An analytical solution to the aeroelastic response of a two-dimensional elastic plate in axial potential flow

2018 ◽  
Vol 845 ◽  
Author(s):  
Cory Medina ◽  
Chang-kwon Kang
Keyword(s):  
Elastic Plate ◽  
Potential Flow ◽  
Aerodynamic Force ◽  
Dynamic Balance ◽  
Input Power ◽  
Flapping Wings ◽  
Aeroelastic Response ◽  
Linear Elastic ◽  
Plate Flutter ◽  
Plate Curvature

This paper presents a novel analytical model that predicts the two-way coupled aeroelastic response of a linear elastic plate in axial potential flow, including the effects of plate curvature. The plate deforms in dynamic balance of the inertia, elastic, and aerodynamic forces. Analytical solutions are obtained by deriving the generalized aerodynamic force with respect to the beam eigenfunctions, which are expressed in a Chebyshev polynomial expansion. Exact expressions are derived for the generated lift, thrust and required input power. The derived solution agrees well with the results reported in the literature for plate flutter and flapping wings.

scholarly journals Scaling of the performance of insect-inspired passive-pitching flapping wings

2019 ◽  
Vol 16 (161) ◽  
pp. 20190609 ◽  
Author(s):  
Kit Sum Wu ◽  
Jerome Nowak ◽  
Kenneth S. Breuer
Keyword(s):  
Scaling Laws ◽  
Aerodynamic Force ◽  
Lift Coefficient ◽  
Angle Of Attack ◽  
Flapping Wing ◽  
Dimensionless Parameters ◽  
Linear Elastic ◽  
Simple Implementation ◽  
Pitch Regulation ◽  
Cauchy Number

Flapping flight using passive pitch regulation is a commonly used mode of thrust and lift generation in insects and has been widely emulated in flying vehicles because it allows for simple implementation of the complex kinematics associated with flapping wing systems. Although robotic flight employing passive pitching to regulate angle of attack has been previously demonstrated, there does not exist a comprehensive understanding of the effectiveness of this mode of aerodynamic force generation, nor a method to accurately predict its performance over a range of relevant scales. Here, we present such scaling laws, incorporating aerodynamic, inertial and structural elements of the flapping-wing system, validating the theoretical considerations using a mechanical model which is tested for a linear elastic hinge and near-sinusoidal stroke kinematics over a range of scales, hinge stiffnesses and flapping frequencies. We find that suitably defined dimensionless parameters, including the Reynolds number, Re , the Cauchy number, Ch , and a newly defined ‘inertial-elastic’ number, IE, can reliably predict the kinematic and aerodynamic performance of the system. Our results also reveal a consistent dependency of pitching kinematics on these dimensionless parameters, providing a connection between lift coefficient and kinematic features such as angle of attack and wing rotation.

A predictive quasi-steady model of aerodynamic loads on flapping wings

2016 ◽  
Vol 800 ◽  
pp. 688-719 ◽  
Author(s):  
Q. Wang ◽  
J. F. L. Goosen ◽  
F. van Keulen
Keyword(s):  
Aerodynamic Force ◽  
Micro Air Vehicles ◽  
Mass Effect ◽  
Reynolds Numbers ◽  
Flapping Wings ◽  
Accurate Estimation ◽  
Pitching Motion ◽  
Aerodynamic Loads ◽  
Design And Optimization ◽  
Aerodynamic Torque

Quasi-steady aerodynamic models play an important role in evaluating aerodynamic performance and conducting design and optimization of flapping wings. The kinematics of flapping wings is generally a resultant motion of wing translation (yaw) and rotation (pitch and roll). Most quasi-steady models are aimed at predicting the lift and thrust generation of flapping wings with prescribed kinematics. Nevertheless, it is insufficient to limit flapping wings to prescribed kinematics only since passive pitching motion is widely observed in natural flapping flights and preferred for the wing design of flapping wing micro air vehicles (FWMAVs). In addition to the aerodynamic forces, an accurate estimation of the aerodynamic torque about the pitching axis is required to study the passive pitching motion of flapping flights. The unsteadiness arising from the wing’s rotation complicates the estimation of the centre of pressure (CP) and the aerodynamic torque within the context of quasi-steady analysis. Although there are a few attempts in literature to model the torque analytically, the involved problems are still not completely solved. In this work, we present an analytical quasi-steady model by including four aerodynamic loading terms. The loads result from the wings translation, rotation, their coupling as well as the added-mass effect. The necessity of including all the four terms in a quasi-steady model in order to predict both the aerodynamic force and torque is demonstrated. Validations indicate a good accuracy of predicting the CP, the aerodynamic loads and the passive pitching motion for various Reynolds numbers. Moreover, compared to the existing quasi-steady models, the presented model does not rely on any empirical parameters and thus is more predictive, which enables application to the shape and kinematics optimization of flapping wings.

Study on the Aerodynamics Mechanism of Passenger Car under Unsteady Crosswind

2013 ◽  
Vol 631-632 ◽  
pp. 809-816
Author(s):  
Chen Shen ◽  
Hui Zhu ◽  
Zhi Gang Yang
Keyword(s):  
Empirical Formula ◽  
Potential Flow ◽  
Aerodynamic Force ◽  
Vortex Motion ◽  
Flow Theory ◽  
Potential Flow Theory ◽  
Practical Engineering ◽  
Precise Prediction ◽  
Engineering Significance ◽  
Semi Empirical

Regular formulae for lateral aerodynamic force cannot give precise prediction under unsteady crosswind. By generalizing potential flow theory and taking the aerodynamic derivative into consideration, the semi-empirical expression for lateral aerodynamic force is derived. In order to determine the coefficients in the semi-empirical formula, the model of a typical double-deck coach is investigated in a sequence of numerical simulations under pure crosswind condition (i.e. linear crosswind, pseudo-step crosswind, sinusoidal crosswind). Moreover, advantages of the semi-empirical formula over the regular one are revealed. Further inspections into the flow field derived from the theory of vortex motion indicate that the deviation between the prediction given by semi-empirical formulae and that by numerical simulation is caused by the non-viscous assumption in potential flow theory. The lateral aerodynamic force depends linearly on the crosswind aerodynamic derivative. Situations in which the coach is moving in the direction perpendicular to the wind velocity are also studied to find the cause of the error in semi-empirical formula. Furthermore, the semi-empirical formula is revised by introducing the “damping model method”. A relatively complete system of prediction for lateral aerodynamic force on a coach, which is of practical engineering significance, has been constructed.

scholarly journals How oscillating aerodynamic forces explain the timbre of the hummingbird’s hum and other animals in flapping flight

eLife ◽  
2021 ◽  
Vol 10 ◽  
Author(s):  
Ben J Hightower ◽  
Patrick W A Wijnings ◽  
Rick Scholte ◽  
Rivers Ingersoll ◽  
Diana D Chin ◽  
...  
Keyword(s):  
Aerodynamic Force ◽  
Microphone Array ◽  
Flapping Wings ◽  
Acoustic Model ◽  
Acoustic Measurements ◽  
Aerodynamic Forces ◽  
Drag Forces ◽  
Radiated Power ◽  
Lift And Drag

How hummingbirds hum is not fully understood, but its biophysical origin is encoded in the acoustic nearfield. Hence, we studied six freely hovering Anna's hummingbirds, performing acoustic nearfield holography using a 2176 microphone array in vivo, while also directly measuring the 3D aerodynamic forces using a new aerodynamic force platform. We corroborate the acoustic measurements by developing an idealized acoustic model that integrates the aerodynamic forces with wing kinematics, which shows how the timbre of the hummingbird's hum arises from the oscillating lift and drag forces on each wing. Comparing birds and insects, we find that the characteristic humming timbre and radiated power of their flapping wings originates from the higher harmonics in the aerodynamic forces that support their bodyweight. Our model analysis across insects and birds shows that allometric deviation makes larger birds quieter and elongated flies louder, while also clarifying complex bioacoustic behavior.

A non-linear elastic plate model of moderate thickness: Existence, uniquenness and duality

1996 ◽  
Vol 42 (3) ◽  
pp. 243-273 ◽  
Author(s):  
W?odzimierz Robert Bielski ◽  
J�zef Joachim Telega
Keyword(s):  
Elastic Plate ◽  
Plate Model ◽  
Linear Elastic ◽  
Non Linear

scholarly journals Experimental Study on Flexible Deformation of a Flapping Wing with a Rectangular Planform

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Wenqing Yang ◽  
Jianlin Xuan ◽  
Bifeng Song
Keyword(s):  
High Speed ◽  
Aerodynamic Force ◽  
Inertial Force ◽  
Aerodynamic Characteristics ◽  
Flapping Wing ◽  
Image Correlation ◽  
Flapping Wings ◽  
Aerodynamic Forces ◽  
Cyclic Movements ◽  
Flexible Deformation

A flexible flapping wing with a rectangular planform was designed to investigate the influence of flexible deformation. This planform is more convenient and easier to define and analyzed its deforming properties in the direction of spanwise and chordwise. The flapping wings were created from carbon fiber skeleton and polyester membrane with similar size to medium birds. Their flexibility of deformations was tested using a pair of high-speed cameras, and the 3D deformations were reconstructed using the digital image correlation technology. To obtain the relationship between the flexible deformation and aerodynamic forces, a force/torque sensor with 6 components was used to test the corresponding aerodynamic forces. Experimental results indicated that the flexible deformations demonstrate apparent cyclic features, in accordance with the flapping cyclic movements. The deformations in spanwise and chordwise are coupled together; a change of chordwise rib stiffness can cause more change in spanwise deformation. A certain lag in phase was observed between the deformation and the flapping movements. This was because the deformation was caused by both the aerodynamic force and the inertial force. The stiffness had a significant effect on the deformation, which in turn, affected the aerodynamic and power characteristics. In the scope of this study, the wing with medium stiffness consumed the least power. The purpose of this research is to explore some fundamental characteristics, as well as the experimental setup is described in detail, which is helpful to understand the basic aerodynamic characteristics of flapping wings. The results of this study can provide an inspiration to further understand and design flapping-wing micro air vehicles with better performance.

Nonlinear Aeroelastic Behavior of Slender Wings Considering a Static Stall Model Based on Wagner Function

2013 ◽  
Vol 325-326 ◽  
pp. 172-179
Author(s):  
D. Badiei ◽  
M.H. Sadr ◽  
Sh. Shams
Keyword(s):  
Equations Of Motion ◽  
Linear Part ◽  
Beam Theory ◽  
Structural Equations ◽  
Aeroelastic Response ◽  
Linear Elastic ◽  
Model Based ◽  
Aerodynamic Model ◽  
Lift Curve ◽  
Nonlinear Aerodynamic

The aeroelastic behavior of high aspect ratio wings in an incompressible flow is investigated. The nonlinear nonplanar bending-bending-twisting motions of beam theory is used for the structural equations assuming large deformations with small strains, small Poisson effects, inextensional beam theory, and linear elastic material characteristics by neglecting warping and shear deformation. An Unsteady nonlinear aerodynamic static stall model based on the Wagner function is introduced and then is used for determination of aerodynamic loading of the wing. In this aerodynamic model, the static lift curve vs. angle of attack is approximated by a piece-wise curve and for each linear part of this curve a corrected Wagner theory is used. Combining these two types of formulation yields fully nonlinear integro-differentials aeroelastic equations of motion. The governing equations will be solved to predict the nonlinear aeroelastic response of a wing in the stall and post stall regions using Galerkin's method and a numerical method without the need of adding any aerodynamic state-space variables and their corresponding equations. The obtained equations are solved for some test cases and the obtained results are compared with the results given in the literature. Also a study is done to show effects of nonlinear aerodynamic static stall model on the limit cycle oscillations.

scholarly journals Aerodynamic effects of flexibility in flapping wings

2009 ◽  
Vol 7 (44) ◽  
pp. 485-497 ◽  
Author(s):  
Liang Zhao ◽  
Qingfeng Huang ◽  
Xinyan Deng ◽  
Sanjay P. Sane
Keyword(s):  
Computational Models ◽  
Aerodynamic Force ◽  
Leading Edge ◽  
Flapping Flight ◽  
Force Generation ◽  
Flapping Wings ◽  
Centre Of Pressure ◽  
Aerodynamic Forces ◽  
Trailing Edge ◽  
High Angles Of Attack

Recent work on the aerodynamics of flapping flight reveals fundamental differences in the mechanisms of aerodynamic force generation between fixed and flapping wings. When fixed wings translate at high angles of attack, they periodically generate and shed leading and trailing edge vortices as reflected in their fluctuating aerodynamic force traces and associated flow visualization. In contrast, wings flapping at high angles of attack generate stable leading edge vorticity, which persists throughout the duration of the stroke and enhances mean aerodynamic forces. Here, we show that aerodynamic forces can be controlled by altering the trailing edge flexibility of a flapping wing. We used a dynamically scaled mechanical model of flapping flight ( Re ≈ 2000) to measure the aerodynamic forces on flapping wings of variable flexural stiffness (EI). For low to medium angles of attack, as flexibility of the wing increases, its ability to generate aerodynamic forces decreases monotonically but its lift-to-drag ratios remain approximately constant. The instantaneous force traces reveal no major differences in the underlying modes of force generation for flexible and rigid wings, but the magnitude of force, the angle of net force vector and centre of pressure all vary systematically with wing flexibility. Even a rudimentary framework of wing veins is sufficient to restore the ability of flexible wings to generate forces at near-rigid values. Thus, the magnitude of force generation can be controlled by modulating the trailing edge flexibility and thereby controlling the magnitude of the leading edge vorticity. To characterize this, we have generated a detailed database of aerodynamic forces as a function of several variables including material properties, kinematics, aerodynamic forces and centre of pressure, which can also be used to help validate computational models of aeroelastic flapping wings. These experiments will also be useful for wing design for small robotic insects and, to a limited extent, in understanding the aerodynamics of flapping insect wings.

scholarly journals Wing and body motion and aerodynamic and leg forces during take-off in droneflies

2013 ◽  
Vol 10 (89) ◽  
pp. 20130808 ◽  
Author(s):  
Mao Wei Chen ◽  
Yan Lai Zhang ◽  
Mao Sun
Keyword(s):  
High Speed ◽  
Aerodynamic Force ◽  
Measured Data ◽  
Body Motion ◽  
Flapping Wings ◽  
Inertia Force ◽  
High Speed Video ◽  
A Value ◽  
Short Time ◽  
Stroke Amplitude

Here, we present a detailed analysis of the take-off mechanics in droneflies performing voluntary take-offs. Wing and body kinematics of the insects during take-off were measured using high-speed video techniques. Based on the measured data, the inertia force acting on the insect was computed and the aerodynamic force of the wings was calculated by the method of computational fluid dynamics. Subtracting the aerodynamic force and the weight from the inertia force gave the leg force. In take-off, a dronefly increases its stroke amplitude gradually in the first 10–14 wingbeats and becomes airborne at about the 12th wingbeat. The aerodynamic force increases monotonously from zero to a value a little larger than its weight, and the leg force decreases monotonously from a value equal to its weight to zero, showing that the droneflies do not jump and only use aerodynamic force of flapping wings to lift themselves into the air. Compared with take-offs in insects in previous studies, in which a very large force (5–10 times of the weight) generated either by jumping legs (locusts, milkweed bugs and fruit flies) or by the ‘fling’ mechanism of the wing pair (butterflies) is used in a short time, the take-off in the droneflies is relatively slow but smoother.

Sign in / Sign up

Export Citation Format

Share Document