1 Department of Applied Mathematics and Computer Science, Technical University of Denmark2 Mathematics, Department of Applied Mathematics and Computer Science, Technical University of Denmark3 Monash University4 Aix-Marseille Université5 unknown6 Monash University
The wake transitions of generic bluff bodies, such as a circular cylinder, near a wall are important because they provide understanding of different transition paths towards turbulence, and give some insight into the effect of surface modifications on the flow past larger downstream structures. In this article, the fundamentals of vorticity generation and transport for the two-dimensional flow of incompressible Newtonian fluids are initially reviewed. Vorticity is generated only at boundaries by tangential pressure gradients or relative acceleration. After generation, it can cross-annihilate with opposite-signed vorticity, and can be stored at a free surface, thus conserving the total vorticity, or circulation. Vorticity generation, diffusion and storage are demonstrated for a cylinder translating and rotating near a wall. The wake characteristics and the wake transitions are shown to change dramatically under the influence of cylinder rotation and wall proximity. At gaps between the cylinder and the wall of less than approximately 0.25 cylinder diameter, the wake becomes three dimensional prior to becoming unsteady, while for larger gaps the initial transition is to an unsteady two-dimensional wake. At a gap of 0.3 cylinder diameter, we observe a sharp increase in the critical Reynolds number at which three-dimensionality sets in. As the gap is further increased, the critical Reynolds number initially decreases before increasing to that for an isolated cylinder. The effect of cylinder rotation on these transitions is also quantified, with forward (prograde) rotation enhancing three-dimensional instability and reverse (retrograde) rotation stabilising the wake. High retrograde rotation leads to suppression of three-dimensional flow until beyond the highest Reynolds number investigated (Re=750).
Journal of Wind Engineering and Industrial Aerodynamics, 2013, Vol 122, p. 2-9
Vorticity; Bluff bodies; Wakes; Stability
Main Research Area:
The Seventh International Colloquium on Bluff Body Aerodynamics and Applications, 2013