On Tumbling of a Two-Dimensional Plate under Free Flight

Abstract

In this study, we experimentally deal with the tumbling, which is a rotating motion of a plate with its axis perpendicular to the falling direction. As the plate, we consider a rectangular-cross-section prism with a depth-to-width ratio λ = 0.3, an aspect ratio AR = 10, and inertia moment ratios I * = 0.75 − 43, together with a wide range of a non-dimensional control parameter C = 7.2×10 1 − 1.6×10 3 . As a result, we specify fundamental aerodynamic characteristics in terminal condition, like the reduced rotating rate Ω * , the lift coefficient C L , the drag coefficient C D and the lift-to-drag ratio C L /C D as functions of both C and I * . Moreover, the relation between the actual Reynolds number Re and the Reynolds number Re(V d) based on V d can be approximately determined, being independent of C and I * . Eventually, we successfully propose a series of empirical formulae to predict Ω * , C L , C D and C L /C D as functions of Re(V d) alone, which is available for a wide parameter range except for large C and small I * .