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.

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.

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.

Wave Decay and Its Characteristics in Surf Zone

In accordance with the similarity between breaking waves and hydraulic jumps, the expressions for estimating wave decay and wave energy dissipation in the surf zone are derived based on the fundamental equations of fluid mechanics. Using the numerical solution of cnoidal wave theory, the various kinematic properties of waves in the surf zone, including the relative wave crest height, wave energy, and radiation stress are discussed. The values calculated with the method proposed in this paper are in good agreement with the experimental data gained by other researchers. The present expressions can be used in the studies of sediment transport on gently sloping beaches, especially on muddy beaches.

Experimental and numerical investigation for energy dissipation of supercritical flow in sudden contractions

Dealing with kinetic energy is one of the most important problems in hydraulic structures,and this energy can damage downstream structures.This study aims to study energy dissipation of supercritical water flow passing through a sudden contraction.The experiments were conducted on a sudden contraction with 15 cm width.A 30 cm wide flume was installed.The relative contraction ranged from 8.9 to 9.7,where relative contraction refers to the ratio of contraction width to initial flow depth.The Froude value in the investigation varied from 2 to 7.The contraction width of numerical simulation was 5~15 cm,the relative contraction was 8.9~12.42,and the Froude value ranged from 8.9~12.42.In order to simulate turbulence,the k-εRNG model was harnessed.The experimental and numerical results demonstrate that the energy dissipation increases with the increase of Froude value.Also,with the sudden contraction,the rate of relative depreciation of energy is increased due to the increase in backwater profile and downstream flow depth.The experimentation verifies the numerical results with a correlation coefficient of 0.99 and the root mean square error is 0.02.

Simulation of open channel flows by an explicit incompressible mesh-free method

In this study,to simulate open channel flows,an explicit incompressible mesh-free method is employed in which the pressure field is obtained by explicitly solving the pressure Poisson equation.To capture the velocity information in open channel flows,the source term in the pressure Poisson equation is modified while the spatial discretization of gradient and Laplacian models is based on the moving particle semi-implicit(MPS)method.The inflow boundary condition is treated by injecting fluid particles into the domain according to the inlet discharge,and the outflow condition is handled by prescribing the pressure distribution and removing the fluid particles beyond the domain.The explicit incompressible mesh-free method is then used to simulate open channel flows,including weir flow,hydraulic jump,and flow over an obstacle.In the simulations,velocity distribution and flow pattern are examined.The simulated results are compared to available experimental measurements and other numerical results.There is a good agreement between the simulated results and the experimental measurements.It shows that the explicit incompressible mesh-free method can reproduce the flow characteristics in the open channel flows.

A NEW HIGH ORDER SCHEME FOR CONVECTION EQUATION AND ITS APPLICATION

With the undetermined coefficient method, a new high order scheme for convection equation named as HAUC was worke d out. The accuracy of the new scheme was analyzed by comparing the computed res ults with the exact solutions of 1-D pure convection equation and nonlinear con vection equation. The effectiveness of the HAUC was also examined by comparing w ith the results obtained by other schemes. Finally, it was applied to simulate 1 -D dam break flow with differenct ratios of initial upstream water depth to do wnstream one. The results show that the scheme has the ability to simulate both undular bores and moving hydraulic jumps.

Particle image velocimetry measurements of vortex structures in stilling basin of multi-horizontal submerged jets

Measurements of turbulent flow fields in a stilling basin of multi-horizontal submerged jets were made with the single- camera Particle Image Velocimetry （PIV）. The particle images were captured, processed, and subsequently used to characterize the flow in terms of the 2-D velocity and vorticity distributions. This study shows that the maximum close-to-bed velocity in the stilling basin is approximately reduced by 60%, comparing to the jet velocity at the outlet of orifices. The jet velocity is distributed evenly at the latter half of the stilling basin and the time-averaged velocity of the cross section is reduced by 77%-85%, comparing to the jet velocity at the outlet of orifices. These results show that the vortices with horizontal axes are continuously repeated during the form-merge-split-disappear process. The vertical vortices are continuously formed and disappeared, they appear randomly near the slab and intermittently reach the slab of the stilling basin. The range of these vortices is small. Vortices with horizontal axes and ver- tical vortices do not coincide in space and the vortices with horizontal axes only affect the position of the tail of the vertical vortices attached to the slab of the stilling basin.