Michael S. Triantafyllou

Oscillating foils of high propulsive efficiency

Thrust-producing harmonically oscillating foils are studied through force and power measurements, as well as visualization data, to classify the principal characteristics of the flow around and in the wake of the foil. Visualization data are obtained using digital particle image velocimetry at Reynolds number 1100, and force and power data are measured at Reynolds number 40 000. The experimental results are compared with theoretical predictions of linear and nonlinear inviscid theory and it is found that agreement between theory and experiment is good over a certain parametric range, when the wake consists of an array of alternating vortices and either very weak or no leading-edge vortices form. High propulsive efficiency, as high as 87%, is measured experimentally under conditions of optimal wake formation. Visualization results elucidate the basic mechanisms involved and show that conditions of high efficiency are associated with the formation on alternating sides of the foil of a moderately strong leading-edge vortex per half-cycle, which is convected downstream and interacts with trailing-edge vorticity, resulting eventually in the formation of a reverse Karman street. The phase angle between transverse oscillation and angular motion is the critical parameter affecting the interaction of leading-edge and trailing-edge vorticity, as well as the efficiency of propulsion.

Drag reduction in fish-like locomotion

We present experimental force and power measurements demonstrating that the power required to propel an actively swimming, streamlined, fish-like body is significantly smaller than the power needed to tow the body straight and rigid at the same speed U . The data have been obtained through accurate force and motion measurements on a laboratory fish-like robotic mechanism, 1.2 m long, covered with a flexible skin and equipped with a tail fin, at Reynolds numbers up to 10 6 , with turbulence stimulation. The lateral motion of the body is in the form of a travelling wave with wavelength λ and varying amplitude along the length, smoothly increasing from the front to the tail end. A parametric investigation shows sensitivity of drag reduction to the non-dimensional frequency (Strouhal number), amplitude of body oscillation and wavelength λ, and angle of attack and phase angle of the tail fin. A necessary condition for drag reduction is that the phase speed of the body wave be greater than the forward speed U . Power estimates using an inviscid numerical scheme compare favourably with the experimental data. The method employs a boundary-integral method for arbitrary flexible body geometry and motions, while the wake shed from the fish-like form is modelled by an evolving desingularized dipole sheet.

Review of experimental work in biomimetic foils

Significant progress has been made in understanding some of the basic mechanisms of force production and flow manipulation in oscillating foils for underwater use. Biomimetic observations, however, show that there is a lot more to be learned, since many of the functions and details of fish fins remain unexplored. This review focuses primarily on experimental studies on some of the, at least partially understood, mechanisms, which include 1) the formation of streets of vortices around and behind two- and three-dimensional propulsive oscillating foils; 2) the formation of vortical structures around and behind two- and three-dimensional foils used for maneuvering, hovering, or fast-starting; 3) the formation of leading-edge vortices in flapping foils, under steady flapping or transient conditions; 4) the interaction of foils with oncoming, externally generated vorticity; multiple foils, or foils operating near a body or wall.

The Kármán gait: novel body kinematics of rainbow trout swimming in a vortex street

SUMMARY Most fishes commonly experience unsteady flows and hydrodynamic perturbations during their lifetime. In this study, we provide evidence that rainbow trout Oncorhynchus mykiss voluntarily alter their body kinematics when interacting with vortices present in the environment that are not self-generated. To demonstrate this, we measured axial swimming kinematics in response to changes in known hydrodynamic wake characteristics. We compared trout swimming in the Kármán street behind different diameter cylinders (2.5 and 5 cm) at two flow speeds (2.5 and 4.5 L s-1, where L is total body length) to trout swimming in the free stream and in the cylinder bow wake. Trout swimming behind cylinders adopt a distinctive, previously undescribed pattern of movement in order to hold station, which we term the Kármán gait. During this gait, body amplitudes and curvatures are much larger than those of trout swimming at an equivalent flow velocity in the absence of a cylinder. Tail-beat frequency is not only lower than might be expected for a trout swimming in the reduced flow behind a cylinder, but also matches the vortex shedding frequency of the cylinder. Therefore, in addition to choosing to be in the slower flow velocity offered behind a cylinder (drafting), trout are also altering their body kinematics to synchronize with the shed vortices (tuning), using a mechanism that may not involve propulsive locomotion. This behavior is most distinctive when cylinder diameter is large relative to fish length. While tuning, trout have a longer body wavelength than the prescribed wake wavelength, indicating that only certain regions of the body may need to be oriented in a consistent manner to the oncoming vortices. Our results suggest that fish can capture energy from vortices generated by the environment to maintain station in downstream flow. Interestingly, trout swimming in front of a cylinder display lower tail-beat amplitudes and body wave speeds than trout subjected to any of the other treatments, implying that the bow wake may be the most energetically favorable region for a fish to hold station near a cylinder.

Wake mechanics for thrust generation in oscillating foils

Foils oscillating transversely to an oncoming uniform flow produce, under certain conditions, thrust. It is shown through experimental data from flapping foils and data from fish observation that thrust develops through the formation of a reverse von Karman street whose preferred Strouhal number is between 0.25 and 0.35, and that optimal foil efficiency is achieved within this Strouhal range.

Forces on oscillating foils for propulsion and maneuvering

Abstract Experiments were performed on an oscillating foil to assess its performance in producing large forces for propulsion and effective maneuvering. First, experiments on a harmonically heaving and pitching foil were performed to determine its propulsive efficiency under conditions of significant thrust production, as function of the principal parameters: the heave amplitude, Strouhal number, angle of attack, and phase angle between heave and pitch. Planform area thrust coefficients of 2.4 were recorded for 35° maximum angle of attack and efficiencies of up to 71.5% were recorded for 15° maximum angle of attack. A plateau of good efficiency, in the range of 50–60%, is noted. A phase angle of 90–100° between pitch and heave is found to produce the best thrust performance. Also, the introduction of higher harmonics in the heave motion, so as to ensure a sinusoidal variation in the angle of attack produced much higher thrust coefficient at high Strouhal numbers. Second, experiments on a harmonically oscillating foil with a superposed pitch bias, as well as experiments on impulsively moving foils in still water, were conducted to assess the capability of the foil to produce large lateral forces for maneuvering. Mean side force coefficients of up to 5.5, and instantaneous lift coefficients of up to 15 were recorded, demonstrating an outstanding capability for maneuvering force production.

Active vorticity control in a shear flow using a flapping foil

It is shown experimentally that free shear flows can be substantially altered through direct control of the large coherent vortices present in the flow. First, flow-visualization experiments are conducted in Kalliroscope fluid at Reynolds number 550. A foil is placed in the wake of a D-section cylinder, sufficiently far behind the cylinder so that it does not interfere with the vortex formation process. The foil performs a heaving and pitching oscillation at a frequency close to the Strouhal frequency of the cylinder, while cylinder and foil also move forward at constant speed. By varying the phase of the foil oscillation, three basic interaction modes are identified

Passive propulsion in vortex wakes

A dead fish is propelled upstream when its flexible body resonates with oncoming vortices formed in the wake of a bluff cylinder, despite being well outside the suction region of the cylinder. Within this passive propulsion mode, the body of the fish extracts sufficient energy from the oncoming vortices to develop thrust to overcome its own drag. In a similar turbulent wake and at roughly the same distance behind a bluff cylinder, a passively mounted high-aspect-ratio foil is also shown to propel itself upstream employing a similar flow energy extraction mechanism. In this case, mechanical energy is extracted from the flow at the same time that thrust is produced. These results prove experimentally that, under proper conditions, a body can follow at a distance or even catch up to another upstream body without expending any energy of its own. This observation is also significant in the development of low-drag energy harvesting devices, and in the energetics of fish dwelling in flowing water and swimming behind wake-forming obstacles.

Three-dimensional flow structures and vorticity control in fish-like swimming

We employ a three-dimensional, nonlinear inviscid numerical method, in conjunction with experimental data from live fish and from a fish-like robotic mechanism, to establish the three-dimensional features of the flow around a fish-like body swimming in a straight line, and to identify the principal mechanisms of vorticity control employed in fish-like swimming. The computations contain no structural model for the fish and hence no recoil correction. First, we show the near-body flow structure produced by the travelling-wave undulations of the bodies of a tuna and a giant danio. As revealed in cross-sectional planes, for tuna the flow contains dominant features resembling the flow around a two-dimensional oscillating plate over most of the length of the fish body. For the giant danio, on the other hand, a mixed longitudinal–transverse structure appears along the hind part of the body. We also investigate the interaction of the body-generated vortices with the oscillating caudal fin and with tail-generated vorticity. Two distinct vorticity interaction modes are identified: the first mode results in high thrust and is generated by constructive pairing of body-generated vorticity with same-sign tail-generated vorticity, resulting in the formation of a strong thrust wake; the second corresponds to high propulsive efficiency and is generated by destructive pairing of body-generated vorticity with opposite-sign tail-generated vorticity, resulting in the formation of a weak thrust wake.

Efficient Foil Propulsion Through Vortex Control

We investigate the problem of a heaving and pitching hydrofoil in an inflow that consists of a uniform velocity field and a staggered array of vortices. The foil can exploit the energy in such a Karman vortex street for efficient propulsion of animals or submarines. Through a two-dimensional inviscid analysis, we find that the phase between foil motion and the arrival of inflow vortices is a critical parameter. Everything else being equal, the highest efficiency is seen when this phase is such that the foil moves in close proximity to the oncoming vortices. Different modes of vortex interaction in the wake results from a variation in this phase, and we show that the flow downstream of the foil is related to the foil input power.