同心环隙有压科特（Couette）流总论

On Couette Flow in a Concentric Circular Clearance With Pressure Gradient

本文利用恒定流动量矩定律以及科特流与槽道流的动力相似性,对外环固定,内环以恒速旋转且压力梯度 p/ θ为正的同心环隙科特流导出了两环面切应力、流速极坏面或流速拐环面及其坐标的方程。这些方程是由2个无因次参变量c_(f1)/c_(f2)·1/η~2,Pr= p/ θ·(η~2-1)/2c_(f1)ρV_0~2所构成的显函数方程组。本文明确地提出了科特数Pr作为环隙科特流的判据与准则的概念,根据它的值,可以把这种流动划分为以下4类: Pr=0 无压( p/ θ=0)环隙科特流。 Pr=1 类似半槽道流的有压环隙科特流,此时静环面切应力为零,流速分布曲线垂直于静环面。 Pr≥1 第1类有压环隙科特流,流扬中存在零切应力环与流速极环面。 0≤Pr≤1 第2类有压环隙科特流,流场中一般地存在流速拐环面。上述分类也把无压平面科特流,有压平面科特流以及槽道流作为特例包括在它的范畴之中。

A universal theory of the steady incompressible Couette flow in an annular Channel with a moving core is presented, the Couette flow with positive pressure gradient is disscused in detail only. By applying the mementum theory and Kinetic analogy of the Couette flow to the channel flow six parameter equations of the Couette flow are derive6, i. e. Two wall-surface Shear stress, the extrenal or the inflexion velocities and their Coordinates, with which the distribution of velocity and shear stress can be easily obtained. All parameters are functions of two-dimensional compound parameters, i. e. cf_1/cf_2η~2 and Pr= p/ θ(η~2-1)/2cf_1ρV_0~2 In which Pr plays a rule of the analogy criterion of the Couette flow designated as the Couette number in memory of its predecesser M. Couette. According to its value the Couette flow can be classified into 4 as Pr0 Non-pressure gradient( p/ θ=0)couette flow Pr=1 The couette flow which is similar to a simi-Channel flow. In such a case the shearing stress of fixed wall-surface is zero and the velocity distribution curve is perpendicular to the fixed wall-surface and forming a boundary of so called first and second Couette flows as follows: Pr≥1 The first Couette flow in which the zero shearing stress point and the extremum point of velocity exist. 0≤Pr≤1 The second Couette flow in which the inflexion point of velocity exists. The plane Couette flow and the channel flow as the special cases of the Couette flow are included in its scope.