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DOI: 10.1615/ICHMT.1995.RadTransfProc.540

Petr M. Krishenik
Institute of Structural Macrokinetics Russian Academy of Sciences, Chernogolovka, Moscow Region, 142432 Russia

Konstantin G. Shkadinskii
Institute of Structural Macrokinetics Russian Academy of Sciences, Chernogolovka, Moscow Region, 142432 Russia


Combustion of dust/air mixture is studied with account of convective, radiative and conductive heat transfer. A two-temperature, one-velocity mathematical model is proposed for the analysis of the unsteady processes occurring in exothermic reactions during propagation of the combustion in the dust/air mixture in an enclosed volume. Temperatures of the particles and gas are assumed to be different. The radiative heat transfer is described by the diffusion approximation. Convective velocity of the mixture is small compared to the velocity of sound and the Mach number M is taken to be M << 1. The pressure of gas is uniform on space (homobaric flow) and only depends on time. We follow this since the high-frequency perturbations are absent and the velocity of gas is small compared to the velocity of sound.
In addition it was assumed that the velocity of the gas is equal to the velocity of particles. The system of differential equations is examined in Lagrangian form. The solutions of differential equations are characterized by two different characteristic time and spatial dimensions. This results in the formation of the time and spatial dimensions boundary layers of a complicated structure that changes with variation parameters. Numerical solution involves an adaptive implicit, finite difference scheme.
Depending on the characteristics of the condensed matter (the sizes and the ignition temperature of the particles, a kinetic law of heterogeneous reaction), modes of unsteady process of combustion for the suspension are investigated. Our theoretical studies are focused on the dynamic regime of combustion two-phase medium. The unsteady combustion regime is determined by combination of the following factors: radiative, convective and conductive heat transfer. If the chemical reaction is accompanied by the intense gasification of condensed phase and the radius of particles exceed the critical value , then the maximum temperature of particles, front velocity and velocity of convective flow increase. At the stage of formation of combustion processes the convective heat transfer results in a decrease of combustion wave velocity. Transition from slow conductive combustion to the fast radiative one has an explosive character.
If the chemical reaction is accompanied by consumption the gaseous oxidizer, then the rate of heterogeneous reaction, the velocity of combustion wave and maximum temperature of particles decrease. If the particle size is smaller than the critical one, the convective flux leads to an increase duration of time initiation and in limiting case this time tends to infinity.

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