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In this paper results of parallel computer simulations on aluminum dust ignition behind a re ected shock wave are presented. Computations show the time-evolution of a complicated ow ÿeld created due to a shock wave collision with a pile of dust, shock re ection from a wall, and its interaction with vortices. Particles, blown away by the incident shock, are heated mainly behind the re ected shock wave. The estimated ignition delay time is of the order of 80 -100 s and is a strong function of the incident shock wave strength. The simulations show that it may be very di cult to ignite aluminum particles when the incident shock wave Mach number is smaller than about M s ≈ 3, while for stronger shocks the estimated ignition delay time quickly decreases.

We present a parametric analysis of a combustion model developed for computer simulations of detonation waves propagating in aluminum-dust-oxygen two-phase mixtures. In this model, consumption of solid and liquid aluminum is limited by its evaporation rate, and, depending on a gas-phase temperature, the fuel can be burned into aluminum oxide or aluminum monoxide. The model is applied for one-dimensional simulations of detonation waves. We analyze the influence of various factors on characteristic parameters of the detonation and compare computed results with those of other models and experimental data. The analyses show a qualitative agreement of the computed results with the Chapman-Jouguet detonation model. A combustion model and an initial solidphase concentration significantly influence the computed solutions. Specifically, a decomposition temperature has a strong effect on the system, because it limits the energy release in the combustion process. An initial particle diameter (with an exception of very fine dust) and an ignition temperature have no influence on the propagation of the detonation waves but are limiting factors for their development. Nomenclature B= universal gas constant C pk = kth species specific heat at constant pressure (k = 1, . . . , n s ) C vs = solid-phase specific heat C x = drag force coefficient c s = solid-phase concentration D = detonation wave velocity D CJ = Chapman-Jouguet detonation wave velocity d = average particle diameter d 0 = initial particle diameter E l = lth phase total specific energy (thermal and kinetic) e l = lth phase specific internal energy (thermal) (l = g, s, where g is gas and s is solid) F = vector of fluxes f = particle breakup (agglomeration) rate, 1/s h = interphase heat transfer factor kg/s 3 · m · K h f 298g k = kth species heat of formation h f 298s = solid-phase heat of formation K r = combustion rate constant, s/m 2 Ma = Mach number M g = average molar mass of gaseous mixture N p = particle number density, 1/m 3 N u = Nusselt number n s = species number p CJ = Chapman-Jouguet detonation pressure p g = gas pressure p vN = peak pressure (von Neumann spike) Re = Reynolds number S = vector of source terms T dec = aluminum oxide decomposition temperature T ign = ignition temperature= kth gaseous species mass fraction c = interphase mass exchange factor, kg/s · m 3 c k = kth species interphase mass exchange factor, kg/s · m 3 δ = interphase drag force factor, kg/s · m 3 λ g = gas-phase heat conduction coefficient π = 3.1415927 . . . ρ g k = kth species partial density ρ l = lth phase material density τ = characteristic combustion time φ s = solid-phase volume fractioṅ ω k = kth species production (consumption) rate due to homogeneous chemical reactions Subscripts CJ = Chapman-Jouguet point g = gas phase k = gaseous species index l = phase index s = solid phase vN = von Neumann spike

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