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 numerically. The effect of the particles is modeled using an ensemble averaged 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 instability (for a given mean shear) depends on two dimensionless parameters: C-f, representing the product of the inverse Stokes number and mass loading, and C-f, representing the inverse Stokes number. For finite values of C-f and large values of C-p, the particles respond as fluid elements and the growth rate is equal to the one of the single-phase flow, while decreasing C-p results in a growth rate decrease. The growth rate also decreases with increasing C-f. Beyond certain critical values of increasing C-f and decreasing C-p, a second unstable low-frequency mode appears which is distinct from the fundamental mode. The fully coupled character of the instability reveals three important aspects of the particle effect on the flow structure: (1) the particle concentration 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 intermediate 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 streamwise fluid velocity for a substantial range of C-p values and every finite C-f, and (3) the modification of the fluid vorticity field structure with respect to the corresponding field in single-phase flow is driven by the divergence of the particle velocity field. (C) 1998 American Institute of Physics.