Global vorticity shedding for a vanishing wing

Abstract

If a moving body were made to vanish within a fluid, its boundary-layer vorticity would be released into the fluid at all locations simultaneously, a phenomenon we call global vorticity shedding. We approximate this process by studying the related problem of rapid vorticity transfer from the boundary layer of a body undergoing a quick change of cross-sectional and surface area. A surface-piercing foil is first towed through water at constant speed, U, and constant angle of attack, then rapidly pulled out of the fluid in the spanwise direction. Viewed within a fixed plane perpendicular to the span, the cross-sectional area of the foil seemingly disappears. The rapid spanwise motion results in the nearly instantaneous shedding of the boundary layer into the surrounding fluid. Particle image velocimetry measurements show that the shed layers quickly transition from free shear layers to form two strong, unequal-strength vortices, formed within non-dimensional time t * = 0.03, based on the foil chord and forward velocity. These vortices are connected to, and interact with, the foil's tip vortex through additional streamwise vorticity formed during the rapid pulling of the foil. Numerical simulations show that two strong spanwise vortices form from the shed vorticity of the boundary layer. The three-dimensional effects of the foil removal process are restricted to the tip of the foil. This method of vorticity transfer may be used for quickly introducing circulation to a fluid to provide forcing for biologically inspired flow control.

Unsteady dynamics of rapid perching manoeuvres

“…The integrated equations are valid over the complete domain and allow for general solid-body dynamics to be simulated. Previous work has validated this approach for a variety of dynamic rigid-body problems such as accelerating aerofoils (Wibawa et al 2012) and deformingbody problems (Weymouth & Triantafyllou 2013). In Maertens & Weymouth (2015) this method was validated against stationary and flapping aerofoil test cases at moderate Re and found to produce accurate and efficient numerical solutions.…”

“…Rapid frontal area change of bodies in acceleratory manoeuvres results in significant added-mass effects, notably the recapture of added-mass energy as demonstrated by in a shrinking cylinder and Weymouth & Triantafyllou (2013) in a squid-like deflating body. Rapid area change can also affect boundary-layer vorticity, causing sudden global shedding of vorticity in a vanishing aerofoil (Wibawa et al 2012) and annihilation of boundary-layer vorticity in a shrinking cylinder .…”

Shape of retracting foils that model morphing bodies controls shed energy and wake structure

“…Finally, in cases of matter phase change, for example in moving bubbles that turn from gas to liquid, the initial energy and vorticity generated by the bubble is shed in the fluid (Eames 2008;Hunt & Eames 2002). All these cases involve transfer of added mass-related kinetic energy to the fluid, as well as simultaneous shedding of boundary layer vorticity over large areas of the body, what is termed "global vorticity shedding" (Wibawa et al 2012;.…”

“…In (Wibawa et al 2012), a high aspect ratio, square-tipped foil was towed with constant angle of attack and steady speed before being rapidly retracted through the free surface of the tank. This experiment was designed as a model problem for morphing bodies that undergo large shape changes, since the cross-section of the body appears to vanish when viewed from a two-dimensional plane within the tank.…”

“…The results from Wibawa et al (2012) showed that a solid, retracting foil, with a rectangular planar form ending with a sharp, square tip, sheds its boundary layer vorticity and added mass energy as it is being retracted, leaving ultimately two strong columnar vortices parallel to its spanwise direction; as well as an additional vortex ring with its axis in the spanwise direction, formed at its sharp tip. The additional ring vortex introduces significant transient three-dimensional flow structures near the tip of the retracting foil.…”