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An unsteady three-dimensional boundary element method is developed to providefast calculations of biological and bio-inspired self-propelled locomotion. Theapproach uniquely combines an unsteady three-dimensional boundary elementmethod, a boundary layer solver and self-propelled equations of motion. Thisnovel implementation allows for the self-propelled speed, power, efficiency andeconomy to be accurately calculated. A Dirichlet formulation is used with acombination of constant strength source and doublet elements to represent adeforming body with a nonlinearly deforming wake. The wake elements aredesingularized to numerically stabilize the evolution of the wake vorticity.Weak coupling is used in solving the equations of motion and in the boundarylayer solution. The boundary layer solver models both laminar and turbulentbehavior along the deforming body to estimate the total skin friction dragacting on the body. The results from the method are validated with analyticalsolutions, computations and experiments. Finally, a bio-inspired self-propelledundulatory fin is modeled. The computed self-propelled speeds and wakestructures agree well with previous experiments. The computations go beyond theexperiments to gain further insight into the propulsive efficiency forself-propelled undulating fins. It is found that the undulating fin produces atime-averaged momentum jet at 76% of the span that accelerates fluid in thestreamwise direction and in turn generates thrust. Additionally, it isdiscovered that high amplitude motions suppress the formation of a bifurcatingmomentum jet and instead form a single core jet. Consequently, this maximizesthe amount of streamwise momentum compared to the amount of wasted lateralmomentum and leads to a propulsive efficiency of 78% during self-propelledlocomotion.

Unsteady three-dimensional boundary element method for self-propelled bio-inspired locomotion