Suryanarayana R. Pakalapati

From a Single Cell to a Stack Modeling

A area (m2) B perimeter of the channel (m) as surface area of solid matrix for unit volume of mixed media (m−1) C product of mass flow rate and specific heat (J/s K) Cp specific heat at constant pressure (J/kg K) Cf friction factor cr condensation rate constant (s−1) e energy per unit mass (J/kg) E open circuit potential (V) E0 potential at standard state conditions (V) Ecor corrected potential (V) Em estimated modeling error F Faraday’s constant (Coulomb/mol), view factor (no units) f flux of a conserved scalar G Gibbs free energy (kJ/Kmol) H dimensionless height (m) h enthalpy (J/kg), grid size (m) hconv heat transfer coefficient (W/m2 K) I current (A) I current density vector i current density (A/m2) i0 exchange current density (A/m2) K permeability k thermal conductivity (W/m K), reaction rate coefficient (mole/m3 s) lw width of control volume (m) L cell length (m) l characteristic length (m) M molecular weight (gm/mole) ṁ mass flow rate (kg/s) ṁ′′ mass flux per area (kg/m2 s) ṁsurf net mass flux through surface (kg/s) n number of participating electrons, number of samples Nu Nusselt number

Effect of Channel Aspect Ratio on Planar SOFC Performance

The optimization process is in general an important issue to show the viability of solid oxide fuel cells (SOFCs) compared to traditional power sources. This optimization process can be done in a faster and cheaper way by making use of numerical simulations. In this study, three-dimensional, non-isothermal, steady state numerical simulations of planar solid oxide fuel cells (SOFC) are performed using the commercial FLUENT software. First, a detailed analysis of grid and iteration-dependent simulations is performed. This analysis predicts a 20% difference between a coarse and fine grid in the velocity magnitude in both anode and cathode gas flow channels, and in the y-component of current density. Then, the performance of a planar SOFC with changing channel aspect ratio is analyzed comparing their V-I curves and critical parameters like temperature, concentration, and current density distributions. The predictions show a 12 degrees difference in temperature at the fuel exhaust between low and high aspect ratio channel simulations. These results suggest that the channel aspect ratio is a significant parameter, worthwhile to be investigated.Copyright

Numerical Investigation of Rotating Detonation Combustion in Annular Chambers

This article presents two dimensional (2D) and three-dimensional (3D) computational analysis of rotating detonation combustion (RDC) in annular chambers using the commercial computational fluid dynamics (CFD) solver ANSYS-Fluent V13. The applicability of ANSYS-Fluent to predict the predominant phenomena taking place in the combustion chamber of a rotating detonation combustor is assessed. Simulations are performed for stoichiometric Hydrogen-Air combustion using two different chemical mechanisms. First, a widely used one-step reaction mechanism that uses mass fraction of the reactant as a progress variable, then a reduced chemical mechanism for H2-Air combustion including NOx chemistry was employed. Time dependent 2D and 3D simulations are carried out by solving Euler equations for compressible flows coupled with chemical reactions. Fluent user defined functions (UDF) were constructed and integrated into the commercial CFD solver in order to model the micro nozzle and slot injection system for fuel and oxidizer, respectively. Predicted pressure and temperature fields and detonation wave velocities are compared for the two reaction mechanisms. Curvature effects on the properties of transverse detonation waves are studied by comparing the 2D and 3D simulations. The effects of diffusion terms on RDC phenomena are assessed by solving full Navier-Stokes equations and comparing the results with those from Euler equations. Computational results are compared with experimentally measured pressure data obtained from the literature. Results show that the detonation wave velocity is over predicted in all the simulations. However, good agreement between computational and experimental data for the pressure field and transverse detonation wave structure proves adequate capabilities of ANSYS-Fluent to predict the main physical characteristics of RDC operation. Finally, various improvements for RDC modeling are postulated, particularly for better prediction of wave velocity.Copyright

A Micro-Scale Model for Oxygen Reduction on LSM-YSZ Cathode

In this study, a micro-scale model is developed to simulate the oxygen reduction on LSM-YSZ composite cathode. The model incorporates the effects of cathode microstructural properties on the local transport phenomena and electrochemistry inside the cathode. A detailed reaction mechanism is used in the model which has two parallel routes for oxygen conversion into oxide ions, namely two-phase boundary and three-phase boundary pathways. The model predicts field distributions of local thermodynamic values, over-potential, Faradaic current and other parameters relevant to cathode performance. Electrochemical impedance simulations are performed using the current model to analyze the contribution of various processes to the overall impedance.

Numerical Evaluation and Comparison of Different Reduced Mechanisms for Predicting the Performance of a SOFC Operating on Coal Syngas

Three-dimensional numerical simulations of an anode supported button solid oxide fuel cell were performed using the code developed in house DREAM SOFC. The cell operates on coal syngas at atmospheric pressure and 1073 K. A gas phase mechanism and a heterogeneous mechanism are studied in this work to assess their influence on the performance of the button cell. Both mechanisms take into account the steam methane reforming reaction and water gas shift reaction. The implemented electrochemistry model allows the cell to simultaneously electrochemically oxidize H2 and CO. Results show that methane reforming from the bulk reactions is negligible compared to the catalyzed reactions. Also with a higher reformation the power delivered by the cell is improved. A small temperature difference of one degree is observed when both mechanisms are compared. The electrochemistry model does not require the ratio between current produced from H2 and CO to be prescribed a priori as an input. Under the operating conditions used in this study the model predicts the ratio to be around 4 for both mechanisms.Copyright

Uncertainty Estimation for Numerical Solutions of Wall Bounded Turbulent Flows

In this study numerical solutions are presented for a steady state, incompressible, 2-D turbulent flow near a wall. For this specific problem a manufactured (exact) solution was provided by the organizers of the 2006 Lisbon Workshop [6]. With the help of manufactured solution, assessment of the true error and other relevant uncertainty measures are possible. The calculations were performed using the commercial flow solver FLUENT along with some user defined functions to define source terms and velocity profiles at boundaries. Though the flow regime is turbulent; the numerical solution is carried out for pseudo-laminar flow. This was done in order to avoid the errors implicit in turbulence models. The transformation from turbulent to laminar flow was done by defining a momentum source term which precludes the pressure gradient term. A detailed grid convergence analysis was performed. Using three-grid triplets the limiting values of the variables solved as the grid size tends to zero were calculated using different extrapolations. The L2 norms of the true error obtained from various extrapolations are assessed. These results exhibit solution convergence as the grid size decreases. It was also shown that cubic spline extrapolation perform the best among the methods considered.© 2006 ASME

Implications of Using Dual Number Derivatives With a Numerical Solution

Dual number arithmetic is a well-known strategy for automatic differentiation of computer codes which gives exact derivatives, to the machine accuracy, of the computed quantities with respect to any of the involved variables. A common application of this concept in Computational Fluid Dynamics, or numerical modeling in general, is to assess the sensitivity of mathematical models to the model parameters. However, dual number arithmetic, in theory, finds the derivatives of the actual mathematical expressions evaluated by the computer code. Thus the sensitivity to a model parameter found by dual number automatic differentiation is essentially that of the combination of the actual mathematical equations, the numerical scheme and the grid used to solve the equations not just that of the model equations alone as implied by some studies. This aspect of the sensitivity analysis of numerical simulations using dual number auto derivation is explored in the current study. A simple one-dimensional advection diffusion equation is discretized using different schemes of finite volume method and the resulting systems of equations are solved numerically. Derivatives of the numerical solutions with respect to parameters are evaluated automatically using dual number automatic differentiation. In addition the derivatives are also estimated using finite differencing for comparison. The analytical solution was also found for the original PDE and derivatives of this solution are also computed analytically. It is shown that a mathematical model could potentially show different sensitivity to a model parameter depending on the numerical method employed to solve the equations and the grid resolution used. This distinction is important since such inter-dependence needs to be carefully addressed to avoid confusion when reporting the sensitivity of predictions to a model parameter using a computer code. A systematic assessment of numerical uncertainty in the sensitivities computed using automatic differentiation is presented.Copyright

A Continuity Outlet Boundary Condition for the Lattice Boltzmann Method

A continuity outlet boundary condition for the Lattice Boltzmann Method (LBM) is proposed based on the assurance of the mass conservation of the system. The main advantage of the proposed boundary condition over the conventional Computational Fluid Dynamics (CFD) techniques is that the macroscopic properties, e.g. velocity, pressure etc. are not needed to be prescribed at the outlet, these properties are automatically calculated with the imposed boundary condition. This is especially useful in practice where the macroscopic properties at the outlet are difficult or impossible to be measured and described as in the biological flows. In order to test the feasibility of the proposed method, the LBM simulations are first verified for its capability to simulate flow in a symmetrically bifurcated channel. Then asymmetrically bifurcated geometries representing the blood vessels have been designed with different bifurcation angles. The new boundary condition is also tested for multi-component LBM simulations. For these cases, LBM predictions have been compared with the predictions for the commercial CFD software, namely ANSYS FLUENT at different Reynolds numbers. The results show that there is a good agreement between the LBM and FLUENT predictions, and this proves the capability of the proposed boundary condition as a viable method that can be used in practice.Copyright

Direct Simulation of Mass Transport in a SOFC Cathode Using Microchannels

Fuel cells are clean and efficient power generation devices which are being widely investigated under the efforts to reduce the impact of greenhouse gases on the environment. Solid oxide fuel cells (SOFCs), especially, are suitable for stationary power generation using a wide range of alternative fuels. Performance of a SOFC strongly depends on the mass transport inside the porous electrodes which are essentially composed of a network of microchannels. In this study the mass transport inside a SOFC cathode is studied using direct simulation of mass transport in microchannels along with statistical analysis. A virtual cathode is built using microchannels that are representative of continuous flow paths between the cathode/air stream interface and cathode/electrolyte interface of a SOFC. Different representative microchannel flow paths are built with varying tortuosity and channel diameters. The numbers of channels of each kind are chosen according to a normal distribution and they are randomly arranged in an appropriately sized cuboid to construct a unit block of the virtual cathode. The normal distribution is modulated with average and standard deviation values for real world electrodes found in literature. Microchannels are tightly packed to achieve the desired porosity. Mass transport in each of the channels is studied separately using commercial CFD software FLUENT. Three dimensional simulations of momentum and specie transport equations (for oxygen and nitrogen) are performed. The results from individual channel simulations are used to assess the global mass transfer characteristics of the virtual cathode. Results obtained using this approach will be compared with those from a continuum Fick’s law type diffusion model used to simulate mass transport in porous media. The primary objective is to test the assumptions employed within the context of continuum mass transport model.Copyright

Comparison of a Multi-Dimensional Model With a Reduced Order Pseudo Three-Dimensional Model for Simulation of Solid Oxide Fuel Cells

Numerical modeling has helped the SOFC research for over a decade in which period the models grew in complexity and detail. Multi-dimensional detailed models such as FLUENT’s SOFC module calculate three dimensional distributions of velocity, temperature, concentration and electric potential inside all components of the fuel cell. Such models while being very helpful in understanding the processes inside the fuel cell may prove to be very expensive for transient simulations and simulations of multi-cell stacks. Hence reduced order modeling is still used for such applications. However, reduced order modeling entails reduction of detail and consequent loss in accuracy. In this paper a multi-dimensional SOFC code, FLUENT’s SOFC module, is compared with a reduced order pseudo three-dimensional model, DREAM SOFC. FLUENT’s SOFC module is a commercial solver built on the popular CFD solver FLUENT. DREAM SOFC is an in house code developed at Computational Fluid Dynamics and Applied Multi Physics (CFD&) Center at West Virginia University. It is a combination of a one dimensional model for channels and three-dimensional models for the rest of the components in a SOFC. This approach avoids having to solve Navier-Stokes equations inside channels but still retains the three-dimensionality inside important components. Same test cases with similar conditions are simulated with these codes and results are compared with each other.Copyright