Mathematical Modeling of the Magnus-Effect-Based Wind Turbine

Abstract

The closed mathematical model of the Magnus-effect-based horizontal axis wind turbine is constructed. The central shaft of the turbine is directed along the wind flow. Several Savonius rotors are mounted in cylindrical joints at the central shaft. Axis of these joints are orthogonal to the wind flow direction. Self-sustained rotation of Savonius rotors induces the Magnus force that sustains the rotation of the central shaft. The rotor of an electric generator is attached to the central shaft. The generator is connected to a local electric circuit. The quasi-steady approach is used to describe the aerodynamic action upon the system. Corresponding aerodynamic coefficients are approximated basing on experimental data. The electromechanical torque acting upon the rotor of the generator is supposed to be linear with respect to the angular speed of the rotor. The coefficient of the electromechanical torque depends on the external resistance in the circuit of the generator. The payload coefficient is introduced as a function of the wind speed and the external resistance in the circuit of the generator. The bifurcation diagram is constructed that describes the mechanical power of the wind turbine depending on the payload coefficient. The maximum power is estimated. The corresponding value of the payload coefficient is calculated.