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.

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。

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。

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.

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

The results presented are obtained from sound velocity measurements, uniaxial compression tests, Brazilian tests and three-point bending tests. The density of microcracks in the heated rock is studied by means of optical microscopy, SEM and differential strain analysis (DSA).

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.

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

Effect of surface roughness on rarefied-gas heat transfer in microbearings

In this Letter, the rarefaction and roughness effects on the heat transfer process in gas microbearings are investigated. A heat transfer model is developed by introducing two-variable Weierstrass-Mandelbrot (W-M) function with fractal geometry. The heat transfer problem in the multiscale self-affine rough microbearings at slip flow regime is analyzed and discussed. The results show that rarefaction has more significant effect on heat transfer in rough microbearings with lower fractal dimension. The negative influence of roughness on heat transfer found to be the Nusselt number reduction. The heat transfer performance can be optimized with increasing fractal dimension of the rough surface. © 2012 Elsevier B.V. All rights reserved.

Shock creation and particle acceleration driven by plasma expansion into a rarefied medium

The expansion of a dense plasma through a more rarefied ionized medium is a phenomenon of interest in various physics environments ranging from astrophysics to high energy density laser-matter laboratory experiments. Here this situation is modeled via a one-dimensional particle-in-cell simulation; a jump in the plasma density of a factor of 100 is introduced in the middle of an otherwise equally dense electron-proton plasma with an uniform proton and electron temperature of 10 eV and 1 keV, respectively. The diffusion of the dense plasma, through the rarefied one, triggers the onset of different nonlinear phenomena such as a strong ion-acoustic shock wave and a rarefaction wave. Secondary structures are detected, some of which are driven by a drift instability of the rarefaction wave. Efficient proton acceleration occurs ahead of the shock, bringing the maximum proton velocity up to 60 times the initial ion thermal speed. (C) 2010 American Institute of Physics. [doi: 10.1063/1.3469762]

Generation of a Purely Electrostatic Collisionless Shock during the Expansion of a Dense Plasma through a Rarefied Medium

A two-dimensional numerical study of the expansion of a dense plasma through a more rarefied one is reported. The electrostatic ion-acoustic shock, which is generated during the expansion, accelerates the electrons of the rarefied plasma inducing a superthermal population which reduces electron thermal anisotropy. The Weibel instability is therefore not triggered and no self-generated magnetic fields are observed, in contrast with published theoretical results dealing with plasma expansion into vacuum. The shock front develops a filamentary structure which is interpreted as the consequence of the electrostatic ion-ion instability, consistently with published analytical models and experimental results.

Two-dimensional particle-in-cell simulation of the expansion of a plasma into a rarefied medium

The expansion of a dense plasma through a more rarefied ionized medium has been studied by means of two-dimensional particle-in-cell simulations. The initial conditions involve a density jump by a factor of 100, located in the middle of an otherwise equally dense electron-proton plasma with uniform proton and electron temperatures of 10 eV and 1 keV, respectively. Simulations show the creation of a purely electrostatic collisionless shock together with an ion-acoustic soliton tied to its downstream region. The shock front is seen to evolve in filamentary structures consistently with the onset of the ion-ion instability. Meanwhile, an un-magnetized drift instability is triggered in the core part of the dense plasma. Such results explain recent experimental laser-plasma experiments, carried out in similar conditions, and are of intrinsic relevance to non-relativistic shock scenarios in the solar and astrophysical systems.

Magnetic field suppression in collision-less shocks generated during the expansion of a dense plasma into a rarefied medium

A two-dimensional numerical study of the expansion of a dense plasma through a more rarefied one is reported. The electrostatic ion-acoustic shock, which is generated during the expansion, accelerates the electrons of the rarefied plasma inducing a superthermal population which reduces electron thermal anisotropy. The Weibel instability is therefore not triggered and no self-generated magnetic fields are observed, in contrast with published theoretical results dealing with plasma expansion into vacuum. © The Author(s) 2013.