基于二阶滑移边界的螺旋槽干气密封泄漏量计算与分析

为解决螺旋槽干气密封流场计算中一阶线性滑移边界条件下得到的泄漏量与实验结果之间存在较大误差的问题,在一阶线性滑移边界条件的基础上,推导出二阶非线性滑移边界条件下的修正的广义雷诺方程,应用迭代法、PH 线性化方法等求解非线性雷诺方程,获得了气膜压力、流速、泄漏量的近似解.利用Maple程序计算了工程实例中不同转速和不同压力情况下的泄漏量,并与一阶线性滑移边界条件下的泄漏量和实验数值进行比较.结果表明:在工程实例中,压力相同时,泄漏量随转速的增大而增大,一、二阶最大相对误差分别为14.4%、5.4%;转速相同时,泄漏量随压力的增大而增大,一、二阶最大相对误差分别为33.3%、13.3%.本文未考虑干气密封内部的振动情况,因此一、二阶理论计算值小于实际测试值.二阶非线性滑移边界条件下的泄漏量值比一阶线性滑移边界条件下的泄漏量值更加接近实验数值,特别是在工程实例中转速、压力较低的工况下更加明显.     

氦气－空气混合环境中微型螺旋槽止推气浮轴承的承载特性分析

针对氦气-空气混合气体环境,分析了不同氦气体积含量下混合气体的黏度和分子平均自由程,利用有限单元法求解雷诺方程二阶滑移修正模型,计算了微型螺旋槽气浮轴承的气压和气膜厚度,研究了氦气体积含量、螺旋槽深度和转速对气浮轴承承载能力的影响.分析结果表明:当螺旋槽深度由1μm增至10μm时,气浮轴承的气膜厚度先增加后减小,槽深为5μm时,气膜厚度最大,气浮轴承的承载能力最佳.此外,当槽深小于5μm时,混合气体的分子平均自由程对气膜厚度的影响较大;当槽深大于5μm时,混合气体黏度的影响起主导作用.     

Navier-Stokes方程二阶速度滑移边界条件的检验

对微尺度气体流动,Navier-Stokes方程和一阶速度滑移边界条件的结果与实验数据相比,在滑移区相互符合,在过渡领域则显著偏离.为改善Navier-Stokes方程在过渡领域的表现,有些研究者尝试引入二阶速度滑移边界条件,如Cercignani模型,Deissler模型和Beskok-Karniadakis模型.以微槽道气体流动为例,将Navier-Stokes方程在不同的二阶速度滑移模型下的结果与动理论的直接模拟Monte Carlo(DSMC)方法和信息保存(IP)方法以及实验数据进行比较.在所考察的3种具有代表性的二阶速度滑移模型中,Cercignani模型表现最好,其所给出的质量流率在Knudsen数为0.4时仍与DSMC和IP结果相符;然而,细致比较表明,Cercignani模型给出的物面滑移速度及其附近的速度分布在滑流区和过渡领域的分界处(Kn=0.1)已明显偏离DSMC和IP的结果.     

不同滑移边界下的页岩渗透率修正模型

页岩中的孔隙直径通常为纳米量级,基于连续流的达西定律已不能描述纳米级孔隙内的气体流动规律,一般采用附加滑移边界条件的Navier-Stokes方程对其进行描述. 由此可导出与压力相关的渗透率公式(称为"视渗透率"),并用来修正达西定律.因而,渗透率修正方法研究成为页岩气流动研究的热点之一.首先,基于Hagen-Poiseuille 流推导出一般形式二阶滑移模型下的速度分布和流量公式,并推导出相应的渗透率修正公式.该渗透率修正公式基本能将现有的滑移速度模型统一表达为对渗透率的修正. 基于一般形式的渗透率修正公式,重点研究了Maxwell, Hsia, Beskok与Ng 滑移模型速度分布渗透率修正系数、及其对井底压力的影响;提出了基于Ng 滑移速度模型的渗透率修正公式. 基于页岩实际储层温压系统及孔隙分布,计算了Kn 范围及储层条件下页岩气的流动形态,表明页岩气流动存在滑移流、过渡流与分子自由流. 而Ng 模型能描述Kn<88 的滑移流、过渡流、自由分子流的流量规律,因此可以用于描述页岩实际储层中页岩气的流动特征. 计算表明,随着Kn 的增加,不同滑移模型下的渗透率修正系数差异增大.Maxwell与Hsia模型适用于滑移流与过渡流早期,Beskok与Ng 模型可描述自由分子流下的流动规律,但二者在虚拟的孔径均为10nm页岩中,井底压力的差别开始显现;在虚拟的孔径均为1nm页岩中,井底压力的差别开始明显.      

基于稀薄效应的微气体径向轴承稳态性能

针对微气体轴承给出参考努森数的定义,根据空气不同温度时的黏度,得到参考努森数的分布范围;考虑气体稀薄效应,给出基于Burgdorfer一阶滑移速度边界的微气体径向轴承润滑Reynolds方程的修正形式; 采用有限差分法求解修正的Reynolds方程,得到不同参考努森数$Kn_0$, 轴承数以及轴颈偏心率情况下轴承的压力分布、无量纲承载能力及偏位角. 数值分析表明:随气体稀薄程度的增强,气体径向轴承的压力明显降低,无量纲承载力降低,而轴承偏位角增大. 当偏心率小于0.6时,轴承偏位角变化平缓,受$Kn_0$数的影响不明显. 当轴承数较小时,气体稀薄程度对轴承的无量纲承载力、偏位角影响较小.      

超薄膜磁头滑块气动力特性

采用有限差分法对广义润滑方程进行数值求解,计算出计算机磁头滑块压强场的分布情况。分析、研究了其稳态和动态气动力特性,并将计算结果分别与求解一阶、二阶修正雷诺方程所得到的结果进行了比较,得到如下三个结论:(1)当飞行高度很小,飞行速度较低时,必须采用广义润滑方程进行磁头滑块的气动力计算,(2)与广义润滑方程结果比较,求解一阶修正雷诺方程所得到的计算结果总是偏高,而求解二阶修正雷诺方程所得到的计算结果总是偏低。此外,还解决了大压缩数下数值失稳问题,使得压缩数可以计算到120万,足以适应任何实际工程的需要。     

热耗散下螺旋槽干气密封气膜刚度的计算与分析

通过二阶非线性滑移边界条件下的雷诺方程并用PH线性化方法和迭代法求得螺旋槽内的气膜推力和气膜压力,并推导了其气膜厚度,得到二阶非线性滑移边界条件下气膜刚度的近似解析式,推导出考虑热耗散下的气膜能量微分方程;利用气膜的压力、能量方程、二阶非线性滑移边界条件下气膜刚度的近似解析式,通过Matlab软件求得螺旋槽内气膜刚度在不同压力、转速、槽深、螺旋角下的分布。结果表明:随着压力、转速、槽深的增大,气膜刚度随之增大,并在槽根部附近达到最大值,且气膜刚度的变化呈非线性;在槽深为6μm、介质压力为0.4MPa、转速为8700r·min-1、环境压力为101.3k Pa的工况下,螺旋角为75°左右时,气膜刚度最大。通过本文设计的在不同介质压力下的试验表明,通过能量微分方程计算所得的考虑热耗散下的气膜刚度数值比不考虑热耗散的气膜刚度数值更接近试验值。本文结果对优化干气密封结构参数、提升干气密封性能十分重要。     

柱面螺旋槽干气密封微尺度流动场稳态近似计算

针对高速、大振动等极端操作工况,提出一种新型柱面螺旋槽干气密封。基于此种干气密封结构特点,建立了考虑滑移边界条件下的微尺度效应稳态柱面雷诺方程,运用PH线性化方法、迭代法对雷诺方程进行近似求解,获得了气体压力的近似解析解,并运用MATLAB软件计算了特定工况下的气膜压力分布。分析了螺旋槽槽数、槽深、偏心率、密封宽度对气膜压力的影响。结果表明:柱面气膜压力先升高后降低,呈现类似抛物线的分布趋势,且在槽区-非槽区交界处出现压力波动;随着槽数和槽深的增加,气膜压力升高且峰值变化较大;随着偏心率的增大,气膜压力相应增大但峰值变化较小;密封宽度对气膜压力影响较小。     

考虑温粘热效应的多瓦轴承模型及其应用

构筑了轴向解析、周向有限元压力分布的一维变粘度场有限宽轴承模型。在绝热边界条件下,忽略泊肃叶流项对速度的影响,不考虑温度轴向变化并沿油膜厚度方向积分,三维能量方程可降阶为平均温度场只沿周向分布的一维形式,结合滑动轴承非线性油膜力的一维直接解法,能量方程与雷诺方程可分别求解,既考虑了温粘效应对滑动轴承非线性动力学性能的影响,又提供了无需迭代直接确定油膜破裂边界和求解非线性油膜力的快速新方法。作为应用,针对进油槽位于水平两侧的椭圆瓦轴承进行了动力润滑热效应分析,与工程数据比较,计算结果吻合,证明该模型合理,适用于工程上多瓦轴承的分析计算。     

基于Circular模型的大剪应变率点接触弹流界面滑移数值分析

采用Circular流变模型,将假定的流体的极限剪应力特性模型拟合入Reynolds方程,编写Fortran语言程序,数值模拟界面滑移效应.计算从弹流润滑(EHL)延展到动压润滑(HL)区域.随着速度增加,摩擦系数曲线出现反常波动,表现为两个异常拐点.在中、高速度下,模拟获得的接触轮廓等值线图中观测到入口凹陷及中心区下凸.进一步讨论了载荷、速度、综合弹性模量、滑滚比等因素对滑移的影响.界面滑移效应被认为是产生反常接触轮廓和摩擦力波动的主因,与试验结果互为验证.     

Forced Convection with Slip-flow in a Channel or Duct Occupied by a Hyper-porous Medium Saturated by a Rarefied Gas

An analytic solution is obtained for forced convection flow in a parallel-plates channel or a circular duct occupied by a hyper-porous medium saturated with a rarefied gas in the slip-flow regime, for the case of uniform flux boundary conditions. As expected, it is found that velocity slip leads in general to increased heat transfer and temperature slip leads to reduced heat transfer.     

Laminar slip flow of an electrically conducting incompressible rarefied gas in a channel with a transverse magnetic field

Summary The effects of a constant external magnetic field on the laminar, fully developed flow of an electrically conducting incompressible rarefied gas in a nonconducting parallel-plate channel are studied. Consideration is given to the slip-flow regime, wherein a gas velocity discontinuity occurs at the channel walls. It is found that the magnitude of the slip velocity is unaffected by the magnetic-field strength for a given pressure drop, but that the mean gas velocity and wall friction coefficient are functions of both the velocity slip coefficient and the magnetic-field strength. The effect of a second-order slip-flow boundary condition is briefly discussed.     

Low speed MHD Couette flow of a slightly rarefied and electrically conducting gas

The effects of an applied magnetic field on the steady, laminar, low speed plane Couette flow of a slightly rarefied and electrically conducting gas are studied. Consideration is given to the slip-flow regime, wherein the gas rarefaction begins to play its important role. The generally accepted method of analysis for slip flows is utilized, i.e. the continuum magnetohydrodynamic equations of motion are used throughout the gas, together with the first and the second order slip velocity and temperature jump boundary conditions. Considerations are further given to (1) the case of zero electric field and (2) the case of a nonconducting channel in which the net current across the channel is zero.     

Mass flow rate measurements in gas micro flows

The main objective of this experimental investigation on the gas flow slip regime is to measure the mass flow rate in isothermal steady flows through cylindrical micro tubes. Two technical procedures devoted to mass flow rate measurements are compared, and the measured values are also compared with the results yielded by different approximated analytical solutions of the gas dynamics continuum equations. Satisfactory results are obtained and the way is clearly opened to measuring mass flow rates for higher Knudsen numbers, over all the micro flow transitional regime.     

Numerical study of aerosol particle deposition in simple and converging-diverging micro-channels with a slip boundary condition at the wall

The design of micro-devices involving aerosol transport requires the study of the deposition of aerosols in micro-channels. In this study, the slip and no-slip boundary conditions for the gas flow regime were applied to the Navier-Stokes equations to obtain the particle deposition in simple and converging-diverging micro-channels. The equation of particle motion included inertial, viscous, Brownian, and gravity terms. It was found that the ratio of gravity to inertial effects controls the deposition of particles with diameters of 0.1-1 μm, and the ratio of diffusion to inertial effects controls the deposition of particles with diameters of 0.01-0.001 i~m. Comparison between the no-slip and slip flow regimes showed that the deposition of 0.1- to 1-μm-diameter particles was less and the deposition of 0.01- to 0.001-1μm-diameter particles was greater for the slip flow regime. There was no significant difference between slip and no-slip flow regimes for the deposition of 0.01- to 0.1-μm-diameter particles. Finally, it was shown that the stagnated gas in the corners of the converging-diverging micro-channel produced similar gas velocity profiles under the slip and no-slip flow regimes.     

Burnett simulation of flow and heat transfer in micro Couette flow using second-order slip conditions

The conventional Burnett equations with second-order velocity slip and temperature jump conditions were applied to the steady-state micro Couette flow of a Maxwellian monatomic gas. An analytical approach as well as a relaxation method was used to determine the velocity slip and temperature jump at the wall. Convergent solutions to the Burnett equations were obtained on arbitrary fine numerical grids for all Knudsen numbers (Kn) up to the limit of the equations’ validity. The Burnett equations with second-order slip conditions indicate a much better agreement with DSMC data over the first-order slip conditions at high Kn. The convergent Burnett solutions were obtained in orders of magnitude quicker than that with the corresponding DSMC simulation. The augmented Burnett equations were also introduced to model the flow but no obvious improvement in the results was found.     

Variational iteration method for two-dimensional steady slip flow in micro-channels

In this paper, the two-dimensional steady slip flow in microchannels is investigated. Research on micro flow, especially on micro slip flow, is very important for designing and optimizing the micro electromechanical system (MEMS). The Navier-Stokes equations for two-dimensional steady slip flow in microchannels are reduced to a nonlinear third-order differential equation by using similarity solution. The variational iteration method (VIM) is used to solve this nonlinear equation analytically. Comparison of the result obtained by the present method with numerical solution reveals that the accuracy and fast convergence of the new method.