The effect of batoid inspired undulating motions on the propulsive forces of a circular planform

This study explores the nature of forces developed by a batoid-inspired undulating circular planform. The forces that arise from this type of fin-based propulsion have two components, one due to added mass effects and a second one due to circulation. The present work studies the impact of specific fin kinematic parameters on the individual contributions of these components. Numerical simulations are performed on a deforming boundary fitted grid around an undulating circular planform. Flow physics and force generation are analyzed at Reynolds numbers up to 500. A detailed analysis is presented of the impact of wavenumber, amplitude of the fin traveling wave, and Strouhal number on propulsive forces using flow contours and pressure distributions on the planform. The sway coefficient increases with decrease in wavenumber, whereas the thrust coefficient reaches a maximum at a wavenumber of one. The yaw moment coefficient increases up to wavenumber of 1.5 and remains nearly constant after. For the cases studied, circulation has a larger impact compared to added mass effects in the overall force generation, and the role of edge vortices is explored in detail. The wake formed during half of the fin flapping cycle has two distinctive parts. One part is shed as an edge vortex toward the planform circumference and the other part is shed from the trailing edge of the planform, where both vortex structures are attached. These two vortices are of same sign. Over the next half-cycle a similar couple, but with opposite sign, is shed and inter-locks with the previous pair. The edge vortices on both sides of the planform are connected like a horse-shoe. The results enable a better understanding of the link between batoid-like undulatory fin kinematics and propulsive force generation and can help in the design and control of bio-inspired underwater vehicles.