Hydroelastic model for fish-like propulsion

The recent development of new technologies in the fields of control, propulsion and communication has enabled the realization of more efficient bio-mimetic autonomous vehicles (AUV) compared to the traditional vehicles used in the naval and marine fields. The fish-like propulsion mechanism is generated through the oscillatory movement of the fish's tail, which interacts elastically with the external fluid. This process generates interaction forces (i.e.: added mass, damping and stiffness) and a wake vortex that produce a high propulsive efficiency jet. Mathematical models behind bio-mimetic AUVs are highly simplified and the fluid-structure interaction effects are usually neglected to create the interface between the models and real-time control logics. For this reason, the purpose of this paper is to evaluate the influence of hydroelastic effects on the propulsive behavior of the fish's fin. An analytical hydroelastic model is developed to evaluate the fish-like propulsion mechanism when its elastic tail is forced to oscillate, with pitching law ?(t), in a flow moving with constant velocity U. The latter comprises a rigid element connected to a flexible caudal fin, whose vibration is responsible for propulsion. The flexible fin is modelled as a Euler-Bernoulli beam and the hydrodynamic loads are computed from the linear potential theory imposing also the Kutta condition to include the release of vortex wake. The final equation of motion is represented by an integro-differential equation in which convolution terms represent the fluid-structure interaction effects and the vorticity. The propulsive performance of the fish-like system is evaluated by computing: (i) the fin's tip amplitude, related to the maximum beam modal deformation, w(x,t), and (ii) the thrust production obtained projecting the force generated by the pressure difference across the fin in the horizontal direction. The proposed hydroelastic propulsive model is validated through experimental and numerical results available from literature evaluating the influence of the model hypotheses (small deformations and high aspect-ratio) and design parameters (i.e., structural stiffness, geometry, oscillation frequency range) on the propulsive characteristics of the fish-like system.