恒定有压扩散流局部非稳态流动研究
|
摘要
扩散流是水工建筑物中常见的水流现象,如抽水蓄能电站上/下水库的进/出水口、有压泄水隧洞的出水口等的水流运动大多属此类流动。在一定边界和较大扩散角条件下,扩散流在边壁处将发生流动分离,一旦扩散水流与边界分离,近边界处将发生漩涡运动;扩散流的主流部分,在漩涡的不稳定位移或其它微小的扰动下,将形成不稳定的横向摆动运动。在恒定流条件下,扩散段内主流部分发生横向摆动运动的现象,我们称之为局部非稳态流动现象。由于局部非稳态流动发生的区域并不局限在边界附近,因此,对水工构造物可能产生的不利影响就较为突出。然而,相对其重要性而言,现今对局部非稳态流动现象的研究,却极为有限。
针对扩散段中存在的局部非稳态流动现象,本文通过模型试验、数值模拟以及理论分析,对其形成条件、产生机理、运动规律等问题进行了较为系统的研究。
(1)某抽水蓄能电站上水库进/出水口模型试验研究。结合某抽水蓄能电站上水库进/出水口物理模型试验,采用ADV三维流速仪,对抽水工况下进/出水口拦污栅处的流速进行测量,同时采用频谱分析,对数据资料进行分析,探讨各点流速的特征,揭示了该有压扩散流中存在局部非稳态流动现象。
(2)有压扩散段局部非稳态流动专门试验研究。对不同平面扩散角的有压扩散段进行试验,研究在一定边界条件下扩散段内产生局部非稳态流动现象的运动特征。应用壁面丝线流动显示技术,对其流动过程进行观测研究;应用ADV三维流速仪记录特征点的流速历时,对测点流速进行分析。探讨局部非稳态流动的运动规律、产生机理及形成条件。
(3)有压扩散段局部非稳态流动数值模拟研究。利用大涡模拟技术,系统研究了有压扩散段内整个流场的变化和发展情况,并结合谱分析方法对恒定有压扩散段中的水流流动特性进行分析,并与试验结果进行比较。
(4)有压扩散段局部非稳态流动理论分析。对试验结果和数值模拟结果进行理论分析,结果表明,一定边界条件下扩散流主流将与边壁分离,并在壁面附近形成不稳定的漩涡区。在这些不稳定漩涡的影响下,流体的主流部分将随着漩涡主体的不规则运动而发生摆动运动,即出现恒定流中的局部非稳态现象。也就是说在有压扩散流中,不仅存在随机的水流脉动,还存在由大涡运移引起的低频拟序的主流整体摆动运动,一般情况下,主流的摆动运动和水流的随机脉动相比具有较低的主频率和较大的摆动幅值,并遵循一定的规律性。
Divergent current is one common flow phenomenon in hydraulic structures, for example the flow movement in intakes/outlets of a pumped-storage power station, outlets of pressure discharge tunnel and so on. Under given boundary condition, flow separation would occur near the boundary. Once the flow separates from the boundary vortex would appear, and under the action of unsteady displacement of the vortex or other little disturbance the major flow would develop to unstable lateral swings. The phenomenon of main flow swinging laterally in divergent segment is called local unsteady-state flow. Due to the region of local unsteady-state flow being not localized near the boundary, the harmful effects of the flow to structures would be evident. However, compared with its importance, the study on the local unsteady-state flow is scarce.
The forming condition, forming mechanism and movement rules of the phonomenon of local unstable-state flow in divergent segment are systemically studied in this paper, according to physical test, numerical simulation and theoretical analysis.
(1) The model experiment study on intakes/outlets of one pumped-storage power station. In the model test of intakes/outlets of one pumped-storage power station, ADV 3-D velocity metre is used to measure the velocity at the outlets under the pumping condition, and through frequency spectrum analysis of data gained, the velocity characters of each point is discussed, the phenomenon of local unsteady-state flow existing in the pressure divergent flow is revealed.
(2) The experimental study on local unsteady-state flow in pressure divergent segment. Based on the pressure divergent segment experiment of different divergent angle, the motion characters of local unsteady-state flow appeared in divergent segment under given boundary condition is studied. The flow pattern is observed by silk thread affixed to the wall, and the velocity duration course of characteristic points recorded by ADV 3-D velocity metre is analysed. The forming condition, forming mechanism and movement rules of the local unsteady-state flow are discussed.
(3) The numerical simulation study on local unsteady-state flow in pressure divergent segment. The movement and development of whole flow field in pressure divergent segment are given through large eddy simulation, flow characters are analysed by spectrum analysis, and the results are compared with the experiment result.
(4) The theoretical analysis of local unsteady-state flow in pressure divergent segment. The results of theoretical analysis on results of experiment and numerical simulation show the main flow of divergent flow would separate from the boundary, and form the unstable vortex region near the boundary. Under the effect of these unstable vortexes, the main flow would swing with the irregular movement of vortex, the phenomenon is namely local unsteady flow in stable flow. In other words, there are low-frequency and pseodu-order unstable swings of main flow, which is caused by the transport and motion of large eddy, besides stochastic flow fluctuation. In common cases, compared with the flow stochastic fluctuation, the swing of main flow shows the lower-frequency and bigger swing range and follows some regularity.
针对扩散段中存在的局部非稳态流动现象,本文通过模型试验、数值模拟以及理论分析,对其形成条件、产生机理、运动规律等问题进行了较为系统的研究。
(1)某抽水蓄能电站上水库进/出水口模型试验研究。结合某抽水蓄能电站上水库进/出水口物理模型试验,采用ADV三维流速仪,对抽水工况下进/出水口拦污栅处的流速进行测量,同时采用频谱分析,对数据资料进行分析,探讨各点流速的特征,揭示了该有压扩散流中存在局部非稳态流动现象。
(2)有压扩散段局部非稳态流动专门试验研究。对不同平面扩散角的有压扩散段进行试验,研究在一定边界条件下扩散段内产生局部非稳态流动现象的运动特征。应用壁面丝线流动显示技术,对其流动过程进行观测研究;应用ADV三维流速仪记录特征点的流速历时,对测点流速进行分析。探讨局部非稳态流动的运动规律、产生机理及形成条件。
(3)有压扩散段局部非稳态流动数值模拟研究。利用大涡模拟技术,系统研究了有压扩散段内整个流场的变化和发展情况,并结合谱分析方法对恒定有压扩散段中的水流流动特性进行分析,并与试验结果进行比较。
(4)有压扩散段局部非稳态流动理论分析。对试验结果和数值模拟结果进行理论分析,结果表明,一定边界条件下扩散流主流将与边壁分离,并在壁面附近形成不稳定的漩涡区。在这些不稳定漩涡的影响下,流体的主流部分将随着漩涡主体的不规则运动而发生摆动运动,即出现恒定流中的局部非稳态现象。也就是说在有压扩散流中,不仅存在随机的水流脉动,还存在由大涡运移引起的低频拟序的主流整体摆动运动,一般情况下,主流的摆动运动和水流的随机脉动相比具有较低的主频率和较大的摆动幅值,并遵循一定的规律性。
Divergent current is one common flow phenomenon in hydraulic structures, for example the flow movement in intakes/outlets of a pumped-storage power station, outlets of pressure discharge tunnel and so on. Under given boundary condition, flow separation would occur near the boundary. Once the flow separates from the boundary vortex would appear, and under the action of unsteady displacement of the vortex or other little disturbance the major flow would develop to unstable lateral swings. The phenomenon of main flow swinging laterally in divergent segment is called local unsteady-state flow. Due to the region of local unsteady-state flow being not localized near the boundary, the harmful effects of the flow to structures would be evident. However, compared with its importance, the study on the local unsteady-state flow is scarce.
The forming condition, forming mechanism and movement rules of the phonomenon of local unstable-state flow in divergent segment are systemically studied in this paper, according to physical test, numerical simulation and theoretical analysis.
(1) The model experiment study on intakes/outlets of one pumped-storage power station. In the model test of intakes/outlets of one pumped-storage power station, ADV 3-D velocity metre is used to measure the velocity at the outlets under the pumping condition, and through frequency spectrum analysis of data gained, the velocity characters of each point is discussed, the phenomenon of local unsteady-state flow existing in the pressure divergent flow is revealed.
(2) The experimental study on local unsteady-state flow in pressure divergent segment. Based on the pressure divergent segment experiment of different divergent angle, the motion characters of local unsteady-state flow appeared in divergent segment under given boundary condition is studied. The flow pattern is observed by silk thread affixed to the wall, and the velocity duration course of characteristic points recorded by ADV 3-D velocity metre is analysed. The forming condition, forming mechanism and movement rules of the local unsteady-state flow are discussed.
(3) The numerical simulation study on local unsteady-state flow in pressure divergent segment. The movement and development of whole flow field in pressure divergent segment are given through large eddy simulation, flow characters are analysed by spectrum analysis, and the results are compared with the experiment result.
(4) The theoretical analysis of local unsteady-state flow in pressure divergent segment. The results of theoretical analysis on results of experiment and numerical simulation show the main flow of divergent flow would separate from the boundary, and form the unstable vortex region near the boundary. Under the effect of these unstable vortexes, the main flow would swing with the irregular movement of vortex, the phenomenon is namely local unsteady flow in stable flow. In other words, there are low-frequency and pseodu-order unstable swings of main flow, which is caused by the transport and motion of large eddy, besides stochastic flow fluctuation. In common cases, compared with the flow stochastic fluctuation, the swing of main flow shows the lower-frequency and bigger swing range and follows some regularity.
引文
[1] 夏雪湔,工程分离流动力学,北京:北京航空航天大学出版社,1991.5
[2] H.史里希廷著,边界层理论,北京:科学出版社,1991.2
[3] Schlichting, H., Boundary layer theory, McGraw-Hill Book Company, 1979
[4] 夏震寰,现代水力学,(三)紊动力学,北京:高等教育出版社,1990.12
[5] 天津大学水力学教研室编,水力学[M].北京:人民教育出版社,1980.
[6] W. 考夫曼,工程流体力学[M]. 北京:科学技术出版社,1957.
[7] 华绍曾,杨学宁编. 实用流体阻力手册[M],北京:国防工业出版社,1985.
[8] D.J. 特里顿,物理流体力学[M].北京:科学出版社,1986.
[9] 周建军,王连祥,林秉南. 明渠不恒定分离流数值模拟及实验验证[J],水动力学研究与进展,1993.8(1): 28-34.
[10] 吕文堂,刘忠潮. 用 K-ε-A 及用 K-ε-E 紊流模型对二维突扩分离流的数值模拟[J],西北水资源与水工程,1994(2): 1～9.
[11] 刘沛清,邓学蓥. 明渠中跌坎后突扩分离流数值研究[J],力学学报,1998,30(1): 9-19.
[12] 刘沛清,工程中的一些复杂流动试验研究与数值模拟,北京航空航天大学,博士学位论文,1997.3
[13] 齐鄂荣,李炜等. 二维后向台阶流的实验研究[C]. 中国环境水力学,2004: 109-117.
[14] 黄明海,齐鄂荣,李炜,PIV 在二维后向台阶流实验研究中的应用,武汉大学学报(工学版),2005.38(2): 35-38
[15] 齐鄂荣,黄明海,李炜等,应用PIV进行二维后向台阶流流动特性的研究(1)二维后向台阶流的旋涡结构的研究,水动力学研究与进展,2004.19(4): 525-532
[16] 齐鄂荣,黄明海,李炜等,应用PIV进行二维后向台阶流流动特性的研究(2)二维后向台阶流的旋涡结构的研究,水动力学研究与进展,2004.19(4): 523-539
[17] 王兵,张会强,王希麟等,不同亚格子模式在后台阶紊流流大涡模拟中的应用,工程热物理学报,2003.24(1): 157-159
[18] 王兵,张会强,王希麟等,后台阶流动再附着过程的大涡模拟研究,应用力学学报,2004.21(3): 17-20
[19] 刘应征, 朴英守, 成亨镇,后台阶分离再附紊流流动的实验研究,上海交通大学学报,2005.39(5): 810-813
[20] 王小华,樊洪明,何钟怡,后台阶流动的数值模拟,计算力学学报,2003.20(3): 361-365
[21] 王小华,鞠硕华,朱文芳. 突扩流的数值模拟[J],低温建筑技术,2003(1): 59-60.
[22] 刘有军,平面突扩流动非稳定的大涡模拟. 计算力学学报[J],1998.15(2): 186-191.
[23] 黄民,匡震邦. 渐缩(扩)直圆管中的发展流动[J],水动力学研究与进展,1996.114(4): 429-438.
[24] 齐清兰,薛运田,张力霆. 有压泄水洞淹没出流出口扩散的水流特征[J],西北水电,2004(4): 53-54.
[25] 王治祥. 陡槽水力扩散特性,西北水资源与水工程[J],1990(4): 23~26.
[26] 徐元利,徐元春,梁兴. Fluent 软件在圆柱绕流模拟中的应用[J],水利电力机械,2005.27(1): 39-41.
[27] 刘松,符松. 串连双圆柱绕流问题的数值模拟[J],计算力学学报,2000, 17(3): 260-266.
[28] Simpson, R.L. Turbulent boundary-layer separation, Ann. Rev. Fluid Mech. 1989,21: 205-234:
[29] 童兵,祝兵,周本宽. 方柱绕流的数值模拟[J],力学季刊,2002, 23(1): 77-81.
[30] 童兵,紊流的三维大涡模拟,西南交通大学,博士学位论文,2001.10
[31] 张柏山,吕志咏,祝立国. 绕丁坝流动结构实验研究[J],北京航空航天大学学报,2002.28(5): 585-588.
[32] 蒋绿林,高玉明,紊流模型在平板边界层分离流动中的应用,江苏石油化工学院学报,2001.13(3): 1-4.
[33] 王小华,何钟怡. 二并列方柱绕流的大涡模拟[J],哈尔滨建筑大学学报,2002.35(2): 49-53.
[34] 魏英杰,朱蒙生,何钟怡. 并列方柱绕流的大涡模拟及频谱分析,应用数学和力学[J],2004.25(8): 824-830.
[35] 张爱社,张陵. 等边布置三圆柱绕流的数值模拟[J],应用力学学报,2003.20(1): 31-36.
[36] 王广超,施保昌,邓滨. 非均匀格子 Boltzmann 方法模拟方柱绕流[J],应用基础与工程科学学报,2003.11(4): 335-344.
[37] Sarpkaya, T. and Schoaff, R.L., Inviscid model of two-dimensional vortex shedding by a circular cylinder, AIAA Journal, 1979, 17: 1193-1201
[38] Zdravkovich, M.M., Review of flow interference between two circular cylindersin various arrangements, Transaction of the ASME Journal of Fluid Engineering, 1977: 618-633
[39] Atsushi Okajima, Flows around two tandem circular cylinders at very high Reynolds Numbers, Bulletin of the JSME. 1979, 22(166): 504-511
[40] 叶春明,吴文权. 数值模拟圆柱绕流旋涡生成、分离演化[J],华东工业大学学报,1995.17(4): 25-30.
[41] 苏铭德,康钦军. 亚临界雷诺数下圆柱绕流的大涡模拟[J],力学学报,1999.31(1): 100-105.
[42] 陈文曲,任安禄,李广望. 串列双圆柱绕流下游圆柱两自由度涡致振动研究[J],力学学报,2004.36(6): 732-738.
[43] Gerrard, J.H., The machanics of the formation region of vortices behind bluff bodies, Fluid Mech. 1966, 25: 401-413
[44] Bearman, P.W., and Trueman, D.M., An investigation of the flow around rectangular cylinders, Aero. Quart. 1972, 23: 229-237
[45] Roshko, A., On the drag and shedding frequency of two-dimensional bluff bodies, NACA TN 3169.
[46] Xia, X.J. and Huang Zheng, Vortex structure in the near wake of the axisymmetric bodies, Proceedings of the third Asian Congress of Fluid Mechanics, Tokyo, 1986
[47] Xia, X.J., and Bearman, P.W., An experimental investigation of the wake of an axisymmetric body with a slanted base, Aero. Quart. 1983, 34
[48] Achenbach, E., Vortex shedding from spheres, Fluid mech. 1974, 62.
[49] 王兵,张会强,虞建丰. 后台阶分离流动中大涡结构演变的数值模拟[J],力学季刊,2003, 24(2): 166-173.
[50] 刘焕芳. 弯道水流的分离[J],武汉水利电力学院学报,1989, 22(6): 50-55.
[51] 刘月琴. 弯道水流紊动特性[J],华南理工大学学报(自然科学版),2003,第 31 卷(12): 89-93.
[52] 王兴奎. 明渠水流的紊动特性[J]. 水力发电学报 1993(4): 12-21.
[53] Anwar H O. Turbulent structure in a river bend[J]. Journal of Hydraulic Engineering, 1986,112(8): 657-669.
[54] 董志勇,须清华. 鹅颈型管道三维水流结构研究[J],水动力学研究与进展,2002.17(1): 25-31.
[55] 窦国仁,紊流力学[M],北京:高等教育出版社,1985.
[56] 张兆顺,崔桂香,许春晓. 湍流理论与模拟[M],北京:清华大学出版社,2005.
[57] 章梓雄,粘性流体力学[M],北京:清华大学出版社,2002.
[58] 闻德逊,工程流体力学[M],北京:高等教育出版社,1990.
[59] L. 普朗特,流体力学概论[M],北京:科学出版社,1987.
[60] J.O. Hinze,Turbulence.McGraw-Hill Publishing Co.,New York, 1975.
[61] P. Spalart and S. Allmaras. ,A one-equation turbulence model for aerodynamic flows.,Technical Report AIAA-92-0439,American Institute of Aeronautics and Astronautics,1992.
[62] W. P. Jones and J. H. Whitelaw,Calculation Methods for Reacting Turbulent Flows: A Review.Combust. Flame,48:1-26,1982.
[63] B. E. Launder, G. J. Reece, and W. Rodi,Progress in the Development of a Reynolds-Stress Turbulence Closure,J. Fluid Mech.,April 197568(3): 537-566.
[64] V. Yakhot and S. A. Orszag,Renormalization Group Analysis of Turbulence,I. Basic Thery. Journal of Scientific Computing,19861(1): 1-51
[65] D. Choudhury , Introduction to the Renormalization Group Method and Turbulence Modeling.,Fluent Inc. Technical Memorandum TM-107,1993.
[66] T.-H. Shih, W. W. Liou, A. Shabbir, and J. Zhu,A New k ?εEddy-Viscosity Model for High Reynolds Number Turbulent Flows - Model Development and Validation,Computers Fluids, 1995, 24(3): 227-238,.
[67] W. C. Reynolds,Fundamentals of turbulence for turbulence modeling and simulation,Lecture Notes for Von Karman Institute Agard Report No,755,1987.
[68] S.-E. Kim, D. Choudhury, and B. Patel,Computations of Complex Turbulent Flows Using the Commercial Code FLUENT , In Proceedings of the ICASE/LaRC/AFOSR Symposium on Modeling Complex Turbulent Flows ,Hampton,Virginia,1997.
[69] M. M. Gibson and B. E. Launder,Ground Effects on Pressure Fluctuations in the Atmospheric Boundary Layer,J. Fluid Mech.,1978, 86: 491-511.
[70] B. E. Launder,Second-Moment Closure: Presentand Future,Inter. J. Heat Fluid Flow,1989, 10(4): 282-300.
[71] Smagorinsky, J., General circulation experiments with the primitive equations. I. The basic experiment [J]. Monthly. Weather. Review., 1963,91(3): 99-104
[72] Dearforff, J.W., A numerical study of three-dimensional turbulent channel flow at large Reynolds number, J. Fluid Mech., 1970. 41 (2): 453-480.
[72] Schumann, U., Results of a numerical simulation of turbulent channel flow. Inint’1. Meeting on Reactor Heat Transfer , 1973, 230-251,
[74] Schumann, U., Subgrid scale modeling for finite difference simulations of turbulent flows in plane channel and annuli. J. Comp. Phys., 1975, 18: 376-404,
[75] Cain, A.B., Reynold, W.C., and Ferziger, J.H., Simulation of the transition and early turbulence regions of a mixer layer. Report TF-14. Department of Mech. Engng., Sranford Univ., Stanford, CA., 1981
[76] Moin, P. and Kim, J., Numerical investigation of turbulent channel flow. J Fluid Mech. 1982, 118: 341-377
[77] McMillan, O.J., and Ferziger, J. H., Direct testing of subgrid scale models. AIAA Journal, 1979, 17: 1340-1354
[78] McMillan, O.J., Ferziger, J. H., and Rogallo, R.S., Tests of new subgrid scale models in strained turbulence. AIAA paper 80: 1339-1344, 1980
[79] Yoshizawa, A. and Horiuti, K., Finite element analysis of two-dimensional non-linear transient water waves, Applied Ocean Research, 1994,Vol.16: 363-372
[80] Yoshizawa, A., Tsubokura, M., Kobayashi, T. and Taniguchi, N., Modeling of the dynamic subgrid-scale viscosity in large eddy simulation. Phys. Fluids. 1996, 8: 2254-2256
[81] Horiuti, K., A proper velocity scale for modeling subgrid-scale eddy viscosities in large eddy simulation. Phy. Fluids A, 1989, Vol.1(2), Feb.: 426-428,
[82] Lilly, D.K., A proposed modification of the Fermano subgrid-scale closure method. Phys. Fluids A,1992, 4(3), March: 633-635
[83] Ghosal, S., Lund, T.S., Moin, P., and Akselvoll, K., A dynamic localization model for large-eddy simulation of turbulent flows. J. Fluid Mech., 1995, 286: 229-255,
[84] Zhang, Y. and Street, R.L., and Koseff, J.R., A dynamic mixed subgrid scale model and its application to turbulent recirculating flows, Phy. of Fluids A (Fluid Dynamics), 1993(5): 3186-3196.
[85] Yuan, M., Song, C.C.S., He, J.M., Numerical analysis of turbulent flow in a two dimensional non-symmetric plane-wall diffuser, Fluids Eng., ASME, 1991, 113: 210-215
[86] Zhao, Q., Tanimoto, K., Numerical simulation of breaking waves by Large eddy simulation and VOF method. Proc. 26th Int. on coastal engineering, ASCE, Copenhagen, 1998, 1: 892-905
[87] Fatica, M., et al, Validation of large-eddy simulation in a plane asymmetrical diffuser. Annual brief center for turbulence research, 22
[88] Prasad, A., Williamson, C.H.K., The instability of the shear layer separating from a bluff body, JFM, 1997: 333-375
[89] Mittal, R., Moin P. Suitability of upwind-biased finite difference schemes for large-eddy simulation of turbulent flows. AIAA. 1997, 35.
[90] Karvchenko A.G., B-spline method and zonal grids for simulation of complex turbulence flows. Computational physics, 1999: 151~757.
[91] Karvchenko, A.G., Moin, P., Numerical studies of flow over a circular cylinder at Re=3900, Physics of Fluids, 2000.
[92] Bardina, J., Ferziger, J.H., Improved subgrid scale models for large-eddy simulation. AIAA paper, 1980: 80-1375
[93] Spezial, C.G., Subgrid scale stress models for the large-eddy simulation of rotating turbulent flow. Geophs. & Astrophys. Fluid Dynamics, 1985, 33: 199-222
[94] 苏铭德,黄诉逸,计算流体力学基础,北京:清华大学出版社,1997
[95] Germano, M., A dynamic subgrid-scale eddy viscosity model. Physics of fluid, 1991, 3.
[96] Yoshizawa, A. andHoriuti, K., A statistically-derived subgrid-scale kinetic energy model for the large-eddy simulation of turbulent flows. Phys. Soc Jpn, 1985, 54: 2834-2839
[97] 金忠青,N-S 方程的数值解法,南京:河海大学出版社,1992.
[98] 王福军,计算流体动力学分析—CFD 软件原理及应用,北京:清华大学出版社,2004
[99] F. 杜斯特,A. 梅林,J. H. 怀特洛著. 激光多普勒流速技术的原理和实践[M],北京:科学出版社,1992.
[100] 周家俞,刘亚辉等.泥沙粒径与水流紊动关系试验研究[J].水动力学研究与进展,2006,21(5): 679-684.
[101] 林鹏,陈立.低含沙水流紊动结构的实验研究[J]. 水动力学研究与进展, 2003,18(2): 209-216.
[102] 金永君,光多普勒效应及应用,现代物理知识,2003,15(4): 14-15
[103] 刘春晶,李丹勋等,过渡区动床明渠流的流速分布,水科学进展,2006,17(1): 49-54
[104] 邓安军,陈立等,紊动强度沿垂线分布规律的分析,泥沙研究,2001,5:33-36
[105] 应怀樵,波形和频谱分析与随机数据处理[M]. 北京:中国铁道出版社,1983.
[106] 俞一彪,孙兵,数字信号处理:理论与应用,南京:东南大学出版社,2005.8
[107] W. 梅尔兹科奇著,流动显示[M],北京:科学出版社,1991.
[108] 中国人民解放军总装备部军事训练教材编辑工作委员会,军事训练教材编辑工作委编,流动显示技术[M],北京:国防工业出版社,2002.
[109] 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.
[110] H.K.Versteeg, W. Malalasekera. An introduction to computational fluid dynamics[M]. New York: Longman Scientific & Technical Press. 1995.
[111] I. Drianski. A simple boundary condition for unbounded hyperbolic flows[J]. Journal of Computational Physics. 1976, 21 (5): 251-269.
[112] H. Wengle, A. Huppertz, G. Barwoff, et al. Numerical simulation (DNS and LES) of manipulated turbulent boundary layer flow over a surface-mounted fence[J]. European Journal of Mechanics B/Fluids, 2001, 20 (1): 25-46.
[2] H.史里希廷著,边界层理论,北京:科学出版社,1991.2
[3] Schlichting, H., Boundary layer theory, McGraw-Hill Book Company, 1979
[4] 夏震寰,现代水力学,(三)紊动力学,北京:高等教育出版社,1990.12
[5] 天津大学水力学教研室编,水力学[M].北京:人民教育出版社,1980.
[6] W. 考夫曼,工程流体力学[M]. 北京:科学技术出版社,1957.
[7] 华绍曾,杨学宁编. 实用流体阻力手册[M],北京:国防工业出版社,1985.
[8] D.J. 特里顿,物理流体力学[M].北京:科学出版社,1986.
[9] 周建军,王连祥,林秉南. 明渠不恒定分离流数值模拟及实验验证[J],水动力学研究与进展,1993.8(1): 28-34.
[10] 吕文堂,刘忠潮. 用 K-ε-A 及用 K-ε-E 紊流模型对二维突扩分离流的数值模拟[J],西北水资源与水工程,1994(2): 1～9.
[11] 刘沛清,邓学蓥. 明渠中跌坎后突扩分离流数值研究[J],力学学报,1998,30(1): 9-19.
[12] 刘沛清,工程中的一些复杂流动试验研究与数值模拟,北京航空航天大学,博士学位论文,1997.3
[13] 齐鄂荣,李炜等. 二维后向台阶流的实验研究[C]. 中国环境水力学,2004: 109-117.
[14] 黄明海,齐鄂荣,李炜,PIV 在二维后向台阶流实验研究中的应用,武汉大学学报(工学版),2005.38(2): 35-38
[15] 齐鄂荣,黄明海,李炜等,应用PIV进行二维后向台阶流流动特性的研究(1)二维后向台阶流的旋涡结构的研究,水动力学研究与进展,2004.19(4): 525-532
[16] 齐鄂荣,黄明海,李炜等,应用PIV进行二维后向台阶流流动特性的研究(2)二维后向台阶流的旋涡结构的研究,水动力学研究与进展,2004.19(4): 523-539
[17] 王兵,张会强,王希麟等,不同亚格子模式在后台阶紊流流大涡模拟中的应用,工程热物理学报,2003.24(1): 157-159
[18] 王兵,张会强,王希麟等,后台阶流动再附着过程的大涡模拟研究,应用力学学报,2004.21(3): 17-20
[19] 刘应征, 朴英守, 成亨镇,后台阶分离再附紊流流动的实验研究,上海交通大学学报,2005.39(5): 810-813
[20] 王小华,樊洪明,何钟怡,后台阶流动的数值模拟,计算力学学报,2003.20(3): 361-365
[21] 王小华,鞠硕华,朱文芳. 突扩流的数值模拟[J],低温建筑技术,2003(1): 59-60.
[22] 刘有军,平面突扩流动非稳定的大涡模拟. 计算力学学报[J],1998.15(2): 186-191.
[23] 黄民,匡震邦. 渐缩(扩)直圆管中的发展流动[J],水动力学研究与进展,1996.114(4): 429-438.
[24] 齐清兰,薛运田,张力霆. 有压泄水洞淹没出流出口扩散的水流特征[J],西北水电,2004(4): 53-54.
[25] 王治祥. 陡槽水力扩散特性,西北水资源与水工程[J],1990(4): 23~26.
[26] 徐元利,徐元春,梁兴. Fluent 软件在圆柱绕流模拟中的应用[J],水利电力机械,2005.27(1): 39-41.
[27] 刘松,符松. 串连双圆柱绕流问题的数值模拟[J],计算力学学报,2000, 17(3): 260-266.
[28] Simpson, R.L. Turbulent boundary-layer separation, Ann. Rev. Fluid Mech. 1989,21: 205-234:
[29] 童兵,祝兵,周本宽. 方柱绕流的数值模拟[J],力学季刊,2002, 23(1): 77-81.
[30] 童兵,紊流的三维大涡模拟,西南交通大学,博士学位论文,2001.10
[31] 张柏山,吕志咏,祝立国. 绕丁坝流动结构实验研究[J],北京航空航天大学学报,2002.28(5): 585-588.
[32] 蒋绿林,高玉明,紊流模型在平板边界层分离流动中的应用,江苏石油化工学院学报,2001.13(3): 1-4.
[33] 王小华,何钟怡. 二并列方柱绕流的大涡模拟[J],哈尔滨建筑大学学报,2002.35(2): 49-53.
[34] 魏英杰,朱蒙生,何钟怡. 并列方柱绕流的大涡模拟及频谱分析,应用数学和力学[J],2004.25(8): 824-830.
[35] 张爱社,张陵. 等边布置三圆柱绕流的数值模拟[J],应用力学学报,2003.20(1): 31-36.
[36] 王广超,施保昌,邓滨. 非均匀格子 Boltzmann 方法模拟方柱绕流[J],应用基础与工程科学学报,2003.11(4): 335-344.
[37] Sarpkaya, T. and Schoaff, R.L., Inviscid model of two-dimensional vortex shedding by a circular cylinder, AIAA Journal, 1979, 17: 1193-1201
[38] Zdravkovich, M.M., Review of flow interference between two circular cylindersin various arrangements, Transaction of the ASME Journal of Fluid Engineering, 1977: 618-633
[39] Atsushi Okajima, Flows around two tandem circular cylinders at very high Reynolds Numbers, Bulletin of the JSME. 1979, 22(166): 504-511
[40] 叶春明,吴文权. 数值模拟圆柱绕流旋涡生成、分离演化[J],华东工业大学学报,1995.17(4): 25-30.
[41] 苏铭德,康钦军. 亚临界雷诺数下圆柱绕流的大涡模拟[J],力学学报,1999.31(1): 100-105.
[42] 陈文曲,任安禄,李广望. 串列双圆柱绕流下游圆柱两自由度涡致振动研究[J],力学学报,2004.36(6): 732-738.
[43] Gerrard, J.H., The machanics of the formation region of vortices behind bluff bodies, Fluid Mech. 1966, 25: 401-413
[44] Bearman, P.W., and Trueman, D.M., An investigation of the flow around rectangular cylinders, Aero. Quart. 1972, 23: 229-237
[45] Roshko, A., On the drag and shedding frequency of two-dimensional bluff bodies, NACA TN 3169.
[46] Xia, X.J. and Huang Zheng, Vortex structure in the near wake of the axisymmetric bodies, Proceedings of the third Asian Congress of Fluid Mechanics, Tokyo, 1986
[47] Xia, X.J., and Bearman, P.W., An experimental investigation of the wake of an axisymmetric body with a slanted base, Aero. Quart. 1983, 34
[48] Achenbach, E., Vortex shedding from spheres, Fluid mech. 1974, 62.
[49] 王兵,张会强,虞建丰. 后台阶分离流动中大涡结构演变的数值模拟[J],力学季刊,2003, 24(2): 166-173.
[50] 刘焕芳. 弯道水流的分离[J],武汉水利电力学院学报,1989, 22(6): 50-55.
[51] 刘月琴. 弯道水流紊动特性[J],华南理工大学学报(自然科学版),2003,第 31 卷(12): 89-93.
[52] 王兴奎. 明渠水流的紊动特性[J]. 水力发电学报 1993(4): 12-21.
[53] Anwar H O. Turbulent structure in a river bend[J]. Journal of Hydraulic Engineering, 1986,112(8): 657-669.
[54] 董志勇,须清华. 鹅颈型管道三维水流结构研究[J],水动力学研究与进展,2002.17(1): 25-31.
[55] 窦国仁,紊流力学[M],北京:高等教育出版社,1985.
[56] 张兆顺,崔桂香,许春晓. 湍流理论与模拟[M],北京:清华大学出版社,2005.
[57] 章梓雄,粘性流体力学[M],北京:清华大学出版社,2002.
[58] 闻德逊,工程流体力学[M],北京:高等教育出版社,1990.
[59] L. 普朗特,流体力学概论[M],北京:科学出版社,1987.
[60] J.O. Hinze,Turbulence.McGraw-Hill Publishing Co.,New York, 1975.
[61] P. Spalart and S. Allmaras. ,A one-equation turbulence model for aerodynamic flows.,Technical Report AIAA-92-0439,American Institute of Aeronautics and Astronautics,1992.
[62] W. P. Jones and J. H. Whitelaw,Calculation Methods for Reacting Turbulent Flows: A Review.Combust. Flame,48:1-26,1982.
[63] B. E. Launder, G. J. Reece, and W. Rodi,Progress in the Development of a Reynolds-Stress Turbulence Closure,J. Fluid Mech.,April 197568(3): 537-566.
[64] V. Yakhot and S. A. Orszag,Renormalization Group Analysis of Turbulence,I. Basic Thery. Journal of Scientific Computing,19861(1): 1-51
[65] D. Choudhury , Introduction to the Renormalization Group Method and Turbulence Modeling.,Fluent Inc. Technical Memorandum TM-107,1993.
[66] T.-H. Shih, W. W. Liou, A. Shabbir, and J. Zhu,A New k ?εEddy-Viscosity Model for High Reynolds Number Turbulent Flows - Model Development and Validation,Computers Fluids, 1995, 24(3): 227-238,.
[67] W. C. Reynolds,Fundamentals of turbulence for turbulence modeling and simulation,Lecture Notes for Von Karman Institute Agard Report No,755,1987.
[68] S.-E. Kim, D. Choudhury, and B. Patel,Computations of Complex Turbulent Flows Using the Commercial Code FLUENT , In Proceedings of the ICASE/LaRC/AFOSR Symposium on Modeling Complex Turbulent Flows ,Hampton,Virginia,1997.
[69] M. M. Gibson and B. E. Launder,Ground Effects on Pressure Fluctuations in the Atmospheric Boundary Layer,J. Fluid Mech.,1978, 86: 491-511.
[70] B. E. Launder,Second-Moment Closure: Presentand Future,Inter. J. Heat Fluid Flow,1989, 10(4): 282-300.
[71] Smagorinsky, J., General circulation experiments with the primitive equations. I. The basic experiment [J]. Monthly. Weather. Review., 1963,91(3): 99-104
[72] Dearforff, J.W., A numerical study of three-dimensional turbulent channel flow at large Reynolds number, J. Fluid Mech., 1970. 41 (2): 453-480.
[72] Schumann, U., Results of a numerical simulation of turbulent channel flow. Inint’1. Meeting on Reactor Heat Transfer , 1973, 230-251,
[74] Schumann, U., Subgrid scale modeling for finite difference simulations of turbulent flows in plane channel and annuli. J. Comp. Phys., 1975, 18: 376-404,
[75] Cain, A.B., Reynold, W.C., and Ferziger, J.H., Simulation of the transition and early turbulence regions of a mixer layer. Report TF-14. Department of Mech. Engng., Sranford Univ., Stanford, CA., 1981
[76] Moin, P. and Kim, J., Numerical investigation of turbulent channel flow. J Fluid Mech. 1982, 118: 341-377
[77] McMillan, O.J., and Ferziger, J. H., Direct testing of subgrid scale models. AIAA Journal, 1979, 17: 1340-1354
[78] McMillan, O.J., Ferziger, J. H., and Rogallo, R.S., Tests of new subgrid scale models in strained turbulence. AIAA paper 80: 1339-1344, 1980
[79] Yoshizawa, A. and Horiuti, K., Finite element analysis of two-dimensional non-linear transient water waves, Applied Ocean Research, 1994,Vol.16: 363-372
[80] Yoshizawa, A., Tsubokura, M., Kobayashi, T. and Taniguchi, N., Modeling of the dynamic subgrid-scale viscosity in large eddy simulation. Phys. Fluids. 1996, 8: 2254-2256
[81] Horiuti, K., A proper velocity scale for modeling subgrid-scale eddy viscosities in large eddy simulation. Phy. Fluids A, 1989, Vol.1(2), Feb.: 426-428,
[82] Lilly, D.K., A proposed modification of the Fermano subgrid-scale closure method. Phys. Fluids A,1992, 4(3), March: 633-635
[83] Ghosal, S., Lund, T.S., Moin, P., and Akselvoll, K., A dynamic localization model for large-eddy simulation of turbulent flows. J. Fluid Mech., 1995, 286: 229-255,
[84] Zhang, Y. and Street, R.L., and Koseff, J.R., A dynamic mixed subgrid scale model and its application to turbulent recirculating flows, Phy. of Fluids A (Fluid Dynamics), 1993(5): 3186-3196.
[85] Yuan, M., Song, C.C.S., He, J.M., Numerical analysis of turbulent flow in a two dimensional non-symmetric plane-wall diffuser, Fluids Eng., ASME, 1991, 113: 210-215
[86] Zhao, Q., Tanimoto, K., Numerical simulation of breaking waves by Large eddy simulation and VOF method. Proc. 26th Int. on coastal engineering, ASCE, Copenhagen, 1998, 1: 892-905
[87] Fatica, M., et al, Validation of large-eddy simulation in a plane asymmetrical diffuser. Annual brief center for turbulence research, 22
[88] Prasad, A., Williamson, C.H.K., The instability of the shear layer separating from a bluff body, JFM, 1997: 333-375
[89] Mittal, R., Moin P. Suitability of upwind-biased finite difference schemes for large-eddy simulation of turbulent flows. AIAA. 1997, 35.
[90] Karvchenko A.G., B-spline method and zonal grids for simulation of complex turbulence flows. Computational physics, 1999: 151~757.
[91] Karvchenko, A.G., Moin, P., Numerical studies of flow over a circular cylinder at Re=3900, Physics of Fluids, 2000.
[92] Bardina, J., Ferziger, J.H., Improved subgrid scale models for large-eddy simulation. AIAA paper, 1980: 80-1375
[93] Spezial, C.G., Subgrid scale stress models for the large-eddy simulation of rotating turbulent flow. Geophs. & Astrophys. Fluid Dynamics, 1985, 33: 199-222
[94] 苏铭德,黄诉逸,计算流体力学基础,北京:清华大学出版社,1997
[95] Germano, M., A dynamic subgrid-scale eddy viscosity model. Physics of fluid, 1991, 3.
[96] Yoshizawa, A. andHoriuti, K., A statistically-derived subgrid-scale kinetic energy model for the large-eddy simulation of turbulent flows. Phys. Soc Jpn, 1985, 54: 2834-2839
[97] 金忠青,N-S 方程的数值解法,南京:河海大学出版社,1992.
[98] 王福军,计算流体动力学分析—CFD 软件原理及应用,北京:清华大学出版社,2004
[99] F. 杜斯特,A. 梅林,J. H. 怀特洛著. 激光多普勒流速技术的原理和实践[M],北京:科学出版社,1992.
[100] 周家俞,刘亚辉等.泥沙粒径与水流紊动关系试验研究[J].水动力学研究与进展,2006,21(5): 679-684.
[101] 林鹏,陈立.低含沙水流紊动结构的实验研究[J]. 水动力学研究与进展, 2003,18(2): 209-216.
[102] 金永君,光多普勒效应及应用,现代物理知识,2003,15(4): 14-15
[103] 刘春晶,李丹勋等,过渡区动床明渠流的流速分布,水科学进展,2006,17(1): 49-54
[104] 邓安军,陈立等,紊动强度沿垂线分布规律的分析,泥沙研究,2001,5:33-36
[105] 应怀樵,波形和频谱分析与随机数据处理[M]. 北京:中国铁道出版社,1983.
[106] 俞一彪,孙兵,数字信号处理:理论与应用,南京:东南大学出版社,2005.8
[107] W. 梅尔兹科奇著,流动显示[M],北京:科学出版社,1991.
[108] 中国人民解放军总装备部军事训练教材编辑工作委员会,军事训练教材编辑工作委编,流动显示技术[M],北京:国防工业出版社,2002.
[109] 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.
[110] H.K.Versteeg, W. Malalasekera. An introduction to computational fluid dynamics[M]. New York: Longman Scientific & Technical Press. 1995.
[111] I. Drianski. A simple boundary condition for unbounded hyperbolic flows[J]. Journal of Computational Physics. 1976, 21 (5): 251-269.
[112] H. Wengle, A. Huppertz, G. Barwoff, et al. Numerical simulation (DNS and LES) of manipulated turbulent boundary layer flow over a surface-mounted fence[J]. European Journal of Mechanics B/Fluids, 2001, 20 (1): 25-46.