Effective Drag Coefficient for Gas-Particle Flow in Shock Tubes

Abstract

Effective drag coefficients for flows of suspensions of spherical glass particles in air were derived from simultaneous measurements of pressure and particle concentration in the flow behind weak shock waves. Average particle diameters were 29 and 62μm. The instantaneous concentration was determined by light scattering, and the results agree well with earlier shock-tube data based on streak records. They exhibit several unexpected features: the correlation between drag coefficient and Reynolds number is much steeper (∝ Re−1.7 ) than the generally used “standard” curve but approaches it at Reynolds numbers of several hundred; the correlation is independent of the particle concentration over the range of the experiments, that is, for particle-to-gas flow rate ratios between about 0.05 and 0.36; if the Reynolds number immediately behind the shock front is changed by varying the shock strength, the points move along the correlation, but if it is changed by changing the particle size, the entire correlation is shifted although to a smaller extent than would correspond to the direct effect of particle diameter on the Reynolds number. To account for the observations, a flow model is developed which allows for microscopic longitudinal and lateral perturbations of the particle motion that are the result of various causes, such as particle interactions with wakes of other particles, lateral forces caused by particle rotation, or electrostatic forces. Because of the nonlinearity of the equation of motion, the averaged particle motion is different from that of a particle without perturbations. The effective drag coefficient for the average particle motion is therefore different from the standard drag coefficient applied along the actual motion. With this model and plausible assumptions for the average lateral velocity component of the particle motion, all features of the experimental data can be qualitatively explained.