【作者】 张广路；

【导师】 吴承伟；

【作者基本信息】 大连理工大学 ， 应用与实验力学， 2009， 硕士

【摘要】 微/纳科技的高速发展对稀薄气体在过渡流区流动的建模提出了迫切需求。气体-固体界面的二阶滑移边界条件将N-S方程的适用范围扩展到过渡流区。由于该模型形式简洁、计算效率高,近年来被广泛应用。本文以二阶滑移边界条件下修正的雷诺方程研究可压缩气体和不可压缩气体的球面挤压特性。对于不可压缩气体流动,气体压强和球面反力的解答根据边界条件分为九种,其中前四种已有报道。本文给出二阶滑移边界条件下的其余五种解答。求解中当完全解析解无法得到时,采用数值解与解析解结合的方法,用数学解析技巧最大限度减少数值解的使用,使求解过程和最终解保持解析形式。算例显示,二阶滑移的影响随着克努森数和二阶滑移系数的增加而增大;在过渡流区,二阶滑移的影响显著。对于符合理想气体状态方程的可压缩气体,本文采用有限差分和直接迭代法求解雷诺方程。数值算例同样显示,二阶滑移的影响在过渡流区不可忽略;而在无滑移边界条件下,气体可压缩性的影响随着最小膜厚与球体半径比值的增加而增大。更多还原

【Abstract】 Development of micro/nanotechnology requires an effective model to investigate rarefied gas flow in the transition regime. Second-order slip boundary condition is used to extend the application scope of Navier-Stokes equations into the transition regime. Recently, this modeling is extensively used due to its simplicity and high-efficiency compared with molecular based theories. In this thesis, a modified Reynolds equation is employed to study the hydrodynamic behavior of incompressible and compressible squeezed gas film confined between spherical surfaces under second-order slip boundary condition.There are nine different cases for incompressible gas flow under no-slip, first-order slip and second-order slip boundary conditions. Gas pressure and hydrodynamic force of the first four cases have been reported in literature. This thesis presents solutions for the other cases. An approach of analytical method associated with numerical computation is supplemented when analytical method is ineffective. Illustrated examples show that a considerable effect of the second-order slip exists in the transition regime. This effect is enhanced by accretion of Knudsen number and the second-order slip coefficient.Finite differential method and iteration procedure are employed to solve compressible gas problem. Numerical examples indicate that a significant effect of the second-order slip occurs in the transition regime. It is also shown that the compressible effect under no-slip condition increases with the ratio of minimum gap height to sphere radius.更多还原