Free-falling autorotating plate - A coupled fluid and flight mechanics problem

Abstract

A computational method coupling the three-degrees-of-freedom flight mechanics equations and the twodimensional, time-dependent Navier-Stokes equations was developed which could be used to predict the autorotating characteristics of a free-falling, 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 Navier-Stokes equations were represented by implicit finite differences and solved using a successive-overrelaxation iteration technique. The resulting aerodynamic coefficients were entered into the three-degrees-of-freedom flight mechanics equations. The system of ordinary differential equations describing the flight mechanics was solved using an Adams-Bashforth explicit method to predict the movement of the plate. New values of the boundary conditions for the Navier-Stokes equations solver were obtained from this movement of the plate. The process was repeated to advance the solution in time. The flight path of a freefalling autorotating plate was predicted using the computational procedure and the validity of the overall approach demonstrated by comparison with experiment.