Stability of Dust Laden Two-Dimensional Laminar Wakes

摘要

The stability of two-dimensional compressible dusty wakes is investigated. An equation is derived for the amplitude of the pressure disturbance. The solution of this equation is sought by perturbing the dust-free solution for small mass fraction of dust to gas. The straightforward perturbation expansion is not uniformly valid far away from the wake axis. A second-order uniformly valid solution is obtained. The results show that the dust can be stabilizing as well as destabilizing, depending on the size of the particles and their distribution. For a uniform distribution of dust and for very small particle size, the dust has a destabilizing effect. As the dust size increases, the destabilizing effect increases to a maximum, and then decreases to zero. As the particle size increases further, the dust will have a stabilizing effect. The quantitative stabilizing or destabilizing effect of the dust depends on the velocity defect and temperature excess at the wake axis. (Author)