The drag on oscillating flat plates in liquids at low Reynolds numbers

Shih, C. C.; Buchanan, H. J.

doi:10.1017/s0022112071001563

Cited by 49 publications

(35 citation statements)

References 3 publications

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“…Therefore, the small wing deformation assumption translates to g ( 1, which corresponds to u ( 1. The drag on a moving body, immersed in viscous fluid can be described by the semi-empirical Morison equation [27,29]. The Morison equation includes both added mass and aerodynamic damping.…”

Section: Small Deformation Assumption and Decoupling Of Lift And Dragmentioning

confidence: 99%

“…The aerodynamic damping coefficient C v depends on k, Re, etc., in general [29] and may also be a function of space and time. Experimental measurements on an oscillating rigid flat plate in a water tank suggest that [29]. In the original formulation, the period number was used, which is equal to the Keulegan -Carpenter number, instead of the reduced frequency, i.e.…”

Section: Small Deformation Assumption and Decoupling Of Lift And Dragmentioning

confidence: 99%

“…In the absence of freestream for hovering flight, we set the maximum translational velocity U of the flat plate at LE as the reference velocity, such that U ¼ 2pfh a [15,16,28]. The reduced frequency becomes a geometrical quantity: k ¼ pfc/U ¼ c/(2h a ) and is inversely proportional to the Keulegan -Carpenter number K C , often used in discussion of the Morison equation [29],…”

Section: Introductionmentioning

confidence: 99%

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Analytical model for instantaneous lift and shape deformation of an insect-scale flapping wing in hover

Kang

Shyy

2014

J. R. Soc. Interface.

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In the analysis of flexible flapping wings of insects, the aerodynamic outcome depends on the combined structural dynamics and unsteady fluid physics. Because the wing shape and hence the resulting effective angle of attack are a priori unknown, predicting aerodynamic performance is challenging. Here, we show that a coupled aerodynamics/structural dynamics model can be established for hovering, based on a linear beam equation with the Morison equation to account for both added mass and aerodynamic damping effects. Lift strongly depends on the instantaneous angle of attack, resulting from passive pitch associated with wing deformation. We show that both instantaneous wing deformation and lift can be predicted in a much simplified framework. Moreover, our analysis suggests that resulting wing kinematics can be explained by the interplay between acceleration-related and aerodynamic damping forces. Interestingly, while both forces combine to create a high angle of attack resulting in high lift around the midstroke, they offset each other for phase control at the end of the stroke.

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Section: Small Deformation Assumption and Decoupling Of Lift And Dragmentioning

confidence: 99%

Section: Small Deformation Assumption and Decoupling Of Lift And Dragmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Analytical model for instantaneous lift and shape deformation of an insect-scale flapping wing in hover

Kang

Shyy

2014

J. R. Soc. Interface.

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“…the wing undergoes unsteady motions [26] and aerodynamic [75] or aeroelastic [73] damping coefficients. These coefficients are empirically determined from various experiments [26,27,73,76].…”

Section: (B) Tandem and Corrugated Wingsmentioning

confidence: 99%

Aerodynamics, sensing and control of insect-scale flapping-wing flight

et al. 2016

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There are nearly a million known species of flying insects and 13 000 species of flying warm-blooded vertebrates, including mammals, birds and bats. While in flight, their wings not only move forward relative to the air, they also flap up and down, plunge and sweep, so that both lift and thrust can be generated and balanced, accommodate uncertain surrounding environment, with superior flight stability and dynamics with highly varied speeds and missions. As the size of a flyer is reduced, the wing-to-body mass ratio tends to decrease as well. Furthermore, these flyers use integrated system consisting of wings to generate aerodynamic forces, muscles to move the wings, and sensing and control systems to guide and manoeuvre. In this article, recent advances in insect-scale flapping-wing aerodynamics, flexible wing structures, unsteady flight environment, sensing, stability and control are reviewed with perspective offered. In particular, the special features of the low Reynolds number flyers associated with small sizes, thin and light structures, slow flight with comparable wind gust speeds, bioinspired fabrication of wing structures, neuron-based sensing and adaptive control are highlighted.

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“…The modulations in the wing kinematics is the primary means by which insects and birds control their flight force. Insects, such as flies, steer and maneuver primarily by altering the wing stroke amplitude and the frequency [GOTZ, 1987, Shih and Buchanan, 1971 as well as the speed and the timing of the wing rotation [Dickinson and Gotz, 1993].…”

Section: Wing Actuationmentioning

confidence: 99%

Wing in the Loop: Integrating the Wing into Dynamics of Insect Flight

Zeyghami

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Insects were the first animals to evolve active flight and remain unsurpassed in many features of flight dynamics and performance. The capacity to move in 3D space provided them with superior abilities in predator-prey interactions and in exploring novel habitats. Among insects, we find animals capable of precise hovering, taking off backwards, flying sideways and landing upside down. In this work, we focused on low flapping frequency insect flight, where the time scales of the wing and body motions are close. The pursuit of our goal is carried out via two different branches.First, we gathered accurate data on the free flight of several species of insects during different aerial maneuvers. Quantitative analysis of the flight behavior was then conducted and comparisons were made with maneuvering flight of high flapping frequency insects. In the second branch of this work, we developed a physics-based model of the insect wing and the mechanical properties of its hinge, and combined it with a model of the unsteady aerodynamics of flapping flight to study actuation of the iv wing pitch. Generation of the aerodynamic force is sensitive to the wing pitch and its dynamics and therefore this motion plays a unique role in executing aerial maneuvers. Quantitative investigations of the wing dynamics were then carried out by varying the wing geometry, kinematics and structural properties. The ratio of the aerodynamic to elastic force, termed as Cauchy number, was identified as the most important parameter in governing wing motion. The analysis of the wing dynamics also revealed a mechanism by which the motions of the wing and body are coupled together. During aerial maneuvers, the body motion alters the balance of forces on the wing, causing the wing kinematics to passively change in response. Furthermore, the changes in the wing kinematics results in altering the force and consequently the body motion. This chain of actions and reactions is the source of coupling in the dynamics of the wing and the body. This phenomenon, which was predicted by our theoretical model and verified by our experimental measurements, cannot be explained by the currently accepted model of the insect flight dynamics. The modifications that were made to the current model based on our analysis and findings resulted in an improved model of the insect flight dynamics that can successfully predict the connection between the wing and body motions during aerial maneuvers.

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The drag on oscillating flat plates in liquids at low Reynolds numbers

Cited by 49 publications

References 3 publications

Analytical model for instantaneous lift and shape deformation of an insect-scale flapping wing in hover

Analytical model for instantaneous lift and shape deformation of an insect-scale flapping wing in hover

Aerodynamics, sensing and control of insect-scale flapping-wing flight

Wing in the Loop: Integrating the Wing into Dynamics of Insect Flight

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