Transonic aeroelasticity analysis using state-space unsteady aerodynamic modeling

An aeroelastic analysis is conducted on a two-degree-of-freedom airfoil in transonic flow using a generalized state-space approximation for the unsteady aerodynamics. The aerodynamic representation is validated against computational fluid dynamic solutions for angle of attack oscillations up to Mach numbers of 0.875 and at reduced frequencies up to 1.0. Despite the inherent nonlinear nature of transonic flow, it is shown that a linear finite-state model with as few as eight states can provide a good approximation to the unsteady lift and moment behavior if appropriate allowance is made for Mach number effects on the airfoil's static lift curve slope and mean aerodynamic center. It is shown how the aerodynamic representation can be coupled to the structural equations of a typical airfoil section with bending and torsional degrees of freedom. The stability of the resulting aeroelastic system is determined by eigenanalysis. This aeroelastic analysis is shown to be in excellent agreement with calculations performed using more sophisticated unsteady aerodynamic theories.

[1]  H. Ashley,et al.  Unsteady aerodynamic modeling for arbitrary motions , 1977 .

[2]  T Y Yang,et al.  Flutter and Time Response Analyses of Three Degree of Freedom Airfoils in Transonic Flow , 1981 .

[3]  Mordechay Karpel.  Design for Active Flutter Suppression and Gust Alleviation Using State-Space Aeroelastic Modeling , 1982 .

[4]  D. Rizzetta,et al.  Time-Dependent Response of a Two-Dimensional Airfoil in Transonic Flow , 1979 .

[5]  B.H.K. Lee.  A Study of Transonic Flutter of a Two-Dimensional Airfoil Using the U-g and p-k Methods (Une Etude sur les Vibrations Aeroelastiques en Regime Transsonique d'Un Profil Aerodynamique Bidimensionnel au Moyen des Methodes U-g et p-k) , 1984 .

[6]  Koji Isogai,et al.  Numerical Study of Transonic Flutter of A Two-dimensional Airfoil , 1980 .

[7]  T. Yang,et al.  Aeroelastic time response analysis of thin airfoils by transonic code LTRAN2 , 1981 .

[8]  S. R. Bland,et al.  Linear/nonlinear behavior in unsteady transonic aerodynamics , 1983 .

[9]  T Y Yang,et al.  Flutter analysis of a NACA 64A006 airfoil in small disturbance transonic flow , 1980 .

[10]  Bernard Mazelsky.  On the Noncirculatory Flow About a Two-Dimensional Airfoil at Subsonic Speeds , 1952 .

[11]  J. Leishman.  Validation of approximate indicial aerodynamic functions for two-dimensional subsonic flow , 1988 .

[12]  Herbert Wagner.  Über die Entstehung des dynamischen Auftriebes von Tragflügeln , 1925 .

[13]  R. T. Jones.  The unsteady lift of a wing of finite aspect ratio , 1940 .

[14]  Earl H. Dowell,et al.  Flutter Analysis Using Nonlinear Aerodynamic Forces , 1984 .

[15]  Robert M. Bennett,et al.  Time-marching transonic flutter solutions including angle-of-attack effects , 1983 .

[17]  P. Goorjian,et al.  Computation of Unsteady Transonic Flows by the Indicial Method , 1977 .

[18]  J. Leishman,et al.  State-space representation of unsteady airfoil behavior , 1990 .

[19]  Louis S. Stivers.  Effects of subsonic Mach number on the forces and pressure distributions on four NACA 64A-series airfoil sections at angles of attack as high as 28 degrees , 1954 .

[20]  T. Theodorsen.  General Theory of Aerodynamic Instability and the Mechanism of Flutter , 1934 .