Direct numerical simulation on the particle dispersion by the vortex structures in a three-dimensional mixing layer: the roll-up

A three-dimensional temporally evolving mixing layer laden with particles was numerically studied by using direct numerical simulation (DNS). The dispersion patterns of particles at different Stokes numbers initially located in the high velocity stream in the process of Kelvin–Helmholtz roll-up was especially investigated. The Lagrangian approach was used to trace the particles and a pseudo-spectral method was employed to directly simulate the coherent structures in the mixing layer. The DNS showed the formation and development of the ‘rib’ structures in the process of the Kelvin–Helmholtz roll-up, and demonstrated the ‘rib’ effect of large-scale vortex structures on the particle dispersion is particle Stokes number dependent. At intermediate Stokes numbers, particles concentrate in sheet-like regions near the outer edges of the large-scale vortex structures, the particle spatial dispersion is much larger than that for both small and large Stokes numbers. Furthermore, the development of pairs of counter-rotating ‘rib’ vortices and three-dimensionality yields a ‘mushroom’-shaped pattern of spanwise particle dispersion.