Session PJ: Bio-Fluids: Undulatory Flapping III

Parameters Governing the Wake Structure of a Low-Aspect-Ratio Pitching Panel at $Re_C=640$

Measurements of the wake structure and thrust performance of a rigid rectangular low-aspect-ratio panel pitching about its leading edge have been previously reported (Buchholz, J.H.J and Smits, A.J, {\em J. Fluid Mech}, 603, pp. 331--365). Such a simplified propulsor has proven to be a useful platform for the investigation of the physics of aquatic animal swimming. Wake visualizations at $Re_C = 640$ yielded vortex skeleton models that were used to understand the structure of the wake at $Re_C = O(10^4)$; however, at this low Reynolds number, only a single value of panel aspect ratio and pitching amplitude were investigated, for three representative Strouhal numbers. In the present work, we investigate variations in aspect ratio and pitching amplitude, and consider additional pitching frequencies in order to further elucidate parameters governing the structure of the wake at $Re_C = 640$.   

Effect of aspect ratio on the hydrodynamics of a self-propelled elliptic foil

Flapping wings or fins are commonly used by birds, insects, fishes and some Micro Air Vehicles to generate propulsive force. In most of the studies on flapping wings, the foil is placed in a steady stream and the motion in the horizontal direction is constrained. However, the condition in these studies is completely different from that in real self-propelled locomotion. Alben and Shelly (PNAS, 102, 11163-11166 (2005)) have performed a pioneering study on fundamental hydrodynamics of a self-propelled flapping foil. In this study, we investigate the effect of geometrical shape on the hydrodynamics by varying the aspect ratio of the elliptical foil. Three different dynamic modes of the foil have been identified with the increase of aspect ratio, i.e. fore-aft symmetry, non-periodic motion and unidirectional motion with periodic velocity oscillation. It is observed that the dynamics of the body are closely related to various vortical patterns around the foil. The formation of the vortices during the starting procedure and their subsequent disposition in the wake will be described. The implication of the current study on the optimization of the foil shape in obtaining locomotion is given.   

3D vortex formation of drag-based propulsors

Three dimensional vortex formation mechanism of impulsively rotating plates is studied experimentally using defocusing digital particle image velocimetry. The plate face is normal to the moving direction to simulate drag-based propulsion and only one power stroke is considered. In order to compare the effect of shape on vortex generation, three different shapes of plate (rectangular, triangular and duck's webbed-foot shapes) are used. These three cases show striking differences in vortex formation process during power stroke. Axial flow is shown to play an important role in the tip vortex formation. Correlation between hydrodynamic forces acting on the plate and vortex formation processes is described.   

Propulsion of a flexible foil in a fluid

The dynamic properties such as time dependent pressure loading, free stream velocity, and local acceleration of the hydrofoil determine the instantaneous deformation of a flexible foil. The present work is concerned with the effect of structural dynamic terms and inertia loads on a flexible foil undergoing large amplitude rigid body harmonic wave-like motion in an unsteady potential flow. The hydrofoil structural dynamics is modeled as an Euler-Bernoulli beam finite element. The unsteady fluid dynamic force is evaluated using a numerical discrete vortex implementation of an unsteady incompressible potential flow model. The hydrofoil is fixed at its leading edge and it moves with velocity parallel to its length in the undeformed state. The propulsion of the hydro-elastic system is studied in terms of the mass ratio of the foil and the fluid, as well as its structural flexibility. It is shown that the thrust coefficient and propulsive efficiency of the flexible foil decreases with increase in structural flexibility. We made a comparison of the effect of structural flexibility on the thrust coefficient and propulsive efficiency considering models of the oscillating foil with inertia and without inertia effects present. Detailed parametric studies of the effect of different parameters on propulsion of the foil were made. Including inertia loads and structural dynamic terms significantly affect the propulsive efficiency and thrust coefficient.   

Effect of Pitching and Heaving Motions of SD8020 Hydrofoil on Thrust and Efficiency for Swimming Propulsion

The thrust producing performance and efficiency of an SD8020 foil hydrofoil that undergoes rotational and translational oscillating motions was studied and optimized through force and torque measurement and dye flow visualization, in the water tunnel at low Reynolds number of 13,000-16,000. The foil was set into pitching and heaving motion under different oscillation patterns to mimick the flapping and swimming motion of the marine creatures. The force and moment data were collected and used as optimization basis for best flapping motion combination. The propulsive efficiency and thrust coefficient of the pitching foil were determined as a function of the Strouhal number, pitch amplitude and angular frequency. Based on the force and efficiency data collected for the pure pitching motion, increasing pitch amplitude and angular frequency was associated with a decrease in propulsive efficiency and an increase in thrust forces produced. A high propulsive efficiency of 70{\%}, accompanied by a thrust coefficient of order one was found at a pitch amplitude of 30\r{ } and angular frequency of 0.873 rad/s, Strouhal number of 0.24, and freestream of 0.1368 m/s (Reynolds number of 16416). This presented the best conditions for thrust production observed at low Strouhal and Reynolds numbers.   

Passive mechanics in jellyfish-like locomotion

The aim of this work is to identify possible benefits of passive flexibility in biologically-inspired locomotion. Substantial energy savings are likely achieved in natural locomotion by allowing a mix of actively controlled and passively responsive deformation. The jellyfish is a useful target of study, due to its relatively simple structure and the availability of recent kinematics and flow-field measurements. In this investigation, the jellyfish consists of a two-dimensional articulated system of rigid bodies linked by hinges. The kinematics -- expressed via the hinge angles -- are adapted from experimentally measured motion. The free swimming system is explored via high-fidelity numerical simulation with a viscous vortex particle method with coupled body dynamics. The computational tool allows the arbitrary designation of individual hinges as ``active'' or ``passive,'' to introduce a mix of flexibility into the system. In some cases, replacing an active hinge with a passive spring can enhance the mean swimming speed, thus reducing the power requirements of the system. Varying the stiffness and damping coefficients of the spring yield different locomotive results. The numerical solution is used to compute the finite-time Lyapunov exponents (FTLE) throughout the field. The FTLE fields reveal manifolds in the flow that act as transport barriers, uncovering otherwise unseen geometric characteristics of the flow field that add new insight into the locomotion mechanics.   

A Propulsive Efficiency Model for Pulsed-Jet Propulsion

Mechanical pulsed jets functionally similar to those utilized by biological jetters such as squid are known to yield elevated thrust in comparison to equivalent steady jets due to the formation of vortex rings with each jet pulse and the concomitant over-pressure at the nozzle exit plane. Although speculated to have advantages for propulsive efficiency as well, the influence of vortex ring formation and over-pressure on propulsive efficiency has not been quantified. The present work proposes a simple model of pulsed jet propulsion where the effect of vortex ring formation on thrust and kinetic energy are accounted for through lumped over-pressure terms in the momentum and energy equations. Time-averaged propulsive efficiency is then formulated from the resulting expressions for thrust and excess kinetic energy. For comparison with steady jet propulsion, it assumed that the vehicle drag is the same for pulsed and steady propulsion at the same vehicle speed. Using measurements of the over-pressure terms from static pulsed jets, the results suggest that the propulsive efficiency of pulsed jets can exceed that for steady jets for short pulses and low vehicle Reynolds number.   

Propulsive efficiency of a self-propelled pulsed jet vehicle at low Re

Steady jet propulsion systems like propellers and jets predominate for large scale systems. The propulsive efficiency of these systems decreases as the Reynolds number (Re) decreases; however, making pulsed jet propulsion appealing at low Re due to its higher thrust compared to an equivalent steady jet. In order to compare the propulsive efficiency of steady and pulsed jets at low Re, a mechanical pulsed-jet underwater vehicle (dubbed ``Robosquid'' after its biological counterpart) was built and tested. The system allows control of piston velocity program, pulsing frequency, and piston stroke-to-nozzle diameter ratio (L/D).The propulsive efficiency of this system was measured using digital particle image velocimetry (DPIV) for L/D = 2 -11 and vehicle Re between 1000 and 2500. The results show that propulsive efficiency increases as L/D decreases, suggesting vortex ring formation plays a key role in increasing propulsive efficiency. Propulsive efficiencies comparable to and above those for steady jet propulsion were obtained for L/D $<$ 3. Results for Robosquid in a more viscous liquid to achieve Re $<$ 1000 will be presented.