Nonlinear Aerodynamics Research Articles

Prediction of the non-linear aeroelastic behavior of a cantilever flat plate and equivalent 2D model

Reducing structure weigh is one of the main strategies for decreasing environmental and manufacturing costs of engineering solutions. The reduction in material is normally related with a higher impact of aeroelastic solicitations. For some industrial cases it is needed to account for non-linear aerodynamics and, therefore, the whole fully coupled set of equations needs to be simulated in order to predict its behavior. One possible way of reducing the high computational cost associated with this problem is the use of an equivalent 2D model, whose derivation is not straightforward. This article presents a methodology for reducing the order from a complete three dimensional arbitrary beam to its equivalent 2D characteristic section. The behavior of both systems is analyzed and it is shown how, when the methodology is applied, the resulting 2D system is capable to predict similar results with a computational cost which is reduced by orders of magnitude.

Modeling and simulating nonstationary thunderstorm winds based on multivariate AR-GARCH

Extreme winds such as thunderstorm winds typically exhibit nonstationary characteristics. When these winds act on the structure, the time domain analysis method is used considering the structural and/or aerodynamic nonlinearity in the wind-induced structural response analysis. Because the time domain analysis method needs a sufficient number of wind speed samples, the efficient simulation of nonstationary winds becomes a crucial task. The time series method is more suitable in generating the nonstationary process due to the high efficiency. As a typical time series model, the autoregressive-generalized autoregressive conditional heteroskedasticity (AR-GARCH) model could be a good candidate to characterize these samples. In this paper, the method based on the multivariate AR-GARCH model is proposed to model and simulate the multivariate nonstationary wind speed process. Specifically, Baba-Engle-Kraft-Kroner (BEKK) model is adopted since it can maintain the positive definiteness of conditional covariance matrix. The numerical simulations based on samples with different time-varying variances obtained by spectral representation method (SRM) are given to demonstrate the applicability of the proposed method. The measured thunderstorm wind speed is adopted to illustrate and validate the accuracy of the proposed method. The results show that the time-varying variance and cross correlation can be satisfactorily maintained.

Nonlinear Flight Dynamics and Control of a Fixed-Wing Micro Air Vehicle: Numerical, System Identification and Experimental Investigations

The flight dynamics of Micro Air Vehicles (MAVs) exhibit significant nonlinear characteristics, which cannot be ignored in simulation or analysis. In this study, a full nonlinear simulation of the flight dynamics characteristics of a fixed-wing MAV is performed. To strengthen the developed nonlinear mathematical modeling, the MAV’s mass properties and propulsion characteristics are experimentally investigated. Moreover, the aerodynamic characteristics of the designed fixed-wing MAV are experimentally measured in a wind tunnel. The experimental aerodynamics investigation includes the propeller wash effect and the same flight conditions of the MAV. These measured data are fed to the nonlinear flight dynamics model to improve its accuracy and ensure the nonlinear aerodynamics effect on the flight dynamics. The enhanced model is then validated against response experimental measurements of the MAV in the wind tunnel that is free to pitch at different control inputs and initial conditions. Furthermore, it is compared to the response of the system identification model. The nonlinear simulation and dynamic testing investigations indicate many nonlinear phenomena, such as the appearance of the limit cycle in the longitudinal flight. This paper shows that the aerodynamic center of MAV with a low aspect ratio in the low Reynolds number regime of flow can move as a response to flap deflection. The validated nonlinear mathematical model was used to evaluate the MAV’s dynamics, design and evaluate a PID controller in flight conditions similar to the MAV’s actual flying mission. Moreover, the presented model can be used for flapping-wing MAVs using time-dependent experimental measurements.

Bifurcation Flight Dynamic Analysis of a Strake-Wing Micro Aerial Vehicle

Non-linear phenomena are particularly important in -flight dynamics of micro-class unmanned aerial vehicles. Susceptibility to atmospheric turbulence and high manoeuvrability of such aircraft under critical flight conditions cover non-linear aerodynamics and inertia coupling. The theory of dynamical systems provides methodology for studying systems of non-linear ordinary differential equations. The bifurcation theory forms part of this theory and deals with stability changes leading to qualitatively different system responses. These changes are called bifurcations. There is a number of papers, the authors of which applied the bifurcation theory for analysing aircraft flight dynamics. This article analyses the dynamics of critical micro aerial vehicle flight regimes. The flight dynamics under such conditions is highly non-linear, therefore the bifurcation theory can be applied in the course of the analysis. The application of the theory of dynamical systems enabled predicting the nature of micro aerial vehicle motion instability caused by bifurcations and analysing the post-bifurcation microdrone motion. This article presents the application of bifurcation analysis, complemented with time-domain simulations, to understand the open-loop dynamics of strake-wing micro aerial vehicle model by identifying the attractors of the dynamic system that manages upset behaviour. A number of factors have been identified to cause potential critical states, including non-oscillating spirals and oscillatory spins. The analysis shows that these spirals and spins are connected in a one-parameter space and that due to improper operation of the autopilot on the spiral, it is possible to enter the oscillatory spin.

Two-Timescale Missile Autopilot Design Based on Suboptimal Control

Aiming at the missile longitudinal motion model with obvious aerodynamic nonlinearity, this paper proposes a two-timescale design method of missile autopilot based on suboptimal control. By dividing the system states into fast and slow states based on different timescales, the corresponding fast and slow control inputs are designed. This paper introduces suboptimal control and robust control to enable the system to have good dynamic response characteristics, and the system’s ability to suppress various uncertainties is guaranteed. By applying the Lyapunov method, the stability conditions of the system are given. Finally, the simulation results show that the system has good dynamic characteristics and robustness.

Experimental and numerical investigations on the nonlinear aeroelastic behavior of high aspect-ratio wings for different chord-wise store positions under stall and follower aerodynamic load models

This study performs an experimental and numerical investigation on the nonlinear aeroelastic response of cantilever high-aspect-ratio beam-like wings with a ballast at their free tips, emulating the effects of a store. As an extent, the effects of different chord-wise ballast positions are experimentally examined for two highly flexible rectangular wings. Furthermore, the numerical model proposed brings forward a nonlinear finite element beam model accounting for aerodynamic nonlinearities, via stall and follower forces models, along with geometrical nonlinearities due to large displacements and rotations. A great variety of analyses were performed: First, the flutter boundaries of the wings were analyzed; second, the limit cycle oscillation amplitudes and frequencies in the oscillating wings were evaluated; third, the coupling behavior and the nonlinear responses obtained were discussed under several attributes. The geometrical nonlinearities were taken into account by a total Lagrangian formulation based on a straightforward and consistent interpolation field in order to describe the exact kinematics of a Timoshenko’s beam. Nonlinear aerodynamic loads were computed via an unsteady strip theory in the time-domain with the Jones approximation for the Wagner’s function along with a follower aerodynamic loads assumption. Additionally, a non-usual stall model based on an experimental quasi-static stall curve for flat plates was used to interpolate the lift-curve slope. The experimental and numerical results indicated a minimum flutter speed for ballast positions about of −5 mm toward the leading edge. Next, different nonlinear post-flutter LCO behaviors were obtained for the different ballast positions tested. To conclude, the good correlation between model and experiments indicated that the nonlinear modeling approach proposed herein was capable to predict the aeroelastic behavior of the tested high aspect-ratio wings.

Static Wind Nonlinear Analysis of Iced Transmission Lines

The torsion of iced transmission line under the action of static wind will affect the configuration of its equilibrium state. This state is very critical for occur of the galloping. The beam element simulation method of iced transmission line is proposed. The stiffness matrix and mass matrix are derived, and the double nonlinear analysis method considering geometric nonlinearity and material nonlinearity is proposed. The static wind stability analysis of iced transmission line show that the aerodynamic nonlinearity caused by the shape is obvious. With the increase of wind loads, the torsion angle of conductor increases and the three component force coefficient changes, which leads to the nonlinear change of displacement and internal force response. At low wind speed, the iced conductor is more sensitive to the initial attack angle of wind, but at high wind speed, the conductor deformation is not sensitive to the initial attack angle of wind, and both will converge to the positive and negative values respectively.

Three dimensional aeroelastic analyses considering free-play nonlinearity using computational fluid dynamics/computational structural dynamics coupling

Most of the previous studies on free-play aeroelasticity were based on the linear aerodynamic theory, which cannot consider the aerodynamic nonlinear effects. This paper proposes a framework of computational fluid dynamics/computational structural dynamics (CFD/CSD) coupling approach that can deal with the three dimensional aeroelastic problems with both the free-play nonlinearity and the aerodynamic nonlinearity. The fictitious mass method is used to construct the reduced structural equations of motion and the switching point is detected using the bisection method. The adaptive time step obtained by the bisection method is returned to the CFD solver so that both the structural and the fluid equations are integrated using the same time step. An all-movable wing with free-play at the root is considered for numerical studies. Results demonstrate the CFD/CSD coupling method can predict the stable limit cycle oscillation (LCO) effectively. The initial condition study shows that the LCO behavior is subcritical and the hysteresis response can be predicted in time domain effectively by the presented method. The viscous effect is shown to increase the LCO boundary and shift the LCO amplitude to a larger velocity in transonic regime. The LCO boundary is determined from subsonic to transonic Mach numbers. The transonic dip in LCO boundary is found by the CFD/CSD coupling method, but the equivalent linearization with doublet lattice method fails to predict this phenomenon. From the results of this study, the LCO boundary is shown to be 43.5% below the flutter boundary at most.

Design of a robustH∞dynamic sliding mode torque observer for the 100 KW wind turbine

This article presents a novel technique for the design of a robust dynamic nonlinear observer in the H ∞ scheme for the Lipschitz nonlinear model of the wind turbine. It is a challenging problem due to the aerodynamic nonlinearity of blades. A drive train of the 100 KW wind turbine benchmark model, developed by Aalborg University and KK-electronic a/c, is conducted to exhibit the effectiveness of the proposed observer approach. The new Lipschitz constant definition for this system is expressed. Based on the new dynamic method, the Lipschitz constant is increased. Therefore, the operating region is increased. A new dynamic sliding mode observer is introduced for torque estimation in the drive train. The design methodology is the use of dynamic gain instead of static one in the sliding mode observer. The dynamic observer design offers an extra degree of freedom over the classical static gain observer. We established the conditions for the suggested dynamic observer stability. The proposed approach provides the observer robustness against nonlinear uncertainties due to the maximizing the Lipschitz constant. Moreover, the design procedure with the effect of system and sensor noises is considered. Results illustrate the advantage of this work in comparison with other observers. Finally, the results are evaluated with the wind turbine simulator software FAST. • The paper studies a new robust sliding mode observer for the nonlinear wind turbine Drivetrain. • Based on the extra degree of freedom the operating region of the wind turbine has been enlarged. • The goal is to obtain a filter to stabilize the error dynamics without loss of performance. • Another contribution is improving the observer behavior by attenuating noise. • To validate the model, the drivetrain model was tested in FAST wind turbine software.

Sparse identification of nonlinear unsteady aerodynamics of the oscillating airfoil

Reduced-order models are widely used in aerospace engineering. A model for unsteady aerodynamics is desirable for designing the blades of wind turbines. Recently, sparse identification of nonlinear dynamics with control was introduced to identify the parameters of an input-output dynamical system. In this paper, two models for attached flows and one for separated flows are identified through this technique. For the unsteady lift of the attached flow, Model I is a linear model that presents the dynamic change of an unsteady lift to a static lift. Model II was built based on Model I in order to obtain a more general system with closed-loop control. It has a first-order inert element that delays the overall input of the static lift. The Model II results replicate the training data very well and give an accurate prediction of other oscillating cases with different oscillation amplitudes, reduced frequency or mean angle of attack. For the unsteady lift of the separated flow, Model III is identified as a nonlinear model, which also has a first-order inert element. This model captures the nonlinear aerodynamics of the separated flow and replicates the training cases well. In addition, the prediction of Model III has good agreement with the numerical results.

Nonlinear modeling of electro-aeroelastic dynamics of composite beams with piezoelectric coupling

Structural and aerodynamic non-linearities can lead to persistent oscillations in aeroelastic systems, which allows the conversion of mechanical energy into electric power. Flexible beams represent an example of structures that can be used as energy harvesters. This work aims to model and analyze the non-linearities induced by the flow-structure interaction of an energy harvester consisting of a laminated beam integrated with a piezoelectric sensor. The cantilevered beam and the piezoelectric lamina are modeled using a nonlinear finite element approach, while unsteady aerodynamic effects are described by a state-space model that allows for arbitrary nonlinear lift characteristics. Wind tunnel tests for a fluttering beam in a broad range of flow speeds and preset angles of incidence were used to validate the electro-aeroelastic model. The matching of experimental and computational results reveals the importance of appropriately modeling structural and aerodynamic non-linearities for reproducing the physical electro-aeroelastic behavior of the system. These findings are of practical and theoretical relevance, and are further supported by the model’s complete inability to reproduce experimental results when either of the non-linearities are “switched off”.

Application of a new empirical model of nonlinear self-excited force to torsional vortex-induced vibration and nonlinear flutter of bluff bridge sections

Long-span bridges are susceptible to vortex-induced vibration (VIV) and flutter in different reduced wind range. Currently, VIV and flutter are considered as two different types of wind-induced vibration and different empirical models were proposed. The possibility of building a universal empirical model for both torsional VIV and nonlinear flutter was explored. In the previous study, a new empirical model was proposed for describing aerodynamic nonlinearities during soft flutter of a bluff bridge section with a medium side ratio. In this study, the empirical model was refined and extended to both torsional VIV and nonlinear flutter for a general bluff body, especially for a flat bridge deck, which is more common in long-span bridges. In the empirical model, aerodynamic nonlinear damping effect was modeled by a cubic velocity term and its applicability was validated by a series of elastically-mounted sectional model tests of a flat twin-side-girder bridge deck. The results indicated that the proposed empirical model was suitable for predicting the stable amplitude of torsional VIV and nonlinear flutter, although the motion-induced “pure force” varies with side ratios. It was found that torsional VIV and soft flutter share the same nonlinear damping mechanism during the development of LCO.

Robust Adaptive Control Barrier Functions: An Adaptive and Data-Driven Approach to Safety

A new framework is developed for control of constrained nonlinear systems with structured parametric uncertainty. Forward invariance of a safe set is achieved through online parameter adaptation and data-driven model estimation. The new adaptive data-driven safety paradigm is merged with a recent adaptive controller for systems nominally contracting in closed-loop. This unification is more general than other safety controllers as contraction does not require the system be invertible or in a particular form. The method is tested on the pitch dynamics of an aircraft with uncertain nonlinear aerodynamics.

Experimental analysis of aircraft directional control effectiveness

Aircraft directional control effectiveness is analyzed through experiments in wind tunnel. Control surfaces on low aspect ratio lifting surfaces exhibit different lifting capabilities compared to those with high aspect ratio. Such behavior must be carefully considered in the preliminary design phase to avoid any overestimation in size, weight, costs and emissions. Traditional sizing methodologies are based on coupling the effects of the wing planform (e.g. aspect ratio) at low angles of control surface deflection with the effects of wing section (e.g. chord ratio) evaluated on section data in the full range of control surface deflection, so that the non-linear aerodynamics is inherited from 2D data, completely neglecting the different aerodynamic behavior of a low aspect ratio wing at high angles of deflection. To fill this gap, an experimental wind tunnel test campaign on a generic regional turboprop aircraft model with a modular vertical tail with rudder has been performed. Results indicate that the aircraft design methodologies present in public literature underestimate the control surface effectiveness at high angle of deflections by 15% to 25%, leading to an average overestimation of control surface size.

Guidance Mechanism for Flexible-Wing Aircraft Using Measurement-Interfaced Machine-Learning Platform

The autonomous operation of flexible-wing aircraft poses theoretical and technical challenges not yet addressed in the literature. The lack of an exact modeling framework is due to the complex nonlinear aerodynamics driven by the deformations of the flexible-wings, which in turn complicates the controls and instrumentation setup of the navigation system. This urges for innovative approaches to interface affordable instrumentation platforms to autonomously control this type of aircraft. This article leverages the ideas from instrumentation and measurements, machine learning, and optimization fields in order to develop an autonomous navigation system for a flexible-wing aircraft. A novel machine-learning process based on a guiding search mechanism is developed to interface real-time measurements of wing-orientation dynamics into control decisions. This process is realized using an online value iteration algorithm based on two improved and interacting model-free control strategies in real time. The first strategy is concerned with achieving the tracking objectives, whereas the second supports the stability of the system. A neural network platform that employs adaptive critics is utilized to approximate the control strategies while approximating the assessments of their values. An experimental actuation system is utilized to test the validity of the proposed platform. The experimental results are shown to be aligned with the stability features of the proposed model-free adaptive learning approach.

Aerodynamic Nonlinearity of Piston Theory in Surface Vibration

AbstractPiston theory is widely used in modeling unsteady aerodynamic force caused by surface vibration. The nonlinearity of piston theory is determined by its high-order terms, which are significa...

Gust Response Computations with Control Surface Freeplay Using Random Input Describing Functions

An analytical and computational investigation of the effect of control surface freeplay on aeroelastic behavior, including random gust response and limit cycle oscillations (LCO), is presented. An efficient method to compute the total gust+LCO response is developed using random input describing functions (RIDF), in a manner analogous to harmonic input describing functions for LCO calculation. Results are obtained for an airfoil with trailing edge flap freeplay and linear potential flow aerodynamics at various gust strengths, freeplay sizes, and flow velocities. Both stable and unstable responses are detected. It is found that LCO coexists with gust response for weak gust/large freeplay combinations, and it is quenched for sufficiently strong gust/small freeplay. Time marching results are provided to validate the RIDF method and confirm the findings. The present work appears to be the first use of RIDF in aeroelasticity although it is well known to nonlinear control systems analysts. Notably the RIDF method in its present form is also applicable when steady flow aerodynamic nonlinearities are included.

Dynamic stability and performance analysis of a galloping-based piezoelectric energy harvester for different order representations of the aerodynamic force

In the present work, a non-linear electromechanical distributed parameter model is proposed for galloping based piezoelectric energy harvester (GPEH) and the impact of different order polynomial representation of aerodynamic force coefficient on the dynamic behavior of the system is investigated. Both geometric and aerodynamic nonlinearity (till9thorder polynomial) is introduced in the proposed model. The derived model is universally valid for both series and parallel connection of piezoelectric bimorph patches. The dynamic responses of the system, for different order representations of aerodynamic force, are extensively studied and then compared with experimental results from the literature. It is shown that a minimum till 7th order polynomial should be chosen for representing the galloping force coefficient in order to get a good agreement with experimental results. It is also shown from the model that the overall efficiency of the system is highest near the onset of galloping speed and decreases with an increase in wind speed. Further, a parametric study is done to find the effect of load resistance on the dynamic behavior of the system. It is seen that the error between experimental and predicted power decreases with an increase in the order of polynomial at a particular value of load resistance. The present analysis based on the proposed model emphasizes the importance of representation of aerodynamic force coefficients and geometric nonlinearity in predicting the accurate response for GPEH.

Nonlinear unsteady bridge aerodynamics: Reduced-order modeling based on deep LSTM networks

Rapid increase in the bridge spans and the attendant innovative bridge deck cross-sections have placed significant importance on effectively modeling of the nonlinear, unsteady bridge aerodynamics. To this end, the deep long short-term memory (LSTM) networks are utilized in this study to develop a reduced-order model of the wind-bridge interaction system, where the model inputs are bridge deck motions and model outputs are motion-induced aerodynamics forces. The deep LSTM networks are first trained using the high-fidelity input-output aerodynamics datasets (e.g., based on the full-order computational fluid dynamics simulations). With the trained LSTM networks, it has been demonstrated that the bridge motion-induced nonlinear unsteady aerodynamics forces can be accurately and efficiently predicted. Numerical examples involving both the linear and nonlinear aerodynamics are employed to explore the flutter and post-flutter behaviors of bridges with the reduced-order model based on deep LSTM networks.

Experimental investigation of wind-induced vibrations of main cables for suspension bridges in construction phases

The main cables of suspension bridges show a changing cross-sectional shape with the evolution of construction phases, and they may suffer from severe wind-induced vibrations at certain conditions. The primary objective of this research was to examine the aerodynamic performance of the main cable in construction phases and to develop appropriate countermeasures to eliminate the potential wind-induced vibrations. Two cross-sections with different shapes of a main cable were chosen, and a series of wind tunnel tests were performed in a reduced wind velocity range of 32–366 using elastically mounted sectional models. Galloping occurred for the two cross-sections under certain wind incidence angles when a critical velocity was reached. No obvious hysteresis phenomenon of galloping was observed in the tests. The steady amplitude of galloping increased linearly with wind velocity and the increasing rate almost kept constant for different structural damping ratios. The aerodynamic nonlinearity, rather than the structural damping nonlinearity, is the main source leading to the limited amplitude oscillation. An empirical expression of galloping amplitudes for the two cross-sections was derived based on the test data. Meanwhile, the critical wind velocity was studied in a Scruton (Sc) number range of 108–4196 (as varied by changing the initial structural damping ratio between 0.093% and 3.62%). Results showed that the Den Hartog criterion was applicable to forecast the possibility of galloping, but not able to estimate the critical wind velocity for the main cable. Linear fitting method can be used to predict the critical velocity based on the experimental data. Finally, three vibration mitigation measures were studied, and a combination of structural and aerodynamic measures was recommended for galloping mitigation of main cables.