Flow map of foil undergoing combined fast and slow pitching

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.