Performance augmentation mechanism of in-line tandem flapping foils

Abstract

The propulsive performance of a pair of tandem flapping foils is sensitively dependent on the spacing and phasing between them. Large increases in thrust and efficiency of the hind foil are possible, but the mechanisms governing these enhancements remain largely unresolved. Two-dimensional numerical simulations of tandem and single foils oscillating in heave and pitch at a Reynolds number of 7,000 are performed over a broad and dense parameter space, allowing the effects of inter-foil spacing (S) and phasing (ϕ) to be investigated over a range of non-dimensional frequencies (or Strouhal number, St). Results indicate that the hind foil can produce from no thrust, to twice the thrust of a single foil depending on its spacing and phasing with respect to the fore foil, which is consistent with previous studies that were carried out over a limited parameter space. Examination of instantaneous flowfields indicate that high thrust occurs when the hind foil weaves in between the vortices that have been shed by the fore foil, and low thrust occurs when the hind foil intercepts these vortices. Contours of high thrust and minimal thrust appear as inclined bands in the S − ϕ parameter space and this behaviour is apparent over the entire range of Strouhal numbers considered (0.2 St 0.5). A novel quasi-steady model that utilises kinematics of a virtual hind foil together with data obtained from simulations of a single flapping foil shows that performance augmentation is primarily determined through modification of the instantaneous angle of attack of the hind foil by the vortex street established by the fore foil. This simple model provides estimates of thrust and efficiency for the hind foil, which is consistent with data obtained through full simulations. The limitations of the virtual hind foil method and its physical significance is also discussed.

Modeling Transverse Gusts Using Pitching, Plunging, and Surging Airfoil Motions

“…[20]) to immerse the dynamic solid boundaries into the fluid domain. This method has been shown to give accurate results for a variety of unsteady airfoil problems closely related to the current work, including unsteady dynamics due to a perching maneuver, as shown by Polet et al [21], and the performance of tandem flapping foils, as shown by Muscutt et al [22].…”

The four-flipper swimming method of plesiosaurs enabled efficient and effective locomotion

“…Furthermore, while we endeavoured to reconstruct flippers with the greatest fidelity, it is important to note that the fundamental flow phenomena that result in the propulsive performance reported herein are relatively insensitive to either the details of the outline or the flexibility of the flippers. The vortex shedding and the interaction between the leading and trailing flippers are apparent in two-dimensional simulations [27], which demonstrate their independence from planform shape. Flexibility has been shown to affect the details of flapping foil propulsion, but not the basic flow patterns [35].…”

“…At the top and bottom of the flapping stroke, these vortices separate from the wing and are shed downstream to create two lines of vortices of alternating sign behind the wing, known as a 'vortex street' [16][17][18]. Thus, if another wing is present behind the first, these vortices and induced velocities will affect the performance (thrust and efficiency) of the hind wing [19][20][21][22][23][24][25][26][27]; this effect is known as performance (or thrust or efficiency) augmentation, and is strongest for certain spacing and phase differences between the wings, shown by a variety of studies [19][20][21][22][23][24][25][26][27][28][29][30], including on dragonfly flight [28,29] and the flocking of migrating birds [30].…”

Flow interactions of two- and three-dimensional networked bio-inspired control elements in an in-line arrangement

“…A performance enhancement was reported for all the arrangements, although the foils in the triangular formation were shown to perform poorly compared with the other arrangements. Finally, exper imental studies have identified that the thrust and efficiency enhancement of in-line foils can be understood simply as alterations in the angle of attack of the follower foil leading to enhancements or degradations in the force production [19][20][21]. All of these studies advanced our knowledge of two-dimensional interactions among propulsors, however, far fewer studies have examined the three-dimensional interactions that occur between fins and in fish schools.…”