Optimal Force Generation with Fluid-Structure Interactions
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Typical computational and experimental methods are unsuitable for studying large scale optimization problems involving complex fluid structure interactions, primarily due to their time-consuming nature. A novel experimental approach is proposed here that provides a high-fidelity and efficient alternative to discover optimal parameters arising from the passive interaction between structural elasticity and fluid dynamic forces. This approach utilizes motors, force transducers, and active controllers to emulate the effects of elasticity, eliminating the physical need to replace structural components in the experiment. A clustering genetic algorithm is then used to tune the structural parameters to achieve desired optimality conditions, resulting in approximated global optimal regions within the search bound. A prototype fluid-structure interaction experiment inspired by the lift generation of flapping wing insects is presented to highlight the capabilities of this approach. The experiment aims to maximize the average lift on a sinusoidally translating plate, by optimizing the damping ratio and natural frequency of the plate's elastic pitching dynamics. Reynolds number, chord length, and stroke length are varied between optimizations to explore their relationships to the optimal structural parameters. The results reveal that only limited ranges of stroke lengths are conducive to lift generation; there also exists consistent trends between optimal stroke length, natural frequency, and damping ratio. The measured lift, pitching angle, and torque on the plate for optimal scenarios exhibit the same frequency as the translation frequency, and the phase angles of the optimal structural parameters at this frequency are found to be independent of the stroke length. This critical phase can be then characterized by a linear function of the chord length and Reynolds number. Particle image velocimetry measurements are acquired for the kinematics generated with optimal and suboptimal structural parameters. By examining the vorticity field and the measured lift, leading edge vortices and added mass are identified as primary lift generation mechanisms under optimality. This is similar to the unsteady lift generating mechanism employed by flapping wing insects. Further analysis reveals that longer stroke lengths rely mainly on vortex formation to maximize average lift, whereas added-mass effects / wing wake interaction become more prominent at shorter stroke lengths.