Asymptotic analysis of non-adiabatic flames: Heat losses towards small inert particles

Abstract

We study the propagation of a flame front into a heterogeneous mixture of dilute premixed reactive gas and small heat-conducting inert particles. Arrhenius kinetics are assumed for the reaction rate. The analysis is performed within the framework of a thermal-diffusional model for large values of the activation temperature of the reaction rate. First, steady propagations are studied. We show that: o (i) particles of small size (or heat capacity) act almost as a gaseous diluent: a monotonous flame speed versus particle concentration curve is obtained. (ii) with particle sizes exceeding well-defined critical values, up to three regimes are possible for the same fresh mixture. (iii) for particles with large thermal inertia, we again encounter the phenomenon of quenching by conductive losses towards isothermal bodies. In a second step, a linear stability analysis is performed by the normal modes method. We obtain the dispersion relation in terms of the Lewis number of the reactant, the activation temperature and the size and concentration of the particles, and show that: (iv) In case of multiple regimes, the intermediate ones are always unstable. (v) with a sufficiently high initial concentration of particles in the fresh mixture, the flame front always exhibits cellular instability. (vi) heavy particles promote the appearance of travelling waves, while light ones tend to suppress them.