流线体外形曲线的参函数表示法

A PARAMETRIC FUNCTION REPRESENTATION FOR THE OUTLINE-CURVES OF STREAMLINED BODIES

本文提出用一个已知函数与参函数的相乘积构造流线体外形曲线解析表达式的一种数学方法。其中参函数由流线体的边界条件决定,反映流线体的边界信息和内部几何特征。在定义范围内,任意一个给定的参函数就对应一条流线体外形曲线。算例证明本文方法不仅可用于流线体外形的设计和建立其型线系列,也可以用于已知流线体型线(离散值)求其近似的解析表达式。对此,本文方法亦具有十分良好的逼近能力。

In this paper, a mathematical representation of the outline-curves of streamlined bodies is given as the product of a known function with a parametric function. The parametric function is decided by the boundary conditions of the streamlined bodies and it reflects the boundary information and internal geometrical characteristics of the streamlined bodies. Within the defined range, a parametric function given arbitrarily corresponds to an outline-curve of streamlined bodies. Results of calculation prove that this method can be used not only for the design-calculation of outline-curves of streamlined bodies, for the construction of curve families, but also for finding out approximate expressions for the outline-curves of streamlined bodies when the outline-curve of streamlined bodies is given. For such cases, this method shows good ability of approximation.