HOPF-BIFURCATION IN VISCOUS, LOW-SPEED FLOWS ABOUT AN AIRFOIL WITH STRUCTURAL COUPLING

The locations of Hopf bifurcation points associated with the viscous, incompressible flow about a NACA 0012 airfoil with structural coupling are computed for very low Re (< 2000). A semi-implicit, first-order-accurate time-integration algorithm is employed to solve the streamfunction-vorticity form of the Navier-Stokes equations. The algorithm is modified to include simple structural elements affixed to the airfoil and the resulting airfoil motion. The equations describing the airfoil motion are integrated in time using a fourth-order Runge-Kutta algorithm. Numerical experiments are performed to determine if the structural model of the airfoil has an effect upon the location of the Hopf bifurcation point when compared with the fixed airfoil. Results are reported for a variety of structural characteristics, including variation of torsional and linear spring constants, inertial properties, structural coupling and structural damping.