收缩螺旋涡线诱导速度的快速收敛法

A RAPID CONVERGENCE METHOD OF INDUCED VELOCITIES BY CONTRACTED HELICAL VORTEX LINES

给出了一种计算收缩涡线（桨尖涡和内部涡线）诱导速度所有组元的快速收敛方法，该方法是由Ｒａｎｄ和Ｃｈｉｕ的方法（计算螺旋涡线诱导速度快速收敛法）发展而来的，它以寻求上下界截断积分解析表达式为基础。其优点是能计算尾迹中任意一点的诱导速度，并且考虑了尾迹收缩。该方法不仅避免了离散涡线引起的截断误差。

A rapid convergence method for calculating all induced velocity components by contracted vortex lines(e.g., tip vortex and inboard vortex) is presented . The advantage of the method is , the induced velocities at any point in the wake can be calculated and the wake contraction is considered. Not only does it avoid the truncation errors associated with discretization of the vortex lines, but also reduces integrand errors corresponding to finite azimuthal angle. Therefore, both numerical precision and integrand convergence rate are obviously improved. This method is developed from Rand and Chiu's method(a rapid convergence method for computing the induced velocity by a helical vortex line ), which is based on finding upper and lower bounds on the truncated integral.