LINEAR INSTABILITY OF A PARTICLE-LADEN MIXING LAYER WITH A DYNAMIC DISPERSED PHASE

The linear, inviscid, spatial instability of a mixing layer uniformly laden with a dilute concentration of heavy particles is studied numeri cally. The effect of the particles is modeled using an ensemble averag ed Eulerian description of the velocity field and Stokes' drag formula to compute an averaged force, and the carrier fluid and the particle motions are assumed to be fully coupled. The behavior of the linear in stability (for a given mean shear) depends on two dimensionless parame ters: C-f, representing the product of the inverse Stokes number and m ass loading, and C-f, representing the inverse Stokes number. For fini te values of C-f and large values of C-p, the particles respond as flu id elements and the growth rate is equal to the one of the single-phas e flow, while decreasing C-p results in a growth rate decrease. The gr owth rate also decreases with increasing C-f. Beyond certain critical values of increasing C-f and decreasing C-p, a second unstable low-fre quency mode appears which is distinct from the fundamental mode. The f ully coupled character of the instability reveals three important aspe cts of the particle effect on the flow structure: (1) the particle con centration field is organized into alternating bands of increased and decreased concentration corresponding to the braid and core regions of the vortices, respectively, with peak perturbations occurring at inte rmediate C-p values (0.01 less than or equal to C(p)less than or equal to 0.1), (2) the streamwise particle velocity is higher than the stre amwise fluid velocity for a substantial range of C-p values and every finite C-f, and (3) the modification of the fluid vorticity field stru cture with respect to the corresponding field in single-phase flow is driven by the divergence of the particle velocity field. (C) 1998 Amer ican Institute of Physics.