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Hydraulic jumps occur in natural systems like streams and rivers as well as manufactured systems. Samples of the latter occurance are jumps in water distribution and irrigation networks formed downstream of hydraulic structures such as spillways, sluice gates, and drops. These structures are usually designed for a specific tailwater depth. Stilling basins with baffle blocks are frequently used as energy dissipators downstream of hydraulic structures. Baffle blocks are often used to stabilize the jump, decrease its length and increase the energy dissipation. If the flow rates become more than the design discharge, the tail water depth will be greater than the one required for a free jump. These situations are common in low head hydraulic structures including low diversion dam spillways and gates. Under such conditions the hydraulic jump will be submerged.  The performance of the blocks in submerged jump (SJ) condition differs from the free jump (FJ) case. According to some factors such as Froude number, block shape and location and submergence factor, flow regimes on baffle blocks in condition of submerged hydraulic jumps which occurs in stilling basins, are classified into two regimes, the deflected surface jet (DSJ) and reattaching wall jet (RWJ). In this article a numerical study was conducted to investigate flow pattern, vortexes and the magnitude of vorticity in submerged hydraulic jumps with baffle blocks downstream of a sluice gate. The results were compared to ones in same conditions without blocks. 3D RANS simulations have been applied by Fluent software. RSM turbulence model were used which illustrated much precise results in verification. Three numerical models have been created; Submerged wall jet without blocks, submerged hydraulic jumps with baffle blocks in the condition of deflected surface jet flow regime and submerged hydraulic jumps with baffle blocks in the condition of reattaching wall jet flow regime. Flow pattern has been exhibited for each model and results were compared with each other. Vortexes formed in such situations classified into three groups according to axis which they whirl around. It was observed that deflected surface jet regime has more vortexes in comparison to the two other conditions. In addition, by measuring the average magnitude of vorticity in cross-sections it has been concluded that z-vortexes –vortexes which rotate around z axis– much more powerful than x- and y-vortexes as they determine the kind of flow regime. Furthermore, this magnitude is about two times larger in deflected surface regime than two other situations. This fact leads to more turbulence in the flow that makes deflected  surface jet  regime the desirable condition in which baffle blocks perform more efficiently as energy dissipators in comparison to two other investigated models. In order that, from energy vantage point, conditions should be provided in a way to form submerged hydraulic jump as deflected surface jet regime.

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One of the most frequently encountered cases of rapid varied flow is the hydraulic jump. Stilling basins are used to dissipate the excess kinetic energy of flow to ensure the safety of overflow spillway, chutes, sluices, pipe outlets etc. in this study the topic of block in stilling basins is investigation in a general approach and it’s effect on energy dissipation and downstream scouring are analyzed. In the present research, the energy dissipation and scouring phenomenon were studied in different hydraulic and geometric conditions. Moreover, the present paper was focused on the effect of presence of blocks as an effective parameter on energy dissipation on stilling basin performance. To analyze and assessment of formed hydraulic jump in the stilling basins, the experimental data of many recent researches were achieved and compared. It was concluded that presence of blocks has significant effect on energy dissipation from 1% to 34%. It is also shown that with increasing the Fr Number, the secondary depth increases and the using a rough bed causes reducing the secondary depth between 18% to 37% in comparison with smooth one. Moreover, installing a rough bed also reduced the length of hydraulic jump between 27% to 67%. Using block in the stilling basins, reduces the scouring depth from USBR standard recommendation. Finally, it was concluded that using blocks increased the efficiency of the stilling basin performance.

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Hydraulic jump is a rapid and sudden transition from a high-velocity supercritical flow to a subcritical flow in an open channel flow. Stilling basins are used to control the hydraulic jump at the downstream of chutes, sluice gates,… End Sills, baffle blocks and negative steps are often used to control hydraulic jumps in stilling basins. The present study focuses on the formation of hydraulic jump in the new type of stilling basins with stepped sills. Extensive experiments were conducted in a rectangular flume 0.6 m wide, 12.0 m long and 1.0 m deep, with various discharges from 30 to 120 l/s. Water was pumped from an underground sump into a head tank and the discharge was measured with a ultrasonic flowmeter. At the downstream end of the head tank there was a sluice gate into the flume. The edge of the sluice gate has a streamlined lip in the shape of a half-cylinder of diameter 20 cm to minimize flow contraction and provide a uniform supercritical flow. A point gauge with an accuracy of 0.1 mm was used to measure water depths. In order to visualize the flow field, the dye-injection method and a high speed camera were employed. A tailgate located at the downstream end of the flume was used to control the tailwater depth. The effects of stepped end sills on hydraulic jumps were investigated experimentally. Firstly, dimentionless parameters affecting the hydraulic jump on stepped sill introduced using Buckingham π theorem. The effect of important parameters such as approach Froude number (Fr1), relative tailwater depth (〖y_t/y〗_2^*) and the end sill geometry (shape and relative height of sill (s/y1)) on hydraulic jump were investigated. The hydraulic jumps over stepped end sills were classified into A-jump, B-jump, minimum B-jump, C-jump and minimum C-jump. By changing the type of flow from A-jump to minimum C-jump, the jump is going to sweepout from basin. A-jump is entirely formed in the basin and at the upstream of sill. In the case of minimum C-jump, most of the surface roller of jump formed at the downstream of sill. The flow types are presented in the form of 6 different diagrams as functions of the relative step height s/y1. By increasing the tailwater depth, sill height, the probability of occurance of hydraulic jump in the stilling basin increased. It was found that the sill with 2 steps have better performance in stabilizing the jump in the stilling basin as compare to sill with 3 steps. By increasing the approach Froude number, the jump began to sweep away from basin. By knowing the initial condition like upstream velocity and upstream froude number, tailwater depth, sill height and its number of steps the toe distance from sill can be found out with desirable accuracy.

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Establishing a bridge in a waterway changes flow characteristics. Most of these changes derive from geometric details of bridge. Circular and pointed (nested) arches have been used as opening geometry in historical bridges. Historical bridges are valuable heritage and protection of them is important because of cultural continuity. Hydraulic study is a tool to recognize these structures and their design philosophy. In this research, effect of three opening geometry on backwater and hydraulic jump phenomena was numerically studied by Flow-3D software. The FLOW-3D software was selected because not only previous studies indicated that flow around a bridge as well as in a compound channel involves significant 3D characteristics but also it is a powerful hydraulic engineering design tool to model 3D free surface flows. The performance of FLOW-3D was tested using of experimental data obtained from test series which were conducted at the Hydraulic Laboratory, Birmingham University on two opening semi circular bridge model in compound channel (AMOSEC) in which the width of model was 0.10 m. Laboratory tests were carried out for low flow conditions without flow contact with the lower bridge deck (21 to 35 lit/sec). In order to study submerged (High Flow) condition, a program has been developed in the MATLAB environment to extrapolate discharges and related normal depth for 40 to 60 lit/sec discharges. Three opening geometry with the same area as AMOSEC model designed in the AutoCAD. DWG files converted into the Stereolithography format and imported into the Flow-3D.The computational domain, 18 m long and 1.213 m wide, was divided into structured grids. This domain involved nonuniform rectangular grids of 950, 100 and 26 to 40 cells in the x-, y- and z-directions, respectively. Inflow boundary condition was specified as discharge. The downstream boundary condition was specified with a constant fluid height equal to the uniform depth. The sidewalls as well as the channel bottom were defined to be no slip boundaries. On the top, the symmetry (atmospheric) boundary condition was assigned to describe the free surface flow condition. Measured uniform flow depth with zero velocities for each run was assigned to each computational cell to set the initial flow condition. Free surface modeled by VOF and turbulence by two equation K-ɛ methods. Then, a total of 27 runs carried out until steady state resulted. The results indicate that pointed arch geometry makes maximum afflux for both low flows (sub-soffit) and high flows (super-soffit) conditions in all models. Emerging Location of afflux at longitudinal axis is the same for all of the models. Length of hydraulic jump for pointed arch geometry is maximum under low flow condition and minimum under high flow condition. Hydraulic jump starts near the pier for rectangular opening geometry in comparison with others. Critical shear stress due to hydraulic jump is minimum for rectangular geometry and maximum for pointed arch in all discharge conditions. Circular opening geometry produces less upstream flooding and less possibility of downstream bed destruction, so it has advantages on pointed arch geometry.Out of the structural reasons, whole of these results may be considered as hydraulic reason of evolution of pointed arch to semi circular geometry from Safavid to Qajar era.

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The hydraulic jump phenomenon is one of the most common phenomena in open channels. Hydraulic jump is a transition state from supercritical to subcritical flow regime, which normally occurs in conjunction with hydraulic structures, such as spillways, weirs, and sluice gates. A hydraulic jump phenomenon serves a variety of purposes, for instance, to dissipate the energy of flow to prevent bed erosion and aerate water or to facilitate the mixing process of chemicals used for the purification of water. Stilling basins are one of the most common structures for energy dissipation of flow with high velocities.The stilling basin has been accepted to be the most powerful hydraulic structure for the dissipation of the flow energy. The size and geometry of the stilling basin affect the formation of flow patterns, which can be influential for hydraulic performance of the whole system. The depth of water after the jump is related to the energy content of the flow, and any reduction in energy content with increased energy dissipation in the jump will reduce the required depth of flow after the jump. Sometimes these basins are supplied with appurtenances that increase the overall roughness of the basins. This in turn increases the energy dissipation, decreases the sequent depth, and requires a shorter basin for the full development of the hydraulic jump. There are plenty of research studies in the literature regarding the classical hydraulic jump in the usual rectangular straight stilling basin, but less for the hydraulic jump in other cross section shape of basins. Expanding gradually basin with the rectangular cross section acts as two separate hydraulic structures including stilling basin and transition. In this type of structures not only the transition can be eliminated, but the length of the basin will be also much smaller than what is designed for the usual straight basins. Researchers’ studies show that divergence in stilling basins reduce the sequent depth and the length of the jump while increasing the energy losses compared to the classic jumps.
In this research, numerical simulation of the hydraulic jump was performed in divergence rectangular sections, and compared with the results of the laboratory, making use of the FLOW-3D software and the standard k-ԑ and RNG k-ԑ turbulence models. The effects of rectangular Strip roughness on the specification of hydraulic jump were evaluated.
The results showed that the standard k-ԑ turbulence model was able to predict the water level profiles in the hydraulic jump in divergence rectangular sections with appropriate and acceptable coincidence. Results showed that the mean relative error of water surface obtained from numerical model and measured values is about 3.55 percent. Also the numerical model showed the vortices that were accrued because of diverging walls as well as experiment investigations. The results show that creating the rectangular Strip roughness, reduces the sequent depth as much as 13.65 % and the length of the hydraulic jump as much as 11.39%, while increasing the energy loss as much as 9.12%, compared to Smooth divergent stilling basin. The results also show that creating the rectangular Strip roughness, reduces the sequent depth as much as 24.63 % and the length of the hydraulic jump as much as 17.64%, while increasing the energy loss as much as 14.46%, compared to the classic hydraulic jumps. Consequently, the use of roughness in stilling basins would be economical.

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The hydraulic jump phenomenon is one of the most common phenomena in open channels. Hydraulic jump is a transition state from supercritical to subcritical flow regime, which normally occurs in conjunction with hydraulic structures, such as spillways, weirs, and sluice gates. A hydraulic jump phenomenon serves a variety of purposes, for instance, to dissipate the energy of flow to prevent bed erosion and aerate water or to facilitate the mixing process of chemicals used for the purification of water. Stilling basins are one of the most common structures for energy dissipation of flow with high velocities. The stilling basin has been accepted to be the most powerful hydraulic structure for the dissipation of the flow energy. The size and geometry of the stilling basin affect the formation of flow patterns, which can be influential for hydraulic performance of the whole system. The depth of water after the jump is related to the energy content of the flow, and any reduction in energy content with increased energy dissipation in the jump will reduce the required depth of flow after the jump. Sometimes these basins are supplied with appurtenances that increase the overall roughness of the basins. This in turn increases the energy dissipation, decreases the sequent depth, and requires a shorter basin for the full development of the hydraulic jump. There are plenty of research studies in the literature regarding the classical hydraulic jump in the usual rectangular straight stilling basin, but less for the hydraulic jump in other cross section shape of basins. Expanding gradually basin with the rectangular cross section acts as two separate hydraulic structures including stilling basin and transition. In this type of structures not only the transition can be eliminated, but the length of the basin will be also much smaller than what is designed for the usual straight basins. Researchers’ studies show that divergence in stilling basins reduce the sequent depth and the length of the jump while increasing the energy losses compared to the classic jumps. In this research, numerical simulation of the hydraulic jump was performed in divergence rectangular sections, and compared with the results of the laboratory, making use of the FLOW-3D software and the standard k-ԑ and RNG k-ԑ turbulence models. The effects of Vertical and Curve blocks on the specification of hydraulic jump were evaluated. The results showed that the standard k-ԑ turbulence model was able to predict the water level profiles in the hydraulic jump in divergence rectangular sections with appropriate and acceptable coincidence. Results showed that the mean relative error of water surface obtained from numerical model and measured values is about 3.55 percent. Also the numerical model showed the vortices that were accrued because of diverging walls as well as experiment investigations. The results show that creating the vertical blocks, reduces the sequent depth as much as 46.27 % and the length of the hydraulic jump as much as 17.64%, while increasing the energy loss as much as 31.57%, compared to the classic hydraulic jumps. The results also show that creating the Curve blocks, reduces the sequent depth as much as 69.76 % and the length of the hydraulic jump as much as 35.29%, while increasing the energy loss as much as 32%, compared to the classic hydraulic jumps.

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The circular hydraulic jump usually forms when a liquid jet impinges on a horizontal flat plate. However, under certain conditions of fluid viscosity, volume flow rate and obstacle height downstream of the jump, the flow changes from super-critical to sub-critical and hydraulic jump changes shape from circular to polygonal. Despite the phenomenon of the hydraulic polygon jump has observed about two decades, the experimental relationship has not been presented to estimate the number of sides of hydraulic polygon jumps. The size and number of sides of a polygonal hydraulic jump depend on various factors such as fluid volume flow rate, jet diameter, fluid height downstream of the jump, and fluid physical properties; in other words, they depend on the dimensionless numbers of Reynolds, Weber, and Bond. Hence, in this study Taguchi analysis, as a Design of Experiment method, was used to investigate the effect of volume flow rate, jet diameter and obstacle height downstream of the jump on the number of the sides of a polygon hydraulic jump and Linear and nonlinear relationships was proposed for estimating the number of the sides of a polygonal hydraulic jump in terms of the above mentioned parameters.

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Walls convergence of stilling basins is one of the ways to improve hydraulic jump to increase tailwater depth and energy dissipation at downstream of spillways of high head dams. On the other hand, occurrence of hydraulic jump in converged sections is accompanied with formation of shock waves. Technically, production and development of the mentioned waves are undesirable due to amplification of mixture of water and air and resulting, disturbance outbreak on occurrence of stable hydraulic jump. Many studies have been conducted on the characteristics of hydraulic jump over gradually expanding cross sections, but comparatively few have been carried out on basins with convergent wall. In this research, occurrence of hydraulic jump in stilling basin with convergent wall was studied using experimental model for three different geometry and initial Froude number equal to 3.17 and 4.46. Experiments were conducted in a flume with a length of 6m, width of 1m and depth of 0.7m. Angels of convergence (7.7º and 19.5º) and type of stilling basins walls (straight and curved) were intended as geometric variables. In all experiments, widths of upstream and downstream channels were considered 80 and 40 cm, respectively (contraction ratio=0.5). The flow discharges were measured by an ultrasonic flow-meter having the accuracy of 0.02 lit/s. Values of instantaneous velocity were measured in 10 vertical sections in centerline of the convergent stilling basins using an electromagnetic 2-D velocity meter having the accuracy of 0.5 cm/s. Maximum height of produced shock waves in the contraction sections and conjugate depths of hydraulic jump were measured by a point gauge having the accuracy of 0.1 mm. The measured values of conjugate depths ratio and energy dissipation were compared with the obtained results of analytical equations presented by Sturm (1985) and Montes and Chanson (1998). The average relative errors of calculation of the mentioned parameters were respectively achieved 9.75% and 17.15%. It should be mentioned that the equations tended to underestimate the conjugate depths ratio and energy dissipation values. The velocity and turbulence intensity profiles were demonstrated and analyzed based on the mean values of instantaneous velocity and minor fluctuation of instantaneous velocity. The effects of convergence angle and curvature of basin wall were investigated on changes trend of the profiles. The results showed that changes of the convergence angle has a considerable impact on the conjugate depths ratio, energy dissipation and length of hydraulic jump. As for a constant Froude number, increasing of the convergence angle to approximately 12º was averagely accompanied with decrease of the conjugate depths ratio and hydraulic jump length to the 34.4% and 35.5%, respectively and increment of the energy dissipation to the 33.2%. It should be mentioned that increasing of the convergence angle caused intensification of the shock waves. Moreover, effects of curvature of basin wall were investigated for an equal convergence angle. As regards it had insignificant impact on improvement of hydraulic jump characteristics and difficulty of its implement, so it is not economical. The obtained results of the present research can be very useful for designer engineers.

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In an open channel, A hydraulic jump is the rapid varied flow which results water surface level increment and energy suppression. In most cases, by this phenomenon energy dissipation process is accomplished in downstream of hydraulic structures such as weirs, sluice gates and so on. The hydraulic jump is controlled by utilizing a structure called stilling basin. Building such structure can be very costly. Several approaches, such as bed roughness, chute blocks, baffle blocks and end sill, have been proposed to reduce the construction cost. For the first time, it is recommended to use the suspended anchored spherical energy dissipator blocks. From a practical point of view, this structure is very similar to baffle blocks but due to having less drag coefficient compared to the baffle blocks, they will suffer less force. Therefore, the slab thickness of basin decreases to a certain extent. Furthermore, due to fluctuations, using such dissipators leads to an increase in energy dissipation. These blocks have a relative density lower than water and are anchored by a thin resistant plastic to the floor of stilling basin. To the best of our knowledge, there are no studies on using these structures in the basin and analysis of their influences on the hydraulic jump characteristics. There are several interesting questions about the effect of such structures on the conjugate depth, jump length, and optimization of the design of the stilling basin as well. The main goal of our study is to answer these queries. In this work, 30 experiments were conducted in the range of froud numbers of 5-8 and in the form of four types of arrangement. It should be noted that, five experiments are concerned with testing the designed bed without any blocks. The Experiments were carried out in a flume with glass walls, 8 m length, 35 cm width and 40 cm heights. In order to form the hydraulic jump, the height of the walls were extended up to 80 cm in the beginning part of the flume and a chute with 30 degree angle and the height of 40 cm was set up. Next, in order to modeling such structures the obstacles diameter was set to 4 cm i.e. 1.2 times more than highest initial depth in classical hydraulic jump of present study. The size of the anchor length was chosen in such a way that the blocks do not enter into the roller environment and remain in front of impinging jet stream into the stilling basin, since no energy dissipation will occur if they enter into the roller ambient. The results showed that the arrangements decrease the jump length and conjugate depth respectively, in average to 31% and 21%. Additionally, the energy dissipation using the suspended blocks in average is around 68% that is approximately 11% greater than smooth bed. In all arrangements for experiments, conjugate depth reduction and energy dissipation increment is not impressive compared to each other, but even so the most and lowest effective arrangement respectively, was type 4 and type 3.

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Abstract
Scope and Background: Dissipating high kinetic energy of supercritical flows for the purpose of protecting downstream structures has always been a concern of hydraulic structure engineers. One of the approaches to tackle this problem is the utilization of hydraulic jump phenomena in which a great amount of kinetic energy is dissipated through turbulence which is more pronounce in roller part and conversion to potential energy in term of depth increase at downstream end and turbulence. A hydraulic jump may occur in prismatic or non-prismatic, converged or diverged and horizontal or inclined channels. However, there are oblique shock waves initiating at the start of a contracted channel, interact with each other and sidewalls and may create a complex flow pattern which is detrimental to the channel itself and downstream facilities. The present research aims at studying hydraulic jumps taken place in a converging inclined channel. The main parameters of a hydraulic jump such as its location, initial depth, ratio of conjugate depths, jump length and energy dissipation are studied for various inclination and convergence ratios and inflow conditions.
Methodology: The experiments were conducted in a channel with different bed slopes of 0, 5, 10, and 15 percent, and convergence angles of 3.66 and 5.4 degrees. The end sills of 0.75 to 11 cm high were installed at the end, depending on the bed slope, to fix the jump location in the channel. The entrance was set carefully to produce the least disturbance due to sharp edges and protruding elements appeared in the flow; hence, a symmetric hydraulic jump may be observed all over a cross section. In order to double-check the accuracy of measurements, clips of various hydraulic jump were shot through sidewalls, converted into the images and digitized using Grapher^TM.
Discussion and Conclusion: The length of a hydraulic jump, was mainly a function of bed slope, such that by increasing the slope to 15%, the increase in the jump length was about 37.5% in average. Specifying a unique initial depth in a converging channel was challenging. There were oblique waves originated from the concave corners and coincided at the center line of the channel. In cases where the hydraulic jump occurred before the coincidence of the oblique waves there were three different depths at the start of the jump. In this work, the centerline depth was selected as depth of reference in the development of equations. By enhancing the bed slope, the mean initial depth decreased and the conjugate depth ratio increased. The energy dissipation increased by both the bed slope and convergence ratio. However, the effect of bed slope was more significant such that the average growth of dissipation in a horizontal bed was about 30% compared to a sloping bed. By increase of initial Froude number the difference between energy dissipation in various bed slopes approached to that of a horizontal bed. Using regression models, empirical relationships were developed for the estimation of length, conjugate depths ratio and energy dissipation of a hydraulic jump in an inclined converging channel. 
 

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One of the most famous hydraulic phenomena to reduce flow energy is hydraulic jump, which is used downstream of dam overflows in river sections and structures established in irrigation and drainage canals. It is very important to control and reduce the kinetic energy resulting from this phenomenon at smaller distances from the place of formation. Among the examples of depreciation structures, we can mention the roughness of the bed and the construction of stilling basin and making expansion, but it must be said that it causes pressure fluctuations and damage to the bed of the canals and river. The existence of the submerged jet can reduce this pressure fluctuation and change the flow downstream to subcritical. The purpose of this research was to investigate the presence of a submerged jet system on the characteristic of asymmetric hydraulic jump in corrugated beds so that this phenomenon can be controlled and ensure the safety of structures and beds downstream. For this reason, the experiments were carried out in a flume with a fixed peak overflow with a central flow rate range of 26 to 67 liters per second and 3 mutual submerged jet flow rates. This investigation showed that the corrugated bed in the region of gradual expansion has reduced the length of the jump compared to its absence and the changes in the flow depth have also decreased. Also, the impact of the opposite jet in the submerged shape improved this process; So that energy consumption was reduced by 25-30% and jump length by 50%. Therefore, the effective role of this combination of jet system and continuous corrugated bed was shown.