基于微分几何水斗内移动网格的时空非定常流动

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

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.

In order to apply the concept of unsteady flow in space and time domains to the design of Pelton buc- kets, 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 non-orthogonal 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 projec- ted 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.