低弗劳德数水跃消能弱化机制及关键技术研究进展Research progress on weakening mechanisms and key technologies of energy dissipation by hydraulic jumps with low Froude numbers
曾清,唐立模,骆国强,林青炜,屈一晗,曹伽
摘要(Abstract):
【目的】水跃作为一种重要的水力现象,在水利工程消能中被广泛应用。低弗劳德数下水跃易形成波状结构且消能率往往不理想,导致下游消能防冲设施受到严重冲刷破坏。【方法】因此分别从力学机制和外部条件作用分析总结了低弗劳德数水跃消能弱化机制,并结合水体结构与气泡引入及其相互作用角度,深化对低弗劳德数水跃结构和消能路径的理解。基于弱化机制的认识,对消力池设计、消力池结构优化、辅助消能工应用和掺气整流消能关键技术及机理进行梳理,以指导工程设计,同时指出了应对辅助消能工空化空蚀、消力池内泥沙淤积、水体过饱和气鱼类致死等衍生问题的关键技术。【结果】研究发现,当前低弗劳德数水跃消能研究由于水跃结构本身的复杂性以及现代流动测试技术局限性,水跃紊流结构与能量耗散机理研究仍存在系统性认知空缺;在工程应用中,目前缺乏普适性设计准则以指导工程优化,同时亟待建立工程生态影响评估体系。【结论】未来可利用物理信息神经网络和机器学习技术在水跃两相流机理的深入、消能工设计方法的优化、工程方案多目标评价体系的建立三方面开展进一步研究。
关键词(KeyWords): 低弗劳德数;水跃消能;弱化机制;关键技术;消能机理;消能率;水力特性;空化
基金项目(Foundation): 江苏省水利厅科研项目“淮河入海水道二期工程枢纽建设质量及安全保障提升关键技术研究”(RHSD2/FW-2024-03);; 国家重点研发计划“长江中下游平原河网区水动力优化再构与自然动能高效利用”(2022YFC3202603)
作者(Author): 曾清,唐立模,骆国强,林青炜,屈一晗,曹伽
DOI: 10.13928/j.cnki.wrahe.2026.03.014
参考文献(References):
- [1] 清华大学水力学教研组.水力学(1980年修订版)下册[M].北京:人民教育出版社,1980.Tsinghua University Hydraulics Teaching and Research Group.Hydraulics (Revised Edition 1980),Volume II [M].Beijing:People’s Education Press,1980.
- [2] 潘家铮.中国大坝50年[M].北京:中国水利水电出版社,2000.PAN Jiazhen.Fifty Years of China’s Dams [M].Beijing:China Water Power Press,2000.
- [3] 杨凡,王均星,陈帅,等.低弗劳德数水流辅助消能工空蚀问题研究[J].水力发电学报,2015,34(2):125-129.YANG Fan,WANG Junxing,CHEN Shuai,et al.Study on cavitation damages of supplementary dissipater under low-Froude-number flows[J].Journal of Hydroelectric Engineering,2015,34(2):125-129.
- [4] 武英豪,王均星,包芬芬,等.清渡河水库溢洪道模型试验研究与体型优化[J].水电能源科学,2022,40(8):131-135.WU Yinghao,WANG Junxing,BAO Fenfen,et al.Model experiment and shape optimization of Qingduhe reservoir spillway [J].Water Resources and Power,2022,40(8):131-135.
- [5] 王文兵,邱勇,周鑫宇,等.格栅高度对底流消能水力特性及消力池体型的影响[J].水电能源科学,2022,40(12):186-189.WANG Wenbing,QIU Yong,ZHOU Xinyu,et al.Effect of grid height on hydraulic characteristics of underflow energy dissipation and shape of stilling pool [J].Water Resources and Power,2022,40(12):186-189.
- [6] 王海阳,傅宗甫.超低弗劳德数闸下消能试验[J].水利水电科技进展,2007,27(6):73-76.WANG Haiyang,FU Zongfu.Experiments on under sluice energy dissipation at ultra-low Froude number[J].Advances in Science and Technology of Water Resources,2007,27(6):73-76.
- [7] 龙建,牛争鸣,李奇龙.增设收缩墩后的跌坎消力池三维流场研究[J].长江科学院院报,2020,37(1):67-72.LONG Jian,NIU Zhengming,LI Qilong.Three-dimensional nu-merical simulation of turbulent flow with contraction jet in stilling basin with step-down floor[J].Journal of Yangtze River Scientific Research Institute,2020,37(1):67-72.
- [8] 刘增文,金瑾,严文博,等.T型墩消力池水力特性数值模拟及结构优化[J].水电能源科学,2023,41(9):103-106.LIU Zengwen,JIN Jin,YAN Wenbo,et al.Numerical simulation of hydraulic characteristics and structural optimization of T-shaped pier stilling pool[J].Water Resources and Power,2023,41(9):103-106.
- [9] 高尚,牧振伟,俞晓伟.趾墩-悬栅消力池水力特性及消能效果研究[J].水电能源科学,2021,39(6):108-111.GAO Shang,MU Zhenwei,YU Xiaowei.Study on hydraulic characteristics and energy dissipation effect of chute block-suspended grid stilling pool[J].Water Resources and Power,2021,39(6):108-111.
- [10] 周凯,牧振伟,周镇,等.底流消力池墩栅联合消能工水力特性数值模拟研究[J].水资源与水工程学报,2023,34(2):142-148.ZHOU Kai,MU Zhenwei,ZHOU Zhen,et al.Numerical simulation of hydraulic characteristics of pier-fence joint dissipators in underflow dissipation basins[J].Journal of Water Resources and Water Engineering,2023,34(2):142-148.
- [11] 郭子中.消能防冲原理与水力设计[M].北京:科学出版社,1982.GUO Zizhong.Energy Dissipation and Scour Protection Principles and Hydraulic Design [M].Beijing:Science Press,1982.
- [12] CHANSON H,MURZYN F.Froude similitude and scale effects affecting air entrainment in hydraulic jumps [C] // American Society of Civil Engineers.World Environmental and Water Resources Congress 2008:Ahupua’a.Reston,VA:American Society of Civil Engineers,2008:1-10.
- [13] 陈帅,王均星,陈利强,等.低弗劳德数水跃耗散涡尺度的物模研究[J].水力发电学报,2013,32(2):179-183.CHEN Shuai,WANG Junxing,CHEN Liqiang,et al.Experimental study on Kolmogorov’s length scale in hydraulic jumps of low Froude numbers[J].Journal of Hydroelectric Engineering,2013,32(2):179-183.
- [14] LIU M,RAJARATNAM N,ZHU D Z.Turbulence structure of hydraulic jumps of low Froude numbers[J].Journal of Hydraulic Engineering,2004,130(6):511-520.
- [15] MISRA S K,KIRBY J T,BROCCHINI M,et al.The mean and turbulent flow structure of a weak hydraulic jump[J].Physics of Fluids,2008,20(3):926-158.
- [16] MIGNOT E,CIENFUEGOS R.Energy dissipation and turbulent production in weak hydraulic jumps[J].Journal of Hydraulic Engineering,2010,136(2):116-121.
- [17] TATEWAR S P,DHATRAK A I,SAKHALKAR S V.Discussion of “Turbulent Jet Energy Dissipation at Vertical Drops” by Mohammad R.Chamani,N.Rajaratnam,and MK Beirami[J].Journal of Hydraulic Engineering,2011,137(8):856-856.
- [18] FELDER S,CHANSON H.Triple decomposition technique in air-water flows:application to instationary flows on a stepped spillway[J].International Journal of Multiphase Flow,2014,58:139-153.
- [19] CHACHEREAU Y,CHANSON H.Free-surface fluctuations and turbulence in hydraulic jumps[J].Experimental Thermal and Fluid Science,2011,35(6):896-909.
- [20] WANG H.Turbulence and Air Entrainment in Hydraulic Jumps[D].Brisbane:University of Queensland,2014.
- [21] DE DIOS M,BOMBARDELLI F A,GARC??A C M,et al.Experimental characterization of three-dimensional flow vortical structures in submerged hydraulic jumps[J].Journal of Hydro-Environment Research,2017,15:1-12.
- [22] CHEN S,WANG J X.On energy dissipation of hydraulic jumps at low Froude numbers considering bubbles formation and transportation process[J].Hydraulic Engineering,2013,139(1):91-96.
- [23] WUTHRICH D,SHI R,CHANSON H.Hydraulic jumps with low inflow Froude numbers:air-water surface patterns and transverse distributions of two-phase flow properties[J].Environmental Fluid Mechanics,2022,22(4):789-818.
- [24] CHACHEREAU Y,CHANSON H.Bubbly flow measurements in hydraulic jumps with small inflow Froude numbers[J].International Journal of Multiphase Flow,2011,37(6):555-564.
- [25] 陈帅.基于掺气作用的低Froude数水跃消能问题研究[D].武汉:武汉大学,2013.CHEN Shuai.Research on the Energy Dissipation of Hydraulic Jumps with Low Froude Numbers based on the Aeration Effect [D].Wuhan:Wuhan University,2013.
- [26] WANG H,MURZYN F,CHANSON H.Interaction between free-surface,two-phase flow and total pressure in hydraulic jump[J].Experimental Thermal and Fluid Science,2015,64:30-41.
- [27] CHANSON H,CHACHEREAU Y.Scale effects affecting two-phase flow properties in hydraulic jump with small inflow Froude number[J].Experimental Thermal and Fluid Science,2013,45:234-242.
- [28] ESTRELLA J,WUTHRICH D,CHANSON H.Flow patterns,roller characteristics,and air entrainment in weak hydraulic jumps:Does size matter?[J].Journal of Fluids Engineering,2022,144(7):071305.
- [29] 莫诗玙,田丽蓉,顾声龙.基于光滑粒子数值方法的坡面水动力过程模拟研究[J].水利水电技术(中英文),2024,55(10):124-136.MO Shiyu,TIAN Lirong,GU Shenglong.Study on SPH method-based numerical simulation of overland flow[J].Water Resources and Hydropower Engineering,2024,55(10):124-136.
- [30] 陈月君,傅宗甫,陈青生,等.大扩散比闸下折冲水流偏折特性试验研究[J].中国农村水利水电,2022(4):92-99.CHEN Yuejun,FU Zongfu,CHEN Qingsheng,et al.Experimental research on the flow deflection features downstream of a sluice with large expansion ratios[J].China Rural Water and Hydropower,2022 (4):92-99.
- [31] GUPTA S K,DWIVEDI V K.Effect of surface roughness and channel slope on hydraulic jump characteristics:An experimental approach towards sustainable environment[J].Iranian Journal of Science and Technology,Transactions of Civil Engineering,2024,48(3):1695-1713.
- [32] 叶炜民.贯彻习近平总书记治水重要论述精神加强河道采砂管理[J].水利发展研究,2024,24(10):29-33.YE W M.Implementing the guidign principles from General Secretary Xi Jinping’s important remarks on water governance and strengthening the management of river sand mining[J].Water Resources Development Research,2024,24(10):29-33.
- [33] 韩小军,卢书慧,史红玲,等.黄河上游宁蒙河段平滩流量变化与水沙过程的响应关系[J].中国水利水电科学研究院学报(中英文),2024,22(4):361-367.HAN Xiaojun,LU Shuhui,SHI Hongling,et al.Variation of bank-full discharge and its response relationship with flow and sediment processes of Ningmeng reach in Upper Yellow River[J].Journal of China Institute of Water Resources and Hydropower Research,2024,22(4):361-367.
- [34] 温志超,黄哲,徐海珏,等.泥沙异重流稳定水跃的耗能与掺混实验研究[J].水力发电学报,2023,42(9):11-21.WEN Zhichao,HUANG Zhe,XU Haijue,et al.Experimental study on energy consumption and entrainment in stable hydraulic jumps of sediment density current[J].Journal of Hydroelectric Engineering,2023,42(9):11-21.
- [35] 缑文娟,沈正中,李会平.低弗劳德数条件下尾坎坡度对消力池内流场结构的影响[J].水资源与水工程学报,2024,35(5):114-122.GOU Wenjuan,SHEN Zhengzhong,LI Huiping.Influence of end sill slope on flow fields in stilling basins under low Froude number conditions[J].Journal of Water Resources and Water Engineering,2024,35(5):114-122.
- [36] 何志亚,向鹏鹏,洪彰华,等.渐扩式消力池体型优化研究[J].中国农村水利水电,2022(5):190-194.HE Zhiya,XIANG Pengpeng,HONG Zhanghua,et al.Research on the optimization of gradual expanding stilling basin[J].China Rural Water and Hydropower,2022(5):190-194.
- [37] FELDER S,MONTANO L,CUI H,et al.Effect of inflow conditions on the free-surface properties of hydraulic jumps[J].Journal of Hydraulic Research,2021,59(6):1004-1017.
- [38] 钟益华,马旭东,聂锐华,等.低弗劳德数水跃的水跃长度计算方法[J].水电能源科学,2019,37(6):84-86.ZHONG Yihua,MA Xudong,NIE Ruihua,et al.Study on hydraulic jump length with low Froude number[J].Water Resources and Power,2019,37(6):84-86.
- [39] BRADLEY J N,PETERKA A J.The hydraulic design of Stilling Basins:Hydraulic jumps on a horizontal apron (Basin I)[J].Journal of Hydraulic Engineering,1957,83:1-24.
- [40] 陈椿庭.平底槽二元水跃长度公式的比较[J].水利水电技术,1964(4):34-38.CHEN Chuntin.Comparison of two-dimensional hydraulic jump length formulas in rectangular channels[J].Water Resources and Hydropower Technology,1964(4):34-38.
- [41] 张春财,杜宇.低佛氏数水跃紊流数值模拟研究[J].西北农林科技大学学报(自然科学版),2012,40(1):227-234.ZHANG Chuncai,DU Yu.Numerical simulation study on turbulence of hydraulic jump with low Froude number[J].Journal of Northwest A&F University (Natural Science Edition),2012,40(1):227-234.
- [42] 张志昌,李若冰,傅铭焕,等.矩形明渠自由水跃长度的理论分析[J].水力发电学报,2013,32(6):108-114.ZHANG Zhichang,LI Ruobing,FU Minghuan,et al.Theoretical analysis on the length of free hydraulic jump in rectangular open channel[J].Journal of Hydroelectric Engineering,2013,32(6):108-114.
- [43] 张志昌,赵莹,傅铭焕.矩形平底明渠水跃长度公式的分析与应用[J].西北农林科技大学学报(自然科学版),2014,42(11):190-198.ZHANG Zhichang,ZHAO Ying,FU Ming-huan.Analysis and application of hydraulic jump length formulas in rectangular flat open channel[J].Journal of Northwest A&F University (Natural Science Edition),2014,42 (11):190-198.
- [44] 王勤香.泄水建筑物下游低弗汝德数水跃长度研究[J].人民长江,2014,45(17):63-65.WANG Qinxiang.Research on length of hydraulic jump at downstream of discharge structurewith low Froude number[J].Yangtze River,2014,45 (17):63-65.
- [45] 黄智敏,付波,陈卓英.低水头水闸下游消力池长度优化研究[J].水资源与水工程学报,2019,30(4):154-158.HUANG Zhimin,FU Bo,CHEN Zhuoying.Optimization research on the length of the downstream stilling basin of low-head sluice[J].Journal of Water Resources and Water Engineering,2019,30 (4):154-158.
- [46] ABDEEN M A M,ABDIN A E D,ABBAS W.Simulation and prediction for energy dissipaters and stilling basins design using artificial intelligence technique[J].Cogent Engineering,2015,2(1):1018705.
- [47] 李倩,石自堂,汪洹湛.水闸底流消能防冲关键技术研究[J].中国农村水利水电,2018(3):132-134.LI Qian,SHI Zitang,WANG Huanzhan.Key technology research on energy dissipation and anti-scour of sluice bottom flow[J].China Rural Water and Hydropower,2018 (3):132-134.
- [48] HABIBZADEH A,WU S,ADE F,et al.Exploratory study of submerged hydraulic jumps with blocks[J].Journal of Hydraulic Engineering,2011,137(6):706-710.
- [49] FATHI-MOGHADAM M,HAGHIGHIPOUR S,LASHKAR-ARA B,et al.Reduction of stilling basin length with tall end sill[J].Journal of Hydrodynamics,2011,23(4):498-502.
- [50] 张志昌,李若冰,赵莹,等.消力坎式消力池淹没系数和坎高的计算[J].长江科学院院报,2013,30(11):50-54.ZHANG Zhichang,LI Ruobing,ZHAO Ying,et al.Calculation of the submergence coefficient and the sill height of sill-type stilling basin[J].Journal of Yangtze River Scientific Research Institute,2013,30 (11):50-54.
- [51] 张志昌,李若冰,赵莹,等.综合式消力池深度和坎高的计算[J].西安理工大学学报,2013,29(1):81-85.ZHANG Zhichang,LI Ruobing,ZHAO Ying,et al.Calculation of the depth of comprehensive stilling basin and the height of ridge[J].Journal of Xi’an University of Technology,2013,29 (1):81-85.
- [52] 傅铭焕,钱家欢.S型水跃局部水头损失系数与跃后水深计算方法[J].水电能源科学,2020,38(1):99-103.FU Minghuan,QIAN Jiahuan.Calculation of local head loss coefficient and the sequent depth of S-type hydraulic jump [J].Water Resources and Power,2020,38(1):99-103.
- [53] 傅铭焕,钱家欢.R型水跃局部水头损失系数与跃后水深的计算[J].长江科学院院报,2020,37(5):79-84.FU Minghuan,QIAN Jiahuan.Calculating local head loss coefficient and sequent depth of R-jump in an abruptly expanding stilling basin [J].Journal of Yangtze River Scientific Research Institute,2020,37(5):79-84.
- [54] 王学斌,张志昌,傅铭焕.综合式消力池常用设计方法存在的问题和应用条件研究[J].应用力学学报,2017,34(3):495-501.WANG Xuebin,ZHANG Zhichang,FU Minghuan.Research on existing problems and application conditions of commonly used design methods for comprehensive stilling basin[J].Chinese Journal of Applied Mechanics,2017,34 (3):495-501.
- [55] 杨金孟,韩旭东,孙一清,等.动能及流速系数对挖深式消力池深度和长度的影响[J].水电能源科学,2021,39(8):133-137.YANG Jinmeng,HAN Xudong,SUN Yiqing,et al.Influence of kinetic energy and velocity coefficient on depth and length of excavated stilling basin[J].Water Resources and Power,2021,39 (8):133-137.
- [56] RAJARATNAM N.Hydraulic jumps on rough beds[J].Transactions of the Engineering Institute of Canada,1968,11(A-2):1-8.
- [57] EAD S A,RAJARATNAM N.Plane turbulent wall jets on rough boundaries with limited tailwater[J].Journal of Engineering Mechanics,2004,130(10):1245-1250.
- [58] CAROLLO F G,FERRO V,PAMPALONE V.Hydraulic jumps on rough beds[J].Journal of Hydraulic Engineering,2007,133(9):989-999.
- [59] 张志昌,傅铭焕,李若冰,等.波状床面消力池的流速分布和壁面阻力系数[J].长江科学院院报,2014,31(8):45-49.ZHANG Zhichang,FU Minghuan,LI Ruobing,et al.Velocity distribution and wall resistance coefficient of corrugated bed stilling basin[J].Journal of Yangtze River Scientific Research Institute,2014,31 (8):45-49.
- [60] 傅铭焕,张志昌.密排加糙床面消力池水跃旋滚长度的计算[J].应用力学学报,2021,38(2):738-741.FU Minghuan,ZHANG Zhichang.Calculation of sewerage roll length of dense roughness bed stilling basin[J].Chinese Journal of Applied Mechanics,2021,38 (2):738-741.
- [61] 魏文礼,李小欢,洪云飞,等.三角形波浪底板消力池自由水跃水力特性的数值模拟[J].武汉大学学报(工学版),2017,50(2):207-212.WEI Wenli,LI Xiaohuan,HONG Yunfei,et al.Numerical simulation study of hydraulic characteristics of free hydraulic jump on triangular corrugated beds of stilling basin[J].Engineering Journal of Wuhan University,2017,50(2):207-212.
- [62] 魏文礼,何永鹏,王长洲,等.梯形断面波浪形底板消力池自由水跃特性研究[J].水动力学研究与进展(A辑),2020,35(3):401-407.WEI Wenli,HE Yongpeng,WANG Changzhou,et al.Numerical study on properties of free hydraulic jumps on corrugated bed of trapezoidal cross-section stilling basin[J].Journal of Hydrodynamics (Series A),2020,35 (3):401-407.
- [63] OMID M H,KOUCHAKZADEH S,GORD-NOSHAHRI A.Sill-controlled hydraulic jump in a gradually expanding channel[J].Water Management,2010,163(10):515-522.
- [64] ANWAR N,DERMAWAN V.Characteristics of the hydraulic jump on serial drops[J].International Journal of Academic Research,2011,3(1):113-116.
- [65] 杨明.三棱柱群尾槛对低弗劳德数河流消力池消能效果的影响[J].水利科学与寒区工程,2024,7(8):21-23.YANG M.The influence of triangular prism group tail sill on the energy dissipation effect of low Froude number river dissipation pools[J].Hydro Science and Cold Zone Engineering,2024,7(8):21-23.
- [66] 谭高文,韩昌海,余凯文.低弗劳德数水流二级消力池体型参数试验研究[J].水科学进展,2018,29(6):848-857.TAN Gaowen,HAN Changhai,YU Kaiwen.Experimental study on the body parameters of the two-stage stilling basin in low Froude number flow[J].Advances in Water Science,2018,29(6):848-857.
- [67] 谭高文,韩昌海,韩康,等.低弗劳德数水流二级消力池水力特性试验研究[J].水科学进展,2020,31(1):71-80.TAN Gaowen,HAN Changhai,HAN Kang,et al.Experimental study on the hydraulic characteristics of the two-stage energy dissipation in low Froude Number flow[J].Advances in Water Science,2020,31 (1):71-80.
- [68] LIN W,CAI F,HAN C,et al.Experimental study on energy dissipation and tailwater wave in two-stage stilling basin with supercritical inflow of low Froude number[J].Journal of Hydro-environment Research,2023,51:25-31.
- [69] 许光祥,崔予达,杨忠超.复式消力池在山区小水电中的应用研究[J].水力发电学报,2007,26(2):88-92.XU Guangxiang,CUI Yuda,YANG Zhongchao.Study on application of compound still basin in small hydropower plants in mountainous area[J].Journal of Hydroelectric Engineering,2007,26(2):88-92.
- [70] ZHOU Z,WANG J.Numerical modeling of 3D flow field among a compound stilling basin[J].Mathematical Problems in Engineering,2019,2019(1):5934274.
- [71] 卢洋亮,尹进步,张曙光,等.跌坎型消力池底板脉动压强试验研究及体型优化[J].人民长江,2021,52(11):196-200.LU Yangliang,YIN Jinbu,ZHANG Shuguang,et al.Experimental study on fluctuating pressure of stilling pool slab with bottom drop and shape optimization[J].Yangtze River,2021,52(11):196-200.
- [72] 张红梅,刘经强,于新雨,等.突扩式跌坎消力池掺气特性试验[J].水利水电科技进展,2021,41(6):82-87.ZHANG Hongmei,LIU Jingqiang,YU Xinyu,et al.Experimental research on aeration characteristics of a stilling pool with drop sill and sudden expansion[J].Advances in Science and Technology of Water Resources,2021,41(6):82-87.
- [73] 刘达,李连侠,黄本胜,等.双浅水垫消力池水力特性的数值模拟与试验研究[J].水利学报,2012,43(5):623-630.LIU Da,LI Lianxia,HUANG Bensheng,et al.Numerical simulation and experimental investigation on stilling basin with double shallow-water cushions[J].Journal of Hydraulic Engineering,2012,43 (5):623-630.
- [74] LI L,LIAO H,LIU D,et al.Experimental investigation of the optimization of stilling basin with shallow-water cushion used for low Froude number energy dissipation[J].Journal of Hydrodynamics,2015,27(4):522-529.
- [75] 吴宇峰,伍超,刘小兵.渐扩散水跃跃长的研究[J].水科学进展,2007,18(2):210-215.WU Yufeng,WU Chao,LIU Xiaobing.Length of hydraulic jump in gradually broadened channel[J].Advances in Water Science,2007,18(2):210-215.
- [76] 梁砚,周赤,段文刚.折坡扩散型消力池的水跃特性试验研究[J].长江科学院院报,2017,34(3):53-57.LIANG Yan,ZHOU Chi,DUAN Wengang.Characteristics of hydraulic jump in stilling basin with upstream diffusion slope[J].Journal of Yangtze River Scientific Research Institute,2017,34 (3):53-57.
- [77] 郑梅玲,李辉成.数值模拟在渐扩式折坡消力池中的应用[J].水利与建筑工程学报,2018,16(2):194-199.ZHENG Meiling,LI Huicheng.Numerical simulation of sloping stilling basin with diffuser wall[J].Journal of Water Resources and Architectural Engineering,2018,16 (2):194-199.
- [78] 杜振康,尹进步,朱光明,等.不同扩散角下单侧渐扩消力池水力特性研究[J].水资源与水工程学报,2022,33(2):144-151.DU Zhenkang,YIN Jinbu,ZHU Guangming,et al.Hydraulic characteristics of unilateral divergent stilling basin under different diffusion angles[J].Journal of Water Resources and Water Engineering,2022,33 (2):144-151.
- [79] LI Q,LI L,LIAO H.Study on the best depth of stilling basin with shallow-water cushion[J].Water,2018,10(12):1801.
- [80] KHANAHMADI E,DEHGHANI A A,HALAGHI M M,et al.Investigating the characteristic of hydraulic T-jump on rough bed based on experimental and numerical modeling[J].Modeling Earth Systems and Environment,2022,8(4):5695-5712.
- [81] 陈希,许光祥.低弗氏数下旋桨式消力墩的应用研究[J].人民长江,2014,45(S2):220-223.CHEN Xi,XU Guangxiang.Application research of spinning-type energy dissipation block at low froude number [J].Yangtze River,2014,45(S2):220-223.
- [82] 刘洪滨,王亚洲,王均星,等.低Froude数新型消能尾坎数值模拟研究[J].中国农村水利水电,2020(8):221-226.LIU Hongbin,WANG Yazhou,WANG Junxing,et al.Numerical simulation of a new type of energy dissipation tail for low froude numbers [J].China Rural Water and Hydropower,2020(8):221-226.
- [83] 杨敏,练继建.拱网水力特性研究[J].水利水电技术,2001,32(12):49-50.YANG Min,LIAN Jijian.Study on hydraulie characteristics of arch mesh barrier [J].Water Resources and Hydropower Engineering,2001,32(12):49-50.
- [84] 赵乾,牧振伟,周凯,等.趾墩-梯形墩联合消能工水力特性[J].长江科学院院报,2025,42(1):120-128.ZHAO Qian,MU Zhenwei,ZHOU Kai,et al.Hydraulic characteristics of chute block-trapezoidal block joint dissipator[J].Journal of Yangtze River Scientific Research Institute,2025,42 (1):120-128.
- [85] 俞晓伟,牧振伟,高尚.梯形墩-悬栅消力池水力特性数值模拟[J].排灌机械工程学报,2025,43(1):66-73.YU Xiaowei,MU Zhenwei,GAO Shang.Numerical simulation on hydraulic characteristics of trapezoidal pier-suspended grid stilling basin[J].Journal of Drainage and Irrigation Machinery Engineering,2025,43(1):66-73.
- [86] 张宗孝,魏文礼.掺气分流墩与消力池联合应用消能机理分析与试验验证[J].武汉大学学报(工学版),2006,29(6):14-17.ZHANG Zongxiao,WEI Wenli.Analysis of mechanism of jointed energy dissipation of stilling basin and aerated baffle and its validation by experiment[J].Engineering Journal of Wuhan University,2006,29 (6):14-17.
- [87] 李阳,李开军,杨磊.X形宽尾墩消能水力特性研究[J].武汉大学学报(工学版),2021,54(12):1111-1118.LI Yang,LI Kaijun,YANG Lei.Research on hydraulic characteristics of energy dissipation of X-shaped flaring gate pier[J].Engineering Journal of Wuhan University,2021,54(12):1111-1118.
- [88] 张建民.高坝泄洪消能技术研究进展和展望[J].水力发电学报,2021,40(3):1-18.ZHANG Jianmin.Hydraulics of high-speed flows:recent achievements and future outlook[J].Journal of Hydroelectric Engineering,2021,40(3):1-18.
- [89] 张声呜.低佛氏数水跃消能中的几个问题[J].人民长江,1992,23(7):39-45.ZHANG Shengwu.Several problems in low froude number hydraulic jump energy dissipation [J].Yangtze River,1992,23(7):39-45.
- [90] IBRAHIM M M,REFAIE M A,IBRAHEEM A M.Flow characteristics downstream stepped back weir with bed water jets[J].Ain Shams Engineering Journal,2022,13(2):101558.
- [91] SCHERES B,SCHUTTRUMPF H,FELDER S.Flow