Direct numerical simulation of turbulent mixing in shear flows

Abstract

This article considers one of the simplest shear flows-ID time-dependent plane mixing layer. Under certain conditions, many more complicated flows are similar to it: timeindependent plane mixing layer, initial portion of plane and round jets, initial mixing phase in cylindrical vortex, etc. This application was previously studied in a 2D approximation. In this computation the turbulence was treated as the result of random perturbations initially applied to the interface of two flows. Numerical simulation used a 2D EGAK code. The computational results were interpreted using the version of semi-empirical turbulent theory with isotropic Reynolds tensor (model 1). This article continues the studies by Bakhrakh; in addition, a similar approach is implemented based on 3D simulation with the TREK method. The data interpretation uses the version of semi-empirical theory with and without Reynolds tensor anisotropy (models 1 and 2, respectively). Computational setupThe setup is similar to that from Bakhrakh et al. (1983): initially two half-spaces separated by the plane are filled with perfect gases (y = 1.4) with densities p t = 0.001 and p 2 > rtpi for the same pressures P o =\. The gas in region 1 moves with the velocity w 0 = dy/dt = 4 parallel to the interface, one in region 2 is at rest.Initially, the random perturbations v = dz/dt = ±0.1 w o of the velocity component normal to the interface are applied to the latter. The computational domain is a cube with the side A = 7.5 and the number of cells N r x Ni x Ni. For the outer domain boundaries normal to the separate plate, the periodicity condition was specified with the period A; the rigid wall was applied to other boundaries.These 3D computations were run where n = p 2 /pi and the number of cells N! varied (see table 1). In addition, two 2D computations were run on a 45 x 45 grid, one of these, like in the 3D case, using the approximation of motion equation with the second-order approximation over spatial variables and the other using the first-order approximation. The setup is similar to the 3D case; the longitudinal coordinate is x, the transversal coordinate is y.Note that the incompressibility condition was approximately met because of the relation Wo « Wo/Poy where p o -min(p 1) p 2 )- Computational resultsThe flow evolution observed in computations 1 and 2 (p, = p 2 ) is similar to that from Bakhrakh et al. (1983). The vortices grow with time (see figures 1 and 2) showing, for the computation 1, the isolines of volume concentrations /? = 0.5 in the plane y = 0.25 and x = 0.25 normal to the interface and the linear variation law is achieved for the turbulent mixing zone (TMZ) width L(t) (figure 3). Here L was defined as the width of the self-similar

Direct numerical simulation of turbulent mixing

“…A detailed description of this problem made by the authors of this paper is presented in [11][12][13][14][15].…”

“…This problem has been considered in a number of papers and has abundant information, both experimental and computational. A detailed description of this problem made by the authors of this paper is presented in [11][12][13][14][15].…”

“…Under certain conditions, many more complicated flows are similar to it: stationary plane mixing layer, the initial section of plane and round jets, initial mixing phase in a cylindrical vortex, etc. Paper [2] discusses the investigation of this problem based on the direct two-dimensional simulation; papers [43][44][45][46] do the same based on the threedimensional simulation. The TMZ width, the velocity profiles, the turbulent energy and the mean quadratic pulsation of the transverse and longitudinal velocity components are compared with the measurements presented in [47][48][49].…”