Ignition and combustion of magnesium particles in a nonuniform thermal field

Abstract

A distributed two-dimensional mathematical model of ignition and combustion of magnesium particles with allowance for the heterogeneous chemical reaction and for the region of the thermal influence of the particle on the gas is developed. Problems of particle ignition under the action of uniform and nonuniform thermal fields in a rectangular microchannel are solved.

Modeling of combustion of a magnesium particle (Stefan Problem)

“…Results on particle ignition calculated by the authors by the distributed mathematical model were discussed in detail elsewhere [2][3][4]. In the present paper, therefore, we focused our attention on result of solving a complex problem of ignition and combustion in formulation (1)- (8).…”

“…approaches make it possible to describe one or two integral parameters and provide a qualitatively correct description of the behavior of other parameters induced by variations of the input parameters of the system, such as the particle radius and ambient temperature. In our opinion, a promising approach is construction of adjoint mathematical models that can correctly describe several integral parameters within the framework of a unified approach [2][3][4].…”

“…As was shown in [2][3][4], the process of ignition (combustion) in the proposed distributed mathematical model starts at the particle boundary, after which the temperature field of the particle becomes equalized rather rapidly: T 2 = T m (T 2 = T b ) (the time of temperaturefield equalization is fractions of a percent of the ignition delay). This circumstance allows us to model the particle combustion stage as a single-phase Stefan problem, namely, to assume that T 2 = T b = const, and the distribution of the temperature T 1 at the beginning of combustion is determined by solving problem (1)- (7).…”

“…Fedorov et al [1] mainly presented point models and partly one-dimensional unsteady models of ignition of small metal particles, where the process of low-temperature oxidation occurs on the particle surface. The processes of ignition under the conditions of nonuniform thermal loads were studied in [2][3][4]; in particular, distributed mathematical models of ignition of a magnesium particle with allowance for a heterogeneous chemical reaction and the area of the thermal influence of the particle onto the gas in one-dimensional and two-dimensional formulations of mechanics of reacting media were proposed. An adjoint mathematical model that takes into account both ignition and combustion of the metal particle was constructed in [4].…”

“…The processes of ignition under the conditions of nonuniform thermal loads were studied in [2][3][4]; in particular, distributed mathematical models of ignition of a magnesium particle with allowance for a heterogeneous chemical reaction and the area of the thermal influence of the particle onto the gas in one-dimensional and two-dimensional formulations of mechanics of reacting media were proposed. An adjoint mathematical model that takes into account both ignition and combustion of the metal particle was constructed in [4]. The process of particle combustion was modeled by the law of d 2 (Sreznevskii's law), i.e., the combustion-front boundary was assumed to change in accordance with an empirical law of the form d 2 − d 2 0 = −αt, where d and d 0 are the current and initial diameters of the drop, α is the heat-transfer coefficient, and t is the time of evaporation.…”