Compressibility effects in a turbulent
annular mixing layer

Jonathan Freund, University of
California, Los Angeles

Mixing between supersonic streams is critical to many technological applications, especially scramjets. This work uses direct numerical simulations of time evolving annular mixing layers, which correspond to the early development of round jets, to study compressibility effects on turbulence dynamics and mixing in free shear flow. Nine cases were considered with convective Mach numbers ranging from 0.1 to 1.8 and turbulent Mach numbers reaching as high as 0.8.

Growth rates of the simulated mixing layers are suppressed with increasing Mach number as observed experimentally. The Reynolds stresses, with exception of the axial normal stress are also suppressed. Flow visualizations show a distinct change in turbulence structure with increasing Mach number. At low Mach numbers, the flow is dominated by large azimuthally correlated rollers whereas at high Mach numbers the flow is dominated by small streamwise oriented structures. Dilatational terms are found to have negligible net effect upon the turbulence energetics despite the fact that shocklets are found at high Mach numbers. The growth rate suppression is analyzed with the Reynolds stress transport equations and a simple relation between mixing layer growth rate and the pressure-strain-rate correlation is found. This correlation is suppressed at higher Mach numbers due to suppressed pressure fluctuations. A change in structure caused by a "communication" breakdown across supersonically deforming eddies is found to be responsible for the suppression of pressure fluctuations and this effect is parameterized with a gradient Mach number defined in terms of large eddy length scale.

Mixing is studied with a passive scalar transport equation. Increasing the Mach number changes the mixture fraction probability density function from non-marching to marching and the mixing efficiency from 0.5 at convective Mach number 0.1 to 0.67 at convective Mach number 1.5. The scalar concentration and the axial velocity perturbations become highly correlated as the Mach number increases and a suppressed role of pressure in the transport of axial momentum is found to be responsible for this.

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