Transonic Aeroelasticity Research Articles

Optimal Sparsity in Nonlinear Nonparametric Reduced Order Models for Transonic Aeroelastic Systems

Machine learning and artificial intelligence algorithms typically require a large amount of data for training. This means that for nonlinear aeroelastic applications, where small training budgets are driven by the high computational burden associated with generating data, the usability of such methods has been limited to highly simplified aeroelastic systems. This paper presents a novel approach for the identification of optimized sparse higher-order polynomial-based aeroelastic reduced order models (ROMs) to significantly reduce the amount of training data needed without sacrificing fidelity. Several sparsity promoting algorithms are considered, including rigid sparsity, least absolute shrinkage and selection operator (LASSO) regression, and orthogonal matching pursuit (OMP). The study demonstrates that through OMP, it is possible to efficiently identify optimized s-sparse nonlinear aerodynamic ROMs using only aerodynamic response information. This approach is exemplified in a three-dimensional aeroelastic stabilator model experiencing high-amplitude freeplay-induced limit cycles. The comparison shows excellent agreement between the ROM and the full-order aeroelastic response, including the ability to generalize to new freeplay and velocity index values, with online computational savings of several orders of magnitude. The development of an optimally sparse ROM extends previous higher-order polynomial-based ROM approaches for feasible application to complex three-dimensional nonlinear aeroelastic problems, without incurring significant computational burdens or loss of accuracy.

Aeroelastic prediction in transonic buffeting flow with data fusion method

The frequency locking in phenomenon will occur in the transonic buffeting flow of the elastically supported airfoil. This phenomenon is usually accompanied by a large oscillation of the structure, eventually leading to the fatigue damage of the structure. Transonic aeroelasticity research based on computational fluid dynamics is extremely time-consuming. At present, the research on nonlinear aeroelastic reduced-order models attracts attention due to its important role in nonlinear limit cycle oscillation amplitude prediction. However, the training process of current nonlinear aeroelastic reduced order model requires massive smooth amplitude-modulated pseudo-random binary signals (SAPRBS), which limits its application in engineering field. This paper proposes a nonlinear aeroelasticity reduced-order model based on the saturated limit cycle oscillation signals (Harmonic Signals) that can be directly obtained in engineering field, providing a new perspective for nonlinear reduced-order models. The model only uses harmonic signals at three frequencies to accurately predict limit cycle oscillation amplitudes within a wide range of the NACA0012 transonic buffeting frequency-locking region. In addition, the model still maintains a certain generalization ability at the extrapolated frequency points.

An efficient evaluation method for wing fuel mass variations effect on transonic aeroelasticity

PurposeThis paper aims to develop an efficient evaluation method to more intuitively and effectively investigate the influence of the wing fuel mass variations because of fuel burn on transonic aeroelasticity.Design/methodology/approachThe proposed efficient aeroelastic evaluation method is developed by extending the standard computational fluid dynamics (CFD)-based proper orthogonal decomposition (POD)/reduced order model (ROM).FindingsThe results of this paper show that the proposed aeroelastic efficient evaluation method can accurately and efficiently predict the aeroelastic response and flutter boundary when the wing fuel mass vary because of fuel burn. It also shows that the wing fuel mass variations have a significant effect on transonic aeroelasticity; the flutter speed increases as the wing fuel mass decreases. Without rebuilding an expensive, time-consuming CFD-based POD/ROM for each wing fuel mass variation, the computational cost of the proposed method is reduced obviously. It also shows that the computational efficiency improvement grows linearly with the number of model cases.Practical implicationsThe paper presents a potentially powerful tool to more intuitively and effectively investigate the influence of the wing fuel mass variation on transonic aeroelasticity, and the results form a theoretical and methodological basis for further research.Originality/valueThe proposed evaluation method makes it a reality to apply the efficient standard CFD-based POD/ROM to investigate the influence of the wing fuel mass variation because of fuel burn on transonic aeroelasticity. The proposed efficient aeroelastic evaluation method, therefore, is ideally suited to deal with the investigation of the influence of wing fuel mass variations on transonic aeroelasticity and may have the potential to reduce the overall cost of aircraft design.

Identification of nonlinear aerodynamic systems with application to transonic aeroelasticity of aircraft structures

In this study, identification of nonlinear aerodynamic systems based on an improved nonlinear state-space modeling approach is presented to predict transonic aeroelastic behaviors of aircraft structures. It starts with identifying a linear state-space aerodynamic model by using the eigensystem realization algorithm and observer/Kalman filter identification methods. Subsequently, the remaining parameters of the nonlinear state-space aerodynamic model are determined through an output error-minimization procedure, based on a new training data generation methodology. To illustrate the approach, two- and three-dimensional transonic aeroelastic configurations are studied. The transonic aeroelastic behaviors predicted via the proposed approach agree well with those obtained via computational fluid dynamics technique in the interested range of dynamic pressure.

CFD-Aided Design of a Transonic Aeroelastic Compressor Rig

Abstract This paper presents the results of computational fluid dynamics (CFD)-aided design calculations of a transonic linear cascade wind tunnel. The purpose of the wind tunnel is to generate data for the validation of numerical methods employed to calculate aerodynamic damping for forced response cases in transonic compressors. It is common for transonic wind tunnels to use transonic walls (perforated walls with controlled suction) to adjust the transonic flow in the experiment. Unfortunately, perforated walls are difficult to model in CFD simulations, and they complicate the validation process. One of the goals of the new tunnel is not to use perforated walls. The main difficulty in the design of a transonic linear cascade is achieving periodic flow for the central blades due to shock reflections from the side walls and the sensitivity of transonic flow to small changes in geometry. Other design constraints are the maximum available mass flow of 4.5 kg/s and the minimum required blade thickness of 2 mm for instrumentation. The purpose of the current CFD simulations is to determine the optimum geometry (sidewalls, tailboards, and throttle) of the tunnel with the goal of achieving near periodic flow conditions for the central blade channels at the similar condition in a typical transonic compressor.

Influence of Transonic Flutter on the Conceptual Design of Next-Generation Transport Aircraft

Transonic aeroelasticity is an important consideration in the conceptual design of next-generation aircraft configurations. This paper develops a low-order physics-based flutter model for swept high-aspect-ratio wings. The approach builds upon a previously developed flutter model that uses the flowfield’s lowest moments of vorticity and volume-source density perturbations as its states. The contribution of this paper is a new formulation of the model for swept high-aspect-ratio wings. The aerodynamic model is calibrated using offline two-dimensional unsteady transonic computational-fluid-dynamics simulations. Combining that aerodynamic model with a beam model results in a low-dimensional overall aeroelastic system. The low computational cost of the model permits its incorporation in a conceptual design tool for next-generation transport aircraft. The model’s capabilities are demonstrated by finding transonic flutter boundaries for different clamped-wing configurations and investigating the influence of transonic flutter on the planform design of next-generation transport aircraft.

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.

The complexity and mechanism of transonic aeroelastic problems

In high-speed flight, transonic aeroelasticity commonly exists, leading to various problems such as transonic flutter, buffeting and buzz. To solve these problems, a good understanding of the underlying physical mechanisms is critical. Unfortunately, the nonlinearity and unsteadiness of airflows complicate this process and consequently impede the development of aircraft design. Here using the numerical simulation and modeling of complex transonic flows, we developed a unified analytical method for aeroelastic stability and response problems. We then explored the mechanisms of three complex aeroelastic phenomena and unveiled their relationships. (1) Transonic buzz is in essence a single degree of freedom (SDOF) flutter caused by the coupling between the most unstable fluid mode and structural mode. SDOF flutter of this kind is possible only when the fluid exhibits sufficiently low damping; that is, the freestream flow is near the buffet boundary or in the low supersonic zone. Besides, the unstable frequency boundaries are determined by zero and pole of the open loop system. (2) The frequency lock-in phenomenon in the transonic buffeting flow is caused by the SDOF flutter in the unstably separated flow rather than resonance. In this process, the response undergoes a transition from the forced vibration to the self-excited flutter, which results in a deviation of the lock-in region from the resonance point. By contrast, the traditional uncoupled method misestimates the risk range and underestimates the amplitude of a vibration. (3) When the pitching degree of freedom is released, transonic buffet will be induced at a lower angle of attack, indicative of the drawbacks of predicting buffet onset by a rigid model. Actually, the elastic characteristic plays a key role in predicting buffet onset in aircraft design. Collectively, the large-amplitude structural vibration in the transonic flow is closely related to aeroelastic instability. The dynamic linear model can correctly predict the boundary of some complex dynamic phenomena. The complexity of transonic aeroelasticity mainly arises from the stability reduction of airflows. Different from classical aeroelastic problems, the new fluid mode is derived from the reduction of fluid stability. The coupling between such a fluid mode and structural mode often leads to complex phenomena in transonic flows.

Transonic Aeroelastic Instability Suppression for a Swept Wing by Targeted Energy Transfer

Targeted energy transfer is studied as a means for suppression of transonic aeroelastic instabilities of a wind-tunnel swept wing, with a focus on designing a lightweight nonlinear energy sink that improves the critical flutter condition. The aeroelastic response modes of the wing with a nonlinear energy sink coupled to the tip are identified and tested for robustness using a medium-fidelity computational aeroelasticity model, and confirm that robust suppression of transonic aeroelastic instabilities is achievable. Accordingly, a nonlinear energy sink is designed based on a parametric study, and its transonic aeroelastic effects are studied using medium- and high-fidelity models. The results of both models indicate an improvement in stability over a broad range of conditions; the high-fidelity model predicts an approximately 40% increase in the dynamic pressure at the critical stability condition. Finally, a prototype winglet-mounted nonlinear energy sink is modeled to examine its aeroelastic effects. The results show that the nonlinear-energy-sink design is robust, but the winglet design plays a critical role that must be considered in the overall effect.

Limit Cycle Oscillation Control for Transonic Aeroelastic Systems Based on Support Vector Machine Reduced Order Model

Limit Cycle Oscillation Control for Transonic Aeroelastic Systems Based on Support Vector Machine Reduced Order Model

Transonic Aeroelastic Instability Searches Using Sampling and Aerodynamic Model Hierarchy

DOI: 10.2514/1.J050509 A hierarchy of flow models is exploited for transonic aeroelastic stability analysis using the kriging interpolation technique applied within the Schur complement eigenvalue framework. In the Schur framework, a modified structural eigenvalue problem describes the coupled aeroelastic system with a precomputed interaction term depending on the response frequency. The interaction term, representing the influence of the high-dimensional computational fluid dynamics system, is approximated by reconstruction based on samples that can be computed using a frequency or time domain solver. The computationally cheap approximation model is developed and discussed in this paper for two-degree-of-freedom aerofoil cases. The approximation model is used for both the parametric blind search of aeroelastic instability and for updating predictions based on aerodynamic models of different fidelities.

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.

Oscillatory Behavior of Transonic Aeroelastic Instability Boundaries

Oscillatory Behavior of Transonic Aeroelastic Instability Boundaries

Calculated Viscous and Scale Effects on Transonic Aeroelasticity

A viscous-inviscid interactive coupling method is used for the computation of unsteady transonic flows. A lagextrainment integral boundary layer method is used with a transonic small disturbance potential code to compute the transonic aeroelastic response for two wing flutter models. By varying the modeled length scale, viscous effects may be studied as the Reynolds number per reference chordlength varies. Appropriate variation of modeled frequencies and generalized masses then allows comparison of responses for varying scales or Reynolds number. Two wing planforms are studied: one a four percent thick swept wing and the other a typical business jet wing. Calculations for both wings show limit cycle oscillations at transonic speeds in the vicinity of minimum flutter speed indices.

Transonic Aeroelastic Analysis of All-Movable Wing with Free Play and Viscous Effects

C = damping matrix CE = entrainment coefficient Cf = skin-friction coefficient Cg = generalized damping matrix Cp = pressure coefficient C = shear stress coefficient H = boundary-layer shape factors H1 = Head’s boundary-layer shape factor K = stiffness matrix K = linear stiffness at the free-play node M = freestream Mach number M = mass matrix Mg = generalized mass matrix fQg = generalized aerodynamic forces vector fqg = generalized modal displacement vector fRg = restoring force vector including structural nonlinearities S = wing area s = free-play angle at the free-play node t = time, nondimensionalized by U=cr U = freestream velocity x, y, z = nondimensional physical coordinates in the streamwise, spanwise, and vertical directions, respectively ip = initial pitch angle at the free-play node = specific heat ratio = boundary-layer momentum thickness = freestream density = disturbance velocity potential b = modal matrix

Fast Prediction of Transonic Aeroelastic Stability and Limit Cycles

The exploitation of computational fluid dynamics for aeroelastic simulations is mainly based on time-domain simulations. There is an intense research effort to overcome the computational cost of this approach. Significant aeroelasticeffectsdrivenbynonlinearaerodynamicsincludethetransonic flutterdipandlimit-cycleoscillations.The paper describes the use of Hopf bifurcation and center manifold theory to compute flutter speeds and limit-cycle responses of wings in transonic flow when the aerodynamics are modeled by the Euler equations. The cost of the calculations is comparable to steady-state calculations based on computational fluid dynamics. The paper describes twomethodsfor findingstabilityboundariesandthenanapproachtoreducingthefull-ordersystemtotwodegreesof freedom in the critical mode. Details of the three methods are given, including the calculation of first, second, and thirdJacobiansandthesolutionofsparselinearsystems.ResultsfortheAGARDwing,asupercriticaltransporttype of wing, and the limit-cycle response of the Goland wing are given. Nomenclature A = Jacobian matrix of R with respect to w B, C = second and third Jacobian operators h = (scalar) increment for finite differences F = quadratic and higher terms in R G = Taylor coefficients of the residual restricted to the critical eigenspace H = Taylor coefficients of the residual restricted to the noncritical eigenspace f = convective flux discretization kij = coefficients in center manifold expansion of y P = right eigenvector of A, P1 � iP2 Q = left eigenvector of A, Q1 � iQ2 qs = constant scaling vector for the augmented system R = residual vector v = vector for the matrix-free product w = vector of unknowns y = part of w in the noncritical eigenspace z = part of w in the critical eigenspace � t = time step � i = sequence of eigenvalues in the inverse power method � = bifurcation parameter (dynamic pressure) ! = frequency of critical eigenvalue or shift for the inverse power method Subscripts

Sensitivity Study of Downwash Weighting Methods for Transonic Aeroelastic Stability Analysis

The aeroelastic behavior of an aircraft is typically more critical in the transonic flight regime. The linearized potential based equations of the fluid flow do not allow accurate predictions of transonic flutter. Downwash weighting methods are adequate tools for approximating the nonlinear behavior of unsteady transonic flows, as far as aeroelastic applications are concerned. The purpose of downwash weighting methods is to correct unsteady pressures computed from linear aerodynamic models, to take into account nonlinear effects. Such methodology is less expensive than time domain computational aeroelasticity simulations. The reduced frequency to be considered in those methods is associated to specific conditions to be investigated for aeroelastic stability. This implies in a less expensive computational simulation, since it may be performed on a single harmonic motion simulation at the specific reduced frequency. The objective of the present work is to perform a sensitivity study with regard to the variation of the dynamic amplitude of the prescribed mode shape. A set of amplitudes of the disturbance in angle of attack is used to generate the non-linear unsteady pressure data. Therefore, it is possible to understand the variation of the computed flutter speeds with respect to the nature of the non-linear unsteady pressures. The flutter speed computation presents significant variations with respect to the nature of the unsteady pressure data. The results presented herein regarding the dependence of the flutter speeds on the amplitude of the motion indicate that the downwash correction method is closely related to the magnitude of such displacements.

Discrete conservation and coupling strategies in nonlinear aeroelasticity

As a model problem of aeroelasticity the panel flutter problem is considered to study the discretization of nonlinear aeroelastic problems and the behaviour of the corresponding solution strategies. A fluid–structure discretization that mimics the energy budget of the continuous problem is derived. The set of equations occurring in each time step are implicit in time over fluid and structure. To solve these equations approximately, we employ predictor strategies and fixed-point iterations. We compare the method with conventional fluid–structure methods, addressing applications from transonic aeroelasticity, concerning in particular the numerical prediction of bifurcations.

Three-Dimensional Transonic Aeroelasticity Using Proper Orthogonal Decomposition-Based Reduced-Order Models

The proper orthogonal decomposition (POD) based reduced order modeling (ROM) technique for modeling unsteady frequency domain aerodynamics is developed for a large scale computational model of an inviscid flow transonic wing configuration. Using the methodology, it is shown that a computational fluid dynamic (CFD) model with over a three quarters of a million degrees of freedom can be reduced to a system with just a few dozen degrees of freedom, while still retaining the accuracy of the unsteady aerodynamics of the full system representation. Furthermore, POD vectors generated from unsteady flow solution snapshots based on one set of structural mode shapes can be used for different structural mode shapes so long as solution snapshots at the endpoints of the frequency range of interest are included in the overall snapshot ensemble. Thus, the snapshot computation aspect of the method, which is the most computationally expensive part of the procedure, does not have to be fully repeated as different structural configurations are considered.

Limit cycle phenomena in computational transonic aeroelasticity

Limit cycle behavior has been observed in past transonic flutter calculations by the authors, using a two degree of freedom typical section model coupled to an unsteady Euler equation solver. In this article, the structural nonlinearity of freeplay has been added to the typical section model, and its effects on the dynamic stability problem are assessed. In addition, limit cycle behavior in the swept wing model of Isogai is demonstrated and related to the observed presence of multiple flutter points in the transonic dip region