton-conducting-ceramic membrane sub-apps via " + "MultiApps that exchange DIR upstream pressure and recovered permeation rates." + [] + [residence_time_fit] + type = RunCommand + command = 'python fit_residence_time.py' + requirement = "The system shall generate the two-parameter residence-time fit for the " + "PCC-enhanced tritium permeation membrane from the component-level flux data." + required_python_packages = 'matplotlib numpy pandas scipy os' + [] + [dir_fraction_pressure] + type = RunCommand + command = 'python plot_dir_fraction_pressure.py' + requirement = "The system shall generate the system-level DIR pressure and recovery-fraction " + "plot for the coupled PCC-enhanced VP and FCU membrane loops." + required_python_packages = 'matplotlib numpy pandas os' + [] + [inventory_comparison] + type = RunCommand + command = 'python plot_inventory_comparison.py' + requirement = "The system shall generate the inventory comparison plot between the baseline " + "fuel-cycle model and the PCC-enhanced multiscale fuel-cycle model." + required_python_packages = 'matplotlib numpy pandas os' + [] +[]