Performance improvement of flapping propulsions from spanwise bending on a low-aspect-ratio foil

Inspired from deformable caudal fins, continuous bending motion is utilized to improve the propulsive performance of flapping foils for underwater vehicles. The propulsive performance of a flapping foil with spanwise bending motion is studied numerically using the immersed boundary-lattice Boltzmann method. Simulations are conducted by varying the bending parameters and phases of motion at Re = 200 in uniform flow. It is found that the spanwise bending significantly affects vortex evolution and wake structures, which results in the variation of the flapping propulsion. For the present model with an aspect ratio of two, the most powerful (highest thrust) bending is achieved when fixing the phase lag between bending and flapping at 150°, while the most efficient (highest propulsive efficiency) bending is reached at a phase lag of 270°. With proper phase lags, the propulsive performance could be improved into 137% in thrust and 111% in efficiency from the rigid one. Under the most efficient phase lag, the efficiency could be furtherly improved into 112% through adjusting the bending amplitude due to the weak vortex tangle. The propulsive performance is also sensitive to the bending shape. This study presents a numerical guide for the high-performance flapping foil design with spanwise bending movement.