Hypersonic flutter analysis using measured static aerodynamic derivatives, and comparison with experiment
Measured static aerodynamic forces for hypersonic flutter analysis on airfoil models in helium flow
Goetz, R. C.↗
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Generalization of the subsonic kernel function in the s-plane, with applications to flutter analysis
A generalized subsonic unsteady aerodynamic kernel function, valid for both growing and decaying oscillatory motions, is developed and applied in a modified flutter analysis computer program to solve the boundaries of constant damping ratio as well as the flutter boundary. Rates of change of damping ratios with respect to dynamic pressure near flutter are substantially lower from the generalized-kernel-function calculations than from the conventional velocity-damping (V-g) calculation. A rational function approximation for aerodynamic forces used in control theory for s-plane analysis gave rather good agreement with kernel-function results, except for strongly damped motion at combinations of high (subsonic) Mach number and reduced frequency.
Cunningham, H. J.↗
A computational procedure for automated flutter analysis
A direct solution procedure for computing the flutter Mach number and the flutter frequency is applied to the aeroelastic analysis of propfans using an unsteady aerodynamic model based on a three-dimensional subsonic compressible lifting surface theory. An approximation to the Jacobian matrix that improves the efficiency of the iterative process is presented. The Jacobian matrix is indirectly approximated from approximate derivatives of the flutter matrix. Examples are used to illustrate the convergence properties. The direct solution procedure facilitates the automated flutter analysis in addition to contributing to the efficient use of computer time as well as the analyst's time.
Murthy, Durbha V.↗
A computational procedure for automated flutter analysis
A direct solution procedure for computing the flutter Mach number and the flutter frequency is applied to the aeroelastic analysis of propfans using a finite element structural model and an unsteady aerodynamic model based on a three-dimensional subsonic compressible lifting surface theory. An approximation to the Jacobian matrix that improves the efficiency of the iterative process is presented. The Jacobian matrix is indirectly approximated from approximate derivatives of the flutter matrix. Examples are used to illustrate the convergence properties. The direct solution procedure facilitates the automated flutter analysis in addition to contributing to the efficient use of computer time as well as the analyst's time.
Murthy, Durbha V.↗
A computational procedure for automated flutter analysis
A direct solution procedure for computing the flutter Mach number and the flutter frequency is applied to the aeroelastic analysis of propfans using a finite element structural model and an unsteady aerodynamic model based on a three-dimensional subsonic compressible lifting surface theory. An approximation to the Jacobian matrix that improves the efficiency of the iterative process is presented. The Jacobian matrix is indirectly approximated from approximate derivatives of the flutter matrix, which are updated only in the direction of the last move. Examples are used to illustrate the convergence properties. The direct solution procedure facilitates the automated flutter analysis in addition to contributing to the efficient use of computer time as well as the analyst's time.
Murthy, Durbha V.↗
Flutter analysis of swept-wing subsonic aircraft with parameter studies of composite wings
A computer program is presented for the flutter analysis, including the effects of rigid-body roll, pitch, and plunge of swept-wing subsonic aircraft with a flexible fuselage and engines mounted on flexible pylons. The program utilizes a direct flutter solution in which the flutter determinant is derived by using finite differences, and the root locus branches of the determinant are searched for the lowest flutter speed. In addition, a preprocessing subroutine is included which evaluates the variable bending and twisting stiffness properties of the wing by using a laminated, balanced ply, filamentary composite plate theory. The program has been substantiated by comparisons with existing flutter solutions. The program has been applied to parameter studies which examine the effect of filament orientation upon the flutter behavior of wings belonging to the following three classes: wings having different angles of sweep, wings having different mass ratios, and wings having variable skin thicknesses. These studies demonstrated that the program can perform a complete parameter study in one computer run. The program is designed to detect abrupt changes in the lowest flutter speed and mode shape as the parameters are varied.
Housner, J. M.↗
State-space formulations for flutter analysis
Various methods are presented and assessed for approximating the aerodynamic forces so that the State Space formulation and off-the-imaginary axis analysis are retained. The advantages of retaining these features are considerable, not only in simplifying the flutter analysis, but especially for more advanced applications such as optimal design of active control in which the flutter is merely a constraint to the optimization problem.
Weiss, S. J.↗
Developing Uncertainty Models for Robust Flutter Analysis Using Ground Vibration Test Data
A ground vibration test can be used to obtain information about structural dynamics that is important for flutter analysis. Traditionally, this information#such as natural frequencies of modes#is used to update analytical models used to predict flutter speeds. The ground vibration test can also be used to obtain uncertainty models, such as natural frequencies and their associated variations, that can update analytical models for the purpose of predicting robust flutter speeds. Analyzing test data using the -norm, rather than the traditional 2-norm, is shown to lead to a minimum-size uncertainty description and, consequently, a least-conservative robust flutter speed. This approach is demonstrated using ground vibration test data for the Aerostructures Test Wing. Different norms are used to formulate uncertainty models and their associated robust flutter speeds to evaluate which norm is least conservative.
Potter, Starr↗
Flutter analysis of supersonic axial flow cascades using a high resolution Euler solver. Part 1: Formulation and validation
This report presents, in two parts, a dynamic aeroelastic stability (flutter) analysis of a cascade of blades in supersonic axial flow. Each blade of the cascade is modeled as a typical section having pitching and plunging degrees of freedom. Aerodynamic forces are obtained from a time accurate, unsteady, two-dimensional cascade solver based on the Euler equations. The solver uses a time marching flux-difference splitting (FDS) scheme. Flutter stability is analyzed in the frequency domain. The unsteady force coefficients required in the analysis are obtained by harmonically oscillating (HO) the blades for a given flow condition, oscillation frequency, and interblade phase angle. The calculated time history of the forces is then Fourier decomposed to give the required unsteady force coefficients. An influence coefficient (IC) method and a pulse response (PR) method are also implemented to reduce the computational time for the calculation of the unsteady force coefficients for any phase angle and oscillation frequency. Part 1, this report, presents these analysis methods and their validation by comparison with results obtained from linear theory for a selected flat plate cascade geometry. A typical calculation for a rotor airfoil is also included to show the applicability of the present solver for airfoil configurations. The predicted unsteady aerodynamic forces for a selected flat plate cascade geometry and flow conditions correlated well with those obtained from linear theory for different interblade phase angles and oscillation frequencies. All the three methods of predicting unsteady force coefficients, namely, HO, IC, and PR, showed good correlations with each other. It was established that only a single calculation with four blade passages is required to calculate the aerodynamic forces for any phase angle for a cascade consisting of any number of blades, for any value of the oscillation frequency. Flutter results, including mistuning effects, for a cascade of stator airfoils are presented in Part 2 of the report.
Reddy, T. S. R.↗
Flutter analysis of a transport wing using XTRAN3S
As part of the continuing process of evaluating and validating the XTRAN3S unsteady transonic aerodynamic computer program, the code has been applied to the flutter analysis of a transport type wing. The configuration analyzed was an aspect ratio 8 wing with a taper ratio of 0.4, a quarter chord sweep of 20 degrees and a NACA 65A-012 airfoil section. The analytical results compare well with the experimental flutter boundary and exhibit the classical 'transonic dip'. A literature search of available transport wing transonic flutter data is included.
Myers, M. R.↗
Flap-lag-torsion flutter analysis of a constant life rotor
The constant lift rotor (CLR) employs a control input of pitch moment to several airfoil sections which are free to pivot on a continuous spar, allowing them to change their pitch to obtain the desired lift. A flap-lag-torsion flutter analysis of a constant lift rotor blade in hover was developed. The blade model assumes rigid body flap and lead-lag motions at the root hinge and each strip undergoes an independent torsional motion. The results are presented in terms of root locus plots of complex eigenvalues as a function of thrust. The effects of several parameters (including structural damping, center of gravity and elastic axis offset from aerodynamic center, compressibility pitch-lag and pitch-flap coupling) on the blade dynamics are examined. With a suitable combination of lag damper and pitch-flap coupling, it is possible to design a constant lift rotor blade free from flutter instability.
Chopra, I.↗
Flutter analysis of advanced turbopropellers
The two-dimensional subsonic cascade unsteady aerodynamic theory of Jones and Rao (1975) has been modified to account for the variable sweep angles of the blades of advanced turbopropellers. The aerodynamics and the structural modal properties have been formally integrated to determine the generalized aerodynamic coefficients matrix for the blade modes. Modal flutter analysis has been conducted for two SR-5 five- and ten-blade propellers, and analytical results have been found to be in very good agreement with wind tunnel test data.
Elchuri, V.↗
Computer program for supersonic Kernel-function flutter analysis of thin lifting surfaces
This report describes a computer program (program D2180) that has been prepared to implement the analysis described in (N71-10866) for calculating the aerodynamic forces on a class of harmonically oscillating planar lifting surfaces in supersonic potential flow. The planforms treated are the delta and modified-delta (arrowhead) planforms with subsonic leading and supersonic trailing edges, and (essentially) pointed tips. The resulting aerodynamic forces are applied in a Galerkin modal flutter analysis. The required input data are the flow and planform parameters including deflection-mode data, modal frequencies, and generalized masses.
Cunningham, H. J.↗
Time domain flutter analysis of cascades using a full-potential solver
A time domain approach is used to determine the dynamic aeroelastic stability of a cascade of blades. The structural model for each blade is a typical section with two degrees of freedom. The aerodynamic model is the unsteady, two-dimensional, full-potential flow through the cascade of airfoils. The unsteady equations of motion for the structure and the fluid are integrated simultaneously in time starting with the steady flowfield and a small initial disturbance applied to the airfoils. The motion of each blade is analyzed to determine the aeroelastic stability of the cascade. The effect of interblade phase angle is included in the analysis by allowing each blade to have an independent motion and considering a number of blade passages. Calculations are made using an airfoil section and structural parameters that are representative of a propfan. The results are compared with those from a separate frequency domain analysis. Good agreement between the results is observed. With the time domain approach, it is possible to consider nonlinear structural models and nonlinear force-displacement relations. The method allows a realistic simulation of the motion of the fluid and the cascade blades for a better physical understanding and it also has the potential for saving computational time when compared to the frequency domain approach for the flutter analysis of cascades.
Bakhle, Milind A.↗
Panel-flutter analysis of a thermal protection-shield concept for the space shuttle.
Analysis of the panel flutter characteristics of a candidate thermal protection system (TPS) for the space shuttle, using piston theory aerodynamics and Lagrange equations. The results show the TPS candidate panel array to be deep in the 'no-flutter' region during launch and, therefore, safe from panel flutter.
Cunningham, H. J.↗
New Flutter Analysis Technique for Time-Domain Computational Aeroelasticity
A new time-domain approach for computing flutter speed is presented. Based on the time-history result of aeroelastic simulation, the unknown unsteady aerodynamics model is estimated using a system identification technique. The full aeroelastic model is generated via coupling the estimated unsteady aerodynamic model with the known linear structure model. The critical dynamic pressure is computed and used in the subsequent simulation until the convergence of the critical dynamic pressure is achieved. The proposed method is applied to a benchmark cantilevered rectangular wing.
HWB aircraft↗
Flutter Analysis for Turbomachinery Using Volterra Series
The objective of this paper is to describe an accurate and efficient reduced order modeling method for aeroelastic (AE) analysis and for determining the flutter boundary. Without losing accuracy, we develop a reduced order model based on the Volterra series to achieve significant savings in computational cost. The aerodynamic force is provided by a high-fidelity solution from the Reynolds-averaged Navier-Stokes (RANS) equations; the structural mode shapes are determined from the finite element analysis. The fluid-structure coupling is then modeled by the state-space formulation with the structural displacement as input and the aerodynamic force as output, which in turn acts as an external force to the aeroelastic displacement equation for providing the structural deformation. NASA's rotor 67 blade is used to study its aeroelastic characteristics under the designated operating condition. First, the CFD results are validated against measured data available for the steady state condition. Then, the accuracy of the developed reduced order model is compared with the full-order solutions. Finally the aeroelastic solutions of the blade are computed and a flutter boundary is identified, suggesting that the rotor, with the material property chosen for the study, is structurally stable at the operating condition, free of encountering flutter.
computational fluid dynamics↗
Modern wing flutter analysis by computational fluid dynamics methods
The application and assessment of the recently developed CAP-TSD transonic small-disturbance code for flutter prediction is described. The CAP-TSD code has been developed for aeroelastic analysis of complete aircraft configurations and was previously applied to the calculation of steady and unsteady pressures with favorable results. Generalized aerodynamic forces and flutter characteristics are calculated and compared with linear theory results and with experimental data for a 45 deg sweptback wing. These results are in good agreement with the experimental flutter data which is the first step toward validating CAP-TSD for general transonic aeroelastic applications. The paper presents these results and comparisons along with general remarks regarding modern wing flutter analysis by computational fluid dynamics methods.
Cunningham, Herbert J.↗