Surface pressure and viscous forces on inclined elliptic cylinders in steady flow

Abstract

Surface pressure characteristics of elliptic cylinders of various thicknesses and orientations are investigated in steady flow regime. A stabilized finite-element method has been used to discretize the conservation equations of incompressible fluid flow in two dimensions. The Reynolds number, Re, is based on the major axis of cylinder and free-stream speed. Results have been presented for $$Re\le 40$$ and $$0^\circ \le \alpha \le 90^\circ $$ , where $$\alpha $$ is the angle of attack. Cylinder aspect ratios AR considered are 0.2 (thin), 0.5 and 0.8 (thick). It is found that a decrease in AR does not significantly alter the location of minimum surface pressure for $$\alpha = 90^\circ $$ , but the value of minimum pressure decreases sharply, resulting in severe adverse pressure gradient. In contrast, for $$\alpha = 0^\circ $$ , the location travels towards the base and the minimum pressure increases, leading to delayed flow separation. In general, the magnitude of forward stagnation pressure at low Re is smaller than the maximum pressure for $$AR\le 0.5$$ . The maximum pressure occurs at the forward stagnation point as the Re and AR increase. However, in most cases, the locations of forward stagnation and maximum pressure points differ even when the pressure coefficients are very close to each other. The forward stagnation and maximum pressure coefficients of an elliptic cylinder decrease monotonically with increasing $$\alpha $$ . The drag of a circular cylinder in most cases exceeds the ones obtained for elliptic cylinders. With increasing AR, the drag increases approximately linearly for small $$\alpha $$ , lift decreases approximately linearly and moment decreases non-linearly. For a thick cylinder, while the effect of Re on lift and moment is insignificant, the drag shows a strong dependence. Roughly $$\alpha = 20^\circ $$ for $$Re = 40$$ flow represents a critical angle of attack below which a cylinder of $$AR\le 0.5$$ acts like a streamlined body and above, like a bluff body.