Numerical analysis of mixing in variable density turbulent flows
In this study, high-resolution direct numerical simulations of mixing in turbulent flows, subject to a change in density, are performed. Attention is focused on the binary mixing between two streams of fluids, with a variable density step, in a decaying homogeneous isotropic turbulent flow. Since experimentation is limited by the length of the wind tunnels and by difficulties in aligning the virtual origins of the scalar and velocity fields, a direct numerical simulation (DNS) box with periodic boundary conditions in two directions and a free slip boundary condition in the density step direction was used and proved able to virtually eliminate these limitations.
The flow field simulated was a temporally developing mixing layer, which avoids the requirement of specifying inflow/outflow-boundary conditions. The temporal layer model in the simulation considers the flow by employing a Galilean space-time transformation to concentrate on the small section of the flow field that moves with average flow velocity. The computational algorithm in the (DNS) uses the Fourier pseudo-spectral method to compute spatial derivatives for the velocity and density fields, and a fractional step method involving the third order Adams-Bashforth-Moulton predictor and corrector to advance the governing equation in time.
We approached this binary mixing problem by assuming Fick's law of diffusion and zero Mach number flow, in which low speed, non-reactive species, small temperature fluctuations, and no heat generation or heat release are applied.
The results demonstrate the variable density effects in three different cases, where the density ratio sρ varies between 2, 5, and 10. Also a comparison with the constant density case, where sρ is equal to one, is shown. Planer statistics results were developed for these cases and comparisons with some existing models and predictions for variable density flow are considered.
Profiles for the kinetic energy (k), kinetic energy dissipation rate (ε), length scale, and time scale across the mixing layer are demonstrated for the variable density simulations. Then, at a given point in time, comparison between variable density cases are presented to show the variable density effects. Also, testing the kinetic energy initialization method and weather constant or variable initial kinetic energy profile across the layer are going to effect the flow is answered. And the variable density effects on the turbulent kinematic viscosity (νt), and turbulent Schmidt number (Sct) are considered.
Enstrophy production as a result of vorticity generation is then examined. Vorticity and enstrophy are computationally and experimentally very demanding to obtain; however, when they are resolved to the proper scale, they can describe the physical phenomena and help to understand more about the nature of the interaction between turbulent structures and density development in variable density turbulent flows.