Onset of vortex shedding in an inline and staggered array of rectangular cylinders

The onset of vortex shedding in a periodic array of rectangular cylinders in both inline and staggered arrangement is considered and results are compared with the corresponding transition in an isolated cylinder. Numerical simulations over varying geometric arrangement of the array of cylinders over a range of Reynolds numbers is considered to establish the stability characteristics and the influence of parameters such as streamwise and transverse pitch of the periodic array. The critical Reynolds number, based on mean flow velocity and cylinder height, for the periodic array decreases significantly below its value for an isolated cylinder in cross flow. An important characteristic of flow over an inline array of cylinders is that for moderate transverse spacing the streamwise velocity profile in the wake becomes nearly sinusoidal, in which case as the transverse spacing increases the critical Reynolds number for the onset of vortex shedding decreases progressively. With further increase in transverse spacing, departure from the near-sinusoidal wake profile will increase and correspondingly the critical Reynolds number can be expected to increase after reaching a minimum to that of an isolated cylinder. A one-dimensional (1D) linear stability analysis of a sinusoidal profile is performed to explain the observed behavior. Neutral curves for the onset of convective and absolute instabilities in the wake are obtained. Based on the 1D stability analysis a unified description for the onset of vortex shedding for the varying periodic array of cylinders is obtained. (C) 2002 American Institute of Physics.