曲率和挠率对圆截面螺旋管道粘性流动的三阶作用  

The Third-Order Effect of Curvature and Torsion on the Flow in Helical Circular Pipe

作　　者：张金锁[1] 章本照[1] 

机构地区：[1]浙江大学力学系,杭州310027

出　　处：《空气动力学学报》2000年第3期288-299,共12页Acta Aerodynamica Sinica

摘　　要：利用Germano的曲线正交坐标系下的完全N S方程 ,采用摄动方法求解了圆截面螺旋管道内的粘性流动 ,得到完全三阶摄动解 ,研究了曲率和挠率对二次流动和轴向速度的一阶、二阶和三阶作用。在曲率一阶项的作用下 ,截面上形成方向相反的两个二次涡 ,轴向速度最大值移向外侧 ;曲率的二阶项使二次涡的中心移向外侧 ;在曲率和挠率的高阶项 (二阶和三阶 )的共同作用下 ,靠近下半截面的涡增加 ,同时 ,二次涡的中心和轴向速度最大值移向上半截面。当轴向压力梯度较小或挠率相对于曲率较大时 ,轴向速度最大值靠近内侧。通过积分轴向速度的摄动解 ,不仅获得流量方程 ,而且获得摄动解的适用范围。挠率的三阶项并不影响管道的流量 ;当轴向压力梯度小于 2 2 .6 7时 ,螺旋管道内的流量比相同情况下直管内流量大。Without simplifying the N S equations of Germano's, we study the flow in a helical circular pipe employing perturbation method. A third perturbation solution is fully presented. The first 、 second and third order effects of curvature κ and torsion τ on the secondary flow and axial velocity are discussed in detail. The first order effect of curvature is to form the two counter rotating cells of the secondary flow and to push the maximum axial velocity to the outer bend. The two cells are pushed to the outer bend by the pure second order effect of curvature. The combined higher order (second , third ) effects of curvature and torsion, are found to be an enlargement of the lower vortex of the secondary flow at expense of the upper one and a clockwise shift of the centers of the secondary vortices and the location of maximum axial velocity. When the axial pressure gradient is small enough or the torsion is sufficiently larger than the curvature, the location of the maximal axial velocity is near the inner bend. Integrating the perturbation solutions of axial velocity, the equation of the volume flux is obtained. From the equation the validity range of the perturbation solutions in this paper can be obtained and the conclusion that the three terms of torsion have no effect on the volume flux is easily made. When the axial pressure gradient is less than 22.67, the volume flux in a helical pipe is larger than that in a straight pipe.

关 键 词：二次流动 螺旋管道 摄动方法 粘性流动 三阶作用 

分 类 号：O357.1[理学—流体力学]