Analysis Of Rarefied Gas Flow Research Articles

A Stochastic Two-Scale Model for Rarefied Gas Flow in Highly Heterogeneous Porous Media

This paper presents the development of a model enabling the analysis of rarefied gas flow through highly heterogeneous porous media. To capture the characteristics associated with the global- and the local-scale topology of the permeable phase in a typical porous medium, the heterogeneous multi-scale method, which is a flexible framework for constructing two-scale models, was employed. The rapid spatial variations associated with the local-scale topology are accounted for stochastically, by treating the permeability of different local-scale domains as a random variable. The results obtained with the present model show that an increase in the spatial variability in the heterogeneous topology of the porous medium significantly reduces the relevance of rarefaction effects. This clearly shows the necessity of considering a realistic description of the pore topology and questions the applicability of the results obtained for topologies exhibiting regular pore patterns. Although the present model is developed to study low Knudsen number flows, i.e. the slip-flow regime, the same development procedure could be readily adapted for other regimes as well.

Role of diffusion on molecular tagging velocimetry technique for rarefied gas flow analysis

The molecular tagging velocimetry (MTV) is a well-suited technique for velocity field measurement in gas flows. Typically, a line is tagged by a laser beam within the gas flow seeded with light emitting acetone molecules. Positions of the luminescent molecules are then observed at successive times and the velocity field is deduced from the analysis of the tagged line displacement and deformation. However, the displacement evolution is expected to be affected by molecular diffusion, when the gas is rarefied. Therefore, there is no direct and simple relationship between the velocity field and the measured displacement of the initial tagged line. This paper addresses the study of tracer molecules diffusion through a background gas flowing in a channel delimited by planar walls. Tracer and background species are supposed to be governed by a system of coupled Boltzmann equations, numerically solved by the direct simulation Monte Carlo (DSMC) method. Simulations confirm that the diffusion of tracer species becomes significant as the degree of rarefaction of the gas flow increases. It is shown that a simple advection–diffusion equation provides an accurate description of tracer molecules behavior, in spite of the non-equilibrium state of the background gas. A simple reconstruction algorithm based on the advection–diffusion equation has been developed to obtain the velocity profile from the displacement field. This reconstruction algorithm has been numerically tested on DSMC generated data. Results help estimating an upper bound on the flow rarefaction degree, above which MTV measurements might become problematic.

1427 シリコンウエハ薄膜形成における希薄ガス流動解析

1427 シリコンウエハ薄膜形成における希薄ガス流動解析

1202 実在表面の統計的表面粗さモデルを用いた平行平板間希薄気体流の解析

1202 実在表面の統計的表面粗さモデルを用いた平行平板間希薄気体流の解析

High Vectorization Ratio Coding of DSMC Method Analysis.

Conventional DSMC method analysis requires huge execution time in spite of its simple calculation method and use of high performance computer. This is because its analysis code has low vectorization ratio. In order to improve the vectorization ratio, in this study, the following ideas were introduced to the code : (1) random access array for particle registration to cell, (2) virtual boundary cell, (3) modification of flow-into and flow-out particle management and (4) lumpgeneration and storage of random numbers. Requiring large memory capacity, these ideas can avoid the execution of recursive procedures and improve the calculation efficiency. As a results, it was confirmed that the vectorization ratio was significantly improved (approximately from 18% to 94%) and the execution time was drastically reduced (acceleration ratio : approximately 11.3). It seems that this code contributes the computing load reduction of rarefied gas flow analysis.

Study on the Deposition Profile Characteristics in the Micron-Scale Trench Using Direct Simulation Monte Carlo Method

As integrated circuits are advancing toward smaller device features, step-coverage in submicron trenches and holes in thin film deposition are becoming of concern. Deposition consists of gas flow in the vapor phase and film growth in the solid phase. A deposition profile simulator using the direct simulation Monte Carlo method has been developed to investigate deposition profile characteristics on small trenches which have nearly the same dimension as the mean free path of molecules. This simulator can be applied to several deposition processes such as sputter deposition, and atmospheric- or low-pressure chemical vapor deposition. In the case of low-pressure processes such as sputter deposition, upstream boundary conditions of the trenches can be calculated by means of rarefied gas flow analysis in the reactor. The effects of upstream boundary conditions, molecular collisions, sticking coefficients, and surface migration on deposition profiles in the trenches were clarified.

Numerical analysis of rarefied gas flow through two-dimensional nozzles

A kinetic-theory analysis is made of the flow of a rarefied gas from one reservoir to another through twodimensional nozzles with arbitrary contour. The Boltzmann equation, simplified by the Bhatnagar, Gross, and Krook model for the collision integral, is solved by means of finite difference approximations with the discrete ordinate method. The physical space is transformed by a general grid-generation technique, and the velocity space is transformed to a polar coordinate system. A numerical code is developed that can be applied to any two-dimensional passage of complicated geometry for the flow regimes from free-molecular to slip. Numerical values of flow quantities can be calculated for the entire physical space, including both inside the nozzle and in the outside plume. Predictions are made for the case of parallel slots and compared with existing literature data. Also, results for the cases of convergent or divergent slots and two-dimensional nozzles with arbitrary contour at arbitrary Knudsen number are presented.

薄膜製造のミクロ機構 : 希薄気体流解析と微小溝部の薄膜形状

薄膜製造のミクロ機構 : 希薄気体流解析と微小溝部の薄膜形状

Generalized scheme of the no-time-counter scheme for the DSMC in rarefied gas flow analysis

Abstract The generalized scheme of the no-time-counter (NTC) scheme for the direct simulation Monte Carlo method in the analysis of rarefied gas flow is proposed. The generalized scheme is theoretically derived from Kac's master equation. This scheme gives the theoretical basis of the NTC scheme, in that the NTC scheme can be derived approximately from the generalized scheme. The applicability of the present scheme is verified through an application to the relaxation problem in which the non-equilibrium distribution function relaxes to an equilibrium one. The present scheme and the NTC scheme show good agreement with respect to the averaged quantities, such as distribution function and collision rate. From the point of view of application, the NTC scheme is sufficient for obtaining a result for the averaged quantities at least.

Rarefied gas flow analysis by direct simulation Monte Carlo method in body-fitted coordinate system

A new method is proposed for the rarefied gas flow analysis by the direct simulation Monte Carlo (DSMC) method in a multidimensional flow. In this method, a body-fitted coordinate system is used and therefore the DSMC method can be applicable to a flow-field analysis around the body of arbitrary configuration. Through an application to the rarefied supersonic flow around the circular cylinder, the present method was found to be reliable and time-saving in computation time.

Mass-flow reduction of rarefied gas by roughness of a slit surface (High-speed calculation of DSMC method on the vector processor).

Mass-flow reduction of rarefied gas through a two dimensional slit by roughness of a slit surface is investigated numerically. The direct simulation Monte-Carlo method is very effective in an analysis of rarefied gas flow but it costs a lot of CPU time, especially for the near-continuum regime. Recently, some super-computers with a vector processor are available and they enable high-speed calculation. It is necessary for using them in the best condition that a program is adequately vectorized. The programming technique called 'collection of data' is used very often, so that the simulation program eight times faster than conventional one is attained. In the transition regime, the effect of roughness of the slit surface on rarefied gas flow becomes clear. An experiment is carried out in order to confirm the effect.

Analysis of rarefied gas flow. Full solutions for burnett equations.

This paper concerns the numerical analysis of rarefied gas flowing through an orifice in a rotating cylinder. The full solutions for the Burnett equations in the steady state are successfully obtained and compared with those for the Navier-Stokes equations. Then, the pressure in the downstream side is chosen as a parameter to give an appropriate Knudsen number and a Much number. The results show construction of the rarefied gas flow, where the Burnett terms, or the higher order of approximation, reduces the contribution of the viscosity term in the equation of motion and of the conduction term in the equation of energy. The criteria of invalidity for the Navier-Stokes equations and the Burnett equations are discussed, too.

Kinetic theory analysis of rarefied gas flow through finite length slots

A kinetic theory analysis is made of the flow of a rarefied monatomic gas through a two‐dimensional slot connecting two reservoirs. Numerical solutions are obtained by the moment and discrete ordinate methods. The former method portrays the transition regime characteristics well, but has limitations in the free molecule regime. The latter method gives accurate results in the free molecule and slip regime and bolsters confidence in the accuracy of the transition regime results. The numerical solution for the mass flux through the slot agrees well with an approximate analytic solution of the moment equations for length‐to‐width ratios from 6 to 0.5, pressure ratios from 0.8 to 0.1, and Knudsen numbers from 5 to 0.5.