Direct numerical simulation of spatially developing highly compressible mixing layer: Structural evolution and turbulent statistics

Abstract

Direct numerical simulation of a spatially developing supersonic mixing layer with a convective Mach number of 1.0 is conducted. The present work focuses on the structural evolution and the turbulent statistics, and both instantaneous and time-averaged data are utilized to obtain further insight into the dynamical behaviors of the flow. The full development process of instability, including the shear action at the flow early stage, the generation of kinds of typical vortex structures in the flow transition region, and the establishment of self-similar turbulence, is clearly presented. The formation and evolution mechanisms of multiple ring-like vortices are reported and analyzed using the Helmholtz first law in compressible mixing layers, and the role they play in the mixing process in the flow transition stage is researched. The mean velocity distribution and the turbulent intensities are found to have close relations with the evolution of the multiple ring-like vortices. The presence of multiple ring-like vortices leads to local strong ejection and sweep regions that create pockets of partially mixed fluid near the tips of the vortices, which contributes much to the huge energy and momentum transfer of the upper and lower streams. Some anisotropy coefficients and turbulent structure parameters are described and analyzed to better reveal the effects of multiple ring-like vortices on flow behaviors. Our results indicate that with the increase in compressibility, though in a fully turbulent region, mixing layer growth and turbulent intensities are both suppressed, the appearance of multiple ring-like vortices and their evolutions can significantly promote mixing in the transition stage, which is usually ignored by previous researchers. Therefore, employing flow control methods to extend the flow transition stage and help sustain multiple ring-like vortices over a longer distance is a possible technique to enhance mixing.