Unsteady Aerodynamic Forces Research Articles

Gust Load Alleviation on a Large Transport Airplane

This study develops an active control technology to reduce the incremental dynamic loads of a large four-engine transport airplane flying through a gust field. The mathematical model of the proposed gust-alleviation system features composite structural motions (for example, rigid-body motions, elastic vibrations, and deflections of control surfaces) and unsteady aerodynamic forces induced by the structural motions and the gusts. A clear outline of the procedure is first provided to determine the aeroservoelastic equation of the system. Then, an adaptive feedforward controller that uses the preview information of the gust sensed by an onboard alpha probe is designed to operate the ailerons symmetrically to alleviate the wing-root bending moment induced by the gust. The rigid-body motions due to travelling gusts are also compensated for using symmetrical deflections of the elevators. To solve the problems of weight drift and weight bias that are commonly encountered in adaptive control, the circular leaky least mean-squared algorithm is applied to update the weights of the adaptive controller. The simulation results show that a large transport airplane equipped with the proposed gust-alleviation system experiences a significantly lower wing-root bending moment in both stationary and nonstationary gusty environments.

Estimation of unsteady aerodynamic forces using pointwise velocity data

A novel method to estimate unsteady aerodynamic force coefficients from pointwise velocity measurements is presented. As opposed to other existing methodologies, time-resolved full velocity fields are not required. The methodology is based on a resolvent-based reduced-order model which requires the mean flow to obtain physical flow structures and pointwise measurement to calibrate their amplitudes. A computationally affordable time-stepping methodology to obtain resolvent modes in non-trivial flow domains is introduced and compared with previous existing matrix-free and matrix-forming strategies. The technique is applied to the unsteady flow around an inclined square cylinder at low Reynolds number. The potential of the methodology is demonstrated through good agreement between the fluctuating pressure distribution on the cylinder and the temporal evolution of the unsteady lift and drag coefficients predicted by the model and those computed by direct numerical simulation.

Identification of Unsteady Aerodynamic Forces from Forced Motion Wind Tunnel Experiments

The Active Aeroelastic Test Bench is used for the study of low subsonic unsteady aerodynamics through forced motion experiments of rigid wings in pitch and plunge. The use of highly dynamic electric linear actuators allows for arbitrary motion in both the pitch and plunge degrees of freedom. In this paper, we discuss the forces measured on a constant section NACA 0018 wing subjected to isolated single and multisine motion in pitch or plunge. A data-driven approach is used, in which the importance of filtering and averaging of the noisy wind tunnel data is discussed. It is concluded from the forced motion experiments that a good agreement between the single and multisine experiments exists. However, only the pitch experiments agree with predictions from Theodorsen’s unsteady aerodynamics theory. The plunge experiments show the presence of major nonlinear contributions in the measured force response. Because of friction in the linear bearings of the setup, it cannot be excluded that these are generated by the plunging mechanism or the setup itself. Additionally, it is illustrated how the use of multisine signals for the identification of unsteady aerodynamic transfer function models allows for a reduction of wind tunnel test time by a factor of 10.

Experimental research on the aerodynamic characteristics of a high-speed train under different turbulence conditions

The aerodynamic characteristics of a high-speed train in an atmospheric boundary layer are investigated in a wind tunnel. In addition, different atmospheric boundary layer simulations are performed by changing the turbulence intensity generated by a collection of spires in a wind tunnel. Turbulent flow information, measured with the Cobra probe, is used to describe the atmospheric boundary layer. Furthermore, the effect of velocity on the atmospheric boundary layer is also studied. Both the train’s unsteady aerodynamic force and surface pressure are measured at a Reynolds number of 7.5×105, and their mean and standard deviation are used to describe and explain the effect of turbulence and observed trends with varying turbulence intensity.

The influence of the elastic vibration of the carrier to the aerodynamics of the external store in air-launch-to-orbit process

The separation between the carrier and store is one of the most important and difficult phases in Air-launch-to-orbit technology. Based on the previous researches, the interference aerodynamic forces of the store caused by the carrier are obvious in the earlier time during the separation. And the interference aerodynamics will be more complex when considering the elastic deformation of the carrier. Focusing on the conditions that in the earlier time during the separation, the steady and unsteady interference aerodynamic forces of the store are calculated at different angle of attacks and relative distances between the carrier and store. During the calculation, the elastic vibrations of the carrier are considered. According to the cause of formations of the interference aerodynamics, the interference aerodynamic forces of the store are divided into several components. The relative magnitude, change rule, sphere of influence and mechanism of interference aerodynamic forces components of the store are analyzed quantitatively. When the relative distance between the carrier and store is small, the interference aerodynamic forces caused by the elastic vibration of the carrier is about half of the total aerodynamic forces of the store. And as the relative distance increases, the value of interference aerodynamic forces decrease. When the relative distance is larger than twice the mean aerodynamic chord of the carrier, the values of interference aerodynamic forces of the store can be ignored. Besides, under the influence of the steady interference aerodynamic forces, the lift characteristics of the store are worse and the static stability margin is poorer.

Transonic limit cycle oscillation behavior of an aeroelastic airfoil with free-play

The limit cycle oscillation (LCO) behaviors of an aeroelastic airfoil with free-play for different Mach numbers are studied. Euler equations are adopted to obtain the unsteady aerodynamic forces. Aerodynamic and structural describing functions are employed to deal with aerodynamic and structural nonlinearities, respectively. Then the flutter speed and flutter frequency are obtained by V-g method. The LCO solutions for the aeroelastic airfoil obtained by using dynamically linear aerodynamics agree well with those obtained directly by using nonlinear aerodynamics. Subsequently, the dynamically linear aerodynamics is assumed, and results show that the LCOs behave variously in different Mach number ranges. A subcritical bifurcation, consisting of both stable and unstable branches, is firstly observed in subsonic and high subsonic regime. Then in a narrow Mach number range, the unstable LCOs with small amplitudes turn to be stable ones dominated by the single degree of freedom flutter. Meanwhile, these LCOs can persist down to very low flutter speeds. When the Mach number is increased further, the stable branch turns back to be unstable. To address the reason of the stability variation for different Mach numbers at small amplitude LCOs, we find that the Mach number freeze phenomenon provides a physics-based explanation and the phase reversal of the aerodynamic forces will trigger the single degree of freedom flutter in the narrow Mach number range between the low and high Mach numbers of the chimney region. The high Mach number can be predicted by the freeze Mach number, and the low one can be estimated by the Mach number at which the aerodynamic center of the airfoil lies near its elastic axis. Influence of angle of attack and viscous effects on the LCO behavior is also discussed.

Aerothermoelastic-Acoustics Simulation of Flight Vehicles

This paper describes a novel computational-fluid-dynamics-based numerical solution procedure for effective simulation of aerothermoacoustics problems with application to aerospace vehicles. A finite element idealization is employed for both fluid and structure domains, which fully accounts for thermal effects. The accuracies of both the fluid and structure capabilities are verified with flight- and ground-test data. A time integration of the structural equations of motion , with the governing flow equations, is conducted for the computation of the unsteady aerodynamic forces, which uses a transpiration boundary condition at the surface nodal points in lieu of the updating of the fluid mesh. Two example problems are presented herein to that effect. The first one relates to a cantilever wing with a NACA 0012 airfoil. The solution results demonstrate the effect of temperature loading that causes a significant increase in acoustic response. A second example, the hypersonic X-43 vehicle, is also analyzed; and relevant results are presented. The common finite element-based aerothermoelastic-acoustics simulation process, its applicability to the efficient and routine solution of complex practical problems, the employment of the effective transpiration boundary condition in the computational fluid dynamics solution, and the development and public domain distribution of an associated code are unique features of this paper.

Development of an Analytical Unsteady Model for Wind Turbine Aerodynamic Response to Linear Pitch Changes

A simple unsteady blade element analysis is used to account for the effect of the trailing wake on the induced velocity of a wind turbine rotor undergoing fast changes in pitch angle. At sufficiently high tip speed ratio, the equation describing the thrust of the element reduces to a first order, nonlinear Riccti's equation which is solved in a closed form for a ramp change in pitch followed by a constant pitch. Finite tip speed ratio results in a first order, nonlinear Abel's equation. The unsteady aerodynamic forces on the NREL VI wind turbine are analyzed at different pitch rates and tip speed ratio, and it is found that the overshoot in the forces increases as the tip speed ratio and/or the pitch angle increase. The analytical solution of the Riccati's equation and numerical solution of Abel's equation gave very similar results at high tip speed ratio but the solutions differ as the tip speed ratio reduces, partly because the Abel's equation was found to magnify the error of assuming linear lift at low tip speed ratio. The unsteady tangential induction factor is expressed in the form of first order differential equation with the time constant estimated using Jowkowsky's vortex model and it was found that it is negligible for large tip speed ratio operation.

Effect of vortex shedding in unsteady aerodynamic forces for a low Reynolds number stationary wing at low angle of attack

This study elucidates the relation between wake vortex shedding and aerodynamic force fluctuations for a low Reynolds number wing from time resolved particle image velocimetry (TR-PIV) experimental measurements. The results reveal a periodic lift and drag variation within the shedding cycle and resolve the frequencies of those fluctuations from a proper orthogonal decomposition (POD) and power spectral density (PSD) analysis. To show the effect of vortex shedding on the body force fluctuations, the evolution of instantaneous aerodynamic forces is compared to the pressure field of the fluid flow and to the vortical structures in the wake of the airfoil. A six step model describing the vortex-force relation is proposed. It shows that changes in lift such as maximum lift and minimum lift are associated with the detachment of a vortex. It also shows that the minimum or local minimum drag value is obtained at the onset formation of a vortex on the airfoil wake. Similarly, the maximum or local maximum drag is obtained at the onset formation of the saddle on the airfoil wake. The model further explains the asymmetry observed in the unsteady drag force evolution. The model can be used to optimize flow control and fluid-structure interaction applications.

지상 플러터 실험을 위한 시간 영역에서의 비정상 공기력 계산

지상 플러터 실험을 위한 시간 영역에서의 비정상 공기력 계산

Nonlinear aeroelastic modeling via conformal mapping and vortex method for a flat-plate airfoil in arbitrary motion

A nonlinear aerodynamic modeling based on conformal mapping is presented to obtain semi-analytical formulas for the unsteady aerodynamic force and pitching moment on a flat-plate airfoil in arbitrary motion. The aerodynamic model accounts for large amplitudes and non-planar wake and is used to study the aeroelastic behavior of a flat-plate airfoil elastically connected to a support. The fluid is assumed to be inviscid and incompressible, while the flow is assumed to be attached, planar, and potential. Within these hypotheses, conformal mapping and a complex-potential representation of unsteady aerodynamics are used to simplify the theoretical formulation. The vorticity shed at the trailing edge is discretized in desingularized point vortices in order to allow free-wake dynamics. The unsteady aerodynamic model is validated with classical linearized formulations based on the assumption of small disturbances, and with experimental data and theoretical predictions for a large-amplitude pitch-up, hold, pitch-down maneuver. The aeroelastic model is then used to simulate the response of a flat-plate airfoil to sudden starts and body–vortex interactions. Numerical results show that the proposed approach can be an effective tool to model the aeroelastic behavior of an arbitrarily-moving wing section in a time-dependent potential stream of incompressible fluid.

Limit cycle oscillation behavior of transonic control surface buzz considering free-play nonlinearity

The limit cycle oscillation (LCO) behaviors of control surface buzz in transonic flow are studied. Euler equations are employed to obtain the unsteady aerodynamic forces for Type B and Type C buzz analyses, and an all-movable control surface model, a wing/control surface model and a three-dimensional wing with a full-span control surface are adopted in the study. Aerodynamic and structural describing functions are used to deal with aerodynamic and structural nonlinearities, respectively. Then the buzz speed and buzz frequency are obtained by V-g method. The LCO behavior of the transonic control surface buzz system with linear structure exhibits subcritical or supercritical bifurcation at different Mach numbers. For nonlinear structural model with a free-play nonlinearity in the control surface deflection stiffness, the double LCO phenomenon is observed in certain range of flutter speed. The free-play nonlinearity changes the stability of LCOs at small amplitudes and turns the unstable LCO into a stable one. The LCO behavior is dominated by the aerodynamic nonlinearity for the case with large control surface oscillation amplitude but by the structural nonlinearity for the case with small amplitude. Good agreements between LCO behaviors obtained by the present method and available experimental data show that our study may help to explain the experimental observation in wind tunnel tests and to understand the physical mechanism of transonic control surface buzz.

Vibration-induced aerodynamic loads on large horizontal axis wind turbine blades

The blades of a large Horizontal Axis Wind Turbine (HAWT) are subjected to significant vibrations during operation. The vibrations affect the dynamic flow field around the blade and consequently alter the aerodynamic forces on the blade. In order to better understand the influence of blade vibrations on the aerodynamic loads, the dynamic stall characteristics of an S809 airfoil undergoing translational motion as well as pitching motion were investigated using Computational Fluid Dynamics (CFD) techniques. Simulation results indicated that both the out-of-plane and in-plane translational motions of the airfoil affect the unsteady aerodynamic forces significantly. In order to investigate the effects of blade vibration on the aerodynamic load on a large-scale HAWT blade during its operating lifetime, an aerodynamic model based on the Blade Element-Momentum (BEM) theory and the Beddoes–Leishman (B–L) dynamic stall model was proposed. The BEM model was revised to account for the vibration-induced velocity components in the calculation of the effective angle of attack. Aerodynamic load analysis of a 5MW wind turbine was then performed and the impact of blade vibration on the lifetime aerodynamic fatigue loads was analysed.

Application of Shunted Piezoelectric Materials in Aeroelasticity

This paper presents a numerical study on the influence of multimodal shunt circuit parameters in the flutter velocity of a typical section under an unsteady airflow. Flutter on typical sections is a kind of self-excited oscillation which can occur due to the interaction with the airflow. In the flutter point, when the critical dynamic pressure is reached, the vibrations of the typical section become unstable and increase fast and significantly in time. As a result, it can lead the structure to failure. Thus, it becomes important to investigate the possibility of reducing the effects of flutter in order to increase the reliability of composite structures during service. In this work, the aero-electromechanical dynamic model formulation is based on the Hamilton principle. The unsteady aerodynamic forces are calculated based on the linearized thin-airfoil theory, proposed by Theodorsen. The passive element responsible for the energy dissipation is a multimodal resonant shunt circuit in series topology, attached to a piezoelectric patch. An iterative solution algorithm is proposed to solve the resultant nonlinear eigenvalue problem. The optimum shunt tuning is firstly performed using Hagood and Flotow’s propositions; then, it is used an heuristic optimization algorithm, based on Differential Evolution. The preliminary results indicate that the flutter speed can be affected by the passive control, both in its mechanical aspect as electrical.

Dynamic Gust Load Analysis for Rotors

Dynamic load of helicopter rotors due to gust directly affects the structural stress and flight performance for helicopters. Based on a large deflection beam theory, an aeroelastic model for isolated helicopter rotors in the time domain is constructed. The dynamic response and structural load for a rotor under the impulse gust and slope-shape gust are calculated, respectively. First, a nonlinear Euler beam model with 36 degrees-of-freedoms per element is applied to depict the structural dynamics for an isolated rotor. The generalized dynamic wake model and Leishman-Beddoes dynamic stall model are applied to calculate the nonlinear unsteady aerodynamic forces on rotors. Then, we transformed the differential aeroelastic governing equation to an algebraic one. Hence, the widely used Newton-Raphson iteration algorithm is employed to simulate the dynamic gust load. An isolated helicopter rotor with four blades is studied to validate the structural model and the aeroelastic model. The modal frequencies based on the Euler beam model agree well with published ones by CAMRAD. The flap deflection due to impulse gust with the speed of 2m/s increases twice to the one without gust. In this numerical example, results indicate that the bending moment at the blade root is alleviated due to elastic effect.

多体气动弹性系统超声速颤振分析

The supersonic flutter of aeroelastic multibody systems was investigated. Based on the theory of multibody dynamics and the piston theory for unsteady aerodynamic forces, the governing differential algebraic equations (DAEs) for the aeroelastic multibody system were established. The supersonic flutter analysis was conducted through solution of the eigenvalue problem in the form of DAEs to discuss the stability of the perturbed motion and the equilibrium of the multibody system. The approach was used for the supersonic flutter problems of a plate wing and a wing with control surfaces. The flutter speed of the wing was obtained with the control surfaces in different positions. The agreement between the simulation results and the experimental ones shows that, the present method has high computational accuracy, and is suitable for the flutter analysis of engineering structures consisting of multiple components.

AERODYNAMIC MODELING OF OSCILLATING WING IN HYPERSONIC FLOW: A NUMERICAL STUDY

Various approximations to unsteady aerodynamics are examined for the unsteady aerodynamic force of a pitching thin double wedge airfoil in hypersonic flow. Results of piston theory, Van Dyke’s second-order theory, Newtonian impact theory, and CFD method are compared in the same motion and Mach number effects. The results indicate that, for this thin double wedge airfoil, Newtonian impact theory is not suitable for these Mach number, while piston theory and Van Dyke’s second-order theory are in good agreement with CFD method for Ma<7.

188 非定常空気力を受けるモーフィング翼のMBDシミュレーション

188 非定常空気力を受けるモーフィング翼のMBDシミュレーション

Vortex-Lift Mechanism in Axial Turbomachinery with Periodically Pitched Stators

Conventional aerodynamic theory of lift is based on the Kutta–Joukowski condition, in which the lift and drag coefficients are predicted based on the assumption that flow is attached and steady-state. Recent research on insect flight indicates, however, that the unsteady motion of a wing can generate much higher unsteady aerodynamic force through the flow induced by the shedding vortices. In the present work, therefore, we propose a novel type of stage consisting of rotor and periodically pitched stator to take advantage of unsteady vortex lift. The numerical results suggest that the flowfield around the leading and trailing edges of the blades are substantially modified by the interactions between the rotor and pitching stator. Several transient lift peaks can be generated for each period. If an appropriate pitching phase is chosen for the stator, stage performance can be improved through unsteady lift mechanism effects.

Empirical Modeling of Pressure Spectra in Adverse Pressure Gradient Turbulent Boundary Layers

This study investigated the unsteady aerodynamic forcing that occurs near the trailing edge of airfoils with chordwise Reynolds numbers between 2 and 6 million. Static pressure, unsteady surface pressure, and velocity measurements were made throughout the trailing-edge region of an airfoil model with three interchangeable, symmetric trailing-edge sections. The data of the present study were used to develop a new model for estimation of fluctuating surface pressure autospectra beneath two-dimensional turbulent boundary layer flow experiencing an adverse pressure gradient of variable strength. This new model has been used to compare with data from six separate experimental investigations from literature, and has been compared against a separately developed empirical model of the fluctuating surface pressure. Additional empirical modeling of the coherent extents of the fluctuating pressure field in the longitudinal and lateral directions, as well as the convection velocity, is presented as a function of nondimensional variables dependent on the adverse pressure gradient flow condition.