Simulations for gas flows in microgeometries using the direct simulation Monte Carlo method

Micro gas flows are often encountered in MEMS devices and classical CFD could not accurately predict the flow and thermal behavior due to the high Knudsen number. Therefore, the gas flow in microgeometries was investigated using the direct simulation Monte Carlo (DSMC) method. New treatments for boundary conditions are verified by simulations of micro-Poiseuille flow, compared with the previous boundary treatments, and slip analytical solutions of the continuum theory. The orifice flow and the corner flow in microchannels are simulated using the modified DSMC codes. The predictions were compared with existing experimental phenomena as well as predictions using continuum theory. The results showed that the channel geometry significantly affects the microgas flow. In the orifice flow, the flow separation occurred at very small Reynolds numbers. In the corner flow, no flow separation occurred even with a high driving pressure. The DSMC results agreed well with existing experimental information.     

Flow instability of nanofuilds in jet

The flow instability of nanofluids in a jet is studied numerically under various shape factors of the velocity profile, Reynolds numbers, nanoparticle mass loadings,Knudsen numbers, and Stokes numbers. The numerical results are compared with the available theoretical results for validation. The results show that the presence of nanoparticles enhances the flow stability, and there exists a critical particle mass loading beyond which the flow is stable. As the shape factor of the velocity profile and the Reynolds number increase, the flow becomes more unstable. However, the flow becomes more stable with the increase of the particle mass loading. The wavenumber corresponding to the maximum of wave amplification becomes large with the increase of the shape factor of the velocity profile, and with the decrease of the particle mass loading and the Reynolds number. The variations of wave amplification with the Stokes number and the Knudsen number are not monotonic increasing or decreasing, and there exists a critical Stokes number and a Knudsen number with which the flow is relatively stable and most unstable,respectively, when other parameters remain unchanged. The perturbation with the first azimuthal mode makes the flow unstable more easily than that with the axisymmetric azimuthal mode. The wavenumbers corresponding to the maximum of wave amplification are more concentrated for the perturbation with the axisymmetric azimuthal mode.     

Study on micronozzle flow and propulsion performance using DSMC and continuum methods

In this paper, both DSMC and Navier–Stokes computational approaches were applied to study micronozzle flow. The effects of inlet condition, wall boundary condition, Reynolds number, micronozzle geometry and Knudsen number on the micronozzle flow field and propulsion performance were studied in detail. It is found that within the Knudsen number range under consideration, both the methods work to predict flow characteristics inside micronozzles. The continuum method with slip boundary conditions has shown good performance in simulating the formation of a boundary layer inside the nozzle. However, in the nozzle exit lip region, the DSMC method is better due to gas rapid expansion. It is found that with decreasing the inlet pressure, the difference between the continuum model and DSMC results increases due to the enhanced rarefaction effect. The coefficient of discharge and the thrust efficiency increase with increasing the Reynolds number. Thrust is almost proportional to the nozzle width. With dimension enlarged, the nozzle performance becomes better while the rarefaction effects would be somewhat weakened.The project supported by the National Natural Science Foundation of China (10372099). The English text was polished by Boyi Wang     

Effects of Knudsen number and geometry on gaseous flow and heat transfer in a constricted microchannel

A flow and heat transfer numerical simulation is performed for a 2D laminar incompressible gas flow through a constricted microchannel in the slip regime with constant wall temperature. The effects of rarefaction, creeping flow, first order slip boundary conditions and hydrodynamically/thermally developing flow are assumed. The effects of Knudsen number and geometry on thermal and hydrodynamic characteristics of flow in a constricted microchannel are explored. SIMPLE algorithm in curvilinear coordinate is used to solve the governing equations including continuity, energy and momentum with the temperature jump and velocity slip conditions at the solid walls in discretized form. The resulting velocity and temperature profiles are then utilized to obtain the microchannel C _f Re and Nusselt number as a function of Knudsen number and geometry. The results show that Knudsen number has declining effect on the C _f Re and Nusselt number in the constricted microchannel. In addition, the temperature jump on wall and slip velocity increase with increasing Knudsen number. Moreover, by decreasing the throttle area, the fluid flow characteristics experience more intense variations in the constricted region. To verify the code a comparison is carried out with available results and good agreement is achieved.     

Burnett simulations of gas flow in microchannels

The Burnett equations with slip boundary conditions are used to model the gas flow in microchannels in transition flow regime. As the Navier-Stokes equations are not appropriate to model the gas flow in this regime, the higher-order Burnett equations are adopted in the present study. In earlier studies, convergent solutions of the Burnett equations of microPoiseuille flow could only be obtained when Knudsen number is less than 0.2. By using a relaxation method on the boundary values, convergent solutions of the Burnett equations can be obtained even when Knudsen number reaches 0.4. The solutions of Burnett equations agree very well with experimental data and direct simulation Monte Carlo (DSMC) results. The pressure distributions and velocity profiles are then discussed in detail.     

复杂微通道气体流动的格子Boltzmann模拟

构建了一个模拟复杂微通道内气体流动的多松弛格子Boltzmann模型。该模型采用动力学曲面滑移边界,考虑了微尺度效应和努森层影响。此外,为了更准确地描述微通道内气体的滑移速度,在模型中引入孔隙局部Kn数来代替平均Kn数。之后采用Poiseuille流对模型进行验证,模拟结果与用直接模拟蒙特卡洛方法和分子模拟结果吻合较好,证明了该模型模拟微通道内处于滑移区和过渡区气体流动的有效性。最后,采用该模型模拟多孔介质内气体渗流过程。结果表明,随着孔隙平均Kn数的增加,多孔介质内的高渗区域增加,且优先从小孔隙中开始增加,这是由于小孔隙中微尺度效应更加明显,相对大孔隙流动阻力更小所致。     

Intense evaporation of a gas from a two-dimensional periodic surface

Evaporation (or condensation) of a gas is said to be intense when the normal component of the velocity of the gas in the Knudsen layer has a value of the order of the thermal velocity of a molecule, c_T=(2kT/m)^1/2. In this case the distribution function of the molecules with respect to their velocities in the Knudsen layer differs from the equilibrium (Maxwellian) value by its own magnitude. As a result of this, over the thickness of the Knudsen layer the macroparameters also vary by their own magnitudes. So in order to obtain the correct boundary conditions for the Euler gas dynamic equations, it is necessary to solve the nonlinear Boltzmann equation in the Knudsen layer. The problem of obtaining such boundary conditions for the case of a plane surface was considered in [1–11]. In the present study this problem is solved for a two-dimensional periodic surface in the case when the dimensions of the inhomogeneities are of the order of the mean free path of the molecules and the inhomogeneities have a rectangular shape. The flow in the Knudsen layer becomes two-dimensional, and this leads to a considerable complication of the solution of the problem.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 132–139, March–April, 1985.In conclusion the author would like to express his gratitude to V. A. Zharov for his valuable advice, and also V. S. Galkin, M. N. Kogan, and N. K. Makashev for discussion of the results obtained.     

Rarefied gas flow in a channel with specular‐diffuse boundary conditions for arbitrary knudsen numbers. Onsager relations

The problem of a rarefied gas flow in a channel for arbitrary Knudsen numbers has been solved analytically for the first time in the case where the scattering of gas molecules on the channel walls can be described by speculardiffuse boundary conditions. The mean free path of gas molecules is assumed to be constant, i.e., the collision frequency is proportional to molecular velocity. The gas moves under the action of a streamwise temperature gradient. Exact relations for heat and mass fluxes and for meanmass velocity are obtained. It is shown that the Onsager relations are valid within the entire range of Knudsen numbers in the problem of heat and mass transfer in a channel. The dependence of heat and mass fluxes on the Knudsen number (channel thickness) is analyzed. A comparison with available results is performed.     

Vapor flows with evaporation and condensation in the continuum limit: effect of a trace of noncondensable gas

Steady flows of a vapor with evaporation and condensation on the boundary consisting of the condensed phase of the vapor are considered in the following situation: (i) the boundary is of arbitrary smooth shape; (ii) the Knudsen number Kn, the ratio of the typical mean free path of the vapor molecules to the characteristic length of the system, is small; (iii) a small amount of a noncondensable gas is contained in the system; more specifically, the amount is such that the average concentration of the noncondensable gas is of the order of Kn in the case of a closed domain (the case of an infinite domain is also discussed). The steady behavior of the vapor and the noncondensable gas, in particular, that in the continuum limit where Kn vanishes, is investigated by means of a systematic asymptotic analysis based on kinetic theory. In this situation, the average concentration of the noncondensable gas becomes infinitely small in the continuum limit in the case of a closed domain. However, it is shown that the noncondensable gas accumulates in the infinitely thin Knudsen layer on the boundary where condensation is taking place and has a significant effect on the global vapor flow in the continuum limit. An example demonstrating such an effect is also given.     

DIAMOND PORT JET INTERACTION WITH SUPERSONIC FLOW

Interaction flow field of the sonic air jet through diamond shaped orifices at different incidence angles （10 degrees, 27.5 degrees, 45 degrees and 90 degrees） and total pressures （0.10 MPa and 0. 46 MPa） with a Mach 5.0 freestream was studied experimentally. A 90 degrees circular injector was examined for comparison. Crosssection Mach number contours were acquired by a Pitot-cone five-hole pressure probe. The results indicate that the low Mach semicircular region close to the wall is the wake region. The boundary layer thinning is in the areas adjacent to the wake. For the detached case, the interaction shock extends further into the freestream, and the shock shape has more curvature, also the low-Mach upwash region is larger. The vortices of the plume and the height of the jet interaction shock increase with increasing incidence angle and jet pressure. 90 degrees diamond and circular injector have stronger plume vorticity, and for the circular injector low-Mach region is smaller than that for the diamond injector. Tapered ramp increases the plume vorticity, and the double ramp reduces the level of vorticity. The three-dimensional interaction shock shape was modeled from the surface shock shape, the center plane shock shape, and crosssectional shock shape. The shock total pressure was estimated with the normal component of the Mach number using normal shock theory. The shock induced total pressure losses decrease with decreasing jet incidence angle and injection pressure, where the largest losses are incurred by the 90 degrees, circular injector.     

基于稀薄效应的微气体径向轴承稳态性能

针对微气体轴承给出参考努森数的定义,根据空气不同温度时的黏度,得到参考努森数的分布范围;考虑气体稀薄效应,给出基于Burgdorfer一阶滑移速度边界的微气体径向轴承润滑Reynolds方程的修正形式; 采用有限差分法求解修正的Reynolds方程,得到不同参考努森数$Kn_0$, 轴承数以及轴颈偏心率情况下轴承的压力分布、无量纲承载能力及偏位角. 数值分析表明:随气体稀薄程度的增强,气体径向轴承的压力明显降低,无量纲承载力降低,而轴承偏位角增大. 当偏心率小于0.6时,轴承偏位角变化平缓,受$Kn_0$数的影响不明显. 当轴承数较小时,气体稀薄程度对轴承的无量纲承载力、偏位角影响较小.      

Thermally developing flow in finned double‐pipe heat exchanger

A numerical solution of the convective heat transfer in the thermal entry region of the finned double‐pipe is carried out for the case of hydro‐dynamically fully developed flow when subjected to uniform wall temperature boundary condition. Adaptive axial grid size is used in order to cater for the variation of large solution gradients in the axial direction. It has been observed that the thermal entrance region is highly effective and there is a substantial enhancement in the heat transfer coefficient. A maximum of 76.4877% increase has been observed in the thermal entrance region as compared with the fully developed region for 24 fins and H*=0.6 when R?=0.25, whereas for R?=0.5 the maximum increase is 75.0308% for the same number of fins of same height. It has been observed that no geometry consistently perform better throughout the entrance region. However, the geometries that have optimal performance in the fully developed region perform better in the developing region on average terms. Results show that the Nusselt number and the thermal entrance length are dependent upon various geometrical parameters such as ratio of radii of the inner and the outer pipe, fin height and the number of fins. The limiting case results match well with the literature results. This validates our numerical procedure and computer code. Copyright © 2010 John Wiley & Sons, Ltd.     

Improved parallel preconditioners for multidisciplinary topology optimisations

Two commonly used preconditioners were evaluated for parallel solution of linear systems of equations with high condition numbers. The test cases were derived from topology optimisation applications in multiple disciplines, where the material distribution finite element methods were used. Because in this optimisation method, the equations rapidly become ill-conditioned due to disappearance of large number of elements from the design space as the optimisations progresses, it is shown that the choice for a suitable preconditioner becomes very crucial. In an earlier work the conjugate gradient (CG) method with a Block-Jacobi preconditioner was used, in which the number of CG iterations increased rapidly with the increasing number processors. Consequently, the parallel scalability of the method deteriorated fast due to the increasing loss of interprocessor information among the increased number of processors. By replacing the Block-Jacobi preconditioner with a sparse approximate inverse preconditioner, it is shown that the number of iterations to converge became independent of the number of processors. Therefore, the parallel scalability is improved.     

Asymptotic theory of the Boltzmann system,for a steady flow of a slightly rarefied gas with a finite Mach number: General theory

A steady rarefied gas flow with Mach number of the order of unity around a body or bodies is considered. The general behaviour of the gas for small Knudsen numbers is studied by asymptotic analysis of the boundary-value problem of the Boltzmann equation for a general domain. The effect of gas rarefaction (or Knudsen number) is expressed as a power series of the square root of the Knudsen number of the system. A series of fluid-dynamic type equations and their associated boundary conditions that determine the component functions of the expansion of the density, flow velocity, and temperature of the gas is obtained by the analysis. The equations up to the order of the square root of the Knudsen number do not contain non-Navier–Stokes stress and heat flow, which differs from the claim by Darrozes (in Rarefied Gas Dynamics, Academic Press, New York, 1969). The contributions up to this order, except in the Knudsen layer, are included in the system of the Navier–Stokes equations and the slip boundary conditions consisting of tangential velocity slip due to the shear of flow and temperature jump due to the temperature gradient normal to the boundary.     

Empirical slip and viscosity model performance for microscale gas flow

For the simple geometries of Couette and Poiseuille flows, the velocity profile maintains a similar shape from continuum to free molecular flow. Therefore, modifications to the fluid viscosity and slip boundary conditions can improve the continuum based Navier–Stokes solution in the non‐continuum non‐equilibrium regime. In this investigation, the optimal modifications are found by a linear least‐squares fit of the Navier–Stokes solution to the non‐equilibrium solution obtained using the direct simulation Monte Carlo (DSMC) method. Models are then constructed for the Knudsen number dependence of the viscosity correction and the slip model from a database of DSMC solutions for Couette and Poiseuille flows of argon and nitrogen gas, with Knudsen numbers ranging from 0.01 to 10. Finally, the accuracy of the models is measured for non‐equilibrium cases both in and outside the DSMC database. Flows outside the database include: combined Couette and Poiseuille flow, partial wall accommodation, helium gas, and non‐zero convective acceleration. The models reproduce the velocity profiles in the DSMC database within an L₂ error norm of 3% for Couette flows and 7% for Poiseuille flows. However, the errors in the model predictions outside the database are up to five times larger. Copyright © 2005 John Wiley & Sons, Ltd.     

Permissible Height of the Surface Roughness in a Turbulent Boundary Layer with a Streamwise Pressure Gradient

The results of an experimental investigation of the effect of the streamwise pressure gradient in a turbulent boundary layer on the permissible height of the surface roughness of bodies in an incompressible fluid flow are presented. The permissible roughness Reynolds number for which the characteristics of the turbulent boundary layer remain the same as in the case of flow past a smooth surface is determined.     

多场作用下输流单层碳纳米管的动力学特性

以非局部弹性理论为基础,采用欧拉-伯努利梁模型,考虑管型区域内滑移边界条件以及碳纳米管的小尺度效应,应用哈密顿原理获得了温度场与轴向磁场共同作用下的输流单层固支碳纳米管（SWCNT）的振动控制方程以及边界条件,依靠微分变换法（DTM法）对此高阶偏微分方程进行求解,通过数值计算研究了多场中单层固支输流碳纳米管的振动与失稳问题。结果表明：温度场、轴向磁场强度、Knudsen数及小尺度参数都会对系统振动频率以及失稳临界流速产生影响。     

Supersonic transverse rarefied gas flow past a strip

The supersonic flow of a monatomic gas consisting of hard spherical particles past a flat strip normal to the flow is investigated using the direct simulation Monte-Carlo (DSMC) method. The calculations are performed over the Knudsen and Mach number ranges 0.015–5 and 1.8–15, respectively. The structure of the compressed layer and the aerodynamic characteristics are systematically studied for the Mach number 5 and various Knudsen numbers. The dependences of the compressed-layer thickness in molecular free paths are found. The nonequilibrium processes in the neighborhood of the strip are described on the basis of the data on the temperature anisotropy with respect to three coordinates.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, 2005, pp. 159–167. Original Russian Text Copyright © 2005 by Maltsev and Rebrov.     

可变节流高度气浮支承结构设计及动态性能分析

为了使气浮支承的承载力动态可调,设计了一种可变节流高度气浮支承. 通过建立气浮支承计算流体动力学(Computational Fluid Dynamics,CFD)模型,利用CFD动网格技术来模拟小孔节流器的运动,研究小孔节流器的结构参数、运动参数及气浮支承的工作参数对可变节流高度气浮支承动态性能的影响. 结果表明:通过调节小孔节流器的节流高度可以明显改变气浮支承的承载力;在只考虑单一变量的前提下,气浮支承承载力的波动量随着小孔节流器的运动幅值、运动频率、节流高度、直径和气浮支承供气压强的增加而增加,但随着气膜厚度的增大而减小;当小孔节流器直径较小时,随着小孔节流器运动频率的增加,气浮支承动刚度的增幅很小,但当小孔节流器直径增大时,随着小孔节流器运动频率的增加,气浮支承动刚度的增幅会明显变大.      

防风网透流风空气动力学特性大涡数值模拟研究

基于有限体积法建立不可压缩粘性流体运动的大涡模拟模型,采用Smagorinsky-Lilly亚格子模型,并引入浸入边界法(IBM)实现无滑移固壁边界条件,对雷诺数30~30000之间防风网透流风进行模拟研究。基于模拟结果,提出蝶型防风网透流风存在4个典型分区结构,流场中存在由蝶型形态引起的大尺度分层剪切流动,加强流体动能耗散。透流风在雷诺数300时发生层流至湍流的转捩,而在雷诺数增长至3000以上时,湍流充分发展,纵向流速脉动强度可达70%。防风网整体空气阻力远大于单个孔口射流阻力的线性叠加,射流间的相互作用以及大尺度的分层剪切结构大大增加流体阻力损失,这为通过优化孔口布置和网板形态来节省材料提供了科学依据。