Simplified geometries can be used to isolate the effects of flexibility in swimming fish. Here we used an oscillating flexible rectangular panel to explore how efficiency is affected by frequency, heave amplitude, pitch amplitude, heave-pitch offset, and swimming speed. We found that optimal swimming occurs when the panel-water system is resonating, the trailing edge vortices are coherent, the amplitude is large but not so much that the flow separates, and pitch lags heave by about 90 degrees. (This work is from PI Quinn’s research prior to the SFS Lab and is archived here for reference.)
Authors: Daniel Quinn, George Lauder, Alexander Smits
Abstract: Experimental gradient-based optimization is used to maximize the propulsive efficiency of a heaving and pitching flexible panel. Optimum and near-optimum conditions are studied via direct force measurements and particle image velocimetry (PIV). The net thrust and power scale predictably with the frequency and amplitude of the leading edge, but the efficiency shows a complex multimodal response. Optimum pitch and heave motions are found to produce nearly twice the efficiencies of optimum heave-only motions. Efficiency is globally optimized when (i) the Strouhal number is within an optimal range that varies weakly with amplitude and boundary conditions; (ii) the panel is actuated at a resonant frequency of the fluid–panel system; (iii) heave amplitude is tuned such that trailing-edge amplitude is maximized while the flow along the body remains attached; and (iv) the maximum pitch angle and phase lag are chosen so that the effective angle of attack is minimized. The multi-dimensionality and multi-modality of the efficiency response demonstrate that experimental optimization is well-suited for the design of flexible underwater propulsors.