Effects of Reynolds number and average angle of attack on the laminar scaling of oscillating foils

Abstract

The variation in thrust generation with respect to Reynolds number was numerically evaluated for an oscillating foil with combined pitching and heaving motion at a range of reduced frequencies, amplitudes, and phase offsets. Laminar scaling (R e - 0.5) was found accurate for a reasonable range of average angle of attack (α ¯ < 20 °). However, quantitative evaluation of laminar scaling using statistical measures indicates that its capability in predicting thrust variation weakens at higher reduced frequencies and amplitudes. This coincides with an increase in α ¯ above 20°. Evaluation of the pressure and viscous forces revealed a dominance of the former toward total thrust generated at high frequencies for all cases, which also coincided with lower coefficient of determination (R2) for laminar scaling. The chordwise variation of pressure and skin friction coefficient provided further evidence indicating that pressure, in contrast to the skin friction, did not achieve an asymptotic trend with increasing Reynolds number, especially at higher frequencies and for all phase offsets. Qualitative evaluation of the developing leading edge vortex structure at increasing reduced frequencies and Reynolds numbers also supported the quantitative assessment of chordwise pressure variations. Empirical incorporation of Reynolds number into the complete scaling model was hence completed, which further validates the laminar scaling (R e - 0.5) of propulsive thrust generation in oscillating foils with a coupled motion.