RADIATION-AFFECTED DYNAMICS OF ENCLOSED SPHERICAL FLAMES PROPAGATING IN PARTICLE-LADEN PREMIXTURES

We study flames expanding radially from the center of a spherical encl osure which is initially filled with a two-phase premixture: premixed reactive gases and an inert solid suspension. An overall Arrhenius rat e is postulated for the burning process, and the radiant exchanges amo ng the particles is assumed to follow an Eddington differential equati on specialized to a grey continuous medium. Different temperatures and velocities are allowed for each phase. Transfers to the walls and hea ting by compression are also accounted for. The problem is analysed by asymptotic methods in a multiple-limit procedure which assumes large Zel'dovich numbers (activation to reaction temperature ratio), small B oltzmann numbers (radiant to convective heat-flux ratio), small loadin gs by the particles, optically very thin flame fronts and specific-hea t ratios in the gas phase that are close to unity. We analytically red uce the whole problem to a single integral equation for the burning sp eed as a function of the fireball radius. Upon numerical integration t he evolution equation yields the front burning speed histories. It is shown that: a) Compression of the fresh medium often yields a dominant source of flame-speed increase, especially at the end of the propagat ion. It also tends to screen the radiant exchanges with the wall signi ficantly. b) The optical properties of the wall only affect the propag ation at the end of the process if the container is large. For small v essels, radiative preheating is thoroughly weak. c) Mainly through hyd rodynamics and compression, the confinement modifies the flame traject ories qualitatively; e.g., it often favors the appearance of jumps in burning speed. In any case, quantitative modifications are brought abo ut.An overall conclusion is that straightforward extrapolations from s mall-scale experiments in enclosures to unconfined explosions do not c onstitute a safe procedure.