基于DSMC方法的多孔介质孔隙规则网络气体传质模型研究
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摘要
多孔介质中的气体传质研究涉及到多个应用领域,如气固催化反应、分子筛、多孔膜气体分离、气体吸附、微反应器等。多孔介质的孔道结构尺寸细小,孔道结构对流体介质的流动和传质规律影响较大,如何对其进行有效的理论描述是人们关注的重要问题之一。本文采用孔隙规则网络模型作为多孔介质的结构模型,以分子模拟方法——直接模拟Monte Carlo(DSMC)方法为研究工具,针对过渡流问题,建立多孔介质中气体流动和传质模型框架,深入研究了该框架的关键问题——“点-键”模型。
首先采用DSMC方法研究微流动的一般特性。编写的MFRBDSMC程序,能对前/后台阶流动、微喷管流动、气体混合过程和多孔介质孔隙规则网络模型等进行DSMC模拟。通过应用扰动分析理论求解带滑移边界条件的N-S方程,研究典型滑移模型对微流动的预测能力。结果表明,二阶滑移模型Cercignani预测结果与DSMC数据最为接近。当出口克努森数(Kn_o数)数较大时,气体流动出现微流动特性:壁面处速度不为零,且沿流动方向逐渐增大;稀薄效应使原本沿流动方向呈非线性分布的压力趋于线性;质量流率随Kn_o数的增加而增大。进而利用DSMC模拟结果提出新的滑移模型,当Kn_o数小于0.254时,该模型对微流动具有较好的预测,带该滑移模型的N-S方程质量流率滑移解与DSMC结果偏差约为5%。
“点-键”模型为多孔介质孔隙规则网络气体传质模型的基本单位,本文根据Kn_o数范围为0.24～47.60的微槽道流动MFRBDSMC程序模拟结果和Beskok等人的修正稀薄系数法,建立“键”的表达式;对Kn_o数范围为0.12～11.3的“十字”形微槽道气体流动进行MFRBDSMC程序的DSMC模拟,将“十字”形微槽道交叉区域(cross)作“点”处理;通过引入无量纲等效长度(L′_e),在“键”的传质公式中考虑cross对传质的影响,进而建立起“点-键”模型。通过对不同压差、不同气体介质、不同高长比微槽道的DSMC模拟,对“点-键”模型进行DSMC验证,“点-键”模型计算结果与DSMC模拟值的偏差范围为3.69%～12.65%。
本文进一步探讨双组分气体在微槽道中的传质过程。He-Ar的MFRBDSMC程序模拟结果表明,双组分气体传质机理不只是Knudsen扩散;沿微槽道流动方向,Ar的摩尔分数大于He,但在出口附近二者均发生剧烈变化,使得出口处的He摩尔分数大于Ar;而Ar的组分分压则一直大于He。在流动中分子量较大的Ar所受He的影响较小,几乎保持纯Ar的流动状态,由此本文通过DSMC模拟结果对混合粘性系数进行修正,并将其应用于单组分“键”的传质公式,以此预测混合组分的质量流率。
The study on gas mass transfer in porous media involves extensive applications, such as gas-solid catalytic reaction, molecular sieves, porous membrane gas separation, gas adsorption, micro-reactor, etc. The pore tructure has great influence on gas flow and mass transfer in porous media, it becomes an important research aspect that how to model the pore structure of porous media efficiently. In this thesis, the framework of modeling gas flow and mass transfer in porous media is established in the transition region. Based on uniform pore network model and direct simulation Monte Carlo(DSMC) method, the basic "Node-Bond" model is studied intensively.
In the first part, DSMC method is applied to study the general characteristic of microscale gas flows. The MFRBDSMC program can be used for simulations of forward/backward step facing flows, micro-nozzle flows, gas mixing, gas flows and mass transfer in uniform pore network structure of porous media, etc. The perturbation analysis is employed to solve two-dimensional Navier-Stokes equation with slip boundary condition, and function expressions of velocity, pressure and mass flow rate are derived. By compared with these perturbation analysis solutions of different typical slip models, the ability of predicting micro-flow is analyzed contrastively, and these results manifest that the Cercignani second slip model agrees with DSMC results optimally. When Kn_o number exceeds 0.052, the general characteristic of microscale gas flows begin to appear, such as the velocity at wall is no longer zero and increases along the flow direction; the pressure profile along the flow direction is nonlinearized by compressible effect, and linearized by rarefied effect; the mass flow rate raises with the increase of Kn_o number due to the rarefied effect. In addition, adopted the velocity profile data of DSMC simulation results in the slip flow regime, a new slip model is presented, which has a good agreement with DSMC simulation results as Kn_o number within 0.254.
The "Node-Bond" model is a basic unit, which can constitute the gas mass transfer model of porous media uniform pore network model. Based on the correction rarefaction coefficient method proposed by Bekok et al. and micro-channel DSMC simulation results with Kn_o number ranging from 0.24 to 47.60, the function expression of "Bond" is derived. Several cross-shape micro-channel flow cases are simulated by DSMC program, and their cross sections are treated as "Node". As a result, the "Node-Bond" model is established resorted to the treatment of "Node" and nondimensional equivalent length(L'e) which accounts for the effect of cross section. Under these different conditions of pressure difference, gas species, height-length proportion, etc., these results calculated by "Node-Bond" model are compared with DSMC simulation results, and it is shown that their errors are between 3.69% and 12.65%.
In the last part, the binary component gas mass transfer process is investigated. The DSMC simulation results of He-Ar indicate that the binary component gas mass transfer process has some other mechanisms except Knudsen diffusion; the molar fraction of Ar is higher than He's along the flow direction except near outlet where the two components vary fiercely, and in consequence, the molar fraction of He is higher than Ar's; the partial pressure of Ar is always higher than He's. Although there are two components in micro-channel, the Ar component which is heavier than He affected hardly by He component, and almost keep the same flow state as pure Ar component. According to above analysis, the gas mixture viscosity coefficient is corrected by DSMC simulation results. The function expression of "Bond" is modified to estimate the total mass flow rate by substituting the corrected gas mixture viscosity coefficient for the pure viscosity coefficient.
首先采用DSMC方法研究微流动的一般特性。编写的MFRBDSMC程序,能对前/后台阶流动、微喷管流动、气体混合过程和多孔介质孔隙规则网络模型等进行DSMC模拟。通过应用扰动分析理论求解带滑移边界条件的N-S方程,研究典型滑移模型对微流动的预测能力。结果表明,二阶滑移模型Cercignani预测结果与DSMC数据最为接近。当出口克努森数(Kn_o数)数较大时,气体流动出现微流动特性:壁面处速度不为零,且沿流动方向逐渐增大;稀薄效应使原本沿流动方向呈非线性分布的压力趋于线性;质量流率随Kn_o数的增加而增大。进而利用DSMC模拟结果提出新的滑移模型,当Kn_o数小于0.254时,该模型对微流动具有较好的预测,带该滑移模型的N-S方程质量流率滑移解与DSMC结果偏差约为5%。
“点-键”模型为多孔介质孔隙规则网络气体传质模型的基本单位,本文根据Kn_o数范围为0.24～47.60的微槽道流动MFRBDSMC程序模拟结果和Beskok等人的修正稀薄系数法,建立“键”的表达式;对Kn_o数范围为0.12～11.3的“十字”形微槽道气体流动进行MFRBDSMC程序的DSMC模拟,将“十字”形微槽道交叉区域(cross)作“点”处理;通过引入无量纲等效长度(L′_e),在“键”的传质公式中考虑cross对传质的影响,进而建立起“点-键”模型。通过对不同压差、不同气体介质、不同高长比微槽道的DSMC模拟,对“点-键”模型进行DSMC验证,“点-键”模型计算结果与DSMC模拟值的偏差范围为3.69%～12.65%。
本文进一步探讨双组分气体在微槽道中的传质过程。He-Ar的MFRBDSMC程序模拟结果表明,双组分气体传质机理不只是Knudsen扩散;沿微槽道流动方向,Ar的摩尔分数大于He,但在出口附近二者均发生剧烈变化,使得出口处的He摩尔分数大于Ar;而Ar的组分分压则一直大于He。在流动中分子量较大的Ar所受He的影响较小,几乎保持纯Ar的流动状态,由此本文通过DSMC模拟结果对混合粘性系数进行修正,并将其应用于单组分“键”的传质公式,以此预测混合组分的质量流率。
The study on gas mass transfer in porous media involves extensive applications, such as gas-solid catalytic reaction, molecular sieves, porous membrane gas separation, gas adsorption, micro-reactor, etc. The pore tructure has great influence on gas flow and mass transfer in porous media, it becomes an important research aspect that how to model the pore structure of porous media efficiently. In this thesis, the framework of modeling gas flow and mass transfer in porous media is established in the transition region. Based on uniform pore network model and direct simulation Monte Carlo(DSMC) method, the basic "Node-Bond" model is studied intensively.
In the first part, DSMC method is applied to study the general characteristic of microscale gas flows. The MFRBDSMC program can be used for simulations of forward/backward step facing flows, micro-nozzle flows, gas mixing, gas flows and mass transfer in uniform pore network structure of porous media, etc. The perturbation analysis is employed to solve two-dimensional Navier-Stokes equation with slip boundary condition, and function expressions of velocity, pressure and mass flow rate are derived. By compared with these perturbation analysis solutions of different typical slip models, the ability of predicting micro-flow is analyzed contrastively, and these results manifest that the Cercignani second slip model agrees with DSMC results optimally. When Kn_o number exceeds 0.052, the general characteristic of microscale gas flows begin to appear, such as the velocity at wall is no longer zero and increases along the flow direction; the pressure profile along the flow direction is nonlinearized by compressible effect, and linearized by rarefied effect; the mass flow rate raises with the increase of Kn_o number due to the rarefied effect. In addition, adopted the velocity profile data of DSMC simulation results in the slip flow regime, a new slip model is presented, which has a good agreement with DSMC simulation results as Kn_o number within 0.254.
The "Node-Bond" model is a basic unit, which can constitute the gas mass transfer model of porous media uniform pore network model. Based on the correction rarefaction coefficient method proposed by Bekok et al. and micro-channel DSMC simulation results with Kn_o number ranging from 0.24 to 47.60, the function expression of "Bond" is derived. Several cross-shape micro-channel flow cases are simulated by DSMC program, and their cross sections are treated as "Node". As a result, the "Node-Bond" model is established resorted to the treatment of "Node" and nondimensional equivalent length(L'e) which accounts for the effect of cross section. Under these different conditions of pressure difference, gas species, height-length proportion, etc., these results calculated by "Node-Bond" model are compared with DSMC simulation results, and it is shown that their errors are between 3.69% and 12.65%.
In the last part, the binary component gas mass transfer process is investigated. The DSMC simulation results of He-Ar indicate that the binary component gas mass transfer process has some other mechanisms except Knudsen diffusion; the molar fraction of Ar is higher than He's along the flow direction except near outlet where the two components vary fiercely, and in consequence, the molar fraction of He is higher than Ar's; the partial pressure of Ar is always higher than He's. Although there are two components in micro-channel, the Ar component which is heavier than He affected hardly by He component, and almost keep the same flow state as pure Ar component. According to above analysis, the gas mixture viscosity coefficient is corrected by DSMC simulation results. The function expression of "Bond" is modified to estimate the total mass flow rate by substituting the corrected gas mixture viscosity coefficient for the pure viscosity coefficient.
引文
[1]徐如人,庞文琴.分子筛与多孔材料化[M].北京:科学出版社,2004
[2]王金勋.应用孔隙水平网络模型研究两相渗流规律[D].北京:中国石油勘探开发研究院,2001,1-49
[3]王克文,关继腾,范业活等.孔隙网络模型在渗流力学研究中的应用[J].力学进展,2005,35(3):353-360
[4]Webb S W.Gas-phase diffusion in porous media-evaluation of an advective-dispersive formulation and the dusty-gas model including comparison to data for binary mixmres[R].Sandia National Laboratories,1996
[5]Kast W,Hohenthanner C R.Mass transfer within the gas-phase of porous media[J].Int J Heat and Mass Transfer,2000,43:807-823
[6]Grad H.On the kinetic theory of rarefied gases[J].Comm Pure Appl Math,1949,2:331-407
[7]Bhatnagar P,Gross E,Krook K.A model for collision processes in gasses[J].Physics Review,1954,94:511-524
[8]Bird G A.Molecular gas dynamics and the direct simulation of gas flows[M].Clarendon:Oxford,1994
[9]Fan J,Shen C.Statistical simulation of low-speed unidirectional flows in transition regime[J].Rarefied Gas Dynamics,1998,2:245-252
[10]Lees A W,Edwards S EThe comnuter study of transport process under extreme condition[J].Phys C,1975,C5:1921-1929
[11]Wong P Z,Koplik J,Tomanic J.Conductivity and permeability of rocks[J].Physical Review B,1984,30(11):6606-6614
[12]郭尚平.渗流力学几个方面的进展和建议[A],李家春.自然、工业与流动[C].北京:气象出版社,2001,11-22
[13]Dullien F A L.现代渗流物理学[M],范玉平,赵东伟译.北京:石油工业出版社,2001
[14]王克文,关继腾,范业活等.孔隙网络模型在渗流力学研究中的应用[J].力学进展,2005,35(3):353-360
[15]陈书荣,王达健,张雄飞等.多孔介质孔隙结构的网络模型应用[J].计算机与应用化学,2001,18(6):531-535
[16]Dias M M,Payatakes A C.Network models for two-phase flow in porousmedia Part 1:Immiscible microdisplacement of non-wetting fluids[J].J Fluid Mechanics,1986,164:305-336
[17]Blunt M J,King P.Relative permeabilities from two- and three-dimensional pore-scale network modeling[J].Transport in Porous Media,1991,6:407-433
[18]Tsakiroglou C D,Payatakes A C.Pore-wall goughness as a fractal surface and theoretical simulation of mercury intrusion/retraction in porous media[J].Journal of Colloid and Interface Setence,1993,159:287-301
[19]Moreira J C,Rajagopal K.Evaporation of a fluid in capillary porous media using a 3d correlated network model[J].Int Journal of Modem Physics C,2006,17(12):1763-1776
[20]Mu Deqiang,Liu Zhongsheng,Huang Cheng.Determination of the effective diffusion coefficient in porous media including Knudsen effects[J].Microfluidics and Nanofluidics,2007,4(3):257-260
[21]Gostick J T,Loannidis M A,Fowler M W,et al.Pore network modeling of fibrous gas diffusion layers for polymer electrolyte membrane fuel cells[J].Journal of Power Sources,2007,173(1):277-290
[22]Joekar N V,Hassanizadeh S M,Pyrak-Nolte L J,et al.Simulating drainage and imbibition experiments in a high-porosity micromodel using an unstructured pore network model[J].Water Resources Research,2009,45(2):182-190
[23]Chambre S.Flow of rarefied gases[M].Princeton:Princeton University Press,1961
[24]Mason E A,Malinauskas A P.Gas transport in pourous media:The dusty-gas model[C].New York:Chem Eng,1983
[25]Jelena M,Radovan O.Applicability of linearized Dusty Gas Model for multicomponent diffusion of gas mixtures in porous solids[J].Acta periodical technological,2007,38:75-84
[26]Krishna R,Wesselingh J A.The Maxwell-Stefan approach to mass transfer[J].Che Eng Sci,1997,52(6):861-911
[27]Krishna R,Baur R.Modelling issues in zeolite based separation processes[J].Separation and Purification Technology,2003,33(3):213-254
[28]Arora G,Sandler S I.Air separation by single wall carbon nanotubes:Mass transport and kinetic selectivity[J].J Chem Phys,2006,124(8):084702
[29]Chen F,Mourhatch R,Tsotsis T T,et al.Pore network model of transport and separation of binary gas mixtures in nanoporous membranes[J].Journal of Membrane Science,2008,315(1-2):48-57
[30]Pruess K.TOUGH User's guide[R].US Nuclear Regulatory Commission,1987
[31]Derjaguin B V,Abrikosova I I.Direct measurement of the molecular attraction of solid bodies.Statement of the problem and measurement of the force by using negative feedback[J].Sov Phys,1957,3:819-829
[32]Pineda C F,Izquierdo-Gil M A,Garcia-Payo M C.Gas permeation and direct contact membrane distillation experiments and their analysis using different models[J].J Membrane Sci,2002,198:33-49
[33]Suwanwarangkul R,Croiset E,Fowler M W,et al.Performance comparison of Fick's,dusty-gas and Stefan-Maxwell models to predict the concentration overpotential of a SOFC anode[J].J Power Sources,2003,122:9-18
[34]Yang J h,Cermakova J,Petr U.Gas phase transport,adsorption and surface diffusion in a porous glass membrane[J].Catalysis in Membrane,2005,104(2-4):344-351
[35]Fernandez-Pineda C,Izquierdo-Gil M A,Garcia-Payo M C.Gas permeation and direct contact membrane distillation experiments and their analysis using different models[J].J Menbrane Science,2002,198:33-49
[36]Van den Berg H R,Seldam C A,Gulik P S.Compressible laminar flow in a capillary[J].Fluid Mech,1993,2 46:1-20
[37]Harley J C,Huang Y,Bau H H,et al.Gas flow in micro-channels[J].Fluid Mech,1995,284:257-274
[38]Zohar Y,Lee S Y,Lee W Y,et al.Subsonic gas flow in a straight and uniform microchannel[J].Fluid Mech,2002,427:125-151
[39]Arkilic E B,Schmidt M A,Breuer K S.Gaseous flow in small channels[J].AIAA paper,1993,93-3270
[40]Arkilic E B,Schmidt M A,Breuer K S.Gaseous slip flow in long microchannels[J].J MEMS,1997,6(2):167-178
[41]沈青,蒋建政.有限长度的过渡领域微槽道流动(-分析预测和试验的比较)[J].空气动力学学报,2008,26(2):257-262
[42]Struchtrup H,Weiss W.Temperature jump and velocity slip in the moment method[J].Continuum Mechanics And Thermodynamics,2000,12(1):1-18
[43 Struchtrup H,Torrilhon M.Regularization of Grad's 13 Moment Equations:Derivation and linear analysis[J].Phys Fluids,2003,15(9):2668-2680
[44]Sun Y H,Chan W K.Analytical modeling of rarefied Poiseuille flow in microchannels[J].Journal Of Vacuum Science&Technology A,2004,22(2):383-394
[45]Gross E P,Ziering S.Kinetic theory of linear shear flow[J].The Physics of Fluids,1958,1(3):215-224
[46]Yu E Y.Rarefied gas flow along a needle[J].AIAA Paper,1974,18:751-758
[47]Bahukudumbi P,Park J H,Beskok A.A unified engineering model for steady and quasi-steady shear-driven gas microflows[J].Microscale Thermophysical Engineering,2003,7(4):291-315
[48]Cercignani C,Daneri A.Flow of a rarefied gas between two parallel plates[J].Journal Of Applied Physics,1963,34(12):3509-3513
[49]Cercignani C,Lampis M,Lorenzani S.Variational approach to gas flows in microchannels[J].Physics of Fluids,2004,16(9):3426-3437
[50 Xu K,Li Z H.Microchannel flow in the slip regime:gas-kinetic BGK-Burnett solutions[J].Journal of Fluid Mechanics,2004,513:87-110
[51]Parrinello M,Rahman A.Crystal structure and pair potentials:a molecular dynamics study[J].Phys Rev Lett,1980,45:1196-1199
[52]Car R,Parrinello M.Unified approach for molecular dynamics and density-functional theory[J].Phys Rev Lett,1985,55:2471-2474
[53]Bird G A.Molecular gas dynamics[M].New York:Oxford University Press,1976
[54]Hadjiconstantinou N G.Validation of a second-order slip model for dilute gas flows[J].Nanoscale and Microscale Thermophysical Engineering,2005,9(2):137-153
[55]Ewart T,Firpo J L,Graur I A,et al.DSMC simulation:Validation and application to low speed gas flow in microchannels[J].J Fluids Eng,2009,131:014501
[56]Hsieh S S,Wang Y T,Tsai H H,et al.DSMC simulation for constant-wall-temperature Heat Transfer in a Short Parallel Plate Microchannel[J].J Chinese Soc Mech Eng,2007,28(1):13-22
[57]Alexeenko A A,Gimelshein S F,Levin D A.Reconsideration of low reynolds number flow-through constriction microcharmels using the DSMC method[J].J MEMS,2005,14(4):847-856
[58]兰旭东,李志信.纳米尺度气体滑动轴承的DSMC模拟[J].摩擦学学报,2008,28(5):411-415
[59]Le M,Hassan I.DSMC simulation of gas mixing in T-shape micromixer[J].Applied Thermal Eng,2007,27(14-15):2370-2377
[60]Zuppardi G.Comparing the chemicalmodels by Fan-Shen and by Bird through a 2D DSMC code[J].AIP Conf Proc,2008,1084:347-352
[61]焦子龙,庞贺伟.海洋卫星水色仪羽流污染DSMC模拟研究[J].宇航学报,2007,28(6):1529-1532
[62]Hsieh S S,Tsai H H,Lin C Y,et al.Gas flow in a long microchannel[J].International Journal of Heat and Mass Transfer,2004,47:3877-3887
[63]杜东兴,李志信,过增元.微细光滑管内的气体流动阻力特性[J].中国科学E,2000,30(2):173-178
[64]秦丰华,姚久成,孙德军等.微尺度圆管内气体流量的实验测量[J].实验力学,2001,16(2):119-1261
[65]沈青.稀薄气体动力学[M].北京:国防工业出版社,2003
[66]樊菁,沈清.直接模拟蒙特卡罗方法中的一个新算法-随机取样频率法.计算流体力学的理论、方法和应用[A].第六届全国计算流体力学会议论文集[C].北京:科学出版社,1992
[67]吴其芬.稀薄气体动力学[M].长沙:国防科技大学出版社,2004
[68]Thomas J O.An investigation of two-dimensional CAD generated models with body decoupled cartesian grids for DSMC[A].34th AIAA Thermophysics Conference[C].Denver:AIAA,2000,23-61
[69]Bird G A.Application of the DSMC method to the full shuttle geometry[J].AIAA Paper,1990,AIAA-90-1692
[70]Laux M,Fasoulas S,Messerschmid E W.Development ofa DSMC code on planar unstructured grids with automatic grid adaptation[J].AIAA Paper,1995,AIAA-95-2053
[71]Celenligil M C,Moss J N.Application of the DSMC method to hypersonic flow about a delta wing[J].AIAA Paper,1995,AIAA-95-2053
[72]冯萍,黄国平,梁德旺.DSMC方法模拟微尺度流动时的特征参数选取[J].南京航空航天大学学报,2006,38(5):557-561
[73]Ikegawa M,Kobayashi J.Development of a rarefied flow simulator using the direct simulation Monte Carlo method[J].JSME International Journal,1990,30:463-467
[74]Nance R P,Hash D B,Hassan H A.Role of Boundary conditions in Monte Carlo simulation of MEMS devices[J].Journal of Thermalphysics and Hear Transfer,1998,12:447-449
[75]Liou W W,Fang Y.Implicit boundary conditions for direct simulation Monte Carlo method in MEMS flow predictions[J].Computer Modeling in Engineering&Science,2000,4:119-128
[76]Wu J S,Tseng K C.Analysis of micro-scale gas flows with pressure boundaries using direct simulation Monte Carlo method[J].J Computers & Fluid,2001,30:711-735
[77]Wang M R,Li Z X.Simulation for gas flows in microgeometries using the direct simulation Monte Carlo method[J].International Journal of Heat and Fluid Flow,2004,25(6)975-985
[78]王沫然,王金库,李志信.DSMC方法的压力边界条件实现[J].计算物理,2004,21(4):316-320
[79]Cercignani C.The boltzmann equation and its applications[M].New York:Springer-Verlag,1988
[80]Deissler R G.An analysis of second-order slip flow and temperature-jump boundary conditions for rarefied gases[J].Int J Heat and Mass Transfer,1964,7:681-694
[81]Schamberg R.The fundamental differential equations and the boundary conditions for high speed slip-flow,and their application to several specific Problems[D].California:California Institute of Technology,1947
[82]Hsia Y T,Domoto G A.An experimental investigation of molecular rarefaction effects in gas lubricated bearings at ultra-low clearances[J].J Lubrication Tech,1983,105:120-130
[83]Shih J C,Ho C M,Liu J Q,et al.Monatomic and polyatomic gas flow through uniform microchannels[J].ASME-DSC,59:197-203
[84]谢翀,樊菁.Navier-Stokes方程二阶速度滑移边界条件的检验[J].力学学报,2007,39(1):1-6
[85]Lengrand J C,Elizarova T G.An expression that is valid from continuum to free molecular regime for the flow-rate through a long channel[A].West-east high speed field conference[C].Moscow:Russian Academy of Science,2007
[86]Karniadakis G E,Beskok A.微流动-基础与模拟[M].中国科学院过程工程研究所多相反应重点试验室多相系统与多尺度方法课题组译.北京:化学工业出版社,2006
[87]Kennard E.Kinetic theory of gases[M].New York:McGraw-Hill Book Co Inc,1938
[88]Hassan M L.DSMC simulation of gas mixing in T-shape micromixer[J].Applied thermal engimeering,2007,27:2370-2377
[89]Yan F,Farouk B.Prediction of mixing of two parallel gas streams in a microchannel using the direct simulation Monte Carlo method[A].Rarefied Gas Dynamics:22nd International Symposium[C].Sydney:Amer Inst of Physics,2001,510-517
[90]Pisani L.Multi-component gas mixture diffusion through porous media:A 1D analytical solusion[J].Int J Heat and mass transfer,2008,51:650-660
[91]Krishna R,Wesselingh J A.The Maxwell-Stefan approach to mass transfer[J].Chemical Engineering Science,1997,52,(6):861-911
[92]Abriola L M,Pinder G F.A multiphase approach to the modeling of porous media contamination by organic compounds,1.Equation development[J].Water Resourc Res,1985,21:11-18
[93]Kerkhof P J.A modified Maxwell-Stefan model for transport through inert membranes:the binary friction model[J].J Chem Eng,1996,64:319-343
[94]Young J B,Todd B.Modelling of multi-component gas flows in capillaries and porous solids[J].Int J Heat and mass transfer,2005,48:5338-5353
[95]王涛,朴香兰,朱慎林.高等传递过程原理[M].北京:化学工业出版社,2005
[2]王金勋.应用孔隙水平网络模型研究两相渗流规律[D].北京:中国石油勘探开发研究院,2001,1-49
[3]王克文,关继腾,范业活等.孔隙网络模型在渗流力学研究中的应用[J].力学进展,2005,35(3):353-360
[4]Webb S W.Gas-phase diffusion in porous media-evaluation of an advective-dispersive formulation and the dusty-gas model including comparison to data for binary mixmres[R].Sandia National Laboratories,1996
[5]Kast W,Hohenthanner C R.Mass transfer within the gas-phase of porous media[J].Int J Heat and Mass Transfer,2000,43:807-823
[6]Grad H.On the kinetic theory of rarefied gases[J].Comm Pure Appl Math,1949,2:331-407
[7]Bhatnagar P,Gross E,Krook K.A model for collision processes in gasses[J].Physics Review,1954,94:511-524
[8]Bird G A.Molecular gas dynamics and the direct simulation of gas flows[M].Clarendon:Oxford,1994
[9]Fan J,Shen C.Statistical simulation of low-speed unidirectional flows in transition regime[J].Rarefied Gas Dynamics,1998,2:245-252
[10]Lees A W,Edwards S EThe comnuter study of transport process under extreme condition[J].Phys C,1975,C5:1921-1929
[11]Wong P Z,Koplik J,Tomanic J.Conductivity and permeability of rocks[J].Physical Review B,1984,30(11):6606-6614
[12]郭尚平.渗流力学几个方面的进展和建议[A],李家春.自然、工业与流动[C].北京:气象出版社,2001,11-22
[13]Dullien F A L.现代渗流物理学[M],范玉平,赵东伟译.北京:石油工业出版社,2001
[14]王克文,关继腾,范业活等.孔隙网络模型在渗流力学研究中的应用[J].力学进展,2005,35(3):353-360
[15]陈书荣,王达健,张雄飞等.多孔介质孔隙结构的网络模型应用[J].计算机与应用化学,2001,18(6):531-535
[16]Dias M M,Payatakes A C.Network models for two-phase flow in porousmedia Part 1:Immiscible microdisplacement of non-wetting fluids[J].J Fluid Mechanics,1986,164:305-336
[17]Blunt M J,King P.Relative permeabilities from two- and three-dimensional pore-scale network modeling[J].Transport in Porous Media,1991,6:407-433
[18]Tsakiroglou C D,Payatakes A C.Pore-wall goughness as a fractal surface and theoretical simulation of mercury intrusion/retraction in porous media[J].Journal of Colloid and Interface Setence,1993,159:287-301
[19]Moreira J C,Rajagopal K.Evaporation of a fluid in capillary porous media using a 3d correlated network model[J].Int Journal of Modem Physics C,2006,17(12):1763-1776
[20]Mu Deqiang,Liu Zhongsheng,Huang Cheng.Determination of the effective diffusion coefficient in porous media including Knudsen effects[J].Microfluidics and Nanofluidics,2007,4(3):257-260
[21]Gostick J T,Loannidis M A,Fowler M W,et al.Pore network modeling of fibrous gas diffusion layers for polymer electrolyte membrane fuel cells[J].Journal of Power Sources,2007,173(1):277-290
[22]Joekar N V,Hassanizadeh S M,Pyrak-Nolte L J,et al.Simulating drainage and imbibition experiments in a high-porosity micromodel using an unstructured pore network model[J].Water Resources Research,2009,45(2):182-190
[23]Chambre S.Flow of rarefied gases[M].Princeton:Princeton University Press,1961
[24]Mason E A,Malinauskas A P.Gas transport in pourous media:The dusty-gas model[C].New York:Chem Eng,1983
[25]Jelena M,Radovan O.Applicability of linearized Dusty Gas Model for multicomponent diffusion of gas mixtures in porous solids[J].Acta periodical technological,2007,38:75-84
[26]Krishna R,Wesselingh J A.The Maxwell-Stefan approach to mass transfer[J].Che Eng Sci,1997,52(6):861-911
[27]Krishna R,Baur R.Modelling issues in zeolite based separation processes[J].Separation and Purification Technology,2003,33(3):213-254
[28]Arora G,Sandler S I.Air separation by single wall carbon nanotubes:Mass transport and kinetic selectivity[J].J Chem Phys,2006,124(8):084702
[29]Chen F,Mourhatch R,Tsotsis T T,et al.Pore network model of transport and separation of binary gas mixtures in nanoporous membranes[J].Journal of Membrane Science,2008,315(1-2):48-57
[30]Pruess K.TOUGH User's guide[R].US Nuclear Regulatory Commission,1987
[31]Derjaguin B V,Abrikosova I I.Direct measurement of the molecular attraction of solid bodies.Statement of the problem and measurement of the force by using negative feedback[J].Sov Phys,1957,3:819-829
[32]Pineda C F,Izquierdo-Gil M A,Garcia-Payo M C.Gas permeation and direct contact membrane distillation experiments and their analysis using different models[J].J Membrane Sci,2002,198:33-49
[33]Suwanwarangkul R,Croiset E,Fowler M W,et al.Performance comparison of Fick's,dusty-gas and Stefan-Maxwell models to predict the concentration overpotential of a SOFC anode[J].J Power Sources,2003,122:9-18
[34]Yang J h,Cermakova J,Petr U.Gas phase transport,adsorption and surface diffusion in a porous glass membrane[J].Catalysis in Membrane,2005,104(2-4):344-351
[35]Fernandez-Pineda C,Izquierdo-Gil M A,Garcia-Payo M C.Gas permeation and direct contact membrane distillation experiments and their analysis using different models[J].J Menbrane Science,2002,198:33-49
[36]Van den Berg H R,Seldam C A,Gulik P S.Compressible laminar flow in a capillary[J].Fluid Mech,1993,2 46:1-20
[37]Harley J C,Huang Y,Bau H H,et al.Gas flow in micro-channels[J].Fluid Mech,1995,284:257-274
[38]Zohar Y,Lee S Y,Lee W Y,et al.Subsonic gas flow in a straight and uniform microchannel[J].Fluid Mech,2002,427:125-151
[39]Arkilic E B,Schmidt M A,Breuer K S.Gaseous flow in small channels[J].AIAA paper,1993,93-3270
[40]Arkilic E B,Schmidt M A,Breuer K S.Gaseous slip flow in long microchannels[J].J MEMS,1997,6(2):167-178
[41]沈青,蒋建政.有限长度的过渡领域微槽道流动(-分析预测和试验的比较)[J].空气动力学学报,2008,26(2):257-262
[42]Struchtrup H,Weiss W.Temperature jump and velocity slip in the moment method[J].Continuum Mechanics And Thermodynamics,2000,12(1):1-18
[43 Struchtrup H,Torrilhon M.Regularization of Grad's 13 Moment Equations:Derivation and linear analysis[J].Phys Fluids,2003,15(9):2668-2680
[44]Sun Y H,Chan W K.Analytical modeling of rarefied Poiseuille flow in microchannels[J].Journal Of Vacuum Science&Technology A,2004,22(2):383-394
[45]Gross E P,Ziering S.Kinetic theory of linear shear flow[J].The Physics of Fluids,1958,1(3):215-224
[46]Yu E Y.Rarefied gas flow along a needle[J].AIAA Paper,1974,18:751-758
[47]Bahukudumbi P,Park J H,Beskok A.A unified engineering model for steady and quasi-steady shear-driven gas microflows[J].Microscale Thermophysical Engineering,2003,7(4):291-315
[48]Cercignani C,Daneri A.Flow of a rarefied gas between two parallel plates[J].Journal Of Applied Physics,1963,34(12):3509-3513
[49]Cercignani C,Lampis M,Lorenzani S.Variational approach to gas flows in microchannels[J].Physics of Fluids,2004,16(9):3426-3437
[50 Xu K,Li Z H.Microchannel flow in the slip regime:gas-kinetic BGK-Burnett solutions[J].Journal of Fluid Mechanics,2004,513:87-110
[51]Parrinello M,Rahman A.Crystal structure and pair potentials:a molecular dynamics study[J].Phys Rev Lett,1980,45:1196-1199
[52]Car R,Parrinello M.Unified approach for molecular dynamics and density-functional theory[J].Phys Rev Lett,1985,55:2471-2474
[53]Bird G A.Molecular gas dynamics[M].New York:Oxford University Press,1976
[54]Hadjiconstantinou N G.Validation of a second-order slip model for dilute gas flows[J].Nanoscale and Microscale Thermophysical Engineering,2005,9(2):137-153
[55]Ewart T,Firpo J L,Graur I A,et al.DSMC simulation:Validation and application to low speed gas flow in microchannels[J].J Fluids Eng,2009,131:014501
[56]Hsieh S S,Wang Y T,Tsai H H,et al.DSMC simulation for constant-wall-temperature Heat Transfer in a Short Parallel Plate Microchannel[J].J Chinese Soc Mech Eng,2007,28(1):13-22
[57]Alexeenko A A,Gimelshein S F,Levin D A.Reconsideration of low reynolds number flow-through constriction microcharmels using the DSMC method[J].J MEMS,2005,14(4):847-856
[58]兰旭东,李志信.纳米尺度气体滑动轴承的DSMC模拟[J].摩擦学学报,2008,28(5):411-415
[59]Le M,Hassan I.DSMC simulation of gas mixing in T-shape micromixer[J].Applied Thermal Eng,2007,27(14-15):2370-2377
[60]Zuppardi G.Comparing the chemicalmodels by Fan-Shen and by Bird through a 2D DSMC code[J].AIP Conf Proc,2008,1084:347-352
[61]焦子龙,庞贺伟.海洋卫星水色仪羽流污染DSMC模拟研究[J].宇航学报,2007,28(6):1529-1532
[62]Hsieh S S,Tsai H H,Lin C Y,et al.Gas flow in a long microchannel[J].International Journal of Heat and Mass Transfer,2004,47:3877-3887
[63]杜东兴,李志信,过增元.微细光滑管内的气体流动阻力特性[J].中国科学E,2000,30(2):173-178
[64]秦丰华,姚久成,孙德军等.微尺度圆管内气体流量的实验测量[J].实验力学,2001,16(2):119-1261
[65]沈青.稀薄气体动力学[M].北京:国防工业出版社,2003
[66]樊菁,沈清.直接模拟蒙特卡罗方法中的一个新算法-随机取样频率法.计算流体力学的理论、方法和应用[A].第六届全国计算流体力学会议论文集[C].北京:科学出版社,1992
[67]吴其芬.稀薄气体动力学[M].长沙:国防科技大学出版社,2004
[68]Thomas J O.An investigation of two-dimensional CAD generated models with body decoupled cartesian grids for DSMC[A].34th AIAA Thermophysics Conference[C].Denver:AIAA,2000,23-61
[69]Bird G A.Application of the DSMC method to the full shuttle geometry[J].AIAA Paper,1990,AIAA-90-1692
[70]Laux M,Fasoulas S,Messerschmid E W.Development ofa DSMC code on planar unstructured grids with automatic grid adaptation[J].AIAA Paper,1995,AIAA-95-2053
[71]Celenligil M C,Moss J N.Application of the DSMC method to hypersonic flow about a delta wing[J].AIAA Paper,1995,AIAA-95-2053
[72]冯萍,黄国平,梁德旺.DSMC方法模拟微尺度流动时的特征参数选取[J].南京航空航天大学学报,2006,38(5):557-561
[73]Ikegawa M,Kobayashi J.Development of a rarefied flow simulator using the direct simulation Monte Carlo method[J].JSME International Journal,1990,30:463-467
[74]Nance R P,Hash D B,Hassan H A.Role of Boundary conditions in Monte Carlo simulation of MEMS devices[J].Journal of Thermalphysics and Hear Transfer,1998,12:447-449
[75]Liou W W,Fang Y.Implicit boundary conditions for direct simulation Monte Carlo method in MEMS flow predictions[J].Computer Modeling in Engineering&Science,2000,4:119-128
[76]Wu J S,Tseng K C.Analysis of micro-scale gas flows with pressure boundaries using direct simulation Monte Carlo method[J].J Computers & Fluid,2001,30:711-735
[77]Wang M R,Li Z X.Simulation for gas flows in microgeometries using the direct simulation Monte Carlo method[J].International Journal of Heat and Fluid Flow,2004,25(6)975-985
[78]王沫然,王金库,李志信.DSMC方法的压力边界条件实现[J].计算物理,2004,21(4):316-320
[79]Cercignani C.The boltzmann equation and its applications[M].New York:Springer-Verlag,1988
[80]Deissler R G.An analysis of second-order slip flow and temperature-jump boundary conditions for rarefied gases[J].Int J Heat and Mass Transfer,1964,7:681-694
[81]Schamberg R.The fundamental differential equations and the boundary conditions for high speed slip-flow,and their application to several specific Problems[D].California:California Institute of Technology,1947
[82]Hsia Y T,Domoto G A.An experimental investigation of molecular rarefaction effects in gas lubricated bearings at ultra-low clearances[J].J Lubrication Tech,1983,105:120-130
[83]Shih J C,Ho C M,Liu J Q,et al.Monatomic and polyatomic gas flow through uniform microchannels[J].ASME-DSC,59:197-203
[84]谢翀,樊菁.Navier-Stokes方程二阶速度滑移边界条件的检验[J].力学学报,2007,39(1):1-6
[85]Lengrand J C,Elizarova T G.An expression that is valid from continuum to free molecular regime for the flow-rate through a long channel[A].West-east high speed field conference[C].Moscow:Russian Academy of Science,2007
[86]Karniadakis G E,Beskok A.微流动-基础与模拟[M].中国科学院过程工程研究所多相反应重点试验室多相系统与多尺度方法课题组译.北京:化学工业出版社,2006
[87]Kennard E.Kinetic theory of gases[M].New York:McGraw-Hill Book Co Inc,1938
[88]Hassan M L.DSMC simulation of gas mixing in T-shape micromixer[J].Applied thermal engimeering,2007,27:2370-2377
[89]Yan F,Farouk B.Prediction of mixing of two parallel gas streams in a microchannel using the direct simulation Monte Carlo method[A].Rarefied Gas Dynamics:22nd International Symposium[C].Sydney:Amer Inst of Physics,2001,510-517
[90]Pisani L.Multi-component gas mixture diffusion through porous media:A 1D analytical solusion[J].Int J Heat and mass transfer,2008,51:650-660
[91]Krishna R,Wesselingh J A.The Maxwell-Stefan approach to mass transfer[J].Chemical Engineering Science,1997,52,(6):861-911
[92]Abriola L M,Pinder G F.A multiphase approach to the modeling of porous media contamination by organic compounds,1.Equation development[J].Water Resourc Res,1985,21:11-18
[93]Kerkhof P J.A modified Maxwell-Stefan model for transport through inert membranes:the binary friction model[J].J Chem Eng,1996,64:319-343
[94]Young J B,Todd B.Modelling of multi-component gas flows in capillaries and porous solids[J].Int J Heat and mass transfer,2005,48:5338-5353
[95]王涛,朴香兰,朱慎林.高等传递过程原理[M].北京:化学工业出版社,2005