Unsteady Aerodynamic Model Research Articles

Nonlinear aeroelastic characteristics of an all-movable fin with freeplay and aerodynamic nonlinearities in hypersonic flow

Nonlinear aeroelastic characteristics of an all-movable fin in hypersonic flow is investigated considering both aerodynamic and freeplay nonlinearities. The unsteady aerodynamic model is developed by the third-order piston theory for accurately obtaining nonlinear aerodynamic loading of all-movable fin with thickness ratio of airfoil, angle of attack and sweep angle. An equivalent temperature model is used to evaluate the effects of aerodynamic heating on structural stiffness and aeroelastic behaviors. The results demonstrate that the temperature elevation is an important parameter that can reduce the flutter boundary and extend the region of chaotic motions. In the observation of limit cycle oscillations (LCO) and evolution of dynamic bifurcation, aerodynamic nonlinearity produces a smaller amplitude response compared with linear piston theory, but has no apparent influence on dynamic bifurcation. When free-plays both in pitch and flap degrees-of-freedom (DOFs) are further considered, the system exhibits more complex bifurcation behaviors, especially the existence of quasi-periodic and chaotic responses in low Mach number range. Chaotic motions are predicted by mean of the Poincare maps and the evolution of the largest Lyapunov exponent. Moreover, the numerical results also show that the nonlinear aeroelastic behaviors are significantly affected by some parameters, such as freeplay magnitude, thickness ratio and sweep angle.

Study of Dynamic Response Characteristics of the Wind Turbine Based on Measured Power Spectrum in the Eyewall Region of Typhoons

The present research envisages a method for calculating the dynamic responses of the wind turbines under typhoon. The measured power spectrum and inverse Fourier transform are used to generate the fluctuating wind field in the eyewall of the typhoon. Based on the beam theory, the unsteady aerodynamic model and the wind turbine dynamic model are coupled to calculate the dynamic response. Furthermore, using this method, the aeroelastic responses of a 6 MW wind turbine at different yaw angles are studied, and a 2 MW wind turbine are also calculated to verify the applicability of the results for different sizes of wind turbines. The results show that the turbulence characteristics of the fluctuating wind simulated by the proposed method is in good agreement with the actual measurement. Compared with the results simulated by the recommended power spectrum like the Kaimal spectrum, the energy distribution and variation characteristics simulated by the proposed method represent the real typhoon in a superior manner. It is found that the blade vibrates most violently at the inflow yaw angle of 30 degrees under the coupled effect of the aerodynamic, inertial and structural loads. In addition, the load on the tower exceeds the design limit values at the yaw angles of both 30 degrees and 120 degrees.

Design of Control Law of Post Stall Maneuver under Unsteady Aerodynamics Based on Improved Dynamic Inverse Method

In this paper, a practical improved dynamic inverse control method is proposed to solve the large control error and control hysteresis of post stall maneuver under unsteady aerodynamics. Firstly, depending on the wind tunnel experimental data of the advanced fighter aircraft model under biaxial coupled large oscillation, an accurate unsteady aerodynamic model is established by using the improved extreme learning machine (ELM) method. Secondly, in terms of the time scale separation, the control error caused by unsteady aerodynamic is reduced by adding integral in the fast loop, and the control delay caused by unsteady aerodynamic is eliminated by applying the lag correction link in the slower loop. The deflections of conventional aerodynamic surface and thrust vector are allocated by the daisy chain method. Finally, the formula of the reduced frequency, which is the key factor in the unsteady aerodynamic modelling process, is derived by analyzing the wind tunnel data. The effectiveness of the present method for the scaled model is verified by herbst post stall maneuver. The present work provides a practical and reliable way for the flight test of post stall maneuver.

Nonlinear flutter and limit-cycle oscillations of damaged highly flexible composite wings

A study on nonlinear flutter of damaged high- wings is presented. Because an undamaged, high- wing is long and slender, it may be properly modeled as a 1D beam, using a geometrically exact beam formulation. However, structural damages in the form of cracks and delaminations are in fact 3D phenomena. Therefore, the area near a crack cannot be accurately modeled as a reduced-dimensional beam. However, finite element analysis of a wing structure modeled entirely as a 3D continuum is computationally expensive. To address this issue, a joined 3D/1D finite element approach has been proposed in which a small area surrounding the crack is regarded as a 3D continuum, and the rest of the wing structure is modeled as a reduced-dimensional 1D beam undergoing large displacements and rotations. The continuity conditions at the intersection between the 3D and 1D models are derived using the variational asymptotic method, by which the two parts are rigorously connected. Hence, the joined 3D/1D method provides a computationally inexpensive, yet accurate, analysis for slender wings. The structural model is then coupled with a reduced-order unsteady aerodynamic model to compute the aerodynamic forces and moments acting on the wing. The resulting nonlinear aeroelastic element is integrated into Abaqus, a commercial finite element computer code as a nonlinear user-defined element. Through nonlinear time-marching, using a generalized $$\alpha $$ method, limit-cycle oscillations associated with the free response of both undamaged and damaged wings undergoing large deformations are studied, and the differences are highlighted.

Deep neural network for unsteady aerodynamic and aeroelastic modeling across multiple Mach numbers

Aerodynamic reduced-order model (ROM) is a useful tool to predict nonlinear unsteady aerodynamics with reasonable accuracy and very low computational cost. The efficacy of this method has been validated by many recent studies. However, the generalization capability of aerodynamic ROMs with respect to different flow conditions and different aeroelastic parameters should be further improved. In order to enhance the predicting capability of ROM for varying operating conditions, this paper presents an unsteady aerodynamic model based on long short-term memory (LSTM) network from deep learning theory for large training dataset and sampling space. This type of network has attractive potential in modeling temporal sequence data, which is well suited for capturing the time-delayed effects of unsteady aerodynamics. Different from traditional reduced-order models, the current model based on LSTM network does not require the selection of delay orders. The performance of the proposed model is evaluated by a NACA 64A010 airfoil pitching and plunging in the transonic flow across multiple Mach numbers. It is demonstrated that the model can accurately capture the dynamic characteristics of aerodynamic and aeroelastic systems for varying flow and structural parameters.

Aeroelastic Response Analysis of Composite Blades Based on Geometrically Exact Beam Theory

The geometrically exact nonlinear beam theory consisting of the latest version of two-dimensional variational asymptotic beam sectional analysis (VABS) and one-dimensional geometrically exact beam theory (GEBT) has been widely used for the structural analysis of composite beam structures. The theory can be used for establishing the aeroelastic model of composite blades undergoing large deflections to improve computational accuracy and efficiency. In this paper, the theory has been extended from structural analysis to aeroelastic analysis of blade, and an accurate and efficient method for aeroelastic response analysis of composite blades has been presented based on the theory and unsteady aerodynamic model. The geometrically exact nonlinear equations of motion and the latest VABS are used to deal with one-dimensional beam analysis and the structural property of blade cross section, respectively. The Peters–He finite state dynamic wake model and the Peters finite state airloads theory are used to calculate the induced velocity and blade airloads, respectively. The presented method has been used to analyze the aeroelastic responses of composite blades, and its accuracy has been verified by experimental data. The influence of transverse shear deformation on the aeroelastic response of composite blades was also investigated, indicating that the transverse shear deformation has a nonnegligible effect on aeroelastic response analysis of hingeless composite rotors in hover.

Unsteady aerodynamic modeling based on fuzzy scalar radial basis function neural networks

In this paper, a fuzzy scalar radial basis function neural network is proposed, in order to overcome the limitation of traditional aerodynamic reduced-order models having difficulty in adapting to input variables with different orders of magnitude. This network is a combination of fuzzy rules and standard radial basis function neural network, and all the basis functions are defined as scalar basis functions. The use of scalar basis function will increase the flexibility of the model, thus enhancing the generalization capability on complex dynamic behaviors. Particle swarm optimization algorithm is used to find the optimal width of the scalar basis function. The constructed reduced-order models are used to model the unsteady aerodynamics of an airfoil in transonic flow. Results indicate that the proposed reduced-order models can capture the dynamic characteristics of lift coefficients at different reduced frequencies and amplitudes very accurately. Compared with the conventional reduced-order model based on recursive radial basis function neural network, the fuzzy scalar radial basis function neural network shows better generalization capability for different test cases with multiple normalization methods.

Prediction of dynamic derivatives for air-breathing hypersonic vehicle using a harmonic balance method

The harmonic balance method is an efficient frequency-domain approach for computing periodically unsteady flows. Applying harmonic balance method to the rapid calculation of forced periodic motions, an efficient prediction method for dynamic derivatives is established based on the Etkin unsteady aerodynamic model. The method is firstly validated by a standard model of the hypersonic missile hyper ballistic shape, and the harmonic balance method results show great consistency with both time-domain results and experimental data, consolidating the efficiency of our numerical algorithm. The method is subsequently applied for an air-breathing hypersonic vehicle to investigate the capability of the harmonic balance method in modeling unsteady flows around complex geometric configurations. Comparisons with the results of the time-domain method demonstrate that the harmonic balance method is capable of resolving such complicated flowfield with both accuracy and efficiency. To be specific, for the air-breathing hypersonic vehicle, the maximum difference of the dynamic derivatives calculated by the harmonic balance method and the time-domain method is only 6.56%, and the harmonic balance method shows at least an order of magnitude efficiency over the general time-domain method in the current study.

CFD-Based Aeroelastic Sensitivity Study of a Low-Speed Flutter Demonstrator

The goal of developing aircraft that are greener, safer and cheaper can only be maintained through significant innovations in aircraft design. An integrated multidisciplinary design approach can lead to an increase in the performance of future derivative aircraft. Advanced aerodynamics and structural design technologies can be achieved by both passive and active suppression of aeroelastic instabilities. To demonstrate the potential of this approach, the EU-funded project Flutter Free Flight Envelope Expansion for Economical Performance Improvement is developing an unmanned aerial vehicle with a high-aspect-ratio-wing and clearly defined flutter characteristics. The aircraft is used as an experimental test platform. The scope of this work is the investigation of the aeroelastic behaviour of the aircraft and the determination of its flutter limits. The modeling of unsteady aerodynamics is performed by means of the small disturbance CFD approach that provides higher fidelity compared to conventional linear-potential-theory-based methods. The CFD-based and the linear-potential-theory-based results are compared and discussed. Furthermore, the sensitivity of the flutter behaviour to the geometric level of detail of the CFD model is evaluated.

Structural and aeroelastic analyses of a wing with tip rotor

Based on parametric studies, this paper studies the structural and aerodynamic properties of a typical wing-rotor system by considering additional coupling effects from the tip rotor. The governing equations are established by virtue of Yamanaka’s theory and Hamilton’s principle in an Euler–Bernoulli precision. In the derivation process, complex mode theory and the Rayleigh–Ritz approach are employed to obtain the analytical solution and the numerical solution, respectively, and a set of trial functions are generated for the sake of reliability. Two aeroelastic models are generated via steady and unsteady aerodynamic models to investigate the divergence and flutter performance, respectively, where the computational p-k method is adopted because of the gyros matrix. In case studies, the effectiveness of the numerical solution is validated through comparative analysis; thereafter, the aeroelastic solutions are further verified. The results demonstrate that the gyro effect and the thrust effect have significant influences on the fundamental structural and aeroelastic performances, and parametric designs have great potential to postpone aeroelastic instabilities.

Nonlinear Responses of a Slender Wing With a Store

The aeroelastic characteristics of the slender wing with store have been studied for several years. However, the nonlinear aeroelastic behaviors of the wing-store system have not been understood thoroughly. In this paper, the nonlinear aeroelastic model of a slender wing with a store is constructed. In the model, the geometric structural nonlinearity of the wing, and the kinematic nonlinearities of the wing and the store are considered. Two unsteady aerodynamic models are both employed to determine the aerodynamic loads. One is the linear unsteady aerodynamic model based on Wagner function, and the other is the nonlinear ONERA aerodynamic model. Simulation results are given to show that for the cases of employing the linear unsteady aerodynamic model based on Wagner function, the bifurcation diagrams are very complex and change with the variations of store position. For the cases of using the nonlinear ONERA model, the bifurcation diagrams are very simple and insensitive to the variations of the store position. Additionally, with the decrease of store spanwise coordinate, the system bending oscillation equilibrium position is reduced to zero, and the maximum absolute value of the bending response peak is also decreased. With the increase of the horizontal distance between the wing elastic center and the store mass center, the system response peak is decreased. Moreover, it is found that for the systems with the linear unsteady aerodynamic model based on Wagner function, the obtained response peak is larger and the nonlinear critical velocity is smaller than those with the ONERA model.

Parametric reduced-order modeling of unsteady aerodynamics for hypersonic vehicles

A novel parametric reduced-order model (ROM) is proposed for efficiently predicting hypersonic unsteady aerodynamic responses under different flight conditions. The construction of the ROM is realized by computational fluid dynamics (CFD) simulations under the prescribed motion of the structure, while the results are processed via the proper orthogonal decomposition (POD) to obtain the predominant flow modes. Subsequently, to obtain the ROM valid for varying flight conditions, the method of interpolation in a tangent space to a Grassmann manifold is used to generate a new POD modal matrix for the arbitrary operating point in the considered parameter space. Finally, the least squares support vector machine (LS-SVM) is carried out to obtain the nonlinear relations between the applied excitations and the resulting POD coefficients. Once the parametric ROM is constructed, it can behave as a substitution of the full-order CFD flow solver in the considered parameter space. For demonstration purposes, the parametric ROM is used to predict hypersonic unsteady aerodynamic loads, flutter boundaries and limit-cycle oscillations of a double wedge airfoil over a wide range of the flight conditions, respectively. Numerical investigations show a good agreement between the results obtained by the ROM methodology in comparison to the full-order CFD solution over a wide range of the parameters. In addition, the ROM approach yields a significant speedup regarding unsteady aerodynamic calculations, which is beneficial for aeroelastic analysis, control and optimization applications.

A Modified Indicial Functions Approximation for Nonlinear Aeroelastic Analysis

The nonlinear dynamic response, Limit Cycle Oscillations (LCOs), of high aspect ratio wings using a novel indicial aerodynamics in subsonic flow is investigated. Using the nonlinear beam theory, the structural model is derived including the in-plane and out-of-plane bending and torsion motions, all nonlinearities up to cubic order arising from large deformation, mass distribution, and cross-sectional mass imbalance. Based on new approximations of the indicial functions, a comprehensive unsteady aerodynamic model is used. Such an indicial aerodynamics while being coupled to nonlinear structural equations can result in a unified nonlinear aeroelastic formulation in both the incompressible and subsonic compressible flow. The effect of flight conditions, wing tip initial disturbances, stiffness ratio between bending modes, and nonlinearity due to inertia and cross-sectional mass imbalance on the characteristics of LCO are discussed. The results show that the compressibility can affect the LCO boundary up to 12 percent which implies that an appropriate Mach-dependent aerodynamics is required to achieve a more reasonable and realistic description of dynamic behavior of the system. It is shown that the presence of LCO before the linear flutter speed depends on initial disturbances as well as wing characteristics.

Ground Flutter Simulation Test Based on Reduced Order Modeling of Aerodynamics by CFD/CSD Coupling Method

Flutter is an aeroelastic phenomenon that may cause severe damage to aircraft. Traditional flutter evaluation methods have many disadvantages (e.g., complex, costly and time-consuming) which could be overcome by ground flutter test technique. In this study, an unsteady aerodynamic model is obtained using computational fluid dynamics (CFD) code according to the procedure of frequency domain aerodynamic calculation. Then, the genetic algorithm (GA) method is adopted to optimize interpolation points for both excitation and response. Furthermore, the minimum-state method is utilized for rational fitting so as to establish an aerodynamic model in time domain. The aerodynamic force is simulated through exciters and the precision of simulation is guaranteed by multi-input and multi-output robust controller. Finally, ground flutter simulation test system is employed to acquire the flutter boundary through response under a range of air speeds. A good agreement is observed for both velocity and frequency of flutter between the test and modeling results.

LPV Modeling and Identification of Unsteady Aerodynamics for Fast Maneuvering Aircrafts

Fast maneuvers at large angles of attack are necessary for modern fighter aircrafts. The aerodynamic coefficients in this situation are unsteady, with the characteristics of hysteresis and fast time-varying. We propose an identification method based on the linear parameter varying (LPV) model. The model takes into account the hysteresis with respect to the angle of attack, and fast time varying with respect to the motion of post-stall maneuvers. By introducing the angular velocity as an exogenous variable, the model can guarantee the tracking ability of fast time-varying variations. We use the instrumental variable least squares (IVLS) algorithm to deal with the estimation problem. Finally, the experimental data obtained from maneuvers at large angles of attack from wind tunnel tests are used to validate the applicability and effectiveness of the proposed method.

Minimum Parameters Learning-Based Dynamic Surface Control for Advanced Aircraft at High Angle of Attack

Aiming at the difficulty of post-stall maneuvering control modeling and control of advanced aircraft under unsteady aerodynamics, a control method with high control accuracy and fast computation speed is proposed based on Radial Basis Function (RBF) network with minimum parameters learning (MPL) and dynamic surface control (DSC) method. Firstly, the aerodynamic characteristics of post-stall maneuvers are analyzed based on the experimental data of large-scale oscillation wind tunnels, and the key factors affecting the unsteady aerodynamic forces are obtained. Then, an accurate unsteady aerodynamic model is established based on the improved extreme learning machine (ELM) method. Secondly, the influence of unsteady aerodynamic forces on the control of post-stall maneuvers is considered. For the uncertainty of advanced aircraft model, high angle of attack flight control laws based on RBF-DSC are designed. In order to improve the calculation speed of the above control law and optimize the parameters, a post-stall maneuver control law method based on MPL-RBF-DSC is designed, and the stability of the method is proved. The coordinated allocation of the conventional aerodynamic surfaces and thrust vectors is realized based on the daisy chain method. Finally, the typical maneuver simulation of “Cobra” is carried out, which highlights the advantages of the design method in this paper, such as high control accuracy, short calculation time and strong robustness.

Design and flight-stability analysis of a closed fixed-wing unmanned aerial vehicle formation controller

This article addresses a flight-stability problem for the multiple unmanned aerial vehicles cooperative formation flight in the process of the closed and high-speed flight. The main objective is to design a cooperative formation controller with known external factors, and this controller can keep the consensus of attitude and position and reduce the communication delay between any two unmanned aerial vehicles and increase unmanned aerial vehicles formation cruise time under the known external factors. Known external factors are taken into consideration, and longitude maneuvers using nonlinear thrust vectors were employed with unsteady aerodynamic models, according to the attitude and position of unmanned aerial vehicles, which were employed as corresponding input signals for studying the dynamic characteristics of unmanned aerial vehicles formation flight. In addition, the relative distance between any two unmanned aerial vehicles was not allowed to exceed their safe distance so that the controller could perform collision avoidance. An analysis of formation flight distance error shows that it converged to a fixed value that well ensured unmanned aerial vehicles formation flight stability. The experimental results show that the controller can improve the speed of a closed formation effectively and maintain the stability of formation flight, which provides a method for closed formation flight controller design and collision avoidance for any two unmanned aerial vehicles. Meanwhile, the effectiveness of proposed controller is fully proved by semi-physical simulation platform.

Unsteady aerodynamic modeling methodology based on dynamic mode interpolation for transonic flutter calculations

A new unsteady aerodynamic modeling methodology for calculating transonic flutter characteristics is presented. The main idea of the methodology is to obtain the unsteady flow response to small amplitude periodic deformations of a structure over a large range of oscillation frequencies through the interpolation of the most dominant fluid dynamic modes obtained from Dynamic Mode Decomposition (DMD) of a few reference unsteady simulations at different oscillation frequencies. These simulations can be carried out by solving the Euler or RANS equations. The methodology can then be used to obtain a frequency-domain generalized aerodynamic force matrix, and stability analysis can be performed using standard flutter analysis methods such as the p-k method. The proposed methodology provides a very good estimate of the flutter boundary for the 2D Isogai airfoil and 3D AGARD 445.6 wing models, but at a lower computational cost than the traditional higher-fidelity Fluid–Structure Interaction (FSI) simulations.

Aeroelastic Stability Analysis of Aircraft Wings with High Aspect Ratios by Transfer Function Method

A new method is developed for the aeroelastic stability analysis of a high-aspect-ratio wing based on the transfer function. First, the flutter governing equations for three types of wing elements including clear wing element, wing element with a control surface and that with an external store are, respectively, established by combining the corresponding bend-twist vibration model with the Theodrosen’s unsteady aerodynamic model. Then, in order to use the transfer function method, the element governing equations are processed by the Fourier transform and are formulated in a state-space form using state vector. Based on the finite element procedure, the global governing equations of the whole wing are obtained. Both the flutter velocity and flutter frequency are derived by solving a complex eigenvalue problem with the graphical approach. Additionally, the torsional divergence of the high-aspect-ratio wing is obtained by solving a real eigenvalue problem, which is a degenerated form of the wing flutter governing equations. Finally, illustrative examples are prepared to demonstrate the validity of the present method, which is insensitive to mesh density and does not require structural modal analysis for aeroelastic stability.

Effects of the pylon–store system on the nonlinear aeroelastic responses of a slender wing

The aeroelastic behaviors of wing–pylon–store system have been researched for several decades. However, the effects of pylon–store system on the nonlinear aeroelastic characteristics of slender wings have not been sufficiently understood. In this paper, the nonlinear aeroelastic properties of a slender wing with a pylon–store system are discussed. The nonlinear equations of motion about the wing–pylon–store system are established, where the nonlinearities about the wing deformation and store motion are considered. The aerodynamic loads on the wing are determined by using two aerodynamic models with strip theory. One is the linear unsteady aerodynamic model based on Wagner function, the other is the nonlinear ONERA aerodynamic model. By comparing the nonlinear responses obtained with different aerodynamic models, it is found that the interaction between the aerodynamic nonlinearities induced by dynamic stall and the structural nonlinearities may simplify the bifurcation diagram structure of the system. For some typical cases of the wing–pylon–store system, the aeroelastic responses are analyzed. It is observed that the store-induced kinematic nonlinearities may affect the bending oscillation equilibrium position of the wing. This effect will be reduced by using soft spring in the pylon. Additionally, in the case of pylon with soft spring, the limit cycle oscillation (LCO) onset velocity and the post-critical response peak of torsional motion are insensitive to the store mass center position. But the post-critical response of store pitch is violent if the store mass center is not under the elastic center. In the case of pylon with hard spring, the post-critical response of store pitch becomes very complex. Though the response peak of the store is small, the LCO onset velocity changes obviously with the variation of the store mass center position. The store-related kinematics will play an important role on the nonlinear responses of the system in this situation.