【作者】 张金锁；

【导师】 章本照；

【作者基本信息】 浙江大学 ， 流体力学， 2001， 博士

【摘要】 在工程应用中存在旋转曲线管道系统。随着旋转性机械在工业中的广泛应用，其中的控制管路系统、输送管路系统、冷却管路系统的流动性质是提高这些机械性能的重要因素，因此这些管路系统中流体运动的特点成为工业应用中迫切需要解决的问题，也成为流体力学中最有前途的研究领域之一。另一方面，旋转曲线管道系统是流体力学非线性的典型模型，在截面上存在形态复杂的二次流动，在某些条件下出现分叉解，深入研究旋转管道流动，具有重要的理论意义。课题具有广阔的应用前景。 本文首先综述了一个世纪以来有关曲线管道流动的研究成果，并在前人文献的基础上，提出一种多参数旋转螺旋管道流动模型。采用摄动方法和数值计算方法，研究了处于多种旋转状态下、多种截面形状(圆截面、椭圆截面、环形截面、矩形截面)、不同几何结构旋转螺旋管道流动。分析了各种流动参数和几何参数对轴向速度、二次流动、壁面摩擦力、摩擦系数比的影响。同时研究了方形截面旋转弯管流动的分叉问题。 研究结果表明：(1)旋转螺旋管道流动特性受Dean数、曲率、挠率(或Germano数)、科氏力与离心力之比F数(或Rossby数)以及截面的形状五种因素的影响。(2)当F变化时，存在确定的数值Fr(Fr在-1左右。曲率、挠率和Dean数对Fr的影响很小)，当F＞Fr时，轴向速度最大值偏向外侧，摩擦系数比随F增大而增大；当F＜Fr时，轴向速度最大值偏向内侧，摩擦系数比随F减小而增大；当F=Fr时，轴向速度的分布和Poiseuille流近似相同，摩擦系数比约为1。(3)F在Fr左右(离心力和科氏力相当的负旋转)，二次流强度最弱，但结构最复杂；对于正旋转和离心力占优的负旋转，二次流速度的方向和静止的情况相同；对于科氏力占优的负旋转，二次流速度的方向和静止的情况相反。(4)当F的绝对值很大(或Rossby数很小)时，流动出现Taloy-Proudman现象，流动结构左右对称。(5)增大挠率，逆时针方向旋转的一二次涡和流函数的负值区域增大，轴向速度最大值的位置按逆时针（环形截面）或顺时针（圆截面）方向旋转，摩擦系数比最终趋向于1。（6）增大Dean数，二次流先趋于对称而后逆时针方向的二次涡增大，轴向速度和流函数等值线趋向于对称，摩擦系数比增大。门）截面的形状对二次流动的结构影响明显。当F在Fr左右时，对于弯管，环形截面上存在八个涡，圆截面上存在四个涡，椭圆截面上存在四个或六个涡；对于螺旋管，圆截面和环形截面上二次流表现为环流，椭圆截面上表现为鞍流。（8）对于正方形截面的分叉问题，本文得到六种无条件稳定和对称稳定的流动分支，Dean数不同，流动分支的极限点不同，发现正方形截面最多可以存在八个涡。 本文摄动解和数值解的结果，均与文献已有的实验结果和数值结果进行了比较，结果吻合良好。 本论文的创新之处主要表现在系统地研究了多参数旋转曲线管道流动特性，分析了各参数对流动特性的影响，获得若干前人没有获得的重要结论。更多还原

【Abstract】 Rotating curved pipes are often encountered in engineering applications. With the popularity of rotary machinery in industry, the characteristics of the flow in the controlling pipe system, the transporting pipe system, and the cooling pipe system are the main factors to improve the efficiencies of the rotary machinery, consequently, fluid flow in rotating pipes has become one of the urgent problems in engineering and one of the challenging research fields in fluid mechanics. On the other hand, this flow is a typical non-linear model and there exists complicated secondary flow on the cross-section, also, a bifurcation will appear on some conditions. This study is signality in theory and has a broad application future.In this dissertation, researches on the flow in curved pipes of the last century are firstly reviewed and then a flow model in a rotating helical pipe with multi-parameters is introduced. Employing perturbation method and numerical simulation, we study the flow in rotating helical pipes including different rotations, different cross sections (circular, elliptical, annular and square cross section), and different geometrical structures. We analyze the effects of the flow parameters and the geometrical parameters on the axial flow, the secondary flow and the friction. We also study the bifurcation solutions of the flow in rotating curved square ducts.The following results are obtained: (1) The flow in rotating helical pipes are affected by Dean number, curvature, torsion (or Germano number), the ratio of the Coriolis force to the centrifugal force F number (or Rossby number) and the geometry of the cross section. (2) With F varying, there exists a number Fr which is about -1 (Curvature, torsion and Dean number have little influence on Fr), when F > Fr , the maximum of the axial velocity is near the outside bent and the friction factor ratio increases with F increasing; when F < Fr, the maximum is near the inner side bent and the ratio increases with F decreasing; when F = Fr, the distributions of the axial velocity are similar to those of Poiseuille flow and the friction ratio is about 1. (3) When F is about Fr, the secondary flow reaches its weakest intensity, but has a most complicated structure. For co-rotation and counter-rotation in which the centrifugal force dominates the flow, the secondary flow in a rotating helical pipe has the same direction with that in a stationary one. Forcounter-rotation in which the Coriolis force dominates the flow, the secondary flow has the opposite directions to that in a stationary one. (4) When |F| is very large orRossby number is very small, the Taloy-Proudman phenomenon appears and the flow is symmetry left and right. (5) As torsion is increased, the anticlockwise secondary vortexes and the negative area of the stream function increase; the axial velocity moves anticlockwise (annular pipe) or clockwise (circular pipe); the friction factor ratio finally reaches the value about 1. (6) As Dean number is increased, the secondary flow firstly becomes symmetry and then the anticlockwise vortexes are enlarged, the contours of axial velocity and the stream function become symmetry, the secondary flow is intensified and the friction factor ratio increases. (7) The cross-section has significant effects on the secondary flow. When F is about Fr, for curved pipes, the secondary flow appears eight vortexes for annular cross section and four for circular and four or six for elliptical; for helical pipe, the secondary flow appears as a loop flow for annular and circular cross section, and a saddle flow for elliptical cross section. (8) Six branches of the flow in a rotating square duct are obtained. The limited points of every branch are different for different Dean number. An eight-vortex phenomenon is also found.Comparisons are made between the results of this study and the valuable results of the other authors, all the results are all in good agreements.The innovation points of this study are that we firstly analyze the flow in rotating helical pipe an更多还原