Theory of Ignition of Gas Suspensions

Abstract

The analytical method of calculation of the critical size of the hot spot is created for greater values of a coefficient of heat exchange of particles and gas. By means of numerical calculations the functional dependence of the critical size of the hot spot on parameters following from the theory is validated; the range of applicability of approximate formulas is determined. Two mechanisms of the ignition of gas suspension by the hot spot are revealed for the first time

• (a) ignition of gas suspension as ignition in quasi-homogeneous single-temperature medium;

• (b) ignition of particles in the center of the hot spot due to violation of thermal balance between the rate of heat allocation from a particle and heat dissipation into the gas.

It is shown that the value of the minimum energy of ignition does not practically depend on the mass concentration of particles in gas suspension at a constant value of initial temperature $\theta_{\text{in}}$. The method of calculation of the critical size of the hot spot $R_{\text{cr}}$ can be used for determination of $R_{\text{cr}}$ for the complex mechanism of interaction of particles with oxidizer (parallel, consecutive, independent reactions). Various mechanisms of critical phenomena for the kinetic and diffusion modes of ignition at pulse energy supply are established. At greater values of a heat exchange coefficient Z (a kinetic ignition mode) the critical duration of an impulse is equal to the time of establishment of a zero gradient on a border: a heater—gas suspension. At small values of a heat exchange coefficient Z (a diffusion mode of an ignition) the critical duration of an impulse is less than $\tau_{0}$ and is found from the equality $\tau_{1} = \tau_{2}$. Here $\tau_{1}$—the time of complete burning out of particles at the dimensionless coordinate $\xi = 0$, and $\tau_{2}$—the ignition time (transition to the diffusion mode of a reaction) of particles at $\xi \to \xi_{\text{g}} + 0$. The expressions allowing to determine necessary and sufficient conditions of the ignition of gas suspension by a heated body at pulse energy supply are obtained. Numerical calculations showed a possibility of application of approximate formulas for determining of minimum duration of an impulse necessary for the ignition of gas suspension. By means of numerical calculations, it is established that the minimum time required to attain the high-temperature combustion mode is reached at $\tau_{\text{pul}} = \tau_{0}$. The investigation described allows calculating the minimum energy of ignition of hybrid gas suspension (oxidizer + combustible gas + combustible particles) with a hot spot using the data on the kinetics and thermal effects of gas-phase and heterogeneous reactions as well as on the amount of condensed phase in a unit of volume. The results of such calculation are necessary for the creation of safe conditions for carrying out technological processes, in which suspensions of combustible particles in gas containing oxidizer and small additives of combustible gas are formed. It was experimentally shown that at 650–750 °C coal gas suspension containing stoichiometric mixture of natural gas and the air does not burn over surface coated with coal powder due to inhibiting effect of gases evolving during thermal treatment of coal powder. The ignition of that gas suspension can be promoted with small amounts of chemically active additive (e.g., dichlorosilane). Thus, we can conclude that the improved model of ignition of gas suspension of solid particles in a mix oxidizer—combustible gas must take into account both inhibiting effect of gases evolving during thermal treatment of coal powder and the branched chain mechanism of gas combustion. However, in the presence of small quantities of methane (lean mixtures) the ignition of volatiles evolved from coal, can provide the subsequent methane ignition, because the volatiles are hydrocarbons, probably, polycyclic aromatic hydrocarbons (PAH).