摘要
为了对阶梯溢流坝面流场特性进行全面的研究，同时探求在大单宽流量下提高阶梯溢流坝消能率的措施，本文采用紊流数值模拟与实验相结合，数值计算为主、实验为辅的研究方法对阶梯溢流坝面流场进行了较系统深入的研究。阶梯溢流坝面流场带有曲线自由水面和复杂边界条件，给数值模拟技术难度很高，本文首次采用三维k-ε双方程紊流模型，引入水气两相流的VOF模型，利用几何重建格式来迭代生成自由水面，对复杂的几何边界采用非结构网格进行处理，成功地对阶梯溢流坝面的紊动流场进行了数值模拟，得出了流场速度、压力、紊动能和紊动耗散率等的分布规律。采用多普勒激光测速仪和测压管分别对阶梯溢流坝面典型速度场和阶梯表面压力进行详细测量。数值模拟与实测结果的对比分析表明，两者吻合较好。
本文首次从紊动能和紊动耗散率在整个流场的变化规律出发，分析了阶梯的消能机理。研究表明，阶梯坝面水流能量耗散较大的重要原因之一是由于势能沿程不断转化为动能，而动能又部分转化为紊动能，进而由紊动耗散的方式而消耗。在每个阶梯上，紊动耗散率的最大值出现在阶梯的突角处，正是由于滑移主流与阶梯突角之间的相互作用使能量不断耗散，从而使阶梯具有良好的消能效果。
通过对工程实例的三维数值模拟，得到了缓坡阶梯坝面上的水压力、紊动能和紊动耗散率的分布规律。三维计算着重体现了流场沿溢洪道宽度方向的变
化规律，进一步验证了VOF模型、非结构网格与卜。紊流模型相结合能够成功
地模拟三维阶梯溢流坝面复杂流场。
本文首次应用数值模拟的方法对影响阶梯溢流坝面流场特性的一些重要因
素，例如坝面坡度、阶梯尺寸、过渡阶梯等，进行了优化计算。通过对计算成
果的分析和讨论，初步弄清了影响阶梯坝面消能率的机理，并提出了增大坝面
消能率的工程措施，得到了一些具有实用价值的结论。
根据坝坡较缓时，阶梯的消能率较高的研究成果，提出把阶梯溢流应用于
一定高度过水土石坝。并以万县鱼背山水库岸边溢洪道为例，计算了溢洪道上
所受的水流荷载及其分布，为土石坝坡和护面的稳定分析提供了依据。通过计
算证实了既使在较大的单宽流量下，缓坡上的阶梯仍有较高的消能率。
In order to study the characteristics of the stepped spillway overflow comprehensively and seek for the measure to increase the energy dissipation of the stepped spillway at large unit discharge, the method of turbulence numerical simulation and model test are used to study the stepped spillway overflow. In view of the curved free water surface, complicated boundary condition and turbulence flow, it very difficult to simulate the stepped spillway overflow. In this paper, the fractional volume of fluid (VOF) model of the air-water two phase flow is introduced to the k-E turbulence model and combined with the geometry reconstruction scheme to solve the free water surface. The unstructured grid is used to treat the irregular boundary. By these methods, the turbulence flow field of stepped spillway is simulated successfully. The distribution of velocity, pressure, turbulence kinetic energy and turbulence dissipation rate are obtained by simulation. The typical velocity field and the pressure on the step surface of the stepped spillway are measured using the Laser Doppler Anemometer and the piezometer tube respectively. The numerical simulation results are analyzed and compared with the test results, and they are agreed well with each other.
According to the distribution of the turbulence kinetic energy and turbulence dissipation rate in the whole flow field, the mechanism of energy dissipation of stepped spillway is analyzed. One of the main reasons of the step spillway having greater energy dissipation is that the potential energy of the flow continuously transforms to the kinetic energy along the spillway and the kinetic energy partially transforms to the turbulence kinetic energy, and the flow energy is finally dissipated by means of turbulence dissipation. On every step, the maximum of the turbulence
dissipation rate is at the step tip. Because the interaction between the skimming flow and the step tips causes the energy to dissipate continuously, so that the step can have better energy dissipation results.
By the three dimensional numerical simulation of a project case, the distribution of pressures, turbulence kinetic energy and turbulence dissipation rate in the gentle slope spillway overflow are obtained. The results of the three dimensional simulation emphatically show flow characteristics change along the spillway width and furthermore verify that the combination of k- E turbulence model with the VOF model and unstructured grid can successfully simulate complex three dimensional turbulent flow on the stepped spillway.
By the turbulence numerical simulation, the optimization calculation of some key factors that influence the stepped spillway overflow, such as the spillway slope, the step size, the transition steps and so on, are carried out. Through the analysis and discussion for the simulation results, the energy dissipation mechanism of the stepped spillway is preliminarily made clear and some engineering measures for increasing the energy dissipation ratio are proposed, and some useful and practical conclusions are obtained.
In the light of the study result that the energy dissipation ratio is higher as the spillway slope is gentle, to applied stepped spillway to overflow earth-rock dams with a certain height is proposed. Taken the bank spillway at Yubeishan reservoir as an example, the water loads acted on the spillway, such as static water pressure, dynamic water pressure, shear stress on the surface of the step and so on, are calculated, which can provide evidence to the stability analysis of the dam slope and slope protection. By the calculation, it is verified that even if the unit discharge is large, the energy dissipation ratio of the step on the gentle slope is higher.
引文
[1] Wegman E. The design of the New Croton Dam. Transactions, ASCE, Paper 1047, June, 1907: 398～457.
[2] Essery I T S and Homer M W. The hydraulic design of stepped spillways. Report No.33, Construction Industry Research and Information Association, London, England.
[3] Young M F. Feasibility study of a stepped spillway. Hydraulic Division Specialty Conference, Jackson, MS, Aug., 1982, 96～105.
[4] Sorensen R M. Stepped spillway hydraulic model investigation. Journal of Hydraulic Engineering, ASCE, 1985, 111(12): 1461～1472.
[5] Ru Shuxun, etc. Steppped dissipator on spillway face. Proceedings of ninth congress of Asian and Pacific Division of the International Association for Hydraulic Research. 24～26, August, 1994, Singapore, Vol.2: 193～200.
[6] 汝树勋等，曲线形阶梯式溢流坝的消能特性．泄水工程与高速水流论文集，1994年9月：98～102．
[7] Morris H M. A new concept of flow in rough conduits. Transactions, ASCE, Vol. 120, 1955, 373～410.
[8] Rajaratnam N. Skimming flow in stepped spillways. Journal of Hydraulic Engineering, ASCE, 1990, 116(4): 587～591.
[9] Peyras L, Royet P and Degoutte G. Flow and energy dissipation over stepped gabion weirs. Journal of Hydraulic Engineering, ASCE, 1992, 118(5): 707～717.
[10] Liao Huasheng and Wu chigong. Numerical model of stepped spillway overflow. Proceeding of 2nd International Conference on Hydro-Science and Engineering, Beijing, Mar. 1995.
[11] Rice C E and Kadavy K C. Model study of a roller compacted concrete stepped spillway. Journal of Hydraulic Engineering, June 1996, 122(6): 292～297.
[12] 蒋晓光．阶梯式溢流消能浅析．泄水工程与高速水流，1992年4月，第4期：37～40．
[13] Zhou hui, Wu Shiqiang and Jiang Shuhai. Hydraulic performances of skimming flow over stepped spillway. Journal of Hydrodynamics, Ser. B, 1997, 9(3): 80～86.
[14] 周辉，吴时强，姜树海．阶梯溢流坝滑移流水力特性初步研究．泄水工程与高速水流(合订本)，1998年9月，25～28．
[15] Pegram G G S, Officer A K and Mottram S R. Hydraulics of skimming flow on modeled stepped spillways. Journal of Hydraulic Engineering, May 1999, 125(5): 500～510.
[16] Houston K L and Richardson A T. Energy dissipation characteristics of a stepped spillway for an RCC dam. Proceedings, The International Symposium of Hydraulics for High Dams, 1988, Benjing, 91～O8.
[17] 才君眉，薛慧涛，冯金鸣．碾压混凝土坝采用台阶式溢洪道消能初探．水利水电技术1994，(4)：19～25．
[18] Stephenson D. Energy dissipation down stepped spillways. Water Power and Dam Construction, Sept. 1991, 27～30.
[19] Chamani M R and Rajaratnam N. Jet flow on stepped spillways. Journal of Hydraulic Engineering, ASCE, 1994, 120(2): 254～259.
[20] Chanson H. Stepped spillway flows and air entrainment. Canadian Journal of Civil Engineering, 20(3): 422～435.
[21] Christodoulou G C. Energy dissipation on stepped spillways. Journal of Hydraulic Engineering, ASCE, 1993, 119(5): 644～651.
[22] Udomsak I and Chaiyuth C. Flow depth and energy loss through stepped chutes. Proceedings of Ninth Congress of Asian and Pacific Division of the International Association for Hydraulic Research. 24～26, August 1994, Singapore, Vol.2:156～163.
[23] D. 耶尔德兹，I. 科斯．台阶式斜槽溢洪道的水力特性(蒯圣堂译自《水电与大坝》)，水利水电快报1999，20(9)：1～4．
[24] D. 耶尔德兹，I. 科斯．台阶式斜槽溢洪道的水力特性(蒯圣堂译自《水电与大坝》)，水利水电快报1999，20(10)：12～14．
[25] Diez-Cascon J etc. Studies on the hydraulic behaviour of stepped spillways. Water Power and Dam Construction, Sept. 1991, 22～26.
[26] Bindo M, Gautier J and Lacroix F. The stepped spillway of M'Bali dam. Water Power and Dam Construction, Jan. 1993, 35～36.
[27] Chanson H. Self-aerated flows on chutes and spillways. Journal of Hydraulic Engineering, ASCE, 1993, 119(2): 220～243.
[28] Chanson H. Comparison of energy dissipation between nappe and skimming flow regimes on stepped chutes. Journal of Hydraulic Research, 1994, 32(2): 213～219.
[29] Chanson H. Hydraulics of skimming flows over stepped channels and spillways. Journal of Hydraulic Research, 1994, 32(3): 445～460.
[30] Tozzi M J. Residual energy in stepped spillways. International Water Power & Dam Construction, May 1994, 32～34.
[31] 廖华胜，汝树勋，吴持恭．阶梯溢流坝水力特性实验研究．泄水工程与高速水流论文集1994年9月：95～97．
[32] 谢省宗，李世琴，李铁洁．宽尾墩和阶梯式溢流坝联合消能新技术．泄水工程与高速水流，1996年3月，第1期：24～30．
[33] Yang S L and Lin F M. Flaring pier-stepped spillways — a bucket type of combined energy dissipater. The 1st International Conference on Hydropower, 1996, October 28-November 2, Beijing, 231～242.
[34] 杨敏等．阶梯溢流面的几个水利学问题 泄水工程与高速水流(合订本)，1998年9月，29～32．
[35] 唐毅等．阶梯式消能工的试验研究及在南果河水电站的应用．水力发电，1998，(4)：33～35．
[36] Chamani M R and Rajaratnam N, Characteristics of skimming flow over stepped spillways. Journal of Hydraulic Engineering, 1999, 125(4): 361～368.
[37] 陈景仁．湍流模型及有限分析法，上海交通大学出版社，1989年4月．
[38] 余常昭．环境流体力学导论，清华大学出版社，1998年1月．
[39] Rodi V. Turbulence Models and Their Applications in Hydraulics, IAHR Publication, Delft. The Netherlands, June, 1984.
[40] 金忠青．N-S方程和数值解和紊流模型，河海大学出版社，1989年6月．
[41] Bradshaw P, Ferriss D H and Atwell N P. Calculation of boundary layer development using the turbulent energy equation. J. Fluid Mech., 1967, Vol.28, 593-616.
[42] Nee V W and Kobasznay L S G. The calculation of the incompressible turbulent boundary layer by a simple theory. Phys. of Fluid, 1969, No. 12, 473.
[43] Chou P Y. On the velocity correlations and the solution of the equations of turbulent fluctuation. Quart. J. Appl. Math, 1945, 3(1): 38-54.
[44] Davidov B I. On the statistical dynamics of an incompressible turbulent fluid. Dokl. AN SSSR, 1961, 136, 47.
[45] Harlow F H and Nakayama P I. Transport of turbulence energy decay rate. Los Alamos Sci. Lab. Univ. California Rep. LA-3854, 1968.
[46] Jones W P and Launder B E. The prediction of laminarisation with a Z-equation model of turbulence. Int. J. Heat Mass Transfer. 1972, Vol.15: 301.
[47] Rotta J C. Statistische thearie nichthomogener turbulenz. Zeitschrift f. Physic, 1951, t92:547-572 and 131: 51-57.
[48] Kolmogorov A N. Equations of turbulent motion of an incompressible fluid. LZV. Ahad. Nauk. SSR, Seria fizicheska Vi., 1942, No.1-2: 56-58.
[49] Spalding D B. The prediction of two-dimensional steady turbulent flows. Imperial College, Heat Transfer Section Rep., EF/TN/A/16, 1969.
[50] Patankar S V, Pratap V S and Spalding D B. Prediction of turbulent flow in curved pipes, Journal of Fluid Mechanics, 1975, 67: 583-595.
[51] Leschziner M A and Rodi W. Calculation of strongly curved open channel flow. Journal of the Hydraulics Division, ASCE, 1979, 105(10): 1297-1314.
[52] 刘清朝，陈椿庭．水跃紊流特性的数值研究．水利学报，1993年1期，1～10．
[53] 张庄，周同明．溢流坝反弧段紊动水流的数值模拟．水利学报，1994，(6)：31～49．
[54] 戴光清，吴持恭，杨永全．多股射流水垫塘三维流动数值模拟及消能．中国科学(A辑)，1995，25(9)：1002～1008．
[55] 戴光清，李建明，陈文梅．水力旋流器湍流场数值模拟．化工学报，1997，48(1)：123～126．
[56] 魏文礼，金忠青．复杂边界河道流速场的数值模拟．水利学报，1994，(11)：26～30．
[57] Xu Weilin and Liao Huasheng. Numerical simulation of flow field of a river with complicated boundaries. Journal of Hydrodynamics, Ser. B, 1996, 8(3): 75～80.
[58] Kolavadin B A and Vatutin I A. Statistical transfer theory in non-homogeneous turbulence. Int. J. of Heat and Mass Transfer, 1972, 15: 2371-2388.
[59] Launder B E et al. Progress in the development of a Reynolds stress turbulence closure. J. Fluid Mech., 1975, 68: 537-566.
[60] Reece G J. A generalized Reynolds-stress model of turbulence. Ph.D. Thesis, University of London, 1977.
[61] Launder B E and Spalding D B. Mathematical models of turbulence. Academic Press, London and New York, 1972.
[62] 倪浩清，周力行等．明渠温差异重流中湍浮力回流的数学模型．中国科学，A辑，1987，(4)．
[63] 倪浩清，周力行等．应力代数模型在各向异性湍浮力回流中的应用．力学学报，1989，21(4)．
[64] 倪浩清，王能家，周力行等．应力代数及低雷诺数的湍流数学模型在重叠式排取水口工程中的模拟计算．水动力学研究进展，1990，(12)．
[65] Naot D and Rodi W. Calculation of secondary currents in channel flow. Journal of Hydraulic Division, ASCE, 1982, 108(8): 948～968.
[66] Naot D, Nezu I and Nakagawa H. Calculation of compound-open-channel flow. Journal of Hydraulic Engineering, ASCE, 1993, 119(12): 1418～1425.
[67] Marble F E. Dynamics of dusty gases. Ann Rev Fluid Mechanics, 1970,2.
[68] Wallis G B. One dimensional two-phase flow chapter 2. McGrawHill, 1969.
[69] Scheidegger A E. The physics of flow through porous media. 3rd ed. Toronto:univ. Toronto Press, 1974
[70] Biesheuvel A and Wijngaarden L V. Two-phase flow equations for a dilute dispersion of gas bubbles in liquid. Journal of Fluid Mechanics, 1984, 148: 301～318.
[71] Wallis G B, Richter H J and Kuo J T. The separated flow model of two-phase flow. Electric Power Research Institute Report EPRI, NP-275,1976.
[72] Drew D A and Lahey Jr R T. Application of general constitutive principles to the derivation of multidimensional two-phase flow equations. International Journal of Multiphase flow, 1979, 5: 243～264.
[73] Ardron K H. One-dimensional two-fluid equations for horizontal stratified two-phase flow. International Journal of Multiphase flow, 1980, 6: 295～304.
[74] Richter H J. Separated two-phase flow model application to critical two-phase flow. International Journal of Multiphase flow, 1983, 9(5): 511～530.
[75] 范正翘，陈越南．两相流基本方程．应用数学和力学，1986, 7(6):477～485.
[76] Nickox C H. Air-entrainment on spillway faces. Civil Engineering, 1945, 15(12): 562～563.
[77] Straub L G and Anderson A G. Experiments in self-aerated flows in open channels. Journal of the Hydraulics Division, ASCE, 1958, 84(7): 1890-1～1890-34.
[78] Nagar S L R, Seetharamiah K and Gangadharaiah T. Characteristics of self-aerated flows. Journal of Hydraulics Division, ASCE, 1970, 96(2): 331～355.
[79] Pinto N L de S, Neidert S H and Ota J J. Aeration at high velocity flows. Water Power & Dam Construction, Mar 1982: 42～44.
[80] Wood I R. Uniform region of self-aerated flow. Journal of Hydraulic Engineering, ASCE, 1983, 109(3):447～461．
[81] 刘宜烈，刘钧．三元空中水舌掺气扩散的试验研究．水利学报，1989年11期．
[82] 杨春宝，王正臬．斜槽掺气坎坎下流场的数值分析．水利水运科学研究，1991，(2)：151～159．
[83] 吴持恭，杨永森．空中自由射流断面含水浓度分布规律研究．水利学报，1994，(7)：1～11．
[84] 罗铭．掺气减蚀挑跌坎与水流紊动特性．水利学报，1995，(7)：1～7．
[85] 郑永刚，方铎，李桂芬．明渠中掺气水流紊流流动规律．水利学报，1997，(3)：33～36．
[86] Gustavo F V and Juan C L. Prototype and model aeration efficiency in a high head outlet for flood flows. The 2nd International Conference on the Hydraulics of Floods and Flood Control, 365～372．
[87] 吴持恭．明渠水气二相流，成都科技大学出版社，1989年6月．
[88] 杨永森．强迫掺气水流的数学模型．清华大学博士后出站总结报告，1993年7月．
[89] 黄建波．渗气对流场压强的影响．水利学报，1987，(5)：43～51．
[90] 黄建波，倪旱根．空泡群溃灭时作用于固壁上的压强．水利水运科学研究，1988，(3)：33～41．
[91] 柴恭纯，夏维洪．特高速掺气水流对空化的影响．水利水运科学研究，1994年9月，第3期：231～237．
[92] 陈椿庭．高坝大流量泄水建筑物，水利电力出版社，1988年9月．
[93] 帅青红．掺气水流音速压缩性及临界免蚀掺气浓度的研究．四川联合大学博士论文，1995年10月．
[94] 杨永森，吴持恭．通气槽挑射水流掺气特性的研究．水利学报，1992，(4)：1～7．
[95] 杨永森，跌坎型掺气槽过流的掺气特性．水利学报，1994，(2)：65～70．
[96] 杨永森，陈长植，于琪洋．掺气槽上射流挟气量的数学模型．水利学报，1996，(3)：13～21．
[97] 王世夏．清水及浑水高速水流掺气和掺气抗磨的研究．水利水电科技进展，1996，16(1)：6～10．
[98] 罗铭．掺气减蚀设施后沿程掺气浓度的数学模拟．水利学报，1987，(9)：17～24．
[99] 汪国风，王正臬．通气坎下游掺气浓度分布的研究．水利水运科学研究，1988，(2)：37～45．
[100] 苑明顺．陡槽自然掺气发展区含气浓度分布计算．水利学报，1992，(10)：1～6．
[101] Pinto N L de S and Neidert S H. Modeling aerator devices-dimensional considerations. Proc. of ⅩⅩ Ⅱ Congress IA HR, Lausanne, Switzerland, 1987.
[102] Bruschin J. Forced aeration of high velocity flows. Journal of Hydraulic Research, 1987, 25(1).
[103] 夏维洪．高速掺气水流的模型相似问题．水动力学研究与进展，A辑，1997．12(1)：47～55．
[104] Xu Weixin and Jin Zhongqing. Numerical method for the computation of unsteady bubble turbulent flow in open channel. The Forth International Symposium on Refined Flow Modeling and Turbulence Measurement, Wuhan, China, 1989.
[105] Zarrati A R. Mathematical modeling of air-water mixture in open channels.
Journal of Hydraulic Research, 33(5), 1994.
[106] 赵文华．几种典型水气两相流动问题的理论分析及数值模拟，成都科技大学博士学位论文，
1992年．
[107] 康琦，申功忻．全场测速技术进展．力学进展，1997，27(1)：106～121．
[108] 周明，李文采．激光多普勒测速技术在气液两相流中的应用．力学学报，1991，23(1)：46
～51．
[109] 路展民等．气泡—水流两相流的激光多普勒法测量．力学学报，1988，20(6)：489～495．
[110] 戴光清，杨永全，吴持恭．掺气射流水气两相流测试研究．四川联合大学学报(工程科学
版)，1997，1(1)：1～6.
[111] Cain P and Wood I R. Measurements of self-aerated flow on a spillway.
Journal of Hydraulic Division, ASCE, 1981, 107(11):1425～1445.
[112] 吴持恭主编．水力学，第二版，高等教育出版社，1983年6月．
[113] Glaister P. A numerical scheme for two-dimensional, open channel flows
with non-rectangular geometries. International Journal of Engineering Science,
1993, 31(7): 1003～1011.
[114] Zhan Jiemin and Zhang Diming, Numerical solution of the Navier-Stokes
equations for 3-D region using body-fitted coordinate system. Journal of
Hydrodynamics, Ser. B, 1991, 3(3): 105～109.
[115] Thomoson J F. Numerical solution of flow problems using body-fitted
coordinates system. Computational Fluid Dynamics, 1980.
[116] Barth T J and Jespersen D. The design and application of upwind schemes on
unstructured meshes. Technical Report AIAA-89-0366.
[117] Kuipers J and Vreug denbil C B. Calculations of two-dimensional horizontal
flow. Delft Hydraulic Laboratory Reports, 163, part 1, 1973.
[118] Eilis J, Numerical simulation of open channel spillway flows. Proceedings,
The International Symposium of Hydraulics for High Dams, 1988, Benjing, 197～
207.
[119] Guo Qingchao and Han Qiwei. The numerical simulation of two-dimension open
channel turbulence. Journal of hydrodynamics, Set. B, 1993, 5(3): 89～97.
[120] Harlow F H, Welch J E, Shannon J P and Daly B J. The MAC Method, Los
Alamos Scientific Laboratory Report, LA-3425, 1965.
[121] Hirt C W and Nichols B D. Volume of fluid (VOF) Method for the Dynamics of
Free Boundaries. J. Comput. Phys., 1981, 39: 201～225.
[122] 金忠青，戴会超．坝下消能工局部水流的数值模拟．水动力学研究与进展，A辑，1994，9
(4)：163～169．
[123] Dai Huichao. The application and study of numerical simulation of
turbulence flow with free surface in hydraulic spillways stricture. Journal of
Hydrodynamics, Ser. B, 1997, 9(4): 54～60.
[124] Xu Weixin and Jin Zhongqing. Numerical simulation of high turbulent free surface flow under the curvilinear coordinates. Journal of Hydrodynamics, Ser. B, 1990, 7(1): 50～55.
[125] Youngs D L. Time-dependent multi-material flow with large fluid distortion. In K. W. Morton and M J Baines, editors, Numerical Methods for Fluid Dynamics. Academic Press, 1982.
[126] Launder B E and Spalding D B. Lectures in Mathematical Models of Turbulence. Academic Press, London, England, 1972.
[127] Chen Qun, Dai Guangqing and Liu Haowu. The turbulence numerical simulation for the stepped spillway overflow. Hydrodynamics, Ser. B (待刊).
[128] Barth T J and Jespersen D. The design and application of upwind schemes on unstructured meshes. Technical Report AIAA-89-0366, AIAA 27th Aerospace Sciences Meeting, Reno, Nevada, 1989.
[129] Vandoormaal J P and Raithby G D. Enhancements of the SIMPLE method for predicting incompressible fluid flows. Numer. Heat Transfer, 1984, 7: 147-163.
[130] Patankar, S V and Spalding D B. A calculation procedure for heat mass and momentum transfer in three-dimensional parabolic flows. Int. J. Heat Mass Transfer, 1972, 15: 1787.
[131] Launder B E and Spalding D B. The numerical computation of turbulent flows. Computer Methods in Applied Mechanics and Engineering, 1974, 3: 269-289.
[132] 唐朝阳．鱼背山水电站溢洪道消能工设计研究．水电站设计，1995年12月，11(4)：30～34．
[133] 李世宁，李长林编著．过水土坝，吉林人民出版社，1983年5月．
[134] Weiss A. Construction technique of passing floods over earth dams. Transactions, ASCE, 1951, 116: 1951.
[135] Wilkins J K. The flow of water through rockfill and its application to the design of dams. Proceedings and Australia-New Zealand Conference or Soil Mechanics and Foundations Engineering, 1956: 141.
[136] Curtis R P and Lawson J. Flow over and through rockfill banks. Journal of the Hydraulic Division, ASCE, Sept. 1967, 93(6): 1～21.
[137] Parkin A K, Trollope D H and Lawson J D, Rockfill Structures subject to water flow. Jouranl of the Soil Mechanics and Foundations Division, ASCE, Nov. 1966, 92(6): 135～151.
[138] Parkin A K. Rockfill dams with inbuilt spillways. Part Ⅰ, Hydraulic characteristics, Report DR2. Department of Civil Engineering, University of Melbourne, Australia.
[139] Parkin A K. Rockfill dams with inbuilt spillways: Part Ⅱ, stability characteristics. Repart DR3, Department of Civil Engineering, University of Melbourne, Australia.
[140] Pravdirets Y P and Slissky S M. Passing floodwaters over embankment dams. International Water Power and Dam Construction, 1981, 33(7): 30～32.
[141] Miller A P. Pravdivets Y P and Saiov V A. Earth overflow dam. Hydrolichnical Construction (English translations of Gidrotekhnicheskoe Stroitel Stvo), 1987, 21(8): 503～507.
[142] Pravdivets Y P. Industrial design of an earth overflow dam. Hydrotechnical Construction (English translations of Gidrotekhnicheskoe Stroitel Stvo), 1988, 21 (12): 685～689.
[143] Frizell K H. Stepped spillway design for flow over embankments. Proceedings of the 1991 National Conferences on Hydraulic Engineering, Naskville, TN, USA. July 29～Aug. 2,1991:118～123.
[144] 陈小冰，陈圣平．混凝土面板堆石坝坝体过水保护．人民长江，1998，(6)：27～29．
[145] 徐天有，张晓宏．过水堆石坝钢筋笼护坡失稳临界条件．西北水电，1998，(2)：34～35．
[146] 侍克斌，肖焕雄．过水土石坝(围堰)下游混凝土板护坡垫层的设计准则．水电站设计，1997，(2)：13～18，29．
[147] Snider S H. RCC overlays for embankment dams. Proceedings of the 1st International Conference on Water Resources, Part 1(of 2), Aug. 14-18, 1995, 323～327.
[148] Hansen K D and Mclean F G. Roller compacted concrete for overtopping protection: and overview. Proceedings of the 1st International Conference on Water Resources, Part 2(of 2), Aug 14-18, 1995, 1016～1020.
[149] 赵启忠．土工膜防渗技术在水利工程中的应用．安徽水利科技，1998，(3)：24～26．
[150] 王昭礼．复合土工薄膜防渗在松子坑水库工程的应用．水力发电，1997，(7)：51～52．
[151] 陈乃仲．复合土工膜在黄粟坑水库土坝防渗工程的应用．人民珠江，1998，(6)：22～23．
[152] 黄国兴，姚伟民．土工膜在水关河水库土坝防渗处理工程中的应用．水利水电技术，1996，(2)：23～27．
[153] 戴光清，杨永全，吴持恭．水垫塘多层淹没射流数值模拟及消能研究．水利学报，1996年第1期：13～19．
[154] 戴光清，杨永全，吴持恭．多股射流水垫塘入流方式优化计算．水利学报，1996年增刊：67～71，95．
[155] 陈群，何昌荣．一种新型楔形拉筋加筋土挡墙的原型观测．岩土工程学报，2000，22(3)：289～293．
[156] Zarrati A R. Mathematical modelling of air-water mixtures in open channels. Journal of Hydraulic Research, 1995, 32(5): 707～720.
[157] Nakoryakov V E etc. Gas-liquid bubbly flow in vertical pipes. Journal of Fluids Engineering. 1996, 118(3): 377～382.
[158] Growe C T, Troutt T R and Chung J N. Numerical models for two-phase turbulent flows. Annu. Rev. Fluid Mech., 1996, 28: 11～43.
[159] 郑邦民，陈飞勇．溢流面陡坡段上紊流边界层数值分析．水利学报，1989年第3期：9～16.
[160] 陈学德．过坝水流全程紊流边界层发展的分析与计算．水利学报，1986年第2期：28～37．
[161] 陶晓峰，董曾南．光滑溢流坝面水流边界层特性试验研究．水利学报，1984年第6期：1～9．
[162] Akai M, Inoue A and Aoki S, The prediction of stratified two-phase flow with a two-equation model of turbulence. International Journal of Multiphase flow, 1981, 7: 21～39.
[163] 翁情达等．溢流坝面紊流边界层的发展极其应用．水利学报，1984年第6期：10～18．
[164] 刘大有．论气体混合物和两相流中的压强和热流．力学学报，1986，18(6)：492～501．
[165] 杨文熊．湍流一般机理极其应用．力学进展，1992，22(4)：489～495．
[166] 廖华胜，许唯临，杨永全．高速水力学研究进展．泄水工程与高速水流，1996年6月，第2期：1～10．
[167] 戴光清．多股射流水垫塘流动结构水力特性及消能机理研究．四川大学工学博士学位论文，1994年11月．
[168] Ardron K H. One-dimensional two-fluid equations for horizontal stratified two-phase flow. International Journal of Multiphase flow, 1980, 6:295～304.
[169] 倪浩清．工程湍流模式理论综述及展望．力学进展，1996，26(2)：145～165．
[170] 马根娣，孙鸿元．气液两相流研究概述．力学进展，1986，16(1)：65～71．
[171] 肖兴斌．高坝泻水建筑物泻洪消能的新发展．东北水利水电，1995，(3)：42～45．
[172] Wallis G B, Review—theoretical models of gas-liquid flows. Journal of Fluid Engineering, Sept. 1982, 104:279～283.