Particle transport and flow modification in planar temporally evolving laminar mixing layers. I. Particle transport under one-way coupling

Simulations of two-dimensional, particle-laden mixing layers were performed for particles with Stokes numbers of 0.3, 0.6, 1, and 2 under the assumption of one-way coupling using the Eulerian-Lagrangian method; two-way coupling is addressed in Part II. Analysis of interphase momentum transfer was performed in the Eulerian frame of reference by looking at the balance of fluid-phase mean momentum, mean kinetic energy, modal kinetic energy, and particle-phase mean momentum. The differences in the dominant mechanisms of vertical transport of streamwise momentum between the fluid and particle phases is clearly brought out. In the fluid phase, growth of the mixing layer is due to energy transfer from the mean flow to the unstable Kelvin-Helmholtz modes, and transport of mean momentum by these modes. In contrast, in the particle phase, the primary mechanism of vertical transport of streamwise momentum is convection due to the mean vertical velocity induced by the centrifuging of particles by the spanwise Kelvin-Helmholtz vortices. Although the drag force and the particle-phase modal stress play an important role in the early stages of the evolution of the mixing layer, their role is shown to decrease during the pairing process. After pairing, the particle-phase mean streamwise momentum balance is accounted for by the convection and drag force term. The particle-phase modal stress term is shown to be strongly connected to the fluid phase modal stress with a Stokes-number-dependent time lag in its evolution.