Characterization of the mixing layer self-similarity with multiple parameters

Abstract

In the paper, results from direct numerical simulation of a planar incompressible mixing layer spatially developing incompressible between two co-flowing laminar boundary layers are used to analyze a possibility for multiple flow parameters to achieve self-similarity within the same flow region. The Reynolds numbers for the boundary layers are 3930 and 2412 based on the free-stream velocities far above and below the splitter plate and the boundary layer thicknesses at the splitter plate trailing edge. The three-dimensional computational domain is sufficiently large for the mixing layer transition to fully turbulent far upstream the domain exit. The mixing layer growth is characterized using various definitions of the mixing layer thickness. It is shown that the proposed mixing layer thickness based on the gradient of the streamwise mean velocity in the transverse direction defines more accurately the area of turbulent mixing. Three regions of the flow linear growth are discovered using a rigorous approach, with only one of them being located within the fully turbulent mixing layer. Other parameters included in the flow self-similarity analysis are the streamwise and transverse mean velocities along with the Reynolds stresses. New normalization is proposed to observe self-similarity of the transverse mean velocity. The flow region where all considered parameters exhibit self-similarity is determined. It is shown that this region is limited by the “pulsating” streamwise distribution of the transverse mean velocity. The computational domain dimension along with the boundary conditions in the transverse direction for all considered parameters are suggested for the Reynolds-averaged Navier–Stokes simulations.