Focal ignition of a layer of metal powder

Abstract

Formulation of the Problem The following model is used to study theoretically the laws of ignition of bulk metal powders by an internal source in terms of such parameters as temperature, the size of the source, the pressure and concentrationof the oxidizer in the gas phase, the porosity of the powder, the filtration and diffusion coefficients, etc. At the center of the layer of metal powder there is a hot spot of size Rm which at the initial instant is at temperature To. The hot spot is surrounded by alayer of metal powder of radius ~ at the initial temperature T1o. The system (hot spot-powder) is in a gaseous medium, characterized by the constant pressure p2o and the relative mass oxidizer concentration a2o, at a temperature equal to the initial temperature of the metal powder. We are given the coefficient of heat transfer from the surface of the powder to the surrounding medium. During the reaction initiated by the internal source and proceeding at the surface of the metal particles, the oxidizer is consumed, and the temperature in the layer of powder increases, which leads to a mass flow of gas. At the center of the system (r = 0) we have adiabatic temperature conditions, at the hot spot-metal powder boundary (r = R ) adjoint boundary conditions, and at the metal powder-gas boundary (r = ~) boundary conditions of the third kind with allowance for heat transfer due to gas filtration. The system of equations describing this model takes the form: energy equation for the hot spot at 0 < r < R m