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The authors present generalized finite-volume-based discretized loss functions integrated into pressure-linked algorithms for physics-based unsupervised training of neural networks (NNs). In contrast to automatic differentiation-based counterparts, discretized loss functions leverage well-developed numerical schemes of computational fluid dynamics (CFD) for tailoring NN training specific to the flow problems. For validation, neural network-based solvers (NN solvers) are trained by posing equations such as the Poisson equation, energy equation, and Spalart–Allmaras model as loss functions. The predictions from the trained NNs agree well with the solutions from CFD solvers while also providing solution time speed-ups of up to seven times. Another application of unsupervised learning is the novel hybrid loss functions presented in this study. Hybrid learning combines the information from sparse or partial observations with a physics-based loss to train the NNs accurately and provides training speed-ups of up to five times compared with a fully unsupervised method. Also, to properly utilize the potential of discretized loss functions, they are formulated in a machine learning (ML) framework (TensorFlow) integrated with a CFD solver (OpenFOAM). The ML-CFD framework created here infuses versatility into the training by giving loss functions access to the different numerical schemes of the OpenFOAM. In addition, this integration allows for offloading the CFD programming to OpenFOAM, circumventing bottlenecks from manually coding new flow conditions in a solely ML-based framework like TensorFlow.

A process where power and biomass are converted to Fischer-Tropsch liquid fuels (PBtL) is compared to a conventional Biomass-to-Liquid (BtL) process concept. Based on detailed process models, it is demonstrated that the carbon efficiency of a conventional Biomass to Liquid process can be increased from 38 to more than 90% by adding hydrogen from renewable energy sources. This means that the amount of fuel can be increased by a factor of 2.4 with the same amount of biomass. Electrical power is applied to split water/steam at high temperature over solid oxide electrolysis cells (SOEC). This technology is selected because part of the required energy can be replaced by available heat. The required electrical power for the extra production is estimated to be 11.6 kWh per liter syncrude . By operating the SOEC iso-thermally close to 850 °C the electric energy may be reduced to 9.5 kWh per liter, which is close to the energy density of jet fuel. A techno-economic analysis is performed where the total investments and operating costs are compared for the BtL and PBtL. With an electrical power price of 0.05 $/kWh and with SOEC investment cost of the 1000 $/kW(el), the levelized cost of producing advanced biofuel with the PBtL concept is 1.7 $/liter, which is approximately 30% lower than for the conventional BtL. Converting excess renewable electric power to advanced biofuel in a PBtL plant is a sensible way of storing energy as a fuel with a relatively high energy density. © 2018 Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/BY/4.0/).

The present work suggests two concepts for producing hydrogen by reverse electrodialysis. Reverse electrodialysis is a technology that uses concentration differences to create electrical energy. In this work, the energy is utilised as direct hydrogen production within a closed-loop system. For both system alternatives, waste heat is used to set up the mentioned concentration differences. The first concept is evaporation, where heat is added to boil off excess water from a concentrated solution and thereby increase its concentration. The second concept removes heat in order to precipitate excess salt. For the precipitation concept to work, a salt where the solubility is highly dependent on temperature must be used. KNO3 fulfils this requirement. As part of a proof of concept, the conductivity of membranes soaked in KNO3 was investigated. The conductivity of the salt in two commercialised membranes, Fumatech FKE-50 and FAS-30, was measured and compared to NaCl in the same membranes. The conductivity of K+ in FKE-50 was found to be 4.5 and 6.6 mS cm−1 at 25◦C and 40◦C respectively. The conductivity of NO−3 in FAS-30 was found to be 4.3 mS cm−1 and 6.5 mS cm−1 at 25◦C and 40◦C respectively. Neither of the membranes change conductivity with soaking concentrations. The conductivity at 40◦C compared to 25◦C is significantly better in the FKE membrane, and seemingly better in the FAS membrane. Potential peak power densities for a RED unit cell is 1.29 W m−2 with the precipitation system, and 28.1 W m−2 when evaporation is used. © 2018. This is the authors' accepted and refereed manuscript to the article. The final authenticated version is available online at: http://dx.doi.org/10.1149/08513.0147ecst

The solid oxide fuel cell is an electro-chemical device which converts chemical energy into electricity and heat. To compete in today's market, design improvements, in terms of performance and life cycle, are required. Numerical prototypes can accelerate design and development progress. In this programme of research, a three- dimensional solid oxide fuel cell prototype, openFuelCell, based on open-source computational fluid dynamics software was developed and applied to a single cell. Transport phenomena, combined with the solution to the local Nernst equation for the open-circuit potential, as well as the Kirchhoff-Ohm relationship for the local current density, allow local electro-chemistry, fluid flow, multi-component species transport, and multi-region thermal analysis to be considered. The underlying physicochemical hydrodynamics, including porous- electrode and electro-chemical effects are described in detail. The openFuelCell program is developed in an object-oriented open- source C++ library. The code is available at http://openfuelcell.sourceforge.net/. The paper also describes domain decomposition techniques considered in the context of highly efficient parallel programming

A combined numerical and experimental investigation has been carried out to study the flow behaviour in a spacer-filled channel, representative of those used in spiral-wound membrane modules. Direct numerical simulation and particle image velocimetry were used to investigate the fluid flow characteristics inside a 2 × 2 cell at Reynolds numbers that range between 100 and 1000. It was found that the flow in this geometry moves parallel to and also rotates between the spacer filaments and that the rate of rotation increases with Reynolds number. The flow mechanisms, transition process and onset of turbulence in a spacer-filled channel are investigated including the use of the velocity spectra at different Reynolds numbers. It is found that the flow is steady for Re < 200 and oscillatory at Re ∼ 250 and increasingly unsteady with further increases in Re before the onset of turbulent flow at Re ∼ 1000.

A modeling framework for the microstructural modeling of infiltrated SOFC electrodes is presented. The model numerically reconstructs infiltrated electrodes through a sedimentation algorithm for the backbone generation and a novel Monte Carlo packing algorithm for the random infiltration. Effective properties are evaluated by means of Monte Carlo geometric analysis and finite volume method as a function of the loading and of the particle size of infiltrated particles. Infiltration into ion-conducting and composite backbones is analyzed in this study. Simulations show that the infiltration can lead to an increase in TPB density of about two orders of magnitude if compared with conventional composite electrodes. In addition, infiltration into monocomponent backbones can lead to a TPB density about twice the TPB achievable when infiltrating composite backbones. On the other hand, a critical loading of nanoparticles must be reached in monocomponent backbones while in a composite backbone the infiltration is always beneficial.

Solid oxide fuel cells represent a potentially important application for ceramic materials. There are, however, some significant issues which can affect the reliability and durability of the cell. The generation of stresses and associated strains in fuel cells is an important concern that needs to be addressed in order to avoid mechanical failure of the cell. Few comprehensive studies have been published on the subject of stress analysis of planar and tubular SOFCs to-date, although various numerical methodologies have been used to obtaining the stress distribution in specific SOFC components over the last 10 years. The objective of this paper is to summarize the state-of-the art of solid oxide fuel cell stress analysis efforts so that the salient issues can be identified.Copyright © 2010 by ASME and NRC Canada

This article presents a numerical framework for the computation of the effective transport properties of solid oxide fuel cells (SOFCs) porous electrodes from three-dimensional (3D) constructions of the microstructure. Realistic models of the 3D microstructure of porous electrodes are first constructed from measured parameters such as porosity and particle size distribution. Then each phase in the model geometries is tessellated with a computational grid. Three different types of grids are considered: Cartesian, octree, and body-fitted/cut-cell with successive levels of surface refinement. Finally, a finite volume method is used to compute the effective transport properties in the three phases (pore, electron, and ion) of the electrode. To validate the numerical approach, results obtained with the finite volume method are compared to those calculated with a random walk simulation for the case of a body-centred cubic lattice of spheres. Then, the influence of the sample size is investigated for random geometries with monosized particle distributions. Finally, effective transport properties are calculated for model geometries with polydisperse particle size distributions similar to those observed in actual SOFC electrodes.

The flow phenomena in a serpentine microchannel segment attached to a porous transport layer in a micro proton-exchange membrane fuel cell is investigated. Due to the presence of a porous transport layer, the fluid flow for this configuration exhibits different characteristics compared with that through a simple serpentine channel. The pressure drop and friction factor variation in the channel is examined for various values of Reynolds number and radii of curvature. Also, the effect of variation of permeability is investigated. There are two modes of fluid transport in this geometry—one through the serpentine channel and other via the porous media. With increasing permeability, more fluid is convected through the porous transport layer.