Abstract
The bio-mimetic propulsion consists in propelling a nautical device by the oscillation of a profiled body (foil), in the way of the caudal fin of cetaceans. The will to reduce energy consumption and pollution generated by maritime transport, actively motivates the exploration of this propulsion principle which is an alternative to propellers. However, experimental Facilities and high-fidelity numerical simulations remain expensive and hard to set up. The work carried out has led to the development of a reduced order model allowing to rapidly simulate the performances of a flapping foil and to study the influence of its flexibility.The developed model is based on a strong coupling between a non-linear 3D lifting-line method and a dynamic stall model. The non-linear 3D lifting-line method allows to quickly estimate the hydrodynamic loading acting on a finite span foil with sweep, dihedral and twist in a stationary flow. It is a numerical version of the Prandtl's lifting-line method. It is enhanced with a 3D version of the Kutta-Jukowski theorem and a non-linear resolution algorithm, allowing non-linear 2D polars to be used. An artificial viscosity has been added to the lifting-line equations to allow the correct representation of the static stall phenomenon. The dynamic stall model used is a modified version of the Beddoes-Leishman model. This model allows to quickly obtain the dynamic coefficients of lift, drag and moment for a 2D profile subjected to any motion. The unsteady simulation of flapping foil is performed by a moving lifting-line simulation, for which the behaviour of each spanwise section is given by the dynamic stall model. An unsteady wake generated by vortex shedding is also added downstream of the foil in order to allow the story of the movement to be taken into account.The conditions of the simulations performed were chosen to be representative of cetacean swimming. That is, the foil motion is composed of heaving and pitching simultaneously. The Reynolds number of the flow is large (Re>10^4). The amplitude of the foil motion is in the same order of magnitude than its chord length, and the Strouhal number of the oscillation is in the order of magnitude St=0.3, consistent with the biological observations.The obtained results revealed the influence of the motion on the Strouhal number maximizing the propulsive efficiency of the foil. Furthermore, the results showed that the benefit provided by the flexibility of the foil is greater for combined heave and pitch motions, compared to pure heave motion. Flexibility is also more favourable when the amplitude of motion is small. The maximum propulsive efficiency obtained is 0.89 and the maximum benefit due to flexibility is 6.6%.