Wake Dynamics 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 freestream flow oriented normal to the cylinder axis. The current paper examines the structure, consequences and validity for yawed cylinder flows of a quasi-two-dimensional 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 quasi-two-dimensional theory can be nondimensionalized to eliminate dependence on yaw angle, such that the cross-stream Reynolds number is the only dimensionless parameter. A perturbation argument is used to justify the quasi-two-dimensional approximation and to develop approximate conditions for validity of the quasi-two-dimensional approximation for finite-length cylinder flows. Computations using the quasi-two-dimensional 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 quasi-two-dimensional flow, that might explain the experimentally observed breakdown of the Independence Principle for large yaw angles.