Alexandra H. Techet

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.

Forces on oscillating uniform and tapered cylinders in cross flow

Forces are measured at both ends of rigid cylinders with span 60 cm, performing transverse oscillations within an oncoming stream of water, at Reynolds number Re 3800. Forced harmonic motions and free vibrations of uniform and tapered cylinders are studied. To study free motions, a novel force-feedback control system has been developed, consisting of: (a) a force transducer, which measures forces on a section of a cylinder moving forward at constant speed; (b) a computer using the measured force signal to drive in real time a numerical simulation of an equivalent mass{dashpot{spring system; (c) a servomotor and linear table which impose, also in real time, the numerically calculated motion on the cylinder section. The apparatus allows very low equivalent system damping and strict control of the parametric values and structure of the equivalent system. Calculation of the cross-correlation coecient between forces at the two ends of the uniform cylinder reveals ve distinct regimes as a function of the nominal reduced velocity Vrn: two regimes, for low and high values of Vrn, and far away from the value of VrS corresponding to the Strouhal frequency, show small correlation; two regimes immediately adjacent to, but excluding, VrS show strong correlation, close to 1; surprisingly, there is a regime containing the Strouhal frequency, within which correlation is low. Free vibrations with a 40:1 tapered cylinder show that the regime of low correlation, containing the Strouhal frequency, stretches to higher reduced velocities, while lock-in starts at lower reduced velocities. When comparing the amplitude and phase of the lift coecient measured for free and then for forced vibrations, we obtain close agreement, both for tapered and uniform cylinders. When comparing the cross-correlation coecient, however, we nd that it is much higher in the forced oscillations, especially for the uniform cylinder. Hence, although the force magnitude and phase may be replicated well in forced vibrations, the correlation data suggest that dierences exist between free and forced vibration cases.

Acoustic measurement of the Deepwater Horizon Macondo well flow rate

On May 31, 2010, a direct acoustic measurement method was used to quantify fluid leakage rate from the Deepwater Horizon Macondo well prior to removal of its broken riser. This method utilized an acoustic imaging sonar and acoustic Doppler sonar operating onboard a remotely operated vehicle for noncontact measurement of flow cross-section and velocity from the well’s two leak sites. Over 2,500 sonar cross-sections and over 85,000 Doppler velocity measurements were recorded during the acquisition process. These data were then applied to turbulent jet and plume flow models to account for entrained water and calculate a combined hydrocarbon flow rate from the two leak sites at seafloor conditions. Based on the chemical composition of end-member samples collected from within the well, this bulk volumetric rate was then normalized to account for contributions from gases and condensates at initial leak source conditions. Results from this investigation indicate that on May 31, 2010, the well’s oil flow rate was approximately 0.10 ± 0.017 m3 s-1 at seafloor conditions, or approximately 85 ± 15 kg s-1 (7.4 ± 1.3 Gg d-1), equivalent to approximately 57,000 ± 9,800 barrels of oil per day at surface conditions. End-member chemical composition indicates that this oil release rate was accompanied by approximately an additional 24 ± 4.2 kg s-1 (2.1 ± 0.37 Gg d-1) of natural gas (methane through pentanes), yielding a total hydrocarbon release rate of 110 ± 19 kg s-1 (9.5 ± 1.6 Gg d-1).

Water entry of spinning spheres

The complex hydrodynamics of water entry by a spinning sphere are investigated experimentally for low Froude numbers. Standard billiard balls are shot down at the free surface with controlled spin around one horizontal axis. High-speed digital video sequences reveal unique hydrodynamic phenomena which vary with spin rate and impact velocity. As anticipated, the spinning motion induces a lift force on the sphere and thus causes significant curvature in the trajectory of the object along its descent, similar to a curveball pitch in baseball. However, the splash and cavity dynamics are highly altered for the spinning case compared to impact of a sphere without spin. As spin rate increases, the splash curtain and cavity form and collapse asymmetrically with a persistent wedge of fluid emerging across the centre of the cavity. The wedge is formed as the sphere drags fluid along the surface, due to the no-slip condition; the wedge crosses the cavity in the same time it takes the sphere to rotate one-half a revolution. The spin rate relaxation time plateaus to a constant for tangential velocities above half the translational velocity of the sphere. Non-dimensional time to pinch off scales with Froude number as does the depth of pinch-off; however, a clear mass ratio dependence is noted in the depth to pinch off data. A force model is used to evaluate the lift and drag forces on the sphere after impact; resulting forces follow similar trends to those found for spinning spheres in oncoming flow, but are altered as a result of the subsurface air cavity. Images of the cavity and splash evolution, as well as force data, are presented for a range of spin rates and impact speeds; the influence of sphere density and diameter are also considered.

Vorticity Control in Fish-like Propulsion and Maneuvering

Abstract Vorticity control is employed by marine animals to enhance performance in maneuvering and propulsion. Studies on fish-like robots and experimental apparatus modelling rigid and flexible fins provide some of the basic mechanisms employed for controlling vorticity.

Review of Hydrodynamic Scaling Laws in Aquatic Locomotion and Fishlike Swimming

We consider observations and data from live fish and cetaceans, as well as data from engineered flapping foils and fishlike robots, and compare them against fluid mechanics based scaling laws. These laws have been derived on theoretical/numerical/experimental grounds to optimize the power needed for propulsion, or the energy needed for turning and fast starting. The rhythmic, oscillatory motion of fish requires an “impedance matching” between the dynamics of the actively controlled musculature and the fluid loads, to arrive at an optimal motion of the fish’s body. Hence, the degree to which data from live fish, optimized robots, and experimental apparatus are in accordance with, or deviate from these flow-based laws, allows one to assess limitations on performance due to control and sensing choices, and material and structural limitations. This review focuses primarily on numerical and experimental studies of steadily flapping foils for propulsion; three-dimensional effects in flapping foils; multiple foils and foils interacting with bodies; maneuvering and fast-starting foils; the interaction of foils with oncoming, externally-generated vorticity; the influence of Reynolds number on foil performance; scaling effects of flexing stiffness of foils; and scaling laws in fishlike swimming. This review article cites 117 references.

Vortical patterns behind a tapered cylinder oscillating transversely to a uniform flow

Visualization studies of the flow behind an oscillating tapered cylinder are performed at Reynolds numbers from 400 to 1500. The cylinder has taper ratio 40[ratio ]1 and is moving at constant forward speed U while being forced to oscillate harmonically in the transverse direction. It is shown that within the lock-in region and above a threshold amplitude, no cells form and, instead, a single frequency of response dominates the entire span. Within certain frequency ranges a single mode dominates in the wake, consisting of shedding along the entire span of either two vortices per cycle (‘2S’ mode), or four vortices per cycle (‘2P’ mode); but within specific parametric ranges a hybrid mode is observed, consisting of a ‘2S’ pattern along the part of the span with the larger diameter and a ‘2P’ pattern along the part of the span with the smaller diameter. A distinct vortex split connects the two patterns which are phase-locked and have the same frequency. The hybrid mode is periodic, unlike vortex dislocations, and the location of the vortex split remains stable and repeatable, within one to two diameters, depending on the amplitude and frequency of oscillation and the Reynolds number.

Propulsive performance of biologically inspired flapping foils at high Reynolds numbers

SUMMARY Propulsion and maneuvering underwater by flapping foil motion, optimized through years of evolution, is ubiquitous in nature, yet marine propulsors inspired by examples of highly maneuverable marine life or aquatic birds are not widely implemented in engineering. Performance data from flapping foils, moving in a rolling and pitching motion, are presented at high Reynolds numbers, Re=Uc/ν, or O(104), where U is the relative inflow velocity, c is the chord length of the foil, and ν is the kinematic viscosity of the fluid, from water tunnel experiments using a foil actuator module designed after an aquatic penguin or turtle fin. The average thrust coefficients and efficiency measurements are recorded over a range of kinematic flapping amplitudes and frequencies. Results reveal a maximum thrust coefficient of 2.09, and for low values of angle of attack the thrust generally increases with Strouhal number, without much penalty to efficiency. Strouhal number is defined as St=2h0f/U, where f is the frequency of flapping, and 2h0 is the peak-to-peak amplitude of flapping. The thrust and efficiency contour plots also present a useful performance trend where, at low angles of attack, high thrust and efficiency can be gained at sufficiently high Strouhal numbers. Understanding the motion of aquatic penguins and turtle wings and emulating these motions mechanically can yield insight into the hydrodynamics of how these animals swim and also improve performance of biologically inspired propulsive devices.

A spin on cavity formation during water entry of hydrophobic and hydrophilic spheres

United States. Office of Naval Research (University Laboratory Initiative Grant No. N00014-06-1-0445)

Separation and Turbulence Control in Biomimetic Flows

The study of the flow around live marine animals and robotic mechanisms which emulate fish motion has revealed a number of mechanisms of flow control, optimised through evolution to minimize the energy required for steady and unsteady motion underwater. We outline some of the mechanisms used to (a) eliminate separation, (b) reduce turbulence, and (c) extract energy from oncoming vortical flows.