Modeling of low-speed rarefied gas flows using a combined ES-BGK/DSMC approach

Modeling of low-speed gas flows at moderate Knudsen numbers, where conventional continuum CFD methods are inapplicable and kinetic methods are either inaccurate of prohibitively expensive, presents a significant challenge for computational modeling. In this work, an approach that combines a finite-volume solution of the ES-BGK model kinetic equation and the statistical DSMC method to accurately predict radiometric forces on a vane in large vacuum chamber filled with rarefied gas is presented. The approach in effect combines the accuracy of a statistical solution of the Boltzmann equation with the numerical efficiency of a deterministic solution of simplified model kinetic equations.     

Rarefied gas flow through channels of finite length at various pressure ratios

A rarefied gas flow through channels (i.e. flow through parallel plates) of finite length has been modeled based on the direct simulation Monte Carlo method. The reduced flow rate and the flow field have been calculated as function of the gas rarefaction, the length-to-height ratio and the pressure ratio upstream and downstream of the channel. The whole range of the gas rarefaction including the free-molecular, transitional and hydrodynamic regimes and a wide range of the length-to-height ratio representing both short and long channels have been considered. Several values of the pressure ratio between 0 and 0.5 have been used in the calculations. It is shown that the rarefaction parameter has the most significant effect on the flow field characteristics and patterns, followed by the pressure ratio, while the length-to-height ratio has a rather modest impact. The Mach belt phenomenon is discussed in detail.     

Computational study of a rarefied gas flow through a long circular pipe into vacuum

The paper presents an analysis of the non-linear rarefied gas flow through a circular pipe into vacuum. The main attention is given to the case of the large length to radius ratio. The problem is studied on the basis of the numerical solution of the S-model kinetic equation. Results are compared with the available DSMC data for short tubes as well as with the asymptotic solution corresponding to the infinitely long pipe.     

TPMC和DSMC方法在真空技术领域的应用

随着计算机技术的发展,蒙特卡罗方法(MC)成为研究稀薄气体流动问题的重要方法.本文着重介绍了试验粒子蒙特卡罗方法(TPMC)和直接模拟蒙特卡罗方法(DSMC).通过一些实际的算例(异形管路传输几率计算、涡轮分子泵模拟优化设计)讨论了它们在与真空技术相关的气体分子流和过渡流研究中的应用情况.     

Heat‐flux‐specified boundary treatment for gas flow and heat transfer in microchannel using direct simulation Monte Carlo method

Direct simulation Monte Carlo (DSMC) method has been widely used to study gaseous flow and heat transfer in micro‐fluidic devices. For flows associated with microelectromechanical systems (MEMS), the heat‐flux‐specified (HFS) boundary condition broadly exists. However, problems with HFS boundary have not been realized in the simulation of microchannel flows with DSMC method. To overcome this problem, a new technique named as inverse temperature sampling (ITS) is developed. This technique provides an approach to calculate the molecular reflective characteristic temperature from the specified heat flux at the wall boundary. Coupling with DSMC method, the ITS technique can treat the HFS boundary condition in DSMC method for both simple gas and gas mixtures. For validation, heat flux obtained from two‐dimensional Poiseuille flows with wall‐temperature‐specified (WTS) boundary condition is employed as the initial thermal boundary condition of our new method. Sampled wall temperature by the ITS method agrees well with the expected value. Pressure, velocity and temperature distributions under these two thermal boundary conditions (WTS and HFS) are compared. Effects of molecule collision model and gas–surface interaction model are also investigated. Results show that the proposed ITS method could accurately simulate gaseous flow and heat transfer in MEMS. Copyright © 2007 John Wiley & Sons, Ltd.     

End corrections for rarefied gas flows through capillaries of finite length

The influence of end effects on rarefied gas flows through moderately long capillaries is investigated by implementing the concept of effective capillary length, representing a sum of the real length of capillary and its increment. To calculate the length increment, a flow field near the inlet cross section of capillary is analyzed on the basis of the linearized kinetic equation. Far from the inlet inside of capillary, the solution is matched at the level of the distribution function with the one-dimensional solution corresponding to the flow in an infinite capillary. Far from the inlet outside of capillary, the gas is assumed to be in equilibrium at a specific pressure and temperature. The capillary length increment has been calculated as a function of the gas rarefaction. Using these results it is possible to estimate a flow rate through a moderately long capillary without hard calculations for the complete geometry.     

Effect of flow pulsation on fluidization degree of gas-solid fluidized beds by using coupled CFD-DEM

In this paper, the effect of inlet flow type on fluidization of a gas-solid fluidized bed was studied by using numerical simulations. Gas-solid fluidized beds are widely used in processes such as heating, cooling, drying, granulation, mixing, segregating and coating. To simulate the gas-particle flows, the unresolved surface CFD‐DEM was used considering Eulerian–Lagrangian approach. The fluid phase was modeled by computational fluid dynamics (CFD) while the solid phase was solved by discrete element method (DEM), and the coupling between gas and solid phases was considered to be four-way. The uniform and pulsed flows were injected through three nozzles located at the bottom of a rectangular bed. Three types of pulsed flow were considered: sinusoidal, rectangular and relocating. The fluidized bed behavior was discussed in terms of minimum fluidization velocity (MFV), pressure drop, bubble formation, bed expansion, particles velocity and, gas-solid interaction and particle contact forces. The results of different simulations indicated that the minimum fluidization velocity of the beds fluidized by pulsed flows was decreased by up to 33%. The influence of the pulsation amplitude on the minimum fluidization velocity was more significant than that of the pulsation frequency. The bed expansion and particles average velocity were increased by the pulsed flows, while the pressure drop and interaction force were decreased. As the pulsation frequency increased, the pressure drop and gas-solid interaction force increased, although size of the bubbles and bed expansion decreased. It was also observed that in large vibration frequencies, the bubbles became more regular. In the sinusoidal flow, the velocity and contact force between the particles were initially increased by frequency and in larger frequencies they were decreased.     

干式罗茨真空泵吸气级内流动的瞬态模拟

基于动网格方法建立了干式真空泵罗茨型吸气级的三维瞬态数值计算模型。模拟结果与抽速曲线对比,入口压力为1000 Pa时误差为11.5%,100 Pa时误差为34.2%,表明计算流体力学(CFD)方法不适用于入口压力较低及极限真空时真空泵内的流动研究,但在入口压力较高时具有较好的数值精度。由于干式真空泵的主要设计问题多集中于入口压力较高,负荷较大的运行工况,应用CFD方法研究干式真空泵的流动特性具有实用价值。文中计算了真空泵的性能参数,分析了泵腔内的流动现象和流场的主要特征。     

Computational fluid dynamics for turbomachinery internal air systems

Considerable progress in development and application of computational fluid dynamics (CFD) for aeroengine internal flow systems has been made in recent years. CFD is regularly used in industry for assessment of air systems, and the performance of CFD for basic axisymmetric rotor/rotor and stator/rotor disc cavities with radial throughflow is largely understood and documented. Incorporation of three-dimensional geometrical features and calculation of unsteady flows are becoming commonplace. Automation of CFD, coupling with thermal models of the solid components, and extension of CFD models to include both air system and main gas path flows are current areas of development. CFD is also being used as a research tool to investigate a number of flow phenomena that are not yet fully understood. These include buoyancy-affected flows in rotating cavities, rim seal flows and mixed air/oil flows. Large eddy simulation has shown considerable promise for the buoyancy-driven flows and its use for air system flows is expected to expand in the future.     

Asymptotic modelling of flows in microchannel by using Navier-Stokes or Burnett equations and comparison with DSMC simulations

The modelling of isothermal gas flows driven by pressure drops, in coplanar microchannels is investigated. The goal is to construct an asymptotic model deduced from Navier-Stokes or Burnett equations for this type of flow, assuming slip boundary conditions along the walls. The dimensionless balance equations are written, taking into account a geometrical parameter introduced in this study. The application of the Principle of Least Degeneracy produces models with small Mach numbers and small or moderate Knudsen numbers and allows the development of asymptotic models. The first and second approximations associated with the Navier-Stokes or Burnett equations are presented and discussed. Navier-Stokes and Burnett second approximations reduce the mass flow rates.Additionally, first asymptotic solutions as against Direct Simulation Monte Carlo (DSMC) simulations show overall satisfactory agreements.     

板翅式换热器封头型式的改造

采用计算流体力学(CFD)方法研究大型板翅式换热器封头内的流体流动,根据流动特征提出在封头段加入导流分布板改善流动分布均匀性的方法.与未加入导流分布板比较结果显示,加入导流分布板后,流体分布得到改善,传热系数亦有显著提高.     

Flow-dependent directional growth of carbon nanotube forests by chemical vapor deposition

We demonstrated that the structural formation of vertically aligned carbon nanotube (CNT) forests is primarily affected by the geometry-related gas flow, leading to the change of growth directions during the chemical vapor deposition (CVD) process. By varying the growing time, flow rate, and direction of the carrier gas, the structures and the formation mechanisms of the vertically aligned CNT forests were carefully investigated. The growth directions of CNTs are found to be highly dependent on the nonlinear local gas flows induced by microchannels. The angle of growth significantly changes with increasing gas flows perpendicular to the microchannel, while the parallel gas flow shows almost no effect. A computational fluid dynamics (CFD) model was employed to explain the flow-dependent growth of CNT forests, revealing that the variation of the local pressure induced by microchannels is an important parameter determining the directionality of the CNT growth. We expect that the present method and analyses would provide useful information to control the micro- and macrostructures of vertically aligned CNTs for various structural/electrical applications.     

Prediction of acceleration length in turbulent gas–solid flows

CFD investigation for gas–solid flows in a horizontal pipe was performed using Euler–Euler approach or two-fluid model and accounting for four-way coupling. Calibration of the numerical model is obtained by confirming the numerical predictions with published experimental data. Based upon the axial profiles of the pressure gradient, the authors investigated the acceleration length for different particle properties and loadings. It is found that acceleration length increases generally with increasing particulate loading and/or decreasing gas phase mean flow velocity. However, the variations of acceleration length with particle diameter are quite different under different operating conditions. Finally, an empirical correlation for acceleration length (L_a) is proposed, which contains two terms: the first-term matches with the entrance length for gas only flow; whereas the second term is regarded as the enhancement due to addition of solids to gas flow. The accuracy of the correlation is approximately ±11%.     

Glow discharge in external magnetic field in hypersonic flow of rarefied gas

A two-dimensional computational model is used to investigate the gasdynamic structure of a rarefied (pressure of several torr) hypersonic flow of molecular nitrogen in a plane channel, with a glow discharge maintained between two surfaces of this channel. An asymmetric configuration of electrodes is considered, namely, the cathode is a narrow strip located on the lower surface of the channel, and the upper surface of the channel is a continuous anode. The fundamental possibility is studied of using an external magnetic field transverse to the flow for modifying the shock-wave structure of flow in the channel.A two-dimensional conjugate electrogasdynamic model is given, which includes equations of continuity, Navier-Stokes equations, equations of conservation of energy, and equations of continuity of charged particles in ambipolar approximation. The real thermophysical and transport properties of molecular nitrogen are included.It is demonstrated that the use of a surface glow discharge in a rarefied hypersonic flow enables one to effectively modify the shock-wave structure of flow and, thereby, consider discharges of this type as additional means of control over rarefied gas flows.     

Plane thermal transpiration of a rarefied gas in the presence of gravitation

Plane thermal transpiration of a rarefied gas that flows horizontally in the presence of gravitation is studied based on the Boltzmann equation. Assuming that the temperature gradient along the walls is small, the asymptotic analysis for a slow variation in the flow direction is conducted. The semi-analytical solution that is valid for arbitrary values of the mean free path and the gravitational strength is derived, and the problem is reduced to solving the spatially one-dimensional Boltzmann equation. This reduced problem is solved numerically for a hard-sphere molecular gas for small values of gravitational strength, and the behavior of the flow is studied based on the numerical solution. The effect of weak gravitation is no longer negligible when the gas is so rarefied that the mean free path is comparable to the maximum range that the molecules travel along the parabolic path within the channel. This phenomenon has been observed in the plane Poiseuille flow of a highly rarefied gas, and a similar phenomenon also occurs in the plane thermal transpiration considered in the present paper.     

Gas flow measurement by the thin orifice and the classical Venturi tube

Many applications of vacuum technology require the generation and measurement of known gas flows. For this purpose, one may use ducts with constrictions. At a constriction, the flow-dependent pressure drop occurs. The gas throughput can be obtained from the inlet and outlet pressures at the constriction, provided its characteristics are known. In the present study, the characteristics of constrictions with basic geometry, i.e. the (infinitely) thin circular orifice and the standardised (DIN 1952) classical Venturi tube were investigated. Experimental methods for measuring the gas flow through a duct are described. The characteristics of individual constrictions were carefully measured and the data quantitatively compared to theoretical calculations. The results are discussed in order to provide a better understanding of the flow phenomena and to make them applicable to thin orifices and to Venturi tubes of any size and arbitrary gas. Over the whole flow range from molecular to viscous, the thin orifice can be used. However, it causes permanent pressure loss and it only has a small aperture in relation to the duct dimensions. In the viscous range, the Venturi tube can be used successfully. Thus, it is possible to establish stable secondary flow standards if the proper constriction is chosen.     

Prediction of micro-channel flows using direct simulation Monte Carlo

The direct simulation Monte Carlo (DSMC) method is a particle-based numerical modeling technique. It is recently used for simulating gaseous flow in micro-electro-mechanical-systems (MEMS) where micron-scale features become important. In this paper, numerical simulations of fluid flow in micro-channels are carried out using the DSMC method. The details in determining the parameters critical for DSMC applications in micro-channels are provided. Streamwise velocity distributions in the slip-flow regime are compared with the analytical solution based on the Navier–Stokes equations with slip velocity boundary condition. Satisfactory agreements have been achieved. Effects of the entrance and exit regions on simulation results are discussed. Simulations are then extended to transition flow regime (Kn>0.1) and compared with the analytical solution. It is shown that the results are distinguished with the analytical solutions, which fail to predict the flow due to the break down of continuum assumption. It is indicated that the gradient of the pressure along the channel direction dominates the motion of the fluid flow.     

三维高超声速稀薄气体流场通量分裂式DSMC-IP方法研究

结合非结构网格对复杂外形精确描述的能力和IP（Information Preservation）方法降低统计耗散的特点,该文在非结构网格的基础上构建了改进型通量分裂式DSMC（Direct Simulation of Monte Carlo）-IP数值方法,对三维高超声速稀薄气体流场进行了数值模拟。采用渐变尺度的非结构网格划分流场区域,在满足DSMC方法对网格尺度需求的同时,对流场的结构特点进行精确描述;另外根据Van Leer格式的思想改进IP方法中的通量计算格式,解决了激波处的数值间断问题;并采用单元信息保存法对IP方法进行补充,提高了计算方法的稳定性。通过对三维圆球绕流和航天飞机头部绕流流场的数值模拟,验证了该文方法的有效性和可行性,并对模型中的气动特性和参数分布规律进行了分析。     

Pressure driven rarefied gas flow through a slit and an orifice

The flow of a monatomic gas through a slit and an orifice due to an arbitrarily large pressure difference is examined on the basis of the nonlinear Bhatnagar-Gross-Krook (BGK) model equation, subject to Maxwell diffuse boundary conditions. The governing kinetic equation is discretized by a second-order control volume scheme in the physical space and the discrete velocity method in the molecular velocity space. The nonlinear fully deterministic algorithm is optimized to reduce the computational effort by introducing memory usage optimization, grid refinement and parallelization in the molecular velocity space. Results for the flow rates and the macroscopic distributions of the flow field are presented in a wide range of the Knudsen number for several pressure ratios. The effect of the various geometric and physical parameters on the flow field is examined. Comparison with previously reported corresponding Direct Simulation Monte Carlo (DSMC) results indicates a very good agreement, which clearly demonstrates the accuracy of the kinetic algorithm and furthermore the reliability of the BGK model for simulating pressure driven flows.