On the hydrodynamic performance of manta ray pectoral fin-inspired foil shapes*

In this research we study the hydrodynamic performance and produced wake structures of 2-D Manta Ray pectoral fin-like foil shapes. First, a class-shape transformation (CST) method was used to generate five airfoil shapes based on a high-fidelity CT scan of a Manta Ray’s pectoral fin. These five airfoil shapes are representative of the spanwise variation of the pectoral fin shape and reflect the changes in thickness and location of maximal thickness of the real manta pectoral fin. Point tracking was performed on the CT scan images to generate five pairs of CST coefficients. that generated symmetric foils. The chord for all foils is normalized to 1. Pitching and heaving motion is introduced to the foil as well, with the heaving motion varying from 0.1c-0.4c, and pitching angle varying from 5-30 degrees.

To resolve the force production and wake structures of the cases, we use an immersed boundary method-based incompressible flow solver. In this solver, the 2-D Navier-Stokes equations are discretized using a cell-centered, collocated arrangement of the primitive variables and are solved using a finite difference-based Cartesian grid immersed boundary method. For each of the cases, the Reynolds number will be set to 500 with a frequency of 1Hz and nondimensional flow velocity of 1.

For these simulations, preliminary results have shown some key differences in the thrust and efficiency between foil 1 (representing the shape nearest the root) and foil 5 (representing the fin shape nearest the tip). Further analysis will be performed on all foil shapes and motions. These findings will be communicated through plots of the hydrodynamic coefficients of thrust as well as visualization of the flow features using post processing tools. We expect to observe variations in the strength, location, and time of formation and shedding of the body vortexes. These observation are an important factor when designing bio-inspired propulsors or energy harvesters.