Walter A. Silva

NACA 0012 benchmark model experimental flutter results with unsteady pressure distributions

The Structural Dynamics Division at NASA Langley Research Center has started a wind tunnel activity referred to as the Benchmark Models Program. The primary objective of this program is to acquire measured dynamic instability and corresponding pressure data that will be useful for developing and evaluating aeroelastic type computational fluid dynamics codes currently in use or under development. The program is a multi-year activity that will involve testing of several different models to investigate various aeroelastic phenomena. This paper describes results obtained from a second wind tunnel test of the first model in the Benchmark Models Program. This first model consisted of a rigid semispan wing having a rectangular planform and a NACA 0012 airfoil shape which was mounted on a flexible two degree of freedom mount system. Experimental flutter boundaries and corresponding unsteady pressure distribution data acquired over two model chords located at the 60 and 95 percent span stations are presented.

Supersonic/Hypersonic Flutter and Postflutter of Geometrically Imperfect Circular Cylindrical Panels

A theoretical investigation of the flutter and postflutter of infinitely long thin-walled circular cylindrical panels in a supersonic/hypersonic flowfield is presented. In this context, third-order piston theory and shockwave aerodynamics are used in conjunction with the geometrically nonlinear shell theory to obtain the pertinent aeroelastic governing equations. The effects of in-plane edge restraints and small initial geometric imperfections are also considered in the model. The objective is twofold: 1) to analyze the implications of nonlinear unsteady aerodynamics and structural nonlinearities on the character of the flutter instability boundary and 2) to outline the effects played, in the same respect, by a number of important geometrical, physical, and aerodynamic parameters characterizing the aeroelastic system. As a by-product of this analysis, the implications of these parameters on the linearized flutter instability behavior of the system are captured and emphasized. The behavior of the aeroelastic system in the vicinity of the flutter boundary is studied via the use of an encompassing methodology based on the Lyapunov first quantity. Numerical illustrations, supplying pertinent information on the implications of geometric and aerodynamic nonlinearities, as well as of other effects, such as curvature and thickness ratios, on the flutter instability and on the character of the flutter boundary are examined, and pertinent conclusions are outlined.

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.

Nonlinear Open-/Closed-Loop Aeroelastic Analysis of Airfoils via Volterra Series

Determination of the subcritical aeroelastic response to arbitrary time-dependent external excitation and determination of the flutter instability of open/closed-loop two-dimensional nonlinear airfoils constitute the main topics. To address these problems, Volterra series and indicial aerodynamic functions are used, and, in the same context, the pertinent aeroelastic nonlinear kernels are determined. Flutter instability predictions obtained within this approach compared with their counterparts generated via the frequency eigenvalue analysis and via experiments reveal excellent agreements. Implications of a number of important parameters characterizing the lifting surface and control law on the aeroelastic response/flutter are discussed, and pertinent conclusions are outlined.

Aeroelastic Response of Nonlinear Wing Sections Using a Functional Series Technique

This paper addresses the problem of the determination of the subcritical aeroelastic response and flutter instability of nonlinear two-dimensional lifting surfaces in an incompressible flow-field via indicial functions and Volterra series approach. The related aeroelastic governing equations are based upon the inclusion of structural and damping nonlinearities in plunging and pitching, of the linear unsteady aerodynamics and consideration of an arbitrary time-dependent external pressure pulse. Unsteady aeroelastic nonlinear kernels are determined, and based on these, frequency and time histories of the subcritical aeroelastic response are obtained, and in this context the influence of the considered nonlinearities is emphasized. Conclusions and results displaying the implications of the considered effects are supplied.

IDENTIFICATION OF LINEAR AND NONLINEAR AERODYNAMIC IMPULSE RESPONSES USING DIGITAL FILTER TECHNIQUES

This paper discusses the mathematical existence and the numerically-correct identification of linear and nonlinear aerodynamic impulse response functions. Differences between continuous-time and discrete-time system theories, which permit the identification and efficient use of these functions, will be detailed. Important input/output definitions and the concept of linear and nonlinear systems with memory will also be discussed. It will be shown that indicial (step or steady) responses (such as Wagners function), forced harmonic responses (such as Theodorsens function or those from doublet lattice theory), and responses to random inputs (such as gusts) can all be obtained from an aerodynamic impulse response function. This paper establishes the aerodynamic impulse response function as the most fundamental, and, therefore, the most computationally efficient, aerodynamic function that can be extracted from any given discrete-time, aerodynamic system. The results presented in this paper help to unify the understanding of classical two-dimensional continuous-time theories with modern three-dimensional, discrete-time theories. First, the method is applied to the nonlinear viscous Burgers equation as an example. Next the method is applied to a three-dimensional aeroelastic model using the CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) code and then to a two-dimensional model using the CFL3D Navier-Stokes code. Comparisons of accuracy and computational cost savings are presented. Because of its mathematical generality, an important attribute of this methodology is that it is applicable to a wide range of nonlinear, discrete-time problems.

Development of Aeroservoelastic Analytical Models and Gust Load Alleviation Control Laws of a SensorCraft Wind-Tunnel Model Using Measured Data

Aeroservoelastic (ASE) analytical models of a SensorCraft wind-tunnel model are generated using measured data. The data was acquired during the ASE wind-tunnel test of the HiLDA (High Lift-to-Drag Active) Wing model, tested in the NASA Langley Transonic Dynamics Tunnel (TDT) in late 2004. Two time-domain system identification techniques are applied to the development of the ASE analytical models: impulse response (IR) method and the Generalized Predictive Control (GPC) method. Using measured control surface inputs (frequency sweeps) and associated sensor responses, the IR method is used to extract corresponding input/output impulse response pairs. These impulse responses are then transformed into state-space models for use in ASE analyses. Similarly, the GPC method transforms measured random control surface inputs and associated sensor responses into an AutoRegressive with eXogenous input (ARX) model. The ARX model is then used to develop the gust load alleviation (GLA) control law. For the IR method, comparison of measured with simulated responses are presented to investigate the accuracy of the ASE analytical models developed. For the GPC method, comparison of simulated open-loop and closed-loop (GLA) time histories are presented.

Linear/Nonlinear Supersonic Panel Flutter in a High-Temperature Field

An analysis of the flutter and postflutter behavior of infinitely long flat panels in a supersonic/hypersonic flowfield exposed to a high-temperature field is presented. In the approach to the problem, the thermal degradation of thermoelastic characteristics of the material is considered. A third-order piston theory aerodynamic model in conjunction with the von Karman nonlinear plate theory is used to obtain the pertinent aerothermoelastic governing equations. The implications of temperature, thermal degradation, and of structural and aerodynamic nonlinearities on the character of the flutter instability boundary are analyzed. As a byproduct, the implications of the temperature on the linearized flutter instability of the system are discussed. The behavior of the structural system in the vicinity of the flutter boundary is studied via the use of an encompassing methodology based on the Lyapunov First Quantity. Numerical illustrations, supplying pertinent information on the implications of the temperature field and of the thermal degradation are presented, and pertinent conclusions are outlined.

Time-Delay Effects on Linear/Nonlinear Feedback Control of Simple Aeroelastic Systems

A study of the effects of time delay on the linear/nonlinear feedback control of two-dimensional lifting surfaces in an incompressible flowfield is presented. Specifically, the case of a one-degree-of-freedom system is considered in detail, and in that context, both the structural and the unsteady aerodynamics models are assumed to be linear. The study of the stability/instability behavior of nonlinear feedback time-delay closed-loop aeroelastic systems

Development of Reduced-Order Models for Aeroelastic Analysis and Flutter Prediction Using the CFL3Dv6.0 Code

ARLY mathematical models of unsteady aerody namic response capitalized on the efficiency and power of superposition of scaled and time shifted fun damental responses, also known as convolution. Chs sical models of two dimensional airfoils in incompress ible flow s include Wagners function2(response to a unit step variation in angle of attack), Kussners func tiona(response to a sharp edged gust), Theodorsens function4(frequency response to sinusoidal pitching motion), and Seats function (frequency response to a sinusoidal gust). As geometric complexity increased from airfoils to wings to complete configurations, the analytical derivation of these types of response func tions became impractical and the numerical computa tion of linear unsteady aerodynamic responses, in the frequency domain, became the method of choice. 5