水泵与水轮机转子低压截面上的结构常数G及流线相似法应用

Structure Constant G and Streamline Similarity Method for Flow Distributions at the Low Pressure Sides of the Pump and the Turbine Impellers

本文从理论上准确地推导了水泵转子入口处流速与压力的不均匀分布。其基本出发点是流动的势流特征以及在转子入口处流线分布的几何相似特性,即不随流量而变化。流线分布的几何相似特性决定了流速分布的几何特性并由几何参数G(s)与第一结构常数G_Ⅰ描述。由已知的流速分布,本文还推导了非额定工况下流体在转子入口处的冲击损失并因此而引入第二结构常数G_Ⅱ。两个结构常数的引入,第一次将解析计算的精度提高了多个数量级。由于流动的势流特征以及流速分布的几何特性,对水泵转子入口处流速的分析计算可以直接应用于混流式水轮机出口的速度分布。本文因此还进一步严谨地计算了欧拉方程中出口项的平均值(u_2c_(2u))。其中,两个结构常数以及综合结构常数再一次得到应用。本文所介绍的计算方法称为流线相似法(SSM)。

Thenon-uniform velocity and pressure distributions at the impeller inlet of a pump have been precisely deduced. The analyses are based on the potential flow theory and the geometrical similarity of the streamline distribution along the leading edge of the impeller blades. This means that all streamlines are independent of the flow. The obtained geometric form of the flow distribution is thus simply described by both the geometric parameter G(s) and the first structural constant G_Ⅰ. From the known flow velocity distribution, the paper also deduced a simple and accurate formula of the shock loss in the flow at the impeller inlet by introducing the secondstructural constant G_Ⅱ. The use of two structural constants contributes immensely to the enhancement of the computational accuracies. Because of the potential flow property and the geometrical feature of the streamline distribution, the flow analyses and calculations for the pump flow can be directly applied to the non-uniform flows at the impeller exit of the Francis turbine. For this reason, this paper also further rigorously presents a computation of the mean value of the exit term(u_2 c_(2u)) of the Euler equation. Two structural constants are applied again.The method presented in this paper is called streamline similarity method(SSM).