Session AB: Biofluid Dynamics II: Flying

Passive Wing Rotation in Dragonfly Flight

We study the aerodynamic force, torque and power calculated from wing kinematics measured for a tethered dragonfly, {\em Libellula pulchella}. This is done using two methods -- by directly solving the Navier-Stokes equations employing the 2D immersed interface method, and a quasi-steady ODE model. Of considerable interest in our results is the wing pitch reversal, the rapid change of angle of attack near stroke transition. Past work has found that this sudden pitching of the wing can play a significant role in lift production during flight, as well as the ability of the insect to maneuver effectively during flight. By analyzing the power requirements of the motion, we find strong evidence that the wing is turned by the fluid torque and requires no additional external power. This passive mechanism for wing rotation suggests an efficient method for reversing wing pitch in flapping flight.   

Pressure distribution, thrust performance, and wake structure of a low-aspect ratio pitching panel

To understand the fluid dynamics of a biologically inspired unsteady low-aspect ratio propulsor, time-averaged thrust performance, unsteady pressure distributions, and wake structures have been measured. Experiments were performed on a rigid rectangular panel pitching in a uniform flow with aspect ratios ranging from 0.54 to 2.38. Peak efficiencies between 9\% and 21\% were measured within a Strouhal number range of 0.13 to 0.34. At peak efficiency conditions, a reverse von K$\acute{a} $rm$\acute{a}$n vortex street pattern was observed in the near wake. However, in contrast to two-dimensional wakes, the wake exhibits transverse growth and spanwise compression with increased downstream distance. At greater Strouhal numbers, the transverse growth increases, yielding a double jet structure. Wake models based on low Reynolds number visualizations explain this behavior. Time resolved measurements of the pressure distribution along the surface were conducted in order to gain insight into optimization of thrust production as well as the generation of wake vorticity.   

Quasi-steady modeling of rolling and pitching foils

Unsteady foils are accurately modeled as the dynamic rendition of the steady state foil lift-drag (thrust) characteristics while retaining its basic pre-stall characteristic. The foil normal force, of which lift and drag are resolved representations, is a cross-stream force which produces leading and trailing edge separated drag vortices at high angles of attack. Primarily rolling and also pitching if present are dynamic strategies for retaining the two drag vortices over the foil. In the process, the foil angle of attack and normal force oscillate and stall is prevented. Steady state, as well as unsteady measurements of forces, power, surface flow critical points and visualization of dynamic stall vortices have been carried out for foils of two different spans. Good agreement between the quasi-steady model and unsteady force and power measurements have been achieved in both instantaneous time signatures and in cycle averaged values at all angles of attack.   

Thrust augmentation in tandem flapping foils by foil-wake interaction

Propulsion by pitching and heaving airfoils and hydrofoils has been a focus of much research in the field of biologically inspired propulsion. Organisms that use this sort of propulsion are self-propelled, so it is difficult to use standard experimental metrics such as thrust and drag to characterize performance. We have constructed a flapping foil robot mounted in a flume on air-bearings that allows for the determination of self-propelled speed as a metric of performance. We have used a pair of these robots to examine the impact of an upstream flapping foil on a downstream flapping foil as might apply to tandem fins of a swimming organism or in-line swimming of schooling organisms. Self-propelled speed and a force transducer confirmed significant thrust augmentation for particular foil-to-foil spacings, phase differences, and flapping frequencies. Flow visualization shows the mechanism to be related to the effective angle of attack of the downstream foil due to the structure of the wake of the upstream foil. This confirms recent computational work and the hypotheses by early investigators of fish fluid dynamics.   

Parametric Dependencies in Aero-Elastic, Articulated, Flapping Flight

Aero-elastic coupling and wing articulation both play a vital role in the generation of lift and propulsion in birds, bats and fish. We present results from a computational study that employs several tools of varying fidelity to explore the role of flexible structures on the performance and efficiency of bird and bat flight mechanics. The tools (both 2-D and 3-D) include a Wake only ``Betz'' analysis following the work of Hall, Pigott and Hall (\emph{J. Aircaft}, 1998), a potential flow model coupled to a free-vortex wake (Willis, Peraire \& White, \emph{AIAA 2005-0854}), and lastly, a discontinuous Galerkin solver (Persson \& Peraire, \emph{AIAA 2006-0113}) for the full Navier-Stokes equations. Structural models include springs, beams and membranes to represent compliant biological structures. The results demonstrate the changes in efficiency that can be achieved by different parametric variations in the flight behavior, including the effects of increasing kinematic degrees of freedom (e.g. articulated wings) and the effect of compliance in wing and skeletal structures.   

Numerical and experimental study of flexion in flapping-wing fluid dynamics

The wings of airborne insects are flexible structures that permit considerable out-of-plane deformation during the flapping cycle. However, it is not clear what aerodynamic role is served by this flexion, nor is it clear to what degree it is coupled with the fluid forcing. In this work we investigate the flapping of a two-dimensional wing composed of two rigid sections connected by a torsion spring. The motion of the leading section is prescribed with hovering-flight kinematics, and the trailing section responds passively. The complexity of a continuously flexible structure is thereby circumvented by isolating the flexion in the deflection of the spring. Numerical simulations of the coupled fluid--body dynamics are performed with a viscous vortex particle method. The wing behavior is studied experimentally with a dynamically-scaled system in a water tank with two-degree-of-freedom motion control. Experimental measurements of the torsion spring deflection are used to validate the numerical methodology, with excellent agreement. The force production and energy consumption are examined by analyzing the numerical simulation results. In comparing the flapping of a flexible wing with a fully rigid one, it is found that the flexible wing generates smaller lift forces and requires considerably less power.   

Coexixtence of two types of flight, hovering, and the stability in the insect's free flight

We study the insect’s free flight using a simple model. This model includes a wing flapping horizontally and the center point of the flapping (oscillation). In this model, all the mass is concentrated at the center point. The point, which is equivalent to the center of mass (CM), is allowed to move in a one-dimensional vertical direction according to the hydrodynamic force generated through flapping. Numerical simulation revealed that the model exhibits two types of flapping flight: a steady flight in which the CM velocity oscillates and a wandering flight in which the CM velocity varies irregularly. These two types of flights can coexist in a parameter region. Moreover, at a certain critical parameter value, the steady flight loses its stability and experiences a drastic transition to the wandering flight. At this critical value, the steady flight can be regarded as hovering. The possible flights are analyzed in terms of bifurcation, and the bifurcation structure is qualitatively explained based on a simple analysis using the tethered model.   

Fluid-Structural dynamics of flapping, flexible airfoils

In recent years, flapping flight has received considerable attention and many studies have been pursued in the fluid dynamics community by using simplified two-dimensional rigid airfoils and three-dimensional rigid wings with prescribed kinematics. Although these studies provide important insights and help explain experimental observations, the coupled fluid-structural dynamics of flexible, flapping wings remains largely unexplored. In order to understand this dynamics as well as to gain insights into insect flight, numerical studies of a two-part hinged plate configuration with a flexural coupling moving in a viscous fluid are conducted. The two-part configuration is described by a set of four coupled, nonlinear second-order differential system, and this system in conjunction with the Navier-Stokes equations and the boundary conditions constitute the complete system. A strongly coupled embedded boundary formulation is used to fully capture the fluid-structure interactions and determine the solution of the coupled system of equations. Parametric studies are undertaken to understand the dependence of the lift and drag coefficients on the relative inertia properties of the fluid and foil systems and stiffness characteristics of the flapping foil system. Instantaneous vortex dynamics is also studied, and the results obtained are compared with prior work.   

Efficiency of flapping flight

We analyze the efficiency of flapping and fixed wing kinematics at Reynolds numbers of about 100, as appropriate for insect flight. In particular we solve the two dimensional Navier-Stokes equations and minimize the average aerodynamic power required to support the typical weight of a fruitfly. We find that carefully designed periodic kinematics can be more efficient than fixed wing kinematics.   

Aerodynamic Performances of Corrugated Dragonfly Wings at Low Reynolds Numbers

The cross-sections of dragonfly wings have well-defined corrugated configurations, which seem to be not very suitable for flight according to traditional airfoil design principles. However, previous studies have led to surprising conclusions of that corrugated dragonfly wings would have better aerodynamic performances compared with traditional technical airfoils in the low Reynolds number regime where dragonflies usually fly. Unlike most of the previous studies of either measuring total aerodynamics forces (lift and drag) or conducting qualitative flow visualization, a series of wind tunnel experiments will be conducted in the present study to investigate the aerodynamic performances of corrugated dragonfly wings at low Reynolds numbers quantitatively. In addition to aerodynamics force measurements, detailed Particle Image Velocimetry (PIV) measurements will be conducted to quantify of the flow field around a two-dimensional corrugated dragonfly wing model to elucidate the fundamental physics associated with the flight features and aerodynamic performances of corrugated dragonfly wings. The aerodynamic performances of the dragonfly wing model will be compared with those of a simple flat plate and a NASA low-speed airfoil at low Reynolds numbers.   

Rationalizing the bumps on whale flippers using basic aerodynamic theory

Recent experiments and numerics demonstrated that bumps on the leading edge of humpback whale flippers can lead to an increase in the lift/drag ratio and an increase in the stall angle, as compared to smooth flippers. Using basic aerodynamic theory (potential flow around a Joukowski profile, combined with lifting-line theory) we attempt to rationalize the experimental and numerical findings. We use this basic theory to find perturbations which could lead to an increase in stall angle.   

Wake Studies of Ornithopters

This paper details experiments using a mechanical ornithopter flying in a low speed wind tunnel. Experiments were conducted for a Strouhal number of 0.3 and Reynolds number of 2300, Particle Image Velocimetry (PIV) and flow visualization was used to develop quantitative and qualitative information about the nature of the wake. The data shows that the wake is made of a series of discrete vortex rings. The impulse of these rings has been estimated with PIV data and the results correlate well with the lift required to sustain the ornithopter in flight.