J0205-3-2 Boundary Element Analysis of Propulsion Efficiency of a Helix Depending on Its Shape

Abstract

Rotating helices are often found as flagella, organs of locomotion, in microorganisms and they are expected to be useful as screws or pumps in the flow of very low Reynolds number. When a helix is rotated by a torque along its helical axis, a propelling force is generated as a reaction of the force exerted on the surrounding fluid by the helix. In this study, we considered the ratio of the propelling force to the input torque as a measure of the efficiency of the helix, and numerically investigated the shape of the helix which maximizes the ratio. The boundary element method was employed to calculate the force and torque. According to our results, the most efficient helix has the wavelength of tenth of the filament's diameter, the pitch angle of 30 degrees, and the number of turns of around 1.