Propulsive Performance of Pitching Foils Investigated with Viscous Vortex Particle Method

Abstract

Unsteady flapping foil based thrusters have emerged as ideal candidates for enabling propulsion in bioinspired and bio-mimetic devices such as autonomous underwater vehicles. To a large extent, this emergence has been driven by the extensive utilization of undulatory body motions in a wide spectrum of small to medium-sized swimming aquatic organisms. In the present work, the propulsive performance and related wake characteristics of both thrust generating towed foils and self-propelling pitching foils are investigated over a wide range of Reynolds numbers (Re) from 10 to 10,000. The effect of geometric and kinematic parameters like Strouhal number (St), amplitude of pitching and density ratio of the foil to fluid have been investigated from an energetic efficiency perspective. The above studies are performed using a high resolution two dimensional viscous vortex particle method (VVPM) based fluid structure interaction solver capable of handling both actively and passively moving bodies. The solver incorporates a new coupling algorithm for passively moving rigid bodies using vortex impulse. In order to reduce the time to solution of the solver, the implementation has been ported onto a graphics processing unit(GPU). For thrust producing towed foils, a sharp increase is observed in the peak energetic efficiency as Re is increased from 50 to 1000, with the efficiency values being nearly constant at higher Re values. The wake shows a variety of different regimes that are dependent on Re and St, and a wake map has been obtained in this two-dimensional parameter space. The map shows that the peak efficiency values at a given Re correspond to the region where the wake is asymmetric, while the von Karman to reverse von Karman wake transition precedes the drag-to-thrust transition at all Re. For thick foils, the number of wake regimes is found to substantially increase primarily due to the generation of a stronger leading edge vortex, which in turn interacts with the trailing edge vortex; this interaction being sensitive to the motion parameters of the pitching foil. An important characteristic of such propulsion systems is the St for the transition from drag to thrust at a given Re, with this value showing a very clear power law scaling with Re. This scaling relation can also be independently derived based on a balance between thrust produced from pitching motions and the viscous skin friction drag. At this transition condition, the net force is zero, and this corresponds to the case when the foil is self-propelling. For such selfpropelling cases, studies have been done with different degrees of freedom, which includes permitting only chordwise motion and the possibility of self-induced heaving motions during the pitching cycle. The average chordwise self-propelled motions of the pitching foil are found to be strongly dependent on the degrees of freedom. This work thus provides a comprehensive characterization of pitching foil based propulsion under both thrust producing towed and self-propelling conditions from both the energetic and the wake perspective.