Numerical Study of 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 for \textit{Re}$\le $300. Reynolds number and angle of incidence (\textit{$\theta $}) are the key parameters which determine the flow characteristics. There exist two kinds of critical Reynolds numbers; flow becomes unsteady at a lower critical Reynolds number (\textit{Re}$_{c1})$ and the two-dimensional time-periodic wake becomes unstable to three-dimensional disturbances at an upper critical Reynolds number (\textit{Re}$_{c2})$. We present the two critical Reynolds numbers as a function of \textit{$\theta $} by using the Stuart-Landau equation for a steady flow and a fully-resolved Floquet stability calculation for a time-periodic wake, respectively. In particular, there are two different instability modes for a time-periodic wake, namely, one (mode A) associated with a long spanwise wavelength and the other (mode B) with a short spanwise wavelength. The spanwise wave numbers of the most unstable (or least stable) wave for the critical case are presented for each \textit{$\theta $} considered. We also report flow-induced forces on the cylinder, and flow patterns past the cylinder for the range of \textit{Re} considered in this investigation, and attempt to present physical explanations about them.