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SCALING LAWS FOR THE PERFORMANCE OF RIGID PROPULSORS INTENDED FOR UNDERWATER LOCOMOTION

Daniel Floryan
Department of Mechanical and Materials Engineering, The University of Western Ontario London, Ontario, Canada; Mechanical and Aerospace Engineering Princeton University Princeton, NJ 08544, USA

Tyler Van Buren
Department of Mechanical and Aerospace Engineering, Princeton University, NJ, USA

Clarence W. Rowley
Mechanical and Aerospace Engineering Princeton University Princeton, NJ 08544, USA

Alexander J. Smits
Department of Mechanical & Aerospace Engineering, Princeton University Princeton, NJ 08544, USA

Abstract

Scaling laws are presented for the propulsive performance of rigid foils undergoing oscillatory motion in water. Water tunnel experiments on a nominally two-dimensional foil show that the scaling laws provide an excellent description of the data for thrust, power, and efficiency. The scaling laws are then extended to account for the effects of non-sinusoidal motions by using a parameter based on the maximum velocity of the trailing edge, which describes the experiments on non-sinusoidal gaits described by Jacobi elliptic functions reasonably well. Lastly, intermittent motions are considered. The thrust and power is shown to scale linearly with the duty cycle, and scaling laws for the energetics are presented. Intermittent motions are generally energetically advantageous over continuous motions, unless metabolic energy losses are sufficiently high.