Vorticity Dynamics in the Wake of a Yawed Cylinder

Abstract

A theoretical and computational study is reported of the effect of cylinder yaw angle on the vorticity and velocity field in the cylinder wake. Previous experimental studies for yawed cylinder flows conclude that, sufficiently far away from the cylinder ends and for small and moderate values of the yaw angle, the near-wake region is dominated by vortex structures aligned parallel to the cylinder. Associated with this observation, experimentalists have proposed the so-called Independence Principle, which asserts that the forces and vortex shedding frequency of a yawed cylinder are the same as for a cylinder with no yaw using only the component of the free-stream flow oriented normal to the cylinder axis. The current paper examines the structure and consequences for yawed cylinder flows of a quasi-two-dimensional (Q2D) approximation in which the velocity and vorticity have three nonzero components, but have vanishing gradient in the direction of the cylinder axis. In this approximation, the cross-stream velocity field is independent of the axial velocity component, thus reproducing the Independence Principle. Both the axial vorticity and axial velocity components are governed by an advection-diffusion equation. The governing equations for vorticity and velocity in the Q2D theory can be nondimensionalized to eliminate dependence on yaw angle, such that the cross-stream Reynolds number is the only dimensionless parameter. Computations using the Q2D theory are performed to examine the evolution of the cross-stream vorticity and associated axial velocity field. The cross-stream vorticity is observed to shed from the cylinder as thin sheets and to wrap around the Ka´rman vortex structures, which in turn induces an axial velocity deficit within the wake vortex cores. The computational results indicate two physical mechanisms, associated with instability of the Q2D flow, that might explain the experimentally observed breakdown of the Independence Principle for large yaw angles.