TRANSONIC AEROELASTIC STABILITY AND RESPONSE OF CONVENTIONAL AND SUPERCRITICAL AIRFOILS INCLUDING ACTIVE CONTROLS

JOHN TERENCE BATINA, Purdue University

Abstract

Transonic aeroelastic stability and response analyses are performed for two conventional airfoils, NACA 64A006 and NACA 64A010, and one supercritical airfoil, MBB A-3. Three d.o.f.'s are considered: plunge, pitch, and aileron pitch. A set of aeroelastic parameters are selected for which the flutter speeds are near the bottom of a transonic dip. A Pade state-space aeroelastic model is formulated using generalized aerodynamic forces approximated by an interpolating function in the variable s. The coefficient matrices of this function are determined by a least-squares curve fit of harmonic transonic aerodynamic data. Three sets of aerodynamic data are computed using three different transonic computational codes (LTRAN2-NLR, LTRAN2-HI, and USTS) for comparison purposes. In general, the Pade interpolating function provides a good approximation of the unsteady aerodynamic coefficients predicted by the transonic codes. The state-space aeroelastic model, formulated by using the Pade interpolating function, results in a set of linear, first-order, constant coefficient, differential equations. These equations are solved in the Laplace domain with the resulting eigenvalues plotted in a "root-locus" type format. Alternatively, the Pade model is solved in the time-domain yielding the aeroelastic time-response histories. As verification of the Pade results, parallel time-marching response calculations are carried out by simultaneously integrating the structural equations of motion along with the unsteady aerodynamic forces of transonic code LTRAN2-NLR. Time-marching and Pade responses are in good agreement, thus demonstrating the ability of the Pade equations to accurately model the aeroelastic system. A modal identification technique is used to identify the aeroelastic modes from the time-marching response curves. Damping and frequency of these estimated modes agree well with Pade model eigenvalues. Stability and response analyses including active controls are performed by adding a simple, constant gain, partial feedback, control law to the aeroelastic equations of motion. Control laws utilizing displacement, velocity, and acceleration sensing are considered. Aeroelastic effects due to a variety of control gains are studied.

Degree

Ph.D.

Subject Area

Aerospace materials

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