离子发动机交换电荷离子分布的数值模拟
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摘要
目前离子发动机已经较多地应用于空间飞行任务中,国外已经开始投入商用与深空探测项目。离子发动机羽流中产生的交换电荷离子会影响航天器的正常工作,准确地评估交换电荷离子分布特性对于离子发动机的应用与发展具有重要作用。离子发动机实验耗时长、成本高,而数值模拟却可以在较短的时间内获得更详尽的信息,目前数值模拟方法主要有质点网格-蒙特卡罗碰撞(PIC-MCC)法与直接模拟蒙特卡罗(DSMC)法。PIC粒子模拟方法需要模拟大量粒子,传统的中央处理器(CPU)串行求解效率很低,并行集群系统造价又十分昂贵。近年来图形处理器(GPU)的性能迅速提高,其性价比高、计算密度大、能耗低等优势十分明显。大规模的并行计算因此得以在个人计算机(PC)上实现,有利于提高科学研究的效率。
为了研究交换电荷离子的分布规律,本文采用PIC-MCC法对离子发动机交换电荷离子进行数值模拟,建立了二维轴对称模型和三维笛卡尔坐标模型,分别采用交替方向隐式迭代(ADI)法与完全近似存储格式的代数多重网格(FAS-AMG)法求解电场方程,MCC碰撞抽样过程中采用并行MT19937算法生成随机数。分别开发了基于CPU的粒子模拟系统和采用计算设备统一架构(CUDA)技术基于GPU的并行粒子模拟系统。模拟结果表明交换电荷离子在电场作用下会向束流区外运动,并在发动机栅极下游形成扩张型电场结构,一部分离子在电场力作用下会向发动机上游运动,其速度超过7000m/s,这些高速返流离子将会对航天器表面造成冲击。在发动机栅极上游约0.4m处获得交换电荷离子数密度为1×1010~5×1010/cm3,与国外相关报道基本一致。GUP并行模拟取得了与CPU串行模拟一致的结果,并获得约4.5~10倍的加速比。
In recent years, ion thruster has been widely used in many commercial and deep-space missions as propulsion system. The interaction between charge-exchange ions and spacecraft will influence solar panels and other instruments. It is very important to evaluate the distribution character of charge-exchange ions for the application and development of ion thruster. Ground and flight tests are very expensive and time-consuming for plume research. Numerical simulation gets more details of propagation character under different conditions for a short time. Particle-in-cell with Monte Carlo collision (PIC-MCC) method and Direct Simulation Monte Carlo (DSMC) method has been used as main approach in most analysises. The efficiency of central processing unit (CPU) is very low, and the use and maintenance costs of parallel cluster system is very expensive.With performances rapidly increasing, general computation ability of graphic processor unit (GPU) has transcended CUP's for its parallel hardware architecture and obvious advantages such as higher efficiency, higher arithmetic intensity and lower energy consumption. For all of these, the large-scale parallel computing can be practiced on personal computer to improve the efficiency of scientific research.
PIC-MCC method is used to simulate the charge-exchange ions to study its distribution. Two-dimensional axisymmetric and three-dimensional Cartesian coordinate models are established. The alternating direction implicit (ADI) method and full approximation storage-algebraic multigrid (FAS-AMG) method are used to update the electric field. Random numbers are generated by the parallel MT19937 algorithm in the process of MCC collision sampling. A particle simulation code based on CPU and a parallel one, which base on GPU by using the Compute Unified Device Architecture (CUDA), has been developed. The result shows that the chage-exchange ions driven by the electrostatic force will move out of the beam zone, and an expansion structure of electric formed in the grid downstream. A part of ions will move to the upstream of thruster with a velocity about 7 kilometers per second. These high speed ions can impact spacecraft surface. The ion number density is 1×1010~5×1010/cm3 in a 0.4m upstream distance from the grid. And GPU's result agrees well with CPU's and foreign related reports. Compared with a single CPU, 16-processor GPU represents 4.5~10 speedup.
为了研究交换电荷离子的分布规律,本文采用PIC-MCC法对离子发动机交换电荷离子进行数值模拟,建立了二维轴对称模型和三维笛卡尔坐标模型,分别采用交替方向隐式迭代(ADI)法与完全近似存储格式的代数多重网格(FAS-AMG)法求解电场方程,MCC碰撞抽样过程中采用并行MT19937算法生成随机数。分别开发了基于CPU的粒子模拟系统和采用计算设备统一架构(CUDA)技术基于GPU的并行粒子模拟系统。模拟结果表明交换电荷离子在电场作用下会向束流区外运动,并在发动机栅极下游形成扩张型电场结构,一部分离子在电场力作用下会向发动机上游运动,其速度超过7000m/s,这些高速返流离子将会对航天器表面造成冲击。在发动机栅极上游约0.4m处获得交换电荷离子数密度为1×1010~5×1010/cm3,与国外相关报道基本一致。GUP并行模拟取得了与CPU串行模拟一致的结果,并获得约4.5~10倍的加速比。
In recent years, ion thruster has been widely used in many commercial and deep-space missions as propulsion system. The interaction between charge-exchange ions and spacecraft will influence solar panels and other instruments. It is very important to evaluate the distribution character of charge-exchange ions for the application and development of ion thruster. Ground and flight tests are very expensive and time-consuming for plume research. Numerical simulation gets more details of propagation character under different conditions for a short time. Particle-in-cell with Monte Carlo collision (PIC-MCC) method and Direct Simulation Monte Carlo (DSMC) method has been used as main approach in most analysises. The efficiency of central processing unit (CPU) is very low, and the use and maintenance costs of parallel cluster system is very expensive.With performances rapidly increasing, general computation ability of graphic processor unit (GPU) has transcended CUP's for its parallel hardware architecture and obvious advantages such as higher efficiency, higher arithmetic intensity and lower energy consumption. For all of these, the large-scale parallel computing can be practiced on personal computer to improve the efficiency of scientific research.
PIC-MCC method is used to simulate the charge-exchange ions to study its distribution. Two-dimensional axisymmetric and three-dimensional Cartesian coordinate models are established. The alternating direction implicit (ADI) method and full approximation storage-algebraic multigrid (FAS-AMG) method are used to update the electric field. Random numbers are generated by the parallel MT19937 algorithm in the process of MCC collision sampling. A particle simulation code based on CPU and a parallel one, which base on GPU by using the Compute Unified Device Architecture (CUDA), has been developed. The result shows that the chage-exchange ions driven by the electrostatic force will move out of the beam zone, and an expansion structure of electric formed in the grid downstream. A part of ions will move to the upstream of thruster with a velocity about 7 kilometers per second. These high speed ions can impact spacecraft surface. The ion number density is 1×1010~5×1010/cm3 in a 0.4m upstream distance from the grid. And GPU's result agrees well with CPU's and foreign related reports. Compared with a single CPU, 16-processor GPU represents 4.5~10 speedup.
引文
[1] Douglas Bryan VanGilder.Numerical Simulations of the Plumes of Electric Propultion Thrusters[D].Cornell University, January 2000.
[2]黄良甫.电推进系统发展概况与趋势[J].真空与低温.2009(1):1-8,49.
[3]刘畅,汤海滨,顾左等.基于PIC方法的离子发动机光学系统粒子模拟[J].北京航空航天大学学报.2006(4)382-386.
[4] Samanta Roy.Numerical Simulation of Ion Thruster Plume Backflow for Spacecraft Contamination Assessment[D].Massachusetts Institute of Technology, June 1995.
[5] John F. Staggs, William P. Gula, William R. Kerslake.The Distributinn of Neutral Atoms and Charge-Exchange Ions Downstream of an Ion Thruster[R].AIAA 82-673,1967.
[6] M.R. Carruth, Jr.A Review of Studies on Ion Thruster Beam and Charge-Exchange Plasmas[R].AIAA 82-1944,1975.
[7] G. K. Komastu and J. M. Sellen, Jr.Beam Efflux Mesurements[R] .NASA CR-135038,1976.
[8] David Younghee Oh.Computational Modeling of Expanding Plasma Plumes in Space Using a PIC-DSMC Algorithm[D].Massachusetts Institute of Technology, February 1997.
[9] N. A. Gatsonis,R. I. Smanta Roy and D. E. Hastings. Numerical Investigation of Ion Thruster Plume Backflow[R].AIAA 94-3140.
[10] Joseph Wang,J. Brophy and D. Brinaza.3-D Simulations of NSTAR Ion Thruster Plasma Environment[R].AIAA 96-3202.
[11]曹勇.电推进发动机羽流对LEO小卫星编队飞行影响的数值模拟[A].2008年第四届电推进会议[C].西安:2008:11-18.
[12]贺碧蛟,张建华,蔡国飙.稳态等离子体推进器羽流场数值模拟[J].北京航空航天大学学报.2005(9):1009-1013.
[13]田东波,沈青,樊菁.稳态等离子体推进器羽流的粒子模拟[J].空气动力学学报.2006(4):425-429.
[14]钱中,王阳平,杜朝辉.Hall推力器羽流数值模拟[J].推进技术.2008(1):93-97.
[15]陈琳英,江豪成,郑茂繁.离子推力器束流密度分布测量[J].真空与低温.2007(3):155-158
[16] Michio Nishida , Toru Hyakutake , Hitoshi Kuninaka and Kyoichiro Toki[C]. DSMC-PIC Analysis of a Plume from a Small Ion Engine[R].IEPC 01-110, 2001.
[17] M. Matsushiro,M. Nishida,H. Kuninaka and K. Toki.Sensitivity of The Behavior of Backflow CEX Ions to Ion Engine Plume Characteristics[R].IEPC 0038-0303, 2003.
[18] F. H. Harlow . The Particle-in-Cell Computing Method for Fluid Dynamics[M].Methods Comput. Phys..1964(3):319–343.
[19]邵福球.等离子体粒子模拟[M].北京:科学出版社, 2002.
[20]冯白明.方向交替隐含法并行计算的一种模型[J].航空计算技术.1999(3):10-13.
[21]鲁晶津,吴小平,Klaus Spitzer.三维泊松方程数值模拟的多重网格法[J].地球物理学进展.2009(1):154-158.
[22]刘超群.多重网格法及其在计算流体力学中的应用[M].北京:清华大学出版社, 1995.
[23]张林波等.并行计算导论[M].北京:清华大学出版社, 2006.
[24]张舒,褚艳利等.GPU高性能运算之CUDA[M] .北京:中国水利水电出版社, 2009.
[25] Hotball.深入浅出CUDA.http:.//cuda.csdn.net, 2008.
[26] NVIDIA Corporation.NVIDIA CUDA Programming Guide(2.2).April 2009.
[27]陈飞国,葛蔚,李静海.复杂多相流动分子动力学模拟在GPU上的实现[J].中国科学B辑:化学.2008(12):1120-1128.
[28] K.霍金,D.阿斯特著,田昱川译.OpenGL游戏程序设计[M].北京:科学出版社,2006.
[29]金畅.蒙特卡洛方法中随机数发生器和随机抽样方法的研究[D].大连理工大学, 2005: 8-16.
[30] Yousef Saad.Iterative Methods for Sparse Linear Systems[M].PWS Publishing, Boston, MA, 1996:364-367.
[31]吴其芬,陈伟芳等.稀薄气体动力学[M].长沙:国防科技大学出版社, 2004.
[32] C. K. Birdsall,A. B. Langdon.Plasma Physics via Computer Simulation[M].Adam Hilger, Bristol, 1991.
[2]黄良甫.电推进系统发展概况与趋势[J].真空与低温.2009(1):1-8,49.
[3]刘畅,汤海滨,顾左等.基于PIC方法的离子发动机光学系统粒子模拟[J].北京航空航天大学学报.2006(4)382-386.
[4] Samanta Roy.Numerical Simulation of Ion Thruster Plume Backflow for Spacecraft Contamination Assessment[D].Massachusetts Institute of Technology, June 1995.
[5] John F. Staggs, William P. Gula, William R. Kerslake.The Distributinn of Neutral Atoms and Charge-Exchange Ions Downstream of an Ion Thruster[R].AIAA 82-673,1967.
[6] M.R. Carruth, Jr.A Review of Studies on Ion Thruster Beam and Charge-Exchange Plasmas[R].AIAA 82-1944,1975.
[7] G. K. Komastu and J. M. Sellen, Jr.Beam Efflux Mesurements[R] .NASA CR-135038,1976.
[8] David Younghee Oh.Computational Modeling of Expanding Plasma Plumes in Space Using a PIC-DSMC Algorithm[D].Massachusetts Institute of Technology, February 1997.
[9] N. A. Gatsonis,R. I. Smanta Roy and D. E. Hastings. Numerical Investigation of Ion Thruster Plume Backflow[R].AIAA 94-3140.
[10] Joseph Wang,J. Brophy and D. Brinaza.3-D Simulations of NSTAR Ion Thruster Plasma Environment[R].AIAA 96-3202.
[11]曹勇.电推进发动机羽流对LEO小卫星编队飞行影响的数值模拟[A].2008年第四届电推进会议[C].西安:2008:11-18.
[12]贺碧蛟,张建华,蔡国飙.稳态等离子体推进器羽流场数值模拟[J].北京航空航天大学学报.2005(9):1009-1013.
[13]田东波,沈青,樊菁.稳态等离子体推进器羽流的粒子模拟[J].空气动力学学报.2006(4):425-429.
[14]钱中,王阳平,杜朝辉.Hall推力器羽流数值模拟[J].推进技术.2008(1):93-97.
[15]陈琳英,江豪成,郑茂繁.离子推力器束流密度分布测量[J].真空与低温.2007(3):155-158
[16] Michio Nishida , Toru Hyakutake , Hitoshi Kuninaka and Kyoichiro Toki[C]. DSMC-PIC Analysis of a Plume from a Small Ion Engine[R].IEPC 01-110, 2001.
[17] M. Matsushiro,M. Nishida,H. Kuninaka and K. Toki.Sensitivity of The Behavior of Backflow CEX Ions to Ion Engine Plume Characteristics[R].IEPC 0038-0303, 2003.
[18] F. H. Harlow . The Particle-in-Cell Computing Method for Fluid Dynamics[M].Methods Comput. Phys..1964(3):319–343.
[19]邵福球.等离子体粒子模拟[M].北京:科学出版社, 2002.
[20]冯白明.方向交替隐含法并行计算的一种模型[J].航空计算技术.1999(3):10-13.
[21]鲁晶津,吴小平,Klaus Spitzer.三维泊松方程数值模拟的多重网格法[J].地球物理学进展.2009(1):154-158.
[22]刘超群.多重网格法及其在计算流体力学中的应用[M].北京:清华大学出版社, 1995.
[23]张林波等.并行计算导论[M].北京:清华大学出版社, 2006.
[24]张舒,褚艳利等.GPU高性能运算之CUDA[M] .北京:中国水利水电出版社, 2009.
[25] Hotball.深入浅出CUDA.http:.//cuda.csdn.net, 2008.
[26] NVIDIA Corporation.NVIDIA CUDA Programming Guide(2.2).April 2009.
[27]陈飞国,葛蔚,李静海.复杂多相流动分子动力学模拟在GPU上的实现[J].中国科学B辑:化学.2008(12):1120-1128.
[28] K.霍金,D.阿斯特著,田昱川译.OpenGL游戏程序设计[M].北京:科学出版社,2006.
[29]金畅.蒙特卡洛方法中随机数发生器和随机抽样方法的研究[D].大连理工大学, 2005: 8-16.
[30] Yousef Saad.Iterative Methods for Sparse Linear Systems[M].PWS Publishing, Boston, MA, 1996:364-367.
[31]吴其芬,陈伟芳等.稀薄气体动力学[M].长沙:国防科技大学出版社, 2004.
[32] C. K. Birdsall,A. B. Langdon.Plasma Physics via Computer Simulation[M].Adam Hilger, Bristol, 1991.