Improved determination of aeroelastic stability properties using a direct method

• Published in: Mathematical and computer modelling 1999-12, Vol.30 (11), p.95-110
• Main Authors: Leger, T.J., Wolff, J.M., Beran, P.S.
• Format: Article
• Language: English
• Subjects: Boundary conditions; Exact sciences and technology; Flutter aeroelasticity; Mathematical analysis; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods in mathematical programming, optimization and calculus of variations; Numerical methods in optimization and calculus of variations; Partial differential equations; Sciences and techniques of general use; Transonic flow; Unsteady aerodynamics
• ISSN: 0895-7177; 1872-9479
• DOI: 10.1016/S0895-7177(99)00200-9

The ability to accurately predict transonic flutter boundaries is investigated using an enhanced direct computational method. Steady characteristic and unsteady approximate nonreflecting characteristic far-field boundary conditions are utilized to more accurately model the aerodynamic flow physics in a direct method. In order to accomplish this, the aerodynamic model is modified to lock the movement of the far-field grid points while allowing the airfoil surface points to move freely. This is accomplished by introducing a linear weighting function in the grid deformation model. The direct method is based on a discretization of the Euler equations and a coupled set of structural dynamics equations representative of a pitch-and-plunge airfoil with trailing edge flap. The coupled equations are expanded to specify a Hopf-bifurcation point, which defines an incipient flutter state. In addition, the direct continuation method is extended by an analytic computation of the path tangent vector for pseudo-arclength continuation (PAC). A flapped NACA 64A006 airfoil, executing pitch and plunge motion, is utilized to demonstrate the ability of the enhanced boundary conditions to accurately calculate flutter boundaries for reduced domain sizes. Both zero and nonzero angle of attack results are shown to highlight the improved accuracy of the boundary conditions. Each boundary condition modification resulted in analysis improvements, with the steady characteristic model demonstrating significant improvements in the nonlinear flow regime. For a 1° static pretwist, analysis at a freestream Mach number of 0.84, the enhanced model resulted in over a 75% decrease in the flutter speed error. In addition, flutter boundary solutions are presented which demonstrate the capability of the PAC model to compute variations in structural parameters. The airfoil-fluid mass ratio and structural damping parameters are varied for both subsonic and transonic flow conditions, with nonlinear effects observed for the transonic results.