Flow past an Inclined Square Cylinder

Numerical investigation has been carried out for laminar flow (\textit{Re}$\le $150) past an inclined square cylinder in cross freestream. The motivation stems from characterization of flow-induced forces on a sharp-edged cylindrical object immersed in cross flow with an angle of attack. From the viewpoint of wind hazards, this study would be the first step towards understanding flow-induced forces on cylindrical structures under a strong gust of wind. In this flow configuration, there exist two kinds of critical Reynolds numbers in laminar regime; flow separation occurs at a lower critical Reynolds number (\textit{Re}$_{c1})$ and flow becomes unsteady at an upper critical Reynolds number (\textit{Re}$_{c2})$. It is seen that the values of \textit{Re}$_{c1}$ and \textit{Re}$_{c2}$ change depending on the inclination angle (\textit{$\theta $}) of the cylinder. In particular, \textit{Re}$_{c2}$ decreases as \textit{$\theta $} increases, being consistent with the instability theory based on Stuart-Landau equation in literature. Furthermore, the cylinder vertices at which flow separation takes place are determined by \textit{$\theta $}. Consequently, key flow characteristics such as drag/lift forces on the cylinder and vortex-shedding frequency could drastically alter depending on \textit{$\theta $}. We propose contour diagrams of mean drag/lift coefficients, Strouhal number (\textit{St}) of vortex shedding, and rms of lift coefficient fluctuation$_{ }$on \textit{Re}--\textit{$\theta $} plane.