Dynamics of a Wheeled Cart Driven by a Savonius Rotor

Abstract

Savonius rotor is one of relatively wide-spread type of wind turbines. The rotation rate of this rotor is considerably lower than that of horizontal axis wind turbines and Darrieus wind turbines. However, it starts rotating at small wind speeds, doesn’t require any additional devices to ensure its re-orientation in case of change of the wind direction, and generates a rather large torque. Therefore, it is suitable for use as a drive in different mechanical and electromechanical systems. In the present paper, dynamics of rectilinear motion of a wheeled cart is studied, which is driven by Savonius rotor installed on it. It is assumed that the wind makes a certain constant angle with the line, along which the cart moves. The aerodynamic load upon the rotor is described with an empirical model, in the context of which the aerodynamic characteristics (aerodynamic torque, drag and lateral force coefficients) are represented as Fourier series with respect to the rotor revolution angle, the coefficients of the series being functions of the rotor tip speed ratio (dimensionless angular speed). Experiments were performed in the subsonic wind tunnel of the Institute of Mechanics of Lomonosov Moscow State University intended to measure aerodynamic characteristics of the rotor at different wind speeds and rotor angular speeds. Based on experimental data, functions were proposed that approximately describe the dependence of the above mentioned coefficients upon the tip speed ratio. The obtained dependences were used for analysis of dynamics of the cart driven by the Savonius rotor. The equations of motion are averaged with respect to the angle of revolution of rotor. Steady solutions of this averaged system are studied. It is shown that, for certain values of parameters, there exist two attracting steady motions corresponding to different directions of the cart velocity. Cart dynamics in the context of the full system of equations of motion is compared with its dynamics in the context of the averaged system.