# Manual Rarefied Gas Dynamics: Fundamentals, Simulations and Micro Flows

Many Particles Dynamics. A semi-continuous Boltzmann equation for particles with general dispersion relations. Kinetic Theory of Soft Matter. The Penetrable-Sphere Model. Investigation of peculiarities of small Reynolds number flows. Light-induced heat and mass transfer of rarefied gas in a flat channel. A reactive BGK-type model: influence of elastic collisions and chemical interactions. Consideration of the vibrationally linked molecular dissociation model based on the kinetic theory.

Continuous inverse kinetic theory for incompressible fluids. On one-dimensional discrete velocity models of the Boltzmann equation for mixtures. Analytical solutions to the full and linearized boltzmann equations for maxwell molecules. Modeling vibrationally favored dissociation with the macroscopic chemistry method. Lattice Boltzmann Method for phase-separating liquid-vapor systems.

Translational nonequilibrium of a gas by flow in vacuum through the constant cross-section channel. Hybrid Molecular Dynamics-Monte Carlo Simulations for the properties of a dense and dilute hard-sphere gas in a microchannel. On the accuracy of DSMC modeling of rarefied flows with real gas effects.

Fundamental study of hypersonic shock interactions about double cones. Recent developements and applications of Doppler Global Velocimetry in hypersonic wind tunnels. A comparison of semiclassical IVR and exact quantum collinear atom diatom transition probabilities for mixed reactive and non reactive regimes. Dynamics of collision-induced dissociation of two molecules with ionic bond. Atomic oxygen recombination and chemical energy accommodation on alumina at high temperature. A combined MD simulation and experimental investigation of the O 2 formation on beta-quartz at high temperature.

Molecular dynamics study on the evaporation part of the kinetic boundary condition at the interface between water and water vapor. Condensation of methanol vapor onto its liquid film on a solid wall behind a reflected shock wave. On the motion of solid particle in rarefied gas, sorbing on its surface.

An analysis and predicting the efficiency of atomic oxygen recombination and chemical energy accommodation on heated silica surfaces. Analytic solutions for the probability of atomic surface recombination as a function of surface parameters. Vibrational populations of the adlayer in exoergic processes at solid surfaces. Stochastic simulation of termoemission from surfaces of dusty grains. Stochastic simulation of fluctuation stage of phase transfer on solid surface during thin film formation. A fully coupled multigroup model for hypersonic radiating flows. Hypersonic transversal flow of rarefied gas mixture past infinite band.

Kinetics of ro-vibrationally excited H 2 molecules and H atoms in a plasma expansion. Experimental Investigation and Modelling of N 2 -thruster plume backflow. Studies on impingement effects of low density jets in transition regime - determination of shear stress and normal pressure. Numerical study of free transitional jets with FCT limited Scheme. DSMC modeling of innermost cometary atmosphere around spherical and non-spherical nucleus.

Analytical solutions for wave propagation in small scale channels. In the world literature the research on gas dynamics on the molecular level and on the internal physical processes inside molecules in the gas flows is very active. Relatively the domestic works on these aspects is fewer.

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From the viewpoint of the prospects of the subject and the demands of the development of science and technology research on gas dynamics on the micro-scale is a direction needs to be strengthened and further developed in our country, and it is appropriate to advocate and promote in the scientific research layout and education arrangement. This book elucidates the methods of molecular gas dynamics or rarefied gas dynamics which treat the problems of gas flows when the discrete molecular effects of the gas prevail under the circumstances of low density, the emphases being stressed on the basis of the methods, the direct simulation Monte Carlo method applied to the simulation of non-equilibrium effects and the frontier subjects related to low speed microscale rarefied gas flows.

As the basis of the discipline two chapters on molecular structure and basic kinetic theory are introduced. The first chapter devotes a minimum space in brief and summarized description of the molecular energy state structure and energy distribution as the necessary basis for the investigation of the non-equilibrium in high enthalpy rarefied gas flows.

The second chapter discusses the basis of the kinetic theory focusing on binary collisbns, Boltzmann equation and the equilibrium state of the gas, including the phenomenological molecular models: the VHS model of G. The third chapter discusses various realistic models of gas surface interactions, including the viii PREFACE reciprocity principle reflecting the detailed equilibrium, the CLL model based on this principle and the application in direct simulation in the cases including incomplete energy accommodation and internal energy exchange.

The fourth chapter deals with the free molecular flows.

## RAREFIED GAS DYNAMICS FUNDAMENTALS, SIMULATIONS AND MICRO FLOWS

Chapter 5 discusses the continuum equations and slip boundary conditions applied for slip flow regime, including Burnett equation the usability of which has been proved to be penetrated to more rarefied range. This chapter also includes the discussion of some simple problems solved by the Navier-Stokes equation plus slip boundary conditions and the problem of thermophoresis. Chapter 6 introduces with fair comprehensiveness and generality various analytical and numerical methods developed in transition regime.

Chapter 7 introduces the direct simulation Monte Carlo DSMC method with emphasis stressed on the specific issues encountered in dealing with non-equilibrium rarefied gas dynamics, including the work of the author and his colleague in treating the excitation and relaxation of the internal energy, the chemical reactions and the general coding of simulation of the flow field around complex configurations, i. Chapter 8 is dedicated to the simulation of low velocity micro scale rarefied gas flows which becomes an actual and urgent task encountered by the rarefied gas dynamics in the 21st century with the rapid development of the micro-electro-mechanical system MEMS.

Some methods of solution of the rarefied flow problems is examined from the point of view of utilization in simulating the flows in MEMS. The information preservation IP method is introduced with a general description, some validation of the method and a program demonstrating the method. The resolving of the boundary condition regulation problem in MEMS by using the conservative scheme and the super relaxation method is illustrated on the example of flow in long micro diannels.

In choosing the contents of the book the author proceeds out of the consideration to elucidate various essential basics of the subject and is influenced by his own interests, so the quotation of literature is far from complete, hoping the forgiveness and understanding of all the scientists having made contributions to the development of the subject. This book provides a solid basis for engaging in the studying of the molecular gas dynamics for the senior students and graduates in the aerospace and the mechanical engineering departments of universities and colleges, giving them an overall acquaintance of the modern development of rarefied gas dynamics in various regimes and leading them to reach the frontier topics of the non-equilibrium rarefied gas dynamics and the low speed microscale gas dynamics.

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It will be also of benefit to the scientific and technical workers engaged in the aerospace high altitude aerodynamic force and heating design and in the research on gas flow in the MEMS when treating practical gas dynamics problems. The author would appreciate Prof. Hu Zhenhua and Prof. Fan Jing for many helpful discussions concerning the contents of some sections of the book. The author thanks Mr. Tian Dongbo, Mr. Jiang Jianzheng, Mr. Xie Chong, and Dr. Liu Hongli who helped in making the drawings and layout of the book. Zhongguancun, Beijing, China September, C.

The properties of gases observed by the ordinary measuring apparatus are continuous and smooth, so the continuum hypothesis is natural. In practice or in the laboratory, the characteristic scale of flow under usual conditions has at least the size of lcm, and the change of physical or dynamic properties of gas in the range of l T3cm would be very small, the sensing volume of 1CT9COT3 would give the measurement of the local properties of the gas. From the fact that the Loschmidt number n0 the number of gas molecules in cm3 under standard -3 state is 2. This number is big enough to ensure that the average property of the gas is not influenced by the concrete number of molecules in this volume.

But under the special condition of extremely low density or when the size of the body is extremely tiny , the discrete particle effect becomes remarkable, and we are obliged to give up the continuum hypothesis and to adopt the discrete model, i. Strictly speaking, the failure of the continuum model happens when the shear stress and the heat flux in the continuum equations of mass, momentum and energy conservations can no longer be characterized by the macroscopic magnitudes of lower order velocity, temperature , that is, when the expressions of the transport coefficients are no longer valid.

This happens when the scale length of the gradients of the macroscopic quantities becomes so small that it is comparable with the molecular mean free path of the gas. When L in Eq. When Kn is less than 0. Such effects also belong to the category of rarefied gas dynamics effects. The density of the high altitude atmosphere decreases with descent of the height, the molecular mean free path increases from about 0.

In the problem of force action and the heating of missiles, spacecrafts, satellites, space shuttles and space stations, rarefied gas dynamics plays an important role. The modern rarefied gas dynamics is initiated from the studying of the force and heating action exerted on bodies flying at high altitude [1, 2]. In vacuum systems, with the enhancement of the vacuum degree, the mean free path becomes comparable with the characteristic length of the flow, and the molecular gas dynamics method is to be applied.

When considering problems like such of the shock wave structure, the macroscopic magnitudes experience consistently drastic change in several mean free paths, so the molecular description is to be invoked even under usual density conditions.

## Direct simulation Monte Carlo - Wikipedia

Generally, under usual density conditions, when the size of the subject of our investigation is small enough to be comparable with the mean free path, the gas discrete effect reveals itself, as in the case of the study of aerosol particles of the size of micrometer or less. In the last ten-odd years, the micro-electro-mechanical-systems MEMS 0. Owing to the tiny size of MEMS, when gas is used as the working media, the study of their properties requires the involvement of the rarefied gas effects. He supposes that these particles are of different sizes and shapes and are in persistent rapid motion, and attributes the differences in the properties of matter to the differences in the kinds of particles and the differences in their motion.

Owing to the absence of any convincing evidence this closest to truth hypothesis could be considered only as one of the many philosophic conjectures about the structure of matter and had been rejected by the authority at that time Aristotle B. The real quantitative argumentation of the kinetic theory of gases can be thought initiated by Daniel Bernoulli In Bernoulli explained Boyle's law, i.

From the fifties to eighties of the 19th century the work of Clausius , Maxwell and Boltzmann accomplished the founding and the overall development of the kinetic theory of gases.

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In Clausius introduced the concept of mean free path the average value of the distance traveled by a molecule between two successive collisions [3]. At the beginning of 20th century the experiments of Perrin el al. Chapman and Enskog in and respectively derived the exact expressions of the transport coefficients through entirely different mathematical ways [6, 7].