Hydrodynamic performance of a fishlike undulating foil in the wake of a cylinder

The hydrodynamic performances of a fishlike undulating foil in the wake of a D-section cylinder are numerically investigated by using a modified immersed boundary method. The results regarding the effects of various controlling parameters, including the distance between the foil and the D-cylinder, the frequency and the phase angle of foil’s undulation, and the phase angle of heaving motion on the thrust and the input power, are reported. It is observed that the foil without undulation in the vortex street can gain a thrust, as a result of the fact that the passing vortices produce reverse flows with respect to the mainstream in vicinity of the foil surface. When an undulating foil is placed at different distances behind the D-section cylinder, different wake structures form behind the cylinder. The wake area can be divided into three domains: suction domain, thrust enhancing domain, and weak influence domain. The undulation of the foil can inhibit the roll-up instability of the shear layers and vortex shedding from the cylinder and consequently significantly enlarge the suction domain, compared to the foil-free case or the stationary foil case. The thrust on the foil first increases and then decreases, as the distance between the foil and the cylinder increases. The undulation plays a negative role in the foil propulsion when the foil is located near the cylinder (largely in the suction domain) and a positive role when the distance between the foil and the cylinder is beyond a critical value. The mean thrusts do not vary significantly with the undulation phase angle when the heaving motion is not considered and the undulation amplitude studied is relatively small, instead, they are significantly affected by the phase angle of the heaving motion. The foil bypassing the vortices undergoes both minimum thrust and input power, whereas the one passing through vortices experiences a larger thrust. The phase angle difference between the heave and the undulation is important.