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

Modelos cinéticos da equação linearizada de Boltzmann e um problema de transferência de calor em microescala

Neste trabalho, um problema de transferência de calor da dinâmica de gases rarefeitos, causado pela diferença de temperaturas nas superfícies de um canal, é abordado. O problema é formulado através dos modelos cinéticos BGK, S e Gross-Jackson da equação linearizada de Boltzmann e resolvido, de forma unificada, pelo método analítico de ordenadas discretas (método ADO). Resultados numéricos para as perturbações de densidade e temperatura e também para o fluxo de calor são apresentados e comparados, mostrando que não se pode dizer que algum dos três modelos seja uma melhor aproximação da solução aos resultados da equação linearizada de Boltzmann.

The spatial distribution of water in the inner coma of Comet 9P/Tempel 1: Comparison between models and observations

The near nucleus coma of Comet 9P/Tempel 1 has been simulated with the 3D Direct Simulation Monte Carlo (DSMC) code PDSC++ (Su, C.-C. [2013]. Parallel Direct Simulation Monte Carlo (DSMC) Methods for Modeling Rarefied Gas Dynamics. PhD Thesis, National Chiao Tung University, Taiwan) and the derived column densities have been compared to observations of the water vapour distribution found by using infrared imaging spectrometer on the Deep Impact spacecraft (Feaga, L.M., A’Hearn, M.F., Sunshine, J.M., Groussin, O., Farnham, T.L. [2007]. Icarus 191(2), 134–145. http://dx.doi.org/10.1016/j.icarus.2007.04.038). Modelled total production rates are also compared to various observations made at the time of the Deep Impact encounter. Three different models were tested. For all models, the shape model constructed from the Deep Impact observations by Thomas et al. (Thomas, P.C., Veverka, J., Belton, M.J.S., Hidy, A., A’Hearn, M.F., Farnham, T.L., et al. [2007]. Icarus, 187(1), 4–15. http://dx.doi.org/10.1016/j.icarus.2006.12.013) was used. Outgassing depending only on the cosine of the solar insolation angle on each shape model facet is shown to provide an unsatisfactory model. Models constructed on the basis of active areas suggested by Kossacki and Szutowicz (Kossacki, K., Szutowicz, S. [2008]. Icarus, 195(2), 705–724. http://dx.doi.org/10.1016/j.icarus.2007.12.014) are shown to be superior. The Kossacki and Szutowicz model, however, also shows deficits which we have sought to improve upon. For the best model we investigate the properties of the outflow.

Drag coefficients with applications to satellite orbits

In the last twenty or so years the results of theory and experiment have produced much information on the characteristics of gas-surface interactions relevant to a satellite in hyperthermal free-molecular flow. This thesis contains reviews of the rarefied gas dynamics applicable to satellites and has attempted to compare existing models of gas-surface interaction with contemporary knowledge of such systems. It is shown that a more natural approach would be to characterise the gas-surface interaction using the normal and tangential momentum accommodation coefficients, igma' and igma respectively, specifically in the form igma = constant , igma' = igma'0 -igma'1sec i where i is the angle subtended between the incident flow and the surface normal and igma,igma'0 and igma'1 are constants. Adopting these relationships, the effects of atmospheric lift on inclination, i, and atmospheric drag on the semi-major axis, a, and eccentricity, e, have been investigated. Applications to ANS-1 (1974-70A) show that the observed perturbation in i can be ascribed primarily to non-zero igma'1 whilst perturbations in a and e produce constraint equations between the three parameters. The numerical results seem to imply that a good theoretical orbit is achieved despite a much lower drag coefficient than anticipated by earlier theories.

The concentration-jump coefficient in a rarefied binary gas-mixture

The problem of the concentration jump of a vapour in the vicinity of a plane wall, which consists of the condensed phase of the vapour, in a rarefied gas mixture of that vapour (A) and another 'inert' gas (B), is considered. The general formulation of the problem of determining the concentration-jump coefficient for dA is given. In the Knudsen layer the simplest model of Boley-Yip theory is used to simplify the Boltzmann equations for the binary gas mixture. The numerical calculation of the concentration jump coefficient for dA for various values of evaporation coefficient of A is illustrated for the case of the equilibrium concentration of B being much greater than that of A, for which experimental data are available.

Couette Gas Flow Between Cylinders with Different Temperature

Петър Господинов, Добри Данков, Владимир Русинов, Стефан Стефанов - Изследвано е стационарно течение на Кует на разреден газ в случая на въртене на вътрешния цилиндър и неподвижен външен цилиндър чрез използване на DSMC метод и числено решение на уравненията на Навие–Стокс за относително малка (дозвукова) скорост на въртене. Изследвани са различни случаи при промяна на температурата на въртящият се цилиндър и числото на Кнудсен. Целта на изследването е да се установи влиянието на малки скорости на въртене върху макрохарактеристиките – плътността, скоростта и температурата на газа. Установено е добро съвпадение на резултатите получени по двата метода за Kn = 0.02. Получените резултати са важни при решаването на неравнинни, задачи от микрофлуидиката с отчитане на ефектите на кривината. Ключови думи: механика на флуидите, кинетична теория, разреден газ, DSMC.

Heat transfer in rarefied couette flow on the basis of discrete ordinate method

The method of discrete ordinates, in conjunction with the modified "half-range" quadrature, is applied to the study of heat transfer in rarefied gas flows. Analytic expressions for the reduced distribution function, the macroscopic temperature profile and the heat flux are obtained in the general n-th approximation. The results for temperature profile and heat flux are in sufficiently good accord both with the results of the previous investigators and with the experimental data.

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.

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.

Monte Carlo Simulation Of Thermal Fluctuations Below The Onset Of Rayleigh-Benard Convection

The density fluctuations below the onset of convection in the Rayleigh-Benard problem are studied with the direct simulation Monte Carlo method. The particle simulation results clearly show the connection between the static correlation functions of fluctuations below the critical Rayleigh number and the flow patterns above the onset of convection for small Knudsen number flows (Kn=0.01 and Kn=0.005). Furthermore, the physical nature for no convection in the Rayleigh-Benard problem under large Knudsen number conditions (Kn>0.028) is explained based on the dynamics of fluctuations.

Simulation of gas flow over a micro cylinder

Gas flow over a micro cylinder is simulated using both a compressible Navier-Stokes solver and a hybrid continuum /particle approach. The micro cylinder flow has low Reynolds number because of the small length scale and the low speed, which also indicates that the rarefied gas effect exists in the flow. A cylinder having a diameter of 20 microns is simulated under several flow conditions where the Reynolds number ranges from 2 to 50 and the Mach number varies from 0.1 to 0.8. It is found that the low Reynolds number flow can be compressible even when the Mach number is less than 0.3, and the drag coefficient of the cylinder increases when the Reynolds number decreases. The compressible effect will increase the pressure drag coefficient although the friction coefficient remains nearly unchanged. The rarefied gas effect will reduce both the friction and pressure drag coefficients, and the vortex in the flow may be shrunk or even disappear.

Development of an efficient particle approach for micro-scale gas flow simulations

The micro-scale gas flows are usually low-speed flows and exhibit rarefied gas effects. It is challenging to simulate these flows because traditional CFD method is unable to capture the rarefied gas effects and the direct simulation Monte Carlo (DSMC) method is very inefficient for low-speed flows. In this study we combine two techniques to improve the efficiency of the DSMC method. The information preservation technique is used to reduce the statistical noise and the cell-size relaxed technique is employed to increase the effective cell size. The new cell-size relaxed IP method is found capable of simulating micro-scale gas flows as shown by the 2D lid-driven cavity flows.

Statistical analysis of microscale gas flows and stock price changes

First, recent studies on the information preservation (IP) method, a particle approach for low-speed micro-scale gas flows, are reviewed. The IP method was validated for benchmark issues such as Couette, Poiseuille and Rayleigh flows, compared well with measured data for typical internal flows through micro-channels and external flows past micro flat plates, and combined with the Navier-Stokes equations to be a hybrid scheme for subsonic, rarefied gas flows. Second, the focus is moved to the microscopic characteristic of China stock market, particularly the price correlation between stock deals. A very interesting phenomenon was found that showed a reverse transition behaviour between two neighbouring price changes. This behaviour significantly differs from the transition rules for atomic and molecular energy levels, and it is very helpful to understand the essential difference between stock markets and nature.

Kinetic Studies of Gas Flows

Our recent studies on kinetic behaviors of gas flows are reviewed in this paper. These flows have a wide range of background, but share a common feature that the flow Knudsen number is larger than 0.01. Thus kinetic approaches such as the direct simulation Monte Carlo method are required for their description. In the past few years, we studied several micro/nano-scale flows by developing novel particle simulation approach, and investigated the flows in low-pressure chambers and at high altitude. In addition, the microscopic behaviors of a couple of classical flow problems were analyzed, which shows the potential for kinetic approaches to reveal the microscopic mechanism of gas flows.