CENTRIFUGAL INERTIA EFFECTS OF THE FLUID FLOW BETWEEN STEPPED SPHERICAL SURFACES

ＣＥＮＴＲＩＦＵＧＡＬＩＮＥＲＴＩＡＥＦＦＥＣＴＳＯＦＴＨＥＦＬＵＩＤＦＬＯＷＢＥＴＷＥＥＮＳＴＥＰＰＥＤＳＰＨＥＲＩＣＡＬＳＵＲＦＡＣＥＳＬｉｕＺｈｉｅｎ－ｂｅｉ（刘震北）（ＨａｒｈｉｎＩｎｓｔｉｔｕｔｅｏｆｔｅｃｈｎｏｌｏｇｙ．Ｈａｒｂｉｎ）（Ｒ...     

An approximate solution considering flow inertia between spherical surfaces

In this paper, the analytical expressions of the pressure distribution, velocity distribution and discharge of the flow between spherical surfaces are found by using the method of iterative approximate solution when the inertia terms of Navier-Stokes equations in spherical coordinates are taken into consideration. Furthermore, using these expressions, we can directly obtain the corresponding analytical expressions of the laminar radial flow between parallel disks, which are fully identical with corresponding results presented by refs. [3,4].     

An analysis on entrance region effect of the laminar radial flow between two parallel disks

In this paper, B. B. Golubef method^[1] is used for calculating the radial diffuse flow between two parallel disks for the first step. The momentum integral equation together with the energy integral equation is derived from the boundary layer momentum equation, and the expression of secondary approximation explicit function in which the channel length of entrance region varies with the boundary layer thickness can be obtained by using Picard iteration[2] in the solution of the energy integral equation. Therefore, this has made it possible to analyze directly and analytically the coefficients of the entrance region effect. In particular, when the outer diameter of disk is smaller than the entrance region length, the advantage of this method can be prominently manifest.Only because the energy integral equation is employed, the terms in the pressure loss coefficient can be independently derived theoretically. The computable value of the pressure loss coefficient presented in this paper is nearer to the testing value than that in ref. [3] when the entrance correction Reynolds number Re<100. Therefore the results in this paper within Re<100 are both reliable and simple.     

阶梯形球面间流体流动的离心惯性效应

本文推广运用了Ｓｏｍｍｅｒｆｅｌｄ代换方法，从而导出了阶梯形球面间流体流动考虑离心惯性效应的解析解，为球形静压推力轴承的精确设计提供了理论基础．     

AN ANALYSIS ON THE FLOW RESISTANCE IN THE ENTRANCE REGION OF DIFFUSE LAMINAR FLOW BETWEEN TWO PARALLEL SPHERICAL SURFACES

In this paper.V.V.Golubef method is first extended to the diffuse laminar flowbetween two parallel spherical surfaces.With the boundary layer motion equation inspherical coordinates,we derive the momentum integral equation together with the energyintegral equation for the laminar boundary layer of the entrance region between twoparallel spherical surfaces.And then by applying Picards gradually approaching methodfor the momentum integral equation,we get the approximate expression which the entranceregion length varies with the thickness of boundary layer.In the end,every coefficient ofentrace region effect is analyzed and calculated.     

AN APPROXIMATE SOLUTION CONSIDERING FLOW INERTIA BETWEEN SPHERICAL SURFACES

In this paper, the analytical expressions of the pressure distribution, velocity distribution and discharge of the flow between spherical surfaces are found by using the method of iterative approximate solution when the inertia terms of Navier-Stokes equations in spherical coordinates are taken into consideration. Furthermore, using these expressions, we can directly obtain the corresponding analytical expressions of the laminar radial flow between parallel disks, which are fully identical with corresponding results presented by refs.     

An analysis on the flow resistance in the entrance region of diffuse laminar flow between two parallel spherical surfaces

In this paper, V.V. Golubef method is first extended to the diffuse laminar flow between two parallel spherical surfaces. With the boundary layer motion equation in spherical coordinates, we derive the momentum integral equation together with the energy integral equation for the laminar boundary layer of the entrance region between two parallel spherical surfaces. And then by applying Picards gradually approaching method for the momentum integral equation, we get the approximate expression which the entrance region length varies with the thickness of boundary layer. In the end every coefficient of entrace region effect is analyzed and calculated. Projects Suported by the Science Fund of the Chinese Academy of Sciences.     

锥面间流体流动考虑流动惯性的近似解

本文采用锥坐标下的Navier-Stokes方程式,利用迭代近似解法,求出了考虑流动惯性时锥面间流体流动的速度分布、压力分布以及流量的解析式;并对轴对称过流流动的外向流和内向流进行了比较.     

球面间流体流动考虑流动惯性的近似解

本文利用球坐标下的Navier-Stokes方程式,采用迭代近似解法,求出了考虑流动惯性时的球面间流动的压力分布、速度分布以及流量的解析式。并利用此式可直接导出平行圆板间径向层流的相应解析表达式,它与文献[3],[4]中所提供的相应结果是完全一致的。     

AN ANALYSIS ON ENTRANCE REGION EFFECT OF THE LAMINAR RADIAL FLOW BETWEEN TWO PARALLEL DISKS

In this paper, B. B. Golubef method is used for calculating the radial diffuse flow between two parallel disks for the first step. The momentum integral equation together with the energy integral equation is derived from the boundary layer momentum equation and the expression of secondary approximation explicit function in which the channel length of entrance region varies with the boundary layer thickness can be obtained by using Picard iteration in the solution of the energy integral equation. Therefore, this has made it possible to analyze directly and analytically the coefficients of the entrance region effect. In particular, when the outer diameter of disk is smaller than the entrance region length, the advantage of this method can be prominently manifest. Only because the energy integral equation is employed, the terms in the pressure loss coefficient can be independently derived theoretically. The computable value of the pressure loss coefficient presented in this paper is nearer to the testing v