基于微分几何水斗内移动网格的时空非定常流动

华南理工大学学报(自然科学版) ›› 2012, Vol. 40 ›› Issue (2): 39-44.

基于微分几何水斗内移动网格的时空非定常流动

沈娜¹韩凤琴²久保田乔²

1．华南理工大学广州学院电气工程学院，广东广州 510800;2．华南理工大学电力学院动力系，广东广州 510640

收稿日期:2011-03-14 出版日期:2012-02-25 发布日期:2012-01-04
通信作者: 沈娜(1984-) ，女，博士，主要从事流体机械数值仿真及优化设计研究． E-mail:ShenNa@ foxmail.com
作者简介:沈娜(1984-) ，女，博士，主要从事流体机械数值仿真及优化设计研究．
基金资助:
浙江省重大科技专项资助项目( 2008C11057) ; 广东省教改委项目( BKYB2011099)

Space-Time Unsteady Flow of Moving Grids in Pelton Bucket Based on Differential Geometry

Shen Na¹Han Feng-qin²Kubota Takashi²

1.School of Electrical Engineering,Guangzhou College of South China University of Technology,Guangzhou 510800,Guangdong,China; 2. School of Electric Power,South China University of Technology,Guangzhou 510640,Guangdong,China

Received:2011-03-14 Online:2012-02-25 Published:2012-01-04
Contact: 沈娜(1984-) ，女，博士，主要从事流体机械数值仿真及优化设计研究． E-mail:ShenNa@ foxmail.com
About author:沈娜(1984-) ，女，博士，主要从事流体机械数值仿真及优化设计研究．
Supported by:
浙江省重大科技专项资助项目( 2008C11057) ; 广东省教改委项目( BKYB2011099)

摘要/Abstract

摘要： 为了把时空非定常流动设计理念用于冲击式水轮机，旋转水斗自由曲面上复杂时空非定常水膜的数值可视化必不可少．文中采用局部非正交边界贴体网格( BFG) 对水斗内表面进行描述，利用微分几何精确计算了网格处的自然基本矢量及其偏微分，得到了水斗表面的局部曲率、沿曲面最短距离以及微小曲面面积; 成功地将流体的水膜移动网格点投影到了水斗内表面上．用建立的投影理论实现了从旋转水斗缺口及分水刃进入的非定常水膜移动网格的数值可视化，与模型试验照片的比较表明，该数值方法是有效的．

关键词: 冲击式水轮机, 旋转水斗, 非定常流动, 水膜流动, 自然基本矢量, 微分几何

Abstract:

In order to apply the concept of unsteady flow in space and time domains to the design of Pelton buckets,a numerical visualization of the complicated unsteady water film flow on the free surface of a rotating bucket is indispensable. In this paper,the inner surface of a bucket is described by using the boundary-fitted grids with nonorthogonal curvilinear local coordinates. Then,the natural basic vectors and their partial differentials are precisely
acquired based on the differential geometry,and the local curvature along the inner surface,the geodesic and the small surface area of the bucket are obtained. Moreover,the moving grids of the water film are successfully projected onto the bucket’s inner surface,and a projection algorithm is proposed to numerically visualize the moving grids of the unsteady water film flowing from the bucket cutout and the water separation edge. The visualization results are finally compared with the photos taken in the model test,which verifies the effectiveness of the proposed method.

Key words: Pelton turbine, rotating bucket, unsteady flow, water film flow, natural basic vector, differential geometry

沈娜韩凤琴久保田乔 . 基于微分几何水斗内移动网格的时空非定常流动[J]. 华南理工大学学报(自然科学版), 2012, 40(2): 39-44.

Shen Na Han Feng-qin Kubota Takashi. Space-Time Unsteady Flow of Moving Grids in Pelton Bucket Based on Differential Geometry[J]. Journal of South China University of Technology(Natural Science Edition), 2012, 40(2): 39-44.

[1]	杨筱沛, 王威, 蒋博彦, 等 . 不同雷诺数下二维翼型尾涡脱落的流动分析[J]. 华南理工大学学报(自然科学版), 2020, 48(10): 96-104,112.
[2]	陈晖沈明. 基于复合滑移的微纳缝隙剪切流研究[J]. 华南理工大学学报（自然科学版）, 2014, 42(7): 68-73.
[3]	韩风琴肖业祥久保田乔. 旋转水斗内的非定常射流干涉[J]. 华南理工大学学报（自然科学版）, 2007, 35(6): 25-28.
[4]	肖业祥郑爱玲韩凤琴丁二喜久保田乔. CFD 法研究多喷嘴冲击式水轮机的射流干涉[J]. 华南理工大学学报（自然科学版）, 2007, 35(3): 66-70.