Multi-component Species Transport Research Articles

Eulerian-Lagrangian modelling of detonative combustion in two-phase gas-droplet mixtures with OpenFOAM: Validations and verifications

A hybrid Eulerian-Lagrangian solver RYrhoCentralFoam is developed based on OpenFOAM® to simulate detonative combustion in two-phase gas-liquid mixtures. For Eulerian gas phase, RYrhoCentralFoam enjoys second order of accuracy in time and space discretizations and is based on finite volume method on polyhedral cells. The following developments are made based on the standard compressible flow solver rhoCentralFoam in OpenFOAM®: (1) multi-component species transport, (2) detailed fuel chemistry for gas phase combustion, and (3) Lagrangian solver for gas-droplet two-phase flows and sub-models for liquid droplets. To extensively verify and validate the developments and implementations of the solver and models, a series of benchmark cases are studied, including non-reacting multi-component gaseous flows, purely gaseous detonations, and two-phase gas-droplet mixtures. The results show that the RYrhoCentralFoam solver can accurately predict the flow discontinuities (e.g. shock wave and expansion wave), molecular diffusion, auto-ignition and shock-induced ignition. Also, the RYrhoCentralFoam solver can accurately simulate gaseous detonation propagation for different fuels (e.g. hydrogen and methane), about propagation speed, detonation frontal structures and cell size. Sub-models related to the droplet phase are verified and/or validated against analytical and experimental data. It is also found that the RYrhoCentralFoam solver is able to capture the main quantities and features of the gas-droplet two-phase detonations, including detonation propagation speed, interphase interactions and detonation frontal structures. As our future work, RYrhoCentralFoam solver can also be extended for simulating two-phase detonations in dense droplet sprays.

Open-source computational model of a solid oxide fuel cell

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.

Enforcing realizability in explicit multi-component species transport

We propose a strategy to guarantee realizability of species mass fractions in explicit time integration of the partial differential equations governing fire dynamics, which is a multi-component transport problem (realizability requires all mass fractions that are greater than or equal to zero and that the sum equals unity). For a mixture of n species, the conventional strategy is to solve for n−1 species mass fractions and to obtain the nth (or “background”) species mass fraction from one minus the sum of the others. The numerical difficulties inherent in the background species approach are discussed and the potential for realizability violations is illustrated. The new strategy solves all n species transport equations and obtains density from the sum of the species mass densities. To guarantee realizability the species mass densities must remain positive (semidefinite). A scalar boundedness correction is proposed that is based on a minimal diffusion operator. The overall scheme is implemented in a publicly available large-eddy simulation code called the Fire Dynamics Simulator. A set of test cases is presented to verify that the new strategy enforces realizability, does not generate spurious mass, and maintains second-order accuracy for transport.

Internal reforming of biogas in SOFC: a model based investigation

This paper presents a multiphysics model for the simulation of solid oxide fuel cell operating on biogas without external reforming. The model accounts for multicomponent species transport, heterogeneous reaction kinetics on Ni cermet anode, H2 electrochemical oxidation, and charge transport in the cermet electrodes and electrolyte. The model uses only three adjustable parameters that are fitted against one set of experimental data and then kept constant throughout the study. The model predicted voltage fluctuations are in excellent agreement with experimental measurements reported in the literature. The model also reveals that the assumption of H2 as the only electrochemically active species is probably inadequate to explain the behavior of cells operating directly on biogas. Thermodynamic analysis is further performed to support this claim made based on model predictions. The model results demonstrate that the thickness of electrochemically active layer is independent of fuel composition under fuel rich conditions, however, thins down as the fuel becomes more and more diluted.

Multi-scale Modeling of Biogas Fueled SOFC

This paper presents a multi-physics model for simulating solid oxide fuel cells operating directly on biogas without the aid of an external reformer. The model accounts for multi-component species transport, electrochemical charge transfer and charge transport within the electrodes and electrolyte. The model uses only 3 adjustable parameters that are fitted against a base set of experimental data and then kept constant throughout the study. The model predicted voltage fluctuations due to composition fluctuation of biogas are in very good agreement with experimentally measured voltage fluctuations. The model reveals that the assumption of H2 as the only electrochemically active species is probably inadequate for explaining the behavior of cells operating directly on biogas. It is also found that the electrochemically active thickness is independent of fuel composition and the ionic current through electrolyte under fuel rich conditions.

Theoretical analysis of hydrogen production by variable volume membrane batch reactors with direct liquid fuel injection

A direct liquid fuel injection/variable volume reactor integrated with a hydrogen selective membrane (CHAMP-DDIR) has been recently shown to be a promising new concept for hydrogen production in portable and distributed applications. The CHAMP-DDIR reactor performance has been analyzed using a simplified transport model with which conditions for maximum performance, e.g. highest volumetric power density, were identified. A prototype reactor demonstrated the ability to realize performance improvement, while also indicating a need for more a rigorous model for accurate exploration of the design and operation space. In this paper, we present a comprehensive reactor model which carefully considers the effects of heat and mass transfer, including rigorous treatment of multi-component species transport. The model is validated against experimental results through comparison of predicted and measured hydrogen production rate, reactor pressure, and temperature. The experimentally validated model is used to identify the relationship between CHAMP-DDIR design and operating parameters and the rate-limiting processes that govern reactor output. In addition, effects of heat and mass transfer limitations on CHAMP-DDIR performance are investigated by comparing the predictions among multiple cases with increasing level of complexity used for modeling the transport phenomena within the reactor.

Numerical solution of multi-component species transport in gases at any total number of components

In Böttcher [K. Böttcher, Numerical solution of a multi-component species transport problem combining diffusion and fluid flow as engineering benchmark, Int. J. Heat Mass Transfer 53 (1–3) (2010) pp. 231–240], one of us described an implementation of ternary multi-component species transport by diffusion and convection and presented benchmark cases and simulation results for these cases computed with software ENTWIFE. In this paper, an implementation of the Stefan–Maxwell equation into the ANSYS CFX software is described in combination with a procedure to numerically calculate the ordinary multi-component diffusion coefficients in gases at any total number of components. Finally, the benchmark for ternary mixtures is extended to a quarternary one. A comparsion to the benchmark results of Böttcher revealed an implementation mistake in Böttcher’s paper leading to wrong results in case of largely different molar masses. The correct benchmark results are presented here and furthermore compared to two different kinds of effective binary diffusion approaches in multi-component gas mixtures.

Direct two-dimensional electrochemical impedance spectra simulation for solid oxide fuel cell

A two-dimensional (2D) EIS simulation approach is developed by solving a SOFC unit cell model with imposed sinusoidal voltage perturbations at different frequencies. The transient SOFC unit cell model describes the intricate interdependency among the ionic/electronic conduction, multi-component species transport, electrochemical reaction processes and electrode microstructure as well as the coupling processes of mass, energy, momentum transport within flow channels. The model calculates the local transient response and impedance spectra as a function of channel position. The effects of the reaction depletion, product accumulation as well as the temperature variation along the flow channels on the EIS spectra are numerically simulated with a counter-flow mode. The results show that the convection-diffusion process along the flow channel has significant effects on the low frequency half circle of the impedance spectra. The temperature oscillations accumulate along the flow channels, and then affect the current responses which probably lead to an electro-thermal impedance effects.

Modeling detailed chemistry and transport for solid-electrolyte-interface (SEI) films in Li–ion batteries

The thin solid-electrolyte-interface (SEI) films that grow around electrode particles play important roles in Li–ion battery performance. The objective of the present paper is to develop and apply models of SEI behavior that incorporate detailed chemical kinetics and multicomponent species transport. Species- and charge-conservation equations are derived and solved within the SEI film. The SEI model is coupled at its boundaries with an intercalation model within the electrode particles and with Li–ion transport and chemistry at the interface between the SEI and the electrolyte solution. The results of the model provide new insights concerning the influences of the intercalation fraction and cycling rate on SEI growth rates. The model also provides new insight concerning the influence of the SEI film on reversible potential and interfacial resistance.

Simulation of Two-Dimensional Electrochemical Impedance Spectra of Solid Oxide Fuel Cells Using Transient Physical Models

A two-dimensional (2D) EIS simulation approach was developed by solving a SOFC unit cell model with imposed sinusoidal voltage perturbations at different frequencies. The transient SOFC unit cell model described the intricate interdependency among the ionic/electronic conduction, multi-component species transport, electrochemical reaction processes and electrode microstructure as well as the coupling processes of mass, energy, momentum transport within flow channels. The model calculates the local transient response and impedance spectra as a function of channel position. The effects of the reaction depletion, product accumulation as well as the temperature variation along the flow channels on the EIS spectra was numerically simulated with a counter-flow mode. The results show that the convection-diffusion process along the flow channel has significant effects on the low frequency circle of the impedance spectra. The temperature oscillations accumulate along the flow channels, and then affect the current response which probably lead to an electro-heat impedance effects.

A Study on Mass Transfer in the Cathode Gas Channel of a Proton Exchange Membrane Fuel Cell

AbstractA two-dimensional, transient mathematical model for the mass transfer of a reactant gas in the cathode gas channel of a PEMFC is developed. This model accounts concurrently for gas flow and multicomponent species (oxygen, water vapor and nitrogen) transport in the gas channel at specified cell current densities. The governing equations along with the boundary and initial conditions are solved numerically by using finite-difference methods. The numerical results show that the oxygen and water vapor concentrations in the gas channel are strong functions of stoichiometry. However, at a fixed stoichiometry, the current density has only a slight influence on the concentration variations. The fully-developed Sherwood number for oxygen mass transfer in the gas channel was found to be 6.0, which agrees well with the Sherwood number estimated from the correlation between mass and heat transfer. The current mathematical model and numerical results are confirmed by the experimental verification of the location of first appearance of liquid water at the channel/GDL interface.

Modeling of an anode-supported Ni–YSZ|Ni–ScSZ|ScSZ|LSM–ScSZ multiple layers SOFC cell: Part I. Experiments, model development and validation

This paper is the first part of a two-part paper and presents the development, calibration and validation of a two-dimensional isothermal mechanistic model of a composite yttria/scandia-stabilized zirconia anode-supported multiple layers solid oxide fuel cell (Ni–YSZ|Ni–ScSZ|ScSZ|LSM–ScSZ). This model was developed to describe the intricate interdependency among the ionic conduction, electronic conduction, multi-component species transport, electrochemical reaction processes and electrode microstructure for intermediate temperatures operation between 750 and 850 °C. This model takes into account the fact that the electrochemical reactions take place throughout the electrodes and not only at the electrolyte/electrode boundaries. The model was calibrated using experimental polarization curves and then validated by comparing each cell component polarizations (anodic, cathodic and electrolyte) determined from the simulation and from specific experiments using a symmetric cell and EIS measurements.

Multiphase Transport Phenomena in the Diffusion Zone of a PEM Fuel Cell

Abstract In this paper, a thorough model for the porous diffusion layer of a polymer electrolyte fuel cell (PEFC) is presented that accounts for multicomponent species diffusion, transport and formation of liquid water, heat transfer, and electronic current transfer. The governing equations are written in nondimensional form to generalize the results. The set of partial differential equations is solved based on the finite volume method. The effect of downscaling of channel width, current collector rib width, and diffusion layer thickness on the performance of polymer electrolyte membrane (PEM) fuel cells is systematically investigated, and optimum geometric length ratios (i.e., optimum diffusion layer thicknesses, optimum channel, and rib widths) are identified at decreasing length scales. A performance number is introduced to quantify losses attributed to mass transfer, the presence of liquid water, charge transfer, and heat transfer. Based on this model it is found that microchannels (e.g., as part of a tree network channel system in a double-staircase PEM fuel cell) together with diffusion layers that are thinner than conventional layers can provide substantially improved current densities compared to conventional channels with diameters on the order of 1 mm, since the transport processes occur at reduced length scales. Possible performance improvements of 29, 53, and 96 % are reported.

Detailed characteristic comparison between planar and MOLB-type SOFCs

Detailed comparisons of fluid flow, concentration, and electric fields between the planar solid oxide fuel cell (planar SOFC) and the mono-block-layer-built solid oxide fuel cell (MOLB-type SOFC) are made in the present study. A multi-physics model is developed to simulate the SOFCs of different geometries. The model couples the electrochemical kinetics with the fluid dynamics and multi-component species transport. Darcy's law governs the flow momentum in the porous electrodes. The Bruggman model depicts the diffusion of reactant species within the electrodes. The electrochemical kinetics and the species transport on the electrode surfaces is connected by the Butler–Volmer equation. Results show that the MOLB-type SOFC has a higher fuel/oxidant utilization than the planar SOFC. The high utilization of the fuel/oxidant reflects the high current through the SOFC.

Heat and mass transfer simulation of SiC boule growth by sublimation

ABSTRACTAn accurate modelling and simulation of the sublimation growth process needs a software taking into account a multitude of highly coupled phenomena: fluid mechanics, convective, conductive and radiative heat transfer, electromagnetic, multicomponent species transport, homogeneous and heterogeneous reactivity and finally thermal and transport databases. The objective of this paper is to combine modelling trends with experimental results to propose explanations and solutions to growth problems. Finally, a simple and generic mechanical approach will show the relations between the density of dislocations and the temperature field.

Electrokinetic Remediation. II: Theoretical Model

A mathematical model is presented for multicomponent species transport under coupled hydraulic, electric, and chemical potential differences. Mass balance of species and pore fluid together with charge balance across the medium result in a set of differential equations. Sorption, aqueous phase, and precipitation reactions are accounted by a set of algebraic equations. Instantaneous chemical equilibrium conditions are assumed. Transport of H + , OH − , Pb 2+ , NO-, the associated chemical reactions, electric potential, and pore pressure distribution across the electrodes in electrokinetic remediation are modeled. Model predictions of acid transport, lead transport, and pore pressure distribution display very good agreement with the pilot-scale test results validating the formalisms offered for multicomponent transport of reactive species under an electric field. The model also bridges the gap between the electrochemistry and mechanics in electroosmotic consolidation of soils.

Remark on algorithm perm

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.