Unsteady two-dimensional theory of a flapping wing

Minotti, F.

doi:10.1103/physreve.66.051907

Cited by 48 publications

(42 citation statements)

References 15 publications

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“…As previously described, an inclined wing moving at a constant angle of attack is subject to aerodynamic forces that can be adequately modeled by accounting for the circulation around the wing using standard potential theory. Other effects such as leading edge separation may also be modeled by a variation of the same approach (see, for example, Minotti, 2002). However, when the wing accelerates, it encounters a reaction force due to the accelerated fluid.…”

Section: Added Massmentioning

confidence: 99%

“…The more recent analytical models (e.g. Zbikowski, 2002;Minotti, 2002) have been able to incorporate the basic phenomenology of the fluid dynamics underlying flapping flight in a more rigorous fashion, as well as take advantage of a fuller database of forces and kinematics (Sane and Dickinson, 2001). …”

Section: Analytical Models Of Insect Flightmentioning

confidence: 99%

“…Methods of calculating added mass have been outlined in various texts, most notably in Sedov (1965), Denny (1993) and Lighthill (1975) or in research articles by Ellington (1984d), Sunada et al (2001), Sane and Dickinson (2002), Zbikowski (2002) and Minotti (2002). The added mass force is typically modeled in quasi-steady terms using a timeinvariant added-mass coefficient, and any time dependence is implicit due to the time course of wing acceleration.…”

Section: Added Massmentioning

confidence: 99%

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The aerodynamics of insect flight

Sane

2003

Journal of Experimental Biology

1,048

759

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Insects owe much of their extraordinary evolutionary success to flight. Compared with their flightless ancestors, flying insects are better equipped to evade predators, search food sources and colonize new habitats. Because their survival and evolution depend so crucially on flight performance, it is hardly surprising that the flight-related sensory, physiological, behavioral and biomechanical traits of insects are among the most compelling illustrations of adaptations found in nature. As a result, insects offer biologists a range of useful examples to elucidate both structure-function relationships and evolutionary constraints in organismal design (Brodsky, 1994;Dudley, 2000).Insects have also stimulated a great deal of interest among physicists and engineers because, at first glance, their flight seems improbable using standard aerodynamic theory. The small size, high stroke frequency and peculiar reciprocal flapping motion of insects have combined to thwart simple 'back-of-the-envelope' explanations of flight aerodynamics.As with many problems in biology, a deep understanding of insect flight depends on subtle details that might be easily overlooked in otherwise thorough theoretical or experimental analyses. In recent years, however, investigators have benefited greatly from the availability of high-speed video for capturing wing kinematics, new methods such as digital particle image velocimetry (DPIV) to quantify flows, and powerful computers for simulation and analysis. Using these and other new methods, researchers can proceed with fewer simplifying assumptions to build more rigorous models of insect flight. It is this more detailed view of kinematics, forces and flows that has led to significant progress in our understanding of insect flight aerodynamics. Experimental challengesBecause of their small size and high wing beat frequencies, it is often quite difficult to quantify the wing motions of free- The flight of insects has fascinated physicists and biologists for more than a century. Yet, until recently, researchers were unable to rigorously quantify the complex wing motions of flapping insects or measure the forces and flows around their wings. However, recent developments in high-speed videography and tools for computational and mechanical modeling have allowed researchers to make rapid progress in advancing our understanding of insect flight. These mechanical and computational fluid dynamic models, combined with modern flow visualization techniques, have revealed that the fluid dynamic phenomena underlying flapping flight are different from those of non-flapping, 2-D wings on which most previous models were based. In particular, even at high angles of attack, a prominent leading edge vortex remains stably attached on the insect wing and does not shed into an unsteady wake, as would be expected from non-flapping 2-D wings. Its presence greatly enhances the forces generated by the wing, thus enabling insects to hover or maneuver. In addition, flight forces are further enhanced by other mechanisms act...

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Section: Added Massmentioning

confidence: 99%

Section: Analytical Models Of Insect Flightmentioning

confidence: 99%

Section: Added Massmentioning

confidence: 99%

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The aerodynamics of insect flight

Sane

2003

Journal of Experimental Biology

1,048

759

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“…Minotti [49] produced a circulation-based analysis for insect-like flapping wings. He divided the problem into the trailing-edge wake and the LEV and summed their respective influences.…”

Section: Analytical Work On Insect Flight Aerodynamicsmentioning

confidence: 99%

Non-linear unsteady aerodynamic model for insect-like flapping wings in the hover. Part 1: Methodology and analysis

Ansari

Żbikowski

Knowles

2006

Proceedings of the Institution of Mechanical Engineers, Part G:

127

148

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The essence of this two-part paper is the analytical, aerodynamic modelling of insectlike flapping wings in the hover for microair vehicle applications. A key feature of such flappingwing flows is their unsteadiness and the formation of a leading-edge vortex in addition to the conventional wake shed from the trailing edge. What ensues is a complex interaction between the shed wakes which, in part, determines the forces and moments on the wing. In an attempt to describe such a flow, two-novel coupled, non-linear, wake-integral equations are developed in this first part of the paper, and these form the foundation upon which the rest of the work stands. The circulation-based model thus developed is unsteady and inviscid in nature and essentially two-dimensional. It is converted to a 'quasi-three-dimensional' model using a blade-element-type method, but with radial chords. The main results from the model are force and moment data for the flapping wing and are derived as part of this article using the method of impulses. These forces and moments have been decomposed into constituent elements. The governing equations developed in the study are exact, but do not have a closed analytic form. Therefore, solutions are found by numerical methods. These are described in the second part of this paper.

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“…In addition to these experiments, there are also several new Computational Fluid Dynamic (or CFD) simulations of flow around flapping insect wings Ramamurti and Sandberg, 2002;Sun and Tang, 2002;Wang et al, 2004;Miller and Peskin, 2005) and a few analytic models (Minotti, 2002;Zbikowski, 2002). Together, these researches have vastly improved our understanding of the near-field mechanisms of force production by flapping wings.…”

Section: Introductionmentioning

confidence: 99%

Induced airflow in flying insects I. A theoretical model of the induced flow

Sane

2006

Journal of Experimental Biology

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SUMMARY A strong induced flow structure envelops the body of insects and birds during flight. This flow influences many physiological processes including delivery of odor and mechanical stimuli to the sensory organs, as well as mass flow processes including heat loss and gas exchange in flying animals. With recent advances in near-field aerodynamics of insect and bird flight, it is now possible to determine how wing kinematics affects induced flow over their body. In this paper, I develop a theoretical model based in rotor theory to estimate the mean induced flow over the body of flapping insects. This model is able to capture some key characteristics of mean induced flow over the body of a flying insect. Specifically, it predicts that induced flow is directly proportional to wing beat frequency and stroke amplitude and is also affected by a wing shape dependent parameter. The derivation of induced flow includes the determination of spanwise variation of circulation on flapping wings. These predictions are tested against the available data on the spanwise distribution of aerodynamic circulation along finite Drosophila melanogaster wings and mean flows over the body of Manduca sexta. To explicitly account for tip losses in finite wings, a formula previously proposed by Prandtl for a finite blade propeller system is tentatively included. Thus, the model described in this paper allows us to estimate how far-field flows are influenced by near-field events in flapping flight.

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Unsteady two-dimensional theory of a flapping wing

Cited by 48 publications

References 15 publications

The aerodynamics of insect flight

The aerodynamics of insect flight

Non-linear unsteady aerodynamic model for insect-like flapping wings in the hover. Part 1: Methodology and analysis

Induced airflow in flying insects I. A theoretical model of the induced flow

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