Lift forces induced by phase lag between the vortex sheddings from two tandem bluff bodies

Flow-induced forces on two tandem circular cylinders of identical diameter are numerically studied at a Reynolds number of 200. The cylinder center-to-center spacing ratio is varied from 2 to 9. We focus on fluctuating (rms) lift coefficient of the upstream cylinder, vortex dynamics in the gap between cylinders, and phase lag between vortex shedding from the two cylinders. The phase lag was a linear function of the spacing ratio as known in the literature; but it is, as proved here, indeed a nonlinear function of the spacing ratio, Strouhal number and convection velocity of vortices in the gap between the cylinders. The shedding from the two cylinders turns out to be inphase and antiphase alternately as the spacing ratio increases. We unearth that both phase lag and spacing ratio influence the fluctuating lift of the upstream cylinder. With an increase in the spacing ratio, while the influence of the spacing ratio on fluctuating lift diminishes rapidly in an overdamped manner, that of the phase lag makes the fluctuating lift variation underdamped sinusoidal. The inphase and antiphase flows correspond to a local maximum and a local minimum, respectively, in the fluctuating lift variation. An equation is deduced, showing the relationship between the fluctuating lift, spacing ratio, and phase lag. The physics behind the damped-sinusoidal variation in the fluctuating lift is discussed. The investigation directs that the streamwise separation between two tandem wings of airplanes/submarines should be taken into account or optimized. It would also be interesting to see whether fish exploits phase-lag-induced lift to enhance its forward thrust.