Numerical model of three-dimensional motion of plate-type wind-borne debris based on quaternions and its improvement in unsteady flow

A numerical model of three-dimensional motion of plate-type wind-borne debris in uniform wind field based on quaternions is proposed in this paper. This model can simulate the complex 3D spinning flight robustly and efficiently with rotational quaternions, which are also free from the gimbal lock that is associated with Euler rotational matrix. The predictions from the model were then compared with the results of another quasi-steady model, and good agreement is found. For the unsteady flow involved in autorotational flight mode, the present model was improved by revising the damping moment in order to simulate the two-dimensional motion of plates with higher accuracy. Calibration of the damping moment coefficient was performed through a direct comparison of the predicted non-dimensional angular velocity with the results of CFD-RBD model. The predictions of the improved model agree reasonably well with the CFD-RBD results, which verifies the accuracy of the improved model in predicting the two-dimensional trajectories of plates.