Journal of Hydraulics
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Journal of Hydraulicsendaily1Tue, 21 Mar 2023 00:00:00 +0330Tue, 21 Mar 2023 00:00:00 +0330Analysis of Water Surface Profiles in Coarse-Grained Porous Media with Radial Flow Using the Gradually Varied Flow Theory
http://jhyd.iha.ir/article_151038.html
IntroductionNon-darcy flows into two categories: parallel flows (such as gravel dams, gabions, etc.) and radial flows (such as flows near wells drilled in coarse-grained alluvial beds, etc.) are divided. In the first category, streamlines are almost parallel so that there is no curvature or contraction of streamlines in the plan view. This type of flow is found in both pressurized and free-surface modes. Radial non-darcy flow analysis has many applications in the fields of civil engineering, geology, oil, and gas. The equations governing the radial non-darcy flow are solved using numerical methods of finite differences, finite elements and finite volumes. Solving these equations requires boundary conditions and a lot of data and is almost bulky, time consuming and costly. While, gradually varied flow theory, requires much less data and is easier and less expensive. For this reason, in the present study, for the first time, using experimental data recorded in a large-scale (almost real) device, the application of the gradually varied flow theory in radial non-darcy flows with free surface has been investigated. In other words, since the calculation of water surface profiles in a radial rockfill is of great importance. In the present study, using large-scale (almost real) experimental data and the gradually varied flow theory, the water surface profile in radial non-darcy flow with free surface and in steady state has been investigated.MethodologyIn the present study, due to the compatibility of cylindrical coordinates and its adaptation to the physics of problems related to radial flows, a device has been constructed in the laboratory of Bu Ali Sina University in the form of a semi-cylinder with a diameter of 6 meters and a height of 3 meters. The dimensions of this device are made on a large scale and the effects limitations have practically no effect on the testing process. To measure piezometric pressure, piezometric grids have been used. The device has a volume of 14,000 liters and a capacity of materials weighing approximately 40 tons. Four pumps are installed in parallel at the top of the device to generate the required flow. Coarse-grained river materials with a diameter between 2 to 10 cm, a porosity of 40%, a Cu of 2.13, and a Cc of 1.016 have been used. To perform the tests, the model is first filled to a certain height (53, 60, 70, 85, 95, 110, 120, 140, 150, and 160 cm) by pumping operations. The flow rate created in these experiments is in the range of 49.94 to 53.16 L/s.Results and DiscussionOne-dimensional analysis of steady-non-darcy flow using gradually varied flow theory and two-dimensional analysis using Parkin equation solution. Most research has been done in parallel flow rockfills. Also, solving the Parkin equation in both parallel and radial flows requires a lot of data such as boundary conditions upstream and downstream, as well as the boundary condition of the water surface profile, and the calculation process is complex and time-consuming. The gradually varied flow theory requires much less data than solving the Parkin equation, and the water surface profile obtained from it is also used as the main boundary condition in solving the Parkin equation. In other words, calculating the water surface profile in a radial rockfill is very important to studying the movement of water. Also, the water surface profile is the main boundary condition in the two-dimensional analysis of steady flow (solving the Parkin equation), and with it, upstream and downstream boundary conditions will be practically available. For this reason, in the present study, using large-scale (almost real) experimental data and the gradually varied flow theory, the water surface profile in the case of radial non-darcy flow has been calculated. To calculate the flow depth at different points (water surface profile) using the gradually varied flow theory, the amount of flow depth at one point and the coefficients m and n must be available. Since the flow depth measurement in the well (downstream of the desired interval) can be measured, in the present study, the calculations started from the downstream (depth of flow in the well).ConclusionIf the gradually varied flow theory is used to calculate the water surface profile in the case of radial non-darcy flow with a free surface, the mean relative error in the case of pumped heights is 53, 60, 70, 85, 95, 110, 120, 140, 150 and 160 cm are equal to 1.56, 0.96, 0.61, 0.45, 0.28, 0.19, 0.13, 0.16, 0.11 and 0.05 are calculated, respectively. In other words, the average mean relative error (MRE) of calculating the water surface profile for different heights of pumped water is equal to 0.45%. Also, according to the obtained results, the greater the depth of water pumped upstream, the higher accuracy of the gradually varied flow theory.KeywordsRadial Non-Darcy Flow, Steady Flow, One-Dimensional Analysis, Gradually Varied Flow Theory.The experimental study of downstream scouring of trapezoidal Piano key weir type A under free and submerged flow
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Introduction: Weir is a structure that is made in the body or support of the dam to safe drain the excess volume of water in the tank. Weirs are mainly considered for free flow mode, but in some cases there is a possibility of immersion in them. Submersion in weirs occurs in two general and local ways. General submersion will occur if the downstream water level is higher than the weir crown level. This is more likely to occur for weirs in canals and rivers and if the weir acts as a diversion dam. Local submersion is observed in the downstream part of weir due to local flow conditions. Weirs are divided into linear and non-linear weirs based on the shape in the plan. Piano key weirs are the newest type of non-linear weirs which recently due to its advantages. Non-linear Piano Key Weirs enjoy not only a higher water passage but also a relatively simple and economic structure compared to linear weirs. Methodology: All experiments of this research were performed in a channel with a long 10 m, wide 0.75 m and high 0.8 m in Tarbiat Modares University hydraulic laboratory. A view of the laboratory flume is shown in Figure (3). The required water was supplied through an underground reservoir. In this research, trapezoidal piano key weir types A, made of thermoplastic with a thickness 1.2 m, slope of the input and output keys 28 degrees and a height 0.2 m was used. The weir has 6 keys (3 input keys and 3 output keys) with the same slope in the input key and the output key. Uniform bed materials with an average diameter 2.2 mm were used. Flow discharge was measured with an ultrasonic flowmeter and flow depth and bed level were measured with a laser level gauge. According to the selected discharges, the flow depth upstream of the weir was considered to be more than 3 cm so that the effect of surface tension is not significant. In this study, experiments were performed with five discharges 30, 40, 50, 60 and 70 liters per second. Under submerged flow for each discharge, two percent submersion and under free flow for each discharge, the tailwater depth was considered to be 0.13 m.Results and discussion: Flow characteristics are affected in case of weir submersion. During the test, after the flow hit from the input switch to the tailwater surface, due to the amount of tailwater depth, surface rotations (at low tailwater depth) and surface turbulence (at high tailwater depth) are observed. Part of the flow moves downwards and after hitting the bed surface, a weak rotational zone is created in the range of the input switches. The flow enters the downstream in the form of a submerged jet after the output switch and, due to the momentum to the upper fluid, causes a severe rotational zone in the range of the output switches. In the free flow, more turbulence is observed in the range of the output switches due to the intersection of the flow passing through the weir lateral wall and the falling current from the upstream and downstream crowns. Less tailwater depth in free flow limits the deep growth and development of the sedimentary hill in downstream of the scouring hole, and sedimentation occurs with longer length and lower elevation. However under the submerged flow, due to the greater tailwater depth and lower fall height, the flow strength is more depleted and the flow strikes the bed with less energy, and result in less scouring. In this case, the flow does not have the power to transfer all the sediments to the downstream and most of the sediments accumulate on top of each other and a sedimentary hill is created as a point. As a result, a sedimentary hill with a higher height and less length is visible under submerged current than free flow. Therefore, in the free flow than in the submerged flow, the length and depth of the scour hole occur more, and sedimentation occurs with less height and longer length. Under submerged flow, most of the sediment bed remains unchanged, while under free flow most of the sediment bed is affected by scouring and sedimentation. Of course, changes vary depending on the hydraulic conditions. In the early times, in both free and submerged currents, scouring occurs with greater intensity, but over time, its severity decreases and scouring reaches a stable state. In this case, sediments are rarely transported downstream. The surface of the sedimentary hill downstream of the scour hole in the open stream is almost smooth and in the submerged stream is sharp. Conclusion: The results showed that most of the scour hole changes occur in 20% of the initial time of the experiment and the changes in the free flow are faster than the submerged flow. The depth and length of the scour hole in free flow is greater than in submerged flow. Relative scour depth with increasing 77% in tailwater depth for Froude numbers of particle 0.029, 0.037, 0.045, 0.052 and 0.058, respectively 42, 45, 21, 28 and 27% and with increasing the tailwater depth 123% is reduced by 95%, 92%, 90%, 75% and 68%, respectively. With increasing 18% in the submersion ratio in the Froude number of particle 0.029 and increasing 96% in the submersion ratio in the Froude number of particle 0.058, the maximum relative scour depth decreases by 92 and 56%, respectively. The location of the maximum scouring is also a function of Froude number of particle and the tailwater depth. Maximum scour depth at the tailwater depth 0.13 m at a distance 0.18 to 0.30 m from the weir toe, at the tailwater depth 0.23 m at a distance 0.18 to 0.36 m from the weir toe and at a tailwater depth 0.29 m is at a distance 0.03 to 0.30 m from the weir toe.Investigation of the effect of treated wastewater injection on the permeability of unsaturated and saturated porous media in the aquifer storage and recovery system
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Extended Abstract:Introduction: The permeability of porous media due to clogging of pores is one of the problems of aquifer storage and recovery (ASR) systems. The more pore clogging occurs when treated wastewater is used as water resources for ASR In addition to physical clogging, the biological clogging also plays an important role in reducing the permeability and hydraulic conductivity of the porous media. In most of previous studies, the infiltration and clogging of the unsaturated zone have been evaluated by measuring the input-output flow from the soil columns. In this study, the permeability and hydraulic conductivity variations due to the passage of treated wastewater through the unsaturated and saturated zone have been evaluated simultaneously. Methodology: The main goal of this study is the investigation of permeability and clogging variations in unsaturated-saturated zones in the aquifer storage and recovery system using the treated wastewater. For this study, an experimental model was designed with 2.5 m vertical height (unsaturated layer) and 12.5 m horizontal length (saturated layer). It was made with a PVC pipe with a diameter of 200 mm.Results and discussion: The input-output flow rates had been measured for a period of 70 days. The reduction of inlet and outlet flow is due to physical and biological clogging of soil pores. The physical clogging usually occurs earlier and in the early parts of the model and then there is a gradual decrease of infiltration velocity and hydraulic conductivity. The rate of increase of biological clogging is slower than physical and with the growth of bacteria, its amount increases to a constant rate. Then, as the bacterial population decreases, the flow rate in the porous media increases and results in a temporary increase in permeability and outlet flow rate. The bacterial growth cycle in a closed environment consists of four stages. This growth pattern corresponds to the fluctuations of the discharge output from the end of the setup. In the first stage (lag phase) when the bacterial population is the smallest, the output discharge is maximum. Then, entering the second stage (log phase), the bacterial population increases up to the maximum. With this increase in growth, the output discharge is reduced to a minimum. After that, the bacterial population enters the third stage (stationary phase) and their population remains constant, and the output discharge in this stage is also almost constant. Then the growth of bacteria enters the fourth stage (death phase) and some of the bacteria die to regain balance and the output flow increases to an almost constant value. This bacterial growth cycle and discharge output continues. In fact, what causes biological clogging is the activity of bacteria. The gases produced by their activity clogged some of the pores of the porous medium. The nitrate concentration decreases to some extent as the treated wastewater passes through the unsaturated soil. Then, as it continues to move in the saturation zone, its concentration decreases much more and at a distance of 7 meters from the beginning of the setup, its value reaches less than 0.5 mg / liter and this concentration is almost constant at the end of the path. The main reason for the large decrease in nitrate concentration is due to denitrification phenomenon. This is also hydraulically justified by the height of the water inside the piezometers along the flow path. The hydraulic head had many fluctuations in piezometers, which are largely proportional to the output flow fluctuations. The quantitative (inlet and outlet flow and pressure) and qualitative (nitrate concentration) measurements on the model indicate the types of clogging in the porous media.Conclusion: The output flow of the experimental model after two days from the start of injection reached its maximum value of about 6.7 liters per day and after 6 days began to decrease to about 2.6-2.1 liters per day and had a variation of the same range for about 30 days. Then, its amount has been increased to 4.1 liters per day for 6 days and decreased to 2.1 liters per day in 70 days after the injection. The hydraulic conductivity of the soil also changes in proportion to the changes in the output flow. Before injecting the treated wastewater into the soil column, the amount was 1.32 meters per day and gradually decreased to 0.47 meters per day. The maximum and minimum soil permeability is 14.8 and 4.33 cm per day, respectively. After the injection of treated wastewater, over time, part of the pores of the porous medium is clogged for physical, chemical and biological reasons and reduces the permeability. This permeability reduction can initially be up to 70%, which is the simultaneous effect of three factors of physical, chemical and biological clogging, but with the entry of bacteria into the fourth phase, the effect of biological clogging decreases and the permeability increases so that the penetration rate is 35% less than its original value. If the clogging of the pores is physical, the reduction of permeability and hydraulic conductivity becomes almost permanent, but if the clogging is biological, the reduction of permeability and hydraulic conductivity is temporary. Therefore, a cycle of biological clogging changes in the treated wastewater injection system and using the dry and wet interval periods in accordance with this cycle, the performance of injection ponds can be significantly increased in terms of quantity and quality.Experimental study of the effect of the apron installation on reducing scour depth at the downstream of stepped weirs with labyrinth sill
http://jhyd.iha.ir/article_154188.html
Introduction: The movement of water flow in rivers and streams of the erodible bed causes the cycle of erosion and sedimentation. Although this is a natural process, its occurrence occurs along sections of a river course that conflict with different uses, ranging from agricultural damage to structures built along rivers or riverbeds (Esmaeili Varaki et al., 2021).Stepped weirs are one of the effective structures in flow energy dissipation. Due to their shape and geometry, these structures implement to reduce energy and erosive power of water flow and also to reduce the cost of energy consuming structures that should be built downstream of dam weirs (Chanson, 1995; Khatsuria, 2005). In the present study, the simultaneous effect of creating an apron at the downstream of a stepped weir and installing sills with different geometries on its stairs on the downstream scour depth under different flow conditions and apron length was examined in a laboratory.Methodology: The experiments of this research were performed in the hydraulic laboratory and physical-hydraulic models of the Department of Water Engineering of the University of Guilan in a flume of 12.5 meters long, 1.5 meters wide and 1 meter high with glass walls and metal floors. In order to provide the flow rate, a centrifugal pump was used that can provide a flow rate of up to 90 L/s. In this research, two different weir slopes (1:2 and 1:3), aprons with lengths of P/3 (0.135 m) and 2P/3 (0.27 m) and sill with different geometries, were examined. In order to supply sediment particles, mineral sand with a uniform diameter of 2.68 mm was prepared and placed in the sediment bed with a length of 2 m, a width of 1.5 m and a height of 0.3 m at the downstream of the weir. Long term experiment was conducted to find the corresponding time of equilibrium scour depth. Comparison of results showed that after 6 hours, the scour depth reached equilibrium condition and no noticeable change occurred, so in all experiments, measurements were performed during the mentioned period. For each experiment, after installing the weir, the sills and aprons the downstream sedimentary bed was leveled. Then, according to the desired flow, the necessary adjustments were made for the relevant engine speed. After the flow entered the flume, the flow depth gradually increased and by adjusting the downstream tail gate, desired tail water depth was adjusted. In each experiment, instantaneous scour profiles were recorded at 5, 10, 15, 30, 45, 60, 90, 120, 180, 270 and 360 minutes from the start of the experiment using digital camera and then digitized using Grapher9 software. The final scour profile was also measured at the end of each experiment using a laser meter with an accuracy of &plusmn; 1 mm.Results and discussion: Experimental observation showed that by installation of sills, nappe thickness increased from yc/2 to yc, in which yc is critical flow depth. Furthermore, installation of sills reduced angle of imping jet to sedimentary bed from 58 to 34 degree. Consideration of the length of falling jet form the last step of weir to the downstream sedimentary bed indicated that by reduction of the weir slope from 1:2 to 1:3, length of falling jet increased. Comparison of the temporal development of scour depth showed that at the low discharge, installation of sill increase temporal scour depth. However, by increasing flow discharge and corresponding flow velocity over steps, installation of sills reduced temporal scour depth. From different geometry of sills and length of apron, weir of S2Si2LA2 have the best performance and decrease dse/p form 0.23 and 0.45 in range of low and high flow discharge to 0.1 and 0.24. by reduction of the weir to 1:3, installation of sill have not positive effect to reduction of the temporal scour depth.Conclusion: Comparison of the results of the installation of apron with different lengths on the maximum scour depth in the range of minimum and maximum flow discharge, i. e., relative critical depth (yc/ h) from 0.06 to 0.34, showed that stepped weir with and without sill at a slope of 1:2 showed by installation apron of lengths LA1 (P/3) and LA2 (2P/3), the relative maximum scour depth (dse/p) reduced from 0.23 to 0.19 and 0.11, respectively. By installation of different sills, the relative maximum scour depth decreased to 0.22 and 0.17, respectively. By reduction of weir slope to 1:3, installation of apron with length of P/3 and 2P/3, reduced the relative scour depth to 0.18 and 0.14. by installation of different sills geometries, dse/p reduced to 0.24 and 0.1, corresponding to the length of aprons P/3 and 2P/3, respectively.Analysis of unsteady flow in open channel using Fourier series
http://jhyd.iha.ir/article_154776.html
Introduction: The shallow-water equations in unidirectional form namely as Saint Venant equations (SVE) are a set of quasi-linear hyperbolic partial differential equations, having a wide range of applications in open channel and river flow analysis. Because of intrinsic non-linearity, there are no analytical solutions for these equations in most practical applications except for simplified versions. On the other hand, numerical solutions by finite difference or finite element methods are time-marching and for forecasting and timely management of floods are relatively lengthy and time-consuming. Recently, new solutions of SVE in frequency domain, using Laplace Transform (LT) or Fourier Series (FS) have been proposed to overcome these difficulties. In the LT method, input wave is converted into a unit hydrograph, a unit step, or a unit pulse. Despite of unconditional stability, the accuracy of this method depends on time step of decomposition of input information. In this research, however, the FT method is proposed to reduce the execution of real-time flood forecasting. Unlike finite difference models, this is not a marching method and the results may be generated at a given time, directly. Moreover, there is not any restriction in the decomposition of input data due to their independence from time.Methodology: The complete form of SVE, namely as full dynamic equations are used in the present work. Initial conditions are non-uniform and the up-and downstream boundary conditions are inflow hydrograph and stage-discharge rating curve. SVE are linearized around a steady-state situation using the Taylor expansion. Assuming that the changes in water depth and discharge follow a sine pattern, the linear equations of continuity and momentum are transferred from time domain to frequency domain using the FS and sine functions. The input wave to the model, not necessarily harmonic and periodic, is converted to a set of periodic waves using Fast Fourier Transform (FFT). Considering the initial condition of non-uniform flow in the model, the channel is divided into some intervals that may have equal or non-equal lengths with uniform flow at each part. All channel characteristics such as mean flow depth are computed at each interval separately. Then, transition matrices are constructed to interconnect the channel intervals at the boundaries. Finally, the frequency response of flow discharge and water level are obtained at each part of the channel.Results and discussion: This method could be used for all kinds of prismatic and non-prismatic channels, natural rivers with various types of flow (critical, sub-critical, and super-critical), different boundary conditions at the up- or downstream ends, and point or distributed lateral inflow. Rashid and Chaudhry (1995) performed their experiments in a rectangular flume. The flow was unsteady and non-uniform. FFT was used to decompose the input hydrograph into a complex sum of periodic waves. In this research, 256 waves with a frequency of 0.002 to 0.5 were used for accurate matching between the input hydrograph of the laboratory model and the hydrograph of the total waves analyzed by the fast Fourier transform. The result of the proposed method was compared with laboratory results of Rashid and Chaudhry, analytical model of Cimorelli, and numerical method of Preissman in time domain. The Nash&ndash;Sutcliffe efficiency coefficient (NSE) in the present study is more accurate than other models and in stations (2) and (5) are equal to 0.9893 and 0.9872, respectively. The peak of hydrograph in our model is more than the Cimorelli analytical model. The lag time of mean peak of hydrograph in the model is equal to the experimental results of Rashid and Chaudhry (1995). Execution time of the model is 11.84 seconds in comparison with Preissmann implicit method that is 54.48 seconds with the same computer. This run time is important in forecasting and warning models of floods. Visual comparison of theoretical and experimental hydrograph curves are satisfactory.Conclusions: The proposed method is unconditionally stable. Full dynamic unsteady flow equations of Saint Venant is solved using FFT and Transition Matrix. The upstream boundary condition is stage-hydrograph and the downstream boundary condition is a stage-discharge relationship. The effects of lateral inflows and non-uniform initial conditions are considered in the model. To evaluate the accuracy of the model, the results compared with experimental data of Rashid and Chaudhry, analytical model of Cimorelli and numerical model of priessmann in time domain, were satisfactory both quantitatively and qualitatively. Regarding the unconditional stability and the appropriate run time of computer, the code is suitable for flood forecasting, warning and optimization models. This method can be used to analyze the flow in natural rivers and irrigation canals with any type of flow regimeNumerical investigation of velocity distribution and flow characteristics over modified steps of stepped spillway
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Introduction: Stepped spillways are a common structure for energy dissipation by creating frictional resistance to flow through the steps. Based on the studies and depending on flow conditions, the flow over a stepped spillway is usually categorized into three regimes: nappe, transition, and skimming. The stepped spillway is often designed for skimming flows. There were different studies investigating various aspects of stepped spillways, but what is important in this type of spillway is increasing the effectiveness of steps in the rate of energy dissipation. This can be done by a new type of step structure (i.e., inclination angles on steps or using a sill on the edge of a step and cases like that) or geometric alteration and change of steps called labyrinth stepped spillways. Therefore, it is scientifically beneficial to modify the shape of the step of the stepped spillway to increase its collision and roll to achieve energy dissipation. The present study deals with the design of step modification by creating cubic elements on the steps in different arrangements and different hydraulic conditions. This has been considered to improve the performance of stepped spillways by increasing the energy dissipation. For this purpose, using FLOW-3D software, the influence of geometric appendance elements on the steps on the velocity distribution, pressure, the turbulent kinetic energy (TKE), and finally the flow resistance and the energy dissipation on modified spillways was investigated and compared with the flat stepped spillway.Methodology: The physical model for verifying the numerical results was carried out in a rectangular flume with a length of 12 m, a width of 1.2 m, and a height of 0.8 m. The experiments were conducted on a stepped spillway with a slope of 26.60&deg; and consisted of 10 steps with step length (l) and height (h) of 0.06 and 0.12 m, respectively. Stepped spillway models in numerical study include flat models and models with cubic elements placed on the steps in four arrangements of two side, zigzag, center, and hybrid AE elements and two heights of elements h/2 and h/4 (h step height). The commercially available CFD program FLOW-3D was used for the numerical simulations. The RNG k-&epsilon; turbulence model was employed for the turbulence calculations. To obtain mesh-independent results, three different mesh sizes were used, and the grid convergence index (GCI) methodology was employed to select the appropriate mesh. As a result, the mesh consisting of a containing block with a cell size of 1.3 cm and a nested block of 0.95 cm was selected. In the fluid domain, the boundary conditions were set according to the experimental conditions. In the upstream of the domain, a discharge flow rate (Q) definition was set. The downstream section was treated as an outflow (O) boundary condition. The bottom and the sides behave as rigid walls (W). For the upper boundary, the atmospheric pressure boundary, and at the inner boundary conditions, symmetry (S) was used.Results and Discussion: The results showed that the appendance elements on the steps cause some fluctuations on the flow surface and increase the intensity of the current collision by deviating the flow from its parallel path. The result is reduced velocity by about 10%, an increase of 54% in TKE, and an increase of 6.42% in energy dissipation on modified models compared to the flat stepped model. There was no negative pressure on the horizontal plane of the steps, and the maximum pressure occurred in the middle of the steps and inclined to the end of the steps. The appendance elements reduce the negative pressure areas on the vertical surface of the steps and reduce the risk of cavitation. The hybrid element model performs best in other arrangements, and reducing the height of the elements improves their behavior.Conclusion: According to the obtained results, it can be concluded that the appendance elements on the steps improved the hydraulic performance of stepped spillways by increasing the roughness of the steps, increasing energy dissipation, reducing the flow velocity over the spillway and reducing the risk of cavitation by reducing the negative pressure in the vertical plane of the steps. The use of cube-shaped elements on the steps and in the hybrid arrangement is suggested.Laboratory study of crossbeam structural design in control of asymmetric S- type jump of sudden expansion sections
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Laboratory study of crossbeam structural design in control of asymmetric S- type jump of sudden expansion sectionsIntroduction This paper presents an experimental study on a proposed dissipation structure, which consists of a series of cross beams, tested in different geometric configurations and hydraulic conditions. First, the effectiveness of this system was analyzed in terms of uniformity of flow and bed velocity and while, observing the dissipating mechanisms, in the next step, the system performance under variable tail water conditions by describing the three-dimensional flow patterns observed in the downstream channel with a gradual decrease in downstream level to 70%, 80% and 90% of tail water depth in the conditions the reference experiments were tested. Measurement of three-dimensional velocities to determine the parameters of flow uniformity, momentum and energy coefficients, and analysis of three-dimensional velocity distributions, turbulent kinetic energy, and supplementary studies on the development of isothermal line concentration and drop energy losses of reference experiments and optimal case compositions were examined. The results showed that in addition the similar qualitative trends of &beta; and &alpha;, the flexibility of the dissipation structure has a high efficiency in the effective homogenization of the flow in the abrupt expansion channel, even in the downstream water level conditions.Methodology The experiments were performed in the hydraulic laboratory of Shahid Chamran University of Ahvaz and in a horizontal rectangular open channel with a length of 12 m and a width of 1 m with a height of 0.87 meters. Flow supply was provided through an open tank with dimensions of 7 m by 5 m at a height of 2.5 m. Hydraulic S-jump was performed with sudden expansion and design and construction of ogee weir. With the formation of S-jump, the conditions for the depth of hS downstream in the end control section were set, equal to 0.19, 0.15 and 0.11 m, respectively, to create three 7.4, 8.7 and 9.5 Froude numbers. Measurement of longitudinal velocity at a fixed height of 0.5 cm from the bottom of canal and longitudinal sections of 0.25 from each other in the first 2 m of downstream canal, and the other ones at distances of 2.5, 3, 4, 6 and 8 m from sudden expansion. Finding the best configurations to achieve a uniform flow and reduce the velocity distribution was done in most of the critical areas downstream of structure. For the levels of reference experiments, 54 geometries of the energy dissipation system with different configurations of beam distances, s, number of beams, N, hb height, position of the first beam from expansion, P, and slope of the system, &theta;, were investigated. Each component of the structure includes an I-shaped beam, with a flange width of 1.5 to 2.5 cm, depending on the hb, in the direction of the channel width and vertically in the direction of the main stream. Results and Discussion The results showed the values of &beta;b and vmb2. &beta;b calculated for three Froude numbers and different geometric parameters of the system, which means the absolute distance of 1.65, 1.85, and 2.55 meters from the expansion section for P = 0.4, 0.6, and 0.8 meters, respectively the effectiveness of the system (beam configurations) in homogenizing the flow and reducing the bed velocity is clearly evident, even for the worst performance settings. When using the structure, the mean &beta;b is almost less than 1.1 with vmb2; the corresponding &beta;b was measured to be approximately 0.1 m2/s2. According to the observed efficiency of the beam system, 3 of the best performance settings of the structures were selected for Fr = 9.5 (which was the most difficult situation regarding the energy characteristics of the input current) to the flow characteristics along with the flow and downstream of the structure. Energy dissipation should be fully described. According to research results, the qualitative trends of &beta; and &alpha; are similar. Three-dimensional velocity distribution analysis showed that this type of structure has the flexibility to effectively homogenize the flow in abruptly expanding channels, even in the conditions of downstream water level varieties.Investigation of the turbulence kinetic energy, smaller vortices that contribute to turbulence at the surface and promote mixing in the flow interface until they reach maximum value during the study period, which was from x = 0.3 m to x = 2 according to the definition of the ratio of energy losses to initial energy as a relative energy loss or jump efficiency (&eta;), it was found that in all tested Froude numbers, the trend of increasing relative energy loss to a cross-section of 2.5 m after expansion section was increasing. Approximately X/Xexp = 4 reaches its peak and extends with a constant almost linear trend to the end of the section and the end.Conclusion In this research, a laboratory simulation application of a new structure with different geometric configurations of cross beams as a series of wide-wing beams to control asymmetric S-jump of sudden expansion sections was experienced. The use of different geometric configurations of cross beams shows the effectiveness of beams' contribution in homogenizing flow and reducing bed velocity.. The concentration of turbulent flow caused by the jet hitting the beam system, particularly the first beam, leads to a significant energy loss in the area between the first and 2nd beams. Before leaving the main system, the bubbles, leaving the system energy in the same evacuate the area and saw a calmer flow in after areas of the structure. The study of turbulent kinetic energy showed that the conversion rate of the high state from the mainstream after the beams (Conversion of mean flow) to turbulent flow occurs in some cases. Also, in all Froude numbers of reference experiments, the trend of increasing the relative energy loss to a cross-section of about 2.5 m after cross-section expansion is increasing. KeywordsSudden expansion, cross beams, hydraulic S-jump, flow patterns, energy dissipation, hydraulic structures, stilling basin.Evaluation of the Discharge Coefficient of Piano Key Weir under the Unsteady - Gradual Varied Flow with Increasing Discharge
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Introduction: Weirs or spillways are one of the most important types of hydraulic structures that are divided into linear and nonlinear weir categories based on the shape of the plan. The most important types of nonlinear wires are labyrinth wires and piano key weirs that increase the discharge of flow by increasing the length of the spillway crown. These types of weirs are usually made outside the dam body. The most important advantages of these weirs is high flow coefficient, speed in construction and economic efficiency. These weirs are one of the most suitable options for dam weir implementation in free-flow mode. Floods, snow melting, performance changes of hydraulic structures and many other unsteady flow factors are observed abundantly in nature. Therefore, in this study, the discharge coefficient of piano key weirs under the unsteady-gradual varied flow with increasing discharge has been evaluated. Also, in this research, the calibration of discharge coefficient due to changes in the weir height and the effect of weir height changes on the discharge coefficient and other effective hydraulic parameters in the upstream of the spillway under the unsteady-gradual varied flow with increasing discharge has been investigated.Methodology: The experiments were carried out in a rectangular channel of Islamic Azad University, Isfahan University (Khorasgan) with a length of 10 meters and a width of 0.6 meters. The height of the channel was the same and unchanged along the way, as well as its floor was made of galvanized sheets and its walls were made of tempered glass and completely sealed. Considering the relationships and previous studies and dimensional analysis, the effect of effective parameters on flow discharge coefficient was investigated. In the current research, three types of A-type rectangular piano key weir with variable heights of 10, 15 and 20 cm were used. Other geometrical parameters were constant and experiments done under the unsteady-gradual varied flow with increasing discharge in the flow range of 30 to 50 Lit/s. The experiments has been studied under the range of discharge changes of 5,3 and 1 liter per second and range of time changes of 5,10 and 15 seconds. Therefore, according to the said contents, 27 different modes have been analyzed in this thesis. Flow depth was reported by laser altimeter sensors at the top of the channel. PLC device was used to measure discharge and water head at different times. A magnetic flow meter is attached to the PLC device, which measures the discharge in liters per second and the height of water from the channel floor by sensors installed in millimeters.Results and Discussion: Discharge coefficient under the unsteady-gradual varied flow with increasing discharge was obtained by deriving from the relationship provided by Machiels et al. Considering that the dc/dt value is not known, the relationships of past researchers for the flow discharge coefficient of type A rectangular piano key weir presented. And comparing the percentage of error in each relationship was done. Finally, it was concluded that the relationship presented by Javaheri and Kabiri-Samani had a lower error percentage. And it was derived from this relationship relative to time, until determine the dc/dt value. Then, according to the experimental data and weir specifications of the discharge coefficient under the unsteady-gradual varied flow with increasing discharge, it was obtained. The results showed that with increasing the weir height, the slope of the discharge charts and the height of the water decreased and the slope of the head-discharge diagrams increased. With increasing the height of the weir, the discharge coefficient increased and in contrast to the froud number and the ratio of water height to the height of the weir decreased. As a result, the height of the weir is directly related to the discharge coefficient and is in contrast to the froud number and the height of the water at the inlet and upstream of the weir. According to the results obtained in the unsteady-gradual varied flow with increasing discharge that led to the calibration of the flow, it was found that the calibrated discharge coefficient (average) in three weirs with heights of 10, 15 and 20 cm is a number between 1.693 and 3.776.Conclusion: By comparing three type A piano key weirs, it was found that the weir with a height of 20 cm is more efficient than the weir with heights of 10 and 15 cm according to the higher discharge coefficient. It can also be stated that the higher height weir is much more applicable in floods and high flow discharges and better diverts the flow. In fact, all the results indicate that the height of the weir plays an important role in the amount of the flow coefficient of the piano key weir. And by increasing it, the efficiency of the flow discharge can be increased.Optimal Estimation of Secondary Flow Coefficient in Compound Channels with Vegetated Floodplains
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This study adopted the Shiono-Knight model (SKM) to estimate the lateral distribution of the depth-averaged velocity within rectangular and trapezoidal compound channels with emergent vegetation in floodplains. To implement the SKM, it was required to estimate the eddy viscosity coefficient, friction coefficient, and secondary flow coefficient. The present study estimated the friction coefficient using the Colebrook&ndash;White equation modified by Rameshwaran and Shiono for vegetated beds. An analysis of eddy viscosity models across compound channels indicated that the model was not sensitive to the eddy viscosity coefficient; thus, the eddy viscosity coefficient could be assumed constant across the channel. However, the negligence of the secondary flow in the model would lead to a significant error, and it was required to calibrate the secondary flow coefficient. Thus, this study used a genetic algorithm (GA) to develop equations for the secondary flow coefficient for different sections of the compound channel under two different approaches: (1) the approach of Abril and Knight (2004), who proposed constant values for the main channel and floodplains, and (2) the equations of Devi and Khatua (2017), which related the secondary flow coefficient to the relative depth and width ratio. It was found that the secondary flow coefficient was dependent on the relative depth and width ratio. As a result, the equation optimized based on the Devi-Khatua approach outperformed the Rameshwaran-Shiono technique in estimating the lateral distribution of the velocity, with a 10.2% lower error. This paper employed SKM to estimate the depth-averaged velocity within three compound channels of rectangular and trapezoidal cross-sections with a vegetated floodplain at small and large scales. To solve the SKM, it was required to calculate the friction coefficient, eddy viscosity coefficient, and secondary flow coefficient. The friction coefficient was calculated using the modified Colebrook&ndash;White equation. Several eddy viscosity models were adopted to implement the SKM. It was found that the eddy viscosity coefficient had no significant effect on the performance of SKM. The present study focused on calibrating the secondary flow coefficient as it played a key role in the flow simulation of compound channels using SKM. Two approaches were adopted to calibrate the secondary flow coefficient: (1) the approach of Abril and Knight (2004) and (2) the approach of Devi and Khatua (2017). The latter defines the secondary flow coefficient as a function of the relative depth and width ratio. The optimal secondary flow coefficient was obtained using a GA and experimental data for different geometric and hydraulic conditions. A comparison of the predicted and observed velocities demonstrated that the Devi-Khatua calibration method improved the predictive accuracy of SKM by nearly 10.2%. The secondary flow coefficient was found to be dependent on the relative depth and width ratio. It was calculated to be positive in both the main channel and floodplain, suggesting clockwise secondary flows. The difference between the observed and predicted velocities was larger in the floodplain than in the main channel, which could have arisen from flow complexities around vegetation.Energy Dissipation of Triangular Piano Key Weir
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Introduction Piano key weirs (PKW) is the newest type of long crest weirs, which achieve more crest length in the same width as congress weirs, and therefore, the capacity of the void is higher than that of the mounted piano key weirs, with the aim of increasing the amount of energy dissipation in them. It was noticed that the piano key weir oscilloscopes are used in the crest of reservoir dams and in irrigation and drainage networks. This has been implemented due to the importance of the issue of energy dissipation in these types of instruments. So far, many studies have been done on the discharge coefficient of the piano key weir, but no research has been done on the relative energy dissipation of the triangular Piano key weir.MethodologyThis research is a continuation of previous research on PK weirs. Figure 1 shows the rotating flume environment, which experiments were performed in that laboratory at the Tarbiat Modares University of Tehran (Dimensions: 10 meters long, 2 meters wide, and 0.9 meters high). Experiments have been performed on a triangular weir with a zero slope (i.e., Tri-Base model) (Fig. 2 and 3) and 10 degrees in the flow direction (Fig. 2 and 4). In this article, PK weir with horizontal and sloped crest is called Tri-Base and Tri-B1 models. The weir characters used in the laboratory are provided in Table1. Eq (3).The upstream depth (ho = P+h) and downstream (h1) was measured with an accuracy of &plusmn; 0.1 mm at a distance of 4P for the upstream depth (Crookston, 2010) and 10P for the downstream of the overflow (Eslinger &amp; Crookston, 2020).Results and DiscussionFor the ∆E/E0 curves, firstly, the relative energy dissipation curves for triangle PK weir with horizontal crest have been plotted (Fig 5) and compared with the present study and other researchers' results. The differences between results are because of the differences in geometric characteristics. Because the head and weir height changes for every discharge, Fig 6 has been plotted curves of (q - E1/E0).The trend of the relative energy dissipation curve of nonlinear weir may be according to a logarithmic curve (Lopes et al., 2011). Figure 5 shows the changes in energy consumption for the Tri-Base and Tri-B1 models and their comparison with the results of other researchers. According to Figure 5, the highest relative consumption of energy is for the Tri-Base model. In other words, at the same flow rate, the highest relative amount of energy dissipation is related to the weir model with a horizontal crest. It is also clear that the highest relative energy loss in all samples occurred at the lowest flow rates.As the flow rate increases, the relative dissipation of energy decreases in both models. The reason for this is that with the increase in flow rate and flow speed, the amount of flow friction is reduced, and as a result, the dissipation of the flow is reduced.With the increase of Froude Number, the acceleration increases, and the flow travels a longer path towards the separation, which causes the separation area to decrease and the Drag force to decrease. Because of the slope of the weir walls, the flow speed in the Tri-B1 model is higher than the Tri-Base model (the flow moves like a slide from the spillway to the downstream side), so the separation area in the Tri-B1 model is reduced, and the Drag force and consequently the relative depreciation The energy in the Tri-B1 model (about 24%) is lower than the Tri-Base model.Figure 6 shows the residual energy curve of the piano key weir in relation to the flow rate per unit of the overflow width. According to Figure 6, the E1/E2 ratio increases with the increase of flow per unit width. In other words, the relative residual energy in both models occurs at high flow rates. Also, in both models, at low flow rates, the increase in E1/E2 ratio is higher than at high flow rates. The reason for this is the local sinking upstream of the weir in high discharges; so that in high heads, the aeration on the weir is reduced.Finally, Fig 7 shows the comparison of measured and calculated values of triangular PK weir.ConclusionIn the triangular piano key weir, by increasing the slope of the side walls (&theta;) from zero to 10 degrees in the flow direction, the relative dissipation of energy has decreased by 24%. Also, the highest dissipation of energy in the weir with a horizontal crest occurred in the lower heads, and this value decreases with the increase of the head.The highest amount of energy dissipation for Tri-Base and Tri-B1 models is 0.74 and 0.85, respectively, in this case. Finally, relationships (9) and (10) are proposed to calculate the relative energy consumption of the overflow of the piano key with horizontal and sloping crest, respectively.