Direct numerical simulation of a three-dimensional temporal mixing layer with particle dispersion

The three-dimensional mixing layer is characterized by both two-dimensional and streamwise large-scale structures. Understanding the effects of those large-scale structures on the dispersion of particles is very important. Using a pseudospectral method, the large-scale structures of a three-dimensional temporally developing mixing layer and the associated dispersion patterns of particles were simulated, The Fourier expansion was used for-spatial derivatives due to the periodic boundary conditions in the streamwise and the spanwise directions and the free-slip boundary condition in the transverse direction. A second-order Adam-Bashforth scheme was used in the time integration. Both a two-dimensional perturbation, which was based on the unstable wavenumbers of the streamwise direction, and a three-dimensional perturbation, derived from an isotropic energy spectrum, were imposed initially, Particles with different Stokes numbers were traced by the Lagrangian approach based on one-way coupling between the continuous and the dispersed phases. The time scale and length scale for the pairing were found to be twice those for the rollup. The streamwise large-scale structures develop from the initial perturbation and the most unstable wavelength in the spanwise direction was found to be about two thirds of that in the streamwise direction. The pairing of the spanwise vortices was also found to have a suppressing effect on the development of the three-dimensionality. Particles with Stokes number of the order of unity were found to have the largest concentration on the circumference of the two-dimensional large-scale structures, The presence of the streamwise large-scale structures causes the variation of the particle concentrations along the spanwise and the transverse directions, The extent of variation also increases with the development of the three-dimensionality, which results in the 'mushroom' shape of the particle distribution.