Performances of ideal wind turbine

Abstract

If there is an ideal wind turbine, its performances will be the pursuit goals for designing the actual wind turbine. In this paper, the wind turbine that has the maximum efficiency is defined as ideal wind turbine, which has three main features: lift-drag ratio is infinite, it has enough number blades so that the blade tip and root losses can be ignored, and its blades are limited in width. Using blade element theory, the differential equations of power, torque, lift and thrust of blade element were derived, and the expressions of power, torque, lift and thrust coefficients of the ideal wind turbine were gained by integrating along the blade span. Research shows that the power, torque and lift coefficients of the ideal wind turbine are functions of tip-speed ratio. When the lift-drag ratio and the tip-speed ratio is approaching infinity, power coefficient of the ideal wind turbine is close to the Betz limit; The torque limit is 0.401 when the tip-speed ratio equals about 0.635; The Lift limit is 0.578 when the tip-speed ratio equals about 0.714; The thrust coefficient is 8/9, which is unrelated with tip-speed ratio. For any wind turbine which tip-speed ratio is less than 10, the power coefficient is unlikely to exceed 0.585, for any high-speed wind turbine which tip-speed ratio is greater than 6, the torque coefficient in steady state is unlikely to exceed 0.1, and the lift coefficient is unlikely to exceed 0.2.