Showing papers by "Earl H. Dowell published in 2001"

Modeling of Fluid-Structure Interaction

Abstract: ▪ Abstract The interaction of a flexible structure with a flowing fluid in which it is submersed or by which it is surrounded gives rise to a rich variety of physical phenomena with applications in many fields of engineering, for example, the stability and response of aircraft wings, the flow of blood through arteries, the response of bridges and tall buildings to winds, the vibration of turbine and compressor blades, and the oscillation of heat exchangers. To understand these phenomena we need to model both the structure and the fluid. However, in keeping with the overall theme of this volume, the emphasis here is on the fluid models. Also, the applications are largely drawn from aerospace engineering although the methods and fundamental physical phenomena have much wider applications. In the present article, we emphasize recent developments and future challenges. To provide a context for these, the article begins with a description of the various physical models for a fluid undergoing time-dependent mot...

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

Abstract: 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

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

Abstract: 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.

System Identification and Proper Orthogonal Decomposition Method Applied to Unsteady Aerodynamics

Abstract: 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.

Effects of Angle of Attack on Nonlinear Flutter of a Delta Wing

Abstract: Limit cycle oscillations (LCOs) have been observed in flight for certain modern high-performance aircraft. The nonlinear physical mechanism responsible for the LCOs is still in doubt, even to the point of it not yet being determined whether the nonlinearity is principally in the flexible elastic structure of the aircraft or due to the fluid behavior in the surrounding aerodynamic flowfield. One observation from flight tests is that by changing the angle of attack of aircraft, the flight velocity at which LCOs begin may be raised or lowered and that the amplitude of the LCOs may be reduced. It has been suggested that this sensitivity to angle of attack indicates the nonlinearity is in the fluid rather than in the structure. We show that such effects of an angle of attack change can be the result of a structural nonlinearity. Specifically, an investigation to determine the effects of a steady angle of attack on nonlinear flutter and LCO of a delta wing-plate model in low subsonic flow has been made. A three-dimensional time domain vortex lattice aerodynamic model and a reduced order aerodynamic technique were used, and the structure is modeled using von Karman plate theory that allows for geometric strain-displacement nonlinearities in the delta wing structure. The results provide new insights into nonlinear aeroelastic phenomena not previously widely appreciated, i.e., LCOs for low aspect ratio wings that have a platelike nonlinear structural behavior. The effects of a steady angle of attack on both the flutter boundary and the LCOs are found to be significant. For a small steady angle of attack, α 0 ≤ 0.1 deg, the flutter onset velocity increases, whereas for larger α 0 , it decreases. Moreover, as α 0 increases, the maximum LCO amplitude decreases substantially. Such effects have been observed by Bunton and Denegri in flight flutter experiments. It is noted that the present theoretical results do not prove that the LCOs phenomena observed in flight are due to structural nonlinearities; however, the results of the present analysis are consistent with those observed in flight and do show that a structural nonlinearity can give rise to the observed effects of angle of attack on the LCOs.

A Parametric Analysis of Reduced Order Models of Potential Flows in Turbomachinery Using Proper Orthogonal Decomposition

Abstract: An unsteady inviscid flow through a cascade of oscillating airfoils is investigated. An inviscid nonlinear subsonic and transonic model is used to compute the steady flow solution. Then a small amplitude motion of the airfoils about their steady flow configuration is considered. The unsteady flow is linearized about the nonlinear steady response based on the observation that in many practical cases the unsteadiness in the flow has a substantially smaller magnitude than the steady component. Several reduced order modal models are constructed in the frequency domain using the proper orthogonal decomposition technique. The dependency of the required number of aerodynamic modes in a reduced order model on the far-field upstream Mach number is investigated. It is shown that the transonic reduced order models require a larger number of modes than the subsonic models for a similar geometry, range of reduced frequencies and interblade phase angles. The increased number of modes may be due to the increased Mach number per se, or the presence of the strong spatial gradients in the region of the shock. These two possible causes are investigated. Also, the geometry of the cascade is shown to influence strongly the shape of the aerodynamic modes, but only weakly the required dimension of the reduced order models.Copyright © 2001 by ASME

Transonic limit cycle oscillation analysis using reduced order aerodynamic models

Abstract: Limit cycle oscillations have been observed in flight operations of modern aircraft, wind tunnel experiments and mathematical models. Both fluid and structural nonlinearities are thought to contribute to these phenomena. With recent advances in reduced order aerodynamic modeling, it is now feasible to analyze limit cycle oscillations that may occur in transonic flow including the effects of structural and fluid nonlinearities. In this paper an airfoil with control surface freeplay (a common structural nonlinearity) is used to investigate transonic flutter and limit cycle oscillations. The reduced order aerodynamic model used in this paper assumes the shock motion is small and in proportion to the structural motions.

Mathematical model of a nanopaddle oscillator

Abstract: A model of a nanopaddle oscillator is developed to determine the resonant frequency (or the modulus of elasticity by inference from a measurement of the resonant frequency). Also modeled is the nonlinear stiffness of the oscillator and its nonlinear response. The approach is based upon a modal expansion of the elastic deformation of the oscillator and a Lagrangian representation. A comparison with recent work by other investigators is made and it appears the present model may help resolve a question about the modulus of elasticity to be inferred from such models.

System Identification and Pod Method Applied to Unsteady Aerodynamics

Abstract: The representation of unsteady aerodynamic flow fields 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 flow field. Eigenmodes and Proper Orthogonal Decomposition (POD) modes have been used for this purpose with good effect. This suggests that system identification models may also be used to represent the aerodynamic flow field. Implicit in the use of a systems identification technique is the notion that a relative small state space model can be useful in describing a dynamical system. The POD model is first 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 POD and the system identification 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. The advantages and limitations of each approach are briefly discussed. Both appear promising and complementary in their characteristics.

Characterizing Aeroelastic Systems Using Eigenanalysis, Explicitly Retaining The Aerodynamic Degrees of Freedom

Abstract: Discrete time aeroelastic models with explicitly retained aerodynamic modes have been generated employing a time marching vortex lattice aerodynamic model This paper presents analytical results from eigenanalysis of these models The potential of these models to calculate the behavior of modes that represent damped system motion (noncritical modes) in addition to the simple harmonic modes is explored A typical section with only structural freedom in pitch is examined The eigenvalues are examined and compared to experimental data Issues regarding the convergence of the solution with regard to refining the aerodynamic discretization are investigated Eigenvector behavior is examined; the eigenvector associated with a particular eigenvalue can be viewed as the set of modal participation factors for that particular mode For the present formulation of the equations of motion, the vorticity for each aerodynamic element appears explicitly as an element of each eigenvector in addition to the structural dynamic generalized coordinates Thus, modal participation of the aerodynamic degrees of freedom can be assessed in M addition to participation of structural degrees of freedom

Characterizing aeroelastic systems using eigenanalysis, explicitly retaining the aerodynamic degrees of freedom

Abstract: Discrete time aeroelastic models with explicitly retained aerodynamic modes have been generated employing a time marching vortex lattice aerodynamic model. This paper presents analytical results from eigenanalysis of these models. The potential of these models to calculate the behavior of modes that represent damped system motion (noncritical modes) in addition to the simple harmonic modes is explored. A typical section with only structural freedom in pitch is examined. The eigenvalues are examined and compared to experimental data. Issues regarding the convergence of the solution with regard to refining the aerodynamic discretization are investigated. Eigenvector behavior is examined; the eigenvector associated with a particular eigenvalue can be viewed as the set of modal participation factors for that particular mode. For the present formulation of the equations of motion, the vorticity for each aerodynamic element appears explicitly as an element of each eigenvector in addition to the structural dynamic generalized coordinates. Thus, modal participation of the aerodynamic degrees of freedom can be assessed in M addition to participation of structural degrees of freedom.

Nonlinear inviscid aerodynamic effects on transonic divergence, flutter and limit cycle oscillations

Abstract: By the use of a state-of-the-art computational e uid dynamic (CFD) method to model nonlinear steady and unsteady transonice owsin conjunction with a linearstructural model,an investigationismadeinto how nonlinear aerodynamics can effect the divergence, e utter, and limit-cycle oscillation (LCO) characteristics of a transonic airfoil cone guration. A single-degree-of-freedom (DOF) model is studied for divergence, and one- and two-DOF models are studied for e utter and LCO. A harmonicbalancemethod in conjunction with the CFD solver is used to determine the aerodynamics for e nite amplitude unsteady excitations of a prescribed frequency. A procedure for determining the LCO solution is also presented. For the cone guration investigated, nonlinear aerodynamic effects are found to produce a favorable transonic divergence trend and unstable and stable LCO solutions, respectively, for the one- and two-DOF e utter models. Nomenclature a = nondimensional location of airfoil elastic axis, e=b b, c = semichord and chord, respectively cl, cm = coefe cients of lift and moment about elastic axis, respectively e = location of airfoil elastic axis, measured positive aft of airfoil midchord h, ® = airfoil plunge and pitch degrees of freedom I® = second moment of inertia of airfoil about elastic axis