Evaluation of Mixing Length in a Planar Mixing Layer Based on Shear-Induced Vortex Quantity

Abstract

An incompressible turbulent planar mixing layer is composed of two different flow types in its flow field, namely a shear layer in the central region and two free streams in the outer high- and low-speed sides. Shear layer, which is of shear turbulence, is formed right after the trailing edge of the splitter plate and develops streamwisely through successively distinct regions, namely the near field (developing) region and the self-preserving (developed) region. A new definition of the mixing length (lω) is proposed on the basis of an effectively pure shear-induced vorticity component (ΩSH) by means of a triple decomposition method, that is, lω = yH - yL where yH and yL are the two transverse positions, at which |ΩSH| normalized with the maximum ∂U/∂y at the trailing edge is equal to 0.06, in the high- and low-speed free stream sides, respectively. It is shown that the linear growth rate of lω along streamwise distance can be now used as one of the necessary and sufficient conditions for justifying the achievement of the self-preserving state in turbulent mixing layer. I. Introduction he incompressible turbulent planar mixing layer is composed of two different flow types in its flow field, namely a shear layer in the central region and two free streams in the outer high- and low-speed sides. Shear layer, which is of shear turbulence, is formed right after the trailing edge of the splitter plate and develops streamwisely through successively distinct regions, namely the near field (developing) region and the self-preserving (developed) region. In contrast, two outer free stream regions are of nearly homogeneous turbulence. The mixing length is used to characterize the sectional range of the shear layer. The usual definition of the mixing length is given by