Fast numerical simulation of vortex shedding in tube arrays using a discrete vortex method

Vortex shedding may occur in tube arrays, resulting in strong excitation forces at discrete frequencies. In the past the Strouhal numbers governing vortex shedding in these systems were determined primarily by experiment. This paper presents a computationally inexpensive method of numerical simulation for the unsteady flow through a rigid normal triangular tube array which determines both the frequency of vortex shedding and the instantaneous flow structure. The technique used is based on a discrete vortex method similar to the cloud-in-cell approach which has been applied to flow problems for small numbers of cylinders. However, in the current implementation the flow velocity calculation is carried out on an unstructured grid using a finite element discretization. Thus, the complex geometry associated with a tube array can be easily accommodated. The method, referred to as the “Cloud-in-element” method, is validated for the standard case of flow over a single cylinder and then applied to flow through a normal triangular array with a pitch-to-diameter of 1.6. The Reynolds number is 2200. The Stouhal number obtained from the numerical simulation is 1.27, which is within 6% of the value available in the literature. Qualitatively, the vortex shedding pattern obtained is in agreement with published flow visualization.