Reduced Order Aerodynamic Models Research Articles

Active flutter suppression of wing with morphing flap

The flutter characteristics of a wing with morphing flap are analyzed based on computational fluid dynamics (CFD) method. The unsteady aerodynamic reduced order model (ROM) is constructed to model the morphing flap with high accuracy, and the effect of flap camber on the wing flutter boundary is investigated. Active suppression of aeroelastic response by controlling the flap deflection is validated through numerical simulations. A Linear Quadratic Gaussian (LQG) compensator is designed to explore the potential of suppressing wing flutter by deflecting the flap actively. The simulation results show that the order of morphing flap camber may change the critical flutter speed and flutter frequency of the wing. Compared with the conventional plain flap, the morphing flap shows higher control efficiency with fewer deflection demands.

Efficient prediction of transonic flutter boundaries for varying Mach number and angle of attack via LSTM network

Transonic aeroelastic analysis can be carried out accurately and efficiently by using the aerodynamic Reduced-Order Modeling (ROM) approach. However, the efficiency and generalization capability of traditional time-dependent ROM should be further enhanced, especially when dealing with the case for varying flight parameters. For such a purpose, a set of flight samples for different Mach numbers and mean angles of attack in transonic regime are selected to cover the concerned parameter space. Subsequently, a typical filtered white Gaussian noise is used as the input signal to excite the dynamical behavior of the aerodynamic system via the direct Computational Fluid Dynamic (CFD) technique, and the corresponding input and output data at all the flight samples are used as the training data set. Afterwards, based on the CFD training data set, the dynamical relationship between aerodynamic output and displacement input for varying Mach number and mean angle of attack can be approximately fitted by using the Long Short Term Memory (LSTM) network, which is a time-series prediction approach of deep learning method. Finally, the transonic flutter boundaries of a NACA 64A010 airfoil are investigated to assess the validity of the proposed approach. The comparison with CFD results shows that, the ROM can predict the unsteady aerodynamic response and aeroelastic characteristics well with low computation cost. In particular, the flutter boundaries of the concerned airfoil at different Mach numbers and mean angles of attack are obtained, due to the absence of time-delay term in surrogate model, the generalization capacity and modeling efficiency of the ROM are improved.

Efficient reduced-order aerodynamic modeling for fast prediction of transonic flutter boundary

In this study, a reduced-order aerodynamic modeling framework by integration of a novel training data interpolation approach and the Eigensystem realization algorithm (ERA) is presented for fast prediction of transonic flutter boundary over a range of flight parameters. First, aerodynamic impulse responses are computed by using the technique of computational fluid dynamics (CFD) at grid points within parameter space, which are selected to cover the transonic regime of concern. Next, the training data interpolation approach by combining the discrete empirical interpolation method with the Kriging technique is used to generate the aerodynamic impulse response at arbitrary flight condition, without performing unsteady CFD simulations. Finally, the interpolated impulse response is used by ERA to extract the linear state-space aerodynamic model, which is coupled with the structural model for flutter characteristics analysis. To illustrate the proposed approach, a NACA 0012 airfoil of two degrees of freedom at zero mean angle of attack is investigated. The transonic flutter boundaries of the airfoil agree well with those obtained by using CFD-based technique.

Transonic flutter characteristics of an airfoil with morphing devices

An investigation into transonic flutter characteristic of an airfoil conceived with the morphing leading and trailing edges has been carried out. Computational fluid dynamics (CFD) is used to calculate the unsteady aerodynamic force in transonic flow. An aerodynamic reduced order model (ROM) based on autoregressive model with exogenous input (ARX) is used in the numerical simulation. The flutter solution is determined by eigenvalue analysis at specific Mach number. The approach is validated by comparing the transonic flutter characteristics of the Isogai wing with relevant literatures before applied to a morphing airfoil. The study reveals that by employing the morphing trailing edge, the shock wave forms and shifts to the trailing edge at a lower Mach number, and aerodynamic force stabilization happens earlier. Meanwhile, the minimum flutter speed increases and transonic dip occurs at a lower Mach number. It is also noted that leading edge morphing has negligible effect on the appearance of the shock wave and transonic flutter. The mechanism of improving the transonic flutter characteristics by morphing technology is discussed by correlating shock wave location on airfoil surface, unsteady aerodynamics with flutter solution.

Aerodynamic Reduced-Order Model of Shape-Change Blade Subjected to Upstream Wake

AbstractThis paper presents a Volterra series reduced-order model method to evaluate aerodynamic forces of aircraft engine blade designs, whose shape changes during design and are always excited by...

Research on Vibration Suppression for AGARD Wing Based on State Space Model

Based on the Observer method, the unsteady aerodynamic reduced order model is established. The aerodynamic, structural and control parts are in the form of state space equations. The state feedback control law is designed by linear quadratic regulator (LQR) method, and the active flutter suppression of aeroelastic system is realized. The three-dimensional AGARD elastic wing is selected as an example. The simulation results show that the active control law designed by the model reduction technique can effectively stabilize the response of the system, and the critical speed of closed-loop flutter increases greatly.

Aerodynamic shape optimization by continually moving ROM

This study presents a multi-round shape optimization method based on the aerodynamic reduced order model. In this method, each optimization round employs the first-order Taylor reduced order model to provide aerodynamic characteristics in the local design space around the baseline point. At the end of each optimization round, the baseline point moves toward the optima and a new reduced order model is built at the new baseline point for the next optimization round. In this way, the provided method explores the whole design space. The NACA0012 airfoils in subsonic and transonic flows are used to verify the method with the lift-drag ratio as optimization objective. The design parameters are the shape control parameters of the airfoil. The optimization algorithm is a genetic algorithm. After a total of 20 simulations by two rounds of optimizations, the lift-drag ratios increase from 0 to 25 and from 0 to 8 in the subsonic case and transonic case, respectively. An additional trick was suggested for addressing shockwave effect in the transonic case, in which the influence of the airfoil shape on the aerodynamic forces is divided into the following two parts: the smoothed part to address the influence of the shape on the smooth aerodynamic distribution, and the shockwave part to address the influence of the shape on shockwave strength, shockwave position, and their effect on the aerodynamic distribution. The optimizations of the airfoils in subsonic and transonic flows yield different trends. The results of the subsonic case tend to increase the airfoil curvature to increase the lift-drag ratio. The results of the transonic case tend to move the upper surface shockwave to the trailing edge, while moving the lower surface shockwave to the leading edge. Independent of the case, the provided optimization method can properly address the resulting trends and increase the efficiency of the optimization.

Verification of a low fidelity fast simulation framework through RANS simulations

Verification and validation of simulation models are critical steps in engineering. This paper aims at verifying the suitability of reduced order aerodynamic models used in an aeroservoelastic framework designed to analyze the flight dynamics of flexible aircraft, known as the Cranfield Accelerated Aircraft Loads Model. This framework is designed for rapid assessment of aircraft configurations at the conceptual design stage. Therefore, it utilizes or relies on methods that are of relatively low fidelity for high computational speeds, such as modified strip theory coupled with Leishmann–Beddoes unsteady aerodynamic model. Hence, verification against higher order methods is required. Although low fidelity models are widely used for conceptual design and loads assessments, the open literature still lacks a comparison against higher fidelity models. This work focuses on steady-trimmed flight conditions and investigates the effect of aerodynamic wing deformation under such loads on aerodynamic performance. Key limitations of the reduced order models used, namely fuselage and interference effects, are discussed. The reasons for the overall agreement between the two approaches are also outlined.

Multi-fidelity modeling framework for nonlinear unsteady aerodynamics of airfoils

• Unsteady multi-fidelity framework for nonlinear aerodynamics is proposed. • Data fusion is introduced to improve the efficiency of model construction. • The correction term is represented by a neural network model. • The framework gives accurate prediction with data from only three harmonic motions . • The framework outperforms reduced-order models when high-fidelity data is limited. Aerodynamic data can be obtained from different sources, which vary in fidelity, availability and cost. As the fidelity of data increases, the cost of data acquisition usually becomes higher. Therefore, to obtain accurate unsteady aerodynamic model with very low cost and the desired level of accuracy, this paper proposes an unsteady multi-fidelity aerodynamic modeling framework. The approach integrates ideas from data fusion, multi-fidelity modeling, nonlinear system identification and machine learning. Data fusion reduces the total cost of data generation for model construction, while multi-fidelity modeling with a nonlinear autoregressive with exogenous input (NARX) description provides a general framework for unsteady aerodynamics. The correction term from the low-fidelity model to the high-fidelity result is then identified by a machine learning approach, i.e., a multi-kernel neural network. To validate the proposed method, unsteady aerodynamics of a NACA0012 airfoil pitching at Mach number 0.8 is modeled. The high-fidelity data is obtained from a Navier–Stokes-equation-based solver, while the low-fidelity solution is taken from an Euler-equation-based flow solver. The main difference between two types of data is that the high-fidelity solution takes into account the viscous effect, while the low-fidelity solution is based the invisicid flow assumption. Besides, to mimic the practical situation where high-fidelity data are limited in amount and diversity due to high cost (e.g., the experimental condition), only three high-fidelity unsteady aerodynamic solutions from harmonic motion are available. After performing a multi-fidelity analysis on a typical harmonic motion, the model is applied to the prediction of aerodynamic loads from either new harmonic motions or random motions. The multi-fidelity model shows a good agreement with the high-fidelity solution, indicating that by using only a few high-fidelity data and a low-fidelity model, high-fidelity results can be accurately reproduced. Furthermore, the model convergence with respect to increasing training data, and the comparison with a single high-fidelity reduced-order model (ROM) are also studied. The proposed approach becomes more accurate as the number of high-fidelity samples increases, and outperforms a single aerodynamic ROM in most of test cases. Compared with ROM method, additional computational cost for the proposed approach is small, therefore the total time cost of model training is still low.

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.

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.

A flutter prediction method with low cost and low risk from test data

The most common approach to flight flutter testing is to track estimated modal damping ratios of an aircraft over a number of fight conditions. However, the risk is inevitable when this method is utilized since the aircraft must fly near the flutter boundary. In this paper, a method with low cost and low risk for flutter boundary prediction is proposed. Based on structural modal parameters from the ground vibration test (GVT) and the structural response at the sub-critical speed, the generalized aerodynamic force coefficient vector can be solved. The generalized displacement vector is designed as the input and the generalized aerodynamic force coefficient vector as the output. System identification is used to construct the reduced-order aerodynamic model. The aeroelastic model based on experimental results can be constructed by coupling the structural motion equation and the aerodynamic equation in state space. Analyzing the characteristics of the fluid–structure coupling system changing with the dynamic pressure, the flutter onset behaviors can be solved by the eigenvalue method. Wind tunnel tests confirm that this method only needs one wind-on test at the sub-critical speed to predict the flutter onset with a certain precision even the reference dynamic pressure is far from the flutter critical point.

An aerodynamic ROM of the blade subjected to wake based on Fourier method for flow

SummaryA reduced‐order model (ROM) is presented based on Fourier method for flow to predict aerodynamic forces of blades subjected to periodic time‐varying upstream wakes. In the method, a time‐varying wake is decomposed into harmonic waves by fast Fourier transformation. Using the Fourier method for flow and neglecting the cross‐coupling between harmonics, the aerodynamic forces caused by the wake are represented by a linear combination of harmonics with the same frequencies as the wake. The coefficients of the aerodynamic force harmonics are interpolated at the per‐fitted curves of the normalized Fourier coefficients (coefficients of aerodynamic forces harmonics corresponding to a unit simple harmonic excitation)–frequency relationship. A blade example is used to show the ability of the proposed method. The results indicate that the ROM method can predict the aerodynamic forces of blades caused by wakes efficiently and accurately. The amplitude levels of wakes have a linear impact on the accuracy of the ROM. Neglecting the higher‐order cross‐coupling between the harmonics in the ROM method is acceptable.

A High Efficient Fluid-Structure Interaction Method for Flutter Analysis of Mistuned

The time cost is very high by direct fluid-structure interaction method for mistuned bladed disk structures, so aerodynamic loads generally are ignored or treated as small perturbations in traditional flutter analysis. In order to analyze the flutter characteristics of mistuned blade rapidly and accurately, this paper presents an efficient fluid-structure interaction method based on aerodynamic reduced order model. system identification technology and two basic assumptions are used to build the unsteady aerodynamic reduced order model. Coupled the structural equations and the aerodynamic model in the state space, the flutter stability of mistuned bladed disk can be obtained by changing the structural parameters. For the STCF 4 example, the response calculated by this method agrees well with the results obtained by the direct CFD, but the computational efficiency is improved by nearly two orders of magnitude. This method is used to study the stiffness mistuned cascade system, and the stability characteristics of the system are obtained by calculating the eigenvalues of the aeroelastic matrix. The results show that the stiffness mistuning can significantly improve the flutter stability of the system, and also lead to the localization of the mode. The mistuning mode, mistuning amplitude and fluid structure interaction can influence the flutter stability obviously.

Efficient Training Data Generation for Reduced-Order Modeling in a Transonic Flight Regime

In this study, a time-dependent surrogate approach is presented to generate the training data for identifying the reduced-order model of an unsteady aerodynamic system with the variation of mean angle of attack and Mach number in a transonic flight regime. For such a purpose, a finite set of flight samples are selected to cover the flight range of concern at first. Subsequently, the unsteady aerodynamic outputs of the system under given inputs of filtered white Gaussian noise at these flight samples are simulated via CFD technique which solves Euler equations. The unsteady aerodynamic outputs, which are viewed as a time-dependent function of flight parameters, can be approximated via the Kriging technique at each time step. By this way, the training data for any combination of flight parameters in the range of concern can be obtained without performing any further CFD simulations. To illustrate the accuracy and validity of the training data generated via the proposed approach, the constructed data are used to identify the reduced-order aerodynamic models of a NACA 64A010 airfoil via a robust subspace identification algorithm. The unsteady aerodynamics and aeroelastic responses under various flight conditions in a transonic flight regime are computed. The results agree well with those obtained by using the training data of CFD technique.

Reduced-Order Modeling for Nonlinear Aeroelasticity with Varying Mach Numbers

AbstractThis paper proposes a nonlinear aerodynamic reduced-order model robust to different Mach numbers based on a recursive neural network. To model the nonlinear features with varying flow param...

A novel unsteady aerodynamic Reduced-Order Modeling method for transonic aeroelastic optimization

In aircraft design, structural optimization concerning transonic aeroelastic issues is computationally impractical, due to a great number of aeroelastic analyses are required in iterative process. Reduced-Order Model (ROM) method is convenient for transonic aeroelastic analyses; however, current ROMs are not reusable during iteration, hence the time consumption is still too high. To solve the problem, this study proposes an improved ROM suitable for Arbitrary Mode Shapes (ROM-AMS), which is reusable in iterative process. By adopting Principal Component Analysis, ROM-AMS method significantly reduces the number of basis mode shapes, while improves the accuracy of flutter analysis. In an optimization case, the weight of a cropped delta wing is reduced by 28.46%, and the efficiency is 900 times higher than that of traditional ROM approaches, which demonstrates the feasibility of this method in aeroelastic optimization.

Nonlinear Reduced-Order Models for Transonic Aeroelastic and Aeroservoelastic Problems

Nonlinear reduced-order modeling approaches have been a promising tool for predicting the transonic aerodynamic and aeroelastic behaviors of aircraft structures. However, the accuracy of the approaches in predicting the transonic limit-cycle oscillations and aeroservoelastic behaviors needs to be further improved. For example, because of the complexity induced by the coupling among deflection of control surfaces, oscillating shock waves, structural vibration, and aerodynamic viscosity, it is difficult to adjust the system order and number of neurons of the Wiener-based reduced-order model. Moreover, the increasing of the system order may lead to overfitting. This paper presents a novel reduced-order aerodynamic modeling methodology based on the theory of nonlinear state-space identification. The accuracy of the method is demonstrated for predicting aerodynamic loads, limit-cycle oscillations, and frequency responses of aeroservoelastic systems at transonic flow conditions. Results are compared with full-order simulations solving the Reynolds-averaged Navier-Stokes equations.

Simulation and Modeling of Rigid Aircraft Aerodynamic Responses to Arbitrary Gust Distributions

The stresses resulting from wind gusts can exceed the limit value and may cause large-scale structural deformation or even failure. All certified airplanes should therefore withstand the increased loads from gusts of considerable intensity. A large factor of safety will make the structure heavy and less economical. Thus, the need for accurate prediction of aerodynamic gust responses is motivated by both safety and economic concerns. This article presents the efforts to simulate and model air vehicle aerodynamic responses to various gust profiles. The computational methods developed and the research outcome will play an important role in the airplane’s structural design and certification. Cobalt is used as the flow solver to simulate aerodynamic responses to wind gusts. The code has a user-defined boundary condition capability that was tested for the first time in the present study to model any gust profile (intensity, direction, and duration) on any arbitrary configuration. Gust profiles considered include sharp edge, one minus cosine, a ramp, and a 1-cosine using tabulated data consisting of gust intensity values at discrete time instants. Test cases considered are a flat plate, a two-dimensional NACA0012 airfoil, and the high Reynolds number aero-structural dynamics (HIRENASD) configuration, which resembles a typical large passenger transport aircraft. Test cases are assumed to be rigid, and only longitudinal gust profiles are considered, though the developed codes can model any gust angle. Time-accurate simulation results show the aerodynamic responses to different gust profiles including transient solutions. Simulation results show that sharp edge responses of the flat plate agree well with the Küssner approximate function, but trends of other test cases do not match because of the thin airfoil assumptions made to derive the analytical function. Reduced order aerodynamic models are then created from the convolution integral of gust amplitude and the time-accurate responses to sharp-edge gusts. Convolution models are next used to predict aerodynamic responses to arbitrary gust profiles without the need of running time-accurate simulations for every gust shape. The results show very good agreement between developed models and simulation data.

Nonlinear identification via connected neural networks for unsteady aerodynamic analysis

In the present work, a nonlinear system identification strategy is proposed which is based on the series connection of a recurrent local linear neuro-fuzzy model (NFM) and a multilayer perceptron (MLP) neural network. The NFM with output feedback is initially used for multi-step ahead predictions, whereas the MLP neural network is a posteriori employed to perform a nonlinear quasi-static correction of the NFM's time-series response. The novel identification approach is utilized exemplarily as a reduced-order modeling (ROM) technique to lower the computational effort of unsteady aerodynamic simulations, although the approach is generally applicable to any nonlinear identification task. In order to demonstrate the method's fidelity for unsteady aerodynamic modeling, the NLR 7301 airfoil is investigated at transonic flow conditions, while the motion-induced aerodynamic forces are considered in particular. Therefore, the pitch and plunge degrees of freedom are simultaneously excited via forced motions to obtain the training data for model calibration, while the respective aerodynamic response is computed using a computational fluid dynamics (CFD) solver. The sequential nonlinear identification process as well as the generalization of the resulting model is presented. Besides, a Monte-Carlo-based training procedure, which is novel in the context of aerodynamic reduced-order modeling, is introduced to estimate statistical errors. It is shown that the essential linear and nonlinear system characteristics are accurately reproduced by the new approach compared to the full-order solution. Moreover, by examining the results in comparison to established ROM methods it is indicated that the connected neural network approach leads to an enhanced simulation and generalization performance.