On Tumbling of a Two-Dimensional Plate under Free Flight

概要

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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 = 7.2×101 - 1.6×103. As a result, we specify fundamental aerodynamic characteristics in terminal condition, like the reduced rotating rate Ω*, the lift coefficient CL, the drag coefficient CD and the lift-to-drag ratio CL/CD as functions of both C and I*. Moreover, the relation between the actual Reynolds number Re and the Reynolds number Re(Vd) based on Vd can be approximately determined, being independent of C and I*. Eventually, we successfully propose a series of empirical formulae to predict Ω*, CL, CD and CL/CD as functions of Re(Vd) alone, which is available for a wide parameter range except for large C and small I*.