Unsteady Aerodynamic Model Research Articles

Unsteady aerodynamic modeling at high angles of attack using support vector machines

Accurate aerodynamic models are the basis of flight simulation and control law design. Mathematically modeling unsteady aerodynamics at high angles of attack bears great difficulties in model structure determination and parameter estimation due to little understanding of the flow mechanism. Support vector machines (SVMs) based on statistical learning theory provide a novel tool for nonlinear system modeling. The work presented here examines the feasibility of applying SVMs to high angle-of-attack unsteady aerodynamic modeling field. Mainly, after a review of SVMs, several issues associated with unsteady aerodynamic modeling by use of SVMs are discussed in detail, such as selection of input variables, selection of output variables and determination of SVM parameters. The least squares SVM (LS-SVM) models are set up from certain dynamic wind tunnel test data of a delta wing and an aircraft configuration, and then used to predict the aerodynamic responses in other tests. The predictions are in good agreement with the test data, which indicates the satisfying learning and generalization performance of LS-SVMs.

Nonlinear Aeroelastic Analysis of Control Surface with Freeplay Using Computational-Fluid-Dynamics-Based Reduced-Order Models

A computational-fluid-dynamics-based aeroelastic analysis method is proposed to simulate control-surface limit-cycle oscillation (LCO) induced by freeplay gap. The present method is based on the previously proposed aeroelastic reduced-order model (ROM), in which an unsteady aerodynamic state-space model is generated from aerodynamic responses to step excitation of individual mode using the eigensystem realization algorithm, and connected to a structural dynamic state-space model within the MATLAB/SIMULINK environment. The aeroelastic ROM is extended to treat structural nonlinearity due to the control-surface freeplay by generating an additional feedback line of generalized residual forces in the SIMULINK model. To reduce the problem size and the computation time, a fictitious-mass modal approach is used, which can afford the possible local change of stiffness. The present method is first validated for its capability to simulate aeroelastic responses of a regional-jet horizontal-tail (HT) model without freeplay, and shows good prediction of flutter characteristics measured in the transonic flutter wind-tunnel testing. The present method is then applied to the HT model with the elevator freeplay gaps. Although there are some differences between the computed and measured limit-cycle-oscillation ranges, the present method well predicts the nonlinear limit-cycle-oscillation behavior in its amplitude and frequency measured in the test, and shows promise toward accurate prediction of control-surface LCO due to its freeplay gap.

Unsteady Vibration Aerodynamic Modeling and Evaluation of Dynamic Derivatives Using Computational Fluid Dynamics

Unsteady aerodynamic system modeling is widely used to solve the dynamic stability problems encountering aircraft design. In this paper, single degree-of-freedom (SDF) vibration model and forced simple harmonic motion (SHM) model for dynamic derivative prediction are developed on the basis of modified Etkin model. In the light of the characteristics of SDF time domain solution, the free vibration identification methods for dynamic stability parameters are extended and applied to the time domain numerical simulation of blunted cone calibration model examples. The dynamic stability parameters by numerical identification are no more than 0.15% deviated from those by experimental simulation, confirming the correctness of SDF vibration model. The acceleration derivatives, rotary derivatives, and combination derivatives of Army-Navy Spinner Rocket are numerically identified by using unsteady N-S equation and solving different SHV patterns. Comparison with the experimental result of Army Ballistic Research Laboratories confirmed the correctness of the SHV model and dynamic derivative identification. The calculation result of forced SHM is better than that by the slender body theory of engineering approximation. SDF vibration model and SHM model for dynamic stability parameters provide a solution to the dynamic stability problem encountering aircraft design.

Review of Research Progresses in Unsteady Aerodynamic Model

Based on the analysis of the flight stability, the research progress of the unsteady aerodynamic model was comprehensively introduced. Bryan, first of all, the aerodynamic load of traditional dynamic derivative model is put forward, still used today in some engineering issues. However, Bryan state parameters of the model is not complete, not exactly reflect the unsteady aerodynamic force time history effect and nonlinear effect. Etkin models, by retaining the item of high order Taylor expansion, including the influence of nonlinear effect. Improved Etkin model can explain the actual flight of some of the common transient response, including due to stall the mutation and aerodynamic force/torque caused by unsteady flow dynamic bifurcation and chaos of the aerodynamic force/torque value and uncertain phenomenon. Finally, the unsteady flow field of a reduced order model development trends and application prospect were analyzed, and pointing out that the CFD simulation is still accurately predict the plane stability and handling the most important method.

Aeroservoelastic Pitch Control of Stall-Induced Flap/Lag Flutter of Wind Turbine Blade Section

The aim of this paper is to analyze aeroelastic stability, especially flutter suppression for aeroelastic instability. Effects of aeroservoelastic pitch control for flutter suppression on wind turbine blade section subjected to combined flap and lag motions are rarely studied. The work is dedicated to solving destructive flapwise and edgewise instability of stall-induced flutter of wind turbine blade by aeroservoelastic pitch control. The aeroelastic governing equations combine a flap/lag structural model and an unsteady nonlinear aerodynamic model. The nonlinear resulting equations are linearized by small perturbation about the equilibrium point. The instability characteristics of stall-induced flap/lag flutter are investigated. Pitch actuator is described by a second-order model. The aeroservoelastic control is analyzed by three types of optimal PID controllers, two types of fuzzy PID controllers, and neural network PID controllers. The fuzzy controllers are developed based on Sugeno model and intuition method with good results achieved. A single neuron PID control strategy with improved Hebb learning algorithm and a radial basic function neural network PID algorithm are applied and performed well in the range of extreme wind speeds.

Modeling of Unsteady Aerodynamics for a Flapping wing

Insect-like flapping flight offers a power-efficient and highly manoeuvrable basis for a micro air vehicle. In this paper, investigation was made into the aerodynamic analysis of a flapping wing applicable to micro aerial vehicles. First, the three dimensional aerodynamic calculation and flow field simulation of a flapping wing were studied. Then, the generation of reduced order models for computing the unsteady and nonlinear aerodynamic loads on the flapping wing from flapping motions is described. The models considered are based on Volterra theory using nonlinear kernels. One of the biggest challenges in creating these reduced order modeling techniques is accurate identification of the Volterra kernels. The validity of models studied was assessed by comparison of the model outputs with unsteady CFD result. It was proved that the percent error between CFD and reduced order model is 8.55.

POD approach for unsteady aerodynamic model updating

A method for aerodynamic model updating is proposed in this paper. The approach is based upon a correction of the eigenvalues of the reduced-order unsteady aerodynamic matrix through an optimization with objective function defined through the difference in the generalized aerodynamic forces or on the aeroelastic poles. The high-fidelity model in reduced-order form is obtained by the proper orthogonal decomposition (POD) technique applied to the computational fluid dynamics Euler-based formulation. Many of the methods that have been developed in the past years for simpler aeroelastic models that use, for example, doublet-lattice method aerodynamics, can be adopted for this purpose as well. However, this model is not able to capture shocks and flow separation in transonic flow. The proposed approach performs the updating of the aerodynamic model by imposing the minimization of a global error between target aerodynamic performances, namely experimental performances, and an aerodynamic model in reduced-order form via POD approach. After a general presentation of the application of the POD method to the linearized Euler equations, the optimization strategy is presented. First, a simple test on a 2D wing section with theoretical biased data is performed, and then, the performances of different optimization strategies are tested on a 3D model updated by wind tunnel data.

Reduced-Order Modeling of Unsteady Aerodynamics Across Multiple Mach Regimes

A reduced-order model for unsteady aerodynamic calculations across a range of Mach regimes based on linear convolution and a nonlinear correction factor is developed. Separate investigations are conducted for the sub-, trans-, and supersonic Mach regimes, and overall good results are seen when reduced-order model results are compared with full-order computational-fluid-dynamics solutions, though the reduced-order model errors tend to decrease as the Mach number increases. To assist reduced-order model construction, the method-of-segments simplified model has been created and tested throughout these same Mach regimes. Finally, a practical example of the reduced-order model’s applicability is presented by following a single test case from subsonic up through supersonic flight.

Dynamics Characterization of Missiles with Control Flaps Based on CFD

Numerical studies were carried out on the dynamics of the Basic Finner missile under supersonic velocity based on the three-dimensional unsteady N-S equation. Second-order upwind NND scheme finite volume was used to discretize the spatial derivative term of the flow-controlled equation group. The LU-SGS containing dual time steps was used to obtain higher efficiency and precision of time solution. A numerical model representing the relationship between the unsteady aerodynamic force/moment coefficients and state variables under single DOF (degree of freedom) pitching and rolling movements was built from the Etkin unsteady aerodynamic model. The numerical algorithm for solving damping-in-pitch derivatives and damping-in-roll derivatives by forced-harmonic analysis was proposed. The M910 target practice, discarding sabot with tracer (TPDS-T) was used as a validation example and proved that the numerical calculation gives the same result as the experiment. By simulating the forced pitching and rolling vibration of Basic Finner, the numerical identification succeeded in obtaining the damping-in-pitch derivative and damping-in-roll derivative to a higher precision than the calculated result obtained by the quasi-steady Euler equation. Besides, to address the longitudinal and horizontal cross coupling induced by the pitching movement, numerical identification was also carried out on the cross coupling derivative of Basic Finner when under forced pitching vibration.

Research on Numerical Simulation of Support Interference for Dynamic Derivatives at Hypersonic Flight Speeds

The research on dynamic derivative under the dynamic unsteady condition is one of the most difficult aspects of the aircraft development process. For the special experiment of dynamic derivatives, no numerical simulation of support interference has yet been systematically studied. The numerical simulation of support interference for identification of dynamic derivatives with 7o blunted cone under the hypersonic condition was done in this paper. The 2-order Roe scheme and the dual-time-step method based on LU-SGS were respectively applied to discrete of the spatial and time derivative of the unsteady flow. A least square method based on the Etkin unsteady aerodynamic model was used for identification of dynamic derivatives. Hypersonic missile module was adopted as a verification example, and the numerical calculation results are consistent with the experimental results. For two different sting support forms with 7o blunted cone, the impact of sting support interference on dynamic derivatives was studied. Results show the moment coefficients of two support forms under static conditions are essentially the same, while there is a big difference in the pitch damping derivatives under dynamic conditions. The support interference of nonlinear aerodynamic loads resulted from the shock wave induced separation and other unsteady flow structures under dynamic conditions is far more complicated than that under static conditions, and the correction law of support interference under static conditions cannot be applied directly to the unsteady dynamic situations.

State-space model identification and feedback control of unsteady aerodynamic forces

Unsteady aerodynamic models are necessary to accurately simulate forces and develop feedback controllers for wings in agile motion; however, these models are often high dimensional or incompatible with modern control techniques. Recently, reduced-order unsteady aerodynamic models have been developed for a pitching and plunging airfoil by linearizing the discretized Navier–Stokes equation with lift-force output. In this work, we extend these reduced-order models to include multiple inputs (pitch, plunge, and surge) and explicit parameterization by the pitch-axis location, inspired by Theodorsen׳s model. Next, we investigate the naïve application of system identification techniques to input–output data and the resulting pitfalls, such as unstable or inaccurate models. Finally, robust feedback controllers are constructed based on these low-dimensional state-space models for simulations of a rigid flat plate at Reynolds number 100. Various controllers are implemented for models linearized at base angles of attack α0=0°,α0=10°, and α0=20°. The resulting control laws are able to track an aggressive reference lift trajectory while attenuating sensor noise and compensating for strong nonlinearities.

Wave propagation in beams with periodic arrays of airfoil-shaped resonating units

This paper presents an analytical and numerical study on the dispersion properties of an Euler–Bernoulli beam immersed in a steady fluid flow with periodic arrays of airfoil-shaped vibration absorbers attached to it. The resonance characteristics of the airfoils generate strong attenuation of flexural waves in the beam occurring at frequencies defined by the properties of the airfoils and the speed of the incident fluid. Analytical and numerical tools are developed to investigate the effects of the incident flow on the dispersion properties and the bandgaps of the system. Both steady and unsteady aerodynamic models are used to model the lift force and the pitching moment acting on the resonators and their effect on the dispersion relations of the system is evaluated. Finally, an effective medium description of the beam is developed to capture its behavior at long-wavelengths. In this regime, the system can be effectively considered as an acoustic metamaterial with adaptive dispersion properties.

Unsteady Aerodynamic Modeling of Aircraft Control Surfaces by Indicial Response Methods

This study is part of a larger effort to create reduced-order models for aerodynamic forces and moments acting on a maneuvering aircraft with moving control surfaces. The aircraft used in this study was inspired by the T-38 jet trainer and includes elevators, rudder, ailerons, and trailing-edge flaps on the wing for landing and takeoff. A hybrid unstructured overset mesh was generated to move these control surfaces and simulate the unsteady flowfields around the aircraft. The static results are first compared to experimental data available at different flap deflection angles, with good agreement obtained at low to moderate angles of attack and deflection angles. Unsteady airloads predictions were then made using the indicial response methods and response functions due to step changes in control surface deflection angles. A time-dependent surrogate model was also used to approximate the response function variation with changes in the angle of attack. The model outputs were then compared with time-accurate simulations of arbitrary control surface motions within the range of data used for model generation. Very good agreement was found between models and computational-fluid-dynamics data for low and high motion rates at low to moderate deflection angles. The results demonstrated that unsteady effects significantly change the amplitude and phase lags of predicted airloads compared with static (or steady-state) predictions.

Validation of DYSTOOL for unsteady aerodynamic modeling of 2D airfoils

From the point of view of wind turbine modeling, an important group of tools is based on blade element momentum (BEM) theory using 2D aerodynamic calculations on the blade elements. Due to the importance of this sectional computation of the blades, the National Renewable Wind Energy Center of Spain (CENER) developed DYSTOOL, an aerodynamic code for 2D airfoil modeling based on the Beddoes-Leishman model. The main focus here is related to the model parameters, whose values depend on the airfoil or the operating conditions. In this work, the values of the parameters are adjusted using available experimental or CFD data. The present document is mainly related to the validation of the results of DYSTOOL for 2D airfoils. The results of the computations have been compared with unsteady experimental data of the S809 and NACA0015 profiles. Some of the cases have also been modeled using the CFD code WMB (Wind Multi Block), within the framework of a collaboration with ACCIONA Windpower. The validation has been performed using pitch oscillations with different reduced frequencies, Reynolds numbers, amplitudes and mean angles of attack. The results have shown a good agreement using the methodology of adjustment for the value of the parameters. DYSTOOL have demonstrated to be a promising tool for 2D airfoil unsteady aerodynamic modeling.

Active flap control on an aeroelastic wind turbine airfoil in gust conditions using both a CFD and an engineering model

In the past year, smart rotor technology has been studied significantly as solution to the ever growing turbines. Aeroservoelastic tools are used to asses and predict the behavior of rotors using trailing edge devices like flaps. In this paper an unsteady aerodynamic model (Beddoes-Leishman type) and an CFD model (URANS) are used to analyze the aeroservoelastic response of a 2D three degree of freedom rigid body wind turbine airfoil with a deforming trailing edge flap encountering deterministic gusts. Both uncontrolled and controlled simulations are used to asses the differences between the two models for 2D aerservoelastic simulations. Results show an increase in the difference between models for the y component if the deforming trailing edge flap is used as control device. Observed flap deflections are significantly larger in the URANS model in certain cases, while the same controller is used. The pitch angle and moment shows large differences in the uncontrolled case, which become smaller, but remain significant when the controller is applied. Both models show similar reductions in vertical displacement, with a penalty of a significant increase in pitch angle deflections.

Unsteady aerodynamic prediction for dynamic stall of wind turbine airfoils with the reduced order modeling

A surrogate based reduced order method is developed for the prediction of the unsteady dynamic loading of wind turbine airfoils under dynamic stall situation. S809 airfoil undergoing sinusoidal pitch oscillation at different reduced frequencies, mean angles of attack and pitch oscillation amplitudes at Re = 106 are simulated by the CFD method. Then, the Kriging function is selected to establish the unsteady and nonlinear aerodynamic model with training cases generated by the CFD method. The results reveal an encouraging agreement between the CFD simulations and the reduced order model predictions. Furthermore, Ohio State University measurement data and Leishman–Beddoes model predictions for test cases are also included. Because CFD has good accuracy simulation for flow field around the airfoil under dynamic stall condition, the reduced order model can more effectively predict the airfoil nonlinear hysteretic behavior than L–B model. In addition, the reduced order method has relatively less computational cost compared with the CFD method. Therefore, it would be useful in engineering conditioning for aero-elastic analysis and design optimization of wind turbines.

Nonlinear aeroelastic analysis of a composite wing by finite element method

The aim of this paper is to develop a modified 1D structural dynamics model for aeroelastic analysis of a composite wing under large deformations. To attain this goal, an accurate available mechanical beam model of a composite wing was considered and improved to simulate large deformation behavior. Also, in aerodynamic aspect of view, a semi-experimental unsteady aerodynamic (ONERA dynamic stall) model has been incorporated to construct the aeroelastic model. To set up a flutter determination tool based on the eigenvalue analysis, Finite Element Method (FEM) has been implemented to discretize the aeroelastic equations. Also, a finite element cross-sectional analysis code VABS (Variational Asymptotical Beam Sectional Analysis) has been applied to determine composite cross-sectional properties across the wing span. Because of the existence of nonlinear terms in the aeroelastic equations, due to the large deformation behavior, the perturbed dynamic equations have been established about the nonlinear static equilibrium to capture the flutter boundaries. The obtained results are in good agreement with the available experimental data. It is found that the present aeroelastic model is appropriate for analysis of composite wings with arbitrary cross-sections.

Experimental and Computational Study on Flapping Wings with Bio-Inspired Hover Kinematics

In this paper, force and particle-image-velocimetry vorticity measurements of biologically inspired hover kinematics are compared to corresponding results of an unsteady aerodynamic vortex model and a Navier–Stokes (NS) solver. The Reynolds number and the reduced frequency are and 0.38, respectively. Three kinematics derived from the measured hovering kinematics of an Agrius convolvuli are considered: 1) without elevation angle, 2) elevation angle accounted in the pitch angle, and 3) pure sinusoidal pitch–plunge neglecting higher harmonics. The Navier–Stokes computations show good qualitative agreement with experiments with consistent underprediction. The time-averaged thrust coefficients obtained using Navier–Stokes computations are 82 to 87% of the corresponding force measurements. The standard deviation of time history of thrust coefficients, also normalized by the measured time-averaged values, is 13 to 20%. The underprediction is possibly due to blockage effects in the experiments, also reflected in lower values of the vorticity compared to particle-image-velocimetry measurements. The unsteady aerodynamic vortex model captures some of the peaks in a qualitative manner. The relative difference in the time-averaged forces and standard deviation are 8 to 18% and 66 to 93%, respectively. The differences in prediction of time histories are not reflected in the estimation of time-averaged forces due to cancellation effects, wherein the forces are underpredicted in the first half of the stroke and overpredicted in the second half. The discrepancies are attributed to the simplifying assumptions in the unsteady aerodynamic vortex model, which overpredicts the vorticity in the leading-edge vortex and results in significant differences in the wing–wake interaction process.

Simulation of Aircraft Encounters with Perturbed Vortices Considering Unsteady Aerodynamic Effects

Today, wake-turbulence-related aircraft separations are a limiting factor for the capacity of airports worldwide. A detailed knowledge about the severity of potential wake encounters is necessary for a safe revision of the current International Civil Aviation Organization separation requirements. Vortex encounter simulation is an important part in building an understanding how the encountering aircraft is adversely affected by the vortex-induced disturbances. Whereas most research has focused on aircraft encounters with a pair of straight vortices, this work focuses on the simulation of encounters with perturbed vortices as they are observed under various atmospheric conditions. In addition, a method to account for unsteady aerodynamic effects during the computation of vortex-induced forces and moments is presented. Those effects are becoming especially important for vortex-induced disturbances of a higher-frequency range as they may appear during encounters with perturbed vortices. This combination of models for vortex deformation due to long-wave Crow instability and unsteady aerodynamic models increases the realism of encounter simulations. The simulation models are suited for real-time and fast-time applications, such as piloted-flight-simulator experiments and fast-time Monte Carlo simulations. The results of a simulator study with airline pilots are discussed concerning the differences between encounters with straight and perturbed vortices.

风力机设计及其空气动力学问题

A multi-objective design framework is presented based on Pareto theory for complicated multiple variables, multiple objectives and multiple constraints in wind turbine optimization. The basic features of the integrated optimization design are discussed through a 1.5 MW large-scale wind turbine blade design as an example. Key issues in both the wind turbine aerodynamic calculation methods and the unsteady aerodynamic modeling are then introduced with a summary of the complexity of wind turbine aerodynamics, followed by a brief review on progress and challenges in the aerodynamic calculations and models one by one.