Daniella E. Raveh

Reduced-order models for nonlinear unsteady aerodynamics

Two reduced-order modeling approaches for the evaluation of nonlinear aerodynamic forces based on CFD computations are presented. These reducedorder models (ROMs) provide a means for rapid calculation of frequency-domain generalized aerodynamic forces, which can be used in traditional flutter analysis scheme, to calculate flutter characteristics about nonlinear steady flows. Two ROMs are presented, one that is based on the Volterra theory for nonlinear systems, and a new ROM that is based on step (indicial) responses. ROM kernels are identified directly from input-output relations, and the study focuses on issues of kernel identification and their effect on the quality of the ROM. First- and second-order ROMs are generated for the response of the AGARD 445.6 wing to forced-harmon ic excitation of its elastic modes. Responses computed from the ROMs are compared to responses obtained directly from a CFD analysis in which the boundary conditions are excited harmonically. Results show that the quality of the Volterra ROM is very sensitive to the amplitudes of the impulse inputs used for identification. The step-response ROM is shown to be more accurate than the Volterra ROM and less sensitive to the amplitude used for its identification.

Fictitious Mass Element in Structural Dynamics

Fictitious masses are used to improve the accuracy and efficiency of modal-based structural analyses that involve substructure synthesis, local excitation, and local structural changes. New formulations, which allow easy applications in various subsequent analyses, are given for two categories of fictitious masses : regular and very large. Regular masses are of the order of entire substructures, whereas very large ones are several orders of magnitude larger. The regular fictitious masses are added to selected coordinates of the finite element model for normal-mode analysis, and then removed in a way that produces modes with local deformations near the selected points, in addition to the nominal natural vibration modes. Subsequent analyses of local nature can then be performed in the standard way. Very large masses are used to generate static constraint modes for fixed-boundary modal coupling, and broken modes are used for representing rigid-body relative motion between structural segments with application to loads analysis. The inclusion of fictitious masses as optional elements in standard structural dynamic procedures is facilitated.

Numerical Simulation and Reduced-Order Modeling of Airfoil Gust Response

I. Abstract Computational Fluid Dynamics (CFD) based simulations, along with parametric and non-parametric Reduced-Order Models (ROM) for gust responses are presented. A CFD code is enhanced to simulate responses of an airfoil to arbitrary shaped gust inputs. Time-domain Auto-Regressive-Moving-Average (ARMA) models are identified based on CFD responses to random gust excitations, using system-identification methods. Responses to discrete gusts of various shapes, amplitudes and gradient lengths are computed via the ROMs and compared to responses simulated directly by the CFD code. The ROMs predict the lift and pitching moment histories accurately throughout the subsonic and transonic regimes. They offer significant savings in computational resources compared to the full CFD simulation, since only one CFD run is required for ROM identification, from which responses to arbitrary shaped gusts can be rapidly estimated. The combination of ROMs and full CFD simulations offers a computationally efficient tool set of various-fidelity time-domain models for gust responses. The ROMs can be used for rapid tuned-gust analyses, and the critical cases can be simulated with a full CFD run, providing pressure distribution for airframe structural design.

Identification of Computational-Fluid-Dynamics Based Unsteady Aerodynamic Models for Aeroelastic Analysis

Three approaches for reduced-order modeling of computational-fluid-dynamics-(CFD) based unsteady aerodynamics, employing system-identification methods, are presented, and used for generation of three models: A frequency-domain model, a time-domain autoregressive-moving-average model, and a discrete-time state-space model. All models are identified based on the same identification data, which consists of the time histories of the generalized aerodynamic forces developed in response to filtered white-Gaussian-noise modal excitation, computed in a CFD analysis. The models are used for rapid flutter analysis via traditional frequency-domain methods, linear stability analysis, and time simulation. The method is applied for flutter analysis of the AGARD 445.6 wing. The filtered white-Gaussian-noise input is found to be applicable within the framework of CFD, yielding informative identification data sets. The identification process is simple, and the resulting reduced-order models closely reproduce the CFD system response to various excitations. Reduced-order model-based flutter analysis is rapid and yields accurate results compared with wind-tunnel test, CFD, and linear aerodynamics results.

Maneuver Trim Optimization Techniques for Active Aeroelastic Wings

Presented at the 41st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference and Exhibit, Atlanta, GA, April 3-6, 2000.

Structural optimization using computational aerodynamics

A recently developed methodology for aircraft structural design, based on nonlinear airloads, is extended to include a modal-based optimization option and is employed with a new computational aerodynamics code for loads analysis. Nonlinear maneuver loads are evaluated by a computational scheme that efficiently combines fluid dynamics iterations with iterations for elastic shape deformations and trim corrections. An efficient design process is obtained by performing several structural optimization runs during one maneuver load analysis, where each optimization is based on the interim nonconverged airloads. To allow for the efficient application of the method with large finite element structural models and many constraints, the discrete-coordinate optimization scheme is replaced by a modal-based optimization where a set of low-frequency vibration modes of the baseline structure is used to represent the structure throughout the optimization, both for response analysis and for sensitivity analysis. Comparative modal-based and discrete-coordinate design cases are shown to converge to the same optimal design variable values, even though they do not follow the same path. Two flow solvers are used, one of which is a newly developed Euler/Navier-Stokes computational aerodynamics code that is capable of handling complex geometries by using the Chimera overset grid method. The method avoids the problem of mesh discontinuities due to elastic shape deformations and control surface deflections because the displacements of each component affect only the components mesh. The method is demonstrated with a wing-fuselage-elevator transport aircraft model performing symmetric and antisymmetric maneuvers at Mach 0.85.

Reynolds-Averaged Navier-Stokes Study of the Shock-Buffet Instability Mechanism

A study of shock-buffet onset and instability mechanism via Reynolds-averaged Navier―Stokes simulations on several airfoils is presented. The numerical setup and the Spalart―AUmaras turbulence closure are validated based on wind-tunnel data from NACA 0012 and RA16SC1 airfoils. The paper presents simulations of the flow past three • airfoils: the subsonic NACA 0012, the supercritical RA16SC1, and the thin, transonic/supersonic NACA 64A204, at pre- and postbuffet conditions, and within a cycle of developed shock buffet. The shock-buffet cycle is found to be »■• similar in nature for all airfoils, originating in unstable interaction of the shock and the separation bubble. Simulation results support the notion that buffet onset is not related to the bursting of the separation bubble behind the shock. Shock-buffet categorizing is posited as a transonic prestall instability phenomenon that depends on the shock strength and location. Shock-buffet onset conditions occur when the shock position is behind and sufficiently close to the upper-surface maximum curvature location. Additionally, it is suggested that offset conditions are when the shock is at an upstream location and the flow aft of it is fully separated.

Efficient aeroelastic analysis using computational unsteady aerodynamics

A methodology for efe cient evaluation of generalized aerodynamic forces (GAFs) in transonic e ows for use in e utter analysis is presented. GAF matrices are evaluated from a reduced-order model (ROM), which comprises the generalized aerodynamic forces recorded from a time-accurate computational e uid dynamics (CFD) analysis in response to a modal step excitation in each structural mode. With the step response database, that is, the ROM, the comprehensive CFD analysis is replaced by a simple convolution scheme to compute the GAFs. The forces due to excitation of one mode at a given Mach number for all reduced frequencies can be computed from a single step response. Comparison of the GAFs computed from the ROM to those computed by direct sinusoidal excitation of the boundary conditions in a CFD run demonstrate, that for small amplitudes of excitation, the ROM is capable of predicting the unsteady aerodynamic forces very accurately. The use of ROM offers a signie cant reduction in computational time and makes the calculation of CFD-based unsteady aerodynamic forces for e utter analysis feasible. The CFD-based GAFs are used to conduct a e utter analysis of the AGARD 445.6 wing at several Mach numbers, and the results are compared to wind tunnel test results.

Numerical Study of an Oscillating Airfoil in Transonic Buffeting Flows

Numerical simulations are conducted to compute the aerodynamic flowfield response that is observed for a NACA0012 airfoil that undergoes prescribed harmonic oscillation at transonic Mach numbers. Large shock oscillations are observed for certain combinations of Mach number and steady mean angle of attack. These are termed as buffet in this paper. Prescribing an airfoil oscillation about the buffeting flowfield reveals a nonlinear interaction between the flowfields induced by the buffet and airfoil motion, respectively. At low airfoil-oscillation amplitudes, the time histories of the aerodynamic coefficients exhibit two frequencies, that of the buffet and that of the oscillating airfoil. As the airfoil amplitude increases, the flowfield response at the buffet frequency decreases. Beyond a certain level of airfoil amplitude, lock-in occurs: the flowfield response at the buffet frequency vanishes, and the flow system response predominantly assumes the frequency of the airfoil motion. The airfoil amplitude that will cause lock-in is dependent on the ratio between the frequency of the airfoil oscillation and the buffet frequency. The closer these frequencies are, the smaller the airfoil-oscillation amplitude that will cause lock-in. There is a broad analogy between this flow phenomenon and the flowfield of the von Karman vortex street found behind a cylinder with the cylinder undergoing a prescribed oscillation. This paper reviews that phenomenon, suggests an aerodynamic gain-phase model for the lock-in region, and suggests a possible relation between this flow mechanism and limit-cycle oscillation.

Application of Active-Aeroelastic-Wing Technology to a Joined-Wing Sensorcraft

A study was conducted to investigate the applicability of active-aeroelastic-wing technology to a joined-wing sensorcraft configuration for the purpose of minimization of embedded antenna deformations. The study was performed using a half-span aeroelastic model of a joined-wing sensorcraft design with six control surfaces. These control surfaces were used concurrently to minimize the elastic deformations at structural nodes corresponding to the antenna tip, while trimming the aircraft to a required 1-g level flight, simultaneously satisfying constraints on the allowable hinge moments and maximum control surface deflections. Comparison of antenna displacements for the optimized and baseline cases (using one control surface at a time) demonstrates that the active-aeroelastic-wing concept can be used to significantly reduce the antenna displacements, potentially improving the performance of the embedded antenna system. Aeroelastic displacements from the trim-optimized system are an order-of-magnitude smaller than those of the baseline. These results demonstrate the feasibility of active-aeroelastic-wing technology for the improvement of embedded antenna performance caused by structural deformations.