TRANSITION TO CHAOS IN AN OPEN UNFORCED 2D FLOW

Unsteady low Reynolds number flow past a two-dimensional airfoil is studied numerically. The purpose is to (1) determine the bifurcation sequence leading from simple periodic flow to complex aperiodic flow as Reynolds number is increased, (2) identify and quantify the chaos present in the aperiodic flow, and (3) evaluate the role of numerics in modifying and controlling the observed bifurcation scenario. The full two-dimensional Navier-Stokes equations are solved for a NACA 0012 airfoil at M∞ = 0.2, α = 20°, and Re < 4000. The Navier-Stokes code ARC2D in an unsteady time-accurate mode is used for most of the computations. For each Reynolds number studied, the asymptotic behavior of the flow is studied using time delay reconstructions, Poincaré sections, and frequency decompositions. The system undergoes a period-doubling bifurcation to chaos as the Reynolds number is increased from 800 to 1600, with windows of periodic behavior in the chaotic regime past 1600. The observed chaotic attractors are further characterized by estimates of the fractal dimension and partial Lyapunov exponent spectra. Tests are made on the effects of varying mesh resolution, added artificial dissipation, and order of spatial or temporal accuracy of the numerical method. It is shown that the observed chaos does not arise due to numerical effects alone, but is a true solution of the model system. Local Lyapunov exponent analysis is used to determine the physical mechanism behind the period-doublings. © 1993 Academic Press, Inc.