Flow map of foil undergoing combined fast and slow pitching

Abstract

The drag-thrust transition and wake structures of a pitching foil undergoing combinations of fast and slow pitching are systematically investigated. The foil locomotion having combinations of fast and slow pitching is made by setting a variable s defined as the fraction of the pitching time required on the upper side of the wake centerline. On the other hand, time 1-s is required for the foil to pitch on the lower side of the wake centerline. Compared to the symmetric pitching (s = 0.5) case, the time-mean thrust rapidly increases and the drag-thrust boundary advances with increasing |s − 0.5|. The Kármán vortex street slants and produces thrust when |s − 0.5| is sufficiently large, which supersedes the previous thumb rule that only reverse Kármán vortex street can produce thrust. The faster forward stroke determines the slant direction of the vortex street. The detailed wake structures produced by the pitching foil are discussed, showing how the combined pitching affects vortex dynamics, drag-thrust transition, slant direction, and wake jet. This work provides a physical basis for understanding the hydrodynamics of native swimmers which may be useful to design bio-inspired underwater robots.

Hydrodynamic performance of slender swimmer: effect of travelling wavelength

“…2019; Chao et al. 2021 b ). The emergence of the 2S aligned wake at the KV–RKV boundary (red dashed line) precedes the drag–thrust boundary (black solid line) in the St -- Re map (figure 17).…”

“…2019; Chao, Alam & Ji 2021 a ; Chao et al. 2021 b ). Alam & Muhammad (2020) analysed the fluid dynamics based on inertia, using relative angular acceleration with respect to the foil, showing that the fluid dynamics is strongly dictated by the inertia of the foil.…”

“…St = 2fA L /U. On the other hand, the propulsive force of a pitching foil is linked to the wake patterns generated by the foil (Zhang 2017;Chao et al 2021b). The Kármán vortex (KV) wake and reverse Kármán vortex (RKV) wake are generally considered to produce drag and thrust, respectively (Von Kármán & Burgers 1934).…”

Effect of combined heaving and pitching on propulsion of single and tandem flapping foils

“…The influence of pitch and heave amplitude on propulsion has not been comprehensively investigated for tandem flapping foils. However, some of the works [38][39][40][41][42][43] deal with the effect of these parameters on a single foil. The St -pitch amplitude parametric space was studied for a single foil and a rich spectrum of wake behavior was observed 40,41 .…”

“…However, some of the works [38][39][40][41][42][43] deal with the effect of these parameters on a single foil. The St -pitch amplitude parametric space was studied for a single foil and a rich spectrum of wake behavior was observed 40,41 . In the case of asymmetric foil motion 42 , the mean thrust coefficient was noted to increase with pitch amplitude at Re = 3000 and Re = 10000.…”