Direct numerical simulation of interactions between a mixing layer and a wake around a cylinder

Abstract

Direct numerical simulations of turbulent flows around a cylinder are performed using the virtual boundary technique to model the presence of the obstacle. This method consists of the imposition of a no-slip boundary condition within the flow field, using a specific forcing term added to the momentum equation. In this paper, two different inflow conditions are considered upstream from the cylinder. In the first case, where the inflow conditions correspond to a constant velocity flow, common features of the cylinder wake dynamics are well recovered (three-dimensional vortex shedding) while turbulent statistics (mean velocity and Reynolds stresses) are in good agreement with previous experimental and numerical results. This clearly shows that a code based on high-order finite difference schemes combined with the virtual boundary method can lead to reliable results even if the grid is not well designed for the shape of the obstacle. In the second case, the inflow conditions correspond to a spatially developing mixing layer reaching a transitional state just upstream from the cylinder. This flow configuration can be schematically decomposed in three basic flows: a low-speed wake, a high-speed wake and a mixing layer flow. It is found that interaction mechanisms between these three flows are predominant. The cylinder induces a strong distortion on the spatial development of the mixing layer. Analysis of the mean flow shows the presence of strong upward and downward streams respectively in front of and behind the cylinder. The downward motion induces strong perturbations on the vortex shedding cycles in the fast wake while the behaviour of the slow wake is similar to a conventional constant flow over a cylinder. In the regions of slow/fast wakes, vortex shedding is found at frequencies which seem to be linked, but no synchronization mechanism can be clearly identified in this study. Despite this difficulty, the vortex dynamics analysis, based on vorticity animations, shows that large scale eddies are the key element of the interaction mechanisms between the three basic flows. This article was chosen from selected Proceedings of the Second International Symposium on Turbulence and Shear Flow Phenomena (KTH-Stockholm, 27-29 June 2001) ed E Lindborg, A Johansson, J Eaton, J Humphrey, N Kasagi, M Leschziner and M Sommerfeld.