摘要
研究流体激励诱发离心泵基座的振动,对进一步减小基座振动传递至其他设备引起的设备故障与传递至板壳结构引起的辐射噪声有重要意义。本文的目的在于从泵内表面-蜗壳-支架-基座与叶轮-转轴-支撑-基座两条流体激励力传递途径分别研究流体激励所诱发垂直于离心泵基座方向的振动,并分析离心泵基座振动的混沌非线性特性。
运用Pro-E与ICEM建立离心泵流域的几何模型与网格,基于计算流体力学运用CFX分析了离心泵的稳态流场与瞬态流场,并积分得出空间三个方向泵内表面所受流体合力与叶轮所受流体合力与合力矩,运用分段拟合的方法建立了泵内表面流体合力数学模型,运用统计方法分析了叶轮各表面对叶轮所受流体合力与合力矩的贡献,通过流域内压力脉动值与转轴振动位移的测试证明了分析结果的准确性。
根据试验台架,建立包括蜗壳、电机模型、电机、支架与离心泵基座系统的FEM模型,通过对比模态分析结果与LMS模态测试验证FEM模型的正确性,基于流场计算所得瞬态流场各时间步泵内表面流体压力,分析了流体激励泵内表面-蜗壳-支架-基座所诱发的瞬态响应。
基于达朗伯原理建立了包含有离心泵基座的四圆盘三轴段、垂直于基座方向的转子动力学模型;基于配重法运用光电传感器、电涡流位移传感器与所构建的LabVIEW刚度辨识虚拟仪器测试了转子支撑的刚度,并分析了叶轮内流体质量对转子系统固有频率与振型的影响;基于Newmark算法运用Matlab分析了流场计算所得叶轮径向流体激励作用下转子系统的瞬态响应,并分析了转子动力学中将流体力简化为圆盘附加质量建模方法的准确性;通过仅电机转动与电机离心泵共同转动的实验对比分析了所设计台架中电机与离心泵对基座振动的贡献量;对比分析了流体力两个途径激励离心泵基座诱发的振动,并与实验结果做了对比。
从统计理论出发,提出三种方法修正两个一维数组所构成平面上,数据对所对应点在该平面上的概率分布矩阵,从而改进Cellucci的互信息算法,并由该改进算法计算了Lorenz序列的最佳延迟时间,而后得出最大Lyapunov指数验证了改进算法的有效性。
运用改进的互信息算法与Tisean3.0伪最近邻点算法工具包对四个测试点所得离心基座振动位移进行了延迟时间与嵌入维数的分析,并依据该延迟时间与嵌入维数重构了相空间,运用Tisean3.0小数据量算法工具包分析了各振动位移时间序列的最大Lyapunov指数以判断系统混沌非线性特性。
通过以上研究得出了以下主要结论:
1)运用CFD计算可以有效地得出离心泵所受流体力与力矩;叶轮径向流体合力主要以叶轮转动频率,而非叶片通过频率进行波动,蜗壳所受流体空间三个方向合力、叶轮所受其它方向流体力与绕三个方向的合力矩均主要以叶片通过频率进行波动;运用分段拟合的方法所得到蜗壳流体力数学模型比单段拟合与正余弦函数逼近有更好的精度;叶片所受流体径向合力是叶轮所受径向流体力的主要来源,叶轮前盖板外表面与后盖板外表面之间的压力差决定叶轮所受轴向力的大小,前盖板流体压力分布的不均匀程度决定叶轮绕径向转矩的大小,运用离心泵转轴振动位移与叶轮径向流体力的对比可以验证流场计算的正确性。
2)建立的蜗壳、电机模型、电机与基座系统FEM模型是可靠的;流体激励泵内表面-蜗壳-支架诱发垂直于基座方向振动的位移幅值与加速度幅值均较小;离心泵起动阶段所产生初始压力脉动在非稳态振动阶段对基座振动有较大影响;泵内表面局部压力脉动是宽频激振源,会诱发出离心泵系统的各阶模态振动。
3)所建立的转子动力学模型是正确有效的;所提出支撑刚度不拆卸测试方法是有效可行的;建立的支撑刚度辨识虚拟仪器系统能够可靠地得出转子支撑刚度;叶轮内流体质量对转子系统的中频固有频率有一定影响,而对系统低频与高频固有频率与各阶振型影响较小;流体力激励叶轮-转轴-基座所诱发的基座振动主要频率为转子的基频;正弦外激励作用下,将流体力简化为叶轮内20%与40%水质量所得基座振动均远小于将流体激励力直接作用于系统所引起的基座振动;流体激励力是诱发离心泵基座振动的主要原因;流体力激励泵内表面-蜗壳-支架-基座所引起的基座振动远小于激励叶轮-转轴-支撑-基座所引起的基座振动;流体激励诱发离心泵基座振动的主要来源是流体激励转子系统所诱发的基座振动;流体激励作用下离心泵基座振动位移的最大峰值频率为转轴转动频率,而振动加速度的最大峰值频率为五倍转动频率;从流体激励力的两条传递途径分别研究其所诱发基座振动的方法是有效可行的。
4)等间距划分时间序列所构成平面会得到错误的互信息值;当时间序列长度不为边缘划分区间个数整数倍时,Cellucci算法将会得到错误的最佳延迟时间;所提出的三种互信息改进算法不仅能够消除Cellucci算法的缺陷,并且计算速度快;并且使用较长序列计算互信息时所得结果更加稳定;三种互信息改进计算方法是有效可靠的;流体激励诱发的离心泵基座振动位移信号具有明显的吸引子存在;各振动位移的最大Lyapunov指数均略大于零,因此本文所研究离心泵系统的基座振动具有混沌特性存在。
Researches on vibration of centrifugal pump base by fluid inciting are significant for reducing equipment faults, which are caused by the vibration transferring from the base, and noise emission of shells which connect with the base. The aims of this dissertation is to investigate the fluid inciting centrifugal-pump-base vibration which is vertical to the base from two different routes, including the route that fluid force transferring to pump base via interior surfaces of pump, volute and brackets as well as that via impeller, rotor and supports, and detect chaos of the base vibration.
To analyses fluid field in centrifugal pump by CFX based on CFD theory, geometry models and mesh of fluid field are built by Pro-E and ICEM respectively. Then three-dimension gross fluid forces on pump interior surfaces and impeller as well as three-dimension gross fluid torques on impeller are integrated by stable and transient CFD results. Also, multi-section curve fitting of gross pump interior fluid forces as well as analysis on the contributions of fluid forces and torques on each surface of impellers to the gross are done. And measurements on pressures of different locations in pump and vibration displacements of shaft on two vertical directions are mad use of affirming the correctness of simulation results.
Base on test bench designed, a FEM model including volute, motor model, motor, bracket and pump base is built. And model test of the bench by LMS is also done for validating the veracity of FEM model by comparing the results of simulation and measurement. With fluid pressure on pump interior surfaces by transiently simulating in CFX, the pump base transient response, which is excited by fluid force via interior surfaces, volute and brackets, is calculated.
Besides, a four-pan and three-shaft-section rotor dynamic model which is on pump base is also built based on Alembdert principle. And stiffness of springs which connect rotor and pump base are measured by photoelectric sensor, electric eddy-current displacement sensors and virtual instrument built by LabVIEW based on additional weight method. With the stiffness and rotor model, influence on inherent frequencies and model shapes by weight of fluid in impeller is studied, too. And then rotor-model transient response incited by radial fluid force on impeller pan is computed by Matlab program based on Newmark algorithm. Accuracy of rotor modeling method, which regards fluid inciting forces as additional weight on impeller, is also discussed. Further, contributions to pump base vibration by motor and centrifugal pump respectively are compared based on measurement two conditions, including motor running only and pump also rotating. At last, compare of vibrations, incited by fluid forces transferring from two routes mentioned above, is finished, and validation by measurement is carried out as well.
With revised probability matrix, which represents distribution that points corresponding to data pairs of two one-dimension arrays land on the plane formed by the two arrays, three improved algorithms of Cellucci mutual information algorithm are upraised base on statistic method for optimal time delay in phase space reconstruction from time series. And validation of the algorithms by maximal Lyapunov exponent with reconstructed phase space by time series of Lorenz is checked out.
By the improved mutual information algorithms and the False Nearest Neighbor (FNN) Algorithm toolbox in Tisean3.0.0, optimal time delays and embed dimensions are calculated for phase space reconstruction from vibration displacement time series measured on four points of pump base. To judge whether chaos is in pump base vibration, the maximal Lyapunov exponent is also computed by the Small Data Quantity (SDQ) Algorithms toolbox in Tiean3.0.0 with the reconstructed phase space.
The conclusions are gained as following from the researches above:
1)The fluid forces and torques can be gained effectively by CFD simulation. And except the radial impeller fluid force which repeats after impeller rotating one circle, frequencies of the other gross fluid forces and torques on impeller and volute are the same as vane pass frequency. Multi-section curve fitting of fluid force on volte can acquire mathematic model which is better than those of sole section curve fitting and Sin function fitting. And the radial fluid force on vanes of impeller is the biggest contribution to radial fluid force on impeller. Difference of pressure on impeller-front-cover out surface and back-cover out surface decides the axial fluid force on impeller. And unsymmetrical distribution of fluid pressure on impeller-front-cover out surface decides the impeller radial torques. Compare between radial vibration displacement of pump shaft and impeller radial fluid forces can validate the correction of CFD results.
2)The FEM model including volute, motor model, rotor and pump base is feasible for simulating transient response analysis. Vibration acceleration and displacement vertical to pump base by fluid force inciting the base via interior surfaces, volute and bracket are gender. But the initial pressure pulsations when pump startups strongly effects the base vibration in the period that base vibrates unsteadily. The fluid pressure pulsations on pump interior surfaces are inciting forces with wide frequencies, and each inherent model of pump system is working when pump is running.
3)The rotor dynamic model is reliable, and the support stiffness measurement method is also feasible. The virtual instrument system for support stiffness discrimination is reliable for the pump rotor system and the . The fluid weight in impeller effects on middle-rang-order inherent frequencies of rotor system obviously, while it has less effect on low-order and high-order inherent frequencies. The frequency of pump base vibration incited by fluid forces via impeller-rotor system is focus on the frequency that rotor rotates. The base vibration with additional Sine incitation when the radial fluid force on impeller is regarded as impeller pan additional weight which equals to 20% and 40% of fluid weight in impeller respectively is much less than that when the radial fluid force is loaded on impeller directly. The vibration of centrifugal pump base is mainly caused by fluid inciting force. And the base vibration caused by fluid force via pump interior surfaces, volute and brackets is much less than that caused by fluid force via impeller, rotor shaft and springs. The pump base vibration is mainly resource from vibration caused by fluid force on rotor system, other than vibration caused by motor running. The frequency with the biggest amplify of centrifugal-pum-base vibration displacement is shaft rotating frequency, while that of vibration acceleration is five times of rotating frequency.The method calculating pump base vibration via two fluid force transfer route is feasible and available.
4)Equal distance partition the plane formed by two column time series may lead to inaccurate mutual information. When length of time series is not multiple of number that the plane is partitioned, Cellucci’s mutual information receive the wrong optimal time delay for phase space reconstruction from time series. The improved three new mutual information algorithms can not only overcome the fault of Cellucci’s algorithm but also much faster than Fraser’s mutual information algorithm. And the improved algorithms can gain more steady results with longer time series length. So the improved algorithms are feasible and available. It also can be known that the attractors of the base vibration displacements exist evidently. And the maximal Lyapunov exponents of the four vibration-displacement signals are a little bigger than zero, so there is chaos existing in the pump vibration system.
引文
[1] Brennen C.E.. Hydrodynamics of Pumps . Oxford University Press, Oxford. 1994.
[2] Larralde, Eduardo,Ocampo Rafael.Centrifugal pump selection process. World Pumps. 2010(2): 24-28.
[3] Larralde, Eduardo,Ocampo Rafael. Pump selection: a real example. World Pumps. 2010(3): 28-33.
[4]关醒凡.现代泵技术手册.宇航出版社.1995,9.
[5]吴仁荣.船用自吸离心泵的结构设计.船舶工程.2000(5):44-50.
[6]李文广.离心泵叶片设计理论与应用研究进展综述.水泵技术.1998(5):20-27.
[7] Larose, Jeffrey A.. Design concepts and principle of operation of the heart ware ventricular assist system. ASAIO Journal. 2010(4): 285-289.
[8] Maeda, Taketoshi. Etc. Early in vivo evaluation of ventricular assistance with a miniature centrifugal blood pump in rabbits. ASAIO Journal. 2010(3): 254-259.
[9] Santolaria Morros, Carlos, Fernández Oro, Jesús Manuel, Argüelles Díaz, Katia María. Numerical modeling and flow analysis of a centrifugal pump running as a turbine: Unsteady flow structures and its effects on the global performance. International Journal for Numerical Methods in Fluids. 2011(5): 542-562.
[10] Nautiyal, Himanshu, Varun, Kumar, Anoop. Reverse running pumps analytical, experimental and computational study: A review. Renewable and Sustainable Energy Reviews. 2010(9): 2059-2067.
[11] Westra, R.W. etc. PIV measurements and CFD computations of secondary flow in a centrifugal pump impeller. Journal of Fluids Engineering, Transactions of the ASME. 2010(6): 0611041-0611048.
[12]何有世,袁寿其,陈池. CFD进展及其在离心泵叶轮内流计算中的应用.水泵技术.2002(3):23-26.
[13] Chantasiriwan, Somchart. Method for estimating energy saving by variable-speed control of centrifugal pump. IASTED International Conference on Modeling, Simulation, and Identification, MSI 2009, October 12, 2009 - October 14, 2009.
[14]张诚,程永清.化工泵节能综述.水泵技术.1995(6):22-28.
[15] Jan Cernetic, Mirko Cudina. Estimating uncertainty of measurements for cavitation detection in a centrifugal pump. Measurement: Journal of the International Measurement Confederation, 2011.
[16] Chivers TC.. Correlation of Cavitating performance for a centrifugal pump handling various liquids. Conference: Inst Mech Eng Proc (Part 1) Gen Proc. 1969(2): 48-68.
[17] Indira V. etc.. A method for calculation of optimum data size and bin size of histogram features in fault diagnosis of mono-block centrifugal pump. Expert Systems with Applications. 2011(6): 7708-7717.
[18] Hasan A.. Occurrence of faults in heating and air conditioning equipment. Heat Vent Eng J Air Cond. 1974(562): 447-455.
[19] Rosen H. Variability of pump system performance. SIAMM - Journal of The South African Institute of Mining and Metallurgy. 2010(2): 79-87.
[20]黄国富,常煜,张海民等.低振动噪声船用离心泵的水力设计.船舶力学. 2009(4):313-318.
[21] Yedidiah S.. Centrifugal pump problems: Causes and cures. Petroleum Publishing Company, Tulsa, Oklahoma, 1980.
[22] Steve Schmitz. Reducing Pump noise in cooling tower applications . World pumps . 2004(9):24- 29.
[23] M.A.Langthjem, N.Olhoff. A numerical Study of Flow-induced noise in a two-dimensional centrifugal pump . Part I: Hydrodynamics. Journal of Fluids and Structures . 2004(19): 349-368.
[24] M.A.Langthjem, N.Olhoff. A numerical Study of Flow-induced noise in a two-dimensional centrifugal pump . Part II: Hydroacoustics. Journal of Fluids and Structures . 2004(19): 369-386.
[25]蒋爱华,张志谊,章艺等.离心泵噪声研究的综述和展望.振动与冲击.2011(2):.77-84.
[26] Magalh?es R.S. etc. A model for three-dimensional simulation of acoustic emissions from rotating machine vibration. Journal of the Acoustical Society of America.2010(6): 3569-3576.
[27]Hsia Shao-Yi, Chiu Shih-Ming, Cheng yin-Wen. Sound field analysis and simulation for fluid machines. Advances in Engineering Software.2009(1):15-22.
[28]袁寿其,司乔瑞,薛菲等.离心泵蜗壳内部流动诱导噪声的数值计算.排灌机械工程学报.2011(3):93-98.
[29] Yedidiah S.. Centrifugal pump problems: Causes and cures. Petroleum Publishing Company, Tulsa, Oklahoma, 1980.
[30]赵万勇,白双宝,马鹏飞.离心泵转子振动研究现状与展望.流体机械.2011(3):37-39.
[31]陈进.机械设备振动监测与故障诊断.上海交通大学出版社.1991,1.
[32]闻邦春.高等转子动力学.机械工业出版社.1998.
[33]黄立权,王维民,苏奕儒.基于电磁自愈力的转子自动平衡方法与实验研究.振动与冲击.2011(1):208-212.
[34] Kunz Donald L., Newkirk Mark C.. A generalized dynamic balancing procedure for the AH-64 tail rotor. Journal of Sound and Vibration.2009(326): 353-366.
[35] Chakraborty, Animesh. Dynamic balancing in NMR double rotor system. Spectrochimica Acta - Part A: Molecular and Biomolecular Spectroscopy.2000(14): 2725-2727.
[36]夏松波,刘永光,李勇等.旋转机械自动动平衡综述.中国机械工程.1999(4):458-461.
[37]欧阳红兵,曾胜,汪希萱.转子系统在线动平衡综述及展望.1997(10):20-24.
[38]马建敏;张文;郑铁生.柔性联轴节在减小转子系统扭转冲击运动中的作用.中国机械工程.2003(4):26-30.
[39]马建敏;吕景林;杨万东.柔性驱动对转子碰摩运动特性的影响.噪声与振动控制.2006(2):15-17.
[40] Xing, Changhu, Braun, Minel J.. Imbalance response of a partially sealed squeeze film damper for the flexible rotor model. Society of Tribologists and Lubrication Engineers Annual Meeting and Exhibition.2009: 581-583.
[41] Wu, Shang-Teh, Shen, Wei-Ming. Speed regulation of an eccentric rotor with a flexible joint. Proceedings of the IEEE International Conference on Control Applications.2004(2): 949-954.
[42]阎超.计算流体力学方法及应用.北京:北京航空航天大学出版社.2007,4.
[43]江春波,张永良,丁则平.计算流体力学.北京:中国电力出版社, 2007.
[44]Fletcher C.A.J..Computational techniques for fluid dynamics. Springer Version. 1991.
[45] J.D. Anderson, Jr.. Computational Fluid Dynamics. Springer Version.1995.
[46] Lucius A. Brenner G.. Unsteady CFD simulations of a pump in part load conditions using scale-adaptive simulation. International Journal of Heat and Fluid Flow.2010(6):1113-1118.
[47] Park Sang Hyun, Morrison Gerald L.. Centrifugal pump pressure pulsation prediction accuracy dependence upon CFD models and boundary conditions. Proceedings of the ASME Fluids Engineering Division Summer Conference.2009,Part A: 207-220.
[48]徐朝晖.高速离心泵内全流道三维流动及其流体诱发压力脉动研究.清华大学博士论文.2004,4
[49]郭鹏程.水力机械内部复杂流动的数值研究与性能预测.西安理工大学博士学位论文.2006,9.
[50] Dyro P.R..Some results of investigating the effect of undissolved air upon the cavitaion. zv Vyssh Ucheb Zaved, Energ. 1970(11): 85-90.
[52] Al-Qutub A., Khalifa A., Khulief, Y.. Experimental investigation of the effect of radial gap and impeller blade exit on flow-induced vibration at the blade-passing frequency in a centrifugal pump. International Journal of Rotating Machinery.2009.
[53] Suzuki Takayuki, Yonezawa Koichi, Horiguchi Hironori, et.. A numerical analysis of rotordynamic fluid forces on an artificial heart pump impeller in whirling motion. Transactions of the Japan Society of Mechanical Engineers.2008(2): 310-316.
[54] Heshmat Hooshang, Walton II James F., Tomaszewski Michael J., et.. Magnetically suspended rotary blood pump. Proceedings of the World Tribology Congress III.2005.
[55] Suzuki Takayuki, Prunières Romain, Horiguchi Hironori, et.. Measurements of rotordynamicforces on an artificial heart pump impeller. Journal of Fluids Engineering, Transactions of the ASME. 2007(11): 1422-1427.
[56] Yoshida Y., Tsujimoto Y., Kawakami T., et.. Unbalanced hydraulic forces caused by geometrical manufacturing deviations of centrifugal impellers. Journal of Fluids Engineering, Transactions of the ASME. 1998(3): 531-537.
[57] Nakamura Youichi, Tsukamoto Hiroshi, Miyazaki Koji. Experimental study of dynamic characteristics of a centrifugal blood pump with a conical spiral groove bearing for a ventricular assist device. 2007 5th Joint ASME/JSME Fluids Engineering Summer Conference. 2007, part B:1187-1194.
[58] Van Bokhorst E., Almasy S.. Root cause analysis of vibrations and pulsations in a naphtha pipe system with centrifugal pumps. Institution of Mechanical Engineers - 11th European Fluid Machinery Congress.2010:169-179.
[59] Timouchev Serguei, DeBotton Gal, Reznik Avi.. Experimental and computational study of pressure pulsation in a centrifugal pump. Proceedings of the Tenth International Congress on Sound and Vibration.2003: 1897-1904.
[60] Spence R., Amaral-Teixeira J.. A CFD parametric study of geometrical variations on the pressure pulsations and performance characteristics of a centrifugal pump. Computers and Fluids.2009(38) 1243-1257.:
[61] Berten S., Farhat M., Dupont P., et.. Rotor-stator interaction induced pressure fluctuations: CFD and hydroacoustic simulations in the stationary components of a multistage centrifugal pump. 2007 Proceedings of the 5th Joint ASME/JSME Fluids Engineering Summer Conference. 2007(2): 963-970.
[62] Shi F., Tsukamoto H.. Numerical Study of Pressure Fluctuations Caused by Impeller-Diffusor PumpStage. Journal of Fluids Engineering, 2001(123): 466-474.
[63] Hansen T.. Comparison of Steady-State and Transient Rotor-Stator Interaction of an Industrial Centrifugal Pump, CFX Users Conference, Berchtesgaden. 2001.
[64] Wu Yulin, Chen Naixiang, Xu Zhaohui. Unsteady flow simulation through a centrifugal pump. Proceedings of the American Society of Mechanical Engineers Fluids Engineering Division Summer Conference.2005(1),part B: 1543-1549.
[65]黄国富,常煜,张海民.基于CFD的船用离心泵流体动力振动噪声源分析.水泵技术.2008(3):20-33.
[66]倪永燕.离心泵非定常湍流场计算及流体诱导振动研究.江苏大学博士学位论文.2008,5.
[67]邵春雷,顾伯勤,陈晔.离心泵内部非定常压力场的数值研究.农业工程学报. 2009(1):75-79.
[68] Rzentkowski G.. Generation and control of pressure pulsations emitted from centrifugal pumps: A review. American Society of Mechanical Engineers, Pressure Vessels and PipingDivision. 1996(328): 439-454.
[69]程光田,刘元义,颜世周. CFD技术在低比转速离心泵中的应用.机械工程与自动化.2009(5):197-200.
[70] Cui Bao-Ling, Lin Yong-Gang, Jin Ying-Zi. Numerical simulation of flow in centrifugal pump with complex impeller. Journal of Thermal Science.2011(1): 47-52.
[71] Gruselle Franois, Steimes Johan, Hendrick, Patrick. Study of a two-phase flow pump and separator system. Journal of Engineering for Gas Turbines and Power.2011(6).
[72]袁建平.离心泵多设计方案下内流PIV测试及其非定常全流场数值模拟.江苏大学博士学位论文.2008,5.
[73]盛森芝,徐月亭,袁辉靖.近十年来流动测量技术的新发展.力学与实践.2002(5):1-13.
[74]袁建平,袁寿其,何志霞.流场测试技术及其在离心泵中的应用进展.水泵技术.2003(4):3-7.
[75]李亚林,袁寿其,汤跃等.离心泵内部流动PIV测试研究进展水泵技术.2010(5):1-4.
[76]杨波,许友谊,刘栋等.离心泵叶轮内流场PIV研究.水泵技术.2006(4):12-18.
[77] R.Dong, S.Chu, J.Katz. Effect of Modification to Tongue and Impeller Geometry on Unsteady Flow, Pressure Fluctuations, and Noise in a Centrifugal Pump . Journal of Turbomachinery. 1997(119):506-515.
[78] R.Dong, S.Chu,, J.Katz. Quantitative Visualization of the Flow Within the Volute of a Centrifugal Pump. Part A: Technique. Journal of Fluids Engineering.1992(3): 390-395.
[79] R.Dong, S.Chu,, J.Katz. Quantitative Visualization of the Flow Within the Volute of a Centrifugal Pump. Part B: Results. Journal of Fluids Engineering.1992(3): 396-403.
[80] S.Chu, R.Dong, J.Katz. Unsteady Flow, Pressure Fluctuation and Noise Associated With the Blade-Tongue Interaction in a Centrifugal Pump. ASME Winter Annual Meeting, New Orleans.1993. Nov. 28-Dec. 3.
[82] S.Chu, R.Dong, J.Katz. Relationship between unsteady flow, pressure fluctuations, and noise in a centrifugal pump Part A: Use of PDV data to compute the pressure field. Journal of fluids engineering.1995(117): 30-35.
[83] S.Chu, R.Dong, J.Katz.Relationship between unsteady flow, pressure fluctuations, and noise in a centrifugal pump PartB: Effects of blade2tongue interactions. Journal of fluids engineering. 1995(117): 24-29.
[84] Y.Y.Jiang, S. Yoshimura, R. Imai, H. Katsura, T. Yoshida, C. Kato. Quantitative evaluation of flow-induced structural vibration and noise in turbomachinery by full-scale weakly coupled simulation . Journal of Fluids and Structures . 2007(23):531-544.
[85]叶建平.离心泵振动噪声分析及声优化设计研究.武汉理工大学硕士学位论文.2006,4.
[86]Gao Jiang-Yong, Wang Fu-Jun, Qu Li-Xia. Prediction of flow-induced vibration in a largedouble-suction centrifugal pump impeller. Journal of Engineering Thermophysics. 2010(31):5-8.
[87]王新,魏述和.大型泵站的流固耦合振动分析.人民长江.2009,40( 22) : 56-59
[88] Wang Xin, Luo Shaoze. Vibration analysis of large bulb tubular pumping station considering flow-structure interaction. 2010 Asia-Pacific Power and Energy Engineering Conference.
[89]邢景棠;周盛;崔尔杰.流固耦合力学概述[J]力学进展, 1997 (1): 19-38
[90]叶睿,王新.大型泵站随机振动频谱分析.黑龙江水专学报.2010(6):5-8.
[91] Shijie Guo, Yoshiyuki Maruta. Experimental Investigations on Pressure Fluctuations and Vibration of the Impeller in a Centrifugal Pump with Vaned Diffusers. JSME International Journal. 2005,48(1):136-143
[92] Berten Stefan, Dupont Philippe, Fabre Laurent, et.. Experimental investigation of flow instabilities and rotating stall in a high-energy centrifugal pump stage. Proceedings of the ASME Fluids Engineering Division Summer Conference.2009: 505-513.
[93]倪永燕,潘中永,李红等.出口压力波动特性在离心泵汽蚀监测中的应用.排灌机械.2006(5):40-43.
[94]朱玉才,曲衍国,邵举平.离心泵叶片边界层分离对水动力特性的影响.应用力学学报.2005(9):466-469.
[95]徐萃萍,刘建成,朱玉才.边界层分离对固液两相流离心泵水力振动的影响.黑龙江科技学院学报.2004(5):149-153
[96] Uchida N., Imaichi K., Shirai T.. Radial force on the impeller of a centrifugal pump. Bull JSME. 1971(76): 1106-1117.
[97]Adkins Douglas R., Brennen Christopher E.. Orings hydrodynamic forces on centrifugal pump impeller. NASA Conference Publication.1986: 467-491.
[98] Adkins D.R., Brennen C.E. Analyses of hydrodynamic radial forces on centrifugal pump impellers. Journal of Fluids Engineering, Transactions of the ASME. 1988(1):22-28.
[99]Kikuyama Koji, Hasegawa Yutaka, Maeda Takao. Unsteady pressure distributions and forces on the impeller blades of a centrifugal pump. Transactions of the Japan Society of Mechanical Engineers. 1988(504): 2038-2046.
[100]Fongang R., Colding-Jorgensen J., Nordmann R.. Investigation of hydrodynamic forces on rotating and whirling centrifugal pump impellers. Proceedings of the 1996 International Gas Turbine and Aeroengine Congress & Exhibition. 1996.
[101]Jude L..The hydrodynamic action of the fluid on the impeller blades in a centrifugal pump. UPB Scientific Bulletin, Series A: Applied Mathematics and Physics.1999(61): 91-96.
[102] Gonzaláz José, Santolaria Carlos, Parrondo Jorge Luis. Unsteady radial forces on the impeller of a centrifugal pump with radial gap variation. Proceedings of the ASME/JSME Joint Fluids Engineering Conference.2003(2): 1173-1181.
[103]Guo Shijie, Okamoto Hidenobu, Maruta Yoshiyuki. Measurement on the fluid forces induced by rotor-stator interaction in a centrifugal pump. Transactions of the Japan Society of Mechanical Engineers. 2005(706): 1603-1610.
[104] Blanco Eduarde, Parrondo Jorge, Barrio Raúl, et. Fluid-dynamic pulsations and radial forces in a centrifugal pump with different impeller diameters. Proceedings of 2005 ASME Fluids Engineering Division Summer Meeting.2005: 1634-1643.
[105] González José, Parrondo Jorge, Santolaria Carlos, et.. Steady and unsteady radial forces for a centrifugal pump with impeller to tongue gap variation. Journal of Fluids Engineering , Transactions of the ASME.2006(3): 454-462.
[106] Raúl Barrio, Eduardo Blanco, Jorge Parrondo, et.. The Effect of Impeller Cutback on the Fluid-Dynamic Pulsations and Load at the Blade-Passing Frequency in a Centrifugal Pump. Journal of Fluids Engineering Transactions of the ASME. 2008(11): 111102-1- 111102-11.
[107]Ji Pei, Shouqi Yuan, Jianping Yuan, et.. Numerical Analysis on Asymmetrical Distribution of Flow Field and Radial Force for a Centrifugal Pump. 2009 International Conference on Energy and Environment Technology.2009:741-744.
[108]刘占生,刘全忠,王洪杰.离心泵变工况流场及叶轮流体激振力研究.哈尔滨工程大学学报.2008(12):1304-1308.
[109]张亮.大型双吸离心泵径向力数值计算.兰州理工硕士学位论文.2009,6.
[110] Wang Hongjie, Liu Quanzhong, Wei Xianzhu, et.. Quasi-steady solution of rotor-dynamic forces generated by discharge-to-suction leakage flows in centrifugal pumps. Proceedings of the 12th International Conference on Engineering, Science, Construction, and Operations in Challenging Environments.2010: 2217-2227.
[111] Torbergsen E., White M. F.. Numerical and Experimental Study of Impeller/Diffuser Interactions in Centrifugal Pumps. Proceedings of the ISROMAC Conference. 1998:1349–1358.
[112] Chamieh D. S.. Forces on a whirling centrifugal pump-impeller. California Institute of Technology University PH.D. Dissertation. 1983.
[113] Moore J. Jeffrey, Ransom David L., Viana Flavia. Rotordynamic force prediction of centrifugal compressor impellers using computational fluid dynamics. Journal of Engineering for Gas Turbines and Power. 2011(4).
[114] Chamieh D.S., Acosta A.J., Brennen C.E., et. Experimental measurement of hydrodynamic stiffness matrix for a centrifugal pump impeller. NASA Conference Publication.1982:382-398.
[115] Chamieh Dimitri S., Acosta Allan J., Brennen Christopher E.. Experimental measurements of hydrodynamic radial forces and stiffness matrices for a centrifugal pump-impeller. Journal of Fluids Engineering, Transactions of the ASME. 1985(3): 307-315.
[116]闻邦椿等.高等转子动力学.北京:机械工业出版社.2000.
[117]徐敏等.船舶动力机械的振动、冲击与测量.北京:国防工业出版社.1981.
[118]胡朋志,李同杰,孙启国.流体激振及其对离心叶轮转子的影响.现代机械.2006(4): 35-38.
[119] Ahmad K., Lidgitt P.J., Dickson H.M.K.. Theoretical and experimental investigation of axial thrusts within a multi-stage centrifugal pump. Mechanical Engineering Publ Ltd.1986: 89-99.
[120]沈小要.超超临界汽轮机组转子系统振动特性及若干故障转子非线性特性的研究.上海交通大学博士论文.2007,9.
[121]蒋庆磊,戴维平,吴大转,王乐勤.离心泵内泄漏流计算及其对转子振动的影响.排灌机械工程学报.2010(5):202-205.
[122] Le Bleu Jr., Julien, Xu Ming. Vibration monitoring of sealess pumps using spike energy. Sound and Vibration.1995(12):10-16.
[123] Akhmetkhanov R., Banakh L., Nikiforov A.. Flow-coupled vibrations of rotor and seal. Journal of Vibration and Control. 2005(7): 887-901.
[124] Tondl Ales. Analysis of self-excited vibration in water machines due to leakage flow. Acta Technica CSAV (Ceskoslovensk Akademie Ved).1989(34): 144-170.
[125] Baskharone E.A., Daniel A.S., Hensel S.J..Rotordynamic effects of the shroud-to-housing leakage flow in centrifugal pumps. Journal of Fluids Engineering, Transactions of the ASME. 1994(116): 558-563.
[126]Childs D.W.. Fluid-structure interaction forces at pump-impeller-shroud surfaces for rotordynamic calculations. Journal of vibration, acoustics, stress, and reliability in design.1989(3):216-225.
[127]Makay Elemer, Nass Douglas. Gap-Narrowing rings make booster pumps quiet at low flow. Power. 1982(9):87-88.
[128] Kaneta Motohiro, Fukahori Masafumi. Fundamental study on non-contact face seal utilizing pumping action. Journal of Japan Society of Lubrication Engineers. 1983(6): 457-464.
[129] Childs D.W.. Finite-length solutions for the rotordynamic coefficients of constant-clearance and convergent-tapered annular seals. Third International Conference on Vibrations in Rotating Machinery. 1984: 223-231.
[130] Berezhnoi I.S.. Investigation of the flow and dynamic characteristics of labyrinth seals. Soviet engineering research. 1986(5):16-18.
[131] Jery B., Acosta A. J., Brennen, C. E., et.. Hydrodynamic Impeller Stiffness, Damping, and Inertia in the Rotordynamics of Centrifugal Pumps. Rotordynamic Instability Problems in High-Performance Turbomachinery, NASA CP2338, proceedings of a workshop held at Texas A & M University, NASA Science and Technical Branch. 1984:137–160.
[132]Uy R. V.. Studies of Rotordynamic Forces Generated by Annular Flows. Ph.D. dissertation, California Institute of Technology. 1998.
[133]Ohashi H., Sakurai A., Nishihama, J.. Influence of Impeller and Diffuser Geometries on the Lateral Fluid Forces of Whirling Centrifugal Impeller. Rotordynamic Instability Problems in High-Performance Turbomachinery, NASA CP3026, proceedings of a workshop held at Texas A&M University, NASA Science and Technical Branch. 1988:285–306.
[134] Bolleter U., Wyss A., Welte L., et..Measurement of Hydrodynamic Interaction Matrices of Boiler Feed Pump Impellers. ASME J. Vibr. Acoust. 1987(109):144–151.
[135] Guinzburg, A.. Rotordynamic Forces Generated By Discharge-to- Suction Leakage Flows in Centrifugal Pumps. Ph.D. dissertation, California Institute of Technology. 1992.
[136] Sivo J. M., Acosta A. J., Brennen, C. E., et..The Influence of Swirl Brakes on the Rotordynamic Forces Generated by Discharge-to-Suction Leakage Flows in Centrifugal Pumps. ASME J. Fluids Eng. 1995(117): 104–108.
[137] Bentlyde, Muszynska A.. Role of circumferential flow in the stability of fluid-handling machine rotors. The 5th Workshop on Rotor dynamic Instability Problems in High Performance Turbo machinery, Taxas A&M University. 1988:1-5.
[138] Muszynska A. Fluid-related rotor/bearing/seal instability problems . BRDRC Report No. 2. Nevada: Bently Rotordynamics Research and Development Corporation,1986.
[139] Moore J.J., Palazzolo A.B.. Rotordynamic force prediction of whirling centrifugal impeller shroud passages using computational fluid dynamic techniques. Journal of Engineering for Gas Turbines and Power. 2001(123):910-913.
[140] Athavale M. M., Przekwas A. J., Hendricks R. C., et..SCISEAL: A three-dimensional CFD Code for Accurate Analysis of Fluid Flow and Forces in Seals. Advance ETO Propulsion Conference. 1994.
[141] Moore J. J., Palazzolo A. B.. CFD Comparison to Three-Dimensional Laser Anemometer and Rotordynamic Force Measurements for Grooved Liquid Annular Seals. ASME/STLE International Tribology Conference. 1998.
[142]平仕良,吴大转,谭善光,王乐勤.大功率高压多级离心转子动力学分析.工程热物理学报.2010(7):1135-1138.
[143] Uy R.V., Bircumshaw B.L., Brennen C.E.. Rotordynamic forces from discharge-to-suction leakage flows in centrifugal pumps: effects of FLXmetry. JSME International Journal, Series B: Fluids and Thermal Engineering.1998(41): 208-213.
[144] Kirk R.G., Guo Z.. Influence of leak path friction on labyrinth seal inlet swirl. Tribology Transactions.2009(52): 139-145.
[145] Jen Chang-Wei. Comparison of the rotor dynamic coefficients of packing and mechanicalseals in centrifugal pumps. Lubrication Engineering.1991(41):616-618.
[146]王斌.基于离心泵内流场模拟的转子临界转速分析与计算.兰州理工大学硕士学位论文.2010,6.
[147] Benra Friedrich-Karl, Dohmen Hans Josef, Schneider Oliver. Calculation of hydrodynamic forces and flow induced vibrations of centrifugal sewage water pumps. Proceedings of the ASME/JSME Joint Fluids Engineering Conference. 2003(1):603-608.
[148] Benra Friedrich-Karl. Dohmen Hans Josef, Schneider Oliver. Experimental investigation of flow induced rotor oscillations in a centrifugal sewage water pump. Proceedings of the ASME Heat Transfer/Fluids Engineering Summer Conference.2004(3):23-28.
[149]孙晓林,于慎波.离心泵转子系统临界转速的计算.福州大学学报. 1999(2):53- 56.
[150]张新敏,王延合,袁宗久等.离心多级泵转子临界转速的计算.水泵技术,1999(3):3-6.
[151]成晓伟.离心泵转子部件临界转速的分析与计算.兰州理工大学硕士学位论文.2009,6.
[152]熊万里,段志善,闻邦椿.用机电耦合模型研究转子系统的非平稳过程.应用力学学报. 2000 ( 4) : 7-12.
[153]李振平,闻邦椿,张金焕等.松动-裂纹故障转子系统的非线性动力学行为研究.中国机械工程.2003 ( 22) : 1891-1895.
[154]刘树英,宋雪萍,闻邦椿.转子系统故障发展过程的突变.东北大学学报.2005 ( 3) : 285-288.
[155]Muszynska A. Rotor-to-Stationary Element Rub-RelatedVibration Phenomena in Rotating Machinery.Shock and Vibration Digest.1989(21): 3-11.
[156]刘献栋,李其汉.转静件碰摩模型及不对中转子局部碰摩的混沌特性.航空动力学报.1998 ( 4) : 361-365.
[157]刘献栋,李其汉,杨绍普.质量偏心旋转机械整圈碰摩的稳定性及其Hopf分叉.振动工程学报. 1999 ( 1) : 40-46.
[158]黄文虎,武新华,焦映厚等.非线性转子动力学研究综述.振动工程学报.2000(12): 497-509.
[159]焦映厚,陈照波,夏松波等.非线性转子动力学的研究现状与展望.哈尔滨工业大学学报,1999(6):1-4.
[160]李同杰,孙启国,王娟.横向流体激振力作用下的不平衡离心叶轮转子分岔特性研究.振动与冲击.2007(11):213-215.
[161]李同杰,王娟,陈云香,孙启国.含转轴裂纹的离心叶轮转子非线性动力学特性研究.振动与冲击.2010(11):213-215.
[162]蒋兆远,孙启国,李同杰,王娟.带有支座松动故障的离心泵叶轮转子分岔特性分析.机械强度.2009(5):707-711.
[163] Yedidiah S.. Oscillations at low NPSH caused by flow-conditions in the suctions in pipe.ASME Cavitation and Polyphase Flow Forum. 1974(5):27-28
[164] Ni Yongyan, et .. Detection of cavitation in centrifugal pump by vibration methods. Chinese Journal of Mechanical Engineering. 2008(5): 46-49.
[165]梁超.压力脉动法在离心泵汽蚀故障诊断中的研究.东北电力大学硕士论文.2010,3.
[166]黄忠富.小波分析在离心泵汽蚀故障诊断中的应用研究.江苏大学硕士学位论文.2004,5.
[167] Chini Seyed Farshid; Rahimzadeh Hassan; Bahrami Mohsen. Cavitation detection of a centrifugal pump using noise spectrum. Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. 2005(1):13-19.
[168] Okamura T., Ohki H., Matsunaga Y. Intensity of cavitaion erosion in centrifugal pumps operating at low flow rate. ASME Cavitation in Hydraulic Structures and Turbomachinery conference.1985(25): 63-70.
[169]苏永生,王永生,段向阳.离心泵空化监测阈值确定方法研究.农业机械学报.2010(5):68-71.
[170]苏永生,王永生,段向阳.离心泵空化试验研究.农业机械学报.2010(3):77-80.
[171] Sebestyen Gy, Rizk M., Szabo A. Some properties form cavitation-vibration test on centrifugal pumps. Conference: Proc Jt Symp on Des and Oper of Fluid Mach.1978(2): 557-566.
[172] Perez Robert X., Akins Robert A., Lee Chung E., et. Fiber-optic pressure sensors detect cavitation and flow instabilities in centrifugal pumps. World Pumps. 1996(359):28-33.
[173] Soyama Hitoshi, et.. Behavior of severe cavitation erosion occurring in a high-specific-speed centrifugal pump due to vibrations and noise. Transactions of the Japan Society of Mechanical Engineers.1995(61): 3276-3281.
[174] Rayan M.A., Mahgob M.M. Mostafa N.H..Cavitation erosive wear in centrifugal pump impeller. ASME Cavitation and Multiphase Flow Forum.1987(50) 92-95.
[175] Rayan M.A., Mahgob M.M., Mostafa N.H. Energetic model for cavitation erosion prediction in centrifugal pump impeller. ASME Cavitation and Multiphase Flow Forum. 1990(98): 133-138.
[176] Pearson A.R.. Experiences with cavitation induced instabilities in centrifugal pumps. 11th Symposium of the Section on Hydraulic Machinery, Equipment and Cavitation.1982.
[177] Kamijo, Kenjiro. Cavitation-induced flow vibration of liquid oxygen pumps for rockets. Transactions of the Japan Society of Mechanical Engineers. 1988(503): 1655-1660.
[178] Kawata Yutaka, Kanki Hiroshi, Kawakami Takashi. Dynamic radial force on the cavitating centrifugal impeller. 12th Symposium on Hydraulic Machinery in the Energy Related Industries. 1984:305-315.
[179] Franz R., Acosta A.J., Brennen C.E., et.. Rotordynamic forces on a centrifugal pumpimpeller in the presence of cavitation. ASME Fluids Engineering Division. 1989(81): 205-211.
[180] Kitamura Noboru, Kubota Naokazu.Cavitation performance of tandem impeller at partial capcities. Proc Jt Symp on Des and Oper of Fluid Mach conference. 1978(2): 621-630.
[181] Dupont, Philippe. Numerical prediction of cavitation: Improving pump design. Design Engineering. 2002(1):15.
[182] Pandit A.B., Niranjan K., Davidson J.F.. Pump-stirred aerator. Chemical Engineering Science. 1991(9): 2293-2301.
[183]刘宜,张文军,杜杰.离心泵内部空化流动的数值预测.排灌机械.2008(5):19-21.
[184]曹潇丽.低温流体汽蚀的CFD模拟及实验研究.浙江大学硕士学位论文.2011,1.
[185] Diang H., Visser F.C., Jiang Y.. Demonstration and validation of a 3D CFD simulation tool predicting pump performance and cavitation for industrial applications. Journal of Fluids Engineering, Transactions of the ASME. 2011(1): 011101
[186] Caridad Jose, Asuaje Miguel, Kenyery Frank. Characterization of a centrifugal pump impeller under two-phase flow conditions. Journal of Petroleum Science and Engineering. 2008(63):18-22.
[187]戎海武,孟光,徐伟等.二自由度耦合线性随机系统的最大Lyapunov指数和稳定性.2000(9):46-53.
[188]闻邦椿,李以农,徐培民.工程非线性振动.北京:科学出版社. 2007,8.
[189]陈佐一.流体激振.北京:清华大学出版社.1998.
[190]陈佐一,王继宏.流体激振的全三维数值分析系统.自然科学进展.1998(1):1-7.
[191]陈佐一,刘红吴,晓峰.叶轮机械叶片流体激振安全性的全功能分析.工程热物理学报.1999(5):304-308.
[192]王梅,江和甫,吕文林.在尾流激振情况下叶片振动应力预估技术.航空动力学报.2007(4):608-613.
[193]杨荣菲,侯安平,周盛等.最大Lyapunov指数用于压气机局部性能的分析.航空学报.2009(4):622-624.
[194]伍友利,董福安,吕建伟等.某型发动机实验数据的Lyapunov指数研究.应用力学学报. 2006(1): 68-71.
[195] Nakanno T , Kodama H . Numerical and experimental investigation of instability in a high speed axial f low compressor using chaos theory . AIAA.2002:4089, 2002.
[196]白长青,许庆余,张小龙.火箭发动机液氢涡轮泵转子密封系统的非线性动力稳定性.西安交通大学学报.2005(9):1016-1020.
[197]白长青,许庆余,张小龙.密封和内阻尼对火箭发动机液氢涡轮泵转子系统动力稳定性的影响.机械工程学报.2006(3):150-155.
[198]刘杰黄,文伟,黄步玉.离心机转子系统的稳定性问题.振动与冲击.1989(1):44-51
[199]刘杰黄,文伟,黄步玉.离心机转子的稳定性试验研究.上海交通大学学报.1992(1):52-58.
[200]何斌辉,王兆伍,涂桥安.高速管式离心机转子动力学稳定性的研究.轻工机械.2010(11):12-14.
[201]田爱梅,朱梓根.涡轮泵转子稳定性计算.推进技术.2000(6):43-45
[202]张兆顺,崔桂香,许春晓.湍流理论与模拟.北京:清华大学出版社.2005,9.
[203]Marizo Piller,EnricoNobile,Thomas J.. DNS study of turbulent transport at low Prandtl numbers in a channel flow. Journal of Fluid Mechanics. 2002(458):419-441.
[204]Wissink J.G.. DNS of separating low Reynolds number flow in a turbine cascade with incoming wakes. International Journal of Heat and Fluid Flow.2003(4):626-435.
[205]Stephane V..Local mesh refinement and penalty methods dedicated to the Direct Numerical Simulation of incompressible multiphase flows. Proceedings of the ASME/JSME Joint Fluids Engineering Conference.2003: 1299-1305.
[206]张兆顺,崔桂香,许春晓.湍流大涡数值模拟的理论与应用.北京:清华大学出版社.2008,1.
[207]Abbott M.B., Basco D.R..Computational Fluid Dynamics-An Introduction for Engineers. Longman Scientific& Techincal ,Harlow, England,1989.
[208]Rollet-Miet P., Laurence D., Ferziger J.. LES and RANS of turbulent flow in tube bundles. International Journal of Heat and Fluid Flow.1999(3):241-254.
[209] Zhang Shu Jia, Tong Yue Ping, He Le. Examine applicability of the RANS and LES method on numerical simulation of centrifugal pump. Applied Mechanics and Materials.2011(55):582-586
[210]Tabib Mandar, Lane Graeme, Yang William, et.. CFD simulation of a solvent extraction pump mixer unit: Evaluating Large Eddy Simulation and RANS based models. Journal of Computational Multiphase Flows.2010(2):165-178.
[211] Brzozowski Daniel, Chow Yi-Chih, et.. A comparison of unsteady RANS simulations with PIV data in an axial turbomachine. Proceedings of 2005 ASME Fluids Engineering Division Summer Meeting.2005:1464-1479.
[212]Lee Y.. A study and improvement of large eddy simulation for practical applications. Ph.D dissertation. Texas A&M University.1992.
[213] Strelets M. Detached eddy simulation of massively separated flows . AIAA Journal. 2001(1)..
[214] Shih Tsan-Hsing, Zhu Jiang, Lumley John L.. New Reynolds stress algebraic equation model. Computer Methods in Applied Mechanics and Engineering.1995(125):287-302.
[215]Versteeg H.K., Malalasekera W. An Introduction to Computational Fluid Dynamics: The Finite Volume Method. Wiley, New York.1995.
[216]Hinze J.O..Turbulence. McGraw-Hill, New York.1975.
[217]陶文铨.数值传热学.西安:西安交通大学出版社,2001.
[218] Smith A.M.O., Cebeci T.. Numerical solution of the turbulent boundary layer equations. Douglas aircraft division report.1967, DAC 33735.
[219]Baldwin B.S., Lomax H..Thin layer approximation and algebraic model for separated turbulent flows. American Institute of Aeronautics and Astronautics, Aerospace Sciences Meeting. 1978:16-18.
[220] Johnson D.A.. King L.S.. A mathematically simple turbulence closure model for attached and separated turbulent boundary layers. AIAA journal.1985(23): 1684-1692.
[221]周云龙,郭婷婷.高等流体力学.北京:中国电力出版社.2007,6.
[222]Flunent Inc..FLUENT User’s Guide. Fluent Inc..2003.
[223] Spalart P. R, Allmaras S. R.. A one equation turbulent model for aerodynamic flows. La Recherche Aerospatiale.1994(1):5-21.
[224] Baldwin Barrett S., Barth Timothy J.. A one-equation turbulence transport model for high Reynolds number wall-bounded flows. AIAA, Aerospace Sciences Meeting, 29th.1991.
[225] Paciorri R.,Dieudonne W., Degrez G., et.. ring the validity of the Spalart-Allmaras turbulence model for hypersonic flows. Journal of Spacecraft and Rockets. 1998(2): 121-126.
[226] Tahsini A.M.. Piloted ignition of solid fuels in turbulent back-step flows. Aerospace Science and Technology.2011,In Press.
[227]张鸣远,景思睿,李国君.高等工程流体力学.西安:西安交通大学出版社.2006,7.
[228]Yakhot V., Orzag S.A.. Renormalization group analysis of turbulence: basic theory. Journal of Scientific Computing. 1986(1):3-51.
[229]Shih T.H., Liou W.W., Shabbir A., et.. A new k -? eddy viscousity model for high Reynolds number turbulent flows. Computers&Fluids. 1995(3):227-238.
[230]Spalding D.B..Concentration fluctuations in a round turbulent free jet. Chemical Engineering Science. 1971(26):96-107.
[231]Hegbusi J.O.. Revised two-equation model of turbulence. CFD unit. 1983,5.
[232]张陈安,史爱明,刘锋等.基于SST湍流模型的三维叶片气动弹性问题研究.第十届全国空气弹性学术交流会.2007:345-351
[233]童秉纲,尹协远,朱克勤.涡运动理论.合肥:中国科学技术大学出版社.1994.
[234]余利仁,张书农,蔡树棠.水环境中紊流污染场深度平均二方程数值模拟新模式及其数值检验.水利学报.1990(3):13-21.
[235]张志伟,刘建军.各种湍流模型在Fluent中的应用.河北水利.2008,10.
[236] Menter F.R.,Two-Equation Eddy-Viscosity Turbulence Models for Engineering Application, AIAA Journal. 1994(8):1598-1605.
[237]张强,杨永,李喜乐.基于新的描述湍流耗散方程的k -?两方程湍流模型的数值算法研究.西北工业大学学报.2009(8):466-470.
[238]陈钱.叶轮机械相关流动中几种湍流模型的预测性能.清华大学硕士学位论文.2007,5.
[239]江春波,张永良,丁则平.计算流体力学.北京:中国电力出版社. 2007.
[240]龙天渝.计算流体力学.重庆:重庆大学出版社,2007.
[241]Patankar S.V.. Numerical Heat Transfer and Fluid Flow. Hemisphere, Washington,1980.
[242]Van Doormal J.P., Raithby G.G.. Enhancement of the SIMPLE method for predicting incompressible fluid flows. Numerical Heat Transfer.1984(7):147-163.
[243]Issa R.I.. Solution of the implicitly discretized fluid flow equations by operator-splitting. Journal of Compute Physic. 1986(62):40-65.
[244]刘应中,缪国平.高等流体力学.上海:上海交通大学出版社.2002,1.
[245] Hansen, T.. Comparison of Steady-State and Transient Rotor-Stator Interaction of an Industrial Centrifugal Pump. CFX Users Conference, Berchtesgaden.2001.
[246] Shi F., Tsukamoto H.. Numerical Study of Pressure Fluctuations Caused by Impeller-Diffusor Pump Stage. Journal of Fluids Engineering.2001(3): 466-474.
[247]Speziale C. G..On nonlinear k -? model of turbulent flows. Fluid Mechanics. 1987(178):459-475.
[248] Wilcox. Multiscale model for turbulent flows. AIAA Journal. 1988(11):1311-1320.
[249] Menter F. R.. Influence of Freestream Values on k -? Turbulence Model Predictions. AIAA Journal. 1992(6):1651-1659.
[250]钱玉琴.高速离心泵流固耦合动力特性的研究.江苏大学硕士论文.2010,12.
[251] Marscher W.D. The relationship of vibration to problems in Centrifugal Pumps. Chemical Engineering. 2004(5):38-44.
[252] Shannon C. E.. Communication in the presence of noise. Proceedings of the IRE. 1949( 37): 10- 21.
[253]傅志方,华宏星.模态分析理论与应用.上海:上海交通大学出版社.2000,7.
[254]刘延柱,陈文良,陈立群.振动力学.北京:高等教育出版社.1998,2.
[255]胡于进,王璋奇.有限元分析及应用.北京:清华大学出版社.2009,4.
[256]孙启国,虞烈.流体机械中浸液转子动力学特性的研究.动力工程.2000(10):906-910.
[257]孙启国,姜培林,虞烈.大间隙环流中壁面摩擦及偏心转子静特性研究.摩擦学学报. 1999 (3) : 261- 265.
[258]孙启国,虞烈.大间隙环流中偏心转子动特性系数的数值分析方法.应用力学学报.2000 (17):45-49.
[259]孙启国,虞烈.有限长大间隙环流中同心转子动特性系数研究.摩擦学学报,2001 (6) : 473-477.
[260]孙启国,虞烈,谢友柏.大间隙环流中偏心转子动特性系数的计算.润滑与密封. 2000(2) :13-15.
[261]Antunes J., Mendes J. ,Moreira M. et cl. A theoretical model for nonlinear planar motions of rotors under fluid confinement. Journal of Fluids and Structures .1999 (13) :103-126.
[262] Moreira M., Antunes J., Pina H.. A theoretical model for nonlinear orbital motions of rotors under fluid confinement. Journal of Fluids and Structures. 2000 (14) : 635-668. [263 ] Moreira M., Antunes J. , Pina H. An improved linear model for rotors subject to dissipative annular flows. Journal of Fluids and Structures. 2003 (17) : 813-832.
[264] Jiang P. N., Wang W. Z., Liu Y. Z., et cl. Influence of stem leakage through vane,gland and shaft seals on rotor dynamics of high-pressure rotor of a 1000MW ultra-supercritical steam turbine. Archive of Applied Mechanics.2011:1-13.
[265] R. Gordon Kirk, Ali A. Alsaeed. Induced unbalance as amethod for improving the dynamic stability of high-speed turbochargers. International journal of rotating machinery.2011:Article ID 952869.
[266]何洪庆,沈达宽,张哲文.涡轮泵转子的临界转速研究(I):均匀支撑转子临界转速的传递矩阵法.推进技术.1998(12):83-87.
[267]何洪庆,张小龙,沈达宽等.涡轮泵转子的临界转速研究(II):非均匀支撑转子临界转速的传递矩阵法.推进技术.1999(2):38-45.
[268]何洪庆,张小龙,沈达宽等.涡轮泵转子的临界转速研究(III):计入液体作用力时涡轮泵转子的临界转速.推进技术.1999(4):42-44.
[269]张小龙,何洪庆.涡轮泵转子的临界转速研究(IV):分布质量轴的传递矩阵法.推进技术.2000(4):52-55.
[270]郭力.子结构传递矩阵法、有限元素法和模态综合发应用于转子动力学特性研究时的对比分析.电站系统工程.1999(15):12-24.
[271]欧园霞,李彦.转子动力特性计算中常用方法的对比分析.航空动力学报.1994(4):142-146.
[272]黄太平.转子动力学中的传递矩阵阻抗耦合法.航空动力学学报.1988(10):315-318.
[273]顾家柳.传递矩阵-直接积分法及其应用.航空学报.1983(4):48-56.
[274]孟光.转子动力学研究的回顾与展望.振动工程学报.2002(3):1-8.
[275] Prohl M.A. A general method of calculating critical speeds of flexible rotors. Journal of applied mechanics, ASME.1945(67): 142-146.
[276]付才高.航空发动机强度设计、试验手册:转轴系统振动试验.北京:航空工业出版社.1987,2.
[277]王海波,陈伯望,余志武.结构动力方程Newmark- ?方法递推简化分析.四川大学学报.2008(5):47-52.
[278]陈伯时.阮毅.陈维钧等.电力拖动自动控制系统:运动控制系统.北京:高等教育出版社.2003.
[279]吕金虎,陆君安,陈士华.混沌时间序列分析及其应用.武汉:武汉大学出版社.2001,10.
[280]孙克辉.混沌同步控制理论及其在信息加密中的应用研究.中山大学博士学位论文.2005,1.
[281]张雨.时间序列的混沌核复合分析及实践.长沙:国防科技大学出版社.2007,3.
[282]韩敏.混沌时间序列预测理论与方法.北京:中国水利水电出版社.2007,5.
[283]陈士华,陆君安.混沌动力学初步.武汉:武汉水利电力大学出版社.1998.
[284]张筑生.微分动力系统原理.北京:科学出版社.1987.
[285] Takens F.. Determing strang attractors in turbulence. Lecture notes in mathematics. 1981(898): 361-381.
[286]Takens F.. On the numerical determination of the dimension of an attractor. Lecture notes in mathematics.1985(1125):99-106.
[287] Ma?éR.. On the dimension of the compact invariant sets of certain non-linear maps. Lecture note in mathematics. 1981(898):230-242.
[288] Abarbanel H.D.I., Brown R., Sidorowich J.J., et al..The analysis of observed chaotic data in physical system. Rev. Mod.Phy..1993(4) : 1331- 1392.
[289] Theiler J. Estimating fractal dimension. JOSA. A. 1990( 6) :1055-1073.
[290] Fraser A. M., Swinney H. L.. Independent coordinates for strange attractors from mutual information. Physical Review A. 1986 (33):1134 - 1140.
[291] Grassberge P., Proeaeeia I..Measuringthestrangenessofstrnageattractors.Physic Review D.1983(9):189-208.
[292]Kennel, Mathew B., Brown R., et al..Determing embedding dimension for phase-space reconstruction using a geometrical construction. Physic review A. 1992(45):3403-3411.
[293]Broomhead D., King G. Extracting qualitative dynamics from experimental data. Physical review D. 1986(20):217-236.
[294]徐自励,王一扬,周激流.估计非线性时间序列嵌入延迟时间和延迟时间窗的C-C平均方法.四川大学学报.2007(1):151-155.
[295] Gao J.B., Zheng Z.M.. Local exponential divegrenee plot and optimal embedding of a chaotic time series. Physics Letters A.1993(181):153-158.
[296]陈铿,韩伯棠.混沌时间学历分析中的相空间重构技术综述.计算机科学.2005(4):67-70.
[297]赵永龙,常晓青,丁晶等.水文动力系统重建相空间嵌入维数研究.人民长江.1999(10): 43-45.
[298]Michael T., Rosenstein, James J.C., et al.. A practical method for calculating largest Lyapunov exponents from small data sets. Physica D:Nonlinear phenomena. 1993(5):117-134.
[299] Wolf A., Swift J.B., Swinney H.L., Vastano J.A.. Determining Lyapunov exponents from a time series.Physical D. 1985 ,16 (3) :285 - 317.
[300] Reggie Brown, Paul Bryant, Henry D.I. Abarbanel. Computing the Lyapunov Spectrum of a Dynamical System from Observed Time Series. Physical Review A. 1991(3):2787-2906.
[301]蒋海峰,马瑞军,魏学业等.一种基于小数据量得快速识别短时交通流混沌特性的方法.铁道学报.2006(4):63-66.
[302]姚凤阁,温红梅.银行业操作风险混沌特征识别-基于小数据量法的研究.中国管理科学.2010(11):264-268.
[303]卢宇,陈宇红,贺国光.应用改进型小数据量法计算交通流的最大Lyapunov指数.系统工程理论与实践.2007(1):85-90.
[304]丁晶,王文圣,赵永龙.长江日流量混沌变化特性研究.水科学进展.2003(7):412-416.
[305] Mosteller F., Tukey J. W.. Data Analysis and Regression. Addison-Wesley. 1977.
[306] Bendat J. B., Piersol A. G.. Measurement and Analysis of Random Data. John Wiley, New York.1966.
[307] Rissanen Y.. Stochastic Complexity in Statistical Inquiry. World Scientific, Singapore. 1992.
[308]Cellucci C.J., Albano A.M., Rapp P.E..Statistical Validation of Mutual Information Calculations: Comparisons of Alternative Numerical Algorithms. Physical Review E. 2005 (71) :1-14.
[309]吕小青,曹彪,曾敏等.确定延迟时间互信息法的一种算法.计算物理.2006(3):184-188.
[310]马红光,李夕海,王国华等.相空间重构中嵌入维和时间延迟的选择.西安交通大学学报.2004(4):335-338.
[311]Viswanath D.. The fractal property of the Lorenz attractor. Physical review D: Nonlinear Phenomena. 2004 (190)115-128.
[312] Hegger R., Kantz H., Schreiber T.. Practical implementation of nonlinear time series methods: The TISEAN package, CHAOS.1999 (9): 413-435.
[313] Kantz H.. A robust method to estimate the maximal Lyapunov exponent of a time series. Phys. Lett. 1994 (77): A 185.
[314]陈予恕.非线性振动.北京:高等教育出版社.2002,12.
[315]王海燕,卢山.非线性时间序列分析及其应用.北京:科学出版社.2006,11.