Locomotion performance for oscillatory swimming in free mode

Abstract

Oscillatory swimming of a fishlike body, whose motion is essentially promoted by the flapping tail, has been studied almost exclusively in axial mode under an incoming uniform stream or, more recently, self-propelled under a virtual body resistance. Obviously, both approaches do not consider the unavoidable recoil motions of the actual body which have to be necessarily accounted for in a design procedure for technological means. Actually, once combined with the prescribed kinematics of the tail, the recoil motions have an essential impact on the resulting swimming performance. An inviscid impulse model, linear in both potential and vortical contributions, is a proper tool to obtain a deeper comprehension of the physical events with respect to more elaborated flow interaction models. In fact, at a first look, the numerical results seem to be quite entangled, since their trends in terms of the main flapping parameters are not easy to be identified and a fair interpretation is obtained by means of the model capability to separate the effects of added mass and vortex shedding. Specifically, a prevailing dependence of the potential contribution on the heave amplitude and of the vortical contribution on the pitch amplitude is instrumental to unravel their combined action. A further aid for a proper interpretation of the data is provided by accounting separately for a geometrical component of the recoil which is expected to follow from the annihilation of any spurious rigid motion in case no fluid interactions occur. The above detailed decomposition of the recoil motions shows, through the numerical results, how the single components are going to influence the main flapping parameters and the locomotion performance as a guide for the design of biomimetic swimmers.

How Free Swimming Fosters the Locomotion of a Purely Oscillating Fish-like Body

“…In case Equations ( 11 ) and ( 12 ) are not satisfied, the resulting spurious motions of the center-of-mass, known as geometrical recoil motions, may be removed as detailed in [ 14 ]. By considering that the second term in Equation ( 8 ) is the force acting on the fluid, which is opposite to the force on the body, and by combining with Equation ( 2a ), we obtain: and, similarly, from Equations ( 9 ) and ( 2b ): where is the body mass and the angular impulse is recast from Equation ( 2b ) in terms of the distance as …”

“…Let us remark that prescribing the body deformation requires two additional mathematical conditions given by the conservation of linear and angular momenta to avoid spurious external actions (see [ 14 ]).…”

“…From a theoretical point of view, this observation is perfectly consistent with the presence of recoil motions, i.e., further rigid motions of the body beyond the main forward locomotion, generated by the fluid interaction to satisfy the equilibrium of the entire system as underlined in the early 1960s by Lighthill [ 12 ] and Wu [ 13 ]. Once in the water frame, these recoil motions are seen to modify the oscillating deformation of the body to establish again a sort of favorable undulation (see also [ 14 ]). In other words, by letting a purely oscillating fish-like body experience all the recoil motions, we find a partial recovery of the self-propulsion capability which, on the contrary, is severely reduced if the swimmer is axially constrained.…”

“…The significance of the recoil, as a beneficial effect on the performance, was previously analyzed ([ 15 , 16 ]) in the realm of plain undulatory swimming by considering several constrained motions, with one or more velocity components totally prevented to force the fish along a compatible trajectory. Analogously, the beneficial effect of the recoil motion, once combined with the prescribed body deformation, has been analyzed for the flapping tail propeller in a typical oscillatory swimming [ 14 ]. The comprehension of all the above issues may be of a certain interest for the design of biomimetic swimmers to suggest the geometrical configuration and the kinematical parameters to obtain the most appropriate swimming style for the desired application.…”

Special issue: bioinspired fluid-structure interaction

“…Han et al [4] show that non-uniformly flexible foils can outperform their rigid and uniformly flexible counterparts, providing guidance for the development of underwater vehicles using simple purely pitching bio-inspired propulsive drives. Paniccia et al [5] compute the recoil reaction during flapping and the locomotion speed of a fish-like body using a simple impulse model able to highlight the added mass and the released vorticity contributions. Their impulse model, linear in both potential and vortical contributions, allows one to understand the capability of the potential terms to attenuate the recoil reaction continuously forced by the vortex shedding which is directly related to the wasted energy.…”