Search

Hydraulic jumps are induced in hydraulic facilities for the purposes of energy dissipation or flow aeration. Presently there is no means for a simple estimate of void fraction distribution and air entrainment flux, without detailed physical modelling. This paper presents a semi-theoretical model to simulate the void fraction and velocity distributions in hydraulic jumps characterized by partially-developed inflow conditions. Relationships were established between the inflow Froude number, jump roller length and key parameters that determine the full expression of void fraction and velocity profiles. The proposed model enables accurate prediction of void fraction, longitudinal velocity, and air flux using the inflow Froude number. The results indicated considerable air flux contribution of free-surface aeration, in addition to the singular air entrainment at the jump toe, for moderate to large Froude numbers. A Froude number between 8 and 9 tended to achieve highest aeration rate with maximum total air flux in the roller.

Hydraulic jumps have complex flow structures, characterised by strong turbulence and large air contents. It is difficult to numerically predict the flows. It is necessary to bolster the existing computer models to emphasise the gas phase in hydraulic jumps, and avoid the pitfall of treating the phenomenon as a single-phase water flow. This paper aims to improve predictions of hydraulic jumps as bubbly two-phase flow. We allow for airflow above the free surface and air mass entrained across it. We use the Reynolds-averaged Navier–Stokes equations to describe fluid motion, the volume of fluid method to track the interface, and the k–e model for turbulence closure. A shear layer is shown to form between the bottom jet flow and the upper recirculation flow. The key to success in predicting the jet flow lies in formulating appropriate bottom boundary conditions. The majority of entrained air bubbles are advected downstream through the shear layer. Predictions of the recirculation region’s length and air volume fraction within the layer are validated by available measurements. The predictions show a linear growth of the shear layer. There is strong turbulence at the impingement, and the bulk of the turbulence kinetic energy is advected to the recirculation region via the shear layer. The predicted bottom-shear-stress distribution, with a peak value upstream of the toe of the jump and a decaying trend downstream, is realistic. This paper reveals a significant transient bottom shear stress associated with temporal fluctuations of mainly flow velocity in the jump. The prediction method discussed is useful for modelling hydraulic jumps and advancing the understanding of the complex flow phenomenon.

Screens, perforated units to dissipate energy in hydraulic structures, are investigated numerically in this study. These units are part of a physical setup exposed to supercritical flows, normally created by sluice gates. The interaction of perforated screens and supercritical flows results in local complex three-dimensional flows, which can be analyzed by the application of RANS-based flow equations. The most important controlling parameters include supercritical Froude number between 2 and 10 and screen porosity of 40% and 50%. Numerical water surface profiles and energy dissipation are validated by the author’s experimental data. This paper derives a set of equations in terms of depth ratio of the hydraulic jump through the perforated screens and assesses the effect of baffles on energy dissipation. This study seeks a proof-of-concept for the application of the RANS-based technique for further application of the result to real hydraulic structures in due course.

The substantive conditions are affecting the subjective process of creating rapid turbulent changes in flow. Such character happens in hydraulic jump phenomenon, which depends on how much of flow kinetic energy changes into potential energy. During this process part of the kinetic energy is dissipated by taking other types of energy in the channel. The quantity of energy dissipated reflects on the height and length of the jump. The effects of lowering the bed of channel by means of square strips of six different spaces (2, 3, 4,5,6,7 cm) respectively are studied experimentally with additional smooth bed. The investigation leads that bed strips increases the energy dissipation by 6%. The energy dissipation increases with the increase of strips spacing, the best spacing is between 5 and 6 cm. Consequently jump height decreases which is reflected by the reduction of the relative sequent depth value by (6%-15%). While the relative length of jump decreases by 22% and 28% compared with the smooth bed. The mean dimensionless depth deficit is 0.15 and normalized jump length is 2.5. Within the limitations of this work, different relationships are suggested to predict hydraulic jump characteristics with coefficient of determination more than 0.9.

In some cases, the flow head loss is not the main concern of design engineers, who instead prefer to exclude the hydraulic jump from super- to subcritical flow due to unfavourable flow conditions. The present study investigates the flow field and hydrodynamic aspects of the transitional region from super- to subcritical flow without a hydraulic jump. It is found that inside the transitional region the velocity and pressure profiles deviate slightly from uniform flow velocity and hydrostatic pressure. According to evaluation of the velocity measurements in conjunction with the continuity equation, the characteristics of the transitional region are determined. Furthermore, Reynolds stresses are analysed and the mechanisms of transition from super- to subcritical flow without a jump are demonstrated qualitatively. Results relating to the profiles of shear stresses, vorticity and the total angular momentum along the transition are developed. Results indicate that the first short part of the flow field downstream of the transition structure floats on the incoming high-speed fluid where the shear stress is maximal. It is observed that, downstream of the structure, both the shear stresses and the vorticity are maximal along the streamlines. Inside the shear layer, the vorticity spreads upward by diffusive mechanisms.

A detailed field investigation of a saline gravity current in the southwest Black Sea has enabled the first complete analysis of three-dimensional flow structure and dynamics of a series of linked hydraulic jumps in stratified, density-driven, flows. These field observations were collected using an acoustic Doppler current profiler mounted on an autonomous underwater vehicle, and reveal that internal mixing processes in hydraulic jumps, including flow expansion and recirculation, provide a previously unrecognised mechanism for grain-size sorting and segregation in stratified density-driven flows. Field observations suggest a newly identified type of hydraulic jump, that is a stratified low Froude number (< 1.5–2) subaqueous hydraulic jump, with an enhanced ability to transport sediment downstream of the jump, in comparison to hydraulic jumps in other subaerial and submarine flows. These novel field data underpin a new process-based conceptual model of channel lobe transition zones (CLTZs) that explains the scattered offset nature of scours within such settings, the temporal variations in infill and erosion between adjacent scours, how bed shear stresses are maintained across the CLTZ, and why the locus of deposition is so far downstream of the scour zone.

The natural phenomena hydraulic jump that is commonly used in spillways as an energy dissipater coupled to hydropower applications has been investigated with Smoothed Particle Hydrodynamics. A new approach was applied based on a periodic open boundary condition. The model consisted of a tank, a gate, a stilling basin and periodic open boundaries at each end of the computational domain. The tank provided a hydraulic head and in turn a specific flow through the gate, and a downstream condition in terms of a depth for the jump. The gate elevation had a major impact and was calibrated to ensure a correct and stable flow rate, when compared to experiments. With the proper flow rate, the position of the jump toe was significantly improved. The jump toe oscillated with a frequency in good agreement with experimental findings found in the literature and the oscillation amplitude increased with Froude number. However, for high Froude number cases the position was still too close to the gate but could be improved by including a correction based on the length of the jump. The depths in both the super- and subcritical zones was in good agreement with experiments and previous numerical studies. Furthermore, the Froude number was in-line with the definition of super- and subcritical flows.

Turbulent intensity and scales of turbulence after hydraulic jump in rectangular channel. Experimental research was undertaken to investigate the changes in spatial turbulence intensity and scales of turbulent eddies (macroeddies) in a rectangular channel and the influence of the hydraulic jump on vertical, lateral and streamwise distributions of relative turbulence intensity and scales of turbulent eddies. The results of three tests for different discharges are presented. An intensive turbulent mixing that arises as a result of a hydraulic jump has a significant effect on instantaneous velocity, turbulent intensities and sizes of eddies, as well as their vertical and longitudinal distributions. In the analysed case the most noticeable changes appeared up to 0.5 m downstream the hydraulic jump. In the vertical dimension such an effect was especially seen near the surface. The smallest streamwise sizes of macroeddies were present near the surface, maximum at the depth of z/h = 0.6 and from that point sizes were decreasing towards the bottom. The intensive turbulent mixing within the hydraulic jump generates macroeddies of small sizes.

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.

Movable weirs have been developed to address the weaknesses of conventional fixed weirs. However, the structures for riverbed protection downstream of movable weirs are designed using the criteria of fixed weirs in most cases, and these applications cause problems, such as scour and deformation of structures, due to misunderstanding the difference between different types of structures. In this study, a hydraulic experiment was conducted to examine weir type-specific hydraulic phenomena, compare hydraulic jumps and downstream flow characteristics according to different weir types, and analyze hydraulic characteristics, such as changes in water levels, velocities and energy. Additionally, to control the flow generated by a sluice gate, energy dissipators were examined herein for their effectiveness in relation to different installation locations and heights. As a result, it was found that although sluice gates generated hydraulic jumps similar to those of fixed weirs, their downstream supercritical flow increased to eventually elongate the overall hydraulic jumps. In energy dissipator installation, installation heights were found to be sensitive to energy dissipation. The most effective energy dissipator height was 10% of the downstream free surface water depth in this experiment. Based on these findings, it seems desirable to use energy dissipators to reduce energy, as such dissipators were found to be effective in reducing hydraulic jumps and protecting the riverbed under sluice gates.

In the present paper, three-dimensional, unsteady, detached eddy simulation (DES) of a submerged hydraulic jump with an inlet Froude number of 8.2 is performed. The volume of fluid (VOF) method with a high-resolution interface capturing (HRIC) scheme is used for free-surface tracking. The mean velocity and turbulence quantities including the Reynolds stresses are compared with available experimental data to validate the results. The three-dimensional nature of the flow in the developing and developed zone of the submerged hydraulic jump is evaluated by examining the coherent structures using the λ2" role="presentation" style="display: inline; line-height: normal; font-size: 12px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px 2px 0px 0px; margin: 0px; font-family: arial, helvetica, clean, sans-serif; background-color: rgb(239, 239, 239); position: relative;">λ2λ2 criteria. Additionally, proper orthogonal decomposition (POD) analysis reveals the dominance of smaller structures in the developed region of the submerged hydraulic jump. The presence of these smaller scales is directly responsible for the energy dissipation characteristic of the submerged hydraulic jump.

Hydraulic jump is a phenomenon which usually occurs in rivers and in correspondence with hydraulic structures. It is characterized by a rapid transition from a super- to sub-critical flow conditions, involving a huge energy dissipation. For its characteristics and its relevance in hydraulics, it has been studied since the early years of the last century. Nevertheless, many features still require a further investigation, e.g., scale effects, air entrainment process, effect of bed roughness on conjugate depths, etc. In particular, in the last few decades, the analysis of the main geometric parameters has been further developed. Nevertheless, no studies dealing with D-jump occurring on a rough sloping channel are present in literature. Therefore, the present paper reports the results of experimental investigations, which allowed to develop a semi-theoretical approach in order to evaluate the D-jump conjugate depth in a wide range of channel bed geometric and boundary configurations.

An analytical solution of nondimensional hydraulic energy equation is derived in cosine form for the flow in rectangular open channels considering nonhydrostatic pressure and nonuniform velocity distributions across flow depth and friction and turbulent losses. The new inverted energy equation is a single equation describing all the three roots of the nondimensional hydraulic energy equation. The energy losses due to turbulence and bed shear are also implicitly accounted. Only two roots out of the three roots are practically significant, which denote the two alternate depths and are distinguishable for subcritical and supercritical flow, respectively. These equations yield direct determination of alternate depths in a single step, avoiding an iterative procedure. The use of the new equations is illustrated through worked-out examples. The new single-term analytical inverted equations are computationally simple and useful for academicians, field engineers, and practitioners in directly solving in a...

Hydraulic computation is required in various phases of irrigation planning especially in the designing of the canal cross-section; channel transition; bridge construction, i.e., constriction in the canal section; hydraulic jump for energy dissipation structures; fixing the bed level for the canal falls; flow through outlets and gates; backwater effects of structures; water profile in the reservoir; etc. This chapter presents an easy-to-understand theoretical description of the methods along with practical application beside the analytical and explicit computation of normal and critical depth and elements of the hydraulic jump with worked examples relevant to the design of a canal system.

Hydraulic jump is generally helped in the dissipation of excess kinetic energy downstream of hydraulic structures such as gates, spillways, and weirs. This paper presents a comprehensive review of the available literature on the hydraulic jump properties on corrugated beds. In the present study the effect of spaced triangular strip corrugated bed on submerged jump characteristics has been experimentally investigated. Thirty experimental runs were carried out considering wide range of Froude numbers ranging from 1.68 to 9.29. Experiments were conducted for both smooth and rough bed. The results confirm that sequent depth and jump length were reduced by average values 15.14% and 21.03%, respectively, whereas, jump efficiency was increased by 50.31% at optimum spaced roughness compared to a classical jump respectively. Dimensionless relationships were deduced to predict the jump characteristics. Results of the present study were agreed satisfactorily with the previous studies.

A hydraulic jump with strong turbulent mixing and air bubble entrainment is regarded as a transition process of a supercritical flow into a subcritical flow. In this study, the three-dimensional submerged hydraulic jumps were investigated numerically. The volume of fluid method and RSM turbulence model were used to simulate the free surface and turbulence structure. And the effects of the near-wall treatment methods including standard-wall functions, non-equilibrium wall function and enhanced-wall treatment on the flow field of the submerged hydraulic jumps were studied. Comparison between the numerical results and experimental measurements showed that the numerical model is adequate for predicting the flow pattern and free surface of the submerged hydraulic jumps. The numerical results showed that the longitudinal velocity and free surface profiles simulated by standard- and non-equilibrium wall functions are approximately similar. In the numerical simulation of the submerged hydraulic jump, the standard-wall functions were reasonably accurate in predicting the free surface, longitudinal turbulence intensity, turbulence shear stress and turbulence kinetic energy along the channel and also simulating the distribution of longitudinal velocity across the channel. The enhanced-wall treatment method despite high computational time is well able to predict the near-wall behavior of the flow such as longitudinal velocity near the channel bed and bed shear stress coefficient. Also maximum mean velocity and vertical turbulence intensity simulated by enhanced-wall treatment are more accurate than wall functions.

There is no doubt that, the gates one of the most important controllers of the flow through regulators. Several studies had been conducted to improve the gates' performance by modifying its features to improve the flow characteristics. It can be said that, no studies focused on the gate as an energy dissipater. The present paper investigates the possibility of using the gate as a tool of the flow controlling through the basin itself. We have provided a new idea based on perforating of a hole in the gate itself. It plays an important rule to improve the hydraulic jump's characteristics and the coefficient of discharge. Theoretical models are built to simulate each of the dissipated energy values and Froude's number. The laboratory experiments achieved promising results. It was found that, the case of sluice gate with a circular opening and plastic hose of inclination angle = 330o reduces the relative jump depth and the relative jump length by 12.3% and 29%, respectively. In addition, it increases the average values of the dissipated energy and the coefficient of discharge by 8% and 16.5%, respectively. Statistical analysis is used in the construction of equations to simulate the above-mentioned parameters.

The hydraulic jump is a transitional state from supercritical to subcritical flow. The phenomenon of the hydraulic jump has been widely studied because of its frequent occurrence in nature and because of its uses in many practical applications. In the present study the momentum principle is used to derive an equation expressed the hydraulic jump (A-jump) occurred in a short horizontal reach of an inverted semicircular open channel. The derived equation indicates that the initial water depth and the tail water depth (conjugate depths) are functions of the critical water depth. Various elements of the hydraulic jump are expressed in dimensionless case. The procedure of dimensionless ratios described in the present paper can be used to determine various elements of A-jump in an inverted semicircular channel when either the discharge and the relative initial depth (or tail water depth) is known or the discharge and the relative dissipated energy are known.

The weir is one of the hydraulic structure which is supposed to be used to store water quantity against drought. To solve the disturbance of flood control caused by soil sediment and environment problems from the severance of moving sediment, movable weir is currently set up so as to solve that serious problem. There have been many studies focusing on the weir in specific target area. however, it is not applicable for all kinds of moveable weir. Therefore, In this study, experiments for moveable weir typed sluice gate are performed and hydraulics characteristics are measured depending on gate operation. According to comparison results between apron length calculated by Bligh`s equation and hydraulic jump length by experiments, hydraulic jump length is bigger than apron length by Bligh`s equation where oscillation jump happens. Therefore, it is necessary to set the energy dissipator up for improving stability of hydraulic structure.

An experimental–analytical investigation was performed to explore whether a hydraulic jump in a transition from super- to subcritical flow regime can be avoided. As the free-surface profile passes the critical depth, the transitional point is a singular point. A transition structure was designed based on the energy principle and the singular point theory to gradually increase the flow depth, thereby eliminating the hydraulic jump. This profile was designed for approach flow Froude numbers between 1.5 and 7. To validate the analytical model, a comprehensive experimental study was conducted. Six hydraulic models of transition structures were experimentally investigated on the basis of the theoretical approach. The analytical results agreed well with the experimental results and those of former investigations. Observations indicated that the hydraulic jump is absent for a certain range of the Froude numbers.

Hydraulic gates are hydraulic control equipments to control the flow of water in any water resources project. The location of horizontal girders are influenced by type of hydraulic loading, fixity of it with gate and interference of hydraulic jump formed downstream of gate. When a high-head vertical lift gate is opened with a small opening, a hydraulic jump forms downstream, which interferes with the bottom-most horizontal girder. In the present paper, an attempt has been made using numerical experiments to highlight the effect of interference of hydraulic jump on horizontal girders of vertical lift hydraulic gate. For the numerical experiments, the design thickness of gate as 1.2 m with water head (H) as 13.7 m (without tail water) is considered. Hydraulic jump profiles for gate openings 0.05, 0.1, 0.2, 0.3, 0.4 and 0.5 m have been discussed. The methodology adopted leads to a bottom slope estimation which for a water pressure head of 13.7 m and a vertical lift gate of thickness 1.2 m leads to a bottom s...

This study derived equations for examining the energy dissipation characteristics of a hydraulic jump after free overfall. Comparison of energy dissipation characteristics was further made between hydraulic flows occurring in a prismatic channel of constant cross-sectional width and that in an expanding channel with gradual increase in width along the length. Results calculated using the derived equations show that the conjugate depth ratio relative energy loss and energy dissipation efficiency ( ) are not only influenced by the pre-jump Froude number and the relative height of the weir but also by pre- and post-jump cross-sectional width ratio. In addition, energy dissipation of hydraulic jump after free overfall is greater in an expanding channel than in a prismatic channel. Hence, future design of stilling basins should consider having a gradually expanding channel so as to achieve lower level of tailwater.

A hydraulic jump is a common phenomenon that can be observed in open channel flows such as rivers and spillways. It can cause damage of the downstream bed and bank of the channel due to the process of continuous erosion and degradation. In order to reduce the hydraulic jump destruction, the energy in the hydraulic jump must be dissipated as much as possible. One method to increase dissipation of energy is using a corrugated bed. In order to know the effect of a corrugated bed on the hydraulic jump, a smoothed particle hydrodynamics (SPH) model is applied to investigate the characteristics of hydraulic jumps in various corrugated beds. A variety of corrugated beds that are smooth, triangular, trapezoidal, and sinusoidal are considered. The opening of a gate is changed to adjust the hydraulic jump. The conjugate depth ratio, the jump length, the bottom shear stress distribution, and the energy dissipation are reported. The results of the present study are in a good agreement with previous studies. E...

The transition from supercritical to subcritical flow is characterised by a strong dissipative mechanism, a hydraulic jump. Herein a comparative analysis of physical data is presented with a focus on a broad range of two-phase flow parameters. The results show that, for hydraulic jumps with Fr-1 = 5.1, the void fraction data obtained with Re < 4 x 10(4) could not be scaled up to Re = 1 x 10(5). Most air-water flow properties measured with Reynolds numbers up to 1.25 x 10(5) could not be extrapolated to large-size prototype structures without significant scale effects in terms of bubble count rate, turbulence, bubble chord time distributions and bubble cluster characteristics. The findings have some implications of civil and sanitary engineering designs, because most hydraulic structures, storm water systems and water treatment facilities operate with Reynolds numbers larger than 10(6) to over 10(8). (C) 2012 Elsevier Inc. All rights reserved.

The velocity field and surface profile of an open channel flow with a submerged hydraulic jump from a vertical sluice gate are investigated for two different flow cases. The governing equations are numerically solved using a finite-volume method for flows having the same conditions with experiments. The volume of fluid method is used to calculate the free surface. In modeling the turbulence stresses, standard k-?, renormalization group k-?, realizable k-?, shear stress transport k-?, and Reynolds stress turbulence closure models are employed. A grid convergence index analysis is carried out to determine the discretization error for the grid-independent solution. Experimental validations of the numerical results show that in predicting the velocity field, the Reynolds stress turbulence model is the most successful among the five. It also estimates the free-surface profile of the flow successfully. © 2015 American Society of Civil Engineers.

【Objective】The calculation of turbulent boundary layer development in hydraulic jump region is put forwarded.【Method】According to the analysis of predecessors’ researches about plane adhesive wall jet flow of rectangular channel, Based on the momentum integral equation of turbulent boundary layer and the velocity distribution formula of adhesive wall jet flow, turbulent boundary layer development of hydraulic jump region in rectangular channel is researched.【Result】Formulas of the development of boundary layer in hydraulic jump region and drag coefficient are obtained, the accuracy of equations are verified by the example. 【Conclusion】The calculation has enlightened effect on the hydraulic characteristics of hydraulic jump.

In this study, the effect of sediment concentration on submerged hydraulic jump (SHJ) characteristics such as jump length, submerged depth on the gate and the energy dissipation is investigated. Experiments were carried out in a flume of 46 cm depth, 12 m length. The width of the flume changes from 10 cm (at the entrance) to 60 cm (at the exit). Sediment load and flow concentration have an influence on submerged hydraulic jump characteristics including submerged depth on the gate, jump length and relative energy dissipation. It is shown that at high Froude numbers increasing the suspended sediment concentration to 28.7 gr/l leads to a reduction in the submerged depth on the gate up to 6% and jump length up to 10%. Also, the energy dissipation of the submerged hydraulic jump increases by 4% and turbulence resulting from the jump leads to upright distribution of concentration at the end of the jump. Also in concentrations higher than 30 gr/l, flow is not able to carry the whole sediments and subsequently leads to their deposition in subcritical area and behind the sluice gate.

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≤F 1≤10.95 and a relative bed roughness ranging 0.22≤K R≤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. Belanger’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%.

In this experimental study, the effect of suspended sediment concentration on the characteristics of a submerged hydraulic jump in a rectangular channel has been investigated, based on the sediment concentrations of 0.43%-16.15% and jet Froude numbers were in the range of 1.9-5. Two grain sizes, 0.15 and 0.03 mm ( ρ s =2.65 g/cm 3 ) have been used in the experiments. Characteristics of the submerged hydraulic jump including the submergence depth at the gate, length of submerged hydraulic jump, energy dissipation, velocity, and concentration distribution have been studied in both smooth and rough beds. Results showed that the submergence depth at the gate and the energy dissipation were constant regardless of sediment concentration. However, in the presence of suspended sediment, the length of the submerged hydraulic jump is smaller than that of clear water flow. It was also found that suspended sediment increase flow resistance, as a result of decreased in the maximum flow velocity.

A hydraulic jump is a sudden transition from supercritical to subcritical flow. It is characterized by a highly turbulent roller region with a bubbly two-phase flow structure. The present study aims to estimate the void fraction in a hydraulic jump using a flow visualization technique. The assumption that the void fraction in a hydraulic jump could be estimated based on images’ pixel intensity was first proposed by Mossa and Tolve (J Fluids Eng 120:160–165, 1998). While Mossa and Tolve (J Fluids Eng 120:160–165, 1998) obtained vertically averaged air concentration values along the hydraulic jump, herein we propose a new visualization technique that provides air concentration values in a vertical 2-D matrix covering the whole area of the jump roller. The results obtained are found to be consistent with new measurements using a dual-tip conductivity probe and show that the image processing procedure (IPP) can be a powerful tool to complement intrusive probe measurements. Advantages of the new IPP include the ability to determine instantaneous and average void fractions simultaneously at different locations along the hydraulic jump without perturbing the flow, although it is acknowledged that the results are likely to be more representative in the vicinity of sidewall than at the center of the flume.

This note presents the general features of velocity and variation in length scales of the transition expanding jump, free jump, and wall jet in the rectangular horizontal open channel. The experiments were performed for a range of Froude numbers from 2 to 6 and at an abrupt expansion ratio of 2. The results indicate that the postdepth y2 required to form an expanding jump is distinctly smaller than that for the corresponding classical jumps. The expanding jump length was 1.25 times the corresponding free jump length. The velocity profiles for the transition jumps were similar to those for the wall jet. For the transitional expanding jumps, the boundary layer thickness δ , normalized by the supercritical flow depth y1 , grows more rapidly relative to the free jumps. The normalized boundary layer thickness δ in terms of the length scale of b equal to the flow depth y , where the velocity u is equal to half of the maximum velocity um , against the longitudinal direction x normalized by y1 , which was stabili...

The streamwise flow structure of a turbulent hydraulic jump over a rough bed rectangular channel has been investigated. The flow is divided into inner and outer layers, where upstream supercritical flow changes to downstream subcritical flow. The analysis is based on depth averaged Reynolds momentum equations. The molecular viscosity on the rough bed imposes the no slip boundary condition, but close to the wall the turbulent process in inner layer provides certain matching conditions with the outer layer, where molecular viscosity has no dominant role. It is shown that the bed roughness in the inner layer has a passive role in imposing wall shear stress during formation of hydraulic jump in the outer layer. The Belanger’s jump condition of rectangular channel has been extended to account for the implications of the drag attributable to channel bed roughness, kinetic energy correction factor, and coefficient of the Reynolds normal stresses. For depth averaged Reynolds normal stress, an eddy viscosity model containing gradient of depth averaged axial velocity is considered. Analytical solutions for sequent depth ratio, jump length, roller length, and profiles of jump depth and velocity were found to depend upon the upstream Froude number, drag owing to bed roughness, and kinetic energy correction factor. On the basis of dynamical similarity, the roller length and aeration length were proposed to be of the same order as the jump length. An effective upstream Froude number, introduced in the present work, yields universal predictions for sequent depth ratio, jump length, roller length, jump profile, and other hydraulic jump characteristics that are explicitly independent of bed roughness drag. Thus, results for hydraulic jump over a rough bed channel can be directly deduced from classical smooth bed hydraulic jump theory, provided the upstream Froude number is replaced by the effective upstream Froude number. These findings of universality have been supported by experimental data over a rough bed rectangular channel.

This study investigates the characteristics of reattached plane turbulent offset jets in channels with rough beds and shallow tailwater depths. The flow consists of a deflecting free jet caused by the Coanda effect and the evolving wall jet past reattachment. In limited tailwater conditions, the jet flow is affected by the relative tailwater depth or the submergence parameter, which is defined with respect to the maximum B-jump at a negative step. The results show that for an offset height larger than the jet thickness, the forward-flow momentum, local maximum velocity, and wall shear stress decrease faster in the longitudinal direction in the offset jet than in plane turbulent wall jets. The influence of roughness on reattached offset jets appears to be less than that in submerged wall jets on a similar rough bed. The presented results and the comparative analysis with respect to wall jets in hydraulic jumps are significant for controlling and implementing similar flows on rough beds with variable downst...

Baffle blocks and sills are commonly used to stabilize the location of a hydraulic jump and shorten its length. However, corrugations or prismatic roughness elements may be effective alternatives to them. In the present study, experiments were performed to determine the effects of corrugations and prismatic roughness elements on fundamental characteristics of jump such as length, tailwater depth, and energy dissipation capacity. Corrugations were placed to cover the entire length of the basin. Prismatic roughness elements were placed in two different arrangements as strip and staggered. The results showed that the length of jump was reduced about 35% by corrugations, 40% by strip roughness, and 35%-55% by staggered roughness. The tailwater depth reduction was 20% for corrugations, 5%-13% for strip roughness, and 7%-15% for the staggered roughness compared to classical jump. The roughness elements induce 3%-10% more energy dissipation than that of classical jump.

This paper is concerned with a mathematical model for numerical simulation of 2D flow accompanied with a hydraulic jump. The governing water equations are solved by the Mac Cormack’s predictor-corrector technique. The mathematical model is used to numerically predict 2D hydraulic jump in a rectangular open channel. The comparison and the analysis show that the proposed method is accurate, reliable and effective in simulation of hydraulic jump flows.

A free-surface flow can change from a supercritical to subcritical flow with a strong dissipative phenomenon called a hydraulic jump. Herein the progress and development in turbulent hydraulic jumps are reviewed with a focus on hydraulic jumps operating at large Reynolds numbers typically encountered in natural streams and hydraulic structures. The key features of the turbulent hydraulic jumps are the highly turbulent flow motion associated with some intense air bubble entrainment at the jump toe. The state-of-the-art on the topic is discussed based upon recent theoretical analyses and physical data.

A hydraulic jump is a sudden, rapid transition from a supercritical flow to a subcritical flow. At large inflow Froude numbers, the jump is characterized by a significant amount of entrained air. For this paper, the bubbly two-phase flow properties of steady and strong hydraulic jumps were investigated experimentally. The results demonstrate that the strong air entrainment rate and the depth-averaged void-fraction data highlight a rapid deaeration of the jump roller. The results suggest that the hydraulic jumps are effective aerators and that the rate of detrainment is comparatively smaller at the largest Froude numbers.

In the present study, the effect of suspended load transport on the characteristics of a hydraulic jump in a rectangular channel was investigated experimentally. Sediment concentration and initial Froude numbers in the range 0·42–16·15% and 2·5–8, respectively, were considered. Two grain sizes, 0·15 and 0·03 mm, were used in the experiments. Hydraulic jump characteristics including velocity and concentration distributions, length of jump, the sequent depth ratio and the energy dissipation were studied for both the smooth and rough channel beds. The results showed that the sequent depth ratio and length of the jump in the presence of suspended sediment were smaller than those due to clear water flow. It was also found that the reduction of sequent depth ratio and the jump length were more in rough beds.

In an open channel, a sudden rise in water level induces a positive surge, or bore, that may develop as a hydraulic jump in translation. When the surge propagates against an adverse slope, it decelerates until it becomes a stationary hydraulic jump. Both hydraulic jumps and decelerating surges induce some intense turbulent mixing and have some major impact on the sediment transport in natural systems. Herein, a physical investigation was conducted in a relatively large rectangular channel. Hydraulic jumps and surges were generated by the rapid closure of a gate at the channel downstream end. The turbulent shear stresses were measured with high temporal and spatial resolution (200 Hz sampling rate) in the jump flow. A comparison between the stationary hydraulic jump, hydraulic jump in translation and decelerating surge measurements showed some marked differences in terms of turbulent mixing. The results highlighted some intense mixing beneath the jump front and roller for all configurations. The levels of turbulent stresses were one to two orders of magnitude larger than a critical threshold for sediment motion. The findings provide some insights into the hydraulic jump migration processes in mobile bed channels, and the complex transformation from a moving jump into a stationary jump. Copyright (C) 2010 John Wiley & Sons, Ltd.

This note presents experimental measurements on the turbulence characteristics in the transition region from the end of a hydraulic jump to open channel flow in a rectangular channel. An acoustic Doppler velocimeter was used to measure mean velocities, turbulent intensities, Reynolds stress and turbulent kinetic energy for two supercritical Froude numbers. General correlations for the variation of the normalized maximum values of the Reynolds normal stresses as well as the shear stress and the turbulent kinetic energy have been developed, using the present results and those from the literature. The supercritical Froude number was found to be an effective scale in addition to the supercritical approach flow velocity in obtaining the general correlations.

This paper deals with the roller length and energy loss of a large variety of hydraulic jumps in horizontal and sloping channels. The supercritical upstream flow originated from a standard ogee weir. A stilling basin with bottom slopes of 0.0, −0.025, −0.050, −0.075, and −0.100 was used to generate the jumps. Based on the energy principle, a semi-empirical method to predict the roller length is presented. Predictions based on the proposed method agree well with the results reported by the authors and other researchers. It is shown that the energy loss in the classical jump is greater than that in any jump forming on negative or positive slopes.

The present experimental investigation focuses on energy dissipation and turbulence production in two undeveloped and a partially developed inflow weak hydraulic jumps, measured with micro-ADVs. For the undeveloped inflow jumps, the turbulence production is mostly confined in the shear layer located in the upper part of the water column. For the partially developed inflow jump, two peak turbulence production regions are observed, one in the upper shear layer and the second in the near-wall region. Moreover, the measured energy dissipation distribution in the jumps reveals a similar longitudinal decay of energy dissipation integrated over the flow sections and of maximum turbulence production values from the intermediate jump region toward its downstream section.

Hydraulic jumps in an inclined rectangular chute contraction were studied in this paper. Theoretical equations for the sequent-area and sequent-depth ratios for hydraulic jumps in the contraction were developed considering the effects of contracting width and sloping bottom. The equation of the sequent-area ratio (instead of the sequent-depth ratio) has the same form as the traditional Belanger equation for the sequent-depth ratio for hydraulic jumps in a horizontal rectangular constant-width channel (HRCW channel). A modified approach Froude number M , including the effects of contracting width and sloping bottom, was introduced to replace the approach Froude number F1 in analyzing hydraulic jumps in the contraction. Laboratory experiments of hydraulic jumps in inclined contractions were also conducted to verify the theoretical sequent-area ratio and also to develop the empirical equations of the location of the start of the jump, flow depth of the start of the jump, length of the jump, and energy loss o...

The dynamics of free surface flow is characterised by the so-called Froude number F, whose value F = 1 separates subcritical (F 1) flows. The transition from F 1 is smooth and continuous, as observed in weir flow. However, the reverse transition from F > 1 to F < 1 is abrupt and discontinuous. In the present research the simplest approximation is proposed to describe hydraulic jump flow. The 2D flow features of the classical hydraulic jump are properly described and favorably compared with experimental data. Based on one-dimensional results, the hydraulic jump flow is rationally related to the critical flow condition and it is proved that the specific energy of the main flow reaches a minimum value at F = 1, whereas the total energy head decreases due to energy dissipation. Further results relate to the effects of air, and the non-uniform pressure and velocity distributions.

Hydraulic jump characteristics were studied experimentally over six corrugated beds with varying wave steepness, which had corrugation and Froude numbers in the range of 0.286–0.625 and 3.8–8.6, respectively. The effects of wave height and length of corrugation on the basic jump characteristics, including free surface location, velocity, shear stress distribution and energy dissipation, were studied for a range of Froude numbers. The dimensionless hydraulic parameters were found to be a function of the Froude number. The results showed that the tailwater depth and the length of the jump on corrugated beds are smaller than those of the corresponding jump on a smooth bed. The analysis of velocity profiles at different sections in the jump showed that the velocity profiles were similar to those of a simple plane wall jet. The normalized boundary layer thickness δ / b was equal to 0.57 for jumps on a corrugated bed, compared to 0.16 for the simple wall jet. The analysis and comparison of the bed shear force and shear stress coefficient showed that shear stress on a corrugated bed is about 10 times that of a smooth bed. The results of this study are in good agreement with previous results and showed that corrugated beds can be used to dissipate the excess hydraulic jump energy in stilling basins.

A hydraulic jump is the rapid and sudden transition from a high-velocity supercritical open channel flow to a subcritical flow. It is characterised by the dynamic interactions of the large-scale eddies with the free-surface. New series of experimental measurements were conducted in hydraulic jumps with Froude numbers between 3.1 and 8.5 to investigate these interactions. The dynamic free surface measurements were performed with a non-intrusive technique while the two-phase flow properties were recorded with a phase-detection probe. The shape of the mean free surface profile was well defined and the turbulent fluctuation profiles highlighted a distinct peak of turbulent intensity in the first part of the jump roller, with free-surface fluctuation levels increasing with increasing Froude number. The dominant free-surface fluctuation frequencies were typically between 1 and 4 Hz. A comparison between the acoustic sensor signals and conductivity probe data suggested that the air-water "free-surface" detected by the acoustic sensor corresponded to about the boundary between the turbulent shear layer and the upper free-surface layer. Simultaneous measurements of free surface and bubbly flow fluctuations for Fr = 5.1 indicated that the frequency ranges of both sensors were similar (F < 5 Hz) whatever the position downstream of the toe. The present results highlighted that the dynamic free-surface measurements can be conducted successfully using acoustic displacement meters, and the time-averaged depth measurements was a physical measure of the free-surface location in hydraulic jumps.