Wake structure and thrust generation of a flapping foil in two-dimensional flow

Abstract

We present a combined numerical (particle vortex method) and experimental (soap film tunnel) study of a symmetric foil undergoing prescribed oscillations in a two-dimensional free stream. We explore pure pitching and pure heaving, and contrast these two generic types of kinematics. We compare measurements and simulations when the foil is forced with pitching oscillations, and we find a close correspondence between flow visualisations using thickness variations in the soap film and the numerically determined vortex structures. Numerically, we determine wake maps spanned by oscillation frequency and amplitude, and we find qualitatively similar maps for pitching and heaving. We determine the drag–thrust transition for both pitching and heaving numerically, and we discuss it in relation to changes in wake structure. For heaving with low oscillation frequency and high amplitude, we find that the drag–thrust transition occurs in a parameter region with wakes in which two vortex pairs are formed per oscillation period, in contrast to the common transition scenario in regions with inverted von Kármán wakes.

Swimmers’ wake structures are not reliable indicators of swimming performance

“…Although the reverse von Kármán vortex street is the most commonly encountered wake vortex pattern, many other patterns are possible. In figure 3 we have sketched some of the patterns observed in the experiments and computations of [10]; even more exotic patterns have been observed. With wildly varying wake patterns, we may expect to see large differences in swimming performance as the wake transitions from one pattern to another.…”

“…Conclusions regarding thrust based on the vertical spacing of vortices are inaccurate, however. Generally speaking, the drag-thrust transition occurs when the wake is already a "thrust-type" wake [10], since some excess streamwise fluid momentum is needed to overcome profile drag or velocity fluctuations and pressure differences in the control volume [11,12]. Furthermore, even "drag-producing" wakes have been observed to produce thrust [10].…”

“…Generally speaking, the drag-thrust transition occurs when the wake is already a "thrust-type" wake [10], since some excess streamwise fluid momentum is needed to overcome profile drag or velocity fluctuations and pressure differences in the control volume [11,12]. Furthermore, even "drag-producing" wakes have been observed to produce thrust [10]. In this context, the recent work by Lagopoulos et al [13] offers an alternative method to distinguish drag-and thrust-producing behavior based on kinematic inputs instead of the vortex arrangement.…”

Universal scaling law for drag-to-thrust wake transition in flapping foils

“…This was also supported by Taylor et al (2003) and Triantafyllou et al (1993) who observed that the majority of natural fliers and swimmers prefer to cruise within this range. According to Andersen et al (2017), BvK reversal occurs at different St A values for pure heave and pure pitch. Therefore, St A cannot be regarded as an expression of self similarity.…”

Footprints of a flapping wing

“…The article by Andersen et al (2017) presents a detailed and revealing investigation of the rich variety of wake structures of a flapping wing, and relates the changes in the wake structure to the transition from drag to thrust.…”