轴流泵叶轮出口轴面速度数学模型的建立与验证

Development and verification of mathematical model for meridional velocity at impeller outlet of axial flow pump

为了获得轴流泵叶轮出口轴面速度分布规律,本文基于圆柱层无关性假设,以轴流泵速度梯度方程为基础,推导了轴面速度分布理论数学模型,考虑到叶顶间隙泄漏流损失和端部二次流损失,引入修正系数对数学模型进行了修正,得到了叶轮损失最小、高汽蚀性能时的轴面速度数学模型;并采用微型五孔球形探分别对比转速550,750,1000和1250的高效叶轮出口轴面速度分布进行了测量。实验结果表明,系列轴流泵叶轮出口轴面速度分布规律一致,轮毂和轮缘侧轴面速度降小,在叶片中部最大,均呈抛物线流型。实验结果验证了轴面速度分布数学模型的正确性,并通过二次回归分析,得出系列模型的轴面速度分布数学方程,可供轴流泵水力设计参考。

A mathematical model is theoretically derived for calculation of meridional velocity distribution at the impeller outlet of an axial flow pump, based on the velocity gradient equations and an assumption of cylindrical layer independence. This model considers the head losses caused by the flow leakage at tip clearances and the secondary flows around the tips, using a correction factor to modify the calculation. It predicts the meridional velocity at minimum impeller loss and high cavitation performance. A miniature fivehole spherical probe was used to measure the meridional velocity at specific speeds of 550, 750, 1000 and 1250. Results show that meridional velocity distributions at the impeller outlet of different axial flow pumps of the same type are very similar, showing a drop near the hub and rim and a peak in the middle of blade. A quadratic regression analysis of the experimental data verified the mathematical model, and thus it would supply reference for hydraulic design of axial flow pump.