The accumulation and dispersion of heavy particles in forced two-dimensional mixing layers. I. The fundamental and subharmonic cases

Abstract

This paper presents detailed computational results for the dispersion of heavy particles in transitional mixing layers forced at both the fundamental and subharmonic frequencies. The results confirm earlier observations of particle streaks forming in the braid region between successive vortices. A scaling argument based on the idealization of the spatially periodic mixing layer as a row of point vortices shows that the formation of these concentrated particle streaks proceeds with optimum efficiency for St≂1. It thereby provides a quantitative basis for experimental and numerical observations of preferential particle dispersion at Stokes numbers of order unity. Both the model and full simulation furthermore exhibit oscillatory particle motion, as well as the formation of two bands of high particle concentrations, for larger Stokes numbers. The particle dispersion as a function of time and the Stokes number is quantified by means of two different integral scales. These show that the number of dispersed particles does not reach a maximum for intermediate Stokes number. However, when the distance is weighted, optimum dispersion is observed for Stokes numbers around unity. By tracing the dispersed particles backwards in time, they are found to originate in inclined, narrow bands that initially stretch from the braid region into the seeded free stream. This suggests that particle dispersion can be optimized by phase coupling the injection device with the forcing signal for the continuous phase. In the presence of a subharmonic perturbation, enhanced particle dispersion is observed as a result of the motion of the vortices, whereby a larger part of the flow field is swept out.