Linear stability analysis of particle-laden mixing layers using Lagrangian particle tracking

This paper presents salient features of the temporal stability of particle-laden mixing layers under uniform particle loadings. Results show the strong stabilizing influence of particles with Stokes numbers of the order of unity. The particles also significantly change the most unstable wavenumber which dominates the initial evolution of the mixing layer. Results from the linear stability analysis were used to evaluate the Eulerian–Lagrangian (particle tracking) methodology and excellent agreement was observed for the instability growth rates. Two methods of implementing the fluid–particle coupling, both based on projecting the coupling force onto the fluid nodes, were compared and found to give almost identical results; indicating little practical difference between the two in the present case. Analyzing the accuracy requirements for the velocity interpolation found second-order interpolation to be inadequate. Converged results were obtained with fourth- and sixth-order accurate interpolation schemes.