Edward J. Bissett

Mathematical model of the thermal regeneration of a wall-flow monolith diesel particulate filter

Abstract A wall-flow monolith filter placed in the exhaust stream of a diesel engine can effectively limit the emission of diesel particles through the monolith. The accumulated particles can then be periodically combusted inside the monolith by directing hot gas from a fuel burner to the monolith while the normal engine exhaust is routed around the burner/monolith system. The resulting low flow rates through the monolith require consideration of gas dynamics through the channels as well as particle combustion to analyze this regeneration process. A mathematical model of the regeneration is formulated as a system of nonlinear partial differential equations describing the conservation of mass, momentum and energy. Numerical solutions are obtained by using a combination of finite element and finite difference techniques for the spatial discretization and using an implicit ordinary differential equation solver for the resulting time integration. A detailed discussion of the solution for a sample regeneration is given.

A three-dimensional model for the analysis of transient thermal and conversion characteristics of monolithic catalytic converters

A transient three-dimensional model has been developed to simulate the thermal and conversion charasteristics of nonadiabatic monolithic converters operating under flow maldistribution conditions. The model accounts for convective heat and mass transport, gas-solid heat and mass transfer, axial and radial heat conduction, chemical reactions and the attendant heat release, and heat loss to the surroundings. The model was used to analyze the transient response of an axisymmetric ceramic monolith system (catalyzed monolith, mat, and steel shell) during converter warm-up, sustained heavy load, and engine misfiring

Electrically heated converters for automotive emission control: determination of the best size regime for the heated element

Abstract In view of the significant cold-start hydrocarbon emission reduction potential of the electrically heated converter (EHC) technology demonstrated in recent studies, there is considerable interest in better understanding the behavior and design aspects of an EHC during the cold-start portion of actual vehicle emission tests. Computer simulations based on the EHC model developed previously (Oh et al., 1993, Industrial and Engineering Chemistry Research 32, 1560–1567) show that although decreasing the volume of an electric heater generally improves the emission performance of the EHC system, there is a critical heater volume below which no significant emission benefit is obtained. This paper examines the EHC sizing issue in more detail by analyzing a simplified version of the EHC model to investigate why the emission benefit of decreasing electric heater volume eventually disappears and how the critical heater volume where this occurs is related to system parameters. Analysis of the simplified EHC model identifies this critical volume, V h , which is proportional to the exhaust flow rate through the EHC and inversely proportional to the product of the interphase (gas–solid) heat transfer coefficient within the heated element and its geometric surface area per unit volume. It is shown that the recommended heater size regime must be where the physical heater volume, V , and V h are comparable in magnitude. When V ≫ V h , the electric heater is clearly too large because the emission performance suffers from the slow heat-up rate caused by the large thermal mass. Also, decreasing the heater volume to values much smaller than V h (i.e., V ≪ V h ) is not desirable because it would simply lead to unnecessarily higher (potentially damaging) solid-phase temperatures without producing additional emission reductions. In this smallest size regime, the emission performance of the EHC system becomes insensitive to heater size variation because the higher solid-phase temperatures within the smaller heater tend to be compensated by its poor interphase (solid-to-gas) heat transfer arising from the insufficient heat transfer area available.

Thermal regeneration of particle filters with large conduction

Abstract Singular perturbation techniques based upon large conductivity are used to analyze model equations for the regeneration of a combustible-particle filter. Analytical formulas are derived for two orders of the solution of the nonlinear system of partial differential equations with a free boundary. These formulas require the numerical solution of just two systems of second order ordinary differential equations, only one of which is nonlinear. Initial conditions for the linear system require a separate solution during the initial time period and asymptotic matching. Results confirm the absence of substantial spatial temperature gradients through the particle⧸substrate system as suggested by previous zeroth order calculations. The first order terms obtained here can be used to estimate the accuracy of the zeroth order terms or, if necessary, to refine the results of the zeroth order calculation.

Analysis of a nonadiabatic flame propagating through gradients of fuel or temperature

Using the analytic techniques of large activation energy asymptotics applied to a slowly-varying flame, an equation is derived that describes the burning rate of an unsteady nonadiabatic flame traveling through shallow gradients in fuel concentration or temperature. Solutions of this equation show that (1) the transient burning rate responds more slowly to these gradients than does the local steady-state burning rate, (2) an unsteady flame in an inhomogeneous mixture propagates into a region where the mixture is outside of the homogeneous flammability limits predicted by the steady theory, and (3) the burning rate of the unsteady flame approaches zero at a finite position in the gradient, even with a single-step Arrhenius reaction mechanism. This behavior arises from the accumulation, of enthalpy in the preheat zone, which in turn arises from the differing rates of heat conduction and mass diffusion.

Automotive applications of chemical reaction engineering and future research needs

The stricter future emission standards require further improvement in emission control performance through the optimization of catalytic converter properties and its operating conditions. The single-channel 1-D monolith model has been used extensively at GM to guide the development and implementation of emission control systems with improved cold-start emission performance while reducing the noble metal usage and hardware development time/iterations. This paper discusses some examples of model applications to three-way catalyst systems as well as future research needs and directions in emission control system modeling, including the development of elementary reaction step-based kinetic models.

The Extinction of Slowly-Varying Nonadiabatic Flames

Abstract Using the techniques of large activation energy asymptotics, we observe that a slowly-varying planar nonadiabatic flame will extinguish (1) as the burning rate approaches zero, rather than at finite burning rate as predicted by the steady theory, and (2) at a finite position, when subjected to a wide class of external stimuli. An example is given in which the external stimuli arises from either fuel or concentration variations ahead of the flame.