William J. Wepfer

A Mathematical Model of a Solid Oxide Fuel Cell

A mathematical model of a tubular solid oxide fuel cell is presented. The complete electrochemical and thermal factors are accounted for in a rigorous manner. All required parameters are determined from independent sources; none are fit from performance data. To verify the accuracy of the model predictions, comparison is made with single cell test data from Westinghouse. Agreement with electrochemical and thermal results are within 5%, and for most points, much better. Predictions are shown for power-voltage, irreversibilities, and temperature and current distributions under various conditions.

Ramp wave analysis of the solid/vapor heat pump

A thermally driven heat pump using a solid/vapor adsorption/desorption compression process in a vapor compression cycle is thermodynamically analyzed. The cycle utilizes a simple heat transfer fluid circulating loop for heating and cooling of two solid adsorbent beds. This heat transfer fluid loop also serves to transmit heat recovered from the adsorbing bed being cooled to the desorbing bed being heated. This heat recovery process greatly improves the efficiency of the single-stage solid/vapor adsorption process without the complication of a two-stage cycle. During the heating and cooling processes a thermal wave profile travels through the beds. Previous studies of this cycle used a square wave model to simulate the thermal wave front. This paper utilizes a more physically realistic ramp wave model to overcome the shortcomings of the square wave model. The ramp wave model is integrated into a thermodynamic cycle which provides detailed information on the performance of the beds as well as the COP and the heating and cooling outputs of the heat pump system. Significant cycle design and operating parameters are varied to determine their effect on cycle performance.

Square wave analysis of the solid-vapor adsorption heat pump

Abstract A thermally driven heat pump using a solid/vapor adsorption/desorption compression process in a vapor compression cycle is thermodynamically analyzed. The cycle utilizes a simple heat transfer fluid circulating loop for heating and cooling two solid adsorbent beds. This heat transfer fluid loop also serves to transmit heat recovered from the adsorbing bed being cooled to the desorbing bed being heated. This heat recovery process greatly improves the efficiency of the single stage solid/vapor adsorption process without the complication of a two stage cycle. During the heating and cooling processes a thermal wave profile travels through the beds. This paper uses a square wave representation for the true shape of the thermal wave. However, this square wave is assumed to stop short of the bed ends to account for realistic finite waveforms. The square wave model is integrated into a thermodynamic cycle which provides detailed information on the performance of the beds as well as the COP and the heating and cooling outputs of the heat pump system. Significant cycle design and operating parameters are varied to determine their effect on cycle performance.

Characterizing heat transfer within a commercial-grade tubular solid oxide fuel cell for enhanced thermal management

A thermal transport model has been developed for analyzing heat transfer and improving thermal management within tubular solid oxide fuel cells (TSOFCs). The model was constructed via a proven electrochemical model and well-established heat transfer correlations. Its predictions compare favorably with other published data. Air temperatures consistently approach that of the fuel cell. This is primarily due to the high operating temperature of the cell (1000°C), the moderate magnitudes of radiation and airflow, and cell geometry. The required inlet air temperature (for thermally steady-state operation) has linear dependence on operating voltage and fuel utilization. Inlet air temperature has an inverse proportionality with respect to air stoichiometric number (i.e., inverse equivalence ratio). The current standard for airflow within TSOFCs was found to be excessive in consideration of the regenerative preheat effect within the supply pipes that feed air to the cell. Thermal management of simple TSOFC systems could be enhanced if commonly used air stoichiometric numbers were decreased.

‘Design for power’ of a commercial grade tubular solid oxide fuel cell

Abstract Fuel cell systems must not only be thermodynamically efficient, but cost competitive as well. Since power plant capital costs are typically measured per unit of rated power (i.e.,

Jet impingement drying of a moist porous solid

/kW), one means of attempting an economically attractive product is to “design for power”. A proven model of a commercial grade tubular solid oxide fuel cell (TSOFC) is presented and verified. The model was used to reveal subtle aspects of enhancing power generation. Internal reformation, while beneficial to system size and integration, hinders power generation. Increasing the electrode thicknesses of the TSOFC design can be beneficial to power generation. Finally, decreasing fuel utilization, at a prescribed operating voltage, is also favorable for power generation. These latter trends are explained in view of the common assertions that thinner electrodes and increased fuel utilizations are the means of fuel cell operation enhancement.

A mathematical model of a tubular solid oxide fuel cell

Abstract This paper investigates the thermal characteristics of a continuous industrial drying process for semi-porous textile composites. The conservation of mass, momentum and energy are written for a partially saturate porous fiber layer attached to a solid-backing layer. The numerical solution of the one-dimensional and transient conservation equations provides the temperature, volumetric saturation and gas phase pressure distributions in the moist porous solid and the temperature distribution in the solid-backing layer. During the wet region drying period, continuous liquid exists in the pore space, the moisture transport within the solid is described by the Darcy form of the momentum equation. The moisture transport in the sorption region is described by a bound liquid diffusion and gas phase transport. For the jet impingement type dryer, it is assumed that the penetration of the flow field into the porous solid is small (assumed valid due to the presence of the solid backing). The enhanced transport coefficients at the drying surface are estimated with the use of the Kolmogoroff theory of isotropic turbulence. This theory provides correlations for the heat and mass transfer coefficients from the fluid properties and the turbulent energy dissipation rate in the fluid. The model results of the continuous industrial drying process are compared to independent experimental temperature and global moisture content measurements taken in an operational industrial dryer. From the model analysis and experimental data, the heat flux conditions at the drying surface dictate the manner in which the solid is dried. The heat transfer coefficients considered are in the range of 20–130 W m−2K−1 and necessarily affect the manner in which moisture transport occurs within the solid. It is seen that the lower heat transfer coefficients more accurately represent the internal transport phenomena occurring during the drying process and the heating of the solid. The transport coefficients are compared to previously obtained empirical results.

EXTERNAL FLUID HEATING OF A POROUS ED

The solid oxide fuel cell shows great potential as an efficient energy conversion system for use in central power stations. These cells can reform most hydrocarbon fuels with air to produce electricity and provide a heat source at 1,000 C while maintaining an efficiency of 60--75 percent. This paper describes a steady-state model for the prediction of voltage, current, and power from a single-cell tube. The model is a distributed parameter electrical network that includes the effects of mass transfer resistance (concentration polarization), chemical kinetic resistance (activation polarization), as well as relevant electrical resistance (ohmic losses). A finite-difference heat transfer model is also incorporated to allow for radial and axial temperature variations. The model computes the fuel and oxidant stream compositions as functions of axial length from energy and mass balances performed on each cell slice. The model yields results that compare favorably with the published experimental data from Westinghouse.

Enhancing the Performance Evaluation and Process Design of a Commercial-Grade Solid Oxide Fuel Cell via Exergy Concepts

This work deals with the thermal analysis of externally heated porous beds of finite length. A one dimensional model was developed that includes conduction and storage in both the fluid and bed, convective exchange between the fluid and bed, and the effect of adsorption/desorption in the bed. This model results in two coupled differential equations for the fluid and bed temperatures as functions of four independent dimensionless parameters. These equations were solved numerically using finite difference approximations. A truncation error analysis was carried out to maintain an accurate solution. The method of normalization is such that the results of this analysis are of use in bed design when the breakthrough characteristics in finite length beds are of interest. A method to measure bed thermal performance is defined and a means to optimize bed thermal performance is presented. An experiment was conducted to validate the numerically obtained results. A comparison of numerical to experimental results is p...

Electrochemical and thermal simulation of a solid oxide fuel cell

Fuel cell technology is a promising means of energy conversion. As the technology matures, process design and analysis are gaining importance. The conventional measures of fuel cell performance (i.e., gross real and voltage efficiencies) are limited indices-of-merit. Contemporary second law concepts (availability/exergy, irreversibility, exergetic efficiency) have been used to enhance fuel cell evaluation. A previously modeled solid oxide fuel cell has been analyzed using both conventional measures and the contemporary thermodynamic measures. Various cell irreversibilities were quantified, and their impact on cell inefficiency was better understood. Exergetic efficiency is more comprehensive than the conventional indices-of- performance. This parameter includes thermal irreversibilities, considers the value of effluent exergy, and has a consistent formulation. Usage of exergetic efficiency led to process design discoveries different from the trends observed in conjunction with the conventional efficiency measures. The decision variables analyzed were operating pressure, air stoichiometric number (inverse equivalence ratio), operating voltage and fuel utilization.