Direct numerical simulation of a three-dimensional spatially evolving compressible mixing layer laden with particles. II. Turbulence anisotropy and growth rate

Abstract

With the Eulerian–Lagrangian point-source method, turbulence modulation by dispersed particles is systematically investigated in a three-dimensional spatially evolving compressible mixing layer with the convective Mach number up to 1.2. Particles interact with the mixing layer through two-way coupling, and three simulations with different particle diameters are conducted and compared with the particle-free simulation. The underlying mechanisms responsible for turbulence modulation are revealed by analyzing the transport equations of the Reynolds stresses and turbulent kinetic energy, especially the two-way coupling terms. The compressible mixing layer turbulence is significantly anisotropic with strong three-dimensionality. The addition of particles augments turbulence anisotropy of the shear layer, and the augmentation becomes greater as the particle inertia increases, which is attributed to the different particle responsive features to the fluid fluctuations in the streamwise, normal, and spanwise directions. Particles respond fast to the fluid streamwise fluctuation but slowly to the normal and spanwise fluctuations because the streamwise turbulent intensity is larger compared with the normal and spanwise turbulent intensities. Consequently, the streamwise fluctuating velocity and the Reynolds shear stress are augmented and the normal and spanwise velocity fluctuations are attenuated. Besides, small particles slightly enhance the growth rate of the mixing layer, while large particles reduce the shear layer growth rate in the fully developed turbulence, which is due to the quick response of small particles and the slow response of large particles to the total fluid fluctuation.