Supersonic Lifting Surface Research Articles

Predicting wing-pylon-nacelle configuration flutter characteristics using adaptive continuation method

In this study, the aeroelastic response of a wing-pylon-nacelle system in subsonic and low supersonic flow regimes is analyzed using the continuation method in conjunction with an adaptive step size control algorithm. Idealizing the pylon and nacelle as a point mass, the computed effects of a standard structural analysis of the wing together with the pylon and nacelle are compared with those of a clean wing to build a reduced-order model for analysis. The aerodynamic forces relating to different reduced frequencies are assessed using the Doublet Lattice Method (DLM) in the subsonic flow regime and supersonic lifting surface theory relying on the unsteady linearized small-disturbance potential flow model in the low supersonic flow regime. The Rational Function Approximation (RFA) method is then utilized for the state-space formulation of the system equations, appended with the continuation method for flutter prediction. Thereafter, the linearized aeroelastic equations are resolved using the continuation method with adaptive step size, the results of which are matched with those obtained from the traditional p-k method to emphasize that the continuation method exhibits a distinct advantage in achieving better accuracy in estimating the flutter speed and identifying the “mode switching” phenomenon.

Nonlinear aeroservoelastic analysis of a supersonic aircraft with control fin free-play by component mode synthesis technique

To investigate the nonlinear aeroservoelastic behaviors of a three-dimensional supersonic aircraft with control fin free-play, a modeling method based on the component-mode synthesis technique is utilized. The most distinctive feature of this method is that the structural nonlinearity can be expressed explicitly in the reduced-order aeroservoelastic model. The unsteady aerodynamic model with discrete gust loads is formulated using the supersonic lifting surface theory and the minimum state approximation. The results validate the feasibility of the reduced-order aeroelastic model for gust response analysis. A hybrid adaptive feedback control algorithm is proposed for the gust load alleviation by integrating the positive position feedback (PPF) and the filtered-x least-mean-square (FxLMS) algorithm. The comparative study demonstrates that the designed PPF-FxLMS algorithm has a better control performance for the alleviation of the pitch attitude angle induced by the gust loads, and it remains effective in the post-flutter regime. Moreover, the effects of free-play nonlinearity on the dynamic behaviors of the aeroservoelastic system are also studied, and numerical results show that the presence of free-play can lead to a larger peak value of gust response. The nonlinear vibration of the control fin induces the aircraft pitch attitude to produce stable limit cycle oscillations with high frequency, and variation in the free-play magnitude significantly influences the gust responses of the nonlinear aeroservoelastic system.

A Continuous Robust Control Strategy for the Active Aeroelastic Vibration Suppression of Supersonic Lifting Surfaces

The model-free control of aeroelastic vibrations of a non-linear 2-D wing-flap system operating in supersonic flight speed regimes is discussed in this paper. A novel continuous robust controller design yields asymptotically stable vibration suppression in both the pitching and plunging degrees of freedom using the flap deflection as a control input. The controller also ensures that all system states remain bounded at all times during closed-loop operation. A Lyapunov method is used to obtain the global asymptotic stability result. The unsteady aerodynamic load is considered by resourcing to the non-linear Piston Theory Aerodynamics (PTA) modified to account for the effect of the flap deflection. Simulation results demonstrate the performance of the robust control strategy in suppressing dynamic aeroelastic instabilities, such as non-linear flutter and limit cycle oscillations.

Stochastic nonlinear aeroelastic analysis of a supersonic lifting surface using an adaptive spectral method

An adaptive stochastic spectral projection method is deployed for the uncertainty quantification in limit-cycle oscillations of an elastically mounted two-dimensional lifting surface in a supersonic flow field. Variabilities in the structural parameters are propagated in the aeroelastic system which accounts for nonlinear restoring force and moment by means of hardening cubic springs. The physical nonlinearities promote sharp and sudden flutter onset for small change of the reduced velocity. In a stochastic context, this behavior translates to steep solution gradients developing in the parametric space. A remedy is to expand the stochastic response of the airfoil on a piecewise generalized polynomial chaos basis. Accurate approximation andaffordable computational costs are obtained using sensitivity-based adaptivity for various types of supersonic stochastic responses depending on the selected values of the Mach number on the bifurcation map. Sensitivity analysis via Sobol' indices shows how the probability density function of the peak pitch amplitude responds to combined uncertainties: e.g. the elastic axis location, torsional stiffness and flap angle. We believe that this work demonstrates the capability and flexibility of the approach for more reliable predictions of realistic aeroelastic systems subject to a moderate number of uncertainties.

Implications of time-delayed feedback control on limit cycle oscillation of a two-dimensional supersonic lifting surface,

In this paper, the problem of implications of time delay feedback control of a two-dimensional supersonic lifting surface on the flutter boundary and on its character, that is, benign or catastrophic, is addressed. In this context, the structural and aerodynamic nonlinearities are included in the aeroelastic governing equations. The model and the associated theory are developed for linear and nonlinear plunging and pitching full-state proportional and velocity feedback controls. Center manifold reduction and normal form theory are applied to investigate the stability in the post-flutter flight speed regimes. Numerical simulations are carried out to determine the implications of time delay in the considered controls, but are restricted to the cases of proportional feedback control and no structural damping.

Aeroelasticity of Time-Delayed Feedback Control of Two-Dimensional Supersonic Lifting Surfaces

Determination of the nature of the critical flutter boundary (benign/catastrophic) and its control constitute important issues that can be addressed within the nonlinear formulation of lifting surface theory. The main attention of this paper consists in the development of a computational approach enabling one to get a better understanding on time-delayed dynamics as applied to this important aeroelastic problem, and more specifically, to two-dimensional supersonic lifting surfaces. The analysis is based on the reduction of the infinite-dimensional problem to one described on a two-dimensional center manifold. Results presenting the implication of the linear/nonlinear timedelayed feedback control on two-dimensional supersonic lifting surfaces are addressed, and pertinent conclusions are drawn.

Flutter, Postflutter, and Control of a Supersonic Wing Section

A number of issues related to the flutter and postflutter of two-dimensional supersonic lifting surfaces are addressed. Among them there are the 1) investigation of the implications of the nonlinear unsteady aerodynamics and structural nonlinearities on the stable/unstable character of the limit cycle and 2) study of the implications of the incorporation of a control capability on both the flutter boundary and the postflutter behavior. To this end, a powerful methodology based on the Lyapunov first quantity is implemented. Such a treatment of the problem enables one to get a better understanding of the various factors involved in the nonlinear aeroelastic problem, including the stable and unstable limit cycle. In addition, it constitutes a first step toward a more general investigation of nonlinear aeroelastic phenomena of three-dimensional lifting surfaces.

Design-Oriented Leading-Edge Thrust Force Prediction for Supersonic Lifting Surfaces

A design-oriented method for evaluating the leading-edge (LE) thrust force on supersonic lifting surfaces with subsonic LE is presented. The method is developed to overcome numerical noise and nonsmooth drag predictions observed when currently attainable LE-thrust techniques are used for wing planform shape optimization. The method is an extension of a design-oriented unsteady supersonic lifting surface capability developed previously for aeroservoelastic shape optimization of wings. It is a panel/lattice method where assumed pressure-weighting functions, taking the LE singularity into account, are prescribed to the LE panels while constant pressure panels are retained elsewhere. Explicit expressions for aerodynamic influence coefficients are retained over most of the wing, except for cases involving the LE panels, where numerical integration must be used. Planform shape sensitivities of the LE thrust and wing pressures are obtained using a combination of analytic and semianalytic techniques.

From Piston Theory to a Unified Hypersonic-Supersonic Lifting Surface Method

A unified hypersonic - supersonic lifting surface method has been developed, where the concept of piston theory is generalized and suitably integrated with the aerodynamic influence coefficient (AIC) matrix due to linear theory. Thus, this unified method can account for the effects of wing thickness and/or flow incidence, upstream influence, and three dimensionality for an arbitrary lifting surface system in an unsteady flow, whereas piston theory fails to account for the latter effects. In particular, the present composite series renders the AIC matrix uniformly valid for all supersonic-hypersonic Mach numbers, thus extending the method applicability to cover both the Ackeret limit at the low supersonic end and the Newtonian limit at the hypersonic end. From various cases studied it is concluded that the present method makes a substantial improvement over the linear lifting surface theory and piston theory in terms of unsteady pressures, stability derivatives, and flutter speeds. Among other theories it also predicts the most conservative flutter boundary and it confirms that the supersonic thickness effect is to reduce the flutter speed.

Application of the finite element technique combined with the collocation method to low supersonic lifting surface problems

AbstractIn the present paper, a finite element technique combined with the collocation method is formulated to obtain numerical solutions of integral equations which determine the airload distributions acting on a wing oscillating sinusoidally in a uniform supersonic flow. This technique, which is formulated by the simultaneous use of two integral equations, is shown to be appropriate especially for the low supersonic regions, i.e., for 1 < M < 1·3, where M is the Mach number of the uniform flow. Although the formulation is made for a sinusoidally oscillating wing, it is obvious that the corresponding formulation for a stationary wing can be derived as a special case of that for the oscillating wing. Problems of determining the airload distributions for stationary as well as sinusoidally oscillating wings are treated, and it is shown that the accuracy of numerical results obtained by the present finite element technique is encouraging.