Initiation and propagation of spherical premixed flames with inert solid particles

Abstract

Spherical flame initiation and propagation in particle-laden mixtures are investigated theoretically in this work. Within the framework of constant density, large activation energy and quasi-steady assumptions, a correlation describing spherical flame propagation speed as a function of flame radius is derived. This correlation is used to assess the influence of gas and particle properties on initiation and propagation of premixed spherical flames. Spherical flame initiation and propagation are shown to be influenced noticeably by the appearance of inert solid particles. It is found that the flame propagation speed and temperature both decrease with increased particle heat capacity and thermal relaxation time. A non-monotonic change of the flame propagation speed with flame radius is observed when there are particles with large heat capacity. Furthermore, the bifurcation of flame propagation speed is observed for particles with large heat capacity and thermal relaxation time. Within a certain flame radius range, there are both strong and weak flame solutions. The abrupt jump from the strong flame to weak flame results from the excessive heat loss caused by the solid particles and the energy balance is re-established along the weak flame branch. The Lewis number strongly affects the flame propagation speed, particularly for small thermal response time and high particle heat capacity. Additionally, the minimum ignition energy of the particle-laden spherical flames is found to increase with the Lewis number. At higher Lewis number, the difference of minimum ignition energy between gaseous and particle-laden situations becomes larger. To validate the theoretical results, one-dimensional transient simulations of particle-laden spherical flames with detailed chemistry have been conducted. Qualitative agreement is achieved for results from numerical simulations and theoretical analysis.