| A Large Eddy Simulation (LES) based on filtered vorticity transport equation formulated using diffusion-velocity method and discrete vortex method has been coupled to filtered density function (FDF) equation for scalar, to predict the velocity and passive scalar field of a spatially developing mixing layer. In the vortex method, the vorticity-based and eddy-viscosity type subgrid scale (SGS) model simulating the enstrophy transfer between the large and small scale appears as a convective term in the diffusion-velocity formulation. The methodology has been tested on a spatially growing mixing layer using the two-dimensional vortex-in-cell method with both Smagorinsky and Dynamic Eddy Viscosity subgrid scale models for an anisotropic flow. The effects on the vorticity contours, momentum thickness, streamwise mean velocity profiles, root-mean-square velocity and vorticity fluctuations and negative cross-stream correlation are discussed. Comparison is made with experimental and numerical works where diffusion is simulated using random walk.; The transport equation for FDF is solved using the Lagrangian Monte Carlo method scheme. The unsolved subgrid scale convective term in FDF equation is modeled using the conventional gradient diffusion model for an anisotropic flow. The subgrid scalar mixing term is modelled using the Modified Curl model. The characteristics of the passive scalar, i.e., mean concentration, root-mean-square concentration fluctuation profiles and probability density function (PDF) are presented and compared with previous numerical and experimental works. The sensitivity of results to SGS model, Schmidt number, constant in mixing frequency and inlet boundary condition is discussed. |
