Rarefied Gas Flows in Micro-Channels

利用基于分子模型的统计模拟方法--信息保存方法(IP)统计模拟了实验条件下微槽道气体流动,仔细讨论了用IP方法模拟长槽道稀薄气流时遇到的问题,并给出了解决的方法,即采取守恒形式的控制方程避免质量流量计算误差积累,并利用超松弛方法使收敛过程加速。将IP计算结果与压力分布和质量流量实验数据进行了比较。

Statistical Simulation of Rarefied Gas Flows in Micro-Channels

Rarefied gas flows through micro-channels are simulated using particle approaches, named as the information preservation (IP) method and the direct simulation Monte Carlo (DSMC) method. In simulating the low speed flows in long micro-channels the DSMC method encounters the problem of large sample size demand and the difficulty of regulating boundary conditions at the inlet and outlet. Some important computational issues in the calculation of long micro-channel flows by using the IP method, such as the use the conservative form of the mass conservation equation to guarantee the adjustment of the inlet and outlet boundary conditions and the super-relaxation scheme to accelerate the convergence process, are addressed. Stream-wise pressure distributions and mass fluxes through micro-channels given by the IP method agree well with experimental data measured in long micro-channels by Pong et al. (with a height to length ratio of 1.2:3000), Shih et al. (l.2:4800), Arkilic et al. and Arkilic (l.3:7500), respectively. The famous Knudsen minimum of normalized mass flux is observed in IP and DSMC calculations of a short micro-channel over the entire flow regime from continuum to free molecular, whereas the slip Navier-Stokes solution fails to predict it.

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.

Rarefied gas dynamics: fundamentals, simulations and micro 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.

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.

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.

Some Exact-Solutions Describing Unsteady Plane Gas-Flows With Shocks

A new class of exact solutions of plane gasdynamic equations is found which describes piston-driven shocks into non-uniform media. The governing equations of these flows are taken in the coordinate system used earlier by Ustinov, and their similarity form is determined by the method of infinitesimal transformations. The solutions give shocks with velocities which either decay or grown in a finite or infinite time depending on the density distribution in the ambient medium, although their strength remains constant. The results of the present study are related to earlier investigations describing the propagation of shocks of constant strength into non-uniform media.

Heat transfer in plane Couette flow of a rarefied gas using Bhatnagar-Gross-Krook model

Using the linearized BGK model and the method of moments of half-range distribution functions the temperature jumps at two plates are determined, and it is found that the results are in fair agreement with those of Gross and Ziering, and Ziering.

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.

Characteristics of Micronozzle Gas Flows

The fluid characteristics of gas flows in the micronozzle whose throat height is 20 μm were investigated by the direct simulation Monte Carlo (DSMC) method. In a series of cases, the dependence of mass flux on the pressure difference was gained, and the DSMC's results show good agreement with the experimental data. The comparison of mass flux and the Mach number contours between the DSMC and Navier-Stokes equations adding slip boundary also reveals quantitatively that the continuum model will be invalid gradually even when the average Knudsen number is smaller than 0.01. As one focus of the present paper, the phenomenon of the multiple expansion-compression waves that comes from the nozzle's divergent part was analyzed in detailed.

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。

Micro-Scale Gas Flows

了解微尺度气体流动特点是微机电系统设计和优化的基础.有关的研究可以上溯到20世纪初Knudsen的平面槽道流动质量流量的测量和Millikan的小球阻力系数的测量,实验结果揭示了稀薄气体效应即尺度效应对气体运动的重要影响.由于流动特征长度很小,微尺度气流经常处于滑流区甚至过渡领域,流动的相似参数为Knudsen数和Mach数.因此可以考虑利用相似准则,通过增大几何尺寸、减小压力的途径,解决微机电系统实验观测遇到的困难.为解决直接模拟MonteCarlo方法分析微机电系统中低速稀薄气流遇到的统计涨落困难,我们提出了信息保存法(IP),该方法能够有效克服统计散布,并已成功用于多种微尺度气流.

Kinetic Assessment of Measured Mass Flow Rates and Streamwise Pressure Distributions in Microchannel Gas Flows

Measured mass flow rates and streamwise pressure distributions of gas flowing through microchannels were reported by many researchers. Assessment of these data is crucial before they are used in the examination of slip models and numerical schemes, and in the design of microchannel elements in various MEMS devices. On the basis of kinetic solutions of the mass flow rates and pressure distributions in microchannel gas flows, the measured data available are properly normalized and then are compared with each other. The 69 normalized data of measured pressure distributions are in excellent agreement, and 67 of them are within 1 +/- 0.05. The normalized data of mass flow-rates ranging between 0.95 and 1 agree well with each other as the inlet Knudsen number Kn (i) < 0.02, but they scatter between 0.85 and 1.15 as Kn (i) > 0.02 with, to some extent, a very interesting bifurcation trend.