Low Peclet number flow of a reacting mixture past an array of catalytic wires

Abstract

We describe the diffusion controlled combustion of a reacting mixture flowing past a two-dimensional array of catalytic wires, as a simple model for the flow through catalytic wire-meshes, of interest for small scale combustion devices. In order to minimize the reactant leakage when using only a few layers of wires, the Peclet number based on the upstream velocity, U, the spacing between the wires, l, and the thermal diffusivity of the mixture, D T, must be Pe=U l/D T≪1. Then, the flow field presents two distinct regions: a convective–diffusive region upstream of the wires, of scale l/Pe, and a reactive–diffusive region near the wires, of thickness of order l. Assuming first that the gas phase homogeneous reactions are frozen, the analysis provides the dependence of the downstream values of the temperature and the reactant mass fractions on the Peclet number, the Lewis number of the reactants, the temperature of the wires, and the ratio of the wire radius to the wire spacing. The analysis is then generalized to include the effect of the homogeneous reactions, showing that the rate of fuel consumption in the gas phase grows with the ratio of the adiabatic laminar flame velocity to the upstream flow velocity, the product of the Zeldovich number and the Peclet number, and the nondimensional temperature of the wires.