RADIATION-AFFECTED DYNAMICS OF UNCONFINED SPHERICAL FLAMES IN PARTICLE-LADEN PREMIXTURES

We consider unconfined spherical flames which expand into reactive gas eous premixtures that are laden with inert solid particles. An overall one-step Arrhenius reaction is adopted as burning process and the rad iative transfer among the emitting/absorbing particles is modeled by a differential approximation of the Eddington type. The formulation acc ounts for the differences in velocity and temperature between the phas es. The system is analyzed by matched asymptotic expansions in a multi ple-limit process which assumes large Zel'dovich numbers (activation t o reaction temperature ratio); small Boltzmann numbers (radiant to con vective heat flux ratio), small loading (solid to gas heat capacity ra tio) by the particles and optically very thin flame fronts. Three main regions can then be distinguished in the flowfield: a thin reaction z one (dominated by molecular transports and reaction)embedded in a thic ker quasi-steady flame-front region (dominated by molecular transports , convection and affected by conductive exchanges between the phases): the latter is itself flanked by even thicker, unsteady radiation-zone s (dominated by radiative transfer and convection). We analytically sh ow that, even for polydisperse particle-clouds, tabulating a one-param eter function once for all allows one to obtain an integral equation f or the flame speed evolutions; the evolution equation is then solved n umerically. Depending on the mixture and/or initial conditions, the in terplays among nonlocal radiative-transfer, chemical nonlinearity, as well as momentum and conductive gas/particle exchanges, lead to smooth or abrupt flame accelerations, everlasting relaxation oscillations in fame speed or transient ones. Cases of trajectory multiplicity are al so encountered.