Three-dimensional study of flow past a square cylinder at low Reynolds numbers

Abstract

The spatial evolution of vortices and transition to three-dimensionality in the wake of a square cylinder have been numerically studied. A Reynolds number range between 150 and 500 has been considered. Starting from the two-dimensional Kármán vortex street, the transition to three-dimensionality is found to take place at a Reynolds number between 150 and 175. The three-dimensional wake of the square cylinder has been characterized using indicators appropriate for the wake of a bluff body as described by the earlier workers. In these terms, the secondary vortices of Mode-A are seen to persist over the Reynolds number range of 175-240. At about a Reynolds number of 250, Mode-B secondary vortices are present, these having predominantly small-scale structures. The transitional flow around a square cylinder exhibits an intermittent low frequency modulation due to the formation of a large-scale irregularity in the near-wake, called vortex dislocation. The superposition of vortex dislocation and the Mode-A vortices leads to a new pattern, labelled as Mode-A with dislocations. The results for the square cylinder are in good accordance with the three-dimensional modes of transition that are well-known in the circular cylinder wake. In the case of a circular cylinder, the transition from periodic vortex shedding to Mode-A is characterized by a discontinuity in the Strouhal number-Reynolds number relationship at about a Reynolds of 190. The transition from Mode-A to Mode-B is characterized by a second discontinuity in the frequency law at a Reynolds number of ≈250. The numerical computations of the present study with a square cylinder show that the values of the Strouhal number and the time-averaged drag-coefficient are closely associated with each other over the range of Reynolds numbers of interest and reflect the spatial structure of the wake.