半透明颗粒相变过程光热耦合特性研究
|
摘要
半透明颗粒相变过程是一个复杂的多场耦合传热过程,往往伴随着辐射吸收和发射等光学行为以及膨胀变形、收缩破裂等力学行为。了解和掌握这些机制和行为对相关工程技术领域的过程控制、优化设计具有重要意义,如热喷涂技术、液滴燃烧、空间液滴散热技术、反应堆事故、太阳能热利用等等。高温颗粒相变过程中的辐射导热耦合传热模拟,对于准确分析高温颗粒的相变过程是非常必要的。由于相变过程中存在相界面移动和变形等问题,传统的基于网格法的数值模拟手段求解这类问题需要复杂和繁琐的网格初置与重构过程,而无网格法不依赖于网格,对于求解域连续变化等复杂问题的求解具有很大优势。
本文主要目的是将无网格SPH法引入到相变过程中的辐射-导热耦合传热过程的分析研究当中来,在此过程中忽略力学效应,假设颗粒在发生相变的过程中不发生形变。论文的主要工作包括:
(1)相变导热问题的无网格SPH法研究推导了相变导热方程及其边界条件的SPH法离散格式,编制了计算程序;对第一类和第三类边界条件下的二维非稳态相变导热过程的温度场、相界面位置进行了数值模拟,与解析解比对分析,考察了SPH法在处理相变导热问题上的计算精度和适应性。
(2)辐射传递方程求解的无网格SPH法研究推导了无散射介质辐射传递方程及边界条件的SPH法离散格式,编制了计算程序;对二维方形空腔内的吸收发射性介质辐射换热进行了模拟计算,与有限体积法的标准程序解进行了比对分析,考察了SPH法在处理辐射传递问题上的适用性。
(3)相变过程辐射导热耦合传热模拟的SPH法研究推导了含辐射源项的相变过程焓方程的SPH离散格式,将相变导热问题的SPH法与辐射传递问题的SPH相结合,编制了计算程序;与二维相变辐射导热耦合换热的有限体积法标准解进行比对,验证了SPH法的可靠性;对半透明颗粒相变过程传热进行了模拟。
It is a complex multi-field coupled heat transfer process for semitransparent particle with phase change, there often accompanied by absorption and emission of radiation and swell distortion and shrinkage splinter of mechanical behavior of fracture. Which is very important to process control and optimization design in related to the field with understand and master these mechanisms and behaviors, such as thermal spraying, droplet combustion, droplet cooling space technology, reactor accidents, solar thermal, etc. The radiation and conduction coupling simulation of particle in the high-temperature is necessary for accurate analysis the process of the phase change. Because there exists the phase interface movement and deformation problem in the process of phase change, the traditional gird method need to build a new gird repeating, this work is complex and fasting time. But meshless method does not depend on gird, so it’s a great advantage for solving complex problems such as continuous field changes.
The purpose of this paper is to solving the radiation-conduction problems with the meshless SPH in the process of the phase change, we can not consider the mechanical behavior of fracture in this work. And suppose it is not phase change in the process of deformation. Thesis include:
(1) The study on the conduction heat transfer problem in the process of phase change by meshless SPH method We build the conduction function with phase change and derived the SPH method discrete format of the boundary conditions, then create a computer program. Calculate the temperature field and interface position of the two-dimensional steady-state conduction heat transfer in the phase change with the fist and third boundary conditions. Compared with the analysis to study the accuracy and adaptability of the meshless SPH method by applied which to phase change.
(2) The study on the radiation heat transfer with meshless SPH method We build the radiation transfer function without scattering media and derive the discrete format SPH method of the boundary conditions, then create the computer program. Calculate the radiation heat transfer of the absorption media of the two-dimensional square cavity. Compared with the finite volume solutions of the standard procedures, to investigate the meshless SPH method is used to dealing with the radiation problem.
(3) Study on the heat transfer of coupled radiation and conduction in the process of phase change with the meshless SPH method We derive the discrete format of the power conduction of the process of the phase change with the sources of the radiation. Combine the conduction heat transfer of the phase change and radiation transfer problem, then create computer program. Calculate the couple radiation and conduction heat transfer of the two-dimension phase change, compared with the finite volume solving of standard to verify the reliability of SPH method. In the last calculate the process of the phase change of the semitransparent particle.
本文主要目的是将无网格SPH法引入到相变过程中的辐射-导热耦合传热过程的分析研究当中来,在此过程中忽略力学效应,假设颗粒在发生相变的过程中不发生形变。论文的主要工作包括:
(1)相变导热问题的无网格SPH法研究推导了相变导热方程及其边界条件的SPH法离散格式,编制了计算程序;对第一类和第三类边界条件下的二维非稳态相变导热过程的温度场、相界面位置进行了数值模拟,与解析解比对分析,考察了SPH法在处理相变导热问题上的计算精度和适应性。
(2)辐射传递方程求解的无网格SPH法研究推导了无散射介质辐射传递方程及边界条件的SPH法离散格式,编制了计算程序;对二维方形空腔内的吸收发射性介质辐射换热进行了模拟计算,与有限体积法的标准程序解进行了比对分析,考察了SPH法在处理辐射传递问题上的适用性。
(3)相变过程辐射导热耦合传热模拟的SPH法研究推导了含辐射源项的相变过程焓方程的SPH离散格式,将相变导热问题的SPH法与辐射传递问题的SPH相结合,编制了计算程序;与二维相变辐射导热耦合换热的有限体积法标准解进行比对,验证了SPH法的可靠性;对半透明颗粒相变过程传热进行了模拟。
It is a complex multi-field coupled heat transfer process for semitransparent particle with phase change, there often accompanied by absorption and emission of radiation and swell distortion and shrinkage splinter of mechanical behavior of fracture. Which is very important to process control and optimization design in related to the field with understand and master these mechanisms and behaviors, such as thermal spraying, droplet combustion, droplet cooling space technology, reactor accidents, solar thermal, etc. The radiation and conduction coupling simulation of particle in the high-temperature is necessary for accurate analysis the process of the phase change. Because there exists the phase interface movement and deformation problem in the process of phase change, the traditional gird method need to build a new gird repeating, this work is complex and fasting time. But meshless method does not depend on gird, so it’s a great advantage for solving complex problems such as continuous field changes.
The purpose of this paper is to solving the radiation-conduction problems with the meshless SPH in the process of the phase change, we can not consider the mechanical behavior of fracture in this work. And suppose it is not phase change in the process of deformation. Thesis include:
(1) The study on the conduction heat transfer problem in the process of phase change by meshless SPH method We build the conduction function with phase change and derived the SPH method discrete format of the boundary conditions, then create a computer program. Calculate the temperature field and interface position of the two-dimensional steady-state conduction heat transfer in the phase change with the fist and third boundary conditions. Compared with the analysis to study the accuracy and adaptability of the meshless SPH method by applied which to phase change.
(2) The study on the radiation heat transfer with meshless SPH method We build the radiation transfer function without scattering media and derive the discrete format SPH method of the boundary conditions, then create the computer program. Calculate the radiation heat transfer of the absorption media of the two-dimensional square cavity. Compared with the finite volume solutions of the standard procedures, to investigate the meshless SPH method is used to dealing with the radiation problem.
(3) Study on the heat transfer of coupled radiation and conduction in the process of phase change with the meshless SPH method We derive the discrete format of the power conduction of the process of the phase change with the sources of the radiation. Combine the conduction heat transfer of the phase change and radiation transfer problem, then create computer program. Calculate the couple radiation and conduction heat transfer of the two-dimension phase change, compared with the finite volume solving of standard to verify the reliability of SPH method. In the last calculate the process of the phase change of the semitransparent particle.
引文
1 L. A. Dombrovsky, M. B. Ignatev. Inclusion of Nonisothermality of Particles in the Calculations and Diagnostics of Two-Phase Jets Used for Spray Edposition of Coatings. High Temperature. 2001, 39(1): 134-141
2 L. A. Dombrovsky.Absorption of Thermal Radiation in Large Semi-transparent Particles at Arbitrary Illumination of the Polydisperse System . Int. J. of Heat and Mass Transfer. 2004,47(25):5511-5522
3 C. C. Tseng, R. Viskanta . Effect of Radiation Absorption on Fuel Droplet Evaporation.Combustion Science and Technology. 2005,177(8):1511-1542
4陈君,彭晓峰,段远源.微尺度热现象可视化教学实验装置制作与实验.实验技术与管理. 2003,20(4):48-51
5刘伟民,毕勤成等.低压闪蒸液滴温度与相变过程的研究.应用基础与工程科学学报. 2005, 13(4):381-387
6余其铮编著.辐射换热原理.哈尔滨工业大学出版社. 2000:1-2:111-113
7 E.B.阿梅季斯托夫, A.C.德米特里耶夫著.单分散颗粒系统与技术.秦仁等译.国家级黑龙江中俄科技合作及产业化中心. 2005年
8王剑锋,杨超,毛在砂. Levelset方法数值模拟单液滴传质中的Marangoni效应.中国科学. 2008,38(2):150-160
9谈和平等编.红外辐射特性与传输的数值计算——计算辐射学.哈尔滨工业大学出版社. 2006:241-246
10 D. W. Mackowski, R. A Altenkirch and M. P. Menguc. A Comparison of Electromagnetic Wave and Radiative Transfer Equation Analyses of a Coal Particle Surrounded by a Soot Cloud.Combustion and Flame. 1989,76:415-420
11 S. Choi and C. H. Kruger. Modeling Coal Particle Behavior under Simultaneous Devolatilization and Combustion.Combustion and Flame. 1985,61:131-144
12 L. A. Dombrovsky and M. B. Ignatev. Inclusion of Nonisothermality of Particles in the Calculations and Diagonstics of Two-Phase Jets Used for Spary Edposition of Coatings. High Temperature. 2001, 39(1): 134-141
13 A. L. Aden and M. Kerker. Scattering of Electromagnetic Waves from Two Concentric Spheres. Journal of Applied Physics. 1951,22(10): 1242-1246
14 P. W. Dusel, M. Kerker and D. D. Cooke.Distribution of Absorption Centers within Irradiated Spheres. Journal of Optical Society of America. 1979,69(1):55-59
15 S. M. Oliver and B. E. Moylan. An Analytical Approach for the Prediction of Gamma-to-Alpha Phase Transformation of Aluminium Oxide (Al2O3) Particles in the Space Shuttle ASRM and RSRM Exhausts. AIAA Paper 1992-2915,1992
16 Y. A. Plastinin, N. A. Anfimov, G. G. Baula, G. F. Karabadzhak, B. A. Khmelinin and A. V. Rodionov. Modeling of Aluminum Oxide Particle Radiation in a Solid Propellant Motor Exhaust. AIAA Paper 1996-1879,1996
17 Y. P. Wan, V. Prasad, G. X. Wang, S. Sampath and J. R. Fincke. Model and Powder Particle Heating/Melting Resolidification and Evaporation in Plasma Spraying Processes. Journal of Heat Transfer. 1999,121:691-699
18 L. Hespel, A. Delfour, S. Gosséand F. Millot. Influence of Alumina Particles Heterogeneity on Particle Sizing and Radiative Properties Evaluation in Solid Rocket Plumes. AIAA Paper 2003-3650,2003
19 C. C. Tseng and R. Viskanta.Heating/Melting of a Semitransparent Particle Including Radiation Effects. International Journal of Thermal Sciences. 2006,45:945-954
20 C. C. Tseng and R. Viskanta. Heating/Melting of a Fused Silica Particle by Convection and Radiation. International Journal of Heat and Mass Transfer. 2006,49:2995-3003
21 S. Sazhin, P. A. Krutitskii , S. B. Martynov , D. Mason , M. R. Heikal and E. M. Sazhina. Transient Heating of a Semitransparent Spherical Body. International Journal of Thermal Sciences. 2007,46:444–457
22 L. A. Dombrovsky and L. S. Wojciech. Transient Temperature and Thermal Stress Profiles in Semi-transparent Particles under High-flux Irradiation. International Journal of Heat and Mass Transfer. 2007,50: 2117–2123
23 L. A. Dombrovsky and T. N. Dinh. The Effect of Thermal Radiation on the Solidification Dynamics of Metal Oxide Melt Droplets. Nuclear Engineering and Design. 2008,238:1421-1429
24 Z. X. Wu and Y. P. Wang. Scattering of Electromagnetic-Plane Waves by Radially Inhomogeneous Spheres: a Finely Stratified Sphere Model. Applied Optics. 1994, 69(1):55-59
25刘长松,刘永合,殷声.火焰喷涂合成TiC-Fe涂层的热力学分析.金属学报. 2000,6(1):62-63
26 L. H. Liu (刘林华), H. P. Tan (谈和平) and Q. Z. Yu (余其铮). Internal Distribution of Radiation Absorption in One-Dimensional Semitransparent Medium. Int. J. of Heat and Mass Transfer. 2002,45(2):417-424
27 L. H. Liu (刘林华), H. P. Tan (谈和平) and T. W. Tong. Internal Distribution of Radiation Absorption in a Semitransparent Spherical Particle. J. of Quant. Spectrosc. Radiative Transfer. 2002,72(6):747-756
28李亦军.单分散系微粒的Mie散射计算.应用光学. 2005,26(1):9-11
29张胤,贺友多,樊俊飞.任三兵金属喷射成形过程的数学模型.过程工程学报. 2008,8增刊(1):110-114
30王剑锋,杨超,毛在砂. Levelset方法数值模拟单液滴传质中的Marangoni效应.中国科学. 2008, 38(2):150-160
31孙慧娟,张海滨,白博峰.高温燃气中单个液滴的蒸发特性.西安交通大学学报. 2008,42:833-837
32丰松江,聂万胜,宋丰华,庄逢辰.固体火箭发动机尾焰红外辐射特性预估研究.固体火箭技术. 2009,32:183-187
33 L. B. Lucy.A Numerical Approach to the Testing of the Fission Hypothesis. The Astron[J]. 1977,8(12):1013-1024
34 R. A. Gingold and J. J. Monaghan. Smoothed Particle Hydrodynamics: Theory and Application to Non-spherical Stars [J]. Mnras . 1977:181-375
35 W. Benz and E. Asphaug. Impact Simulations with Fracture. I methods and Test, ICARUS. 1994, 107:98-116
36 J. J. Monaghan. Simulation Free Surface Flow with SPH. Journal of Computational Physics. 1994,110-339
37 J. J. Monaghan. Simulating Gravity Currents with SPH Lock Gates. Applied Mathematics Reports and Preprints, Monash University. 1995a
38 J. J. Monaghan. Heat Conduction with Discontinuous Conductivity. Applied Mathematics Reports and Preprints, Monash University. 1995b
39 P. W. Cleary. Modeling Confined Multi-material Heat and Mass Flows Using SPH. Applied Mathematical Modeling. 1998, 22:981-993
40 W. K. Liu, S. Jun and Y. F. Zhang. Reroducing Kernel Particle Methods. International Journal for Numerical Methods in Fluids. 1995a,20: 1081-1106
41 W. K. Liu, S. Jun, S. Li, J. Adee and T. Belytschko. Reproducing Kernel Particle Methods for Structural Dynamics. International Journal for Numerical Methods in Engineering. 1995b, 38:1655-1679
42 W. K. Liu, Y. Chen, C. T. Chang and T. Belytschko. Adbances in Multiple Scale Kernel Particle Methods, Computationa Mechanics. 1996a, 18(2):73-111.
43 W. K. Liu, Y. Chen, S. Jun, J. S. chen, T. Belyschko, C. Pan, R. A. Uras and C. T. Chang. Overvies and Applications of the Reproducing Kernel Particle Methods. Archives of Computational Methods in Engineering State of the Art, Reviews. 1996b,3:3-80
44 W. k. Liu, Y. Chen, R. A. Uras and C. T. Chang. Generalized Multiple Scale Reproducing KernelParticle Methods. Computer Methods in Applied Mechanics and Engineering. 1996c,139:91-157
45 Benedict. SPH for Naval Hydrodynamics[C]. Proc, 18th IWWWFB. Le Croisic. France 2003
46 M. Gomez-Gesteira. Green Water Overtopping Analyzed with a SPH Model[J]. Ocean Engineering. 2005,32:223-238
47 G. Oger. Two-dimensional SPH Simulation of Wedge Water Entries[J]. J Computational Physics. 2006, 213:803-822
48 S. Potapov, B. Maurel, A. Combescure and J. Fabis. Modeling Accidental-type Fluid–structure Interaction Problems with the SPH Method. Computers and Structures. 2009,87:721-734
49 M. Calamaz, J. Limido, M. Nouari, C. Espinosa, D. Coupard, M. Salaün, F. Girot and R. Chieragatti. Toward a Better Understanding of Tool Wear Effect Through a Comparison between Experiments and SPH Numerical Modelling of Machining Hard Materials. Int. Journal of Refractory Metals & Hard Materials. 2009,27:595-604
50贝新源,岳宗五.平滑粒子流体动力学(一种数值模拟方法)[A].高科技研究中的数值计算[C].国防科技大学出版社. 1995
51张锁春.光滑质点流体动力学(SPH)方法[J].计算物理. 1996,13(4):385–397
52毛益明,汤文辉.自由表面流动问题的SPH方法数值模拟.解放军理工大学学报(自然科学版). 2001,2(5):92-94
53邓嘉胤,杨健,王乐勤,杜红霞,王娜.光滑粒子动力学方法的固液二相流研究.浙江大学学报(工学版). 2007,41(5):853-858
54 S. Wong and Y. Shie. Galerkin Based Smoothed Particle Hydrodynamics. Computers and Structures. 2009,87:1111-1118
55郑兴,许国冬,段文洋.自由表面翻卷与破碎流动的SPH数值模拟.哈尔滨工程大学学报. 2010,31:301-306
56毛益明.光滑粒子流体动力学数值模拟方法研究.国防科学技术大学.硕士学位论文. 2000
57邓方钢.柱坐标系下光滑粒子流体动力学数值模拟.国防科学技术大学.硕士学位论文. 2002
58张姝慧,汪继文. SPH方法中初始时粒子配置的分析.计算机技术与发展. 2007,17(6): 36-38
59田瑜,傅学金,关正西.一维SPH的稳定性分析.力学与实践. 2008, 30(4):73-75
60郑兴,段文洋.光滑粒子流体动力学二阶算法精度研究.水科学进展. 2008,19(6):821-827
61郑俊,张嘉钟,于开平,魏英杰. SPH离散误差的线性形式及稳定性分析.四川大学学报(工程科学版). 2010,42(1):91-97
62 J. K. Chen, J. E. Beraun and T. C. Carney. A Corrective Smoothed Particle Method for BoundaryValue Problems in Heat Conduction. Compuer Methods in Applied Mechanics and Engineering. 1999a,46:231-252
63 J. K. Chen, J. E. Beraun and C. J. Jih. An Improvement for Tensile Instaability in Smoothed Particle Hydrodynamics. Computational Mechanics. 1999b,23:279-287
64 J. K. Chen, J. E. Beraun and C. J. Jih. Completeness of Corrective Smoothed Particle Method for Linear Elastodynamics. Computational Mechanics. 1999c,24:273-285
65 J. K. Chen and J. E. Beraun. A Generalized Smoothed Particle Hydrodynamics Method for Nonlinear Dynamic Problems. Computer Methods in Applied Mechanics and Engineering. 2000,190:225-239
66 G. R. Liu and M. B. Liu.光滑粒子流体动力学——一种无网格粒子法.韩旭,杨刚,强洪夫.湖南大学出版社. 2005:35-37
67杨世明,陶文铨.传热学(第四版).高等教育出版社. 2006,12
68叶宏,何汉峰等.利用焓法和有效热容法对定形相变材料熔解过程分析的比较研究.太阳能学报. 2004, 25(4):488-491
69 H. Yang and Y. Q. He. Solving Heat Transfer Problems with Phase Change Via Smoothed Effective Heat Capacity and Element-free Galerkin Methods. International Communications in Heat and Mass Transfer. 2010,37:385-392.
70王雁明,谈和平,帅永等.基于红外辐射特性的尾喷焰组分分析.中国工程热物理学会.编号:073337
71 J. Y. Li, S. K. Dong and H. P. Tan. Effective Optical Constant of Alumina Particle Containing Cafbon. AIAA J. of Thermophysics and Heat Transfer. 2009,23(1):216-219
72 J. C. Chai. A General-purpose Computer Program for Radiative Transfer(User Manual). 2002
73易红亮,何凯,谈和平.有限元求解二维介质内辐射-相变耦合传热. 2009年中国工程热物理学会传热传质学学术会议.
2 L. A. Dombrovsky.Absorption of Thermal Radiation in Large Semi-transparent Particles at Arbitrary Illumination of the Polydisperse System . Int. J. of Heat and Mass Transfer. 2004,47(25):5511-5522
3 C. C. Tseng, R. Viskanta . Effect of Radiation Absorption on Fuel Droplet Evaporation.Combustion Science and Technology. 2005,177(8):1511-1542
4陈君,彭晓峰,段远源.微尺度热现象可视化教学实验装置制作与实验.实验技术与管理. 2003,20(4):48-51
5刘伟民,毕勤成等.低压闪蒸液滴温度与相变过程的研究.应用基础与工程科学学报. 2005, 13(4):381-387
6余其铮编著.辐射换热原理.哈尔滨工业大学出版社. 2000:1-2:111-113
7 E.B.阿梅季斯托夫, A.C.德米特里耶夫著.单分散颗粒系统与技术.秦仁等译.国家级黑龙江中俄科技合作及产业化中心. 2005年
8王剑锋,杨超,毛在砂. Levelset方法数值模拟单液滴传质中的Marangoni效应.中国科学. 2008,38(2):150-160
9谈和平等编.红外辐射特性与传输的数值计算——计算辐射学.哈尔滨工业大学出版社. 2006:241-246
10 D. W. Mackowski, R. A Altenkirch and M. P. Menguc. A Comparison of Electromagnetic Wave and Radiative Transfer Equation Analyses of a Coal Particle Surrounded by a Soot Cloud.Combustion and Flame. 1989,76:415-420
11 S. Choi and C. H. Kruger. Modeling Coal Particle Behavior under Simultaneous Devolatilization and Combustion.Combustion and Flame. 1985,61:131-144
12 L. A. Dombrovsky and M. B. Ignatev. Inclusion of Nonisothermality of Particles in the Calculations and Diagonstics of Two-Phase Jets Used for Spary Edposition of Coatings. High Temperature. 2001, 39(1): 134-141
13 A. L. Aden and M. Kerker. Scattering of Electromagnetic Waves from Two Concentric Spheres. Journal of Applied Physics. 1951,22(10): 1242-1246
14 P. W. Dusel, M. Kerker and D. D. Cooke.Distribution of Absorption Centers within Irradiated Spheres. Journal of Optical Society of America. 1979,69(1):55-59
15 S. M. Oliver and B. E. Moylan. An Analytical Approach for the Prediction of Gamma-to-Alpha Phase Transformation of Aluminium Oxide (Al2O3) Particles in the Space Shuttle ASRM and RSRM Exhausts. AIAA Paper 1992-2915,1992
16 Y. A. Plastinin, N. A. Anfimov, G. G. Baula, G. F. Karabadzhak, B. A. Khmelinin and A. V. Rodionov. Modeling of Aluminum Oxide Particle Radiation in a Solid Propellant Motor Exhaust. AIAA Paper 1996-1879,1996
17 Y. P. Wan, V. Prasad, G. X. Wang, S. Sampath and J. R. Fincke. Model and Powder Particle Heating/Melting Resolidification and Evaporation in Plasma Spraying Processes. Journal of Heat Transfer. 1999,121:691-699
18 L. Hespel, A. Delfour, S. Gosséand F. Millot. Influence of Alumina Particles Heterogeneity on Particle Sizing and Radiative Properties Evaluation in Solid Rocket Plumes. AIAA Paper 2003-3650,2003
19 C. C. Tseng and R. Viskanta.Heating/Melting of a Semitransparent Particle Including Radiation Effects. International Journal of Thermal Sciences. 2006,45:945-954
20 C. C. Tseng and R. Viskanta. Heating/Melting of a Fused Silica Particle by Convection and Radiation. International Journal of Heat and Mass Transfer. 2006,49:2995-3003
21 S. Sazhin, P. A. Krutitskii , S. B. Martynov , D. Mason , M. R. Heikal and E. M. Sazhina. Transient Heating of a Semitransparent Spherical Body. International Journal of Thermal Sciences. 2007,46:444–457
22 L. A. Dombrovsky and L. S. Wojciech. Transient Temperature and Thermal Stress Profiles in Semi-transparent Particles under High-flux Irradiation. International Journal of Heat and Mass Transfer. 2007,50: 2117–2123
23 L. A. Dombrovsky and T. N. Dinh. The Effect of Thermal Radiation on the Solidification Dynamics of Metal Oxide Melt Droplets. Nuclear Engineering and Design. 2008,238:1421-1429
24 Z. X. Wu and Y. P. Wang. Scattering of Electromagnetic-Plane Waves by Radially Inhomogeneous Spheres: a Finely Stratified Sphere Model. Applied Optics. 1994, 69(1):55-59
25刘长松,刘永合,殷声.火焰喷涂合成TiC-Fe涂层的热力学分析.金属学报. 2000,6(1):62-63
26 L. H. Liu (刘林华), H. P. Tan (谈和平) and Q. Z. Yu (余其铮). Internal Distribution of Radiation Absorption in One-Dimensional Semitransparent Medium. Int. J. of Heat and Mass Transfer. 2002,45(2):417-424
27 L. H. Liu (刘林华), H. P. Tan (谈和平) and T. W. Tong. Internal Distribution of Radiation Absorption in a Semitransparent Spherical Particle. J. of Quant. Spectrosc. Radiative Transfer. 2002,72(6):747-756
28李亦军.单分散系微粒的Mie散射计算.应用光学. 2005,26(1):9-11
29张胤,贺友多,樊俊飞.任三兵金属喷射成形过程的数学模型.过程工程学报. 2008,8增刊(1):110-114
30王剑锋,杨超,毛在砂. Levelset方法数值模拟单液滴传质中的Marangoni效应.中国科学. 2008, 38(2):150-160
31孙慧娟,张海滨,白博峰.高温燃气中单个液滴的蒸发特性.西安交通大学学报. 2008,42:833-837
32丰松江,聂万胜,宋丰华,庄逢辰.固体火箭发动机尾焰红外辐射特性预估研究.固体火箭技术. 2009,32:183-187
33 L. B. Lucy.A Numerical Approach to the Testing of the Fission Hypothesis. The Astron[J]. 1977,8(12):1013-1024
34 R. A. Gingold and J. J. Monaghan. Smoothed Particle Hydrodynamics: Theory and Application to Non-spherical Stars [J]. Mnras . 1977:181-375
35 W. Benz and E. Asphaug. Impact Simulations with Fracture. I methods and Test, ICARUS. 1994, 107:98-116
36 J. J. Monaghan. Simulation Free Surface Flow with SPH. Journal of Computational Physics. 1994,110-339
37 J. J. Monaghan. Simulating Gravity Currents with SPH Lock Gates. Applied Mathematics Reports and Preprints, Monash University. 1995a
38 J. J. Monaghan. Heat Conduction with Discontinuous Conductivity. Applied Mathematics Reports and Preprints, Monash University. 1995b
39 P. W. Cleary. Modeling Confined Multi-material Heat and Mass Flows Using SPH. Applied Mathematical Modeling. 1998, 22:981-993
40 W. K. Liu, S. Jun and Y. F. Zhang. Reroducing Kernel Particle Methods. International Journal for Numerical Methods in Fluids. 1995a,20: 1081-1106
41 W. K. Liu, S. Jun, S. Li, J. Adee and T. Belytschko. Reproducing Kernel Particle Methods for Structural Dynamics. International Journal for Numerical Methods in Engineering. 1995b, 38:1655-1679
42 W. K. Liu, Y. Chen, C. T. Chang and T. Belytschko. Adbances in Multiple Scale Kernel Particle Methods, Computationa Mechanics. 1996a, 18(2):73-111.
43 W. K. Liu, Y. Chen, S. Jun, J. S. chen, T. Belyschko, C. Pan, R. A. Uras and C. T. Chang. Overvies and Applications of the Reproducing Kernel Particle Methods. Archives of Computational Methods in Engineering State of the Art, Reviews. 1996b,3:3-80
44 W. k. Liu, Y. Chen, R. A. Uras and C. T. Chang. Generalized Multiple Scale Reproducing KernelParticle Methods. Computer Methods in Applied Mechanics and Engineering. 1996c,139:91-157
45 Benedict. SPH for Naval Hydrodynamics[C]. Proc, 18th IWWWFB. Le Croisic. France 2003
46 M. Gomez-Gesteira. Green Water Overtopping Analyzed with a SPH Model[J]. Ocean Engineering. 2005,32:223-238
47 G. Oger. Two-dimensional SPH Simulation of Wedge Water Entries[J]. J Computational Physics. 2006, 213:803-822
48 S. Potapov, B. Maurel, A. Combescure and J. Fabis. Modeling Accidental-type Fluid–structure Interaction Problems with the SPH Method. Computers and Structures. 2009,87:721-734
49 M. Calamaz, J. Limido, M. Nouari, C. Espinosa, D. Coupard, M. Salaün, F. Girot and R. Chieragatti. Toward a Better Understanding of Tool Wear Effect Through a Comparison between Experiments and SPH Numerical Modelling of Machining Hard Materials. Int. Journal of Refractory Metals & Hard Materials. 2009,27:595-604
50贝新源,岳宗五.平滑粒子流体动力学(一种数值模拟方法)[A].高科技研究中的数值计算[C].国防科技大学出版社. 1995
51张锁春.光滑质点流体动力学(SPH)方法[J].计算物理. 1996,13(4):385–397
52毛益明,汤文辉.自由表面流动问题的SPH方法数值模拟.解放军理工大学学报(自然科学版). 2001,2(5):92-94
53邓嘉胤,杨健,王乐勤,杜红霞,王娜.光滑粒子动力学方法的固液二相流研究.浙江大学学报(工学版). 2007,41(5):853-858
54 S. Wong and Y. Shie. Galerkin Based Smoothed Particle Hydrodynamics. Computers and Structures. 2009,87:1111-1118
55郑兴,许国冬,段文洋.自由表面翻卷与破碎流动的SPH数值模拟.哈尔滨工程大学学报. 2010,31:301-306
56毛益明.光滑粒子流体动力学数值模拟方法研究.国防科学技术大学.硕士学位论文. 2000
57邓方钢.柱坐标系下光滑粒子流体动力学数值模拟.国防科学技术大学.硕士学位论文. 2002
58张姝慧,汪继文. SPH方法中初始时粒子配置的分析.计算机技术与发展. 2007,17(6): 36-38
59田瑜,傅学金,关正西.一维SPH的稳定性分析.力学与实践. 2008, 30(4):73-75
60郑兴,段文洋.光滑粒子流体动力学二阶算法精度研究.水科学进展. 2008,19(6):821-827
61郑俊,张嘉钟,于开平,魏英杰. SPH离散误差的线性形式及稳定性分析.四川大学学报(工程科学版). 2010,42(1):91-97
62 J. K. Chen, J. E. Beraun and T. C. Carney. A Corrective Smoothed Particle Method for BoundaryValue Problems in Heat Conduction. Compuer Methods in Applied Mechanics and Engineering. 1999a,46:231-252
63 J. K. Chen, J. E. Beraun and C. J. Jih. An Improvement for Tensile Instaability in Smoothed Particle Hydrodynamics. Computational Mechanics. 1999b,23:279-287
64 J. K. Chen, J. E. Beraun and C. J. Jih. Completeness of Corrective Smoothed Particle Method for Linear Elastodynamics. Computational Mechanics. 1999c,24:273-285
65 J. K. Chen and J. E. Beraun. A Generalized Smoothed Particle Hydrodynamics Method for Nonlinear Dynamic Problems. Computer Methods in Applied Mechanics and Engineering. 2000,190:225-239
66 G. R. Liu and M. B. Liu.光滑粒子流体动力学——一种无网格粒子法.韩旭,杨刚,强洪夫.湖南大学出版社. 2005:35-37
67杨世明,陶文铨.传热学(第四版).高等教育出版社. 2006,12
68叶宏,何汉峰等.利用焓法和有效热容法对定形相变材料熔解过程分析的比较研究.太阳能学报. 2004, 25(4):488-491
69 H. Yang and Y. Q. He. Solving Heat Transfer Problems with Phase Change Via Smoothed Effective Heat Capacity and Element-free Galerkin Methods. International Communications in Heat and Mass Transfer. 2010,37:385-392.
70王雁明,谈和平,帅永等.基于红外辐射特性的尾喷焰组分分析.中国工程热物理学会.编号:073337
71 J. Y. Li, S. K. Dong and H. P. Tan. Effective Optical Constant of Alumina Particle Containing Cafbon. AIAA J. of Thermophysics and Heat Transfer. 2009,23(1):216-219
72 J. C. Chai. A General-purpose Computer Program for Radiative Transfer(User Manual). 2002
73易红亮,何凯,谈和平.有限元求解二维介质内辐射-相变耦合传热. 2009年中国工程热物理学会传热传质学学术会议.