Flapping motion of a three-dimensional foil for propulsion and maneuvering of underwater vehicles

Abstract

Experiments were performed on a three-dimensional NACA 0015 foil with a 5.5 cm average chord and 24.3 cm span performing a combined roll and pitch motion. The trailing edge of the foil was tapered. The motion was produced by harmonically rolling and pitching the foil near the root using two-axis control. Tests to determine the mean thrust coefficient of the foil were conducted over a wide parametric space. This parameter space included two roll amplitudes, with induced heave (at the 0.7 span) to chord ratio of hO.7 / c = 1.00 and 1.50; respectively, with Strouhal numbers ranging from 0.20 to 0.80; and maximum angle of attack varying between 15 and 50 degrees. The angle of attack and Strouhal number were also defined using the motion at the 0.7 span. A planform area mean thrust coefficient of 2.07 was recorded for 40 degrees maximum angle of attack and h0.7 / c = 1.50. Experiments to measure the mean lift and thrust coefficient were performed after adding a static bias to the foil pitch. Mean lift coefficients of near 4 were achieved in this manner. Further maneuvering tests were accomplished by measuring the forces produced by an impulsively starting foil in still water and at U = 0.4 m/s. Peak forces and impulse were measured for pitch angles between 30 and 90 degrees and for three different roll velocities. The highest propulsive impulse measured was 2.25 Newton-seconds at a maximum roll amplitude of 1.28 m/s and pitch angle of 40 degrees. Wake velocities were measured using Laser Doppler Velocimetry (LDV) and Digital Particle Imaging Velocimetry (DPIV) in three ancillary experiments. First, mean velocities across the wake at five spanwise locations were recorded using LDV. The wake width was found to be the excursion of the foil at the 70% span, validating our previous assumption. In the second experiment, using LDV, we measured the phase-average velocity and produced a three-dimensional plot of the wake behind the foil at the 0.7 span. Finally, DPIV for the same flapping parameters map the velocity field in the wake for various foil positions in a half-cycle.