Get Acquaited with Rarefied Gas Dynamics

以通俗易懂的方式介绍了空气动力学当气体间断分子效应显著时发展起来的特殊分支--稀薄气体动力学。讨论了非平衡现象与稀薄气体动力学的关系。通过与8速度气体模型的间断Boltzmann方程的对比,解释了Boltzmann方程碰撞项的物理意义和数学困难,简要综述了其一般解法。讨论了分子在物体表面的反射和问题的边界条件,着重介绍了直接模拟Monte Carlo(DSMC)方法和为克服低速稀薄流动(如MEMS中流动)中模拟困难的信息保存(IP)方法。

Rarefied gas dynamics: fundamentals, simulations and micro flows

Shock wave diffraction by a square cavity filled with dusty gas

A simple two-dimensional square cavity model is used to study shock attenuating effects of dust suspension in air. The GRP scheme for compressible flows was extended to simulate the fluid dynamics of dilute dust suspensions, employing the conventional two-phase approximation. A planar shock of constant intensity propagated in pure air over Aat ground and diffracted into a square cavity filled with a dusty quiescent suspension. Shock intensities were M-s = 1.30 and M-s = 2.032, dust loading ratios were alpha = 1 and alpha = 5, and particle diameters were d = 1, 10 and 50 mum. It was found that the diffraction patterns in the cavity were decisively attenuated by the dust suspension, particularly for the higher loading ratio. The particle size has a pronounced effect on the flow and wave pattern developed inside the cavity. Wall pressure historics were recorded for each of the three cavity walls, showing a clear attenuating effect of the dust suspension.

Information preservation (IP) method in simulation of internal rarefied gas flows in MEMS

This paper reviews firstly methods for treating low speed rarefied gas flows: the linearised Boltzmann equation, the Lattice Boltzmann method (LBM), the Navier-Stokes equation plus slip boundary conditions and the DSMC method, and discusses the difficulties in simulating low speed transitional MEMS flows, especially the internal flows. In particular, the present version of the LBM is shown unfeasible for simulation of MEMS flow in transitional regime. The information preservation (IP) method overcomes the difficulty of the statistical simulation caused by the small information to noise ratio for low speed flows by preserving the average information of the enormous number of molecules a simulated molecule represents. A kind of validation of the method is given in this paper. The specificities of the internal flows in MEMS, i.e. the low speed and the large length to width ratio, result in the problem of elliptic nature of the necessity to regulate the inlet and outlet boundary conditions that influence each other. Through the example of the IP calculation of the microchannel (thousands m ? long) flow it is shown that the adoption of the conservative scheme of the mass conservation equation and the super relaxation method resolves this problem successfully. With employment of the same measures the IP method solves the thin film air bearing problem in transitional regime for authentic hard disc write/read head length ( 1000 L m ? = ) and provides pressure distribution in full agreement with the generalized Reynolds equation, while before this the DSMC check of the validity of the Reynolds equation was done only for short ( 5 L m ? = ) drive head. The author suggests degenerate the Reynolds equation to solve the microchannel flow problem in transitional regime, thus provides a means with merit of strict kinetic theory for testing various methods intending to treat the internal MEMS flows.

IP Simulation of Micro Gas Flows under 3-D Head Sliders

Gas film lubrication of a three-dimensional flat read-write head slider is calculated using the information preservation (IP) method and the direct simulation Monte Carlo (DSMC) method, respectively. The pressure distributions on the head slider surface at different velocities and flying heights obtained by the two methods are in excellent agreement. IP method is also employed to deal with head slider with three-dimensional complex configuration. The pressure distribution on the head slider surface and the net lifting force obtained by the IP method also agree well with those of DSMC method. Much less (of the order about 10(2) less) computational time (the sum of the time used to reach a steady stage and the time used in sampling process) is needed by the IP method than the DSMC method and such an advantage is more remarkable as the gas velocity decreases.

Drag on an ellipsoid particle in free-molecular plasma flow

Based on the analysis of molecular gas dynamics, the drag and moment acting on an ellipsoid particle of revolution X-2/a(2) + Y-2/a(2) + Z(2)/c(2) = 1, as an example of nonspherical particles, are studied under the condition of free-molecular plasma flow with thin plasma sheaths. A nonzero moment which causes nonspherical particle self-oscillation and self-rotation around its own axis in the plasma flow-similar to the pitching moment in aerodynamics-is discovered for the first time. When the ratio of axis length c/a is unity, the moment is zero and the drag formula are reduced to the well-known results of spherical particles. The effects of the particle-plasma relative velocity, the plasma temperature, and the particle materials on the drag and moment are also investigated.

Non-linear theory of a positive-column in a magnetic-field

A nonlinear theory of an intermediate pressure discharge column in a magnetic field is presented. Motion of the neutral gas is considered. The continuity and momentum transfer equations for charged particles and neutral particles are solved by numerical methods. The main result obtained is that the rotating velocities of ionic gas and neutral gas are approximately equal. Bohm's criterion and potential inversion in the presence of neutral gas motion are also discussed.

认识稀薄气体动力学

以通俗易懂的方式介绍了空气动力学当气体间断分子效应显著时发展起来的特殊分支－－稀薄气体动力学。讨论了非平衡现象与稀薄气体动力学的。通过与8速度气体模型的间断Boltzmann方程的对比，解释了Boltzmann方程碰撞项的物理意义和数学困难，简要综述了其一般解法。讨论了分在物体表面的反射和问题的边界条件，着重介绍了直接模拟Monte Carlo (DSMC)方法和为克服低速稀薄流动（如MEMS中流动）中模拟困难的信息保存（IP）方法。

第24届国际稀薄气体动力学会议简介

第24届国际稀薄气体动力学会议于2004年7月11日至16日在意大利巴里市召开.会议主席为巴里大学化学系主任马里奥?卡彼特利教授.

Statistical Simulation of Thin-Film Bearings

The information preservation (IP) method and the direct simulation Monte Carlo (DSMC) method are used to simulate the gas flows between the write/read head and the platter of the disk drive (the slider bearing problem). The results of both methods are in good agreement with numerical solution of the Reynolds equation in the cases studied. However, the DSMC method owing to the problem of large sample size demand and the difficulty in regulating boundary conditions at the inlet and outlet was able to simulate only short bearings, while IP simulates the bearing of authentic length ~1000 m ? and can provide more detailed flow information.

Development of a Cell Size Relaxed Scheme for the Direct Simulation Monte Carlo Method

The conventional direct simulation Monte Carlo (DSMC) method has a strong restriction on the cell size because simulated particles are selected randomly within the cell for collisions. Cells with size larger than the molecular mean free path are generally not allowed in correct DSMC simulations. However, the cell-size induced numerical error can be controlled if the gradients of flow properties are properly involved during collisions. In this study, a large cell DSMC scheme is proposed to relax the cell size restriction. The scheme is applied to simulate several test problems and promising results are obtained even when the cell size is greater than 10 mean free paths of gas molecules. However, it is still necessary, of course, that the cell size be small with respect to the flow field structures that must be resolved.

Information Preservation Modeling of Rayleigh-Benard Transition from Thermal Conduction to Convection

Onset and evolution of the Rayleigh-Benard (R-B) convection are investigated using the Information Preservation (IP) method. The information velocity and temperature are updated using the Octant Flux Splitting (OFS) model developed by Masters & Ye based on the Maxwell transport equation suggested by Sun & Boyd. Statistical noise inherent in particle approaches such as the direct simulation Monte Carlo (DSMC) method is effectively reduced by the IP method, and therefore the evolutions from an initial quiescent fluid to a final steady state are shown clearly. An interesting phenomenon is observed: when the Rayleigh number (Ra) exceeds its critical value, there exists an obvious incubation stage. During the incubation stage, the vortex structure clearly appears and evolves, whereas the Nusselt number (Nu) of the lower plate is close to unity. After the incubation stage, the vortex velocity and Nu rapidly increase, and the flow field quickly reaches a steady, convective state. A relation of Nu to Ra given by IP agrees with those given by DSMC, the classical theory and experimental data.

A Breakdown Criterion of Free Molecular Flows and an Optimum Analysis of EBPVD

Two important issues in electron beam physical vapor deposition (EBPVD) are addressed. The first issue is a validity condition of the classical cosine law widely used in the engineering context. This requires a breakdown criterion of the free molecular assumption on which the cosine law is established. Using the analytical solution of free molecular effusion flow, the number of collisions (N-c) for a particle moving from an evaporative source to a substrate is estimated that is proven inversely proportional to the local Knudsen number at the evaporation surface. N-c = 1 is adopted as a breakdown criterion of the free molecular assumption, and it is verified by experimental data and DSMC results. The second issue is how to realize the uniform distributions of thickness and component over a large-area thin film. Our analysis shows that at relatively low evaporation rates the goal is easy achieved through arranging the evaporative source positions properly and rotating the substrate.

稀薄气体动力学

通常的气体动力学方法，当气体分子的平均自由程与流场特征长度相比不可忽略时，不再适用，要采用稀薄气体动力学的方法。这适用于航天飞行器在高空飞行时受的力和热，也适用于微机电系统和真空系统等离子体材料加工等21世纪技术前沿领域。本书系统、简明地阐述稀薄气体动力学方法，给出方法的基础并着重介绍直接模拟Monte Carlo(DSMC)方法以及与低速稀薄气体流动相关的前沿课题。全书共分7章。前两章是作为学科的基础引入的，第1章以空气为对象对于分子能态结构、能态分布以极小篇幅作了简要概括的叙述，以作为了解稀薄气流非平衡现象物理基础的初步。第2章对包括双体碰撞、Boltzmann方程以及气体的平衡态等分子动理论的基础做了必要的讨论，其中包括了对唯像论分子相互作用模型、变径硬球（VHS）、变径软球（VSS）和概括化硬球（GHS）等模型的介绍。第3章讨论了各种分子和表面的相互作用模型，包括反映细致平衡的互易原理和基于此原理的CLL模型的阐述。第4章讨论自由分子流。第5章讨论应用于滑流领域的各连续介质方程及滑流边界条件，一些简单解以及热泳问题。第6章则较全面、概括地介绍了求解过程领域中的各种解析和数值方法。第7章介绍了直接模拟Monte Carlo(DSMC)方法，讨论了非平衡流动及低速稀薄流动等前沿课题，包括处理内能松弛、化学反应的方法、用于复杂流场通用软件的方法、低速稀薄流动的信息保存（IP）方法等。　　本书适合高等学校力学一航空航天专业高年级学生、研究生及从事气动力学和航天研究的科研人员参考阅读。

通常的气体动力学方法，当气体分子的平均自由程与流场特征长度相比不可忽略时，不再适用，要采用稀薄气体动力学的方法。这适用于航天飞行器在高空飞行时受的力和热，也适用于微机电系统和真空系统等离子体材料加工等21世纪技术前沿领域。本书系统、简明地阐述稀薄气体动力学方法，给出方法的基础并着重介绍直接模拟Monte Carlo(DSMC)方法以及与低速稀薄气体流动相关的前沿课题。

符号表
绪论
第1节 稀薄气体动力学的提出
第2节 气体的分子模型
第3节 分子平均自由程
第4节 流动的领域划分
第5节 非平衡现象与稀薄气体动力学
第6节 相似准则
第1章 分子结构与能态
第1节 双原子分子
第2节 分子的能态分布
第3节 分子的内能、内自由度和内能分布函数
第2章 分子动理论基础
第1节 速度分布函数
第2节 宏观量的表达
第3节 分子的双体碰撞模型
第4节 碰撞截面与分子模型
第5节 Boltzmann方程
第6节 碰撞积分与气体分子的总碰撞数
第7节 碰撞积分的计算
第8节 Maxwell输运方程——矩方程
第9节 Maxwell分布
第10节 气体的平衡态
第11节 8速度气体模型
第12节 混合气体
第3章 分子表面相互作用
第1节 引言
第2节 镜面反射与漫反射，适应系数
第3节 互易性原理
第4节 CLL分子表面相互作用模型
第4章 自由分子流
第1节 气体中的分子数目通量和动量通量
第2节 作用于物体的气动力
第3节 表面元素的热传导
第4节 自由分子流出与热流逸
第5节 Couette流动与平板间的传热问题
第6节 无碰撞Boltzmann方程的通解，非定常流动
第5章 连续介质模型
第1节 引言
第2节 基本方程
第3节 滑流边界条件
第4节 一些简单问题的求解
第5节 热蠕动与热泳
第6章 过渡领域
第1节 概述
第2节 线化的BoltzmanN方程
第3节 矩方法
第4节 模型方程
第5节 有限差分法
第6节 间断纵坐标方法
第7节 积分方法
第8节 直接模拟方法
第7章 直接模拟Monte方法
第1节 引言
第2节 碰撞的取样
第3节 DSMC方法求解问题实例
第4节 内能的激发与松弛
第5节 化学反应的模拟
第6节 复杂流场的计算，位置元方法
第7节 微尺度低速气体流动，信息保存法
附录I 气体的性质和分子性质
附录II 分布函数求矩遇到的积分
附录III 具有给定分布的随机数的取样
附录IV Couette问题程序
参考文献
主题词索引