用户名: 密码: 验证码:
大型混流式水轮机水力稳定性研究
详细信息    本馆镜像全文|  推荐本文 |  |   获取CNKI官网全文
摘要
随着水电机组单机容量的提高,机组尺寸的逐步增大,比转速的不断提高,相对刚度的减弱,人们对于大型混流式水轮机的运行稳定性日益重视,同时,随着技术的高速发展,机组运行的自动化程度越来越高,无人值班、少人值守,远程控制的水电厂日益增多,对机组运行稳定性的要求亦日趋严格。另一方面,国内外许多大型混流式水轮发电机组相继出现振动问题,不仅影响了正常的生产运行,有的还危及到机组的安全,因此,水力稳定性已经引起电力及制造行业的普遍关注,也给行业内的专家学者提出了新的研究课题,本文的研究就是基于这样的背景下进行的。
     大型混流式水轮机水力稳定性有关的原因比较复杂,在电站的表现形式也多种多样,如尾水管低频压力脉动、卡门涡、叶道涡等,在这些水力原因中,尾水管涡带又是机组振动最主要的原因,其危害性也最大。而对水力稳定性的研究方法主要有模型试验研究、真机试验研究、CFD数值解析这三种。本文针对东江水电厂机组出现的振动问题,采用以上三种方法相结合的手段,对机组振动的原因进行了综合研究。
     水轮机模型试验是研究真机水力稳定性的重要手段。尽管现在已经具备对水轮机进行较准确的数值模拟及性能预测的手段及仿真技术,但是最终仍需进行模型试验来确定模型转轮的能量特性、汽蚀特性以及水力稳定性等。对于已运行的机组,通过模型试验可以模拟电厂的运行工况以研究真机运行的各种特性。通过对电厂的模型机组进行多方面试验研究的结果表明,转轮的能量特性较差;在小开度下,模型机组尾水管内存在较大的低频压力脉动;不同形状的泄水锥对模型机组尾水管的低频压力脉动有较大的影响;针对具体情况,采用不同的补气方法可减轻机组的振动。
     真机试验是研究真机水力稳定性的直接手段,模型试验固然重要,但也有其局限性,如真机与模型几何相似的假定条件就是相对的,加上水轮机过流部件内的流动极为复杂,各电站水轮机结构的设计也差别很大,由水轮机模型试验的振动特性很难预估真机的运行稳定性,使水轮机振动的真机试验研究为国内外专家所重视。通过大量的研究表明,水轮机振动有其共性,也有其个性。可见,通过模型试验并不能全面了解真机的所有性能,尤其是和机组振动密切相关的动态特性,因此,虽然相比模型试验来说,真机试验受到许多实际条件的限制,但是在研究具体电站的具体问题,特别是要了解机组的制造质量、安装质量等模型上没有的信息对机组运行稳定性的影响时,真机试验必不可少。本论文对电厂的真机做了多方面的试验研究,包括过流部件的实测;不同水头下的变负荷、变励磁试验研究;机组振动的频率特性分析;补气对真机稳定性的影响以及机组振动与大坝振动的之间的关系分析。试验的结果表明,东江水电厂机组的制造及安装质量存在较大的缺陷;机组在每个水头下均存在两个振动工况区,且随着水头的升高,振动工况区有向小出力偏移的趋势;在部分负荷时,尾水管中产生偏心涡,引起尾水管低频压力脉动;采用合适的补气方法及补气量,对于减轻东江水电厂机组的振动是有效的。
     与模型试验和真机试验相比,CFD数值解析在成本与周期、所获得的信息量等方面有着巨大的优势,因此,这一方法的应用也越来越普遍、深入,也使得人们对于大型混流式水轮机过流部件中主流内特性的了解日益加深。本文通过“部分耦合”的方法对真机在不同运行工况下的稳定场进行了数值解析,并全面的分析了各过流部件内的流动特性以及其能量特性。
     仅仅对机组的过流部件进行稳定场的CFD数值分析还不足以解决所有与水轮机水力稳定性有关的问题,因此在本论文的最后,采用雷诺应力湍流模型对真机尾水管在不同运行工况下进行了非稳定场的CFD数值解析,分析涡带的运动规律及其产生的低频压力脉动特性,并与真机的试验结果进行了比较,结果比较吻合。
Along with the increase of the unit installed capacity, the unit size, the specific speed and the weaken of the relative rigidity of hydraulic power unit, the operating stability of large-scale Francis turbine received much more attention increasingly. Meanwhile, the rapid development of technology makes the automaticity of unit operation more and more higher and appears a large amount of hydropower stations with nobody or a few on duty, remote control, so the requirement of the unit operating stability becomes strict increasingly. On the other hand, there come forth vibration problems in many large-scale Francis turbines at home and abroad, which influence the normal operation not only, some of them endanger the units but also, therefore, the hydraulic stability has brought more attention in trades of electricity and manufacturing, the new research field has been brought about to the professionals and scholars also. This paper’s research is based on the background.
     The concerned reasons about the hydraulic stability in large-scale hydropower unit are complicated and the phenomenon are varied, such as the low-frequency pressure pulsation in draft tube, the Karman vortex and the vortex between blades etc. In which of these, the draft tube vortex is the primary reason to bring about the unit vibration. The research methods of hydraulic stability are mainly model test, field test and CFD numerical simulation. Aiming at the vibration problem appeared in DongJiang hydropower unit, this paper comprehensively analyzed the reasons applying the combination of above three methods.
     The model test of hydraulic turbine is the very important way to study the prototype’s hydraulic stability. Although there can be provided the means and simulation technologies now to give the relatively accurate numerical simulation and the performance prediction of hydraulic turbines, finally the model test is required to determine the energy performance, cavitation performance as well as hydraulic stability of model runner. As to the units in use, it can research the prototype’s operating performance by means of model test to simulate the operating condition of units. The results of model test in many aspects indicate that the energy performance of the runner is relatively low; in small opening condition, there exist low-frequency pressure pulsation in draft tube; the draft cone with different configuration has great influence with the low-frequency pressure pulsation in draft tube; the application of different supplying air method can abate the vibration of the units.
     The field test is the direct way to research the prototype’s hydraulic stability. The model test is very important but with limitations, for example, the assumption condition of the geometric similarity between model and prototype is relatively, meanwhile, the flow in passing components of hydraulic turbine is very complicated, the structural design difference among the hydraulic turbines is great and it’s difficult to predict the prototype’s operating stability from the vibration performance of the model, all of those make the research of field test received more attention for professionals. Many results of research indicate that the characteristics of hydraulic units’vibration have not only commonness but also individuality. Obviously, it is impossible to reveal the prototype’s general performance by means of model test especially the transient performance related to the unit vibration. Thus, although the field test has many limitations comparing with model test, but it is necessary in order to research the specific problem especially to find out the influence to unit operating stability of the manufacturing and installation quality without in model test information. The paper carried out many field test research including the passing components measurement, the test of load variation and excitation variation with different head, the frequency characteristic analysis of unit vibration, the influence supplying air to prototype’s stability and the analysis of the relationship between unit vibration and dam vibration. The results indicate that there exist important objections in manufacturing and installation quality of DongJiang units, the units have two vibration region in different head, which has the tendency to offset to lower load with the increase of head, under part-load conditions, it brings about eccentric vortex in draft tube, which causes the low-frequency pressure pulsation, it is available to abate the vibration of DongJian units by means of suitable method and quantity of supplying air.
     The CFD numerical simulation has great advantageous in cost, periods and information content comparing with the model test and field test, so this method becomes more and more popular and ingoing, it also makes the main flow performance in large-scale Francis turbines clear increasingly. The paper numerically simulated the prototype’s stable flow field in different operating conditions by means of partly coupling method and generally analyzed the flow and energy performance in passing components.
     It is not enough to resolve all of the problems related to the hydraulic stability only to analyze the stable field in passing components. Finally, the paper numerically simulated the transient field in prototype’s draft tube under different operating conditions by means of Reynolds stress turbulence model and analyzed the law of motion of vortex rope as well as the performance of low-frequency pressure pulsation and compared with field test results.
引文
[1]徐建龙.开发水电资源实现持续发展.青海社会科学,1999(3):P52~54
    [2]黄艳. 21世纪初我国电力发展趋势及分析.海南大学学报自然科学版,2000,Vol.18(4):P346~352
    [3]刘东波,于雪梅,程玉双.论水电开发与可持续发展战略.黑龙江水利科技,2002(3):P15~16
    [4]李吉川.我国水电事业的发展概况.广西电力技术,2001(4):P61~63
    [5]沙锡林.中国水电设备发展的成就和展望.水力发电,1999(10):P57~60
    [6]汤献华,周厚贵,杨卫东.水电开发与可持续发展战略.水利水电科技进展,2000,Vol.20(3):P18~20
    [7]曹楚生.我国水利和水电可持续发展新的开发前景.中国水利,2000(9):P69~72
    [8]张超,陈武.关于我国2050年水电能源发展战略的思考.北京理工大学学报(社会科学版),2002,Vol.4(增刊):P63~66
    [9] R.Lafitte.世界水电发展展望.西北水电,1998(3):P61~63
    [10]陈宗梁.国外水电技术的发展.中国工程科学,2002,Vol.4(4):P86~92
    [11]何璟. 21世纪中国水电发展战略探讨.中国电力,2002,Vol.35(1):P13~17
    [12]陈尊理,陈建国,马文辉.我国水电已到最佳发展期.四川水力发电,2002,Vol.21(1):P1~5
    [13]陈济生.美国水力发展趋势联想.人民长江,1995,Vol.26(9):P80~83
    [14]华英,刘文.欧洲水电业的发展前景.水利水电快报,1999,Vol.20(1):P28~29
    [15]沃德·拜尔斯.世界目前水电开发概况.水利水电快报,1998,Vol.19(1):P19~22
    [16]李世东.水电比重大的电力系统建抽水蓄能电站的必要性.水力发电,2002(11):P5~8
    [17]覃大清,赵洪田,赵阳.关于混流式水轮机稳定性的几点新认识.大电机技术,1998(3):P43~50
    [18]潘罗平,高明.水轮机水力稳定性分析.长春工程学院学报(自然科学版),2002,Vol.3(4):P41~43
    [19]陶星明,刘光宁.关于混流式水轮机水力稳定性的几点建议.大电机技术,2002(2):P40~44
    [20] Richard.K.FISHER, Ulrich SELDEL, Gilbert Grosse et al. A case study in resonant hydroelastic vibration: The causes of Runner cracks and the solutions implemented for the XIAOLANGDI Hydroelectric Project. Proceedings of the 21nd IAHR Symposium, Lausanne, Switzerland, 2002
    [21] Dan T HUYNH. Vibration Characteristics of Hydro Plant Equipment. Proceedings of the 21nd IAHR Symposium, Lausanne, Switzerland, 2002
    [22] E.Egusquiza, A.Estevez, J.Cabrera, R.Vega. Vibration behavior in Hydro Power Plants. Field Data Analysis. Proceedings of the 20nd IAHR Symposium, Charlotte, United States, 2000
    [23] Skoták A, Mikulasek, J., Troubil, P. Unsteady flow in the draft tube with elbow. Part A–Experimental investigation. Proceedings of the 10th International Meeting of the Work Group on The Behavior on hydraulic machinery under steady oscillatory conditions, Trondheim, Norway, 2001
    [24]王珂仑.水力机组振动.(第1版),北京:水利电力出版社,1986. P36~151
    [25]郑建兴.浅析中小型水力机组运行稳定性.中国农村水利水电,2002(6):P56~58
    [26]沈东.水力机组故障分析. (第1版),北京:中国水利水电出版社,1996. P39~59
    [27] Thomas Vekve, Hermod Brekke, Per Egil Skare. Pressure Pulsation Measurements on a Prototype Francis Turbine. 20nd IAHR Symposium, Charlotte, United States, 2000
    [28]关于东江电厂水轮机振动研究总结报告.华中科技大学,1999.11
    [29]大东江水轮发电机组减振改造报告.湖南省东江水力发电厂. 1999.4
    [30]湖南省东江水电厂真机振动试验研究报告.湖南省电力试验研究所,1999.4
    [31]谭月灿,韦彩新,唐穗平等.改善柘溪电站混流式水轮机水力稳定性的研究.水力发电,1998(2):P47~51
    [32] Wang Zhengw, Qiu Hua, He Chenglian. Experimental Study on Pressure Surge in Draft Tube. Proceedings of the 21nd IAHR Symposium, Lausanne, Switzerland, 2002
    [33] Jorge ARPE, Francois AVELLAN. Pressure Wall Measurements in the Whole Draft Tube: Steady and Unsteady Analysis. Proceedings of the 21nd IAHR Symposium,Lausanne, Switzerland, 2002
    [34] Tenekes H, Lumley J L. A First Course in Turbulent. Cambridge, MIT Pree. 1973
    [35] Siebert Etter, John H. Gummer, U. Seidel. Measurements of the forces on the shaft of a model hydraulic turbine and their application to the prototype. Proceedings of the 20nd IAHR Symposium, Charlotte, United States, 2000
    [36] Monica Sanda lliescu, Gabriel Dan Ciocan. Experimental study of the runner blade to blade shear flow turbulent mixing in the cone of Francis turbine scale model. 22nd IAHR Symposium, Stockholm-Sweden, 2004
    [37] Conny Larson. Experimental investigation of the transient inlet flow field of a Francis turbine runner. 22nd IAHR Symposium, Stockholm-Sweden, 2004
    [38] Carvalho, I.S, Heitor. M.V. Visualization of vortex breakdown in turbulent unconfined jet flows, Journal Optical Diagnostics in Engineering, 1996, Vol.1 (2), P22~30
    [39] B.Rikard, L.Hakan, I.Karlsson, Report from Turbine 99-Workshop on draft tube flow. Proceedings of the 20nd IAHR Symposium, Charlotte, United States, 2000
    [40] Abdel-Ilah RHRICH, Morten KJEKDSEN, Hermod BREKKE. Frequency response measurements and theoretical analysis of the conduit/turbine system at Tonstad Power Plant (Norway). 21nd IAHR Symposium, Lausanne, Switzerland, 2002
    [41]韦彩新,韩凤琴,陈贞石.水轮机转轮不同泄水锥的特性研究.大电机技术,2001(1):P36~39
    [42]王贵.水轮机振动与稳定性及其试验技术的研究.博士学位论文,武汉:华中科技大学图书馆,2002
    [43]韩国明,张信志,刘保国.大型水轮发电机组振动稳定性分析与设计准则.中国机械工程,2002,Vol.13(8):P634~637
    [44] R.Schilling, S.Thum. Design Optimization of Hydraulic Machinery Blade by Multi Level CFD-Technique. Proceedings of the 22nd IAHR Symposium, Lausanne, Switzerland, 2002
    [45]朱云,郭维. CFD技术在水轮机设计及改造中的应用.陕西师范大学学报(自然科学版),2001(5):P45~48
    [46]章梓雄.粘性流体力学.北京:清华大学出版社,1996
    [47] Thompson J.F, Thames F.C, Mastin C.W. Automatic numerical generation of body fitted curvilinear coordinate system for field containing any number of arbitrary 2-D bodies. J Comput Phys, 1974, 15: P299~319
    [48] Thompson J.F, Warsi Z.U.A, marstin C.W. Numerical grid generation foundation and applications. New York: North-Holland, 1985: P95~140
    [49] Dener C., Hirsch CH. An interactive 3-D Surface Modelling and Grid Generation System. AIAA 92, 0073
    [50] Thompson J.F, Warsi E.U.A, Masrtin C.W. Numerical Grid Generation. Elsevier Science Publishing Co., 1985
    [51] Sorenson R. L., McCann K. A Method for Interactive Specification of Multiple Block Topologies. AIAA 91, 0147
    [52]刘超群.多重网格法及其在计算流体力学中的应用.北京:清华大学出版社,1995
    [53]梁在潮.工程湍流.武汉:华中理工大学出版社,1999
    [54] GAO G., Yong Y. Unilateral-Statistical-Average Based Analysis of Flat-Plate Turbulent Flow [C]. MCME’’99, Florida (USA), July 25, 1999
    [55] Yang Jianming, Liu Wenjun, Wu Yulin et al. Unsteady turbulent flow analysis through Three-Gorge draft tube by using LES. Proceedings of the 20nd IAHR Symposium, Charlotte, United States, 2000
    [56]曾实,A. Manners. 180°方形弯管中湍流流动的大涡模拟.清华大学学报(自然科学版),1999,Vol.39(4):P28~34
    [57]陈义良.湍流计算模型.合肥:中国科学技术大学出版社,1991
    [58]蔡树棠,刘宇陆.湍流理论.上海:上海交通大学出版社,1993
    [59]朱自强.应用计算流体力学.北京:北京航空航天大学出版社,1998
    [60]张兆顺.湍流北京:国防工业出版社,2002
    [61]刘导治.计算流体力学基础.北京:北京航空航天大学出版社,1989
    [62]高殿荣,吴晓明.工程流体力学.北京:机械工业出版社,1999
    [63] FLUENT Theory Documentation, Version 6.0, 2002
    [64] CFX-TASCFlow Theory Documentation, Version 2.10, 2000
    [65] STAR-CD Methodology Documentation, Version 3.10, 2000
    [66] CFX Help Documentation, Solver Modeling, Version 5.6
    [67]王晋军,符松.湍流研究最新进展—中国科学技术协会青年科学家论坛第41次活动文集.北京:科学出版社,1999
    [68] Kwank, P., Chang, J.L.C, Shanks, S.P. A three-dimensional incompressible Navier-Strokes flow solver using primitive variables. AIAA, 1986, vol.24, P390~396
    [69] Hughes, T.J.R, Liu, W.R, Brouks, A. A finite element analysis of incompressible viscous flow by penalty for mulation. J. Compt. Phys. 1979, vol.34, P1~60
    [70] Kwank, P., Chang, J.L.C, Shanks, S.P. A three-dimensional incompressible Navier-Strokes flow solver using primitive variables. AIAA, 1986, vol.24, P390~396
    [71] Jiang Y, Prekwas A J. Implicit pressure-based incompressible Navier-Stokes equations solver for unstructured meshes. AIAA, 1994, P94~103
    [72] Steger J L., Warming R.F. Flux vector splitting of the inviscid gasdynamic equations with application to finite difference methods. J Comp Phys, 1981, (40): P263~293
    [73] Versteeg H K, Malalasekera W. An Introduction to Computational Fluid Dynamics: The Finite Volume Method [M]. London: Longman Group Ltd, 1995
    [74]肖若富.中比转速混流式水轮机内流场数值模拟及性能改善研究.博士学位论文,武汉:华中科技大学,2004
    [75] Skotak A. Draft Tube Swirl Flow Modelling. 9th International Meeting of the IAHR WGl, Bron. 1999: Paper D-4
    [76] Nishi M,Wang X, Takahashi T.A. Short Note on the Rotating Frequency of the Vortex Rope in a Draft Tube. 7th International Meeting of the IAHR WG1, Ljubljana. 1995: Paper G-13
    [77] Rheingans, W.J, Power Swings in Hydroelectric Power Plants, ASME, Philadelphia, USA, 1904
    [78] Driaz, P., A Contribution to the Understanding of Flow in Draft Tube of Francis Turbine, IAHR Symposium. Nice, France, 1960
    [79] Kubota, T., Cavitation Characteristics of Force Core in the Flow of Francis Turbine,Fuji Electric Co., Review Vol.18, No3, 1972
    [80] Nlith, P., Contribution to Clarifying the Incepting of Non-stationary Flow Phenomenain the Draft tube of High Specific Speed Francis Turbines at Partly Load Operation. Voith, Heidenheim, Frg, 1973
    [81] Hosoi, Y., Contributions to Model Test of Draft Tube Surges of Francis Turbines, ISCE/IAHR/ASME joint Symposium, Forts Collins, USA, 1978
    [82] W.Shyy., EBaaten.. Three Dimensional analysis of the Flow in the Curved Hydraulic Turbine Draft tube. Int.J Num. Meth. in Fluid. 1986, (6): P861-882
    [83] T.C Vu., W Shyy., Viscous Flow Analysis for the hydraulic Turbine Draft tube. Proceedings of the 19th IAHR Symposium, Trondheim, Norway, 1998
    [84]朱斌.三维不可压缩粘性流动的一种数值计算方法及其在水轮机尾水管中的应用.博士学位论文,北京:清华大学,1992
    [85] X M Wang., M.Nish., H. Tsukamoto., A Simple model for Predicting the Draft tube Surge, Proceedings of the 17th IAHR Symposium, Beijing, China, 1994
    [86]倪浩清,沈永明.工程湍流流动、传热及传质的数值模拟.北京:中国水利水电出版社, 1996
    [87] Ales Skotak. Of the Helical Vortex in the Turbine Draft Tube Modeling. Proceedings of the 20th IAHR Symposium, Charlotte, United States, 2000
    [88] Albert RUPRECHT, Thomas HELMRICH, Thomas SCHERER. Simulation of Vortex Rope in a Turbine Draft Tube. Proceedings of the 22th IAHR Symposium, Lausanne, Switzerland, 2002
    [89] Mirjam SICK, Peter DOERFLER, Michael CASEY. CFD Simulation of the Draft Tube Vortex. Proceedings of the 22th IAHR Symposium, Lausanne, Switzerland, 2002
    [90] Skotak A. The New Possibilities for Draft Tube Performance Prediction, Modeling Testing and Monitoring for HPP III Conference, Aix-enProvence, France. 1998: P456~457
    [91] Shi Qinghua. Experimental Investigation of Frequency Characteristics if Draft Tube Pressure Pulsations for Francis Turbines. 18th IAHR Symposium, Beijing. 1994, Vol.2
    [92]秦云川.大朝山电站水轮机顶盖减压措施探讨.云南水力发电,2004(2):P84~82
    [93]王泉龙.浅谈水轮机振动的研究.大电机技术, 2000(7):P12~16
    [94]于波,刘忠贤.水轮机在高水头低负荷工况下振动问题的研究.水力发电学报,2001, Vol.72(1): P58~84
    [95]沈炜良,龙国平,宋咏春.大型水轮发电机组的减振研究.实用测试技术,2000(2):P8~11
    [96]费修渔.水轮机补气短管掉落故障的分析和出力.浙江电力,1998(4):P24~26
    [97]吴钢,张克危,戴勇峰,谭月灿.小流量工况尾水管补气对混流式水轮机出力的影响.水力发电,2000(12):P37~39
    [98]王海.水轮发电机组状态监测、诊断及综合试验分析系统研究.博士学位论文,华中科技大学图书馆,2001
    [99] G. Pedrizeti, G. Angellco. Model for Vortex Rope Dynamics in Francis Turbine Outlet. 18th IAHR Symposium, Netherlands. 1996: P915-923
    [100]韦彩新,谭月灿.主轴中心孔补气装置的研究.大电机技术,1998(2):P41~45
    [101]东江水电厂大坝动力特性测试报告.武汉水利电力大学,1998
    [102] Sebastian Muntean, Romeo Susan-Resiga, Sandor Bernod et al. 3D Turbulent flow analysis of the GAMM Francis turbine for variable discharge. Proceeding of the 22nd IAHR Symposium, Stockholm-Sweden, 2004
    [103]魏显著,刘毅杰,吴限明.混流式水轮机转轮内全三维粘性流动的数值解析.大电机技术,1999(4):P44~49
    [104]赵永智,韦彩新.葛州坝电站ZZ500转轮的CFD分析及翼型优化.四川水力发电,2003(12):P34~37
    [105]赵永智.万安电站5#水轮机转轮的CFD设计.硕士学位论文,武汉:华中科技大学,2003
    [106]韩凤琴,久保田·乔.混流式水轮机整体三维粘性解析-最高效率点的流动.大电机技术,2000(2):P56~60
    [107]周凌九.水轮机转轮流场计算及性能预测.博士学位论文,北京:中国农业大学,1999
    [108]刘宇,吴玉林,刘树红.混流式水轮机全流道三维定场湍流计算.中国工程热物理学会,2000(027029)
    [109]张梁,吴玉林,刘树红.混流式水轮机三维非定场湍流计算.中国工程热物理学会,2000(027024)
    [110]周凌九,王正伟等.水轮机转轮叶片几何参数及与能量性能的关系—三维粘性流场计算在水轮机中的应用.浙江水利水电专科学校学报. 2000(6):P36~39
    [111] Dragica Jo?t M.Sc., Leopold ?kerget. Separate and Coupled CFD Simulation of a Flow in a Francis Turbine. Proceedings of the 20th IAHR Symposium, Charlotte, United States, 2000
    [112] Nishi M., Wang X., Okamoto M., Matsunaga S. Further Investigations on the Pressure Fluctuation Caused by Cavitated Vortex Rope in an Elbow Draft Tube.ASME FED, 1994, Vol.190: P63-70
    [113]郑津生. 200米水头段水轮机尾水管的CFD研究.硕士学位论文,武汉:华中科技大学,2003
    [114]焦德勇,冯国泰.叶轮机械内部流场数值计算.哈尔滨工业大学出版社,1989
    [115] Joongcheol Paik, Fotis Sotiropoulos, Michael J.Sale. Numerical simulation of flow in a hydroturbine draft tube using unsteady statistical turbulence models. Proceeding of the 22nd IAHR Symposium, Stockholm-Sweden, 2004
    [116] Maryse Page, Enc Theroux, Jean-Yevs Trepanier. Unsteady rotor-stator analysis of a Francis turbine. Proceeding of the 22nd IAHR Symposium, Stockholm-Sweden, 2004
    [117]张大本,李吉川.混流式水轮机尾水管涡带引起的水力振动。广西电力技术,1996(4):P17~21
    [118]吴刚,韦彩新,张克危等.水轮机尾水管水压脉动与运行工况的关系.华中理工大学学报,1998,Vol.26(1):P88~91
    [119]林建忠.湍流的拟序结构.北京:机械工业出版社,1995
    [120] S. V. Patankar.传热与流体流动的数值计算.北京:科学出版社,1984
    [121] Spezaile C. G. On Nonlinear k ?εModel of Turbulent. Journal of Fluid Mechanics, Vol. 178, 1987, P459~475
    [122] Yakhot V., Orsxag S. A. On Nonlinear k ?εModel of Turbulent. International Journal of Heat Mass Transfer, Vol.15, 1972, P301~210
    [123]李连超,崔学明,常近时.湍流理论的发展及其在水轮机中的应用.

© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号

地址:北京市海淀区学院路29号 邮编:100083

电话:办公室:(+86 10)66554848;文献借阅、咨询服务、科技查新:66554700