离心叶轮内相对运动伯努利方程的研究

Analysis in relative Bernoulli’s equation inside centrifugal impellers

离心泵基本方程是研究叶轮流场及设计叶轮的基础性方程,利用运动坐标系下的相对运动伯努利方程导出离心泵基本方程是一种典型的常用方法。已有众多文献以不同途径导出了叶轮内相对流动的伯努利方程,但是,所有这些推导中,在假设流体理想的同时,都给出了流体沿一条相对流线运动的假设。严格地说,在这样条件下取得的结果实际上已不能代表离心叶轮内一般流动规律。为克服过去研究的这一不足和获得具有普遍意义的相对运动伯努利方程,通过矢量分析方法计算理想流体欧拉方程中的三项加速度矢量,得到相对运动伯努利方程中数量性之和的梯度表达式,最终获得了旋转坐标系下的相对运动伯努利方程。这一推导中扬弃了过去积分沿一条相对流线的假设,所获得的结果适合于全流场。这一证明在方法和结果都与过去有显著区别,从而为离心泵基本方程提供了更可靠的基础。

Euler＇s equation is a foundation-stone in investigating flow field within centrifugal impellers and impeller design. Employing relative Bemoulli＇s equation in motive coordinate system to deduce Euler＇s equation is a typical approach, Many means to obtain relative Bemoulli＇s equation were reported in past literatures, but in all these researches, in addition to the assumption of ideal fluid, the fluid must follow a relation streamline. Strictly speaking, the result derived under these conditions can＇t represent the real situation in impellers. To overcome drawback in the past and attain universal relative Bemoulli＇s equation, authors of this paper computed three sorts of accelerations by using vectored analysis, got the gradient of magnitudes contained in relative Bemoulli＇s equation and finally attained relative Bemoulli＇s equation in relative coordinate system, The results obtained in this paper are applicable to the whole flow field, without the restriction of one relative streamline. Both the methods and process presented in this paper are different from those in previous means and can formulate a more reliable foundation for Euler＇s equation of centrifugal pumps.