Flow past a square cylinder with an angle of incidence

A parametric study has been carried out to elucidate the characteristics of flow past a square cylinder inclined with respect to the main flow in the laminar flow regime. Reynolds number and angle of incidence are the key parameters which determine the flow characteristics. Location of separation point is greatly affected by angle of incidence, thus determining the flow field around the square cylinder. The critical Reynolds number for periodic vortex shedding at each angle of incidence considered is obtained by using Stuart-Landau equation. Attempt is made to classify the related flow patterns from a topological point of view, resulting in three distinct patterns in total. A comprehensive analysis of the effects of Reynolds number and angle of incidence on flow-induced forces on the square cylinder is presented. Collecting all the results obtained, contour diagrams of force and moment coefficients, Strouhal number, rms of lift-coefficient fluctuation, as well as a flow-pattern diagram are proposed for the ranges of the two parameters considered in the current investigation. Finally, a Floquet stability analysis is presented to detect the onset of the secondary instability leading to three-dimensional flow. The proposed diagrams and the Floquet stability analysis shed light on better physical understanding of the flow past a square cylinder, which should be useful in many engineering applications.