【作者】 张家忠； 孙旭； 雷鹏飞；

【Author】 Zhang Jia-zhong, Sun Xu, Lei Peng-fei (1.College of Energy and Power Engineering, Xi’an Jiaotong University, Shanxi 710049, China)

【机构】 西安交通大学能源与动力工程学院；

【摘要】 给出了一种低速来流下二元叶片颤振数值模拟、运动稳定性分析的方法:流场方面,以速度势函数形式的Laplace方程、非定常Bernoulli方程作为流动控制方程,利用有限单元法进行数值模拟,计算二元叶片所受气动载荷;结构方面,根据已有二元叶片沉浮、扭转结构动力模型,应用四阶Runge-Kutta法对振动方程积分一步,得到下一时刻叶片振动的位移和速度;流动和结构方程迭代求解,实现低速来流中叶片振动的数值模拟。最后,从非线性动力学角度,利用动力系统稳定性理论、分岔理论,在相平面上对叶片振动平衡位置稳定性进行分析,对颤振发生的机理进行了研究。作为算例,着重分析了来流速度对叶片振动的影响,分析表明:来流速度增加而导致的叶片颤振是以来流速度为分岔参数的Hopf分岔产生的结果。更多还原

【Abstract】 A numerical method is proposed to simulate the Flutter-type oscillation, and investigate the fundamental nature of the nonlinear phenomena from the viewpoint of Hopf bifurcation. The finite element method is used to approach the solution of Laplace equation, in terms of velocity potential, and the unsteady aerodynamic loads can be then obtained through the unsteady Bernoulli equation. Further, the Runge-Kutta method is applied to solve the equation of structural dynamics. Calculating the flow and structure equations alternately, the orbits of the two-dimensional blade in the flow are obtained. Finally, the flutter-type oscillation is studied in detail based on Hopf bifurcation. In particular, the stability of the equilibrium position is analyzed and some explanations for such oscillation are given. As the results, it can be concluded that the appearance of flutter-type oscillation of two-dimensional blade in the flow is the result of the occurrence of Hopf bifurcation, as the velocity of the flow is increasing.更多还原