Improved determination of aeroelastic stability properties using a direct method

The ability to accurately predict transonic flutter boundaries is investiga ted using an enhanced direct computational method. Steady characteristic an d unsteady approximate nonreflecting characteristic far-field boundary cond itions are utilized to more accurately model the aerodynamic Row physics in a direct method. In order to accomplish this, the aerodynamic model is mod ified 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 metho d 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 Ho pf-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 demo nstrate the ability of the enhanced boundary conditions to accurately calcu late flutter boundaries for reduced domain sizes. Both zero and nonzero ang le of attack results are shown to highlight the improved accuracy of the bo undary conditions. Each boundary condition modification resulted in analysi s improvements, with the steady characteristic model demonstrating signific ant improvements in the nonlinear flow regime. For a 1 degrees static pretw ist analysis at a freestream Mach number of 0.84, the enhanced model result ed in over a 75% decrease in the flutter speed error. In addition, flutter boundary solutions are presented which demonstrate the capability of the PA C model to compute variations in structural parameters. The airfoil-fluid m ass ratio and structural damping parameters are varied for both subsonic an d transonic flow conditions, with nonlinear effects observed for the transo nic results. (C) 1999 Elsevier Science Ltd All rights reserved.