Asymptotic analysis of the shock wave ignition of dust particles

Abstract

The critical energy required to initiate dust detonations in tubes of finite diameter depends on the structure of the reaction zone, and especially upon the length of the induction zone, which, in turn, is determined by the ignition delay time of the dust particles. To establish the induction zone length in dust detonations, the shock wave ignition of dust particles was investigated theoretically. In the theoretical model the particle acceleration, subsequent convective heating by the hot gas flow, and chemical exothermic surface reaction in the pores as well as on the surface of the particle were considered. An asymptotic analysis for the limit of large activation energy was carried out for spherical particles with constant average values of the gas recovery temperature and the convective heat transfer coefficient. A formula for calculating the ignition delay times was determined and the asymptotic results were compared with a numerical solution of the governing equations and with experimental ignition delay data for coal dust.