Add pcc multiscale example

doc/content/bib/tmap8.bib

@@ -799,3 +799,153 @@ @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}
+}
+
+@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}
+}

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

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