Study of a Hydraulic Jump in an Asymmetric Trapezoidal Channel with Different Sluice Gates

In this study,the main properties of the hydraulic jump in an asymmetric trapezoidal flume are analyzed experimentally,including the so-called sequent depths,characteristic lengths,and efficiency.In particular,an asymmetric trapezoidal flume with a length of 7 m and a width of 0.304 m is considered,with the bottom of the flume transversely inclined at an angle of m=0.296 and vertical lateral sides.The corresponding inflow Froude number is allowed to range in the interval(1.40<F1<6.11).The properties of this jump are compared to those of hydraulic jumps in channels with other types of cross-sections.A relationship for calculating hydraulic jump efficiency is proposed for the considered flume.For F1>5,the hydraulic jump is found to be more effective than that occurring in triangular and symmetric trapezoidal channels.Also,when■mes>8 and■>5,the hydraulic jump in the asymmetrical trapezoidal channel downstream of a parallelogram sluice gate is completely formed as opposed to the situation where a triangular sluice is considered.

Experiments on two-phase flow in hydraulic jump on pebbled rough bed:Part 2–Bubble clustering

A survey on bubble clustering in air–water flow processes may provide significant insights into turbulent two-phaseflow.These processes have been studied in plunging jets,dropshafts,and hydraulic jumps on a smooth bed.As a first attempt,this study examined the bubble clustering process in hydraulic jumps on a pebbled rough bed using experimental data for 1.70<Fr_(1)<2.84(with Fr_(1) denoting the inflow Froude number).The basic properties of particle grouping and clustering,including the number of clusters,the dimensionless number of clusters per second,the percentage of clustered bubbles,and the number of bubbles per cluster,were analyzed based on two criteria.For both criteria,the maximum cluster count rate was greater on the rough bed than on the smooth bed,suggesting greater interactions between turbulence and bubbly flow on the rough bed.The results were consistent with the longitudinal distribution of the interfacial velocity using one of the criteria.In addition,the clustering process was analyzed using a different approach:the interparticle arrival time of bubbles.The comparison showed that the bubbly flow structure had a greater density of bubbles per unitflux on the rough bed than on the smooth bed.Bed roughness was the dominant parameter close to the jump toe.Further downstream,Fr_(1) predominated.Thus,the rate of bubble density decreased more rapidly for the hydraulic jump with the lowest Fr_(1).

Experiments on two-phase flow in hydraulic jump on pebbled rough bed:Part 1–Turbulence properties and particle chord time and length

This study reported and discussed turbulence characteristics,such as turbulence intensity,correlation time scales,and advective length scales.The characteristic air–water time scale,including the particle chord time and length and their probability density functions(PDFs),was investigated.The results demonstrated that turbulence intensity was relatively greater on a rough bed in the roller length,whereas further downstream,the decay rate was higher.In addition,the relationship between turbulence intensity and dimensionless bubble count rate reflected an increase in turbulence intensity associated with the number of entrained particles.Triple decomposition analysis(TDA)was performed to determine the contributions of slow and fast turbulent components.The TDA results indicated that,regardless of bed type and inflow conditions,the sum of the band-pass(T'_(u))and high-pass(T″_(u))filtered turbulence intensities was equal to the turbulence intensity of the raw signal data(T_(u)).T″_(u) highlighted a higher turbulence intensity and larger vorticities on the rough bed for an identical inflow Froude number.Additional TDA results were presented in terms of the interfacial velocity,auto-and cross-correlation time scales,and longitudinal advection length scale,with the effects of low-and high-frequency signal components on each highlighted parameter.The analysis of the air chord time indicated an increase in the proportion of small bubbles moving downstream.The second part of this research focused on the basic properties of particle grouping and clustering.

Characterizing three-dimensional features of Antarctic subglacial lakes from the inversion of hydraulic potential——Lake Vostok as a case study

To estimate basal water storage beneath the Antarctic ice sheet, it is essential to have data on the three-dimensional characteristics of subglacial lakes. We present a method to estimate the water depth and surface area of Antarctic subglacial lakes from the inversion of hydraulic potential method. Lake Vostok is chosen as a case study because of the diverse and comprehensive measurements that have been obtained over and around the lake. The average depth of Lake Vostok is around 345±4 m. We estimated the surface area of Lake Vostok beneath the ice sheet to be about 13300±594 km^2. The lake consists of two sub-basins separated by a ridge at water depths of about 200–300 m. The surface area of the northern sub-basin is estimated to be about half of that of the southern basin. The maximum depths of the northern and southern sub-basins are estimated to be about 450 and 850 m, respectively. Total water volume is estimated to be about 4658±204 km^3. These estimates are compared with previous estimates obtained from seismic data and inversion of aerogravity data. In general, our estimates are closer to those obtained from the inversion of aerogravity data than those from seismic data, indicating the applicability of our method to the estimation of water depths of other subglacial lakes.

Dynamic hydraulic jump and retrograde sedimentation in an open channel induced by sediment supply: experimental study and SPH simulation

Mountainous torrents often carry large amounts of loose materials into the rivers, thus causing strong sediment transport. Experimentally it was found for the first time that when the intensive sediment motion occurs downstream over a gentle slope, the siltation of the riverbed is induced and the sediment particles can move upstream rapidly in the form of a retrograde sand wave, resulting in a higher water level along the river. To further study the complex mechanisms of this problem, a sediment mass model in the framework of the Smoothed Particle Hydrodynamics(SPH) method was presented to simulate the riverbed evolution, sediment particle motion, and the generation and development of dynamic hydraulic jump under the condition of sufficient sediment supply over a steep slope with varying angles. Because the sediment is not a continuous medium, the marker particle tracking approach was proposed to represent a piece of sediment with a marked sediment particle. The twophase SPH model realizes the interaction between the sediment and fluid by moving the bed boundary particles up and down, so it can reasonably treat the fluid-sediment interfaces with high CPU efficiency. The critical triggering condition of sediment motion, the propagation of the hydraulic jump and the initial siltation position were all systematically studied. The experimental and numerical results revealed the extra disastrous sediment effect in a mountainous flood. The findings will be useful references to the disaster prevention and mitigation in mountainous rivers.

Effect of buried plates on scour profiles downstream of hydraulic jump in open channels with horizontal and reverse bed slopes

Local scour downstream of sluice gates in erosive beds is one of the main concerns of hydraulic engineers because it can cause considerable damage to structures.Many researchers have conducted various studies to predict the maximum depth and length of scour holes and to develop new methods to control this phenomenon.In the methods that have recently been examined,embedded buried plates are used to control the scour in the erosive beds.In this study,using a physical model,the effect of buried plates in erosive beds on the depth of scour downstream of a hydraulic jump was studied.Several experiments were performed in which plates were buried at 50° and 90° angles at different distances from the apron in open channels with horizontal and reverse bed slopes.The results of experiments in which the scour profiles were drawn in dimensionless forms show that the angle and position of the plates are important to controlling and reducing scour depth.In fact,by reducing the angle of buried plates,the maximum depth of scour is also reduced.Also,comparison of the results of a single buried plate and double buried plates shows that using two buried plates at the distances of 30 and 45 cm from the non-erodible bed is more effective in reducing the scour depth.The best distances of the buried plates with angles of 90° and 50° from the non-erodible bed are 45 cm and 30 cm,respectively,in the condition with a single buried plate.

Bubble entrainment, spray and splashing at hydraulic jumps

The sudden transition from a high-velocity, supercritical open channel flow into a slow-moving sub-critical flow is a hydraulic jump. Such a flow is characterised by a sudden rise of the free-surface, with some strong energy dissipation and air entrainment, waves and spray. New two-phase flow measurements were performed in the developing flow region using a large-size facility operating at large Reynolds numbers. The experimental results demonstrated the complexity of the flow with a developing mixing layer in which entrained bubbles are advected in a high shear stress flow. The relationship between bubble count rates and void fractions was non-unique in the shear zone, supporting earlier observations of some form of double diffusion process between momentum and air bubbles. In the upper region, the flow consisted primarily of water drops and packets sur-rounded by air. Visually significant pray and splashing were significant above the jump roller. The present study is the first com-prehensive study detailing the two-phase flow properties of both the bubbly and spray regions of hydraulic jumps, a first step towards understanding the interactions between bubble entrainment and droplet ejection processes.

Study on the Mathematical Model of Hydraulic Jump Atomization

An equation of atomization quantity from energy dissipation by hydraulic jump was derived from the dimensional analysis. By applying Gauss diffusion equation, the spray diffusion rule in valley was studied under the condition of continuous linear source and random wind direction.By considering the spray rain switching process, coagulation, condensation and evaporation of droplets, the air temperature, air relative humidity, spray density and the rainfall intensity in the lower reaches of the linear source were calculated. The 3 D numerical simulation fitted well with prototype monitoring. Finally, the prediction of atomization influence on environments for Xiangjiaba Hydropower Station was conducted.

Dissipative preparation of a steady three-dimensional entangled state via quantum-jump-based feedback

A robust and scalable scheme to generate a steady three-dimensional entangled state for a V-type atom and a A- type atom trapped in a strongly dissipative bimodal cavity is proposed by direct feedback control based on quantum-jump detection. The robustness of this scheme reflects in the insensitivity to detection inefficiencies and the strong ability against the parameter fluctuations in the feedback, driving, and coupling strengths. The influence of atomic spontaneous emission can be suppressed by using the local feedback control. The scalability is ensured that N-dimensional entangled states of two atoms can be deterministically generated.

Proposed Equation to Estimate the Length of a Hydraulic Jump in a Rectangular Open Channel Hydraulic with Variable Slope, and Its Comparison with Seven Theoretical Equations of Specialized Literature

A hydraulic jump is a localized phenomenon that generates on an open hydraulic channel;however, its mathematical demonstration is not possible in the turbulent area of the phenomenon, especially in the area where the jump occurs and where its length is measured, so the data must be obtained with direct measurements in a laboratory and through empiric equations. This work presents the results of the generated hydraulic jumps and the measure of its length in a series of tests, where we input different flow rates in a transportable open channel hydraulic with a constant gate opening “a” and a slope of S = 0.0035, in the Engineering Faculty Research Centre of the Autonomous University of Chiapas. We also present the experimental method to generate a hydraulic jump, the measure of its length and a comparison with seven empirical equations, including the Sie&ntilde;chi equation used in H-Canales, the most used software for hydraulic channels design in Latin America. The results show that the calculus of L with the proposed equation has a mean squared error (MSE) of 0.1337, a Bias of -0.0049, a model efficiency (ME) of 0.9991 and a determination coefficient (R2) of 0.9993 when compared with the experimental model. Meanwhile, the comparison of L calculated with the Sie&ntilde;chi equation versus the experimental model resulted in a MSE of 0.1741, a bias of -0.0437, a ME of 0.9984 and a R2 of 0.9997. Both equations are highly recommended to estimate L in rectangular channels under the conditions presented in this paper, thus, the proposed equation can be applied if??y . Finally, it must be stated that we also proved that the Pavlosky equation is comparable in precision and accuracy concerning to proposed equation and Sie&ntilde;chi equation.

Hydraulic Jump in the Gulf of California

Acoustic Doppler current profiles and water density profiles were measured over the 280 m deep continental slope of the Gulf of California to elucidate the bathymetric effect on zooplankton distribution. These measurements were combined with water velocity and density simulations from the Regional Ocean Model System with and without the influence of Coriolis acceleration. The data revealed an acceleration of the near-bottom flow as it moved toward increasing depths. This acceleration was produced by the adjustment of the isopycnals to bathymetry (hydraulic jump). Zooplankton patches moved downward at the continental slope and then upward, thus exhibiting wave patterns. Model outputs without the effect of Coriolis acceleration also suggested that vertical zooplankton concentration followed a wave pattern. However, when Coriolis acceleration was added to the momentum equation, the horizontal zooplankton distribution was enhanced, which reduced the vertical zooplankton concentration observed over irregular bathymetries. Coriolis acceleration was responsible for horizontal dispersal of up to 20% of the total zooplankton concentration located over the wave trough.

Estimation of hydraulic jump on corrugated bed using artificial neural networks and genetic programming

Artificial neural networks （ANNs） and genetic programming （GP） have recently been used for the estimation of hydraulic data. In this study, they were used as alternative tools to estimate the characteristics of hydraulic jumps, such as the free surface location and energy dissipation. The dimensionless hydraulic parameters, including jump depth, jump length, and energy dissipation, were determined as functions of the Froude number and the height and length of corrugations. The estimations of the ANN and GP models were found to be in good agreement with the measured data. The results of the ANN model were compared with those of the GP model, showing that the proposed ANN models are much more accurate than the GP models.

Geometry and Dynamic Forces along an Inclined Hydraulic Jump over a Rough Channel Bed

In this investigation, based on previous measurements, the geometry and dynamic forces along an inclined （angle φ, with 0^0 〈 qφ φ 8^0 ） hydraulic jump over a variation of rough and smooth channel beds, are examined and compared among them. The roughness is produced through transverse strips （of square cross section） covering the entire channel width and at various normal distributions along the channel. Froude numbers are varying up to 18.5 and conjugate depths＇ ratios up to 18.4. The water free surface profiles, the conjugate depths＇ ratios, the jumps＇ dimensionless lengths are examined and a prediction of exercised forces, in dimensionless terms, is also presented. The results and especially the latter force prediction may help the hydraulic and structural engineers when dealing with such hydraulic jumps.

Smoothed Particle Hydrodynamic Modelling of Hydraulic Jumps: Bulk Parameters and Free Surface Fluctuations

A hydraulic jump is a rapid transition from supercritical flow to subcritical flow characterized by the development of large scale turbulence, surface waves, spray, energy dissipation and considerable air entrainment. Hydraulic jumps can be found in waterways such as spillways connected to hydropower plants and are an effective way to eliminate problems caused by high velocity flow, e.g. erosion. Due to the importance of the hydropower sector as a major contributor to the Swedish electricity production, the present study focuses on Smoothed Particle Hydrodynamic (SPH) modelling of 2D hydraulic jumps in horizontal open channels. Four cases with different spatial resolution of the SPH particles were investigated by comparing the conjugate depth in the subcritical section with theoretical results. These showed generally good agreement with theory. The coarsest case was run for a longer time and a quasi-stationary state was achieved, which facilitated an extended study of additional variables. The mean vertical velocity distribution in the horizontal direction compared favorably with experiments and the maximum velocity for the SPH-simulations indicated a too rapid decrease in the horizontal direction and poor agreement to experiments was obtained. Furthermore, the mean and the standard deviation of the free surface fluctuation showed generally good agreement with experimental results even though some discrepancies were found regarding the peak in the maximum standard deviation. The free surface fluctuation frequencies were over predicted and the model could not capture the decay of the fluctuations in the horizontal direction.

An extended J-integral for evaluating fluid-driven cracks in hydraulic fracturing

J-integral has served as a powerful tool in characterizing crack tip status. The main feature, i.e. path- independence, makes it one of the foremost fracture parameters. In order to remain the path- independence for fluid-driven cracks, J-integral is revised. In this paper, we present an extended J-in- tegral explicitly for fluid-driven cracks, e.g. hydraulically induced fractures in petroleum reservoirs, for three-dimensional （3D） problems. Particularly, point-wise 3D extended J-integral is proposed to char- acterize the state of a point along crack front. Besides, applications of the extended J-integral to porous media and thermally induced stress conditions are explored. Numerical results show that the extended J- integral is indeed path-independent, and they are in good agreement with those of equivalent domain integral under linear elastic and elastoplastic conditions. In addition, two distance-independent circular integrals in the K-dominance zone are established, which can be used to calculate the stress intensity factor （SIF）.

Three-dimensional stochastic seepage field for embankment engineering

Owing to the complexity of geo-engineering seepage problems influenced by different random factors, three-dimensional simulation and analysis of the stochastic seepage field plays an important role in engineering applications. A three-dimensional anisotropic heterogeneous steady random seepage model was developed on the basis of the finite element method. A statistical analysis of the distribution characteristics of soil parameters sampled from the main embankment of the Yangtze River in the Southern Jingzhou zone of China was conducted. The Kolomogorov-Smirnov test verified the statistical hypothesis that the permeability coefficient tensor has a Gaussian distribution. With the help of numerical analysis of the stochastic seepage field using the developed model, various statistical and random characteristics of the stochastic seepage field of the main embankment of the Yangtze River in the Southern Jingzhou zone of China were investigated. The model was also examined with statistical testing. Through the introduction of random variation of the upstream and downstream water levels into the model, the effects of the boundary randomness due to variation of the downstream and upstream water levels on the variation of simulated results presented with a vector series of the random seepage field were analyzed. Furthermore, the combined influence of the variation of the soil permeability coefficient and such seepage resistance measures as the cut-off wall and relief ditch on the hydraulic head distribution was analyzed and compared with the results obtained by determinate analysis. Meanwhile, sensitivities of the hydraulic gradient and downstream exit height to the variation of boundary water level were studied. The validity of the simulated results was verified by stochastic testing and measured data. The developed model provides more detail and a full stochastic algorithm to characterize and analyze three-dimensional stochastic seepage field problems.

低弗劳德数条件下尾坎坡度对消力池内流场结构的影响

低水头、大流量条件下泄洪,易形成低弗劳德数水流,对下游河床和边坡造成冲刷风险。基于某水利枢纽工程,采用数值模拟的方法,应用RNG k-ε数值模型,研究了不同尾坎坡度体型下消力池内低弗劳德数水跃的流场特征。研究结果表明:低弗劳德数来流条件下,消力池内形成的淹没式水跃沿水流方向可分为核心区、发展区和回流区;核心区在水深方向上按流速特性又分为射流内层、射流外层、旋滚内层和旋滚外层;不同尾坎坡度的消力池中,均遵循时均压强沿程增大、临底流速自收缩断面后沿程减小的规律;尾坎坡度变陡会使得水跃的旋滚起始断面向上游移动,旋滚终止断面向下游移动,从而使得旋滚长度增大;当尾坎坡度为1∶3时,尾坎斜坡段临底流速梯度为0,当尾坎坡度小于1∶3时,尾坎斜坡段临底流速梯度为负,当坡度大于1∶3时,流速梯度为正,其原因是尾坎坡度变陡使得尾坎对水体的阻力在平行于尾坎坡面方向的分量减小,从而使得流速梯度逐渐增大。研究成果可为类似工程中消力池的设计选型提供参考。

窄河谷大夹角挑流消能工体型优化研究

针对窄河谷大夹角条件下挑流消能易出现冲击两岸、冲坑过深的问题,采用水工整体模型试验方法对具有代表性的某水利枢纽深孔放水冲沙洞挑流鼻坎体型开展优化研究,并对比分析了水舌形态和下游河道冲刷特性。结果表明,不对称收缩的异型窄缝式消能工可使水流在狭窄河道归槽,水舌纵向拉伸效果较好,大幅减轻了河床冲刷;提出了收缩比、收缩角差、斜切面积比等特征参数适宜的挑流消能工体型,可供窄河谷大夹角条件下挑流消能设计参考。

消力坎对跌坎消力池坎控水跃影响的试验研究

跌坎消力池的设计一直是水利工程领域的热点问题,设计合理的消力池可以保证在短距离内有相当大的消能。笔者通过模型试验研究了跌坎消力池中不同高度和不同位置的消力坎对坎控水跃的影响,并与不加消力坎时消力池内相同水跃流态进行对比。结果表明:增设消力坎可有效缩短越长,减小共轭水深比,增大水跃消能率。随着消力坎距跃首距离的减小或者消力坎高度的增加,消力坎在减小水跃长、共轭水深比,增大消能率方面的作用越来越大。同时经过无量纲分析得出了消力坎设置在不同位置和高度条件下,相对水跃长度、共轭水深比和消能率的经验公式。该研究结果可为类似水工建筑物的设计提供参考。

中心有孔金属圆盘在水面漂浮现象的研究

本文从理论和实验两方面研究了中心有孔的金属圆盘能够漂浮于水面这一现象.建立了湍流模型以及VOF模型,并通过对漂浮于水面的金属圆盘进行受力分析,得到金属圆盘漂浮的临界条件.研究结果表明,小孔半径差、圆盘自身密度、水流量大小以及出水口大小是影响金属圆盘漂浮水面的主要因素.根据理论分析,建立模型进行了仿真分析和实验,对实验结果误差进行了分析.结果表明,所得实验结论及仿真结论与理论分析一致,具有一定的应用价值.