Non-linear aeroelastic response of high aspect-ratio wings in the frequency domain

2017 ◽  
Vol 121 (1240) ◽  
pp. 858-876 ◽  
Author(s):  
F. Afonso ◽  
J. Vale ◽  
É. Oliveira ◽  
F. Lau ◽  
A. Suleman
Keyword(s):  
Aspect Ratio ◽  
Current Trend ◽  
Commercial Aircraft ◽  
Aeroelastic Response ◽  
Flutter Speed ◽  
Wing Model ◽  
Induced Drag ◽  
Non Linear ◽  
Flutter Boundary ◽  
Wing Aspect Ratio

ABSTRACTA current trend in the aeronautic industry is to increase the wing aspect ratio to enhance aerodynamic efficiency by reducing the induced drag and thus reduce fuel consumption. Despite the associated benefits of a large aspect ratio, such as higher lift-to-drag ratios and range, commercial aircraft usually have a relatively low aspect ratio. This is partially explained by the fact that the wing becomes more flexible with increasing aspect ratio and thus more prone to large deflections, which can cause aeroelastic instability problems such as flutter. In this work, an aeroelastic study is conducted on a rectangular wing model of 20 m span and variable chord for a low subsonic speed condition to evaluate the differences between linear and non-linear static aeroelastic responses. Comparisons between linear and non-linear displacements, natural frequencies and flutter boundary are performed. An in-house non-linear aeroelastic framework was employed for this purpose. In this work, the influence of the aspect ratio and geometric non-linearity (highly deformed states) is assessed in terms of aeroelastic performance parameters: flutter speed and divergence speed. A nearly linear correlation of flutter speed difference (relative to linear analysis results) with vertical-tip displacement difference is observed. The flutter and divergence speeds vary substantially as the wing aspect ratio increases, and the divergence speeds always remain above the flutter speed. Furthermore, the flutter mechanism was observed to change as the wing chord is decreased.

Non-linear aeroelastic analysis in the time domain of high-aspect-ratio wings: Effect of chord and taper-ratio variation

2016 ◽  
Vol 121 (1235) ◽  
pp. 21-53 ◽  
Author(s):  
A. Suleman ◽  
F. Afonso ◽  
J. Vale ◽  
É. Oliveira ◽  
F. Lau
Keyword(s):  
Aspect Ratio ◽  
High Aspect Ratio ◽  
Bending Moment ◽  
Equilibrium Solutions ◽  
Computational Framework ◽  
Wing Model ◽  
Aeroelastic Analysis ◽  
Non Linear ◽  
Time Marching ◽  
The Time Domain

ABSTRACTCommercial jets usually have relatively low-aspect-ratio wings, in spite of the associated benefits of increasing the wing aspect-ratio, such as higher lift-to-drag ratios and ranges. This is partially explained by the fact that the wing becomes more flexible by increasing the aspect-ratio that results in higher deflections which can cause aeroelastic instability problems such as flutter. An aeroelastic computational framework capable of evaluating the effects of geometric non-linearities on the aeroelastic performance of high-aspect-ratio wings has been developed and validated using numerical and experimental data. In this work, the aeroelastic performance of a base wing model with 20 m span and 1 m chord is analysed and the effect of changing the wing chord or the taper-ratio is determined. The non-linear static aeroelastic equilibrium solutions are compared in terms of drag polar, root bending moment and natural frequencies, and the change in the flutter speed boundary is assessed as a function of aspect-ratio using a time-marching approach.

The effect of stiffness and geometric parameters on the nonlinear aeroelastic performance of high aspect ratio wings

2016 ◽  
Vol 231 (10) ◽  
pp. 1824-1850 ◽  
Author(s):  
F Afonso ◽  
G Leal ◽  
J Vale ◽  
É Oliveira ◽  
F Lau ◽  
...  
Keyword(s):  
Aspect Ratio ◽  
High Aspect Ratio ◽  
Nonlinear Behavior ◽  
Geometric Parameters ◽  
Torsional Stiffness ◽  
Design Parameters ◽  
Sweep Angle ◽  
Flutter Speed ◽  
Wing Model ◽  
Aspect Ratios

The increase in wing aspect ratio is gaining interest among aircraft designers in conventional and joined-wing configurations due to the higher lift-to-drag ratios and longer ranges. However, current transport aircraft have relatively small aspect ratios due their increased structural stiffness. The more flexible the wing is more prone to higher deflections under the same operating condition, which may result in a geometrical nonlinear behavior. This nonlinear effect can lead to the occurrence of aeroelastic instabilities such as flutter sooner than in an equivalent stiffer wing. In this work, the effect of important stiffness (inertia ratio and torsional stiffness) and geometric (sweep and dihedral angles) design parameters on aeroelastic performance of a rectangular high aspect ratio wing model is assessed. The torsional stiffness was observed to present a higher influence on the flutter speed than the inertia ratio. Here, the decrease of the inertia ratio and the increase of the torsional stiffness results in higher flutter and divergence speeds. With respect to the geometric parameters, it was observed that neither the sweep angle nor the dihedral angle variations caused a substantial influence on the flutter speed, which is mainly supported by the resulting smaller variations in torsion and bending stiffness due to the geometric changes.

Aeroelastic response of a swept wing with cubic structural non-linearities

2008 ◽  
Vol 222 (2) ◽  
pp. 229-248 ◽  
Author(s):  
M Razi ◽  
B Ghadiri
Keyword(s):  
Numerical Solution ◽  
Degrees Of Freedom ◽  
Linear Analysis ◽  
Swept Wing ◽  
Governing Equations ◽  
Aeroelastic Response ◽  
Runge Kutta Method ◽  
Non Linear ◽  
Flutter Boundary ◽  
The Time Domain

Linear and non-linear aeroelastic analyses of swept cantilever wings containing a cubic non-linearity in an incompressible flow are investigated. Expressions of aerodynamic forces and moments for an element of the swept wing are derived in the time domain using a relation between Theodorsen and Wagner's functions. Consequently, the governing aeroelastic equations of two degrees of freedom wings are derived for both swept backward and forward wings. Linear analysis is carried out via solving the governing equations with the standard fourth-order Runge—Kutta method. For the sake of verification of the derived formulas, the results of the numerical solution for a linear flutter boundary are compared with the experimental data in several cases. Considering softening and hardening cubic structural non-linearities, non-linear analysis of the swept wing is studied. For the wings containing hardening cubic non-linearities, the first- and third-order harmonic balance (HB) methods are employed to find the amplitude and frequency of limit cycle oscillations (LCOs). Comparison between results of the HB method and those of the numerical solution of the governing equations indicates a close agreement. Finally, few parameters on the linear and non-linear flutter boundaries and also the amplitude and frequency of the LCO are studied.

scholarly journals On the Investigation of State Space Reconstruction of Nonlinear Aeroelastic Response Time Series

2006 ◽  
Vol 13 (4-5) ◽  
pp. 393-407 ◽  
Author(s):  
Flávio D. Marques ◽  
Eduardo M. Belo ◽  
Vilma A. Oliveira ◽  
José R. Rosolen ◽  
Andréia R. Simoni
Keyword(s):  
Experimental Data ◽  
Time Series ◽  
Response Time ◽  
State Space ◽  
The State ◽  
Aeroelastic Response ◽  
State Space Reconstruction ◽  
Wing Model ◽  
Linear Behavior ◽  
Non Linear

Stall-induced aeroelastic motion may present severe non-linear behavior. Mathematical models for predicting such phenomena are still not available for practical applications and they are not enough reliable to capture physical effects. Experimental data can provide suitable information to help the understanding of typical non-linear aeroelastic phenomena. Dynamic systems techniques based on time series analysis can be adequately applied to non-linear aeroelasticity. When experimental data are available, the methods of state space reconstruction have been widely considered. This paper presents the state space reconstruction approach for the characterization of the stall-induced aeroelastic non-linear behavior. A wind tunnel scaled wing model has been tested. The wing model is subjected to different airspeeds and dynamic incidence angle variations. The method of delays is used to identify an embedded attractor in the state space from experimentally acquired aeroelastic response time series. To obtain an estimate of the time delay used in the state space reconstruction from time series, the autocorrelation function analyis is used. For the calculation of the embedding dimension the correlation integral approach is considered. The reconstructed attractors can reveal typical non-linear structures associated, for instance, to chaos or limit cycles.

Investigation of Computational Non-Linear Aeroelastic Response of High Aspect Ratio Wing

2013 ◽  
Vol 419 ◽  
pp. 55-61
Author(s):  
Hammad Rahman ◽  
Min Li
Keyword(s):  
Aspect Ratio ◽  
High Aspect Ratio ◽  
Parametric Design ◽  
Aerodynamic Load ◽  
Linear Deformation ◽  
Aeroelastic Response ◽  
Simplified Approach ◽  
Strip Theory ◽  
Non Linear ◽  
The Impact

Aircrafts with high aspect ratio wings are most eligible candidates for high altitude and long endurance flights. Such wings show a non-linear deformation behavior because of structural geometric non-linearity. In the present study both linear and non-linear static aeroelastic behaviors of a high aspect ratio rectangular flat plate wing are analyzed using a simplified approach. The main emphasis lies in the tremendous change of lift distribution on the flexible high aspect ratio wing when large deflections are incorporated in the static aeroelastic analysis. The computational static aeroelastic simulations are performed in the finite element method based commercial software ANSYS-14. The aerodynamic load is calculated using the strip theory. Since the aero-load changes with the twisting deformation hence a user defined script is written using ANSYS parametric design language (APDL). The computationally achieved divergence velocity results are compared with the analytical results. The results of parametric study at different flight load conditions and angles of attack have highlighted the role of geometric nonlinearities in both bending and twisting deformations. The impact of follower pressure forces on the aeroelastic response is also investigated.

Experimental Nonlinear Flutter Analysis of a Cantilever Wing/Store

2020 ◽  
Vol 20 (07) ◽  
pp. 2050082
Author(s):  
A. Alizadeh ◽  
Z. Ebrahimi ◽  
A. Mazidi ◽  
S. Ahmad Fazelzadeh
Keyword(s):  
Time History ◽  
Sweep Angle ◽  
Aeroelastic Response ◽  
Nonlinear Flutter ◽  
Wing Model ◽  
Subsonic Wind Tunnel ◽  
Structural Nonlinearities ◽  
Flutter Boundary ◽  
Store Location ◽  
Bending Modes

This paper studies experimentally the nonlinear aeroelastic and flutter behavior of a cantilever plate wing with an external store. The wing model that is constructed from plexiglass sheet is designed and tested in a closed-circuit subsonic wind tunnel. To deal with the structural nonlinearities of the model, various analysis tools such as time history plots, phase-plane projections and Fast Fourier Transform (FFT) have been used for detecting the critical and post-critical behaviors of the structure. The results show that flutter takes place by the coupling between the torsional and bending modes. A good correlation between the present experiments and previous numerical results is obtained. The nonlinear aeroelastic response and flutter boundary are investigated for different sweep angles. The flutter velocity and amplitudes of limit cycle oscillations (LCOs) increase rapidly with increasing sweep angle. The nonlinear response of the wing with an external store is also investigated, with the effect of store location on the nonlinear flutter boundary evaluated.

scholarly journals Preliminary investigation of use of flexible folding wing tips for static and dynamic load alleviation

2016 ◽  
Vol 121 (1235) ◽  
pp. 73-94 ◽  
Author(s):  
A. Castrichini ◽  
V. Hodigere Siddaramaiah ◽  
D.E. Calderon ◽  
J.E. Cooper ◽  
T. Wilson ◽  
...  
Keyword(s):  
Aspect Ratio ◽  
Preliminary Investigation ◽  
Aircraft Design ◽  
Dynamic Loads ◽  
Induced Drag ◽  
Aeroelastic Model ◽  
Static And Dynamic Loads ◽  
Folding Wing ◽  
Wing Tips ◽  
Wing Tip

ABSTRACTA recent consideration in aircraft design is the use of folding wing-tips with the aim of enabling higher aspect ratio aircraft with less induced drag while also meeting airport gate limitations. This study investigates the effect of exploiting folding wing-tips in flight as a device to reduce both static and dynamic loads. A representative civil jet aircraft aeroelastic model was used to explore the effect of introducing a wing-tip device, connected to the wings with an elastic hinge, on the load behaviour. For the dynamic cases, vertical discrete gusts and continuous turbulence were considered. The effects of hinge orientation, stiffness, damping and wing-tip weight on the static and dynamic response were investigated. It was found that significant reductions in both the static and dynamic loads were possible. For the case considered, a 25% increase in span using folding wing-tips resulted in almost no increase in loads.

Robust Flutter Analysis of an Airfoil with Flap Freeplay Uncertainty

2008 ◽  
Vol 33-37 ◽  
pp. 1247-1252 ◽  
Author(s):  
Zhi Chun Yang ◽  
Ying Song Gu
Keyword(s):  
Control Surface ◽  
Two Dimensional ◽  
Advanced Technique ◽  
Worst Case ◽  
Wing Model ◽  
Freeplay Nonlinearity ◽  
Flutter Analysis ◽  
Flutter Boundary ◽  
Nominal Parameter ◽  
Flutter Margin

Modern robust flutter method is an advanced technique for flutter margin estimation. It always gives the worst-case flutter speed with respect to potential modeling errors. Most literatures are focused on linear parameter uncertainty in mass, stiffness and damping parameters, etc. But the uncertainties of some structural nonlinear parameters, the freeplay in control surface for example, have not been taken into account. A robust flutter analysis approach in μ-framework with uncertain nonlinear operator is proposed in this study. Using describing function method the equivalent stiffness formulation is derived for a two dimensional wing model with freeplay nonlinearity in its flap rotating stiffness. The robust flutter margin is calculated for the two dimensional wing with flap freeplay uncertainty and the results are compared with that obtained with nominal parameter values. It is found that by considering the perturbation of freeplay parameter more conservative flutter boundary can be obtained, and the proposed method in μ-framework can be applied in flutter analysis with other types of concentrated nonlinearities.

Numerical Study of Winglet at Low Reynolds Numbers

2013 ◽  
Author(s):  
Sina Pooladsanj ◽  
Mehran Tadjfar
Keyword(s):  
Aspect Ratio ◽  
Flow Field ◽  
Vortex Flow ◽  
Numerical Study ◽  
Reynolds Numbers ◽  
Flow Zone ◽  
Low Reynolds Numbers ◽  
Structured Grid ◽  
Flow Field Characteristics ◽  
Wing Aspect Ratio

A numerical study has been performed to evaluate the aerodynamics coefficients of a winglet in the range of Reynolds numbers below 30,000. In this study some parameters on winglet design have been considered. The effect of winglet-tip airfoil thickness has been investigated on aerodynamics coefficients. In order to explore this effect, two different airfoils (NACA0002 and NACA0012) were employed at the winglet-tip. The influence of varying the winglet connection angle to the wing on aerodynamics coefficients and flow field characteristics in the vortex flow zone such as; circulation magnitude and vorticity magnitude in the vortex core have been studied. Six connection angles including 20°, 30°, 40°, 50°, 60° and 70° have been studied. Negative values of these angles have also been considered. In addition, the effect of changing wing aspect ratio on aerodynamics coefficients has been investigated. To solve the flow field around the studied geometry a fully structured grid was used which consists of 84 blocks.

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