圆截面曲线管道内二次流动的 Galerkin 解

Galerkin Solutions of Laminar Flow in Helical Circular Pipes

本文推导了曲线直角坐标系内的Ｎ－Ｓ方程。并采用Ｇａｌｅｒｋｉｎ方法和计算机符号运算技术求解了圆截面螺旋管道（包括弧形弯管）内的二次流动。结果表明Ｇａｌｅｒｋｉｎ方法可以克服摄动法的小参数局限，得到了纯数值法无法求得的半解析解。

The Navier Stokes equations in the curvilinear coordinate system are established in tensorial form.The fully developed laminar flow in helical circular pipes under the influence of both curvature and torsion is analyzed.The solutions are obtained by the Galerkin weighted residual method which are realized by using computerized symbolic manipulation technique.The results indicate that the Galerkin method can effectively overcome the limitation of small parameters for perturbation method.Based on the Galerkin semi analytical solutions obtained,the characteristics of the secondary flow in pipes are discussed.