Mechanism of dust ignition in incident shock waves

A study is made of dust ignition during transient interaction of an incident shock wave with an extended dust cloud. It has been shown experimentally that in the presence of dispersed phase with volume concentration of $\sim10^{-3}$ the temperature behind a shock wave with Mach number $\mathrm{M}_s = 4.5$ can exceed the ambient one by $400$ K or more. A physical mechanism is proposed for carrier phase heating, based on the effect of supersonic flow braking behind the shock wave under constraints created by dust particles during velocity relaxation. The gasdynamic functions are obtained as analytic functions of the flow Mach number $\mathrm{M}$. In particular, it is shown that the equation $T/T_0=\mathrm{M}_0/\mathrm{M}$ is valid for the temperature. The form of $\mathrm{M}$ as a function of dispersed-phase parameters and the quantitative nonsteadiness criterion are found. The function $\mathrm{M}$ was found to agree well with experiment.