旋转圆筒泄漏流模型研究

An Analytical Model of Leakage Flow Between Coaxial Rotating Cylinders

为获得叶轮机叶尖泄漏流动规律,对周向压差作用下同轴旋转圆筒间泄漏流进行研究。以二维周向压差同轴旋转圆筒为模型,求解流动控制方程组获得以转速比和半径比量纲一化函数表达的圆筒间周向流动速度解析解;导出考虑周向压力梯度和圆筒旋转共同作用引起的周向量纲一泄漏流流量解析表达式;获得内外圆筒转速比、半径比、流体介质和流体温度等因素对泄漏流量的影响规律。结果表明:旋转圆筒间泄漏流量随转速比增加而增加,随半径比增加而减少;介质黏性较小时旋转圆筒的转动对泄漏流量的影响较小,周向压力梯度对泄漏流量的影响较大;介质黏性较大时周向压力梯度对泄漏流量的影响较小,圆筒的转动对泄漏流量的影响较大。

In order to obtain the tip leakage flow characteristics of turbomachines,the leakage flow between coaxial rotating cylinders under circumferential pressure difference was studied.By using a two-dimensional,circumferential pressure differential,coaxial rotating cylinder as a model,the analytical solutions for the circumferential flow velocity between cylinders expressed by the non-dimensional function of the rotational speed ratio and the radius ratio were obtained by solving the flow control equations.The analytical expression of the circumferential leakage flow,which is jointly caused by the circumferential pressure gradient and cylinder rotation,was derived.The influence of rotational speed ratio,radius ratio,fluid medium and fluid temperature on the leakage flow were determined.The results show that the leakage flow between rotating cylinders is increased with the increase of the rotation speed and decreased with the increase of the radius ratio.When the viscosity of the medium is low,the rotation of the cylinder has little effect on the leakage flow while the circumferential pressure gradient has a great influence on the leakage flow.When the viscosity of the medium is large,leakage flow is impacted greatly by the cylinder rotation while the circumferential pressure gradient impacts the leakage flow less.