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.

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.

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.

Local hydraulic jump effects on sediment deposition in open-channel flume experiments

When a river channel is narrow,bifurcated,or intersected,or when extreme weather or geological disasters cause shed rock masses to occupy a river flood channel,local hydraulic jumps may develop in the channel.Natural disasters such as landslides,floods,and debris flows occur upstream,will result in large transport rate of large-sized gravel particles.Those particles may be blocked in hydraulic jump areas,causing river channel water depth to rise.In this study,the effect of local hydraulic jumps on the sediment deposition rate was investigated in flume experiments.The ratio of upstream and downstream Froude numbers,particle size,Sediment supply intensity,and flow discharge all affected the sediment deposition rate.With increases in the ratio of upstream and downstream Froude numbers,particle size,and sediment supply intensity,the sediment deposition rate increased.The sediment deposition rate decreased with an increase in flow discharge.Approach hydraulic conditions and particle properties jointly determined the sediment deposition rate in a hydraulic jump section,and an empirical formula was developed using those parameters to calculate the sediment deposition rate.Thus,to identify risks and prevent disasters in mountain rivers,local changes in hydraulic conditions and particle properties need to be jointly evaluated.

Air entrainment of hydraulic jump aeration basin

In order to avoid the cavitation damage and the decrease of the energy dissipation of the stepped spillways with a large unit discharge, the air entrainments of the hydraulic jump aeration basin （HJAB） are theoretically and experimentally investigated for the hydraulic-jump-stepped spillway developed by the authors. It is shown that the submerged degree of the hydraulic jump and the air concentration in the measuring section are all functions of the dimensionless discharge, the length and the end sill height of the H JAB. The submerged degree odecreases with the increase of the dimensionless discharge or the dimensionless length of the H JAB, but increases with the increase of the dimensionless height of the end sill of the HJAB. The flow regimes near the critical hydraulic jump, namely, at or= 1.0, have the best effect of the air entrainment for the flow at the measuring section and then that of the stepped spillway.

A GENERALIZED EXPLICIT SOLUTION OF THE SEQUENT DEPTH RATIO FOR THE HYDRAULIC JUMP

By use of the property of the momentum equation describing the hydraulic jump in rectangular channels, a generalized solution of the sequent depth ratio was given. On the basis of the generalized solution the explicit solutions of the sequent depth ratio were obtained for the hydraulic jump in gradual enlargements, the corresponding relative energy losses were also presented, and a method to determine the location of hydraulic jump in gradual enlargements was proposed.

Hydraulic jump basins with wedge-shaped baffles

This laboratory study deals with the hydraulic jump properties for an artificially roughened bed with wedge-shaped baffle blocks. The experiments were conducted for both smooth and rough beds with a Froude number in the range of 3.06≤F1≤10.95 and a relative bed roughness ranging 0.22≤KR≤1.4. The data from this study were compared with those of rectangular baffle blocks. New experimental formulae were developed for determining the sequent depth ratio and the hydraulic jump length in terms of the inflow Froude number and relative bed roughness. Bélanger's jump equation of a rectangular channel was extended to account for the implications of the bed shear stress coefficient attributable to channel bed roughness. It was found that, in comparison with the smooth bed, the wedge-shaped bed roughness reduced the sequent depth of the hydraulic jump by approximately 16.5% to 30% and the hydraulic jump length by approximately 30% to 53%.

PRESSURE FLUCTUATIONS BENEATH SPATIAL HYDRAULIC JUMPS

This article deals with statistical analysis of pressure fluctuations at the bottom of spatial hydraulic jumps with abrupt lateral expansions. The effects of the channel expansion ratio and inflow condition on the power spectral and dominant frequency were examined. Pressure data were recorded for different Froude numbers ranging from 3.52 to 6.86 and channel expansion ratios ranging from 1.5 to 3.0. A sampling frequency of 100 Hz was selected. The measurements were conducted in the bed of a glass-walled laboratory flume by means of pressure transducers and data acquisition systems. Power spectra as well as dominant frequency and some other statistical characteristics of fluctuating pressure beneath hydraulic jumps were obtained. Test results were compared with those of classical jump, which indicates that the peak frequencies and intensity coefficients of pressure fluctuations are higher than those of the corresponding classical jumps.

A STUDY OF WAVE CHARACTERISTICS AFTER HYDRAULIC JUMP

An experimental study of wave characteristics after jump in energy dissipation of hydraulic jump is presentedinthis paper.It was completed in a trough with a horizontal bed, 40cm in width.Various elements of wave were measured,the wave form,period,spectrum and its attenuation along course are analyzed,and the physical mechanism of wave is discussed. An expression of the maximum wave height after jump is given,based on the measured data. Some measures to diminish wave are discussed preliminarily also.

SPH numerical investigation of the characteristics of an oscillating hydraulic jump at an abrupt drop

This paper shows the results of the smooth particle hydrodynamics（SPH） modelling of the hydraulic jump at an abrupt drop,where the transition from supercritical to subcritical flow is characterised by several flow patterns depending upon the inflow and tailwater conditions. SPH simulations are obtained by a pseudo-compressible XSPH scheme with pressure smoothing; turbulent stresses are represented either by an algebraic mixing-length model, or by a two-equation k-ε model. The numerical model is applied to analyse the occurrence of oscillatory flow conditions between two different jump types characterised by quasi-periodic oscillation,and the results are compared with experiments performed at the hydraulics laboratory of Bari Technical University. The purpose of this paper is to obtain a deeper understanding of the physical features of a flow which is in general difficult to be reproduced numerically,owing to its unstable character： in particular, vorticity and turbulent kinetic energy fields, velocity, water depth and pressure spectra downstream of the jump, and velocity and pressure cross-correlations can be computed and analysed.

SIMILARITY LAW OF FLUCTUATING PRESSURE WITHIN HYDRAULIC JUMP AREA

For further study of the similarity law of fluctuating pressure, a series of model tests with more scales, covering a wide range of Reynolds number and Froude number have been completed. The data of the fluctuating pressure acting the floor level within 2-D free hydraulic jump were obtained. Froude number varied from 2.94 to 8.61, and Reynolds number ranged from 2×104 to 6×105. The tests were conducted in a glass flume with 0.2 m in width and six fluctuating pressure probes (Type CYG-01) were installed on the floor within the jump. Experimental results indicate that the amplitude scale of fluctuating pressure is the length of the model, i.e., Pr=Lr, which agrees with gravity similarity law. The frequency scale of the fluctuating pressure is an unity i.e., fr=1, which does not satisfy the gravity similarity law.

Hydraulic jump and choking of flow in pipe with a change of slope

This paper investigates hydraulic jumps in sloping pipes by means of wall-resolved large eddy simulation(LES).The purpose is to achieve an improved understanding of jump behaviours driven by pipe discharge and slope.The LES model predicts the hydraulic jump as a 3-D two-phase flow,with air as the gas phase and water as the liquid phase.The predictions yield instantaneous velocity and pressure fields as well as fluid volume fraction.The instantaneous flow variables allow ensemble averages,which quantify the internal structures and integral properties of the hydraulic jump.The predicted instantaneous velocity shows spectra in consistency with the well-known Kolmogorov−5/3 law.The ensemble averages of air and water velocities,free-surface profile,roller length and aeration length,compare well with available experimental data.The jump behaviours are complex.Some aspects such as free-surface fluctuation and jump-toe oscillation resemble the classical hydraulic jump on horizontal floors.Others like the 3-D distributions of core jet,vorticity and aeration are much more complicated.Depending on the pipe discharge and slope,the resulting jump can be a complete or an incomplete jump.The incomplete hydraulic jump causes choked flow downstream.This has severe consequences on drainage conditions in sewer pipes laid on sloping terrain.This paper proposes using the Okubo-Weiss parameter as a new way to subtly delineate the region of hydraulic jump.It is much more efficient and less ambiguous,compared with traditional visual inspections.

STUDIES ON THE TWO-DIMENSIONAL FREE HYDRAULIC JUMP TAKING ACCOUNT OF TURBULENCE INTENSITY AND OTHER FACTORS

Taking account of turbulence intensity, non-uniformity of velocity distribution at the initial and sequent section of hydraulic jump and frictional drag on the floor within jump range, this paper derives new formulas for calculating the ratio of conjugate depths and the efficiency of energy dissipation in the two-dimensional free hydraulic jump. It has been verified by test data that the new formulas are not only exact in theory but also still better in conformity with practice.

Analogy Between Hydraulic Jump in Films Formed by Impinging Liquid Jet and Critical Flow in Internal Flows

Formulated are simple models for the flow in liquid film, formed by impinging jet, and a two-phase downward flow in pipe. The models are based on simplified equations of mass, momentum and energy. The solutions of such conservation equations may have regular points belonging to one integral curve only as well as turning points can be found amongst them, which refer to extreme values in the appropriate co-ordinate system. The solutions can also have singular points belonging to none or more than one integral curve. Both the turning and singular points have a clear physical meaning. They could be linked to critical flow conditions in the pipe flow or to the so-called hydraulic jump. Analogy existing between critical conditions in the pipe and the flow of liquid films formed by the liquid jet have been shown in the paper.

Theoretical Analysis of Hydraulic Jump on ExtremelySmall Size Liquid Jet Impingement

A theoretical study was conducted to characterize hydraulic jump of laminar circular liquid jets. The objective of this research was to determine the jump location in a simple explicit form. The effects of many factors were investigated including nozzle diameter, jet exit pressure, nozzle-to-plate spacing, jet velocity and Reynolds number. It was found that the theoretical data collapsed well over the range of jet Reynolds number 500 Re 1800 with previous data.