Unsteady Aerodynamic Loads Research Articles

Reduced-Order-Model-Based Flutter Analysis at High Angle of Attack

C ONFIGURATIONS with a highly flexible delta wing are considered for the next generation of unmanned air vehicles (UAV). Delta wing flowfield is dominated by vortical structures at high angle of attack, the most prominent is called leading-edge vortex. Ye and Zhao [1] used a nonlinear lifting line method to compute the aerodynamic loads of the delta wing at high angle of attack. With the development of computer technology, computational fluid dynamics (CFD) technique has been used in the simulation of delta wing-induced vortical flow. The study [2] shows that the Reynolds number affects primary vortex slightly, and so Euler codes can be employed to simulate the vortex and aerodynamic loads; the shortness is that it cannot simulate the secondary vortex caused by the effect of viscosity. The CFD and computational structural dynamics (CSD) direct coupling method has been used in aeroelastic analysis of deltawing.Gordnier et al. [3,4] coupled Euler/ Navier–Stokes codes and nonlinear plant element to study the buffet problem of the flexible delta wing at high angle of attack. The CFD and CSD direct coupling method [5–7] has also been used in the nonlinear flutter simulation of delta wing at small angle of attack (<5 deg). The limitation of the direct aeroelastic simulation method is the high cost of the computational time. To solve the contradiction between computational efficiency and computational quality, many researchers turn to CFD-based unsteady aerodynamic reduced-order modeling (ROM) to improve the aeroelastic computational efficiency in the last decade. Dowell and Hall [8], Lucia et al. [9], and Zhang and Ye [10] present some overviews of ROM and its applications on nonlinear aeroelastic research. There are two kinds of methods for ROMof unsteady aerodynamic loads at the present time. The one is the proper orthogonal decomposition (POD) based reduced-order modeling method, the other is aerodynamic modeling based on structural modes by using identification technology. The second method is used in this work. Zhang [11] compared the efficiency between the ROM-based method and the CFD direct simulation method. Efficiency can be improved by 1 2 orders with accuracy still retained by ROM-based method. Zhang used CFDbased ROM to perform aeroservoelastic analysis [12] and transonic flutter suppression by active control [13].

Vehicle dynamics of a high-speed passenger car due to aerodynamics inside tunnels

High train speeds inside narrow double-track tunnels using light car bodies can reduce the ride comfort of trains as a consequence of the unsteadiness of the aerodynamics. This fact was substantiated in Japan with the introduction of the series 300 Shinkansen trains more than a decade ago, where the train speed is very high also in relatively narrow tunnels on the Sanyo line. The current work considers the resulting effects of vehicle dynamics and ride comfort with multi-body dynamics using a model of the end car of the German high-speed train ICE 2. The present efforts are different from traditional vehicle dynamic studies, where disturbances are introduced through the track only. Here disturbances are also applied to the car body, which conventional suspension systems are not designed to cope with. Vehicle dynamic implications of unsteady aerodynamic loads from a previous study are examined. These loads were obtained with large eddy simulations based on the geometry of the ICE 2 and Shinkansen 300 trains. A sensitivity study of some relevant vehicle parameters is carried out with frequency response analysis (FRA) and time domain simulations. A comparison of these two approaches shows that results which are obtained with the much swifter FRA technique are accurate also for sizable unsteady aerodynamic loads. FRA is, therefore, shown to be a useful tool to predict ride comfort in the current context. The car body mass is found to be a key parameter for car body vibrations, where loads are applied directly to the car body. For the current vehicle model, a mass reduction of the car body is predicted to be most momentous in the vicinity of 2 Hz.

Active Flutter Suppression by Feedback Compensation of Transport Logs

A IRCRAFT wings are deigned to be flexible, and as a consequence of this feature they are known to be continuously oscillating under the action of wind loads leading to the well-known phenomenon of “flutter.” Flutter in wings was conventionally inhibited by passive design techniques based on altering the mass and stiffness distributions of the wing. However, the recent trend in building highly flexible aircraft has demonstrated the inadequacy of passive techniques for inhibiting the occurrence of flutter. To overcome the inadequacy of passive techniques in inhibiting the occurrence of flutter within the design envelope of the aircraft, a new technique, based on feedback control, was developed in the early 1970s, called “active flutter suppression.” Two distinct approaches emerged for the design of the control law for activeflutter suppression, the first based on optimal control, and the second approach [1], emerging from the concept of passivity, considers the energy flowing in and out of the “system.” There are several applications of this method to real aircraft, and [2] is archetypal of these examples. References [3,4] are typical examples in which the techniques based on the modeling methods were applied to the synthesis of optimal and near-optimal control laws for active flutter suppression. In this paper we propose a third approach towards controlling flutter. By careful consideration of the unsteady aerodynamic loading, those components that contribute to the delay in the growth of the loading in response to changes in the wingmotion are isolated. These delays or transport lags are then eliminated by an appropriate control law that ensures the constancy of circulatory component of the unsteady lift. With secondary compensation one could increase the flutter speed, which is the primary objective of active flutter suppression. Furthermore, the constancy of the circulatory component implies that the flow is less likely to separate and the circulation is more likely to remain steady. To evaluate the method we consider the archetypal problem of the typical section and implement such a control law. Themotivation for this work arose from the need to develop smart, flexibly actuated morphing control surfaces for future aircraft wings in low-speed flight. The method described in this paper can be routinely implemented with control surfaces. Morphing control surfaces can be deflected in a multitude of modes and the method itself is based on observations of bird flight.

Development of an indicial function approach for the two-dimensional incompressible/compressible aerodynamic load modelling

By using a combined analytical-computational methodology, a unified modelling of aerodynamic indicial functions covering the incompressible, subsonic compressible, transonic, and supersonic flight speed regimes is presented. The procedure is carried out in conjunction with a computational fluid dynamic analysis. For a plunging-pitching airfoil, selected unsteady aerodynamic load expressions have been supplied, and appropriate procedures enabling one to obtain these loads via the indicial function approach have been presented. While a single indicial function is needed to describe the aerodynamic loads in the incompressible flight speed regime, for cases where the compressibility effects play a dominant role, four indicial functions are needed. Having in view the usefulness of indicial functions towards determination of unsteady aerodynamics loads in both time and frequency domains, and implicitly for aeroelastic response and flutter predictions, the advantages of their implementation and use appear evident. Comparisons and validations of the aerodynamic model against numerical, analytical, and experimental results are presented, and pertinent conclusions are drawn.

Effect of Flap Motion on Unsteady Aerodynamic Loads

Effect of Flap Motion on Unsteady Aerodynamic Loads

On unsteady aerodynamic airfoil loads in the design of a control system for minimizing the effect of wind perturbations using the rudder on the trailing edge of the wing

The problem of minimizing wind perturbations using the control on the trailing edge of the airfoil is considered for an airfoil passing through a short wind gust. It is considered that the airfoil movement is bounded by two degrees of freedom, viz. in pitch and height, and each channel has an elastic spring that simulates torsional and bending stiffness of the wing. The study is held on the basis of the developed mathematical model for unsteady aerodynamic loads (the lift coefficient and the pitching moment) when a thin two-dimensional airfoil is flowed without separation by a flow of ideal incompressible fluid. The results obtained using this mathematical model and the conventional quasi-steady model on the basis of aerodynamic derivatives are compared. It is shown that the stability properties for the quasi-steady and unsteady aerodynamics models differ in a wide range of parameters of the airfoil movement considered. Moreover, taking into account the unsteadiness of aerodynamics when designing a control system allows us to suppress the wind perturbations more efficiently and counts when determining the requirements on the actuator rates necessary to suppress wind gusts of high amplitude.

ACTIVE AEROELASTIC CONTROL OF LIFTING SURFACES VIA JET REACTION LIMITER CONTROL

In this paper we present, the design and modeling of the novel nonlinear limiter control feedback control plant [Myneni et al., 1999; Corron et al., 2000; Corron &amp; Pethel, 2002], applied for the first time here in an aeroelastic system, and actuated as a jet reaction torquer control of a wing with potentially chaotic dynamics. This study will provide a better understanding of the nonlinear dynamics of the open/closed-loop aeroelasticity of flexible wings with either steady or unsteady aerodynamic loads. The limiter control can be applied to either the plunging or pitching characteristic of the wing or to both of them. We show that the control can effectively suppress Limit Cycle Oscillations (LCO) and chaos well beyond the nominal flutter speed. This could lead to a practical implementation of the control mechanism on actual and future generation aircraft wings via implementation of a combination of propulsive/jet type forces, micro surface effectors and fluidic devices. Analysis of this control produced favorable results in the suppression of LCO amplitude and increased flutter boundaries for plunging and pitching motion. The limiting control has asymptotically zero power, and is simply implemented, making it a feasible solution to the problem of the chaotic dynamics of the oscillating airfoil.

Structural health monitoring based on sensitivity vector fields and attractor morphing

The dynamic responses of a thermo-shielding panel forced by unsteady aerodynamic loads and a classical Duffing oscillator are investigated to detect structural damage. A nonlinear aeroelastic model is obtained for the panel by using third-order piston theory to model the unsteady supersonic flow, which interacts with the panel. To identify damage, we analyse the morphology (deformation and movement) of the attractor of the dynamics of the aeroelastic system and the Duffing oscillator. Damages of various locations, extents and levels are shown to be revealed by the attractor-based analysis. For the panel, the type of damage considered is a local reduction in the bending stiffness. For the Duffing oscillator, variations in the linear and nonlinear stiffnesses and damping are considered as damage. Present studies of such problems are based on linear theories. In contrast, the presented approach using nonlinear dynamics has the potential of enhancing accuracy and sensitivity of detection.

Aerodynamic Loads on Airfoil with Trailing-Edge Flap Pitching with Different Frequencies

Unsteady aerodynamic loads on NACA 0012 airfoil with a trailing-edge flap were measured in wind tunnel and calculated from a simple theoretical model. The airfoil model of 0.18 m chord length used in wind-tunnel test was oscillating in pitch about an axis located at 35% chord length from the airfoil leading edge. The length of trailingedge flap was 22.6% of airfoil chord. The flap was also deflecting harmonically, but with frequency different from airfoil pitching motion. The influence of phase delay between airfoil angle of incidence and flap deflection at the beginning of the motion was considered. The theoretical method used for calculation of unsteady airfoil loads is based on two-dimensional, inviscid, incompressible flow model at subsonic Mach numbers. The expressions for unsteady aerodynamic loads calculations on the airfoil and on the flap were obtained in a closed form using distribution of flow velocity potential along the airfoil chord and along the flap length. Lift and aerodynamic moment measured in the wind tunnel were compared with results of calculations. The correlation between experimental and theoretical results is adequate.

Stochastic analysis of two dimensional nonlinear panels with structural damping under random excitation

Stochastic behavior of panels in supersonic flow is investigated to assess the significance of including the damping caused by the strains resulting from axial extension of the panel. The governing equations of motion are based on the Von Karman's large deflection equation and are considered with Kelvin's model of structural damping. The panel under study is two dimensional and simply supported for which the first order piston theory is used to account for the unsteady aerodynamic loading. Transformation of the governing partial differential equation to a set of ordinary differential equations is performed through the Galerkin averaging technique. The statistical response moment equations are generated for two modes using the Fokker–Planck equation with a Gaussian closure scheme. The response moments history and their steady state values are considered. Comparison with previous studies shows that the new nonlinear damping term developed through modeling has a significant effect on the response moments. This is verified through analysis of the effects of external pressure and in-plane force spectral density, air-to-structure mass ratio and structural damping ratio on the mean square value of modal amplitudes.

Minimum-State Unsteady Aerodynamics for Aeroservoelastic Configuration Shape Optimization of Flight Vehicles

The Minimum State technique for creating linear time invariant state space models of unsteady aerodynamic loads leads to major savings in terms of the dimension of the resulting aeroservoelastic systems compared to alternative techniques. The upfront effort of the generation of minimum state approximants, however, is large, and involves an iterative double least squares function fitting process. When the overall shape of a configuration varies, during the repetitive analysis required for configuration design optimization, the cost of creating new minimum state approximations becomes prohibitive. This paper presents an efficient method for obtaining shape sensitivity analysis of minimum state approximants. The resulting sensitivities are then used, based on a single detailed analysis and sensitivity analysis at some reference design to generate approximate aeroelastic poles, divergence speed, and flutter speed results for configurations that are subject to considerable planform shape changes.

Calculation of the transonic dip of airfoils using viscous-inviscid aerodynamic interaction method

A numerical procedure for the calculation of the transonic dip of airfoils in the time domain is presented. A viscous-inviscid aerodynamic interaction method is taken to calculate the unsteady aerodynamic loads. In the present case the integral boundary layer equations are coupled with the Transonic Small Disturbance (TSD) Potential Equation. The coupling between structural motion and aerodynamic loads is carried out using State Space equation. It is solved by State Transition Matrix technique. Results are presented for NACA 64A010 and NLR 7301 airfoils with structural data from Isogai and DLR, respectively. Comparisons show good agreement with other numerical results. Certain deviations of experimental data taken from literature need more insight in the detailed test conditions.

Structural Modeling and Aeroelastic Analysis of High-Aspect-Ratio Composite Wings

A unified structural model for high-aspect-ratio composite wing with arbitrary cross-section is developed. Two types of lay-ups of the composite wing, namely, circumferentially uniform stiffness (CUS) configuration and circumferentially asymmetric stiffness (CAS) configuration, are investigated. The present structural modeling method is validated through ANSYS FEM software for the case of a composite box beam. Then, the case of a single-cell composite wing with NACA0012 airfoil shape is considered. To investigate the aeroelastic problem of high-aspect-ratio composite wings, the linear ONERA aerodynamic model is used to model the unsteady aerodynamic loads under the case of small angle of attack. Finally, flutter speeds of the high-aspect-ratio wing with various composite ply angles are determined by using U-g method.

Study on Unsteady Flow around a HAWT Rotor by Panel Method (Calculation of Yawed Inflow Effects and Evaluation of Angle of Attack in the Three-Dimensional Flow Field)

The precise prediction of the performance of a wind turbine largely depends on the accurate knowledge of the flow around the rotor as it is subject to the induced velocity caused by the spiral vortex wake and the unsteady aerodynamic loads caused by the rapid change of wind direction. In this paper the flow around a horizontal axis wind turbine (HAWT) rotor in a yawed flow condition is analyzed by a panel method with a free wake model and the cyclic fluctuations of the aerodynamic load due to the asymmetric inflow condition are obtained. To include the viscous effects in the calculated results, the local angle of attack is investigated and is found to be defined well by the angle of incidence at a quarter chord point in the non-yawed condition. In the yawed condition the effects of highly skewed vortex wake on angle of attack are also discussed.

Influence of Shock Wave on Turbomachinery Blade Row Flutter

The influence and effect of a shock wave on the flutter characteristics of a turbomachinery blade row is described. High-fidelity numerical analysis is used to understand the behavior of turbomachinery blade row flutter in the presence of an oscillating shock wave. The unsteady Navier-Stokes equations are solved on a dynamically deforming, body-fitted grid to obtain the unsteady aerodynamic load on a vibrating blade. An energy exchange method is used for calculating the aerodynamic damping to determine the blade row flutter characteristics. A transonic forward swept fan configuration, which showed flutter at part speed conditions in wind-tunnel tests, is analyzed. The shock wave was found to influence strongly the aerodynamic damping, with outboard stations providing the main contribution. The interblade phase angle of blade motion and the location of shock wave determined the influence of shock wave on blade stability. The influence of shock motion was found to be linear for a small amplitude of blade oscillation. The observations from the numerical analysis are used to develop an algebraic model for calculating the work done on the blade because of an oscillating shock wave.

Aerodynamic Interference of a Large and a Small Aircraft.

The influence of wake from a leading aircraft, Boeing 757, on a following aircraft, Cessna 750 Citation X, is investigated using the unsteady vortex lattice method. The effect of the wakes from both wings and each other is considered and the new position of the wakes from both aircraft calculated. As the midspan of the Cessna wing approaches the Boeing 757 trailing vortex core, the roll moment increases to its maximum value. Strong changes appear in aerodynamic loads of the Cessna as it moves near the Boeing 757’s wake. Rapid change occurs as the Cessna moves in transverse or vertical directions near the Boeing’s wake. The unsteady aerodynamic loads on wings moving along different paths are calculated. The Boeing 757’s wake strongly affects the aerodynamic loads and the wake of the Cessna. Also included in the present results are numerical simulations of wakes and velocity vectors in the Trefftz plane detailing the influence of the wake from the leading aircraft, the Boeing 757.

Studies of Store-Induced Limit-Cycle Oscillations Using a Model with Full System Nonlinearities

The authors investigate limit-cycle oscillations of a wing/store configuration. Unlike typical aeroelastic studies that are based upon a linearized form of the governing equations, herein full system nonlinearities are retained, and include transonic flow effects, coupled responses from the structure, and store-related kinematics and dynamics. Unsteady aerodynamic loads are modeled with the equations from transonic small disturbance theory. The structural dynamics for the cantilevered wing are modeled by the nonlinear equations of motion for a beam. The effects of general store-placement are modeled by the nonlinear equations of motion related to the position-induced nonlinear kinematics. Chordwise deformations of the wing surface, as well as pylon and store flexibility, are assumed negligible. Nonlinear responses are studied by examining bifurcation and related response characteristics using direct simulation. Particular attention is given to cases for which large-time, time-dependent behavior is dependent on initial conditions, as observed for some configurations in flight test. Comparisons of results in which selective nonlinearities are excluded indicate that the accurate prediction of nonlinear responses such as limit cycle oscillations (LCOs) may depend upon consideration of all nonlinearities related to the full system.

Flex Circuit Sensor Array for Surface Unsteady Pressure Measurements

Introduction T HE acquisition of high-fidelity, high-frequency response surface pressure measurements are of interest to experimentalists in gas-turbine aeromechanical research because these data provide a means to measure indirectly the unsteady aerodynamic loading acting on an airfoil. Airfoils are typically (traditionally) instrumented from commercially available miniature pressure transducers that are flush mounted to the airfoil to prevent the transducer from aerodynamically disturbing the flow. Cavities are machined into the airfoil to accommodate the transducers, and trenches are machined to route the lead wires away from the transducer.1−5 The main difficulty in the use of traditional transducers for high spatial resolution comes from the congestion and interference caused by the cavities and trenches required for each sensor location and the number of locations desired. A high spatial resolution array of high-frequency pressure transducers was designed and fabricated that eliminates most of the difficulty associated with having a large concentration of transducers in a given area. Two pressure sensor arrays were applied to the suction and pressure surfaces of two inlet guide vanes (IGVs) of a transonic research compressor to measure the unsteady loading distribution induced by the passage of the bow shocks and the potential field emanating from the downstream rotor.

Numerical model for the simulation of fixed wings aeroelastic response

A numerical model for the simulation of fixed wings aeroelastic response is presented. The methodology used in the work is to treat the aerodynamics and the structural dynamics separately and then couple them in the equations of motion. The dynamic characterization of the wing structure is done by the finite element method and the equations of motion are written in modal coordinates. The unsteady aerodynamic loads are predicted using the vortex lattice method. The exchange of information between the aerodynamic and structural meshes is done by the surface splines interpolation scheme, and the equations of motion are solved iteratively in the time domain, employing a predictor-corrector method. Numerical simulations are performed for a prototype aircraft wing. The aeroelastic response is represented by time histories of the modal coordinates for different airspeeds, and the flutter occurrence is verified when the time histories diverge (i.e. the amplitudes keep growing). Fast Fourier Transforms of these time histories show the coupling of frequencies typical of the flutter phenomenon.

Unsteady Aerodynamic Loading on a Helicopter Fuselage in a Ship Airwake

Unsteady Aerodynamic Loading on a Helicopter Fuselage in a Ship Airwake