基于分子运动模拟的二维微尺度流动数值计算研究
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摘要
DSMC方法为数值求解稀薄气体动力学问题有效方法。所以本文根据该算法发展了一套计算二维微尺度流动的数值计算程序FSMM2D(Flow Simulation based on Molecule Movement, 2-Dimensional),并针对微尺度流动的特点进行了相关的改进研究。
首先,编程实现了基本DSMC方法对二维流动的计算,给出了所用算法的原理、相关模型,并结合程序结构流程图,分别介绍了初始化流场、计算分子的运动、边界的处理、分子的排序、抽样计算分子的碰撞、流场参数采样统计各个功能模块在FSMM2D中的实现,并对该程序进行了算例校验。
其次,分析推导了特征波理论用于处理DSMC算法边界条件的过程。并针对影响程序计算的主要特征参数(采样循环数、模拟分子数、子网格数)进行研究,对采样循环数、模拟分子数、子网格数对计算结果的准确性和所耗机时进行了分析比较,结果表明:采样循环数的取值多少不仅会影响计算的准确性还会影响计算机时,本文建议取在8左右为宜;单位网格内粒子数太少会增加总循环步数从而增加计算时间,太多虽不增加总循环步数,但每个循环耗时增加,也会增加计算时间,故单位网格内粒子数选取应该适中,本文建议取为5个左右为宜;子网格数对流场计算结果的准确性一般没有影响,但是对运算时间影响很大,取得恰当能节约计算时间,取4时最节约计算时间。
然后,分析了DSMC产生统计噪声的机制,采用信息保存技术有效抑制了计算的统计噪声,保证计算的准确性且提高了计算收敛速度。通过微尺度通道低速流动模拟效果的对比,验证了DSMC-IP算法比原算法的准确性和速度都有明显提高。
最后,为了拓宽本文发展的数值计算二维微尺度流动程序的使用范围,使其具备能够模拟不规则复杂形状流场的能力,讨论分析了可对任意几何形状、多块结构化网格进行计算的相关算法。
Two dimension flow simulation based on molecule movement (FSMM2D) is presented in this paper, which is developed from DSMC method.
Firstly the basic concepts and theories of DSMC have been introduced. Then a general description of FSMM2D is provided. With the flowchart the program can be divided into six parts and it includes initial flow field, computation of molecular motion, boundary treatment, re-sort of molecular, sample and computation of molecular collision. Several cases have been simulated to certify the correctness of the program.
DSMC method is improved using method of characteristics to modify the boundary condition and gets the goal as expected. Investigations on the selection of three key parameters are carried out. Results show that the best values for the number of sampling loop、the number of simulated particle per cell and the number of sub-cell are about eight、five and four respectively. Micro-plate layer, and flow through micro vertical plate are simulated and it is clear that the improved program with the optimal parameters can not only get the same results as those of other researchers but can greatly enhance the computational accuracy and efficiency.
DSMC method inherently involves the restriction of statistical noise problem and IP method is an improvement algorithm of DSMC method. Descriptions of suppression of statistical noise and algorithm realization of IP method are provided. DSMC-IP method is a reasonable and reliable tool for simulation of low velocity micro flow through comparing and verifying several cases. Moreover, the advantage of this method is obvious and outstanding in computational resolution and efficiency.
At the end of this paper the feasibility and possibility to enlarge the range of application of DSMC-IP method to structural grid with curvature geometry are discussed.
首先,编程实现了基本DSMC方法对二维流动的计算,给出了所用算法的原理、相关模型,并结合程序结构流程图,分别介绍了初始化流场、计算分子的运动、边界的处理、分子的排序、抽样计算分子的碰撞、流场参数采样统计各个功能模块在FSMM2D中的实现,并对该程序进行了算例校验。
其次,分析推导了特征波理论用于处理DSMC算法边界条件的过程。并针对影响程序计算的主要特征参数(采样循环数、模拟分子数、子网格数)进行研究,对采样循环数、模拟分子数、子网格数对计算结果的准确性和所耗机时进行了分析比较,结果表明:采样循环数的取值多少不仅会影响计算的准确性还会影响计算机时,本文建议取在8左右为宜;单位网格内粒子数太少会增加总循环步数从而增加计算时间,太多虽不增加总循环步数,但每个循环耗时增加,也会增加计算时间,故单位网格内粒子数选取应该适中,本文建议取为5个左右为宜;子网格数对流场计算结果的准确性一般没有影响,但是对运算时间影响很大,取得恰当能节约计算时间,取4时最节约计算时间。
然后,分析了DSMC产生统计噪声的机制,采用信息保存技术有效抑制了计算的统计噪声,保证计算的准确性且提高了计算收敛速度。通过微尺度通道低速流动模拟效果的对比,验证了DSMC-IP算法比原算法的准确性和速度都有明显提高。
最后,为了拓宽本文发展的数值计算二维微尺度流动程序的使用范围,使其具备能够模拟不规则复杂形状流场的能力,讨论分析了可对任意几何形状、多块结构化网格进行计算的相关算法。
Two dimension flow simulation based on molecule movement (FSMM2D) is presented in this paper, which is developed from DSMC method.
Firstly the basic concepts and theories of DSMC have been introduced. Then a general description of FSMM2D is provided. With the flowchart the program can be divided into six parts and it includes initial flow field, computation of molecular motion, boundary treatment, re-sort of molecular, sample and computation of molecular collision. Several cases have been simulated to certify the correctness of the program.
DSMC method is improved using method of characteristics to modify the boundary condition and gets the goal as expected. Investigations on the selection of three key parameters are carried out. Results show that the best values for the number of sampling loop、the number of simulated particle per cell and the number of sub-cell are about eight、five and four respectively. Micro-plate layer, and flow through micro vertical plate are simulated and it is clear that the improved program with the optimal parameters can not only get the same results as those of other researchers but can greatly enhance the computational accuracy and efficiency.
DSMC method inherently involves the restriction of statistical noise problem and IP method is an improvement algorithm of DSMC method. Descriptions of suppression of statistical noise and algorithm realization of IP method are provided. DSMC-IP method is a reasonable and reliable tool for simulation of low velocity micro flow through comparing and verifying several cases. Moreover, the advantage of this method is obvious and outstanding in computational resolution and efficiency.
At the end of this paper the feasibility and possibility to enlarge the range of application of DSMC-IP method to structural grid with curvature geometry are discussed.
引文
[1] 崔之华,小燃气轮机-燃起轮机的一个特殊领域,国际航空,1986(3):34
[2] 吴怀宇,周兆英等,微型飞行器的研究现状及其关键技术,武汉科技大学学报(自然科学版),2000,23(2):170-174
[3] Jack H, Military Look to Flying Insect Robots,[J].Industrical Robot,1998,25(2):124-128
[4] StevenA.,Palm-sizeSpyPlanes,[J].MechanicalEngineering,1998,120(2):74-78
[5] Alan H Epstein. Micro Turbine Engines For Soldier Power[R]. The Defense Science and Technology Seminar, 2000.
[6] Epstein A H, etc. Micro Gas Turbine Generators [R]. Massachusetts Inst. of Tech. , Gas Turbine Lab, Final Rept.1995- 2000.
[7] HanSòjrg Schlip, Fabrication of Turbine-Comp ressor-Shaft Assembly For Micro Gas Turbine Engine[D]. Mater’ s Thesis, Stanford Univ. ,December 2000.
[8] HanS ò jrg Schlip, Kang S, Stampfl [J] , Cooper A G, Prinz F B. Application of the Mold SDM Process to the Fabrication of Ceramic Parts for Micro Gas Turbine engine[R]. Heinrich J G(ed.) , Proceedings Ceramics Materials and Components for Engines, Germany, 2000.
[9] Miklos Gerendas, Ralph Pfister. Development of a Very Small Aero-Engine[R]. Proceedings of ASME Turbo Expo 2000,45th ASME International Gas Turbine and A ero-EngineTechnical Congress and Exposition, 2000- GT- 0536.
[10] Mindi Farber De Anda, Christina TerMaath, N deye K Fall. Distributed Energy Technology Simulator Microturbine Demonstration[R]. Energetics, Inc. Washington,DC, 2001.
[11] Wu Pittle W A. Mesurement of Friction Fcetors for the Flow of Gases in Very Fine Channels Used for Microminiature Joule — Thomson Refrigeration [J].Cryogenics,1983,23:273-277
[12] Pfahler J N , Harley J ,Bau H , et al. Liquid and GasTransport in Small Channels[J] . ASME DSC ,1990 ,19 :149-157
[13] Pfahler J N ,Harley J ,Bau H , et al. Gas and Liquid Flow in Small Channels[J] . ASME DSC ,1991 ,32 :49 - 601
[14] Choi S B ,Barrori R F ,Warrington R O. Fluid Flow and Heat Transfer in Microtubes [J] . ASME DSC , 1991 ,32:123-134
[15] Harley J C ,Huang Y F ,Bau H ,et al. Gas Flow in Micro-channels[J] . J Fluid Mech ,1995 ,284 :257 – 2741.
[16] 邬小波,过增元. 微细光滑圆管内气体的流动与传热特性研究[J] . 工程热物理学报,1997,18(5):326-330
[17] 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
[18] 杜东兴. 可压缩性及粗糙度对微细管内流动及换热特性的影响[D] . 北京:清华大学工程力学系,20001
[19] Fan J , Shen C. Statistical simulation of low - speed rarefied gas flows[ J ]. J Coputational Physics, 2001, 16 ( 9) : 393 -398.
[20] Beskok A,Karniadakis G E. A model for flows in channels,pipes,and ducts at micro and nano scales[J].Microscale Thermophysical Engineering,1999,3(1):43～77.
[21] Berg H R,Seldam C A,Gulik P S.Compressible lam inar flow in a capillary [J]. Fluid Mech.,1993,24:1～20.
[22] Gad-el-hak M . The fluid mechanics of micro devices . J . Fluids Engineering, ASME,1999,Vol.121,pp.5-33.
[23] Tsien H S( 钱 学 森 ).Superaerodynamics,mechanics of rarefied J.Aero.Sci,13.12.653-664(1964)
[24] G.A. Bird, Approach to Translational Equilibrium in a Rigid Sphere Gas[J]. Phys.Fluids, 1963,6(10):1518-1519.
[25] Bird GA. Application of the DSMC method to the full shuttle gemertry .AIAA paper,90-1692,1990
[26] Oran E S, Oh C K and Cybyk B Z. Direct Simulation Monte Carlo: Recent Advances andApplications. Annual Review of Fluid Mechanics. 1998. 30: 403-441
[27] Bird G.A. Molecular Gas Dynamics and the Direct Simulation of Gas Flows. Clarendon Press,Oxford,1994.
[28] 沈青. 稀薄气体动力学. 北京:国防工业出版社. 2003
[29] Bird G A. Rarefied Gas dynamics. Invited Paper 221 at the 12th International Symposium on Rarefied Gas Dynamics,,Charlotesville, July,1980.
[30] Koura K, Matsumoto H. Variable soft sphere molecular model for inverse-power-law or Lennard-Jones potential. Phys. Fluids A, 1991,3:2459-2465.
[31] Koura K, Matsumoto H. Variable soft sphere molecular model for air species. Phys. Fluids A, 1992, 4: 1083-1085.
[32] Cercignani C, and Lampis M. Kinetic models for gas-surface interactions, TransportTheory. Statist. Phys., 1971, 2: 505
[33] Bird G A. Recent advances and current challenges for DSMC. Computers Math. Applic.1998, 35: 1-14
[34] KouraK.Null-collision technique in the DSMC method .Phys.Fluids,29:3529,1986.
[35] Ivanov M S,Rogazinskii S V.Comparative analysis of algorithms of DSMC in rarefied gas dynamics. Comput Math and Math phys.,23(7):1058,1988.
[36] Larsen P S and Borgnakke C. Staistical collision model for model for simulation polyatomic gas with restricted energy exchange. Rarefied Gas Dynamics,ed. By M. Becker and M. Fiebig,A.7-1,DFVLR-Press,1974
[37] Yichuan Fang,Parallel Simulation of Mcroflows by DSMC and Burnett Equations[D],Western Michigan University,June 2003
[38] Ikegawa M, and Kobayashi J. Development of a rarefied flow simulator using thedirect-simulation Monte Carlo method. JSME International Journal, 1990, 30: 463-467
[39] J.-S.Wu,K.-C.Tseng Analysis of micro-scale flows with pressure boundaries using direct simulation Monte Carlo method[J].Computers& Fluids 2001,30(7):711-735
[40] A. A. Alexeenko , Reconsideration of Flows through Constriction Micro-channels Using the DSMC Method,33rd AIAA Fluid Dynamics Conference and Exhibit23-26 June 2003, Orlando,Florida
[41] 王沫然,王金库,李志信 DSMC 方法的压力边界条件实现[J].2004,21(4):316-321
[42] Liou W W and Fang Y C. Computations of the Flow and Heat Transfer in Micro devices Using DSMC with Implicit Boundary Conditions. J. Heat Transfer. 2002, 124: 338-345
[43] A. Beskok, Validation of a New Velocity-Slip Condition for Separated Gas Microflows,Numer. Heat Transfer B, vol. 40, pp. 451-471, 2001.
[44] Haas B L, Hash D B, Bird G A, Lumpkin F E. Rates of thermal relaxation in directsimulation Monte Carlo methods. Phys. Fluids, 1994, 6(6): 2191-2201
[45] Ozgur Aktas and N. R. Aluru. A Combined Continuum/DSMC TechniqueforMultiscale Analysis of Microfluidic Filters[J]. Computational Physics 178, 342–372 (2002)
[46] Quanhua Sun, Iain D. Boyd, Jing Fan.Development of an Information Preservation Method forSubsonic, Micro-Scale Gas Flows,
[47] Wen-Lan Wang and Iain D. Boyd,A New Energy Flux Model in theDSMC-IP Method for Nonequilibrium Flows,36th.AIAA Thermophysics ConferenceJune 23–26, 2003 / Orlando, FL
[48] Quan hua Sun Information Preservation Methods for Modeling Micro-scale Gas Flows[D],Western Michigan University,June 2003
[2] 吴怀宇,周兆英等,微型飞行器的研究现状及其关键技术,武汉科技大学学报(自然科学版),2000,23(2):170-174
[3] Jack H, Military Look to Flying Insect Robots,[J].Industrical Robot,1998,25(2):124-128
[4] StevenA.,Palm-sizeSpyPlanes,[J].MechanicalEngineering,1998,120(2):74-78
[5] Alan H Epstein. Micro Turbine Engines For Soldier Power[R]. The Defense Science and Technology Seminar, 2000.
[6] Epstein A H, etc. Micro Gas Turbine Generators [R]. Massachusetts Inst. of Tech. , Gas Turbine Lab, Final Rept.1995- 2000.
[7] HanSòjrg Schlip, Fabrication of Turbine-Comp ressor-Shaft Assembly For Micro Gas Turbine Engine[D]. Mater’ s Thesis, Stanford Univ. ,December 2000.
[8] HanS ò jrg Schlip, Kang S, Stampfl [J] , Cooper A G, Prinz F B. Application of the Mold SDM Process to the Fabrication of Ceramic Parts for Micro Gas Turbine engine[R]. Heinrich J G(ed.) , Proceedings Ceramics Materials and Components for Engines, Germany, 2000.
[9] Miklos Gerendas, Ralph Pfister. Development of a Very Small Aero-Engine[R]. Proceedings of ASME Turbo Expo 2000,45th ASME International Gas Turbine and A ero-EngineTechnical Congress and Exposition, 2000- GT- 0536.
[10] Mindi Farber De Anda, Christina TerMaath, N deye K Fall. Distributed Energy Technology Simulator Microturbine Demonstration[R]. Energetics, Inc. Washington,DC, 2001.
[11] Wu Pittle W A. Mesurement of Friction Fcetors for the Flow of Gases in Very Fine Channels Used for Microminiature Joule — Thomson Refrigeration [J].Cryogenics,1983,23:273-277
[12] Pfahler J N , Harley J ,Bau H , et al. Liquid and GasTransport in Small Channels[J] . ASME DSC ,1990 ,19 :149-157
[13] Pfahler J N ,Harley J ,Bau H , et al. Gas and Liquid Flow in Small Channels[J] . ASME DSC ,1991 ,32 :49 - 601
[14] Choi S B ,Barrori R F ,Warrington R O. Fluid Flow and Heat Transfer in Microtubes [J] . ASME DSC , 1991 ,32:123-134
[15] Harley J C ,Huang Y F ,Bau H ,et al. Gas Flow in Micro-channels[J] . J Fluid Mech ,1995 ,284 :257 – 2741.
[16] 邬小波,过增元. 微细光滑圆管内气体的流动与传热特性研究[J] . 工程热物理学报,1997,18(5):326-330
[17] 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
[18] 杜东兴. 可压缩性及粗糙度对微细管内流动及换热特性的影响[D] . 北京:清华大学工程力学系,20001
[19] Fan J , Shen C. Statistical simulation of low - speed rarefied gas flows[ J ]. J Coputational Physics, 2001, 16 ( 9) : 393 -398.
[20] Beskok A,Karniadakis G E. A model for flows in channels,pipes,and ducts at micro and nano scales[J].Microscale Thermophysical Engineering,1999,3(1):43～77.
[21] Berg H R,Seldam C A,Gulik P S.Compressible lam inar flow in a capillary [J]. Fluid Mech.,1993,24:1～20.
[22] Gad-el-hak M . The fluid mechanics of micro devices . J . Fluids Engineering, ASME,1999,Vol.121,pp.5-33.
[23] Tsien H S( 钱 学 森 ).Superaerodynamics,mechanics of rarefied J.Aero.Sci,13.12.653-664(1964)
[24] G.A. Bird, Approach to Translational Equilibrium in a Rigid Sphere Gas[J]. Phys.Fluids, 1963,6(10):1518-1519.
[25] Bird GA. Application of the DSMC method to the full shuttle gemertry .AIAA paper,90-1692,1990
[26] Oran E S, Oh C K and Cybyk B Z. Direct Simulation Monte Carlo: Recent Advances andApplications. Annual Review of Fluid Mechanics. 1998. 30: 403-441
[27] Bird G.A. Molecular Gas Dynamics and the Direct Simulation of Gas Flows. Clarendon Press,Oxford,1994.
[28] 沈青. 稀薄气体动力学. 北京:国防工业出版社. 2003
[29] Bird G A. Rarefied Gas dynamics. Invited Paper 221 at the 12th International Symposium on Rarefied Gas Dynamics,,Charlotesville, July,1980.
[30] Koura K, Matsumoto H. Variable soft sphere molecular model for inverse-power-law or Lennard-Jones potential. Phys. Fluids A, 1991,3:2459-2465.
[31] Koura K, Matsumoto H. Variable soft sphere molecular model for air species. Phys. Fluids A, 1992, 4: 1083-1085.
[32] Cercignani C, and Lampis M. Kinetic models for gas-surface interactions, TransportTheory. Statist. Phys., 1971, 2: 505
[33] Bird G A. Recent advances and current challenges for DSMC. Computers Math. Applic.1998, 35: 1-14
[34] KouraK.Null-collision technique in the DSMC method .Phys.Fluids,29:3529,1986.
[35] Ivanov M S,Rogazinskii S V.Comparative analysis of algorithms of DSMC in rarefied gas dynamics. Comput Math and Math phys.,23(7):1058,1988.
[36] Larsen P S and Borgnakke C. Staistical collision model for model for simulation polyatomic gas with restricted energy exchange. Rarefied Gas Dynamics,ed. By M. Becker and M. Fiebig,A.7-1,DFVLR-Press,1974
[37] Yichuan Fang,Parallel Simulation of Mcroflows by DSMC and Burnett Equations[D],Western Michigan University,June 2003
[38] Ikegawa M, and Kobayashi J. Development of a rarefied flow simulator using thedirect-simulation Monte Carlo method. JSME International Journal, 1990, 30: 463-467
[39] J.-S.Wu,K.-C.Tseng Analysis of micro-scale flows with pressure boundaries using direct simulation Monte Carlo method[J].Computers& Fluids 2001,30(7):711-735
[40] A. A. Alexeenko , Reconsideration of Flows through Constriction Micro-channels Using the DSMC Method,33rd AIAA Fluid Dynamics Conference and Exhibit23-26 June 2003, Orlando,Florida
[41] 王沫然,王金库,李志信 DSMC 方法的压力边界条件实现[J].2004,21(4):316-321
[42] Liou W W and Fang Y C. Computations of the Flow and Heat Transfer in Micro devices Using DSMC with Implicit Boundary Conditions. J. Heat Transfer. 2002, 124: 338-345
[43] A. Beskok, Validation of a New Velocity-Slip Condition for Separated Gas Microflows,Numer. Heat Transfer B, vol. 40, pp. 451-471, 2001.
[44] Haas B L, Hash D B, Bird G A, Lumpkin F E. Rates of thermal relaxation in directsimulation Monte Carlo methods. Phys. Fluids, 1994, 6(6): 2191-2201
[45] Ozgur Aktas and N. R. Aluru. A Combined Continuum/DSMC TechniqueforMultiscale Analysis of Microfluidic Filters[J]. Computational Physics 178, 342–372 (2002)
[46] Quanhua Sun, Iain D. Boyd, Jing Fan.Development of an Information Preservation Method forSubsonic, Micro-Scale Gas Flows,
[47] Wen-Lan Wang and Iain D. Boyd,A New Energy Flux Model in theDSMC-IP Method for Nonequilibrium Flows,36th.AIAA Thermophysics ConferenceJune 23–26, 2003 / Orlando, FL
[48] Quan hua Sun Information Preservation Methods for Modeling Micro-scale Gas Flows[D],Western Michigan University,June 2003