离心泵内部三维复杂流场的数值研究
|
摘要
离心泵在国民经济各部门与日常生活中发挥着举足轻重的作用，本文以离心泵内部的三维流动为研究对象，应用适合于求解离心泵内部数值流动的有效算法，对离心泵内动静耦合的定常和非定常三维流动进行了详细的数值研究。主要完成以下几方面的工作：
本文详细介绍了基于MDT的离心泵过流部件三维实体造型的求解方法及处理技术，并利用MDT三维实体造型技术软件建立了离心泵内部过流部件进口管、叶轮、蜗壳和扩散管的三维实体。进一步采用多块网格技术，根据离心泵结构特点，把复杂的离心泵结构划分成几个简单的块，采用对复杂结构适应性强的非结构化网格对计算域进行离散，然后采用网格生成软件完成离心泵过流部件内部的网格生成，为数值计算打下基础。
采用Frozen-Rotor冻结转子模式和Rotor-Stator滑移界面模式系统开展了不同工况下离心泵内叶轮与蜗壳耦合的定常和非定常流动研究，结果表明由于叶轮与蜗壳的干扰蜗壳进口周向流动的不均匀性是非常强烈的，特别是叶轮与蜗舌间的相互干扰最为强烈，一直影响到叶轮进口和蜗壳扩散管出口的流场；在蜗壳内整个流动是以旋涡形式向出口推进的，并随着包角的变化旋涡表现出十分复杂的产生、发展和耗散的演化过程，导致蜗壳内较大的流动损失。
The centrifugal pump is playing a very important role in every department of national economy and daily life. In this paper the numerical investigation on three-dimensional steady and unsteady rotor-stator interaction flow fields in a centrifugal pump were performed. The following aspects were studied mainly.
The resolution methods and treatment technology of three-dimensional entity's modeling of the through-flow components of the centrifugal pump based on MDT were introduced in detail in this paper and the three-dimensional entity's modeling software based on MDT was utilized to create the three-dimensional entity of the through flow components of the pump include inlet tube, impeller, volute and diffuser.
According to the structure characteristic of the through-flow components of the centrifugal pump and adopting multi-block grids generating technique further, the complicated centrifugal pump structure topology was divided into several simple blocks, and then the grids generating was achieved in these blocks of the centrifugal pump by adopting a unstructured grid generating software which has a good and strong adaptability to the complicated geometry. It is available to carry out numerical simulation and fluid dynamic analysis further.
Based on Frozen-Rotor Approach and Rotor-Stator Approach, the numerical simulation was carried out in the centrifugal pump and the numerical results showed that the flow in the impeller and volute of centrifugal pump is periodically unsteady. Due to the interaction between impeller and volute the flow is characterized by pressure fluctuations and it is the strongest at impeller outlet and at the vicinity of the tongue. The unsteady pressure fluctuations are also one of the most important reasons to induce vibration and noise. Secondly, the flow field of the volute is characteristic of the vortex flow, and the vortex flow presents very complicated developing process which is creating, increasing and dissipating every now and then. All these lead to very large flow loss in the volute.
本文详细介绍了基于MDT的离心泵过流部件三维实体造型的求解方法及处理技术，并利用MDT三维实体造型技术软件建立了离心泵内部过流部件进口管、叶轮、蜗壳和扩散管的三维实体。进一步采用多块网格技术，根据离心泵结构特点，把复杂的离心泵结构划分成几个简单的块，采用对复杂结构适应性强的非结构化网格对计算域进行离散，然后采用网格生成软件完成离心泵过流部件内部的网格生成，为数值计算打下基础。
采用Frozen-Rotor冻结转子模式和Rotor-Stator滑移界面模式系统开展了不同工况下离心泵内叶轮与蜗壳耦合的定常和非定常流动研究，结果表明由于叶轮与蜗壳的干扰蜗壳进口周向流动的不均匀性是非常强烈的，特别是叶轮与蜗舌间的相互干扰最为强烈，一直影响到叶轮进口和蜗壳扩散管出口的流场；在蜗壳内整个流动是以旋涡形式向出口推进的，并随着包角的变化旋涡表现出十分复杂的产生、发展和耗散的演化过程，导致蜗壳内较大的流动损失。
The centrifugal pump is playing a very important role in every department of national economy and daily life. In this paper the numerical investigation on three-dimensional steady and unsteady rotor-stator interaction flow fields in a centrifugal pump were performed. The following aspects were studied mainly.
The resolution methods and treatment technology of three-dimensional entity's modeling of the through-flow components of the centrifugal pump based on MDT were introduced in detail in this paper and the three-dimensional entity's modeling software based on MDT was utilized to create the three-dimensional entity of the through flow components of the pump include inlet tube, impeller, volute and diffuser.
According to the structure characteristic of the through-flow components of the centrifugal pump and adopting multi-block grids generating technique further, the complicated centrifugal pump structure topology was divided into several simple blocks, and then the grids generating was achieved in these blocks of the centrifugal pump by adopting a unstructured grid generating software which has a good and strong adaptability to the complicated geometry. It is available to carry out numerical simulation and fluid dynamic analysis further.
Based on Frozen-Rotor Approach and Rotor-Stator Approach, the numerical simulation was carried out in the centrifugal pump and the numerical results showed that the flow in the impeller and volute of centrifugal pump is periodically unsteady. Due to the interaction between impeller and volute the flow is characterized by pressure fluctuations and it is the strongest at impeller outlet and at the vicinity of the tongue. The unsteady pressure fluctuations are also one of the most important reasons to induce vibration and noise. Secondly, the flow field of the volute is characteristic of the vortex flow, and the vortex flow presents very complicated developing process which is creating, increasing and dissipating every now and then. All these lead to very large flow loss in the volute.
引文
[1] 关醒凡．泵的理论与设计[M]．机械工业出版社，1986
[2] 孙寿．水泵汽蚀及其防治[M]．水利电力出版社，1987．
[3] 查森．叶片泵原理及水力设计[M]．机械工业出版社，1988．
[4] 陈振铭等译．苏尔寿离心泵手册[M]．上海科学技术文献出版社，1987．
[5] 袁寿其著．低比速离心泵理论与设计[M]．机械工业出版社，1997．
[6] 杨敦敏．离心泵内两相流流动特性的图像测量[D]．西安理工大学硕士学位论文，2004
[7] 渭南市东雷抽黄管理局．水泵防磨蚀综合治理措施的实验研究[R]．2001．5．20．
[8] 陆勇，王忠亮．黄河泥沙对水泵的影响和防磨措施[J]．山东建筑工程学院学报，2000，Vol．15，No．1：30-33．
[9] 李仁年等．含沙水流对离心泵能量特性的影响[J]．甘肃工业大学学报，1996，22(6)：27-31．
[10] 于长辉．多泥沙河流泵站选型设计若干问题的探讨[J]．山西水利科技，No．109，1995：74-76．
[11] 戴江．离心泵叶轮内固液两相紊流流动规律研究[J]．水力发电学报，1994(1)．
[12] 王春龙，薛建欣等．离心泵抽送含沙水时工作特性的试验研究[J]．甘肃工业大学学报，1994，20(4)：29-33．
[13] 陈次昌，刘正英，刘天宝，袁寿其．两相流泵的理论与设计[M]．北京：兵器工业出版社，1993．
[14] 林汝长等．水泵水轮机转轮内流动的分析[J]．水力发电学报，1982(1)．
[15] Borges J E. PH. Dissertation, Department of Engineering[M]. Cambridge University, 1986.
[16] Moore. J. and Moore. J. G. Calculation of Three-Dimensional Viscous Flow and Wake Development in a Centrifugal Impeller[J]. ASME J. of Engr. For Power, 1981, Vol.103.
[17] Tanabe.S., et al. A study on Internal Flow of a Centrifugal Runner[C]. Proc. of IAHR Symposium, 1986, No.49.
[18] Wu J C. Beijing: Proceeding of International Conference on Pump and Systems. 1992, 456～461
[19] 戴江．关于离心泵叶轮固液两相流的数值计算与实验研究[D]．清华大学博士学位论文，1993．
[20] 李海锋，吴玉林．利用三维紊流数值模拟进行离心叶轮设计比较[J]．流体机械，2001，29(9)：18-21．
[21] 胡寿根，蒋旭平，韩百顺．离心式水泵内部流场的面元法数值计算[J]．流体工程，1988(10)：20-23．
[22] 陈胜利，吴达人．离心泵叶轮内流场的计算[J]．水泵技术，1988，(2)：1-7．
[23] 朱世灿．离心式水泵叶轮三元流场计算[J]．流体工程，1998，(6)：29-31．
[24] 陈次昌，陈红勋，关醒凡．一种离心泵叶轮内部流动的方法[J]．流体工程，1990，(3)：20-26．
[25] 袁卫星，张克危，贾宗谟．离心泵射流—尾流模型的三元流动计算[J]．水泵技术，1990，(1)：12-18．
[26] Goede E. et al. Navier-Stokes Flow Analysis For a Pump Impeller[C]. Proc.of IAHR Symposium, 1992, pp513-523.
[27] 孙自祥．离心泵叶轮内部粘性／紊流流动分块隐式计算和实验量测研究[D]．清华大学博士学位论文，1994．
[28] 吴玉林，曹树良．离心泵叶轮中紊流的计算[J]．水泵技术，1997，(1)：9-11．
[29] 孙自强，吴玉林，薛敦松．离心泵叶轮内部紊流数值计算[J]．工程热物理学报，1996，17(7)．
[30] 李文广．离心泵叶轮内部三维紊流数值计算[J]．水泵技术，1997，(5)：20-29．
[31] 张楚华，刘正先，谷传纲，苗永淼．旋转离心叶轮内湍流的非结构化网格数值计算[J]．航空学报，1998，19(5)：556～559．
[32] 胡春波，姜培正，魏进家．离心泵叶轮内宾汉流体湍流流场的数值计算[J]．应用力学学报，1999，16(2)．
[33] 袁寿其，陈池，郑铭．无过载离心泵叶轮内三维不可压湍流场计算[J]．机械工程学报，2000，36(5)．
[34] 刘先正．曹淑珍．离心叶轮内三维湍流流场的数值计算与实验比较[J]．流体机械，2000，28(4)：9-12．
[35] A.Wahba and A.Tourlidakis. A genetic algorithm applied to the design of blade profiles for centrifugal pump impellers[C]. AIAA Computational Fluid Dynamics Conference, 15th, Anaheim, CA, June 11-14, 2001.
[36] 吴玉林，葛亮，陈乃祥．离心泵叶轮内部固液两相流动的大涡模拟[J]．清华大学学报(自然科学版)，2001，41(10)：93～96．
[37] 李文广．流体机械及工程国际学术会泵论文述评[J]．水泵技术，2001，(1)：3～8．
[38] 陈池，袁寿其，郑铭．低比速离心泵叶轮内三维不可压湍流场计算[J]．动力工程，2001，21(4)：1346～1378．
[39] Chung Ho Liu. Numerical solution of three-dimentional Navier-Stokes equations by a velocity vorticity method[J]. International Journal.for Numerical Methods in Fluid, 2001, 35: 533-557.
[40] Masamichi and Kazuhiro and Kazuyoshi and Takeshi. Numerical Analysis of Unstable Phenomena in A Centrifugal Pump[C]. Proceedings of the XXIst IAHR Symposium on Hydraulic Machinery and Systems, September 9-12, 2002.
[41] 陈池，袁寿其，金树德．离心泵叶轮内流计算方法综述．流体机械[J]．1999，Vol．27，No．2．
[42] 赵兴艳，苏莫明，张楚华，苗永淼．CFD方法在流体机械设计中的应用[J]．流体机械，2000，28(3)：22～25．
[43] 罗兴镝，廖伟丽，林汝长，陈乃祥．流体机械叶轮设计的研究与发展[J]．力学进展，1997，27(3)：372～388．
[44] 何有世，袁寿其，陈池．CFD进展及其在离心泵叶轮内部计算中的应用[J]．水泵技术，2002，(3)：23～26．
[45] 阎超．流体机械内部流动数值计算方法的新进展[J]．流体机械，1994，Vol．22，No．8
[46] Lakshminarayana B. An Assessment of Computational Fluid Dynamic Techniques in the Analysis and Design of Turbomachinery[J]. ASME J. Fluid Engng., Sept. 1991, 113: 315～352.
[47] Bradshaw, P. Effects of Streamline Curvature on Turbulent Flow, AGARDograph[R]. No. 169, 1973, A. D. Young (Ed.).
[48] Bradshaw, P. The Analogy between Streamline Curvature and buoyancy in Turbulent Shear Flow[J]. J Fluid Mech. Vol. 36, 1969.
[49] 周力行．多相湍流反应流流体力学[M]．国防工业出版社，2002．
[50] Durst, F., and Rastogi, A. K. Turbulent Flow over Two-Dimen-Sional Fences[M]. Turbulent Shear Flows,Vol.2, 1980, L. J. S. Bradburg, F. Durst, P. E. launder, f.w.schmidt and J. H. Whitelaw(Eds), Springer-Verlag, New York.
[51] Rodi, W. and Scheuerer, G Calculation of Curved Shear Layerswith Two-Equation Turbulence Models[J]. Physics Fluids, Vol.26,1983, Springer-verlag, New York
[52] Lilley, d. G Primitive Pressure-Velocity Code for the Computation of Strongly Swirling Flows[J]. AIAAJ.Vol.14,1976.
[53] Lilley,d. G. Prediction of Inert Turbulent Swirl Flows[J]. AIAA J.vol.11,1973.
[54] Leschziner, M. A. and Rodi, W. Calculation of Annular and Twin Parallel jets using various Discretization schemes and Turbulence-model Variationss[J]. J Fluids ENGR.,Vol.103,1981.
[55] Sloan, D. G., et al. Modelling Swirl in Turbulent Flow[J]. Prog. Energy and Combustion Science,Vol,12,1986.
[56] Lauder, B. E., et al. the UMIST/UCD Computations for the AFOSRHTTM-Stanford Conf. on Complex Turbulent Flows[R]. Rep.No. TFDfd/82/1.
[57] Rodi, W. Influence of Buoyancy and Rotation on Equation for the Turbulent Length Scale[C]. Proc. of 2 nd Symposium of Turbulent Shear Flows, Imperial College, London, 1979.
[58] Launder, B.E. Reece, G J., and Rodi, W. Progress in the Development of Reynolds Stress Turbulence Closure[J]. J. Fluid Mech., Vol.68,1975.
[59] Chorin, A. J. A Numerical Method for Solving Incompressible Flow Problem[J]. J. Comp. Phy. Vol. 2,1967.
[60] Arakawa, C. et al. Numerical Simulation of Francis Runner Using Pseudo compressibility[C]. 15th Symposium of the IAHR, Paper C1,1990.
[61] Jacoben, O., et al Three-Dimensional Turbulent Flow Simulation in Hydraulic Machinery[C], 15~(th) Symposium of the IAHR, Paper C, 1990.
[62] Stantal, O., and Avellan, f. Hydraulic Analysis of Flow Computation Results[C]. Proc. of 16~(th) Symposium of the IAHR, 1992.
[63] Kirtlry, K. R., and lakashminarayana, B. Computation of Three-Dimensional Turbulent Turbomachinery Flow Using a Coupled Parabolic-Marching Method[J]. ASME J. of turbomachinery, Vol. 110,1988.
[64] Chorin, A. J. Numerical Solution of the Navier-Stokes Equations[J]. Mathematics of Computation, Vol.22,1968.
[65] Shin, B. R., etal. An Efficient Implicit Finite-Difference Scheme for Incompressible Navier-Stokes Equations Using an Improved Factorization Scheme[C]. proc. of the 5th Inte. Symp. on Computation Fluid Dynamics (CFD), 1993, Vol. 3, Sendai.
[66] Rhie, C. M., and Choe, W. L. Numerical Study of the Turbulent Flow Past Airfoil with Trailing Edge Separation[J]. AIAA. J. Vol.21, No.11, 1983.
[67] Rhie, C. M., Pressure-Based Navier-Stokes Solver Using the Multigrid Method[J]. AIAA. J., 1989, Vol.27, No.8.
[68] Kaiki, K. C., and Patankar, S. V., Pressure-Based Calculation Procedure for Viscous Flows at All Speed in Arbitrary Configuration[C]. AIAA. J. Vol.27, No.9., 1989.
[69] Vank, S. P., and leaf, G. K., An Efficient Finite-Difference Calculation Procedure for Multi-Dimensional Fluid Flow[C]. AIAA-84-1242,1984
[70] Thompson J.F., Warsi Z.V.A. and Mastin C.W., Boundary-fitted coordinates systems for numerical solutions of partial differential equations-A Review[J]. Journal of Computational Physics, 1982, 47(1):101-108.
[71] Thompson J. F., Grid generation techniques in computational fluid dynamics[J]. AIAA J., 1994, 22(11): 1505-1514.
[72] Thomas P.D., Middlecoff J. F., Direct control of grid point distribution in meshes generated by elliptic equations[J]. AIAA J., 1980,18(4):652-656.
[73] 周天孝,白文,CFD多块网格生成新进展[J]. 力学进展, 1999, 29(3):344-368.
[74] Rebay S., Efficient unstructured mesh generation by means of Delaunay triangulation and Bowyer-Watson algorithm[J]. J. Computational Physics, 1993,106(1):125-138.
[75] Bowyer. A., Computing Dirichlet tessellations[J]. The Computer J., 1981,24(2): 162-166.
[76] Watson D.F., Computing the n-dimensional Delaunay tessellation with application to voronoi polytypes[J]. The Computer J., 1981,24(2): 167-172.
[77] Weatherdill N.P., Hassan O., Efficient three-dimensional Delaunay triangulation with automatic point creation and imposed boundary constraints[J]. Int. J. Numerical Methods Engineering, 1994, 37(12):2005-2039.
[78] Weatherdill N.P., A method for generating irregular computational grids in multiply connected planar domains[J]. Int. J. Numerical Methods Engineering, 1988, 8(2):181-197.
[79] Weatherdill N.P., Hassan O., Compressible flowfield solutions with unstructured grids generated by Delaunay triangulation[J]. AIAA Journal, 1995,33(7): 1196-1204.
[80] Anderson W.K., A grid generation and flow solution method for Euler equation on unstructured grids[J]. J. Computational Physics, 1994, 110(1):23-38.
[81] Subramanian G., Raveendra V.V.S., Gopolakrishna K., Robust boundary triangulation and Delannay triangulation of arbitrary planar domains[J]. Int. J. Numerical Methods Engineering, 1994, 37(10):1779-1789.
[82] Lohner R., Parikh P., Generation of three-dimensional unstructured grids by the Advancing-Front method[J]. Int. J. for Numerical Methods in Fluids, Vol.8,1988.
[83] Peraire J., Peiro J., Finite Element Euler computations in three dimensions[J]. Int. J. for Numerical Methods in Engineering, 1988,26(10):2135-2159.
[84] Pirzadeh S., structured background grids for generation of unstructured grids by Advancing-Front method[J]. AIAA Journal, 1993, 31(2):257-265.
[85] Pirzadeh S., Unstructured viscous grid generation by the advancing layers methods[J]. AIAA J. 1994, 32(8):1735-1737.
[86] George P.L., Serone E., The Advancing Front Mesh Generation Method Revisited[J]. Int J. Num Methods of Eng., 1994, 37(21):3605-3619.
[87] Pirzadeh S., Three-Dimensional Unstructured viscous grids by the advancing layers method[J]. AIAA J., 1996, 34(1):43-49.
[88] Mavriplis D J., An advancing front Delaunay triangulation algorithm designed for robustness[C]. AIAA paper 93-0671.
[89] 陶文铨．计算传热学的近代进展[M]，北京：科学出版社，2000，6．
[90] Sielari M.J., Guidice P.D., Hybrid finite volume approach to Euler solutions for supersonic flows[J]. J. AIAA, 1990, 28(1): 66-74.
[91] Weatherdill N.P., Mixed structured-unstructured meshes for aerodynamic flow simulation[J]. The Aeronautics J., 1990, 94: 111-123.
[92] Erdos JI,Alzner E. Computation of Unsteady Transonic Flows Through Rotating and Stationary Cascades[C]. 1977, NASA CR-2900
[93] Adamczyk J J. Model Equation for Simulating Flows in Multistage Turbomachinery[C]. ASME 85-GT-226, 1985.
[94] Rhie C M,etal. Developmentand Application of a Multistage Deterministic Stresses[C]. ASME95-GT-342,1995
[95] Rai M M. A Conservative Treatment of Zonal Boundaries for Euler Equation Calculations[J]. J. of Computational Physics, 1996, 62: 472-503
[96] 季路成，孟庆国，周盛．叶轮机通流计算的时间推进方法[J]．航空动力学报，1999，Vol．14，No．1
[97] 刘宝杰，邹正平等．叶轮机计算流体动力学技术现状与发展趋势[J]．航空学报，2002，Vol．23，No．5
[98] Riedelbauch, S., Klemm, D., Hauff, C. Importance of interaction between turbine components in flow field simulation[C]. 18th IAHR..Symposium Hydraulic Machinery and Cavitation, Valencia, 1996.
[99] Ruprecht, A., Heitele, M., Helmrich, T., Moser, W., Aschenbrenner, T. Numerical Simulation of a Complete Francis Turbine including unsteady rotor/stator interactions[C]. Proceedings of the 20th IAHR Symposium on Hydraulic Machinery and Systems, Charlotte, North Carolina, U.S.A. August, 2000
[100] Ruprecht, A., Heitele, M., Helmrich, T., Moser, W., Aschenbrenner, T. Numerical Simulation of a Complete Francis Turbine including unsteady rotor/stator interactions[C]. Proceedings of the 20th IAHR Symposium on Hydraulic Machinery and Systems, Charlotte, North Carolina, U.S.A. August, 2000
[101] Martin K., Florian M., et al. Numerical investigation of turbomachinery performance of a pump-turbine[C]. Proceedings of the 21st IAHR Symposium on Hydraulic Machinery and Systems, Lausanne, Switzerland, Sept. 2002
[102] Alex G., Jean-Louis, K., et al. Unsteady rotor-stator analysis of a hydraulic pump-turbine-CFD and experimental approach[C]. Proceedings of the 21st IAHR Symposium on Hydraulic Machinery and Systems, Lausanne, Switzerland, Sept. 2002
[103] M. Piller, E. Nobile, J. Thomas. DNS study of turbulent transport at low Prandtl numbers in a channel flow[J]. Journal of Fluid Mechanics, 2002(458): 419-441
[104] J.Cx Wissink. DNS "of separating low Reynolds number flow in a turbine cascade with incoming wakes[C]. International Journal of Heat and Fluid Flow, 2003, 24(4): 626-635.
[105] Launder, B. E. and Spalding, D. E. The Numerical Computation of Turbulent Flows[J]. Computer Methods in Applied Mechanics and Engineering, 1974, Vol.3: 269-289.
[106] 陶文铨．数值传热学(第二版)[M]．西安：西安交通大学出版社，2001，5．
[107] Menter, ER., Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications[J]. AIAA J., Vol.32, pp1598-1605, 1994
[108] Menter, F.R., Zonal Two Equation k-ω Turbulence Models for Aerodynamic Flows[R]. AIAA Paper 93-2906, 1993
[109] Rhie, C.M. and Chow, W.L., A numerical study of the turbulent flow past an isolated airfoil with trailing edge separation[C]. AIAA Paper 82-0998, 1982.
[110] Dawes W N. Toward improved throughflow capability: the use of three-dimensional viscous flow solvers in a multistage environment[J].ASME Journal Turbomachinery, 1992, 114(1): 8-17.
[111] 周天孝，白文，CFD多块网格生成新进展[J]．力学进展，1999年第3期．
[112] 党政，叶轮机械非等栅距动／静相干叶排内部非定常流动的数值分析[D]．西安交通大学博士学位论文，2000
[113] 刘胡瑶，仲梁维．基于MDT的参数化产品设计[J]．机械设计与制造工程，2000，29(6)：5-6．
[114] 董仁扬等．MDT基础、应用和技巧[M]．北京：机械工业出版社，2001．6．
[115] 王兆辉，李明宇．计算机辅助夹具编码系统设计[J]．机械制造，1997，(6)：34-35．
[116] 周善记，张胜文．基于MDT平台的参数化夹具设计系统的开发[J]．华东船舶工业学院学报，2004，18(2)：90-94．
[2] 孙寿．水泵汽蚀及其防治[M]．水利电力出版社，1987．
[3] 查森．叶片泵原理及水力设计[M]．机械工业出版社，1988．
[4] 陈振铭等译．苏尔寿离心泵手册[M]．上海科学技术文献出版社，1987．
[5] 袁寿其著．低比速离心泵理论与设计[M]．机械工业出版社，1997．
[6] 杨敦敏．离心泵内两相流流动特性的图像测量[D]．西安理工大学硕士学位论文，2004
[7] 渭南市东雷抽黄管理局．水泵防磨蚀综合治理措施的实验研究[R]．2001．5．20．
[8] 陆勇，王忠亮．黄河泥沙对水泵的影响和防磨措施[J]．山东建筑工程学院学报，2000，Vol．15，No．1：30-33．
[9] 李仁年等．含沙水流对离心泵能量特性的影响[J]．甘肃工业大学学报，1996，22(6)：27-31．
[10] 于长辉．多泥沙河流泵站选型设计若干问题的探讨[J]．山西水利科技，No．109，1995：74-76．
[11] 戴江．离心泵叶轮内固液两相紊流流动规律研究[J]．水力发电学报，1994(1)．
[12] 王春龙，薛建欣等．离心泵抽送含沙水时工作特性的试验研究[J]．甘肃工业大学学报，1994，20(4)：29-33．
[13] 陈次昌，刘正英，刘天宝，袁寿其．两相流泵的理论与设计[M]．北京：兵器工业出版社，1993．
[14] 林汝长等．水泵水轮机转轮内流动的分析[J]．水力发电学报，1982(1)．
[15] Borges J E. PH. Dissertation, Department of Engineering[M]. Cambridge University, 1986.
[16] Moore. J. and Moore. J. G. Calculation of Three-Dimensional Viscous Flow and Wake Development in a Centrifugal Impeller[J]. ASME J. of Engr. For Power, 1981, Vol.103.
[17] Tanabe.S., et al. A study on Internal Flow of a Centrifugal Runner[C]. Proc. of IAHR Symposium, 1986, No.49.
[18] Wu J C. Beijing: Proceeding of International Conference on Pump and Systems. 1992, 456～461
[19] 戴江．关于离心泵叶轮固液两相流的数值计算与实验研究[D]．清华大学博士学位论文，1993．
[20] 李海锋，吴玉林．利用三维紊流数值模拟进行离心叶轮设计比较[J]．流体机械，2001，29(9)：18-21．
[21] 胡寿根，蒋旭平，韩百顺．离心式水泵内部流场的面元法数值计算[J]．流体工程，1988(10)：20-23．
[22] 陈胜利，吴达人．离心泵叶轮内流场的计算[J]．水泵技术，1988，(2)：1-7．
[23] 朱世灿．离心式水泵叶轮三元流场计算[J]．流体工程，1998，(6)：29-31．
[24] 陈次昌，陈红勋，关醒凡．一种离心泵叶轮内部流动的方法[J]．流体工程，1990，(3)：20-26．
[25] 袁卫星，张克危，贾宗谟．离心泵射流—尾流模型的三元流动计算[J]．水泵技术，1990，(1)：12-18．
[26] Goede E. et al. Navier-Stokes Flow Analysis For a Pump Impeller[C]. Proc.of IAHR Symposium, 1992, pp513-523.
[27] 孙自祥．离心泵叶轮内部粘性／紊流流动分块隐式计算和实验量测研究[D]．清华大学博士学位论文，1994．
[28] 吴玉林，曹树良．离心泵叶轮中紊流的计算[J]．水泵技术，1997，(1)：9-11．
[29] 孙自强，吴玉林，薛敦松．离心泵叶轮内部紊流数值计算[J]．工程热物理学报，1996，17(7)．
[30] 李文广．离心泵叶轮内部三维紊流数值计算[J]．水泵技术，1997，(5)：20-29．
[31] 张楚华，刘正先，谷传纲，苗永淼．旋转离心叶轮内湍流的非结构化网格数值计算[J]．航空学报，1998，19(5)：556～559．
[32] 胡春波，姜培正，魏进家．离心泵叶轮内宾汉流体湍流流场的数值计算[J]．应用力学学报，1999，16(2)．
[33] 袁寿其，陈池，郑铭．无过载离心泵叶轮内三维不可压湍流场计算[J]．机械工程学报，2000，36(5)．
[34] 刘先正．曹淑珍．离心叶轮内三维湍流流场的数值计算与实验比较[J]．流体机械，2000，28(4)：9-12．
[35] A.Wahba and A.Tourlidakis. A genetic algorithm applied to the design of blade profiles for centrifugal pump impellers[C]. AIAA Computational Fluid Dynamics Conference, 15th, Anaheim, CA, June 11-14, 2001.
[36] 吴玉林，葛亮，陈乃祥．离心泵叶轮内部固液两相流动的大涡模拟[J]．清华大学学报(自然科学版)，2001，41(10)：93～96．
[37] 李文广．流体机械及工程国际学术会泵论文述评[J]．水泵技术，2001，(1)：3～8．
[38] 陈池，袁寿其，郑铭．低比速离心泵叶轮内三维不可压湍流场计算[J]．动力工程，2001，21(4)：1346～1378．
[39] Chung Ho Liu. Numerical solution of three-dimentional Navier-Stokes equations by a velocity vorticity method[J]. International Journal.for Numerical Methods in Fluid, 2001, 35: 533-557.
[40] Masamichi and Kazuhiro and Kazuyoshi and Takeshi. Numerical Analysis of Unstable Phenomena in A Centrifugal Pump[C]. Proceedings of the XXIst IAHR Symposium on Hydraulic Machinery and Systems, September 9-12, 2002.
[41] 陈池，袁寿其，金树德．离心泵叶轮内流计算方法综述．流体机械[J]．1999，Vol．27，No．2．
[42] 赵兴艳，苏莫明，张楚华，苗永淼．CFD方法在流体机械设计中的应用[J]．流体机械，2000，28(3)：22～25．
[43] 罗兴镝，廖伟丽，林汝长，陈乃祥．流体机械叶轮设计的研究与发展[J]．力学进展，1997，27(3)：372～388．
[44] 何有世，袁寿其，陈池．CFD进展及其在离心泵叶轮内部计算中的应用[J]．水泵技术，2002，(3)：23～26．
[45] 阎超．流体机械内部流动数值计算方法的新进展[J]．流体机械，1994，Vol．22，No．8
[46] Lakshminarayana B. An Assessment of Computational Fluid Dynamic Techniques in the Analysis and Design of Turbomachinery[J]. ASME J. Fluid Engng., Sept. 1991, 113: 315～352.
[47] Bradshaw, P. Effects of Streamline Curvature on Turbulent Flow, AGARDograph[R]. No. 169, 1973, A. D. Young (Ed.).
[48] Bradshaw, P. The Analogy between Streamline Curvature and buoyancy in Turbulent Shear Flow[J]. J Fluid Mech. Vol. 36, 1969.
[49] 周力行．多相湍流反应流流体力学[M]．国防工业出版社，2002．
[50] Durst, F., and Rastogi, A. K. Turbulent Flow over Two-Dimen-Sional Fences[M]. Turbulent Shear Flows,Vol.2, 1980, L. J. S. Bradburg, F. Durst, P. E. launder, f.w.schmidt and J. H. Whitelaw(Eds), Springer-Verlag, New York.
[51] Rodi, W. and Scheuerer, G Calculation of Curved Shear Layerswith Two-Equation Turbulence Models[J]. Physics Fluids, Vol.26,1983, Springer-verlag, New York
[52] Lilley, d. G Primitive Pressure-Velocity Code for the Computation of Strongly Swirling Flows[J]. AIAAJ.Vol.14,1976.
[53] Lilley,d. G. Prediction of Inert Turbulent Swirl Flows[J]. AIAA J.vol.11,1973.
[54] Leschziner, M. A. and Rodi, W. Calculation of Annular and Twin Parallel jets using various Discretization schemes and Turbulence-model Variationss[J]. J Fluids ENGR.,Vol.103,1981.
[55] Sloan, D. G., et al. Modelling Swirl in Turbulent Flow[J]. Prog. Energy and Combustion Science,Vol,12,1986.
[56] Lauder, B. E., et al. the UMIST/UCD Computations for the AFOSRHTTM-Stanford Conf. on Complex Turbulent Flows[R]. Rep.No. TFDfd/82/1.
[57] Rodi, W. Influence of Buoyancy and Rotation on Equation for the Turbulent Length Scale[C]. Proc. of 2 nd Symposium of Turbulent Shear Flows, Imperial College, London, 1979.
[58] Launder, B.E. Reece, G J., and Rodi, W. Progress in the Development of Reynolds Stress Turbulence Closure[J]. J. Fluid Mech., Vol.68,1975.
[59] Chorin, A. J. A Numerical Method for Solving Incompressible Flow Problem[J]. J. Comp. Phy. Vol. 2,1967.
[60] Arakawa, C. et al. Numerical Simulation of Francis Runner Using Pseudo compressibility[C]. 15th Symposium of the IAHR, Paper C1,1990.
[61] Jacoben, O., et al Three-Dimensional Turbulent Flow Simulation in Hydraulic Machinery[C], 15~(th) Symposium of the IAHR, Paper C, 1990.
[62] Stantal, O., and Avellan, f. Hydraulic Analysis of Flow Computation Results[C]. Proc. of 16~(th) Symposium of the IAHR, 1992.
[63] Kirtlry, K. R., and lakashminarayana, B. Computation of Three-Dimensional Turbulent Turbomachinery Flow Using a Coupled Parabolic-Marching Method[J]. ASME J. of turbomachinery, Vol. 110,1988.
[64] Chorin, A. J. Numerical Solution of the Navier-Stokes Equations[J]. Mathematics of Computation, Vol.22,1968.
[65] Shin, B. R., etal. An Efficient Implicit Finite-Difference Scheme for Incompressible Navier-Stokes Equations Using an Improved Factorization Scheme[C]. proc. of the 5th Inte. Symp. on Computation Fluid Dynamics (CFD), 1993, Vol. 3, Sendai.
[66] Rhie, C. M., and Choe, W. L. Numerical Study of the Turbulent Flow Past Airfoil with Trailing Edge Separation[J]. AIAA. J. Vol.21, No.11, 1983.
[67] Rhie, C. M., Pressure-Based Navier-Stokes Solver Using the Multigrid Method[J]. AIAA. J., 1989, Vol.27, No.8.
[68] Kaiki, K. C., and Patankar, S. V., Pressure-Based Calculation Procedure for Viscous Flows at All Speed in Arbitrary Configuration[C]. AIAA. J. Vol.27, No.9., 1989.
[69] Vank, S. P., and leaf, G. K., An Efficient Finite-Difference Calculation Procedure for Multi-Dimensional Fluid Flow[C]. AIAA-84-1242,1984
[70] Thompson J.F., Warsi Z.V.A. and Mastin C.W., Boundary-fitted coordinates systems for numerical solutions of partial differential equations-A Review[J]. Journal of Computational Physics, 1982, 47(1):101-108.
[71] Thompson J. F., Grid generation techniques in computational fluid dynamics[J]. AIAA J., 1994, 22(11): 1505-1514.
[72] Thomas P.D., Middlecoff J. F., Direct control of grid point distribution in meshes generated by elliptic equations[J]. AIAA J., 1980,18(4):652-656.
[73] 周天孝,白文,CFD多块网格生成新进展[J]. 力学进展, 1999, 29(3):344-368.
[74] Rebay S., Efficient unstructured mesh generation by means of Delaunay triangulation and Bowyer-Watson algorithm[J]. J. Computational Physics, 1993,106(1):125-138.
[75] Bowyer. A., Computing Dirichlet tessellations[J]. The Computer J., 1981,24(2): 162-166.
[76] Watson D.F., Computing the n-dimensional Delaunay tessellation with application to voronoi polytypes[J]. The Computer J., 1981,24(2): 167-172.
[77] Weatherdill N.P., Hassan O., Efficient three-dimensional Delaunay triangulation with automatic point creation and imposed boundary constraints[J]. Int. J. Numerical Methods Engineering, 1994, 37(12):2005-2039.
[78] Weatherdill N.P., A method for generating irregular computational grids in multiply connected planar domains[J]. Int. J. Numerical Methods Engineering, 1988, 8(2):181-197.
[79] Weatherdill N.P., Hassan O., Compressible flowfield solutions with unstructured grids generated by Delaunay triangulation[J]. AIAA Journal, 1995,33(7): 1196-1204.
[80] Anderson W.K., A grid generation and flow solution method for Euler equation on unstructured grids[J]. J. Computational Physics, 1994, 110(1):23-38.
[81] Subramanian G., Raveendra V.V.S., Gopolakrishna K., Robust boundary triangulation and Delannay triangulation of arbitrary planar domains[J]. Int. J. Numerical Methods Engineering, 1994, 37(10):1779-1789.
[82] Lohner R., Parikh P., Generation of three-dimensional unstructured grids by the Advancing-Front method[J]. Int. J. for Numerical Methods in Fluids, Vol.8,1988.
[83] Peraire J., Peiro J., Finite Element Euler computations in three dimensions[J]. Int. J. for Numerical Methods in Engineering, 1988,26(10):2135-2159.
[84] Pirzadeh S., structured background grids for generation of unstructured grids by Advancing-Front method[J]. AIAA Journal, 1993, 31(2):257-265.
[85] Pirzadeh S., Unstructured viscous grid generation by the advancing layers methods[J]. AIAA J. 1994, 32(8):1735-1737.
[86] George P.L., Serone E., The Advancing Front Mesh Generation Method Revisited[J]. Int J. Num Methods of Eng., 1994, 37(21):3605-3619.
[87] Pirzadeh S., Three-Dimensional Unstructured viscous grids by the advancing layers method[J]. AIAA J., 1996, 34(1):43-49.
[88] Mavriplis D J., An advancing front Delaunay triangulation algorithm designed for robustness[C]. AIAA paper 93-0671.
[89] 陶文铨．计算传热学的近代进展[M]，北京：科学出版社，2000，6．
[90] Sielari M.J., Guidice P.D., Hybrid finite volume approach to Euler solutions for supersonic flows[J]. J. AIAA, 1990, 28(1): 66-74.
[91] Weatherdill N.P., Mixed structured-unstructured meshes for aerodynamic flow simulation[J]. The Aeronautics J., 1990, 94: 111-123.
[92] Erdos JI,Alzner E. Computation of Unsteady Transonic Flows Through Rotating and Stationary Cascades[C]. 1977, NASA CR-2900
[93] Adamczyk J J. Model Equation for Simulating Flows in Multistage Turbomachinery[C]. ASME 85-GT-226, 1985.
[94] Rhie C M,etal. Developmentand Application of a Multistage Deterministic Stresses[C]. ASME95-GT-342,1995
[95] Rai M M. A Conservative Treatment of Zonal Boundaries for Euler Equation Calculations[J]. J. of Computational Physics, 1996, 62: 472-503
[96] 季路成，孟庆国，周盛．叶轮机通流计算的时间推进方法[J]．航空动力学报，1999，Vol．14，No．1
[97] 刘宝杰，邹正平等．叶轮机计算流体动力学技术现状与发展趋势[J]．航空学报，2002，Vol．23，No．5
[98] Riedelbauch, S., Klemm, D., Hauff, C. Importance of interaction between turbine components in flow field simulation[C]. 18th IAHR..Symposium Hydraulic Machinery and Cavitation, Valencia, 1996.
[99] Ruprecht, A., Heitele, M., Helmrich, T., Moser, W., Aschenbrenner, T. Numerical Simulation of a Complete Francis Turbine including unsteady rotor/stator interactions[C]. Proceedings of the 20th IAHR Symposium on Hydraulic Machinery and Systems, Charlotte, North Carolina, U.S.A. August, 2000
[100] Ruprecht, A., Heitele, M., Helmrich, T., Moser, W., Aschenbrenner, T. Numerical Simulation of a Complete Francis Turbine including unsteady rotor/stator interactions[C]. Proceedings of the 20th IAHR Symposium on Hydraulic Machinery and Systems, Charlotte, North Carolina, U.S.A. August, 2000
[101] Martin K., Florian M., et al. Numerical investigation of turbomachinery performance of a pump-turbine[C]. Proceedings of the 21st IAHR Symposium on Hydraulic Machinery and Systems, Lausanne, Switzerland, Sept. 2002
[102] Alex G., Jean-Louis, K., et al. Unsteady rotor-stator analysis of a hydraulic pump-turbine-CFD and experimental approach[C]. Proceedings of the 21st IAHR Symposium on Hydraulic Machinery and Systems, Lausanne, Switzerland, Sept. 2002
[103] M. Piller, E. Nobile, J. Thomas. DNS study of turbulent transport at low Prandtl numbers in a channel flow[J]. Journal of Fluid Mechanics, 2002(458): 419-441
[104] J.Cx Wissink. DNS "of separating low Reynolds number flow in a turbine cascade with incoming wakes[C]. International Journal of Heat and Fluid Flow, 2003, 24(4): 626-635.
[105] Launder, B. E. and Spalding, D. E. The Numerical Computation of Turbulent Flows[J]. Computer Methods in Applied Mechanics and Engineering, 1974, Vol.3: 269-289.
[106] 陶文铨．数值传热学(第二版)[M]．西安：西安交通大学出版社，2001，5．
[107] Menter, ER., Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications[J]. AIAA J., Vol.32, pp1598-1605, 1994
[108] Menter, F.R., Zonal Two Equation k-ω Turbulence Models for Aerodynamic Flows[R]. AIAA Paper 93-2906, 1993
[109] Rhie, C.M. and Chow, W.L., A numerical study of the turbulent flow past an isolated airfoil with trailing edge separation[C]. AIAA Paper 82-0998, 1982.
[110] Dawes W N. Toward improved throughflow capability: the use of three-dimensional viscous flow solvers in a multistage environment[J].ASME Journal Turbomachinery, 1992, 114(1): 8-17.
[111] 周天孝，白文，CFD多块网格生成新进展[J]．力学进展，1999年第3期．
[112] 党政，叶轮机械非等栅距动／静相干叶排内部非定常流动的数值分析[D]．西安交通大学博士学位论文，2000
[113] 刘胡瑶，仲梁维．基于MDT的参数化产品设计[J]．机械设计与制造工程，2000，29(6)：5-6．
[114] 董仁扬等．MDT基础、应用和技巧[M]．北京：机械工业出版社，2001．6．
[115] 王兆辉，李明宇．计算机辅助夹具编码系统设计[J]．机械制造，1997，(6)：34-35．
[116] 周善记，张胜文．基于MDT平台的参数化夹具设计系统的开发[J]．华东船舶工业学院学报，2004，18(2)：90-94．