NUMERICAL STUDY OF THE FLOW IN THE WAKE OF AN IMPULSIVELY STARTED ROTATING AND TRANSLATING CIRCULAR CYLINDER

In the present work, a detailed investigation in the wake region of the flow for the case of a two dimensional, laminar incompressible flow past a rotating and translating circular cylinder has been carried out by applying a second order time accurate finite difference method using primitive variable formulation for different values of alpha ranging between 0 and 8 for Re = 200, where alpha is a nondimensional peripheral velocity of the cylinder It has been observed that lift coefficient increases monotonically with alpha. But the effect of rotational speed on the steadiness of the flow is found significantly critical. Within the present range of alpha it is found that there have been back and forth regimes of unsteadiness in the flow. The flow remains unsteady for alpha < 1.95, becomes steady for 1.95 <= alpha <= 4.33 and is unsteady again for 4.33 <= alpha <= 4.73. For alpha > 4.73 the flow is again steady. It is found that while the first steady regime of flow is characterised by two oppositely rotating static vortices, the second steady regime is characterised by only one rotating static vortex wrapping around the cylinder It is also found that the nature of two unsteady regimes are not same. Detailed investigation reveals that in the first mode of vortex shedding, vortices are shed alternatively from both top and bottom surfaces, while in the second mode, the shedding occurs only from the bottom surface. Investigation also explains the cause behind increase of lift, decrease of drag with respect to alpha. From FFT analysis it can be concluded that lift curves corresponding to the first unsteady regime are simple sinusoidal waves, while those corresponding to the second unsteady regime are combinations of different harmonics. On the other hand, simple sinusoidal nature of the drag variation is found only when alpha is zero. By tracking the vortex shedding process closely, it is observed that during the process of formation, a small anticlockwise vortex is formed inside a large anticlockwise wrapping vortex around the cylinder to result into a higher pressure stagnation region just below the cylinder which in turn, effects maximum lift and detaches the small vortex from the lower surface of the cylinder resulting into vortex shedding from the bottom surface.