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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Data-Driven Generic Turbines for Distributed Wind Modeling, Optimization, and Economic Studies

As distributed energy resources (DER) become less expensive and more popular, utilities, project developers, and customers have an increasing need to model the performance of existing and proposed DER systems. Distributed wind has been shown to have widespread economic potential but is often represented by a simplified model in - or excluded from - DER modeling tools and studies. There is often no economic imperative to extend models and studies to give full consideration to distributed wind. We present a set of data-driven generic turbines derived from 16 years of annual distributed wind market survey data. The proposed methodology can be used to derive generic turbines from separate or updated data sets. Finally, a mixed-integer linear programming approach to optimal distributed wind project sizing is used to demonstrate the generic turbine models. Combined, these models and methods can reduce barriers to considering distributed wind in modeling tools and studies.

Reiman, Andrew P.↗
DOE OSTI2020

Model Package Report: Central Plateau Vadose Zone Models

This model package report describes concisely the modeling objectives, conceptualization, implementation, uncertainty and sensitivity, configuration control, limitations, data needs, and recommendations for improvement of the Central Plateau Vadose Zone Models. This collection of models is developed to meet the vadose zone simulation needs of the Hanford Site Composite Analysis (CA), the Hanford Site Cumulative Impact Evaluation (CIE), and are expected to find other applications in Hanford Site remedial cleanup decision-making processes. This model package report describes and documents the development of the models themselves to fulfill technical approaches defined for the CA and the CIE. This report does not document any specific calculation using these models: instead, applications of individual vadose models to perform specific calculations will be documented in environmental calculation files, including inputs and results, as appropriate. Configuration management for the Central Plateau Vadose Zone Models is managed through assignment of unique sequential numerical version numbers and archival of the models in the Environmental Modeling Management Archive.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2024

Developing Platinum-Group-Metal-Free Catalysts for Oxygen Reduction Reaction in Acid: Beyond the Single Metal Site

This project is to develop M (x) -N-C catalysts with dense multiple metal center (MMC) sites to meet the DOE 2025 activity target of 0.044 mA/cm 2 at 0.9 V IR-free ., as well as other goals such as durability. We have made important contributions to both catalyst development and fundamental understandings of the active sites in M-N-C catalysts in this project. We successfully made M (x) -N-C catalysts with some multiple metal center (MMC) sites by combining ionothermal carbonization with chemical vapor deposition (CVD). These catalysts, however, are not as active as the most active single-atom Fe-N-C catalysts made by the similar CVD process, owing likely to the low site density and the presence of inorganic Fe species such as iron carbides and nanoparticles. The most significant accomplishments we achieved in this project are: (1) we unraveled the formation pathway of Fe-N 4 sites during pyrolysis step-by-step and identified the trans-metalation mechanism, in collaboration with Deborah Myers and her colleagues at Argonne National Laboratory (ANL); (2) inspired by this finding, we pioneered the CVD synthesis of M-N-C catalysts (M = Mn, Fe, and Co), in which the Fe-N-C catalyst by CVD demonstrated an ORR activity of 33 mA/cm 2 at 0.9 V in H 2 -O 2 proton exchange membrane fuel cells (PEMFCs), very close to the ultimate goal of 35 mA/cm 2 of our project. This catalyst is the first Fe-N-C catalyst that contains only D1 sites without the D2 sites; whereas D1 and D2 sites have been always identified by Mossbauer in previous Fe-N-C catalysts. This finding helps to understand what the D1 and D2 sites are and their roles in catalyzing the ORR. (3) by improving the mass transport of the carbon matrix prior to the CVD process, the revised Fe-N-C catalyst made by CVD delivered a maximum power density of 0.53 W/cm 2 in H 2 -air PEMFCs. The improvement strategy was partly inspired by the computational modeling work by Adam Weber from LBNL, the Co-PI of this project, by developing, coding, and exercising a continuum level model of transport phenomena within a PGM-free catalyst layer. The model demonstrated that local resistances combined with limited site density of the PGM-free catalyst can result in limiting currents and poor polarization performance. The model also gave design guidance for impact of ECSA and overall catalyst-layer thickness. However, both Fe-N-C and Co-N-C catalysts developed by CVD showed poor durability in PEMFCS, in comparison with the traditional M-N-C catalysts synthesized via regular pyrolysis process. Consequently, we did not achieve the proposed durability targets. Despite so, we believe the FeNC-CVD catalysts with the poor durability and D1 sites only provides an excellent platform to understand the degradation mechanism of Fe-N-C in PEMFCs, the most important challenge in the development of M-N-C catalysts.

08 HYDROGEN↗
DOE OSTI2023

Machine Learning Downscaling of SoilMERGE in the United States Southern Great Plains

SoilMERGE (SMERGE) is a root-zone soil moisture (RZSM) product that covers the entire continental United States and spans 1978 to 2019. Machine learning techniques, Random Forest (RF), eXtreme Gradient Boosting (XGBoost), and Gradient Boost (GBoost) downscaled SMERGE to spatial resolutions straddling the field scale domain (100 to 3000 m). Study area was northern Oklahoma and southern Kansas. The coarse resolution of SMERGE (0.125 degree) limits this product’s utility. To validate downscaled results in situ data from four sources were used that included: United States Department of Energy Atmospheric Radiation Measurement (ARM) observatory, United States Climate Reference Network (USCRN), Soil Climate Analysis Network (SCAN), and Soil moisture Sensing Controller and oPtimal Estimator (SoilSCAPE). In addition, RZSM retrievals from NASA’s Airborne Microwave Observatory of Subcanopy and Surface (AirMOSS) campaign provided a nearly spatially continuous comparison. Three periods were examined: era 1 (2016 to 2019), era 2 (2012 to 2015), and era 3 (2003 to 2007). During eras 1 and 2, RF outperformed XGBoost and GBoost, whereas during era 3 no model dominated. Performance was better during eras 1 and 2 as opposed to the pre-L band era 3. Improvements across all eras, regions, and models realized from downscaling included an increase in correlation from 0.03 to 0.42 and a decrease in ub RMSE from -0.0005 to -0.0118 m 3 /m 3 . This study demonstrates the feasibility of SMERGE downscaling opening the prospect for the development of a long-term RZSM dataset at a more desirable field-scale resolution with the potential to support diverse hydrometeorological and agricultural applications.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

E-Area Low-Level Waste Facility GoldSim System Model

This report documents the development of the E-Area Low-Level Waste Facility (ELLWF) trench system model. The GoldSim® Monte Carlo simulation software is utilized to model the release and transport of radiological inventory disposed (both currently and in the future) within Engineered and Slit Trenches. This model is in support of the sensitivity and uncertainty analysis for the ELLWF Performance Assessment. The ELLWF system model utilizes a hybrid-approach to accurately describe the disposal system. The Hydrologic Evaluation of Landfill Performance model provides the infiltration data to both PORFLOW and GoldSim. PORFLOW is used to calibrate the GoldSim model to ensure confidence in the stochastic results. Finally, the concentrations from GoldSim transport simulations are fed into the SRNL Dose Toolkit to calculate dose impacts and assess plume interaction

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2022

Semi-Annual Report for Modular Integrated Gas High Temperature Reactor Development during Performance Period April 2022 - September 2022

Horizontal Compact High Temperature Gas Reactor (HC-HTGR) is being designed by a multidisciplinary team of nuclear, mechanical, and structural engineers under the support of a DOE-NE Advanced Reactor Demonstration Program’s Advanced Reactor Concepts-20 (ARC-20) award. The objective of this ARC-20 project is to deliver a conceptual design for the proposed HC-HTGR in 3 years and support its commercialization as a safe, low-cost HTGR. Argonne National Laboratory (Argonne) is responsible for the design and analysis of the reactor cavity cooling system (RCCS) as a safety system for passive decay heat removal of the reactor concept. Additionally, Argonne is providing analysis of the primary coolant system to ensure temperatures within the core remain below safety margins during steady-state and potential accident scenarios. This second semi-annual report summarized the progress made at Argonne on the two tasks during the second half of FY22. As a part of the RCCS design task, a scoping calculation in estimating HVAC capability for the HC-HTGR reactor building was performed. A water panel modeling study was first performed with the test case, which confirms the capability of the RELAP5-3D modeling approach to explore various design options of the HC-HTGR RCCS under consideration. Then, a reference RELAP5-3D model for the unit geometry of the preliminary design of the HC-HTGR RCCS was developed. A preliminary performance analysis was conducted to evaluate the performances of a single-phase natural circulation and panel conduction in various operating conditions. For the primary coolant system analysis task, preliminary thermal hydraulic analysis of the HC-HTGR core design was performed with a high resolution 1D fluid-3D solid coupled model using the System Analysis Module (SAM) to assess the assembly coolant channel and bypass flow mass flow rate distribution. Some preliminary work on the development of a full core reduced order model was discussed following the assembly level model to predict the core wide coolant flow distribution and to model certain operational and accidental transients.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2022

Using machine learning to identify extragalactic globular cluster candidates from ground-based photometric surveys of M87

Globular clusters (GCs) have been at the heart of many longstanding questions in many sub-fields of astronomy and, as such, systematic identification of GCs in external galaxies has immense impacts. In this study, we take advantage of M87’s well-studied GC system to implement supervised machine learning (ML) classification algorithms – specifically random forest and neural networks – to identify GCs from foreground stars and background galaxies, using ground-based photometry from the Canada–France–Hawaii Telescope (CFHT). We compare these two ML classification methods to studies of ‘human-selected’ GCs and find that the best-performing random forest model can reselect 61.2 per cent ± 8.0 per cent of GCs selected from HST data (ACSVCS) and the best-performing neural network model reselects 95.0 per cent ± 3.4 per cent. When compared to human-classified GCs and contaminants selected from CFHT data – independent of our training data – the best-performing random forest model can correctly classify 91.0 per cent ± 1.2 per cent and the best-performing neural network model can correctly classify 57.3 per cent ± 1.1 per cent. ML methods in astronomy have been receiving much interest as Vera C. Rubin Observatory prepares for first light. The observables in this study are selected to be directly comparable to early Rubin Observatory data and the prospects for running ML algorithms on the upcoming data set yields promising results.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Thermodynamic modeling with uncertainty quantification using the modified quasichemical model in quadruplet approximation: Implementation into PyCalphad and ESPEI

The modified quasichemical model in the quadruplet approximation (MQMQA) considers the first- and the second-nearest-neighbor coordination and interactions, particularly useful in describing short-range ordering (SRO) in complex liquids such as molten salts, slag in metal processing, and electrolytic solutions. Here, the present work implements the MQMQA into the Python based open-source software PyCalphad for thermodynamic calculations. This endeavor facilitates the development of MQMQA-based thermodynamic database with uncertainty quantification (UQ) and propagation (UP) using the open-source software ESPEI. A new database structure based on Extensible Markup Language (XML) is proposed for ESPEI evaluation of MQMQA model parameters. Using the KF-NiF 2 , KCl-NaCl-MgCl 2 , and CaCl 2 -CaF 2 -LiCl-LiF salt systems as examples, we demonstrate the successful implementation of MQMQA in PyCalphad through thermodynamic calculations of Gibbs energy, equilibrium quadruplet fractions, and phase diagram, as well as database development with UQ and UP using ESPEI. Furthermore, as an application of the present implementation, both the LiF–TbF 3 and LiF-HoF 3 systems have been modeled by MQMQA for the first time, which are in good agreement with experiments. The present implementation hence offers an open-source capability for performing CALPHAD modeling for complex liquids with SRO using MQMQA plus a new XML database structure.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Implementation of a Drift Flux Model into SAM with Development of a Verification and Validation Test Suite for Modeling of Noncondensable Gas Mixtures

The advanced thermal-hydraulic system code, System Analysis Module (SAM), was originally developed for the modeling of single-phase flow in advanced reactors. It has since been expanded to include a four-equation drift flux model for the modeling of two-phase flows containing a noncondensable gas. The model was expanded to support the modeling of molten salt reactor (MSR) designs in which the fuel is directly dissolved in the circulating coolant. These designs have shown that circulating gas bubbles can play an important role in the management of fission products and the operational behavior of the reactor. A drift flux model was implemented to more accurately capture the localized behavior of the void in the core and its impact on the mass transfer of fission products. A thorough assessment of the new model was performed by developing a verification and validation test suite. Verification problems were designed to test all major terms in the new governing equations. The new model converged to the correct solution at the expected order of accuracy for all verification cases. The validation cases included a wide range of flow and void conditions in different pipe geometries. Although higher void experiments show a slight underprediction of void by the drift flux model, experiments that aim to reproduce Molten Salt Reactor Experiment (MSRE) experimental conditions show good agreement with the model. The gas transport model was activated for a SAM model of the MSRE to demonstrate that it can be used in a more complex model. Finally, this gas transport model will be used along with an interfacial area transport equation being implemented in SAM for the prediction of mass transport behavior in MSR conditions.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2021

International Collaboration Activities in Geologic Disposal Research: FY2021 Progress

This report describes the FY21 status of international collaboration regarding geologic disposal research in the Spent Fuel and Waste Disposition (SFWD) Campaign. Since 2012, in an effort coordinated by Lawrence Berkeley National Laboratory, SFWD has advanced active collaboration with several international geologic disposal programs across the world. Such collaboration has allowed the SFWD Campaign to benefit from a deep knowledge base in regards to alternative repository environments developed over decades and has provided a framework for active peer-to-peer research participation in international groups which conduct, analyze, and model performance-relevant processes. Via international collaboration, the SFWD Campaign also benefits from substantial international investments in research facilities (such as underground research laboratory testing and modeling) and achieves cost savings via joint funding of expensive field experiments. To date, SFWD’s International Disposal R&D Program has established formal collaboration agreements with multiple international initiatives and various international partners, and national lab scientists associated with SFWD have conducted a large number of specific collaborative R&D activities that align well with its R&D priorities.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2024

Modelling and analysis of nuclear reactor system coupled with a liquid metal battery

Traditionally, nuclear power plants in the U.S. provide baseload power to the power grid because they have less flexibility for ramping their output power than natural gas peaking plants. However, achieving climate goals to reduce the consumption of fossil‐based natural gas places pressure on nuclear power plants and other power generators to ramp up their power output to balance grid generation with demand. This paper presents the modelling and performance analysis of a nuclear reactor system (NRS) coupled to a liquid‐metal battery (LMB) to improve its dynamic response and enable its black start capability. The NRS and LMB thermal behaviour are modelled in Dymola, while the electrical dynamics of the LMB and power grid are modelled in RTDS‐RSCAD. Both simulation platforms are coupled and share their thermal and electrical data using a Transmission Control Protocol/Internet Protocol (TCP/IP) communication protocol. The dynamic performance of the NRS‐LMB integration is tested on the IEEE 9 bus, which demonstrates its ability to respond and provide frequency and voltage regulation. The black start capability of the NRS‐LMB is also evaluated by simulating a grid outage and using the LMB to supply the auxiliary loads required to bring the NRS back online as soon as possible. The results show that coupling an NRS to an LMB improves the system dynamic performance and enables it to black start after being disconnected from the grid for several days.

25 ENERGY STORAGE↗
DOE OSTI2022

Numerical study of multi-component flow and mixing in a scaled fission product venting system

Numerical simulation of isothermal multi-component gas flow was conducted to study fluid flow and mixing in a scaled low-pressure, low-temperature test facility for the fission product venting system (FPVS) of a gas cooled fast reactor (GFR). The geometry of FPVS test facility was an open loop including gradual expansion coupling and two 90°pipe elbows. First, the validation of large eddy simulation (LES) wall-adapting local eddy-viscosity (WALE) turbulent model was performed for transitional flow in a circular pipe with gradual expansion. The reactingFOAM solver in OpenFOAM v8 was employed. By introducing appropriate turbulence disturbance at the flow inlet, such as turbulence intensity, the numerical results showed good agreement in (1) the velocity profile downstream of the pipe expansion measured by particle image velocimetry (PIV) in this study, and (2) the reattachment length reported in the literature. Using this validated model, the numerical simulation of flow and component mixing was performed for the FPVS with an inlet flowrate corresponding to a Reynolds number of 2,400 to investigate the flow behavior and component mixing. Standard deviation of the mass fraction of component, referred to as absolute mixing index (AMI), was calculated to quantify the mixing of components, showing that the component mixing length determined by AMI is related to the reattachment length downstream of the expansion. Additionally, this study was able to identify the best location in the FPVS test facility to measure the velocity and concentration profies where multicomponent flow is well mixed.

15 GEOTHERMAL ENERGY↗
DOE OSTI2022

Fast Gaussian Process Estimation for Large-Scale In Situ Inference using Convolutional Neural Networks

Exascale computing will bring with it significant I/O limitations. One foreseeable consequence of such restrictions is that the user can save only a small fraction of complex simulation data to disk for subsequent analysis. An alternative is to fit statistical models to data in situ, that is, inside the simulation as it runs. This option requires extremely fast statistical estimation to avoid slowing down the simulation. Gaussian processes (GPs) have state-of-the-art predictive performance for modeling spatial data. However, standard estimation methods for GPs scale quite poorly to large data sets as parameter estimation requires inverting a covariance matrix to the size of the data set. In the presented work, we use a convolutional neural network (CNN) to predict the GP parameters for a spatial data set, from a simulation or otherwise, rather than optimize the parameters directly. Here, our presented case study models spatial data from E3SM, the Department of Energy’s Exascale climate model. The CNN is trained on synthetic data simulated from GP models with known parameters and then applied to data from the climate simulation. In the presented examples, the neural network scheme produces parameter estimates that compare well with standard methods such as maximum likelihood estimation in predictive performance but is obtained four orders of magnitude faster.

big data↗
DOE OSTI2024

Designing complex concentrated alloys with quantum machine learning and language modeling

Designing novel complex concentrated alloys (CCAs) is an essential topic in materials science. However, due to the complicated high-dimensional component-property relationship, tuning material properties by researchers’ experience is challenging, even when guided by physical or empirical rules. Here, we adopt quantum computing (QC) technology and machine learning models to provide a proof-of-concept application of QC in physical metallurgy. We propose a quantum support vector machine (QSVM) model to predict single-phase CCAs. We show that fine-tuned quantum kernels with entanglement deliver promising performance, with a maximum accuracy of 89.4%. The QSVM model is then used to identify 1,741 lightweight CCAs jointly with a new text-mining-based method. Meanwhile, we devise a controllable approach to study the effect of noise on model performance and find that the noise level needs to be minimized for high-performance QSVM models. Finally, this study provides a practical and general approach to designing CCAs based on quantum technologies.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Verification Testing of OLI Systems Mixed Solvent Electrolyte Model for the Na-K-Mg-Ca-H-Cl-SO 4 -OH-HCO 3 -CO 3 -CO 2 -H 2 ) System to High Ionic Strength at 25°C

This technical report summarizes model verification results and summary statistics for 41 evaporite mineral solubility cases evaluated by Savannah River National Laboratory using OLI Systems’ aqueous electrolyte thermodynamic modeling software. The 41 verification cases containing a total of 60 solubility curves comprise mineral solubility data from low to high ionic strength at 25°C for the eight-component system Na-K-Mg-Ca-H-Cl-SO 4 -OH-HCO 3 -CO 3 -CO 2 -H 2 O as reported by Harvie et al. (1984). Thermodynamic calculations were executed using OLI Systems’ Stream Analyzer computation module within the OLI Studio software platform (Ver. 11.0, Rev. 11.0.1.9). The Mixed Solvent Electrolyte (MSE) thermodynamic framework was chosen for this investigation because of its superiority in modeling high ionic-strength inorganic salt solutions and actinide redox chemistry and solubility, both of which are relevant to the geological repository conditions at the Waste Isolation Pilot Plant in Carlsbad, New Mexico. Mineral solubility data in various inorganic salt solutions were digitized and extracted from figures generated by Harvie et al. (1984). For each of the 60 solubility curves, a case-specific chemistry model and input file were generated in OLI Studio using OLI Stream Analyzer and the MSE (H 3 O + ion) public databank provided by OLI Systems. Model simulation results were exported to Microsoft Excel to calculate summary statistics and to generate graphs comparing the OLI model predictions to the solubility data. Summary statistics include residuals (model – data) and concordance (accuracy × precision, where precision is indicated by the Pearson correlation coefficient and accuracy accounts for bias and scale differential). Private databanks were not developed, and activity coefficient model regressions were not performed to improve OLI model fits to the data. Of the 41 model verification plots, 83% have a mean of the percent residuals less than or equal to 25%. Similarly, 75% display a concordance greater than or equal to 0.75. Only seven of the 41 verification plots fail to show good agreement between the model and data. Of these seven, three are relevant to the WIPP repository because they involve the Mg-OH-Cl-SO 4 -CO 3 aqueous system. The remaining four address salt solubilities at the pH extremes (strong acid and strong base). It should be noted that in two of the three Mg-OH-Cl-SO 4 -CO 3 system cases, the regressed Harvie et al. (1984) solubility curve also deviated from the data. Lack of agreement between the OLI model-predicted solubility curves and the data is attributable to one or more of the following: specific solid species are not included in the OLI MSE databank; there is significant variation among the different solubility datasets chosen by Harvie et al. (1984); the OLI MSE model’s thermodynamic parameters were determined using different solubility datasets; and the activity coefficient parameters for certain relevant ion-ion and ion-molecule pairs have not been optimized via data regression. Two recommendations for future work are to (1) evaluate solubility data for the Mg-OH-Cl-SO 4 -CO 3 system at high ionic strength and, if necessary, develop a private OLI MSE database that includes missing species and, where necessary, regressed standard state properties and interaction parameters; (2) perform similar verification testing of the OLI model for actinide solubility data.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2020

A digital twin based on OpenFAST linearizations for real-time load and fatigue estimation of land-based turbines

Monitoring a wind turbine requires intensive instrumentation, which would be too cost-prohibitive to deploy to an entire wind plant. This work presents a technique that uses readily available measurements to estimate signals that would otherwise require additional instrumentation. This study presents a digital twin concept with a focus on estimating wind speed, thrust, torque, tower-top position, and loads in the tower using supervisory control and data acquisition (SCADA) measurements. The model combines a linear state-space model obtained using OpenFAST linearizations, a wind speed estimator, and a Kalman filter algorithm that integrates measurements with the state model to perform state estimations. The measurements are: top acceleration, generator torque, pitch, and rotational speed. The article extends previous work that derived the linear state-space model using a different method. The new implementation, based on OpenFAST linearization capability, allows for a systematic extension of the method to more states, inputs, outputs, and to the offshore environment. Results from the two methods are compared, and the validation is made with additional measurements using the GE 1.5-MW turbine located at the National Renewable Energy Laboratory test site. Real-time damage equivalent loads of the tower bottom moment are estimated with an average accuracy of approximately 10%. Overall, the results from this proof of concept are encouraging, and further application of the model will be considered.

17 WIND ENERGY↗
DOE OSTI2020

Modeling Water Electrolysis in Bipolar Membranes

Bipolar membranes (BPMs) have proven useful in numerous electrochemical energy conversion and storage applications, including fuel cells and electrolyzers. However, water dissociation in bipolar membrane electrolysis cells (BPMECs) is a complicated phenomenon that occurs via several different pathways. In this work, we develop a model based on the Poisson-Nernst-Planck system that includes a multistep water-dissociation mechanism to observe the fundamental processes that contribute to BPMEC performance. The model, which is validated to in-house experimental data, demonstrates that the junction potential is the most significant contributor to the total electrolysis voltage. We investigated the effects of water-dissociation catalysts and found that the optimal catalyst $p{K}_{a}$ depends on how the catalyst is integrated into the BPM (although values near 7 are typically best, in accordance with conventional wisdom). We also simulated the water content across the BPM and found that dry-out is not a significant issue when the membrane is in contact with liquid water on both sides. The species conservation approach taken here leads to a physical understanding of the system without using any fitting parameters.

25 ENERGY STORAGE↗