Analytical modeling of self-similar compressible turbulent mixing layers

Self-similar features of compressible turbulent variable-density mixing layers are studied to provide a validation tool for CFD codes. Self-similar solution is obtained for 2D steady Reynolds averaged Navier-Stokes equations simplified with the boundary layer approximation. Turbulence is treated with eddy viscosity model approach. Two variable turbulent viscosity models are proposed as a refinement of the classical constant turbulent viscosity model: bi-quadratic and Gaussian turbulent viscosity models. Validation of the proposed turbulence models is performed by comparing self-similar solution with experimental data of a helium/air coaxial supersonic jet. Good agreement between the self-similar solution with bi-quadratic turbulent viscosity and experimental data is found. As a consequence, bi-quadratic turbulent viscosity model is selected as turbulence closure for the analytical model. A multi-species CFD code is finally validated by a self-similar solution reproducing a supersonic carbon dioxide axial jet issuing into slow moving air.