Deman Tang

Experimental and Theoretical Study on Aeroelastic Response of High-Aspect-Ratio Wings

An experimental high-aspect-ratio wing aeroelastic model with a slender body at the tip has been constructed, and the response due to flutter and limit-cycle oscillations (LCO) has been measured in a wind-tunnel test. A theoretical model has been developed and calculations made to correlate with the experimental data. Structural equations of motion based on nonlinear beam theory are combined with the ONERA aerodynamic stall model to study the effects of geometric structural nonlinearity and steady angle of attack on flutter and LCO of high-aspect-ratio wings. Static deformations in the vertical and torsional directions caused by a steady angle of attack and gravity are measured, and results from theory and experiment are compared. A dynamic perturbation analysis about a nonlinear static equilibrium is used to determine the small perturbation flutter boundary, which is compared to the experimentally determined flutter velocity and oscillation frequency. Time simulation is used to compute the LCO response. The results between the theory and experiment are in good agreement for static aeroelastic response, the onset of flutter, and dynamic LCO amplitude and frequency.

Nonlinear Aeroelasticity and Unsteady Aerodynamics

In this von Karman lecture, a subject is addressed whose foundations were significantly influenced by the work of Theodore von Karman. A classic paper by von Karman and Sears first considered the determination of aerodynamic forces on an airfoil undergoing general time-dependent motion. Also, early in his career, von Karman investigated fundamental issues in structural mechanics and derived the celebrated von Karman plate equations for determining the large (nonlinear) deflections of an elastic plate under a distributed force. Finally, he authored a widely cited paper on the importance of nonlinearities for engineers and engineering. In this lecture, these themes are recalled and the current state of the art in nonlinear aeroelasticity and unsteady aerodynamics is discussed. Several of the most significant nonlinearities arising in a structure or in an aerodynamic flow field are identified. Recent and relevant theoretical and experimental studies are reviewed and future developments are projected that are expected to have a significant impact on our ability to understand and beneficially use nonlinear dynamic aeroelastic behavior

Flutter and limit cycle oscillations of two-dimensional panels in three-dimensional axial flow

Abstract Experimental flutter and limit cycle oscillations (LCO) of two-dimensional elastic plates in three-dimensional axial flow were observed. The plate is clamped at its leading edge and free at its trailing edge, i.e., it is a “flag” albeit one dominated by its bending stiffness. In the companion theoretical model the structural nonlinearity arises in both the bending stiffness and the mass inertia. Aerodynamic nonlinearities are neglected, however, and linear three-dimensional incompressible vortex lattice aerodynamic theory and a corresponding reduced order aerodynamic model were used to calculate the linear flutter boundary and also the LCO (that occur beyond the linear flutter boundary). The results from the theory and experiment are in good agreement for the onset of flutter, including the critical flow velocity at which the aeroelastic system becomes unstable, as well as the aeroelastic mode of oscillation and frequency. However, there are significant differences between the present theory and experiment for large-amplitude LCO. It is hypothesized that aerodynamic nonlinearities (not modelled in the present theory) are the primary cause of these differences.

LIMIT CYCLE OSCILLATIONS OF DELTA WING MODELS IN LOW SUBSONIC FLOW

A nonlinear, aeroelastic analysis of a low aspect, delta wing modeled as a plate of constant thickness demonstrates that limit cycle oscillations (LCO) of the order of the plate thickness are possible. The structural nonlinearity arises from double bending in both the chordwise and spanwise directions. The present results using a vortex lattice aerodynamic model for a low Mach number flow complement earlier studies for rectangular wing platforms that showed similar qualitative results. The theoretical results for the flutter boundary (beyond which LCO occurs) have been validated by comparison to the experimental data reported by other investigators for low aspect ratio delta wings. Also the limit cycle oscillations found experimentally by previous investigators (but not previously quantified prior to the present work) are consistent with the theoretical results reported here. Reduced order aerodynamic and structural models are used to substantially decrease computational cost with no loss in accuracy. Without the use of reduced order models, calculations of the LCO would be impractical. A wind tunnel model is tested to provide a quantitative experimental correlation with the theoretical results for the LCO response itself.

Limit Cycle Oscillations of a Cantilevered Wing in Low Subsonic Flow

A nonlinear, aeroelastic analysis of a low-aspect, rectangular wing modeled as a plate of constant thickness demonstratesthatlimitcycleoscillationsoftheorderoftheplatethicknessarepossible.Thestructuralnonlinearity arisesfrom doublebendinginboth thechordwiseand spanwisedirections.Thepresentresultsusing a vortex lattice aerodynamic model for low-Mach-numbere owscomplementearlierstudiesforhigh supersonicspeed thatshowed similar qualitative results. Also, the theoretical results are consistent with experimental data reported by other investigators for low-aspect-ratio delta wings.

Experimental and Theoretical Study of Gust Response for High-Aspect-Ratio Wing

A nonlinear response analysis of a high-aspect-ratio wing aeroelastic model excited by gust loads is presented along with a companion wind-tunnel test program. For the wind-tunnel tests, a high-aspect-ratio wing aeroelastic experimental model with a slender body at the tip has been constructed, and a rotating slotted cylinder gust generator has been used to generate a gust excitation field. A LabVIEW 5.1 measurement and analysis system is used to measure the gust response, flutter boundary, and limit-cycle oscillation behavior. Structural equations of motion based on a nonlinear beam theory are combined with the ONERA aerodynamic stall model to study the effects of geometric structural nonlinearity and steady angle of attack on nonlinear gust response of high-aspect-ratio wings. Also a dynamic perturbation analysis about a nonlinear static equilibrium is used to determine the small perturbation flutter boundary. The fair to good quantitative agreement between theory and experiment demonstrates that the present analysis method has reasonable accuracy.

Dynamics of very high dimensional systems

Linear and Nonlinear Dynamics of the String - A Prototypical Example Convergence of a Modal Series Orthogonality Normal Forms for Kinetic and Potential Energy Component Modal Analysis Asymptotic Modal Analysis (AMA) Modelling of Acoustic-Structural Interaction: Acoustoelasticity Modelling of Fluid-Structural Interaction: Aeroelasticity Nonlinear Aeroelasticity and other topics.

System Identification and Proper Orthogonal Decomposition Method Applied to Unsteady Aerodynamics

The representation of unsteady aerodynamic e owe elds in terms of global aerodynamic modes has proven to be a useful method for reducing the size of the aerodynamic model over those representations that use local variables at discrete grid points in the e ow e eld. Eigenmodes and proper orthogonal decomposition modes have been used for this purpose with good effect. This suggests that system identie cation models may also be used to represent the aerodynamic e owe eld. Implicit in the use of a systems identie cation technique is the notion that a relative small state-space model can be useful in describing a dynamical system. The proper orthogonal decomposition model is e rst used to show that indeed a reduced-order model can be obtained from a much larger numerical aerodynamical model (the vortex lattice method is used for illustrative purposes ), and the results from the proper orthogonal decomposition model and the system identie cation methods are then compared. For the example considered the two methods are shown to give comparable results in terms of accuracy and reduced model size. Theadvantagesand limitationsofeachapproacharebriee y discussed.Both appearpromisingandcomplementary in their characteristics.

Reduced-Order Aerodynamic Model and Its Application to a Nonlinear Aeroelastic System

Starting from a finite state model for a two-dimensional aerodynamic flow over an airfoil, the eigen-modes of the aerodynamic flow are determined. Using a small number of these aerodynamic eigenmodes, i.e., a reduced-order model, the aeroelastic model is formed by coupling them to a typical section structural model with a trailing-edge flap. A free-play nonlinearity is modeled. Results are shown from the finite state model, the reduced-order model, and previous theoretical and experimental work. All results are in good agreement.

Aerodynamic Loading for an Airfoil with an Oscillating Gurney Flap

A study of aerodynamic loadings on a NACA 0012 airfoil with a static and an oscillating trailing-edge Gurney flap was made. The focus is on the experimental measurement of the static and dynamic-pressure distributions on the airfoil surface. The experimental results are also correlated with theoretical results obtained using the Navier-Stokes code INS2D, developed by NASA. A Reynolds number of 348,000, a flow velocity of 20 m/s (65.6 ft/s), and a reduced frequency from 0 to 0.4 based upon half-chord b and freestream velocity U are used. The experimental results show that the effect of the static and oscillating strips located near the trailing edge of the airfoil is to enhance the maximum lift and pitching-moment coefficients for both unstalled and stalled angles of attack. An increase of the oscillating frequency also enhances the aerodynamic loading. Reasonably good agreement between the experiment and theory is obtained. The experimental results confirm the idea that an oscillating small strip located near the trailing edge can be a useful tool for active aerodynamic flow control for a wing.