Vortex Dynamics of a Vortex Pair in Wall Effect and Flapping Airfoil Propulsion

Abstract

Vorticity provides the means to exchange momentum between objects and their surrounding fluid. As such, vorticity can be potentially harmful, as seen in the hazard posed by strong counter-rotating vortex pairs generated behind aircraft in flight. Conversely, the production of strong vortical wakes is beneficial to birds and fish, which exploit their generation to produce thrust. In this work, we will examine two classes of flows in which vorticity plays a key role. In the first flow, we simulate the trailing vortex pair of an aircraft in a water tank. Such counter-rotating vortex pairs are commonly observed to undergo an instability involving a sinusoidal displacement, which ultimately leads to the generation of a series of large vortex rings. As these trailing vortices are most dangerous when aircraft are in close proximity, such as near the ground, we study the behavior of this instability when it is interrupted by a solid wall. In the presence of the wall, the interaction between the primary vortex pair and secondary vorticity generated in the boundary layer leads to significant topological changes and the production of arrays of smaller-scale vortex rings, the precise configuration of which depends on the extent of development of the instability before wall interaction. In the second flow, we examine the behavior of an airfoil oscillating with pitching and heaving motions. Many animal studies have shown that such flapping airfoils enable high agility and are also quite effective in producing thrust. Similar vehicles are under development for applications such as search and rescue, environmental monitoring, and reconnaissance. In order to reduce weight and complexity of the propulsive mechanism, however, we equip the airfoil with an actuator in the heave direction but allow it to pitch passively under the control of a torsion spring. In this system, variation of the spring stiffness and the chordwise pivot location allows control of the vortex wake produced by the airfoil, enabling it to produce either thrust or drag as desired. If these parameters are well selected, performance can even be comparable to that of a system with two actively controlled degrees of freedom. Finally, the majority of existing studies of flapping airfoils use a fixed incoming flow velocity, achieved either by towing the vehicle at a constant speed or by placing it in a water channel. This imposed velocity does not necessarily correspond to that at which the vehicle would naturally travel, determined by a balance of the vehicle's drag and the thrust produced by the airfoil. Using a cyber-physical fluid dynamics technique, in which force-feedback determines the acceleration of the airfoil in real time, we can simulate self-propulsion for a wide range of heaving and pitching amplitudes. For a given cruising velocity, we determine the combination of pitch and heave that enables the most efficient propulsion and examine the characteristics of the forces and vorticity produced that correspond to this condition.