Large Eddy Simulations of a spatially developing incompressible 3D mixing layer using the v-ω formulation

摘要

The LES of a 3D mixing layer spatially developing downstream of a flat plate has been conducted for a high Reynolds number (Re{sub}θ = 28.35). To overcome the problem of the pressure condition on the free boundaries, use of the (v-ω) formulation of the Navier-Stokes equations has been preferred over the primitive (v-p) formulation. To deal with the difficult problem of the divergence free constraint on both the velocity and the vorticity field, a new and efficient numerical algorithm has been devised which turns out to be very attractive. The velocity components are computed as a solution of a Cauchy-Riemann problem using a fractional step method. As one of the main advantages of the vorticity-based formulation is the treatment of the free flow boundary conditions, special care has been devoted to these boundary conditions. An optimum approximation of the outflow boundary condition has been carried out which satisfies the conservation of mass, making the long time integration easier and more accurate. The numerical results are compared to a reference experiment [Appl. Sci. Res. 53 (1994) 263; J. Delville, PhD thesis, University of Poitiers, 1995] for a rather high Reynolds number. Using inlet perturbations and the mixed scale model, the LES results agree very well with the reference experiments. The validation of the numerical procedure is reviewed on the mean and fluctuating quantities. Good prediction of the spatial evolution is demonstrated for the distribution of the vorticity thickness as well as for the Reynolds stress profiles and spatial correlations. In order to estimate the quality of the spatio-temporal development, a spectral analysis is also reported on the space and time spectra, pointing out a highly 3D arrangement with length scales and frequencies in rather good agreement with the ones generally admitted.