Direct numerical simulation of turbulence anisotropy and growth rate in the supersonic non-isothermal mixing layer

Abstract

By direct numerical simulations, non-isothermal effects on turbulence anisotropy and growth rate are investigated in three-dimensional spatially developing supersonic mixing layers with high convective Mach numbers (Mc > 0.6). Hot air is blown into the high-speed stream, and cold air is added on the low-speed side. Two non-isothermal simulations with different temperature gradients are conducted and compared with the isothermal mixing layer. The Reynolds stress transport is analyzed to reveal the underlying modulation mechanisms by temperature gradients. The supersonic mixing layer is significantly anisotropic, and the streamwise turbulent intensity is larger than the transverse and spanwise turbulent intensities. The non-isothermal effects enhance the energy transfer from the streamwise Reynolds stress to transverse and spanwise Reynolds stresses in the initial shear layer, and the mixing layer anisotropy is intensely attenuated, which is attributed to the increment of the flow instability. Thus, the shear layer growth is initially accelerated, and the supersonic mixing layer is destabilized. However, the fluid viscosity and the viscous dissipation are enhanced, and the Reynolds stresses decay more strongly in the fully developed region. The transverse and spanwise turbulent intensities decrease more than the streamwise turbulent intensity due to the attenuation of the correlation between pressure and dilatation fluctuations. Consequently, the shear layer turbulence anisotropy is augmented with stronger three-dimensionality. As the Reynolds shear stress is reduced and the entrainment of irrotational fluid from the free streams into the shear layer is attenuated, the mixing layer growth rate is decreased in the self-similar turbulence.