Evaluation of dynamics of fluttering and autorotation of a rigid plate in a flow using far-field method

摘要

The rotation of a non-circular body through a fluid flow is affected by different types of moment. In this paper, the total moment applied on the body into the fluid current is derived using far-field technique which uses the integral balance of the momentum equations. Such a complex expression of moment which is composed of many parameters is simplified in the case of a 2D rotating plate as moment due to pressure coefficient and moment due to vorticity field. Analytical expressions are obtained for each moment. The total torque on a rotating plate is decomposed to three parts included current effect, rotational effect, and mutual effect so that the last one is the contribution of the current velocity and the plate rotation simultaneously. The current effect represents the torque due to either the plate translates without rotation through a still fluid or the fluid passes over a stationary plate while the rotational effect deals with the torque generated by the pure rotation of the plate in the still fluid. To consider how different dynamical modes included fluttering (oscillatory rotation) and autorotation (continuous rotation) occur on a 1 DOF plate when is encountered by the current, we present a detailed discussion on the genesis and shed of vortices associated with each mode. We propose a condition related to torques by which the happening of each mode of rotation can be explained. Stability analysis shows that the transcritical bifurcation governs mainly on such physics; however, saddle node bifurcation might happen locally. A threshold is found for this physics.