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为得到风力机功率、转矩和推力等性能随尖速比和翼型升阻比变化的极限公式,需求解叶片的理想扭角和弦长沿翼展变化的解析表达式,同时这项研究也可为叶片外形设计提供理论参考。为此首先从效率最大化的原则出发,用极值的微分算法证明最佳攻角就是使翼型升阻比最大的攻角;其次利用最佳攻角和入流角公式推导出叶片理想扭角沿展向的解析表达式;然后根据动量-叶素理论,推导出叶片理想弦长沿展向的解析表达式。研究表明:叶片理想扭角是设计尖速比、最佳攻角和风轮半径的函数,叶片理想弦长是设计尖速比、风轮半径以及对应最佳攻角的升力和阻力系数的函数。这两个表达式均可表示为显函数的形式。
In order to obtain the limit formula of the variation of power, torque and thrust of wind turbine with tip speed ratio and lift-drag ratio of airfoil, the analytical expression of the ideal twist angle and chord length variation along the span of the blade is required. It can provide theoretical reference for blade profile design. To this end, starting from the principle of maximizing the efficiency, the best angle of attack is proved by the differential algorithm of extreme value, which is the angle of attack of the airfoil with the largest ratio of lift-drag ratio. Secondly, the optimal angle of attack Then according to the momentum-leaf element theory, the analytic expression of the ideal chord length and direction of the blade is deduced. The results show that the ideal torsion angle of the blade is a function of the design tip speed ratio, the best angle of attack and the radius of the rotor. The ideal chord length of the blade is a function of the design speed ratio, radius of the rotor and the lift and drag coefficient corresponding to the best angle of attack. Both of these expressions can be expressed in the form of explicit functions.