CRITERION FOR IGNITION OF A FUEL MIXTURE BY ACOUSTIC STREAMING

Abstract

The ignition of a fuel mixture enclosed between two horizontal walls, which are kept at the same constant temperature, is considered. A first-order Arrhenius reaction with large activation energy represents the chemistry and accounts for the reactant depletion. The Frank–Kamenetskii parameter is assumed small and a thermal explosion is not expected without the intervention of some external source. A standing plane sonic wave is imposed in the longitudinal direction, and Rayleigh-type vortical acoustic streaming that appears in the region induces forced heat convection. The effect of this convection in the presence of the heat sources, which represent the chemical reaction, is analyzed. The Lewis number is assumed equal to unity. A criterion for the ignition of the fuel mixture by acoustic streaming is obtained in terms of an inequality involving characteristic dimensionless parameters, that is, the Frank–Kametetskii parameter, the dimensionless combustion temperature, and the streaming Reynolds number. The latter is proportional to the frequency of the oscillations. It is shown that the streaming Reynolds number necessary to induce ignition increases as the distances between the walls of the channel decrease.

Keywords:

• acoustics
• fuel
• ignition
• mixture
• streaming

Acknowledgments

This research was supported by the Fund for Promotion of Research at Technion—Israel Institute of Technology and by Israel Science Foundation Grant no. 034-162.