Self-similar solutions for mixing layers in supersonic flow and in subsonic flow with variable density are examined. The equation for the velocity profile is derived for a unity turbulent Prandtl number and/or prescribed density distributions. It is found that the shape of the velocity profile is not sensitive to Mach number and is nearly the same for supersonic layers with moderate convective Mach numbers and in low speed flows with variable density: in such conditions, the only compressibility effect is found on the rate of spread. It is also found that turbulent friction is a function of Mach number and of velocity and density ratios. The effect of these last parameters on turbulent friction in low speed layers is proposed. Finally the scaling for turbulent shear stress last parameters on turbulent friction in low speed layers is proposed. Finally the scaling for turbulent shear strees in supersonic mixing layer is discussed. A simple formulation is proposed, in which the effects of density ratio and convective Mach number can be sepearated, as it is usually done for the rate of spread.
Density and Compressibility Effects on the Structure of Supersonic Mixing Layer: Experimental Results and Similarity Analysis
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Menaa, M, & Dussauge, JP. "Density and Compressibility Effects on the Structure of Supersonic Mixing Layer: Experimental Results and Similarity Analysis." Proceedings of the ASME 2003 International Mechanical Engineering Congress and Exposition. Fluids Engineering. Washington, DC, USA. November 15–21, 2003. pp. 359-378. ASME. https://doi.org/10.1115/IMECE2003-42509
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