Unsteady Aerodynamic Reduced-order Models Research Articles

Mechanism of single-mode panel flutter in low supersonic flow

Supersonic panel flutter can be of two possible types: single-mode flutter and coupled-mode flutter. Compared to coupled-mode flutter, the physical mechanism of single-mode flutter is less studied at present. In order to reveal the inducing mechanism of single-mode flutter, the present paper constructed a reduced-order fluid model by using the system identification and the Auto Regressive with eXogenous input (ARX) model. Coupling the reduced-order model (ROM) for unsteady aerodynamics in low supersonic flow with the structural equation, a highly efficient ROM-based aeroelastic model in state space is formulated, then the flutter boundaries are obtained and the stability of aeroelastic modes are investigated by the complex eigenvalue analysis. According to the physical meaning of relevant parameters in unsteady aerodynamic reduced order model ARX, it is found that the unsteady characteristic of the flow, specifically the history effects of the unsteady aerodynamic forces, plays a dominant role in causing the single-mode panel flutter at low supersonic speeds. It is also shown that the higher modes are indeed weakly unstable in the absence of any structural damping or a viscous boundary layer.

Unsteady aerodynamic reduced-order modeling based on machine learning across multiple airfoils

Computational-fluid-dynamics-based prediction of unsteady aerodynamics is an essential research topic in the design of aircraft, which usually requires very high computational cost. Therefore, developing efficient and accurate reduced-order models (ROMs) for unsteady aerodynamics is important. With recent progress in modeling unsteady aerodynamics for a fixed configuration, there is a need of developing reduced-order models across multiple geometrical shapes. In this work, the long short-term memory (LSTM) network, a traditional model in machine learning for modeling time-dependent dynamics, is utilized to construct the unsteady aerodynamic reduced-order model, which takes into account the variation of airfoil geometry. The proposed approach is illustrated by some NACA 6-series airfoils under pitching and plunging motions in the transonic flow, where the geometrical parametrization is based on the maximum camber and thickness. Results show that the model can accurately capture the unsteady aerodynamics for varying shape parameters. Finally, as a proof of concept, the constructed ROM is applied to uncertainty and sensitivity analysis with respect to the variation of geometry parameters.

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.

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.

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 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 reduced-order modeling of unsteady aerodynamics under light dynamic stall conditions

In this research, a reduced-order modeling is developed to predict the unsteady aerodynamic forces under light dynamic stall conditions at low-speed regimes. The filtered white Gaussian noise is selected as input signals for computational fluid dynamics solver in order to generate training data, containing the information of reduced frequency and amplitude. Because of the time history influences, the reduced-order modeling combines the Kriging function and recurrence framework together in this approach. An airfoil NACA0012 undergoing pitching motions with different reduced frequency, amplitude, and mean angle of attack is designed to illustrate the methodology. The developed model can predict the lift, drag, and moment coefficients in seconds on a single-core computer processor. To reduce the prediction errors between reduced-order modeling predictions and computational fluid dynamics simulations, the aerodynamic loads in static conditions are applied as initial inputs. The predictions via the proposed approach are in agreement with the results using a high precision computational fluid dynamics solver over the designed ranges of amplitude and reduced frequency, which is suitable for engineering applications, such as fluid-structure interaction, and aircraft design optimizations.

Uncertain reduced-order modeling for unsteady aerodynamics with interval parameters and its application on robust flutter boundary prediction

Computational fluid dynamics based unsteady aerodynamic reduced-order models can significantly improve the efficiency of transonic aeroelastic analysis. In this paper, the concept of the conventional model reduction method based on the system identification theory is extended to aerodynamic subsystems with the consideration of computational fluid dynamics-induced interval uncertainties in simulation to get the aerodynamic reduced-order model as uncertain as the original aerodynamic subsystem. The interval estimation of identified coefficients involved in the uncertain reduced-order model is obtained by utilizing the first-order interval perturbation method. The stability problem of the interval aeroelastic state-space model formulated based on the constructed uncertain aerodynamic reduced-order model is equivalently transformed into a standard interval eigenvalue problem associated with a real non-symmetric interval matrix in which the interval bounds of eigenvalues are evaluated by virtue of the first-order interval matrix perturbation algorithm. A new stability criterion for the interval aeroelastic state matrix is defined to predict the robust flutter boundary of the concerned uncertain aeroelastic system. Two numerical examples with respect to the uncertain aerodynamic ROM constructions and robust flutter boundary predictions of the two-dimensional Isogai wing and the three-dimensional AGARD 445.6 wing in transonic regime are implemented to assess the validity and accuracy of the presented approach. The obtained results are also compared with Monte Carlo simulation solutions as well as numerical and experimental results in the literatures indicating that the proposed method can provide a more robust and conservative prediction on the flutter boundary of an aeroelastic system compared with conventional deterministic aeroelastic analysis approaches.

Reduced-order modeling of unsteady aerodynamics of a flapping wing based on the Volterra theory

Flapping flight mechanisms offers a power-efficient and highly manoeuvrable basis for the development of micro air vehicles. The aerodynamic knowledge and prediction tools of the flapping wing are quite important for the design of micro air vehicles. In this paper, the unsteady aerodynamics of a flapping wing is investigated by numerical simulations and the generation of reduced-order model based on the Volterra theory for predicting the unsteady aerodynamic of a flapping wing is described. The three dimensional aerodynamic calculation is performed by solving the unsteady Reynolds-averaged Navier-Stokes equations and the user-defined functions were employed to simulate the flapping motion. The training maneuver is a flapping motion with a linearly increasing flapping frequency. Based on the Volterra theory and numerical simulation results, a reduced-order model is generated to predict the unsteady aerodynamics of a flapping wing. The system identification method is employed to generate the Volterra theory reduced-order model. The results show that the Volterra theory reduced-order model agrees well with the training data and the Volterra theory reduced-order model works well to predict the unsteady aerodynamics of a flapping wing.

Reduced-Order Modeling of Unsteady Aerodynamics for an Elastic Wing with Control Surfaces

AbstractIn this paper, a reduced-order modeling approach based on computational fluid dynamics is presented for an elastic wing with control surfaces in the transonic regime. To treat the computational fluid dynamics grid around the geometrical discontinuities, due to the deflection of control surfaces, the constant volume tetrahedron method and the transpiration method are combined together without deforming the grid. Based on the input–output data from the computational fluid dynamics solver, one multiple-input/multiple-output discrete-time state-space model for the wing is identified via a robust subspace algorithm. For each control surface, one one-input/multiple-output discrete-time state-space model is identified using the same algorithm. With the precomputed state-space models for a few flight parameters, the generalized aerodynamic forces over a range of flight parameters can be computed by interpolating the output data. The methodology is applied to an elastic wing model with two control surfaces...

Unsteady aerodynamic reduced-order modeling of an aeroelastic wing using arbitrary mode shapes

Computational fluid dynamics (CFD) based unsteady aerodynamic reduced-order model (ROM) can offer significant improvements to the efficiency of transonic aeroelastic analysis. To construct a ROM based on mode shapes, one run of CFD solver is needed to compute aerodynamic responses corresponding to mode excitations. When mode shapes change with structure, another run of the CFD solver is required to construct the new ROM. The typically large computational cost associated with repeated runs of the CFD solver impedes the application of existing unsteady aerodynamic reduced-order modeling methods to transonic aeroelastic design optimization and aeroelastic uncertainty analysis. This paper demonstrates a method that can replace the CFD solver used in the process of existing unsteady aerodynamic reduced-order modeling. It can produce aerodynamic responses corresponding to mode excitations for arbitrary mode shapes within a few seconds. Computational cost can be reduced by two orders of magnitude using the mode excitations and the corresponding aerodynamic responses computed by the method to construct the ROMs used for flutter analyses in aeroelastic design optimization or aeroelastic uncertainty analysis in transonic regime compared with the existing unsteady aerodynamic reduced-order modeling methods. Results show that the method can accurately produce the aerodynamic responses corresponding to the mode excitations and predict the flutter characteristics of AGARD 445.6 wings root-attached in three different ways.

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.

Effect of control surface on airfoil flutter in transonic flow

Based on aerodynamic identification technology in which unsteady CFD (computational fluid dynamics) is used, the unsteady aerodynamic reduced order models (ROM) are constructed. Coupled with structural equations, we get the analyzable models for transonic aeroelasticity in state-space. A Mach number flutter trend of a typical airfoil section with a control surface is analyzed and agrees well with that of CFD/CSD (computational structural dynamics) direct coupling method. Then we study the effect of the structural parameters (natural frequency and the flap static unbalance) of the control surface on the transonic flutter system. We find some classical structural design rules are unfavorable for transonic flutter problem. For transonic flutter problem, the flap rotating mode becomes the predominant mode of aeroelastic system. Classical technology of mass static balance or over-balance maybe reduces the stability of transonic aeroelasticity.

Reliability and Sensitivity Analysis of Transonic Flutter Using Improved Line Sampling Technique

The improved line sampling (LS) technique, an effective numerical simulation method, is employed to analyze the probabilistic characteristics and reliability sensitivity of flutter with random structural parameter in transonic flow. The improved LS technique is a novel methodology for reliability and sensitivity analysis of high dimensionality and low probability problem with implicit limit state function, and it does not require any approximating surrogate of the implicit limit state equation. The improved LS is used to estimate the flutter reliability and the sensitivity of a two-dimensional wing, in which some structural properties, such as frequency, parameters of gravity center and mass ratio, are considered as random variables. Computational fluid dynamics (CFD) based unsteady aerodynamic reduced order model (ROM) method is used to construct the aerodynamic state equations. Coupling structural state equations with aerodynamic state equations, the safety margin of flutter is founded by using the critical velocity of flutter. The results show that the improved LS technique can effectively decrease the computational cost in the random uncertainty analysis of flutter. The reliability sensitivity, defined by the partial derivative of the failure probability with respect to the distribution parameter of random variable, can help to identify the important parameters and guide the structural optimization design.

Simultaneous Excitation of Multiple-Input/Multiple-Output CFD-Based Unsteady Aerodynamic Systems

A significant improvement to the development of computational-fluid-dynamics-based unsteady aerodynamic reduced-order models is presented. The improvement involves the simultaneous excitation of the structural modes of the computational-fluid-dynamics-based unsteady aerodynamic system. This improvement enables the computation of the unsteady aerodynamic state-space model using a single computational fluid dynamics execution, independent of the number of structural modes. Two new types of input functions are presented that can be used for the simultaneous excitation of the unsteady aerodynamic system via the excitation of the structural modes. Results are presented for a semispan configuration using the CFL3Dv6.4 code.

Control law design for transonic aeroservoelasticity

Existing computational transonic aeroservoelastic researches focus on directly coupling the structural dynamic equations, CFD solver and servo system in time domain, study the effect of the given feedback control laws on the responses of the aeroelastic system. These works have not involved the design of the flutter active control law. The non-linearity of transonic flow brings great difficulties to aeroservoelastic analysis and design. Recent research of the unsteady aerodynamic reduced order models (ROM) based on CFD provides a challenging approach for transonic aeroservoelastic analysis and design. Coupling the structural state equations with the aerodynamic state equations of the wing and the control surface based on the ROM, we construct a transonic aeroservoelastic model in state-space. Then the sub-optimal control method based on output feedback is used to design the flutter suppressing law. The study first demonstrates the open loop of the Benchmark Active Controls Technology (BACT) wing. The computational results of the CFD direct simulation method and the ROM analysis method are both agree well with the experimental data. Then both the closed loop time responses and the flutter results by ROM technique are compared with those of numerical aeroservoelastic simulation based on Euler codes to validate the correctness of the design method of the control law and aeroservoelastic analysis method. An increase of up to 20% of the speed index can be achieved by the control law designed by sub-optimal control method for this model.

Static/Dynamic Correction Approach for Reduced-Order Modeling of Unsteady Aerodynamics

Presented is a newly devised static/dynamic correction approach for eigenvector expansion based reduced-order modeling (ROM). When compared to the fundamental Ritz ROM formulation, along with the static and multiple static correction ROM approaches, the technique is demonstrated to have much better performance in modeling unsteady linearized frequency-domain aerodynamics in regions of the complex frequency plane near the imaginary axis, and up to a prescribed frequency of interest. As with the static and multiple static correction approaches, the method requires a directly computed solution at zero frequency. The method then requires one additional direct solution to be computed at some nonzero frequency, which typically is the maximum frequency of interest. When compared to the multiple static corrections method, the method circumvents the necessity of having to determine each of the multiple static corrections, which require a solution to an alternate set of equations that must be formulated and which can be costly to solve for large systems. We also consider the feasibility of using a proper orthogonal decomposition (POD) to determine approximations for the least damped fluid-dynamic eigenvectors. We demonstrate that in certain situations these approximate eigenvectors can be used in conjunction with the static/dynamic correction ROM approach to achieve an improvement in performance over the recently devised POD/ROM method where the POD shapes alone are used as ROM shape vectors. Finally, we illustrate how the method can be coupled with a structural model to compute the Mach-number flutter speed trend for a large computational-fluid-dynamics model of a three-dimensional transonic wing configuration.