On the method of indirectly measuring gas and particulate phase velocities in shock induced dusty-gas flows

A method of indirectly measuring the temporally varying velocities of the gas and particulate phases in the nonequilibrium region of a shock wave moving at constant speed in a dusty-gas flow is described, and this method is assessed by using experimental data from shock-induced air flows containing 40-m-diameter glass beads in a dusty-gas shock-tube facility featuring a large horizontal channel (19.7-cm by 7.6-cm in cross-section). Simultaneous measurements of the shock-front speed with time-of-arrival gauges, particle concentration by light extinctiometry and gas-particle mixture density by beta-ray absorption are used in conjunction with two mass conservation laws to obtain the indirect velocity measurements of both phases. A second indirect measurement of the gas-phase velocity is obtained when the gas pressure is simultaneously recorded along with the particle concentration and shock-front speed when used in conjunction with the conservation of mixture momentum. Direct measurements of the particulate-phase velocity by laser-Doppler velocimetry are also presented, as a means of assessing the indirect velocity measurement method.List of symbols a_f frozen speed of sound - D particle diameter - d_f LDV interference fringe spacing - d_m LDV probe-volume diameter - l_m LDV probe-volume length - M_sf frozen shock Mach number - M_se equilibrium shock Mach number - Ñ(D) probability density distribution by number - p pressure - R gas constant - t time - T temperature - S LDV-signal amplitude - v_g gas velocity in laboratory frame of reference - v_p particle velocity in laboratory frame of reference - V_s shock-front velocity - ratio of specific heats of particles and gas - ratio of specific heats of gas - equilibrium specific heats ratio - particle-to-air loading ratio - half-angle between incident laser beams - laser light wavelength - _g gas density - _p particle material density - _g gas concentration - _m mixture concentration - _m^app apparent mixture concentration - _p particle concentration - particle volume fraction - (D) probability density distribution by volume