Chaotic Response of an Airfoil due to Aeroelastic Coupling and Dynamic Stall
01 Jan 2007-AIAA Journal (American Institute of Aeronautics and Astronautics (AIAA))-Vol. 45, Iss: 1, pp 271-280
TL;DR: In this article, the effects of dynamic stall and aeroelastic couplings on the response of a 2D airfoil undergoing pitching and plunging motion in a pulsating oncoming flow are analyzed.
Abstract: Flight-test data of helicopters indicate that vibratory levels in the fuselage exhibit a wide spectrum of frequencies, including a few below the rotor revolutions per minute. It is well known that helicopter blades operate in a complex aerodynamic environment, involving time-varying heave, pitch, and pulsating oncoming flow. During operation, some sections of the rotor blade undergo dynamic stall once in a revolution. This paper attempts to understand the reason for the existence of several frequencies in the response of the fuselage and the possible cause for this observed phenomenon by analyzing the effects of dynamic stall and aeroelastic couplings on the response of 2-D airfoil. The ONERA dynamic stall model developed by Petot is modified by incorporating a higher-order rational approximation of Theodorsen's lift deficiency function. This improved model is shown to provide a better correlation with experimental stall data. The response characteristics of a 2-D airfoil undergoing pitching and plunging motion in a pulsating oncoming flow, simulating the response of a cross section of a helicopter rotor blade in forward flight are analyzed. This study shows significant difference in the response characteristics of the airfoil for unsteady (dynamic stall model) and quasi-steady aerodynamic models. It is observed that the nonlinear aerodynamics (dynamic stall effects) in association with aeroelastic couplings above a certain level lead to a bounded chaotic motion of the airfoil.
Citations
More filters
TL;DR: In this paper, a computational aeroelastic tool aimed at the analysis of the response of rotary wings in arbitrary steady motion was developed by coupling a nonlinear beam model for blades structural dynamics with a potential-flow boundary integral equation solver for the prediction of unsteady aerodynamic loads around three-dimensional lifting bodies.
47 citations
TL;DR: In this article, a first-order, state-space model is developed by combining a geometrically exact, nonlinear anisotropic beam model with nonlinear ONERA (Edlin) dynamic stall model.
37 citations
01 Dec 2009
TL;DR: In this article, different approaches include displacement-based, strain-based and intrinsic geometrically-nonlinear beam models for the large structural deformations of aircraft with high-aspect-ratio composite wings.
Abstract: Dissimilar analysis models are considered for the large structural deformations of aircraft with high-aspect-ratio composite wings. The different approaches include displacementbased, strain-based, and intrinsic geometrically-nonlinear beam models. Comparisons are made in terms of numerical efficiency and simplicity for integration of full aircraft flexibility in flight dynamics models. An analysis procedure is proposed based on model substructuring with a (linear) modal representation of both fuselage and tail and (nonlinear) intrinsic beam elements for the flexible wings.
21 citations
TL;DR: In this paper, a flexible half-span Delta wing is tested in a low speed wind tunnel in order to investigate its dynamic response, and three types of bifurcations are observed for the first time for such an aeroelastic system: subcritical, period-doubling/period-halving and nontypical Bifurcation.
21 citations
TL;DR: In this paper, the effect of different unsteady parameters, namely, amplitude (A), reduced frequency (k), Reynolds number (Re), and asymmetry parameter (S) for pitching motion on the force coefficients was investigated.
Abstract: The expanding application in micro-air vehicles has encouraged many researchers to understand the unsteady flow around a flapping foil at a low Reynolds number. We numerically investigate an incompressible unsteady flow around a two-dimensional pitching airfoil (SD7003) at high reduced frequency (k ≥ 3) in the laminar regime. This study interrogates the effect of different unsteady parameters, namely, amplitude (A), reduced frequency (k), Reynolds number (Re), and asymmetry parameter (S) for pitching motion on the force coefficients. The inviscid theoretical model is utilized to calculate the lift coefficient for sinusoidal motion in the viscous regime, and a comparison is made with the numerical results. The theoretical analysis identifies the influence of the non-circulatory lift over circulatory lift at a high reduced frequency. Furthermore, the results indicate that the reduced frequency (k) and asymmetry parameter (S) have a significant impact on the instantaneous and time-averaged force coefficients as well as on the vortex structure in the wake. Finally, the fast Fourier transformation analysis is carried out over a simulated case with fixed amplitude and Reynolds number for distinct k and S values. The findings confirm that the dominant frequency in the flow (k*) has a direct correlation to the airfoil pitching frequency (k).
19 citations
References
More filters
Book•
01 Jan 1994
TL;DR: The logistic map, a canonical one-dimensional system exhibiting surprisingly complex and aperiodic behavior, is modeled as a function of its chaotic parameter, and the progression through period-doubling bifurcations to the onset of chaos is considered.
Abstract: We explore several basic aspects of chaos, chaotic systems, and non-linear dynamics through three different setups. The logistic map, a canonical one-dimensional system exhibiting surprisingly complex and aperiodic behavior, is modeled as a function of its chaotic parameter. We consider maps of its phase space, and the progression through period-doubling bifurcations to the onset of chaos. The Feigenbaum ratio of successive bifurcation periods is estimated at 4.674, in good agreement with the accepted value. The Liapunov exponent, governing the exponential growth of small perturbations in chaotic systems, is calculated and its fractal structure compared to the corresponding bifurcation diagram for the logistic map. Using a non-linear p-n junction circuit we analyze the return maps and power spectrums of the resulting time series at various types of system behavior. Similarly, an electronic analog to a ball bouncing on a vertically driven table provides insight into real-world applications of chaotic motion. For both systems we calculate the fractal information dimension and compare with theoretical behavior for dissipative versus Hamiltonian systems. Subject headings: non-linear dynamics; non-linear dynamical systems; fractal dimension; chaos; strange attractors; logistic map
5,372 citations
02 May 1934
TL;DR: In this paper, the Kutta condition was used to analyze the aerodynamic forces on an oscillating airfoil or an air-foil-aileron combination of three independent degrees of freedom.
Abstract: The aerodynamic forces on an oscillating airfoil or airfoil-aileron combination of three independent degrees of freedom were determined. The problem resolves itself into the solution of certain definite integrals, which were identified as Bessel functions of the first and second kind, and of zero and first order. The theory, based on potential flow and the Kutta condition, is fundamentally equivalent to the conventional wing section theory relating to the steady case. The air forces being known, the mechanism of aerodynamic instability was analyzed. An exact solution, involving potential flow and the adoption of the Kutta condition, was derived. The solution is of a simple form and is expressed by means of an auxiliary parameter k. The flutter velocity, treated as the unknown quantity, was determined as a function of a certain ratio of the frequencies in the separate degrees of freedom for any magnitudes and combinations of the airfoil-aileron parameters.
2,153 citations
"Chaotic Response of an Airfoil due ..." refers background in this paper
...The expressions LNC and LC are, respectively, identical to the noncirculatory and circulatory parts of the unsteady lift obtained by Theodorsen [31], except for the lift deficiency function C k ....
[...]
TL;DR: In this article, the leading edge geometry of an NACA 0012 airfoil has been studied in incompressible flow at moderately large Reynolds numbers and three different types of stall were produced.
Abstract: Dynamic stall and unsteady boundary layer separation have been studied in incompressible flow at moderately large Reynolds numbers. By varying the leading-edge geometry of an NACA 0012 airfoil, three different types of stall were produced. For most of the configurations studied, including the basic NACA 0012 profile, dynamic stall was found not to originate with the bursting of a leading-edge laminar separation bubble, as is commonly believed. Instead, the vortex shedding phenomenon, which is the predominant feature of dynamic stall, appears to be fed its vorticity by the breakdown of the turbulent boundary layer.
462 citations
"Chaotic Response of an Airfoil due ..." refers background in this paper
...Several experimental [5–9] and theoretical [10–21] studies are available in Presented as Paper 1866 at the 47 AIAA/ASME/ASCE/AHS/ASC SDM Conference, Newport, RI, 1–4 May 2006; received 12 April 2006; revision received 23 August 2006; accepted for publication 4 October 2006....
[...]
...Most of the experimental studies on dynamic stall phenomenon have focused on airfoils oscillating only in pitching motion [5,6]....
[...]
01 Jan 1935
TL;DR: In this paper, the Kutta condition was used to analyze the aerodynamic forces on an oscillating airfoil or an air-foil-aileron combination of three independent degrees of freedom.
Abstract: The aerodynamic forces on an oscillating airfoil or airfoil-aileron combination of three independent degrees of freedom were determined. The problem resolves itself into the solution of certain definite integrals, which were identified as Bessel functions of the first and second kind, and of zero and first order. The theory, based on potential flow and the Kutta condition, is fundamentally equivalent to the conventional wing section theory relating to the steady case. The air forces being known, the mechanism of aerodynamic instability was analyzed. An exact solution, involving potential flow and the adoption of the Kutta condition, was derived. The solution is of a simple form and is expressed by means of an auxiliary parameter k. The flutter velocity, treated as the unknown quantity, was determined as a function of a certain ratio of the frequencies in the separate degrees of freedom for any magnitudes and combinations of the airfoil-aileron parameters.
351 citations
TL;DR: In this paper, the authors present the major approaches and results obtained in recent years and to point out existing deficiencies and possibilities for improvements for the prediction of dynamic stall in aerodynamic bodies such as airfoils and wings.
347 citations
"Chaotic Response of an Airfoil due ..." refers background in this paper
...Several experimental [5–9] and theoretical [10–21] studies are available in Presented as Paper 1866 at the 47 AIAA/ASME/ASCE/AHS/ASC SDM Conference, Newport, RI, 1–4 May 2006; received 12 April 2006; revision received 23 August 2006; accepted for publication 4 October 2006....
[...]
...Recently CFDmethods [20,21] are applied to predict dynamic stall in airfoils....
[...]