磨料水射流结构特性与破岩机理研究
|
摘要
磨料水射流切割破碎技术在国民经济建设的诸多领域中都获得了广泛应用,但由于磨料水射流切割破碎物料的影响因素众多,目前磨料水射流的结构特性和破岩机理的物理机制尚不清晰,这在相当程度上限制了磨料水射流切割破碎技术的发展。本文运用多相流体动力学和颗粒动理学等理论,推导得出了磨料水射流的双流体模型,形成了分析磨料水射流结构特性和两相作用机理的数值方法,采用数值模拟和实验研究相结合的技术路线,较系统地研究了磨料水射流中两相速度分布和湍流参量分布,并运用连续介质力学、损伤力学和非线性冲击动力学等理论,建立了磨料水射流冲击破碎岩石的有限元模型,采用数值模拟的方法结合前人研究成果,较为系统地研究了磨料水射流破岩过程中的细观机理和不同宏观参量对冲蚀体积的影响,进一步发展和完善了磨料水射流冲击破岩理论。
综合分析表明,磨料颗粒所受的惯性力、重力、压差力和Stokes阻力对其运动具有重要影响。喷嘴内液固两相间存在速度滑移,磨料颗粒在相间力的作用下速度趋向液相速度。
非旋转和弱旋转磨料水射流中,液相轴向速度分布类似于高斯型,液相轴向速度仍然满足一定的自相似性。液相径向速度分量很小,沿半径分布规律十分复杂。射流轴对称面上液相湍流强度分布表现出一定的对称性,靠近射流边界处湍流强度较高,射流断面上沿径向方向湍流强度呈“M”形分布。弱旋转磨料水射流中,液相切向速度沿半径方向表现为Rankine复合涡形式。本文条件下,液相切向速度在喷距大于2d后,具有自相似性。磨料颗粒速度沿半径的变化趋势与流体微团的基本一致,沿半径方向呈高斯分布。随着喷距的增加,磨料颗粒速度逐渐降低,速度剖面逐渐平缓。
磨料水射流破岩过程中,岩石在冲击波压力、环向拉应力以及应力波反射拉应力等作用下经历了产生破碎、产生初始裂隙、裂隙贯穿等几个过程并最终形成冲蚀漏斗。在其他条件相同时,冲蚀体积随磨料颗粒速度的增大而非线性增加,随冲击角度的增大呈现非线性增加的趋势,随磨料颗粒粒径的增大也呈非线性增加。
本文采用数值模拟的方法对磨料水射流结构特性和破岩机理进行了较为系统的研究,模拟分析得到了实验结果和前人研究结果的验证和支持,表明本文所建立的磨料水射流结构特性和冲击破岩的理论体系合理可行,从而为研究磨料水射流流场结构和破岩机理提供了一条新途径。
Abrasive water jet technology has found its applications in many fields, for example, the petroleum engineering, the mining and the construction industry. The influencing factors and the complex mechanisms in the abrasive water jet have hindered its development. With the application of fluid dynamics, multiphase flow theory and particle kinematics theory, a two-fluid model was provided and the numerical method was formed. Systematic analysis was performed on the flow properties and the turbulence parameters distributions. Furthermore, a finite element model describing the rock-breaking process of abrasive water jet was provided with the help of finite element method, continuum mechanics and non-linear shock dynamics. The influences of different working parameters on the volume loss were also studied in this dissertation.
It is found that the inertia force, the gravity force, the pressure difference force and the Stokes force have vital influence on the movement of abrasive particles. It’s unsuitable to neglect the force exerted on the fluid phase by the abrasive particles. Velocity difference was observed when the abrasive water jet moves along in the nozzle. The particle’s velocity tends to approximate to the fluid velocity with the drag force acting on it, but the accelerating process is slower than the fluid phase. Fluid velocity distributions in fluid-particle flow on the axis line and nozzle exit are found similar to the single phase.
The axial velocity distributions of fluid phase in abrasive water jet (non-swirling and swirling) take on a Gaussian distribution. With the increase of standoff distance, the axial velocity decreases. The self-similarity characteristic of axial velocity is observed in the simulation. The radial velocity of the fluid phase is small in amplitude and shows complex distributions in the flow domain. Symmetrical characteristics of turbulence intensity are observed, high amplitude of turbulence intensity is found near the flow periphery and the turbulence intensity distributions in the radial direction take on an “M”shape. The tangential velocities of the fluid phase in the swirling abrasive water jet take on the Rankine vortex form. Under current condition, the self-similarity characteristic of the fluid tangential velocities is observed when the standoff distance is larger than 2d, where d is the diameter of the nozzle. The velocity distributions of particle phase are similar to the fluid phase and take on a Gaussian distribution in the radial direction. With the increase of standoff distance, the particle velocity decreases and the velocity profiles tend to be flat.
In the process of rock-breaking with abrasive water jet, fail, initial crack generation and crack propagation are obversed when the rock is hit by the shock wave pressure, the tensial stress in the radial direction and the reflecting tensile stress. Non-linear relations are found between the volume loss and the particle velocity, angle of attack and particle size.
It is the first time that the numerical simulation is applied to the systematic research on the flow property and rock-breaking mechanism of abrasive water jet. Numerical results are validated by the experimental data and former researchers’conclusions, which prove that the theoretical architecture built in this thesis is both reasonable and feasible.
综合分析表明,磨料颗粒所受的惯性力、重力、压差力和Stokes阻力对其运动具有重要影响。喷嘴内液固两相间存在速度滑移,磨料颗粒在相间力的作用下速度趋向液相速度。
非旋转和弱旋转磨料水射流中,液相轴向速度分布类似于高斯型,液相轴向速度仍然满足一定的自相似性。液相径向速度分量很小,沿半径分布规律十分复杂。射流轴对称面上液相湍流强度分布表现出一定的对称性,靠近射流边界处湍流强度较高,射流断面上沿径向方向湍流强度呈“M”形分布。弱旋转磨料水射流中,液相切向速度沿半径方向表现为Rankine复合涡形式。本文条件下,液相切向速度在喷距大于2d后,具有自相似性。磨料颗粒速度沿半径的变化趋势与流体微团的基本一致,沿半径方向呈高斯分布。随着喷距的增加,磨料颗粒速度逐渐降低,速度剖面逐渐平缓。
磨料水射流破岩过程中,岩石在冲击波压力、环向拉应力以及应力波反射拉应力等作用下经历了产生破碎、产生初始裂隙、裂隙贯穿等几个过程并最终形成冲蚀漏斗。在其他条件相同时,冲蚀体积随磨料颗粒速度的增大而非线性增加,随冲击角度的增大呈现非线性增加的趋势,随磨料颗粒粒径的增大也呈非线性增加。
本文采用数值模拟的方法对磨料水射流结构特性和破岩机理进行了较为系统的研究,模拟分析得到了实验结果和前人研究结果的验证和支持,表明本文所建立的磨料水射流结构特性和冲击破岩的理论体系合理可行,从而为研究磨料水射流流场结构和破岩机理提供了一条新途径。
Abrasive water jet technology has found its applications in many fields, for example, the petroleum engineering, the mining and the construction industry. The influencing factors and the complex mechanisms in the abrasive water jet have hindered its development. With the application of fluid dynamics, multiphase flow theory and particle kinematics theory, a two-fluid model was provided and the numerical method was formed. Systematic analysis was performed on the flow properties and the turbulence parameters distributions. Furthermore, a finite element model describing the rock-breaking process of abrasive water jet was provided with the help of finite element method, continuum mechanics and non-linear shock dynamics. The influences of different working parameters on the volume loss were also studied in this dissertation.
It is found that the inertia force, the gravity force, the pressure difference force and the Stokes force have vital influence on the movement of abrasive particles. It’s unsuitable to neglect the force exerted on the fluid phase by the abrasive particles. Velocity difference was observed when the abrasive water jet moves along in the nozzle. The particle’s velocity tends to approximate to the fluid velocity with the drag force acting on it, but the accelerating process is slower than the fluid phase. Fluid velocity distributions in fluid-particle flow on the axis line and nozzle exit are found similar to the single phase.
The axial velocity distributions of fluid phase in abrasive water jet (non-swirling and swirling) take on a Gaussian distribution. With the increase of standoff distance, the axial velocity decreases. The self-similarity characteristic of axial velocity is observed in the simulation. The radial velocity of the fluid phase is small in amplitude and shows complex distributions in the flow domain. Symmetrical characteristics of turbulence intensity are observed, high amplitude of turbulence intensity is found near the flow periphery and the turbulence intensity distributions in the radial direction take on an “M”shape. The tangential velocities of the fluid phase in the swirling abrasive water jet take on the Rankine vortex form. Under current condition, the self-similarity characteristic of the fluid tangential velocities is observed when the standoff distance is larger than 2d, where d is the diameter of the nozzle. The velocity distributions of particle phase are similar to the fluid phase and take on a Gaussian distribution in the radial direction. With the increase of standoff distance, the particle velocity decreases and the velocity profiles tend to be flat.
In the process of rock-breaking with abrasive water jet, fail, initial crack generation and crack propagation are obversed when the rock is hit by the shock wave pressure, the tensial stress in the radial direction and the reflecting tensile stress. Non-linear relations are found between the volume loss and the particle velocity, angle of attack and particle size.
It is the first time that the numerical simulation is applied to the systematic research on the flow property and rock-breaking mechanism of abrasive water jet. Numerical results are validated by the experimental data and former researchers’conclusions, which prove that the theoretical architecture built in this thesis is both reasonable and feasible.
引文
1 沈忠厚. 水射流理论与技术. 东营:石油大学出版社,1998: 205-333
2 孙家骏. 水射流切割技术. 北京:中国矿业大学出版社, 1992: 52-150
3 周卫东. 磨料射流切割套管的实验研究[硕士学位论文]. 石油大学(华东),东营:1999
4 董星. 前混合式磨料水射流磨料颗粒运动的理论分析. 黑龙江科技学院学报, 2001,11(3):4-6
5 Swanson R K, Kilman M, Cerwin S, et al. Study of particle velocities in water driven abrasive jet cutting. Proceedings of the 4th U.S. Water Jet Conference, the 4th U. S. Water Jet Conference, Berkeley, 1987. 103-107
6 Miller A L, Achibald J H. Measurement of particle velocities in an abrasive jet cutting system. Proceedings of the 6th American Water Jet Conference,the 6th American Water Jet Conference,Houston, 1991. 291-304
7 Himmelreich U. Fluiddynamische Untersuchungen an Wasserabrasivstrahlen [博士学位论文]. University of Hannover,Hannover: 1992
8 Chen W L, Geskin E S. Measurements of the velocity of abrasive waterjet by the use of laser transit anemometer. Jet Cutting Technology. London:Elsevier Science Publications, 1991: 23-36
9 Chen W L, Geskin E S. Correlation between particle velocity and conditions of abrasive water jet formation. Proceedings of the 6th American Water Jet Conference,the 6th American Water Jet Conference ,Houston,1991. 305-313
10 Neusen K F, Gores T J, Labus T J. Measurement of particle and drop velocities in a mixed abrasive waterjet using a forward-scatter LDV system. Jet Cutting Technology. Dordrecht: Kluwer Academic Publishing,1992: 63-74
11 王瑞和. 旋转水射流破岩钻孔技术研究[博士学位论文],石油大学(北京),北京:1995
12 Franz Durst. Fluid mechanics developments and advancements in the 20th Century. Proceedings of the 10th International Symposium on Applications of LaserTechniques to Fluid Mechanics,the 10th International Symposium on Applications of Laser Techniques to Fluid Mechanics,Lisbon, 2000: 25-37
13 Anand U, Katz J. Using porous lubricated nozzles to prevent nozzle wear in abrasive water suspension jets (AWSJ). Proceedings of 2001 WJTA American Waterjet Conference, 2001 WJTA American Waterjet Conference, Minneapolis, 2001: Paper13
14 Stevenson A N J, Hutchings I M. Scaling laws for particle velocity in the gas-blast erosion test. Wear, 1995, 181-183: 56-62
15 Liu H -T, Miles P J, Cooksey N, et al. Measurements of water-droplet and abrasive speeds in a ultrahigh-pressure abrasive-waterjets. Proceedings of the 10th American Waterjet Conference, the 10th American Waterjet Conference, Houston, 1999: Paper14
16 Momber A, Kovacevic R. Energy dissipative processes in high speed water-solid particle erosion. Proceedings of ASME Heat Transfer and Fluids Engineering Division, Annual Meeting of American Society of Mechanical Engineers, New York, 1995: 243-256
17 杨永印. 磨料浆体旋转射流结构特性及应用研究[博士学位论文]. 石油大学(华东),东营:2003
18 Hamatani G, Ramulu M. Machinability of high temperature composites by abrasive waterjet. ASME Journal of Engineering Materials and Technology, 1990, 112: 381-386
19 Kahlman L, Karlsson S, Carlsson R, et al. Wear and machining of engineering ceramics by abrasive waterjets. American Ceramics Society Bulletin, 1993, 72(8):93-98
20 Lichtarowicz A. Jet Cutting Technology. Dordrecht:Kluwer Academic Press,1992: 483-501
21 Momber A W, Eusch I, Kovacevic R. Cutting refractory ceramics with abrasive water jets—a preliminary investigation, Proceedings of the 8th American Water Jet Conference, the 8th American Water Jet Conference, Houston, 1995: 229-244
22 Hashish M. 磨料水射流切割的数学模型,高压水射流,1986,4:11-21
23 Blickwedel H. Erzeugung und Wirkung von Hochdruck-Abrasivstrahlen [博士学位论文]. Universiy of Hannov,Hannov: 1990
24 Arola D, Ramulu M. Mechanisms of material removal in abrasive waterjet machining of common aerospace materials. Proceedings of the 7th American Water Jet Conference, the 7th American Water Jet Conference, St. Louis, 1993: 43-64
25 Raju S P, Ramulu M. Predicting hydro-abrasive erosive wear during abrasive waterjet cutting. PED, 1994, 68(1): 381-396
26 Bitter J G A. A study of erosion phenomena. Wear, 1963, 6: 5-21
27 Finnie I. The mechanism of erosion of ductile metals. Proceedings of the 3rd U.S. National Congress of Applied Mechanics, the 3rd U.S. National Congress of Applied Mechanics, New York, 1958: 527-532
28 Hutchings I M. Mechanical and metallurgical aspects of the erosion of metals. Proceedings of Conference on Corrosion/Erosion of Coal Conversion System Materials,Conference on Corresion/Erosion of Coal Conversion System Materials, Houston, 1979: 393-428
29 Miller A L, Archibald J H. Measurement of particle velocities in an abrasive jet cutting system. Proceedings of the 6th American Water Jet Conference, the 6th American Water Jet Conference, Houston, 1991: 45-77
30 Hashish M. Turning with abrasive waterjets—a first investigation. Transactions of ASME,Journal of Engineering for Industry, 1987, 109: 281-290
31 Laurinat A, Louis H, Meier-Wiechert G. A model for milling with abrasive water jet. Proceedings of the 7th American Water Jet Conference, the 7th American Water Jet Conference, St Louis, 1993: 119-139
32 Blickwedel H, Guo N S, Louis H. Prediction of abrasive jet cutting performance and quality. Proceedings of the 10th International Symposium on Jet Cutting Technology, the 10th International Conference on Jet Cutting Technology, Amsterdam, 1990: 163-179
33 Chung Y, Geskin E S, Singh P. Prediction of the geometry of the kerf created in the course of abrasive waterjet machining of ductile materials. Jet Cutting Technology, Dordrecht: Kluwer Academic Press, 1992: 525-541
34 Kovacevic R. Monitoring the depth of abrasive waterjet penetration. International Journal of Machine Tools and Manufacturing, 1992, 32: 725-736
35 Kovacevic R, Mohan R, Hirscher J. Rehabilitation of concrete pavements assistedwith abrasive waterjets. Jet Cutting Technology, Dordrecht: Kluwer Academic Publishing, 1992: 425-442
36 Matsui S, Matsumura H, Ikemoto Y, etc. Prediction equations for depth of cut made by abrasive water jet. Proceedings of the 6th American Water Jet Conference,the 6th American Water Jet Conference, Houston, 1991: 78-93
37 周卫东,王瑞和,杨永印等. 前混式磨料水射流切割套管的深度计算模型. 石油大学学报(自然科学版),2001,25(2): 3-5
38 Momber A W. A generalized abrasive water jet cutting model. Proceedings of the 8th American Water Jet Conference, the 8th American Water Jet Conference, St. Louis, 1995: 359-376
39 杨清文,廖振方,秦文学. 前混和磨料射流切割的灰关联分析. 重庆大学学报(自然科学版),1996,19(2): 48-50
40 董星,马安昌,吴财芳等. 基于神经网络的前混和磨料射流切割深度的研究. 煤炭学报, 2002, 27(4): 430-433
41 Mazurkiewicz M. Study of a leading edge profile for a slot formed during hydo-abrasive cutting. Proceedings of the 6th American Water Jet Conference, the 6th American Water Jet Conference, St. Louis, 1991: 43-49
42 Corcoran M, Mazurkiewicz M, Karlic P. Computer simulation of an abrasive waterjet cutting process. Proceedings of the 9th International Symposium of Jet Cutting Technology, the 9th International Symposium of Jet Cutting Technology, Cranfield, 1988: 49-59
43 Yong Z, Kovacevic R. Simulation of chaotic particles motion in particle-laden jetflow and application to abrasive waterjet machining. ASME Journal of Fluid Engineering, 1997, 119: 435-442
44 Yong Z, Kovacevic R. Modeling of 3D abrasive waterjet machining, part I+II. Jetting Technology, London: Mechanical Engineers Publishing, 1996: 73-89
45 Babets K, Geskin E. Numerical study of the turbulent flow inside a pure waterjet. Proceedings of 2001 WJTA American Waterjet Conference, 2001 WJTA American Waterjet Conference, Minneapolis, 2001: Paper19
46 Ahmed D H, Siores E, Chen F L. Numerical simulation of abrasive water jet. Proceedings of 2001 WJTA American Waterjet Conference, 2001 WJTA AmericanWaterjet Conference, Minneapolis, 2001: Paper17
47高激飞,胡寿根,宁原林. 基于CFD的淹没磨料射流的数值模拟与流动特性研究. 中国机械工程, 2003, 14(14): 1188-1191
48 刘大有. 二相流体动力学. 北京:高等教育出版社,1993:16-528
49 岑可法,樊建人. 工程气固多相流动的理论与计算. 杭州:浙江大学出版社,1990:87-610
50 Tangren R F, Dodge C H, Seifert H S. Compressibility effects in two-phase flow. Journal of Applied Physics, 1949, 20: 637-645
51 周力行. 燃烧理论和化学流体力学. 北京:科学出版社,1986:88-254
52 Soo S L. Fluid dynamics of multiphase systems. Waltham:Blaisdell Publishing Company,1967:45-88
53 Drew D A, Segel L A. Averaged equations for two-phase flows. Studies in Applied Mathematics, 1971, 50(3): 133-166
54 Soo S L. Multiphase fluid dynamics [博士学位论文]. University of Illinois, Urbana: 1983
55 周力行. 有相变的颗粒群多相流体力学. 力学进展,1982,12(2):141-150
56 周力行. 欧拉坐标系中有相变的颗粒群多相流的多连续介质模型, 第二届全国多相流体力学、非牛顿流体力学和物理化学流体力学学术会议文集,第二届全国多相流体力学、非牛顿流体力学和物理化学流体力学学术会议,北京,1982:007 号稿件
57 Crowe C T, Sharma M P, Stock D E. The Particle-Source-in-CELL (PSI-CELL) for gas-droplet flows. Journal of Fluids Engineering, 1977, 99: 325-331
58 Smoot LD, Pratt DT. Pulverized coal combustion and gasification. New York: Plenum Press, 1979: 45-132
59 杨清文, 曲玉琨, 张雪华. 淹没和非淹没下前混合磨料射流切割混凝土.兵工学报,2002, 23(1): 120-122
60 张东速, 刘本立. 旋转锥形磨料射流钻孔性能的研究. 煤炭学报, 2001, 26(4): 409-413
61 王瑞和, 曹砚锋, 周卫东等. 磨料射流切割井下套管的模拟实验研究. 石油大学学报(自然科学版),2001, 25(6): 35-37
62 岳湘安. 液-固两相流基础. 北京:石油工业出版社,1996: 24-156
63 赵建福, 李炜. 变速运动颗粒所受非恒定作用力分析. 力学与实践,1998,20(3):43-44
64 张东速. 前混合磨料射流除锈技术的实验研究. 材料保护,1995,28(8):4-7
65 Rubinow S I, Keller J B. The transverse force on a spinning sphere moving in a viscous fluid. Journal of Fluid Mechanics, 1961, 11: 447-459
66 Lin C J, Peery J H, Schowalter W R. Simple shear flow round a rigid sphere: inertial effects and suspension rheology. Journal of Fluid Mechanics, 1970, 44: 1-17
67 施学贵,徐旭常,冯俊凯. 湍流气流中颗粒受力分析. 工程热物理学报,1989,10(3): 320-325
68 Patankar SV 著,张政译. 传热与流动的数值计算. 北京:科学出版社,1984:25-96
69 陶文铨. 数值传热学(第 2 版). 西安: 西安交通大学出版社, 2001: 28-187, 310-402
70 由常福, 祁海鹰, 徐旭常. 煤粉颗粒所受 Magnus 力的数值模拟. 2001,22(5):625-628
71 高德利. 21 世纪油气钻井技术展望. 石油化工动态,2000,8(2):31-34, 50
72 左新华. 油气科学钻井技术现状及发展方向综述. 段块油气田,1994,1(3): 39-44
73 Rizk M A, Elghobashi S E. A two-equation turbulence model for dispersed dilute confined two-phase flows. International Journal of Multiphase Flow, 1989, 15(1): 119-133
74 张东速, 贾北华, 刘本立. 前混合磨料射流液压支架清洗除锈系统. 煤矿机电,1995, 5: 21-23
75 Babets K, Geskin E. Numerical study of the turbulent flow inside a pure waterjet. Proceedings of 2001 WJTA American Waterjet Conference, 2001 WJTA American Waterjet Conference, Minneapolis, 2001: Paper 19
76 王建生. 磨料参数对准直磨料射流切割性能的影响. 水动力学研究与进展,2000,15(1):89-93
77 Crowe C T, Review-numerical models for dilute gas particle flows. Journal of Fluids Engineering, 1982, 104(3):297-303
78 岳湘安. 钻井液携屑的双流体模型. 石油学报,1996,17(1): 133-138
79 Ding J, Gidaspow D. A bubbling fluidlization model using kinetic theory of granular flow. AIChE Journal, 1990, 36(4): 523-538
80 Crowe C T, Sommerfeld M, Tsujinaka Y. Multiphase flow with droplets and particles. Boca Raton: CRC Press, 1998: 59-187
81 吴望一. 流体力学(上册). 北京:北京大学出版社,1982:161-171
82 Givler R C. An interpretation for the solid-phase pressure in slow, fluid-particle flows. International Journal of Multiphase Flow, 1987, 13(5): 717-722
83 Pritchett J W, Blake T R, Garg S K. A Numerical Model of Gas Fluidized Beds. AIChE Symposium Series, 1978, 176(74): 134-148
84 Gidaspow D, Ettahadieh B. Fluidization in two-dimensional beds with a jet. Industrial and Engineering Chemistry, Fundamentals, 1983, 22: 193-201
85 Massoudi M, Rajagopal K R, Ekmann J M, et al. Remarks on the modeling of fluidized systems, AIChE Journal, 1992, 38: 471-472
86 Syamlal M, O'Brien T J. Simulation of granular layer inversion in liquid fluidized beds. International Journal of Multiphase Flow, 1988, 14(4): 473-481
87 Johnson P C, Jackson R. Frictional-collisional constitutive relations for granular materials with application to plane shearing. Journal of Fluid Mechanics, 1987, 176: 67-93
88 Gidaspow D, Lu Huilin. Collisional viscosity of FCC particles in a CFB. AIChE Journal, 1996, 42 (9): 2503-2510
89 Chapman S, Cowling T G. The mathematical theory of non-uniform gases. 3rd Edition. Cambridge, England: Cambridge University Press, 1990: 86-147
90 Jenike A W. A theory of flow of particulate solids in converging and diverging channels based on a conical yield function. Powder Technology, 1987, 50: 229-236
91 Gray D D, Stiles J M. On the constitutive relation for frictional flow of granular materials, Topical Report DOE/MC/21353-2584, NTIS/DE88001089, Springfield,Virgnia: National Technical Information Service, 1988: 45-77
92 Schaeffer D G. Instability in the evolution equations describing incompressible granular flow. Journal of Differential Equations, 1987, 66(1): 19-50
93 Dalla Valle, Joseph Marius. Micromeritics, the technology of fine particles. New York: Pitman Publishing Corporation, 1948: 23-78
94 Savage S B, Jeffrey D J. The stress tensor in a granular flow at high shear rates. Journal of Fluid Mechanics, 1981, 110: 255-272
95 Lun C K K, Savage S B, Jeffrey D J, et al. Kinetic theory for granular flow: inelastic particles in Couette flow and slightly inelastic particles in a general flow field. Journal of Fluid Mechanics, 1984, 140: 223-256
96 Drew D A, Lahey R T. Application of general constitute principles to the derivation of multidimensional two-phase flow equations. Studies in Applied Mathematics, 1979, 58(3): 201-223
97 Kakac S, Mayinger F, Veziroglu T N. Two-phase Flow and Heat Transfer. Washington: Hemisphere Publishing Corporation, 1977: 125-248
98 Lumley J L. Modeling turbulent flux of passive scalar quantities in inhomogeneous flows. Physics of Fluid, 1975, 18(6): 619-621
99 Elghobashi S E, Abou-Arab T W. A two-equation turbulence model for two-phase flows. Physics of Fluid, 1983, 26(4): 931-938
100 曾卓雄. 密相可压气固两相湍流流动的理论分析及其数值模拟[博士学位论文]. 西安交通大学, 西安: 2001
101 Launder B E, Spalding D B. The numerical computation of turbulent flows. Computer Methods in Applied Mechanics and Engineering, 1974, 3(2): 269-289
102 Harlow F H, Nakayama P I. Turbulence transport equations. The Physics of Fluids, 1967, 10(11): 2323-2332
103 Taylor C, Morgan K. Computational techniques in transient and turbulent flows. Swansea: Pineridge Press, Limited, 1981: 1-35
104 Leonard B P, Mokhtari S. Beyond first-order upwinding: the ultra sharp alternative for non-oscillatory steady-state simulation of convection. International Journal for Numerical Methods in Engineering, 1990, 30: 729-766
105 Bram van Leer. Toward the ultimate conservative difference scheme. V:A second-order sequel to Godunov's method. Journal of Computational Physics, 1979, 32: 101-136
106 Taylor C, Morgan K. Recent advances in numerical methods in fluids. Swansea: Pineridge Press Limited, 1980: 144-345
107 Bolio E J, Yasuna J A, Sinclair J L. Dilute turbulent gas-solid flow in risers with particle-particle interactions. AIChE Journal, 1995, 41(6): 1375-1388
108 Tu J Y, Fletcher C A J. Numerical computation of turbulent gas-solid particle flow in a 90°bend. AIChE Journal, 1995, 41(10): 2187-2197
109 Sinclair J L, Jackson R. Gas-particle flow in a vertical pipe with particle-particle interaction. AIChE Journal, 1989, 35(9): 1473-1486
110 铁占绪. 磨料射流中磨料粒子的加速机理和运动规律. 焦作矿业学院学报, 1995, 14(4): 39-42
111 崔谟慎, 李春卉. 前混合式磨料射流喷嘴的基础研究. 中国安全科学学报, 1995, 5(5): 138-145
112 尤明庆. 前混合式磨料射流喷嘴内流动状况的理论研究. 流体机械, 1996, 24(12): 17-20
113 Albertson M L, Dai Y B, Jensen R A, et al. Diffusion of submerged jets. Transactions of American Society of Civil Engineers, 1950, 115: 639-664
114 董志勇. 射流力学. 北京: 科学出版社, 2005: 11-95
115 Choudhury D. Introduction to the Renormalization Group Method and turbulence modeling. Technical Memorandum, TM-107, Lebonon: Fluent Inc, 1993: 75-99
116 陶文铨. 数值传热学. 西安: 西安交通大学出版社, 1988: 78-177
117 Leonard B P. A stable and accurate convective modeling procedure based on quadratic upstream interpolation. Computer Methods in Applied Mechanics and Engineering, 1979, 19: 59-98
118 van Leer B. Upwind-difference methods for aerodynamics problems governed by the Euler equations. Lectures in Applied Mathematics, 1985, 22: 327-336
119 Hinze J O. Turbulence (2nd Edition). New York: McGraw-Hill Companies, 1975: 114-158
120 Farokhi S, Taghavi R, Rice E J. Effects of initial swirl distribution on the evolution of a turbulent jet. AIAA Journal, 1989, 27(6): 700-706
121 Rose W G. A swirling round turbulent jet. Journal of Applied Mechanics, 1962, 29: 615-625
122 Rubin A M, Ahrens T J. Dynamic tensile failure induced velocity deficits in rock. Geophysical Research Letters, 1991, 18(2): 219-222
123 Ahrens T J, Rubin A M. Impact-induced tensional failure in rock. Journal of Geophysical Research, 1993, 98(E1): 1185-1203
124 章本照. 流体力学中的有限元方法. 北京: 机械工业出版社, 1986: 29-77
125 马晓青, 韩峰. 高速碰撞动力学. 北京: 国防工业出版社, 1998: 124-247
126 杨军, 金乾坤, 黄风雷. 岩石爆破理论模型及数值计算. 北京: 科学出版社, 1999: 55-110
127 王爱俊,戴棣,乔新. 高速碰撞中 Lagrange 有限元方法及其应用. 南京航空航天大学学报, 1998, 30(6): 675-679
128 高文学, 刘运通. 爆炸荷载下岩石损伤机理及其力学特性研究. 岩土力学, 2003, 24(增刊): 585-588
129 高文学, 刘运通. 岩石动态损伤的数值模拟. 北京工业大学学报, 2000, 26(2): 5-10
130 高文学,刘运通. 脆性岩石冲击损伤模型研究. 岩石力学与工程学报, 2000, 19(2): 153-156
131 余寿文, 冯西桥. 损伤力学. 北京:清华大学出版社, 1997: 1-10
132 卢春生, 白以龙. 材料损伤断裂中的分形行为. 力学进展, 1990, 20(5): 468-477
133 凌建明. 压缩荷载下岩石细观损伤特征的研究. 同济大学学报, 1993, 21(2): 219-225
134 高文学. 岩石动态响应特性及损伤模型研究[博士学位论文]. 北京理工大学, 北京:1999
135 王介强, 宋守志. 岩石料层动态冲击粉碎的应变率效应. 东北大学学报(自然科学版), 1999, 20(6): 605-607
136 谢和平. 岩石混凝土损伤力学. 徐州: 中国矿业大学出版社, 1990: 29-57
137 黄筑平,杨黎明,潘客麟.材料的动态损伤和失效.力学进展,1993, 23(4): 433-460
138 Yelamanchall Chandra. Computational model of brittle erosion [硕士学位论文]. West Virginia University, Morgantown: 1997
139 Selvakumaresan Veluswamy. Computational model of erosion of oxide layers by impact [硕士学位论文]. West Virginia University, Morgantown: 1994
140 Hutchings I M. A model for the erosion of metals by spherical particles at normal incidence. Wear, 1981, 70(3): 269-281
2 孙家骏. 水射流切割技术. 北京:中国矿业大学出版社, 1992: 52-150
3 周卫东. 磨料射流切割套管的实验研究[硕士学位论文]. 石油大学(华东),东营:1999
4 董星. 前混合式磨料水射流磨料颗粒运动的理论分析. 黑龙江科技学院学报, 2001,11(3):4-6
5 Swanson R K, Kilman M, Cerwin S, et al. Study of particle velocities in water driven abrasive jet cutting. Proceedings of the 4th U.S. Water Jet Conference, the 4th U. S. Water Jet Conference, Berkeley, 1987. 103-107
6 Miller A L, Achibald J H. Measurement of particle velocities in an abrasive jet cutting system. Proceedings of the 6th American Water Jet Conference,the 6th American Water Jet Conference,Houston, 1991. 291-304
7 Himmelreich U. Fluiddynamische Untersuchungen an Wasserabrasivstrahlen [博士学位论文]. University of Hannover,Hannover: 1992
8 Chen W L, Geskin E S. Measurements of the velocity of abrasive waterjet by the use of laser transit anemometer. Jet Cutting Technology. London:Elsevier Science Publications, 1991: 23-36
9 Chen W L, Geskin E S. Correlation between particle velocity and conditions of abrasive water jet formation. Proceedings of the 6th American Water Jet Conference,the 6th American Water Jet Conference ,Houston,1991. 305-313
10 Neusen K F, Gores T J, Labus T J. Measurement of particle and drop velocities in a mixed abrasive waterjet using a forward-scatter LDV system. Jet Cutting Technology. Dordrecht: Kluwer Academic Publishing,1992: 63-74
11 王瑞和. 旋转水射流破岩钻孔技术研究[博士学位论文],石油大学(北京),北京:1995
12 Franz Durst. Fluid mechanics developments and advancements in the 20th Century. Proceedings of the 10th International Symposium on Applications of LaserTechniques to Fluid Mechanics,the 10th International Symposium on Applications of Laser Techniques to Fluid Mechanics,Lisbon, 2000: 25-37
13 Anand U, Katz J. Using porous lubricated nozzles to prevent nozzle wear in abrasive water suspension jets (AWSJ). Proceedings of 2001 WJTA American Waterjet Conference, 2001 WJTA American Waterjet Conference, Minneapolis, 2001: Paper13
14 Stevenson A N J, Hutchings I M. Scaling laws for particle velocity in the gas-blast erosion test. Wear, 1995, 181-183: 56-62
15 Liu H -T, Miles P J, Cooksey N, et al. Measurements of water-droplet and abrasive speeds in a ultrahigh-pressure abrasive-waterjets. Proceedings of the 10th American Waterjet Conference, the 10th American Waterjet Conference, Houston, 1999: Paper14
16 Momber A, Kovacevic R. Energy dissipative processes in high speed water-solid particle erosion. Proceedings of ASME Heat Transfer and Fluids Engineering Division, Annual Meeting of American Society of Mechanical Engineers, New York, 1995: 243-256
17 杨永印. 磨料浆体旋转射流结构特性及应用研究[博士学位论文]. 石油大学(华东),东营:2003
18 Hamatani G, Ramulu M. Machinability of high temperature composites by abrasive waterjet. ASME Journal of Engineering Materials and Technology, 1990, 112: 381-386
19 Kahlman L, Karlsson S, Carlsson R, et al. Wear and machining of engineering ceramics by abrasive waterjets. American Ceramics Society Bulletin, 1993, 72(8):93-98
20 Lichtarowicz A. Jet Cutting Technology. Dordrecht:Kluwer Academic Press,1992: 483-501
21 Momber A W, Eusch I, Kovacevic R. Cutting refractory ceramics with abrasive water jets—a preliminary investigation, Proceedings of the 8th American Water Jet Conference, the 8th American Water Jet Conference, Houston, 1995: 229-244
22 Hashish M. 磨料水射流切割的数学模型,高压水射流,1986,4:11-21
23 Blickwedel H. Erzeugung und Wirkung von Hochdruck-Abrasivstrahlen [博士学位论文]. Universiy of Hannov,Hannov: 1990
24 Arola D, Ramulu M. Mechanisms of material removal in abrasive waterjet machining of common aerospace materials. Proceedings of the 7th American Water Jet Conference, the 7th American Water Jet Conference, St. Louis, 1993: 43-64
25 Raju S P, Ramulu M. Predicting hydro-abrasive erosive wear during abrasive waterjet cutting. PED, 1994, 68(1): 381-396
26 Bitter J G A. A study of erosion phenomena. Wear, 1963, 6: 5-21
27 Finnie I. The mechanism of erosion of ductile metals. Proceedings of the 3rd U.S. National Congress of Applied Mechanics, the 3rd U.S. National Congress of Applied Mechanics, New York, 1958: 527-532
28 Hutchings I M. Mechanical and metallurgical aspects of the erosion of metals. Proceedings of Conference on Corrosion/Erosion of Coal Conversion System Materials,Conference on Corresion/Erosion of Coal Conversion System Materials, Houston, 1979: 393-428
29 Miller A L, Archibald J H. Measurement of particle velocities in an abrasive jet cutting system. Proceedings of the 6th American Water Jet Conference, the 6th American Water Jet Conference, Houston, 1991: 45-77
30 Hashish M. Turning with abrasive waterjets—a first investigation. Transactions of ASME,Journal of Engineering for Industry, 1987, 109: 281-290
31 Laurinat A, Louis H, Meier-Wiechert G. A model for milling with abrasive water jet. Proceedings of the 7th American Water Jet Conference, the 7th American Water Jet Conference, St Louis, 1993: 119-139
32 Blickwedel H, Guo N S, Louis H. Prediction of abrasive jet cutting performance and quality. Proceedings of the 10th International Symposium on Jet Cutting Technology, the 10th International Conference on Jet Cutting Technology, Amsterdam, 1990: 163-179
33 Chung Y, Geskin E S, Singh P. Prediction of the geometry of the kerf created in the course of abrasive waterjet machining of ductile materials. Jet Cutting Technology, Dordrecht: Kluwer Academic Press, 1992: 525-541
34 Kovacevic R. Monitoring the depth of abrasive waterjet penetration. International Journal of Machine Tools and Manufacturing, 1992, 32: 725-736
35 Kovacevic R, Mohan R, Hirscher J. Rehabilitation of concrete pavements assistedwith abrasive waterjets. Jet Cutting Technology, Dordrecht: Kluwer Academic Publishing, 1992: 425-442
36 Matsui S, Matsumura H, Ikemoto Y, etc. Prediction equations for depth of cut made by abrasive water jet. Proceedings of the 6th American Water Jet Conference,the 6th American Water Jet Conference, Houston, 1991: 78-93
37 周卫东,王瑞和,杨永印等. 前混式磨料水射流切割套管的深度计算模型. 石油大学学报(自然科学版),2001,25(2): 3-5
38 Momber A W. A generalized abrasive water jet cutting model. Proceedings of the 8th American Water Jet Conference, the 8th American Water Jet Conference, St. Louis, 1995: 359-376
39 杨清文,廖振方,秦文学. 前混和磨料射流切割的灰关联分析. 重庆大学学报(自然科学版),1996,19(2): 48-50
40 董星,马安昌,吴财芳等. 基于神经网络的前混和磨料射流切割深度的研究. 煤炭学报, 2002, 27(4): 430-433
41 Mazurkiewicz M. Study of a leading edge profile for a slot formed during hydo-abrasive cutting. Proceedings of the 6th American Water Jet Conference, the 6th American Water Jet Conference, St. Louis, 1991: 43-49
42 Corcoran M, Mazurkiewicz M, Karlic P. Computer simulation of an abrasive waterjet cutting process. Proceedings of the 9th International Symposium of Jet Cutting Technology, the 9th International Symposium of Jet Cutting Technology, Cranfield, 1988: 49-59
43 Yong Z, Kovacevic R. Simulation of chaotic particles motion in particle-laden jetflow and application to abrasive waterjet machining. ASME Journal of Fluid Engineering, 1997, 119: 435-442
44 Yong Z, Kovacevic R. Modeling of 3D abrasive waterjet machining, part I+II. Jetting Technology, London: Mechanical Engineers Publishing, 1996: 73-89
45 Babets K, Geskin E. Numerical study of the turbulent flow inside a pure waterjet. Proceedings of 2001 WJTA American Waterjet Conference, 2001 WJTA American Waterjet Conference, Minneapolis, 2001: Paper19
46 Ahmed D H, Siores E, Chen F L. Numerical simulation of abrasive water jet. Proceedings of 2001 WJTA American Waterjet Conference, 2001 WJTA AmericanWaterjet Conference, Minneapolis, 2001: Paper17
47高激飞,胡寿根,宁原林. 基于CFD的淹没磨料射流的数值模拟与流动特性研究. 中国机械工程, 2003, 14(14): 1188-1191
48 刘大有. 二相流体动力学. 北京:高等教育出版社,1993:16-528
49 岑可法,樊建人. 工程气固多相流动的理论与计算. 杭州:浙江大学出版社,1990:87-610
50 Tangren R F, Dodge C H, Seifert H S. Compressibility effects in two-phase flow. Journal of Applied Physics, 1949, 20: 637-645
51 周力行. 燃烧理论和化学流体力学. 北京:科学出版社,1986:88-254
52 Soo S L. Fluid dynamics of multiphase systems. Waltham:Blaisdell Publishing Company,1967:45-88
53 Drew D A, Segel L A. Averaged equations for two-phase flows. Studies in Applied Mathematics, 1971, 50(3): 133-166
54 Soo S L. Multiphase fluid dynamics [博士学位论文]. University of Illinois, Urbana: 1983
55 周力行. 有相变的颗粒群多相流体力学. 力学进展,1982,12(2):141-150
56 周力行. 欧拉坐标系中有相变的颗粒群多相流的多连续介质模型, 第二届全国多相流体力学、非牛顿流体力学和物理化学流体力学学术会议文集,第二届全国多相流体力学、非牛顿流体力学和物理化学流体力学学术会议,北京,1982:007 号稿件
57 Crowe C T, Sharma M P, Stock D E. The Particle-Source-in-CELL (PSI-CELL) for gas-droplet flows. Journal of Fluids Engineering, 1977, 99: 325-331
58 Smoot LD, Pratt DT. Pulverized coal combustion and gasification. New York: Plenum Press, 1979: 45-132
59 杨清文, 曲玉琨, 张雪华. 淹没和非淹没下前混合磨料射流切割混凝土.兵工学报,2002, 23(1): 120-122
60 张东速, 刘本立. 旋转锥形磨料射流钻孔性能的研究. 煤炭学报, 2001, 26(4): 409-413
61 王瑞和, 曹砚锋, 周卫东等. 磨料射流切割井下套管的模拟实验研究. 石油大学学报(自然科学版),2001, 25(6): 35-37
62 岳湘安. 液-固两相流基础. 北京:石油工业出版社,1996: 24-156
63 赵建福, 李炜. 变速运动颗粒所受非恒定作用力分析. 力学与实践,1998,20(3):43-44
64 张东速. 前混合磨料射流除锈技术的实验研究. 材料保护,1995,28(8):4-7
65 Rubinow S I, Keller J B. The transverse force on a spinning sphere moving in a viscous fluid. Journal of Fluid Mechanics, 1961, 11: 447-459
66 Lin C J, Peery J H, Schowalter W R. Simple shear flow round a rigid sphere: inertial effects and suspension rheology. Journal of Fluid Mechanics, 1970, 44: 1-17
67 施学贵,徐旭常,冯俊凯. 湍流气流中颗粒受力分析. 工程热物理学报,1989,10(3): 320-325
68 Patankar SV 著,张政译. 传热与流动的数值计算. 北京:科学出版社,1984:25-96
69 陶文铨. 数值传热学(第 2 版). 西安: 西安交通大学出版社, 2001: 28-187, 310-402
70 由常福, 祁海鹰, 徐旭常. 煤粉颗粒所受 Magnus 力的数值模拟. 2001,22(5):625-628
71 高德利. 21 世纪油气钻井技术展望. 石油化工动态,2000,8(2):31-34, 50
72 左新华. 油气科学钻井技术现状及发展方向综述. 段块油气田,1994,1(3): 39-44
73 Rizk M A, Elghobashi S E. A two-equation turbulence model for dispersed dilute confined two-phase flows. International Journal of Multiphase Flow, 1989, 15(1): 119-133
74 张东速, 贾北华, 刘本立. 前混合磨料射流液压支架清洗除锈系统. 煤矿机电,1995, 5: 21-23
75 Babets K, Geskin E. Numerical study of the turbulent flow inside a pure waterjet. Proceedings of 2001 WJTA American Waterjet Conference, 2001 WJTA American Waterjet Conference, Minneapolis, 2001: Paper 19
76 王建生. 磨料参数对准直磨料射流切割性能的影响. 水动力学研究与进展,2000,15(1):89-93
77 Crowe C T, Review-numerical models for dilute gas particle flows. Journal of Fluids Engineering, 1982, 104(3):297-303
78 岳湘安. 钻井液携屑的双流体模型. 石油学报,1996,17(1): 133-138
79 Ding J, Gidaspow D. A bubbling fluidlization model using kinetic theory of granular flow. AIChE Journal, 1990, 36(4): 523-538
80 Crowe C T, Sommerfeld M, Tsujinaka Y. Multiphase flow with droplets and particles. Boca Raton: CRC Press, 1998: 59-187
81 吴望一. 流体力学(上册). 北京:北京大学出版社,1982:161-171
82 Givler R C. An interpretation for the solid-phase pressure in slow, fluid-particle flows. International Journal of Multiphase Flow, 1987, 13(5): 717-722
83 Pritchett J W, Blake T R, Garg S K. A Numerical Model of Gas Fluidized Beds. AIChE Symposium Series, 1978, 176(74): 134-148
84 Gidaspow D, Ettahadieh B. Fluidization in two-dimensional beds with a jet. Industrial and Engineering Chemistry, Fundamentals, 1983, 22: 193-201
85 Massoudi M, Rajagopal K R, Ekmann J M, et al. Remarks on the modeling of fluidized systems, AIChE Journal, 1992, 38: 471-472
86 Syamlal M, O'Brien T J. Simulation of granular layer inversion in liquid fluidized beds. International Journal of Multiphase Flow, 1988, 14(4): 473-481
87 Johnson P C, Jackson R. Frictional-collisional constitutive relations for granular materials with application to plane shearing. Journal of Fluid Mechanics, 1987, 176: 67-93
88 Gidaspow D, Lu Huilin. Collisional viscosity of FCC particles in a CFB. AIChE Journal, 1996, 42 (9): 2503-2510
89 Chapman S, Cowling T G. The mathematical theory of non-uniform gases. 3rd Edition. Cambridge, England: Cambridge University Press, 1990: 86-147
90 Jenike A W. A theory of flow of particulate solids in converging and diverging channels based on a conical yield function. Powder Technology, 1987, 50: 229-236
91 Gray D D, Stiles J M. On the constitutive relation for frictional flow of granular materials, Topical Report DOE/MC/21353-2584, NTIS/DE88001089, Springfield,Virgnia: National Technical Information Service, 1988: 45-77
92 Schaeffer D G. Instability in the evolution equations describing incompressible granular flow. Journal of Differential Equations, 1987, 66(1): 19-50
93 Dalla Valle, Joseph Marius. Micromeritics, the technology of fine particles. New York: Pitman Publishing Corporation, 1948: 23-78
94 Savage S B, Jeffrey D J. The stress tensor in a granular flow at high shear rates. Journal of Fluid Mechanics, 1981, 110: 255-272
95 Lun C K K, Savage S B, Jeffrey D J, et al. Kinetic theory for granular flow: inelastic particles in Couette flow and slightly inelastic particles in a general flow field. Journal of Fluid Mechanics, 1984, 140: 223-256
96 Drew D A, Lahey R T. Application of general constitute principles to the derivation of multidimensional two-phase flow equations. Studies in Applied Mathematics, 1979, 58(3): 201-223
97 Kakac S, Mayinger F, Veziroglu T N. Two-phase Flow and Heat Transfer. Washington: Hemisphere Publishing Corporation, 1977: 125-248
98 Lumley J L. Modeling turbulent flux of passive scalar quantities in inhomogeneous flows. Physics of Fluid, 1975, 18(6): 619-621
99 Elghobashi S E, Abou-Arab T W. A two-equation turbulence model for two-phase flows. Physics of Fluid, 1983, 26(4): 931-938
100 曾卓雄. 密相可压气固两相湍流流动的理论分析及其数值模拟[博士学位论文]. 西安交通大学, 西安: 2001
101 Launder B E, Spalding D B. The numerical computation of turbulent flows. Computer Methods in Applied Mechanics and Engineering, 1974, 3(2): 269-289
102 Harlow F H, Nakayama P I. Turbulence transport equations. The Physics of Fluids, 1967, 10(11): 2323-2332
103 Taylor C, Morgan K. Computational techniques in transient and turbulent flows. Swansea: Pineridge Press, Limited, 1981: 1-35
104 Leonard B P, Mokhtari S. Beyond first-order upwinding: the ultra sharp alternative for non-oscillatory steady-state simulation of convection. International Journal for Numerical Methods in Engineering, 1990, 30: 729-766
105 Bram van Leer. Toward the ultimate conservative difference scheme. V:A second-order sequel to Godunov's method. Journal of Computational Physics, 1979, 32: 101-136
106 Taylor C, Morgan K. Recent advances in numerical methods in fluids. Swansea: Pineridge Press Limited, 1980: 144-345
107 Bolio E J, Yasuna J A, Sinclair J L. Dilute turbulent gas-solid flow in risers with particle-particle interactions. AIChE Journal, 1995, 41(6): 1375-1388
108 Tu J Y, Fletcher C A J. Numerical computation of turbulent gas-solid particle flow in a 90°bend. AIChE Journal, 1995, 41(10): 2187-2197
109 Sinclair J L, Jackson R. Gas-particle flow in a vertical pipe with particle-particle interaction. AIChE Journal, 1989, 35(9): 1473-1486
110 铁占绪. 磨料射流中磨料粒子的加速机理和运动规律. 焦作矿业学院学报, 1995, 14(4): 39-42
111 崔谟慎, 李春卉. 前混合式磨料射流喷嘴的基础研究. 中国安全科学学报, 1995, 5(5): 138-145
112 尤明庆. 前混合式磨料射流喷嘴内流动状况的理论研究. 流体机械, 1996, 24(12): 17-20
113 Albertson M L, Dai Y B, Jensen R A, et al. Diffusion of submerged jets. Transactions of American Society of Civil Engineers, 1950, 115: 639-664
114 董志勇. 射流力学. 北京: 科学出版社, 2005: 11-95
115 Choudhury D. Introduction to the Renormalization Group Method and turbulence modeling. Technical Memorandum, TM-107, Lebonon: Fluent Inc, 1993: 75-99
116 陶文铨. 数值传热学. 西安: 西安交通大学出版社, 1988: 78-177
117 Leonard B P. A stable and accurate convective modeling procedure based on quadratic upstream interpolation. Computer Methods in Applied Mechanics and Engineering, 1979, 19: 59-98
118 van Leer B. Upwind-difference methods for aerodynamics problems governed by the Euler equations. Lectures in Applied Mathematics, 1985, 22: 327-336
119 Hinze J O. Turbulence (2nd Edition). New York: McGraw-Hill Companies, 1975: 114-158
120 Farokhi S, Taghavi R, Rice E J. Effects of initial swirl distribution on the evolution of a turbulent jet. AIAA Journal, 1989, 27(6): 700-706
121 Rose W G. A swirling round turbulent jet. Journal of Applied Mechanics, 1962, 29: 615-625
122 Rubin A M, Ahrens T J. Dynamic tensile failure induced velocity deficits in rock. Geophysical Research Letters, 1991, 18(2): 219-222
123 Ahrens T J, Rubin A M. Impact-induced tensional failure in rock. Journal of Geophysical Research, 1993, 98(E1): 1185-1203
124 章本照. 流体力学中的有限元方法. 北京: 机械工业出版社, 1986: 29-77
125 马晓青, 韩峰. 高速碰撞动力学. 北京: 国防工业出版社, 1998: 124-247
126 杨军, 金乾坤, 黄风雷. 岩石爆破理论模型及数值计算. 北京: 科学出版社, 1999: 55-110
127 王爱俊,戴棣,乔新. 高速碰撞中 Lagrange 有限元方法及其应用. 南京航空航天大学学报, 1998, 30(6): 675-679
128 高文学, 刘运通. 爆炸荷载下岩石损伤机理及其力学特性研究. 岩土力学, 2003, 24(增刊): 585-588
129 高文学, 刘运通. 岩石动态损伤的数值模拟. 北京工业大学学报, 2000, 26(2): 5-10
130 高文学,刘运通. 脆性岩石冲击损伤模型研究. 岩石力学与工程学报, 2000, 19(2): 153-156
131 余寿文, 冯西桥. 损伤力学. 北京:清华大学出版社, 1997: 1-10
132 卢春生, 白以龙. 材料损伤断裂中的分形行为. 力学进展, 1990, 20(5): 468-477
133 凌建明. 压缩荷载下岩石细观损伤特征的研究. 同济大学学报, 1993, 21(2): 219-225
134 高文学. 岩石动态响应特性及损伤模型研究[博士学位论文]. 北京理工大学, 北京:1999
135 王介强, 宋守志. 岩石料层动态冲击粉碎的应变率效应. 东北大学学报(自然科学版), 1999, 20(6): 605-607
136 谢和平. 岩石混凝土损伤力学. 徐州: 中国矿业大学出版社, 1990: 29-57
137 黄筑平,杨黎明,潘客麟.材料的动态损伤和失效.力学进展,1993, 23(4): 433-460
138 Yelamanchall Chandra. Computational model of brittle erosion [硕士学位论文]. West Virginia University, Morgantown: 1997
139 Selvakumaresan Veluswamy. Computational model of erosion of oxide layers by impact [硕士学位论文]. West Virginia University, Morgantown: 1994
140 Hutchings I M. A model for the erosion of metals by spherical particles at normal incidence. Wear, 1981, 70(3): 269-281