Numerical simulation of a plane "Canonical" mixing layer using a vortex sheet model

Abstract

A novel method for computing mixinglayer flow in the limit of infinite Reynolds number using a twodimensional vortexsheet technique is presented here. The method computes the evolution of the sheet by dividing it into constantstrength short linear elements joined endtoend, and moving each according to velocities given by the Biot-Savart law. As the sheet stretches or shrinks, the number of elements is changed to preserve a given level of computational accuracy. Extensive results are presented for what is termed a “canonical” mixing layer, defined as one that, in the limit of Re , forms downstream of a semiinfinite splitter plate. This definition ensures that the results, in principle, do not depend on the extent of the computational domain. The downstream farfield is modeled by a steady vorticity distribution scaled conically from calculations in the computational domain, with a variable buffer space providing a “soft” coupling between the domain and the farfield. The boundary condition of vanishing normal velocity on the splitter plate is satisfied rigorously using a doublet sheet. The present model avoids the extraneous coresize parameter introduced in the vortexblob method. Whereas previous simulations of the mixing layer using vortex blobs reported Reynolds stresses and thirdorder moments up to about twice and eight times higher than experimental data, the present model yields Reynolds stresses of the correct order and reduces discrepancies in thirdorder moments to half or less. The computed autocorrelations are qualitatively similar to experimental findings. The oscillatory nature of the correlations is manifest not only at the edges of the mixing layer but (contrary to experiments) also along its centerline. The accuracy of the computation is independently established by showing that the changes in the five invariants (including the Hamiltonian) known in vortex dynamics are small. The superiority of the present method is attributable to the avoidance of very large velocities induced in the neighbourhood of discrete vortices. A direct comparison-independent of published numerical results-between the present vortexsheet model and a pointvortex scheme highlights the nature of the errors in the latter. These errors generally result in highly irregular rollup and unduly high Reynolds stresses and thirdorder moments. It is evident that discrepancies between measured values of second and thirdorder moments and those computed by previous discretevortex simulations arise, in part, from the very nature of the discretevortex approximation. Finally, forced mixing layers are studied using a slightly modified vortexsheet model. The computed effects of forcing amplitude and frequency on mixinglayer growth are found to be similar to experimental observations, thereby further demonstrating the effectiveness of the present technique.