摘要
本文用参数B样条来表示任意四边形网格上的曲面,并给出了曲面偏导数的计算公式,数值实验证明了这种表示方法是合理的、可靠的,插值效果很好.对混流式水轮机HL220转轮叶片工作面的实际应用表明,这种表示方法能够用来表示叶片式流体机械叶片形状,其效果令人满意.
The mathematical representation of the surfaces on an arbitrary quadrangular grid with the parametric B-spline is derived and the formulae of the partial derivatives of the surfaces are given. The periphery of an arbitrar-y quadrangular grid is transformed into a square or rectangular one with parameters u and v on the grid as variables by mapping transformation. The method with which two curves belonging to the t and s family respectively are obtained for an arbitrary point p on an arbitrary quadrangular grid is given. It is the basis for the interpolation on the grid. By numeri-cal check of z = l/(x + y) ,Z =1/(x +y2)and Z = x+y, it is proved that the representation proposed is rational. The relative error is less than 0.2% for Z and less than 2% for the first order partial derivative. It is shown that such a representation can be used to represent the blade of fluid machinery by modelling the pressure side of the blade of the Francis turbine type HL220. The result is found to be satisfactory.
出处
《华中理工大学学报》
CSCD
北大核心
1992年第6期87-92,共6页
Journal of Huazhong University of Science and Technology
关键词
流体机械
叶片
fluid machinery
blade
grid
parametric 5-spline
interpolation
