Numerical Aerodynamic Analysis of a Free Falling Autorotating Plate

摘要

A computational method coupling the three degrees of freedom flight mechanics equations and the two dimensional Navier-Stokes equations was developed which could be used to predict the flight path of a free falling, autorotating, two dimensional flat plate. The two dimensional incompressible Navier-Stokes equations were cast in a body fixed coordinate system. The corresponding velocities were cast in an inertial reference system. The equations were represented by backward-time-central-space finite differences and solved using a successive-over-relaxation iteration technique. The resulting aerodynamic coefficients were entered into the three degrees of freedom flight mechanics equations. The system of ordinary differential equations was solved using an Adams open formula to predict the movement of the plate. New boundary conditions for the Navier-Stokes equations solver were derived from the movement of the plate. The process was repeated to advance the solution in time. The computation method was used to calculate the flow field around a flat plate forced to rotate at nondimensional angular velocities of 1.0, 2.0, and 4.0. Finally, the flight path of a free falling autorotating plate was predicted using the computational procedure. The validity of the overall approach was demonstrated by comparison with experiment.