On the absence of asymmetric wakes for periodically plunging finite wings

Abstract

It has previously been shown that, at high Strouhal numbers, oscillating airfoils can produce deflected jets that can create very high lift-coefficients for otherwise symmetric scenarios. These deflected jets form through pairing of the trailing-edge vortices to create asymmetric vortex couples that self-propel at an angle to the freestream, resulting in an asymmetric flow field and non-zero lift. In this paper results are presented that indicate these high-lift deflected jets cannot form for finite wings. Instead of the straight vortex tubes that pair and convect at an angle to the freestream observed for effectively infinite wings, finite wings exhibit vortex tubes that break into two branches near the tip forming double helix structures. One branch connects with the last vortex; one branch connects with the next vortex. This creates a long “daisy chain” of interconnected trailing edge vortices forming a long series of vortex loops. These symmetric flow fields are shown to persist for finite wings even to Strouhal numbers more than twice those required to produce asymmetric wakes on plunging airfoils. Two contributing reasons are discussed for why deflected jets are not observed. First the tip vortex creates three-dimensionality that discourages vortex coupling. Second, the symmetry of the circulation of the interconnected vortex loops, which has been confirmed by the experiments, is a natural consequence of the vortex topology. Therefore, the asymmetry in trailing edge vortex strength previously observed as characteristic of deflected jets cannot be supported for finite wings.

Computational Investigation of Vortex Dynamics and Aerodynamic Performance in Flapping Propulsion

“…In those previous studies, only single interconnected vortex loops were observed around the trailing edge during each half cycle, and the loops exhibited symmetry about the spanwise central plane [21,27]. In the current study, however, the rolling motion results in a faster development of the leading-edge vortex However, according to the top view ( Figure 4-7 (c)), two key features differentiate the current wake structures from those of previous studies.…”

“…The wake topology and force production for the flapping circular plate is examined at Note that the "double-C"-shaped vortex structures generated around the plate trailing edge are distinct from the observations in previous studies on purely pitching [24,25,102,103], purely heaving [21], and pitching-heaving [23,26,27] panels/foils. In those previous studies, only single interconnected vortex loops were observed around the trailing edge during each half cycle, and the loops exhibited symmetry about the spanwise central plane [21,27].…”

“…At higher Strouhal numbers, the shed vortex pairs propagate at an angle to the streamwise axis, and the inverse von Ká rmá n vortex pattern gives rise to an asymmetric wake [16,17,18,19,20], as shown in Figure 1-3 (c). However, for finite-aspect-ratio plates undergoing identical motions, the asymmetric wakes are absent due to the suppression of vortex coupling by the three dimensionality and the symmetric circulation distribution along the interconnected vortex loops [21]. Numerous studies have been conducted to understand the wake structures and the propulsive performance of finite-aspect-ratio plates undergoing pitching and/or heaving motions.…”

“…In the current study, however, the rolling motion results in a faster development of the leading-edge vortex However, according to the top view ( Figure 4-7 (c)), two key features differentiate the current wake structures from those of previous studies. First, in previous pitching and/or heaving studies [21,25,26], the vorticity generated by the streamwise edges dominates the evolution of the wake.…”

Aerodynamics of bird flight

“…Naturally, in this case interaction with the spanwise oriented vortices cannot be avoided (see, e.g., Fig. 12), as apparent from the complex wake structure [11].…”