可旋轉葉片之垂直軸風力發電機之動力分析

Abstract

本研究提出一個新的垂直軸風力發電機具有連桿連接可旋轉的阻力型葉片之設計與理論及數值分析。最大的特色是：除了旋轉風機的中心軸裝有發電機外，每個旋轉葉片的轉軸亦裝上發電機，其尺寸比中心主發電機小。如此可比傳統單一中心主發電機的發電量大。每一雙連接的葉片有不同的姿態，受風下因兩者攻角不同，會有不同的圓周切線力，因為產生轉矩差，可自行啟動。空氣動力學的壓力中心會隨azimuth angle而改變，它不在平板葉片的中心轉軸上，會造成葉片自轉。一片旋轉時透過連桿推或拉動另一葉片永久保持攻角差異。透過用尤拉旋轉運動方程式來建立整體風機與各雙連接的葉片旋轉運動方程式。利用Fluent泛熱流軟體來進行葉片的計算流體力學（CFD）的求解，給定不同組的風速與葉尖周速比的值，找出葉片壓力中心，升力，阻力與力矩。再轉換到葉片轉軸點上去。最後進入尤拉旋轉運動方程式裡。連桿連接會產生約束方程式，是非線性代數式，要跟偏微分方程式的旋轉運動方程式聯立解。根據高斯最小作用原理來將約束力以explicit form表示之。則整體運動方程式就會不含約束方程式與對應的Lagrange multiplier之未知數，較容易進行數值解。數值分析來瞭解系統的風能擷取功率Cp值並與固定葉片的功率值比較。可加裝固定仰俯角升力型葉片成為複合型VAWT以提升Cp值。

This project proposes the design, and theoretical as well as numerical analysis of a novel vertical axis wind turbine in which each pair of rotatable drag-force-driven-type blades are linked by a rigid rod. The important feature is that each rotating blade can be equipped with an electric generator of which the size is smaller than the main generator. So this new system can harness more wind energy than the traditional one with single main generator. Each of the linked blades have different orientations such that they have different angles of attack under the wind flow and suffer different tangential forces which causes a net torque to the VAWT; therefore, this new VAWT has the self-starting ability. Since the center of the aerodynamic pressure varies with the azimuth angle, the instantaneous center is not always located at the center of the flat plate-type blade and will cause the blade to rotate. When one blade rotates, it will pull or push the other linked one to simultaneously rotate so that their angles of attack are always different. We employ the Euler rotational equations of motion to establish the governing equations of the whole system. We use the Fluent software to perform computational fluid dynamic simulation. Given the wind velocity and the tip speed ratio we can find the center of pressure of the blades, lift force, drag force, and torque on each blade, which are needed in the equations of motion. The pair of linked blades produces a constraint equation which is a nonlinear algebraic equation. We use the Gauss Principle of least action to express the constraint force in explicit form such that the governing equations will be free of the unknown Lagrange multiplier associated with the constraint and the constraint equation to facilitate numerical simulation. Through these numerical analysis we can obtain the power rate Cp extracted from the wind and compare it with the VAWT of fixed pitch blades. The novel VAWT can also be equipped with lift-force-driven-type blades to become a hybrid VAWT so as to enhance the power rate of the whole system.