Continuation Method for Calculation of Transonic Airfoil Flutter Boundaries

Flutter boundaries, through variations in aerodynamic and structural dynamic parameters, are computed for a NACA 64A006 airfoil at transonic freestream Mach numbers with pitch-and-plunge structural coupling. These e utter boundaries are obtained with a new continuation algorithm that specie cally accounts for e utter onset. The algorithm, which is based on pseudoarclength continuation, solves an extended form of the Euler equations for the reduced velocity at e utter onset, the corresponding base-e ow solution, the destabilizing mode at e utter onset, and thecritical valueofa secondarystructural parameter, e.g., structural damping. Thealgorithm providesa relatively automated procedure for computing e utter boundaries directly, which avoids a trial-and-error, e utter-detection process typical of time-domain techniques. The current method is validated through comparison with independent e utter-boundary computations. Grid-sensitivity studies are carried out to assess the numerical accuracy of computed solutions.

[1]  Scott A. Morton,et al.  A continuation method for the calculation of airfoil flutter boundaries , 1997 .

[2]  Scott A. Morton,et al.  Nonlinear Analysis of Airfoil Flutter at Transonic Speeds. , 1995 .

[3]  John W. Edwards,et al.  Transonic Shock Oscillations and Wing Flutter Calculated with an Interactive Boundary Layer Coupling Method , 1996 .

[4]  Earl H. Dowell,et al.  Eigenmode analysis in unsteady aerodynamics - Reduced-order models , 1995 .

[5]  John W. Edwards,et al.  Current status of computational methods for transonic unsteady aerodynamics and aeroelastic applications , 1992 .

[6]  Andreas Griewank,et al.  The Calculation of Hopf Points by a Direct Method , 1983 .

[7]  Philip Beran,et al.  Domain-decomposition methods for bifurcation analysis , 1997 .

[8]  Lakshmi N. Sankar,et al.  A technique for the prediction of airfoil flutter characteristics inseparated flow , 1987 .

[9]  H. C. Yee,et al.  A class of high resolution explicit and implicit shock-capturing methods , 1989 .

[10]  C. P. Jackson.  A finite-element study of the onset of vortex shedding in flow past variously shaped bodies , 1987, Journal of Fluid Mechanics.

[11]  Timothy J. Barth,et al.  Description of a Hyperbolic Grid Generating Procedure for Arbitrary Two-Dimensional Bodies , 1984 .

[12]  Herbert B. Keller.  Continuation Methods in Computational Fluid Dynamics , 1982 .

[13]  K. K. Gupta,et al.  Development of a finite element aeroelastic analysis capability , 1996 .

[14]  Guru P. Guruswamy,et al.  Navier-Stokes computations on flexible advanced transport wings in transonic regime , 1996 .

[15]  P. Beran,et al.  Hoph Bifurcation in Viscous, Low Speed Flows About an Airfoil with Structural Coupling , 1994 .

[16]  J. Batina.  Unsteady transonic algorithm improvements for realistic aircraft applications , 1989 .

[17]  David M. Schuster,et al.  Static aeroelastic analysis of fighter aircraft using a three-dimensional Navier-Stokes algorithm , 1990 .

[18]  R. Seydel.  From Equilibrium to Chaos: Practical Bifurcation and Stability Analysis , 1988 .

[19]  P. Beran,et al.  Hopf bifurcation in viscous flows about airfoils at low speeds , 1991 .