Downstream Flow Depth Research Articles

Experimental study on the drag force on bridge abutments

The drag force exerted on a bridge abutment, representative of wall-attached structures, is studied with different geometries in various flow conditions. The drag force was quantified by two methods here: (1) direct method by using strain gauges and (2) employing the conservation of momentum equation that takes advantage of the flow characteristics. The momentum equation results differed considerably from the direct method, mainly related to even the smallest inaccuracy in depth measurements. We suggest a modified momentum equation to enhance accuracy because of its independence on downstream flow depth measurement. The experimental results also revealed that the constriction ratio at the bridge abutment section and the abutments geometric shape are the most influential parameters on the drag coefficient. On the other hand, the effect of flow characteristics is negligible. Finally, we proposed an empirical relationship to estimate the drag coefficient.

The discharge coefficient of SMBF flumes under free and submerged conditions

In this study, the discharge coefficients (Cd) of SMBF flumes under free and submerged flow conditions were analytically investigated. The dimensionless parameters involved in the discharge coefficient, derived from the dimensional analysis, are the contraction ratio [rcrn = ratio of flume width (w) to channel width (B)], relative head (hw: the ratio of the upstream head (h) to the w\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$w$$\\end{document}) and, in the case of submerged flow, also the submergence ratio [Sr=ht/hu\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$S_{{\ ext{r}}} = h_{{\ ext{t}}} /h_{{\ ext{u}}}$$\\end{document}: downstream flow depth (ht\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$h_{{\ ext{t}}}$$\\end{document}) to upstream flow depth (hu)]. Cd decreases logarithmically from 1.2 to 0.75 in the range of hw\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$h_{w}$$\\end{document} between 0.4 and 1.8. The submerged condition does not reduce the Cd\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C_{{\ ext{d}}}$$\\end{document}, but it reduces the discharge capacity (up to 50%), so that in some cases, to pass a given flow discharge, hu\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$h_{{\ ext{u}}}$$\\end{document} should increase by about 100% compared to the free condition.

An efficient hybrid grey wolf optimization-based KELM approach for prediction of the discharge coefficient of submerged radial gates

Accurately prediction of discharge coefficient through radial gates is considered as a challenging hydraulic subject, particularly under highly submerged flow conditions. Incurring the advantages of kernel-depend extreme learning machine (KELM), this study offers a grey wolf optimization-based KELM (GWO-KELM) for effective prediction of discharge coefficient through submerged radial gates. Additionally, support vector machine (SVM) and Gaussian process regression (GPR) methods are also presented for comparative purposes. To build prediction models using GWO-KELM, GPR, and SVM, an extensive experimental database was established, consisting of 2125 data samples gathered by the US Bureau of Reclamation. From simulation results, it is observed that the proposed GWO-KELM approach with radial basis function and input parameters of the ratio of the downstream flow depth to the gate opening and submergence ratio provides the best performance with the correlation coefficient (R) of 0.983, the determination coefficient (DC) of 0.966 and the root-mean-squared error (RMSE) of 0.027. The obtained results showed that the proposed GWO-KELM with RBF kernel function gives better prediction accuracy than employed GPR and SVM approaches. Furthermore, the obtained results showed that the employed kernel-depend methods are capable of a statistically predicting the discharge coefficient under varied submergence conditions with satisfactory level of accuracy. Amon theme, proposed hybrid GWO-KELM method gave the most accurate results (R = 0.873, DC = 0.744, and RMSE = 0.035) for extremely highly submerged flow. Moreover, the results reflected that the employed kernel-depend methods give better predictions than the developed dimensionless formulas.

Numerical study of the weir angle on the flow pattern and scour around the submerged weirs

In this study, the flow pattern and scouring around the submerged sharp edge weir, with different slope angles, have been numerically simulated using the Flow-3D model. After validating the results of the numerical model in simulating the flow pattern and scour around the weir with a 90∘ angle, the effect of the weir angles relative to the upstream and downstream on the flow and scour field had been investigated. The results showed upstream and downstream of the weir, vortex flows were formed and by taking an angle of 90∘, the vortex flows were weakened. In addition, the downstream slope of the weir had little effect on the upstream water level and most changes occurred in the downstream flow depth with a 90∘ angle. The downstream scour depth was independent of the upstream slope angle and the upstream scour depth was independent of the downstream slope. When the upstream angle became closer to the horizon, scouring was reduced in this area. The depth of scour downstream was greater than the depth of scouring upstream. Angles of 50∘, 70∘, 110∘ and 130∘ had slight changes in the depth of the downstream scour, but compared to the angle of 90∘, the depth of the downstream scour for these angles decreased significantly.

Hydraulic model experiment of energy dissipation on the horizontal and USBR II stilling basin

Flow conditions on overflow systems can result in construction failure, mainly due to the high flow energy. Stilling basin at downstream of the spillway is useful for reducing flow energy. It can reduce the destructive force of water flow. Controlling the hydraulic jump is an important part that includes the jump’s energy, length, and height. The physical hydraulic model was carried out with several series, by making a series of bottom lowering of horizontal and USBR II stilling basin. The experimental study is expected to represent flow behavior in the overflow system regarding flow conditions and energy dissipation. Based on the analytical calculation of flow velocity, the amount of flow energy that occurs at each control point is calculated. The control points are the starting point of the spillway, the chute way toe, and flow depth after the hydraulic jump. The energy loss can be calculated for each control point, while the efficiency of energy dissipation on stilling basin is calculated at the downstream flow depth after the hydraulic jump. Velocity calculated by dividing discharge per unit width by water depth which is based on the flow depth measurement data in the hydraulic model.

Experimental and theoretical modeling of a quarter-circular gate flow

Gates are important hydraulic structures and used for flow measurement, water delivery, and water level regulation in open channels and irrigation networks. In this study, the quarter-circular gate is introduced and investigated. The cross section of this gate consists of a quarter circular arc and the lip angle of the gate equals to zero. Discharge coefficient, variation of downstream flow depth, and velocity distribution at opening section of gate were experimentally measured. Using potential flow theory supported by dimensional analysis, equations for discharge coefficient and velocity distribution at gate opening section of quarter-circular gate were derived and then validated using experimental data. The mean percentage error (MPE) of obtained equation for discharge coefficient of quarter-circular gate was calculated as 2.24%, indicating the high precision of the proposed theory. Based on obtained results, downstream flow depth of quarter-circular gate is uniform. Also, velocity distribution at gate opening section is nearly uniform. Discharge coefficient of quarter-circular gate was averagely obtained 55% larger than that of sluice gate. It was also obtained larger than that of radial gate. Elimination of contraction section at downstream of gate opening, which is the main source for energy loss and therefore discharge capacity reduction, is the main reason for larger discharge coefficient of quarter-circular gate.

Embedded fuzzy-based models in hydraulic jump prediction

Abstract This study aims to evaluate the learning ability and performance of five meta-heuristic optimization algorithms in training forward and recurrent fuzzy-based machine learning models, such as adaptive neuro-fuzzy inference system (ANFIS) and RANFIS (recurrent ANFIS), to predict hydraulic jump characteristics, i.e., downstream flow depth (h2) and jump length (Lj). To meet this end, the firefly algorithm (FA), particle swarm algorithm (PSO), whale optimization algorithm (WOA), genetic algorithm (GA), and moth-flame optimization algorithm (MFO) are embedded with the fuzzy-based models, which represent the main contribution of this study. The analysis of the results of predicting hydraulic jump characteristics shows that the embedded ANFIS and RANFIS models are more accurate than the empirical relations proposed by the previous researchers. Comparing the performance of the embedded RANFISs and ANFISs methods in predicting Lj represents the superiority of the RANFIS models to the ANFISs. The results of the sensitivity analysis show that among the input independent parameters, flow discharge (Q) is the most important factor in predicting downstream flow depth in weak, oscillating, and steady hydraulic jumps (1.7 < Froude number < 9), while the upstream flow depth (h1) is more important than the other input parameters in strong hydraulic jumps (Froude number > 9).

Experimental modeling of flumes with two semi-cylinder contractions (free and submerged flows)

In this study, the flow through a simple low-cost flume constructed using two semi-cylinder contractions on either side of a rectangular channel was experimentally investigated. In practice, these flumes may operate under free- or submerged-flow conditions depending on the downstream flow depth. To reliably estimate the flume discharge, free- and submerged-flow conditions should be accurately distinguished. At present, there is no equation to estimate the submergence threshold. This study investigates the possibilities of using these flumes under submerged-flow conditions. The discharge of the submerged flume may be calculated on the basis of the free-flow discharge equation. Thus, two new free-flow discharge equations were deduced: a general equation by considering the contraction ratio with an average error of 2.25%, and another one by neglecting it with an average error of 4.88%. Compared with the existing discharge equations, the proposed free-flow equations are the best ones. Under submerged-flow conditions, the submergence ratio affects the flow discharge. Using the measurements carried out in this study, the submergence threshold ratio and submerged-flow discharge were formulated and calibrated with the average errors of 2.96% and 3.80%, respectively. The equation to distinguish the free- and submerged-flow conditions was also deduced by equating the submerged- and free-flow discharge equations yielding a novel real solution.

Three-Dimensional Numerical Simulation of Dam Discharge and Flood Routing in Wudu Reservoir

The main objectives of the present work are to investigate the hydraulic characteristics of the dam discharge flow and its impact downstream. Building information modeling technology is adopted to generate the terrain entity and hydraulic structures. The calculation of the dam discharge and flood routing simulation is achieved by employing Reynolds-Averaged Navier-Stokes equations with the RNG k-ε eddy viscosity model for its turbulence closure, as well as the Volume of Fluid method. An urban flood experiment and the field measurement records are utilized and validated the model accuracy. The flow field is obtained to assess the dam working conditions under different water levels. The results show that the maximum downstream flow depth, the maximum discharge capacity and the hydraulic jump length under normal water level is 18.6 m, 13,800 m3/s, and 108 m, respectively. The dam satisfies the safety demand under different water levels but close attention should be paid to the dam foundation, especially around the incident points of the discharge flow. Complex turbulent flow patterns, including collision, reflection, and vortices, are captured by three-dimensional simulation. The numerical simulation can assist the reservoir management vividly, so as to guarantee the stability of the dam operation.

Predicting Hydraulic Jump Length on Rough Beds Using Data-Driven Models

The hydraulic jump can be used for some purpose such as dissipating the flow energy in order to prevent bed erosion; aerating water and facilitating the mixing procedure of chemical that used for water purification. In this paper, various artificial intelligence (AI) models including gene expression programming (GEP), adaptive-neuro-fuzzy inference system with grid partition (ANFIS-GP), and neural networks (ANNs) were used to estimate developed and non-developed hydraulic jump length. Four various GEP, ANFIS-GP and ANN models including different combinations of Froude number, bed roughness height, upstream and downstream flow depth based on measured experimental data-set were developed to estimate hydraulic jump length variations. The root mean squared error (RMSE) and determination coefficient (R2) indices were applied for testing models’ accuracy. Regarding the comparison results, it was seen that the ANFIS-GP, ANN, and GEP models could be employed successfully in estimating hydraulic jump length. The comparison between three AI approaches emphasized the superiority of ANNs and ANFIS-GP over the other intelligent models for modeling developed and non-developed hydraulic jump length, respectively. For non-developed hydraulic jump, the R2 and RMSE values obtained as 0.87 and 2.84 for ANFIS-GP model.

Hyporheic flow path response to hydraulic jumps at river steps: Flume and hydrodynamic models

The conceptual model of hyporheic exchange below river steps may oversimplify exchange flow paths if it depicts a uniform pattern of downstream‐directed upwelling. This research used nonmobile, porous bed flume experiments and hydrodynamic simulation (CFD) to characterize hyporheic flow paths below a river step with a hydraulic jump. Bed slope was 1%, step height was 4 cm, downstream flow depth was 4 cm, substrate was 1 cm median diameter gravel, and hydraulic jump length was 25 cm in the flume and CFD experiments. With the hydraulic jump, flow paths changed to include downwelling beneath the water plunging into the pool and upstream‐directed upwelling at the base of the step and beneath the length of jump. Failure to represent the influence of static and dynamic pressures associated with hydraulic jumps leads to erroneous prediction of subsurface flow paths in 75% of the streambed beneath the jump. A refined conceptual model for hyporheic flow paths below a step with a hydraulic jump includes reversed hyporheic circulation cells, in which downwelling water moves upstream and then upwells, and flow reversals, in which the larger flow net of downstream‐directed upwelling encounters a nested flow path of upstream‐directed upwelling. Heterogeneity in hyporheic flow paths at hydraulic jumps has the potential to explain field‐observed mosaics in streambed redox patterns and expand structure‐function relationships used in river management and restoration.

An experimental study of flow, bedload transport and bed topography under conditions of erosion and deposition and comparison with theoretical models

ABSTRACTThe nature of flow, sediment transport and bed texture and topography was studied in a laboratory flume using a mixed size‐density sediment under equilibrium and non‐equilibrium (aggradational, degradational) conditions and compared with theoretical models. During each experiment, water depth, bed and water surface elevation, flow velocity, bed shear stress, bedload transport and bed state were continuously monitored. Equilibrium, uniform flow was established with a discharge of about 0.05 m3 s−1, a flow depth of about 0.01 m, a flow velocity of about 0.81–0.88 m s−1, a spatially averaged bed shear stress of about 1.7–2.2 Pa and a sediment transport rate of about 0.005–0.013 kg m−1 s−1 (i.e. close to the threshold of sediment transport). Such equilibrium flow conditions were established prior to and at the end of each aggradation or degradation experiment. Pebble clusters, bedload sheets and low‐lying bars were ubiquitous in the experiments. Heavy minerals were relatively immobile and occurred locally in high concentrations on the bed surface as lag deposits.Aggradation was induced by (1) increasing the downstream flow depth (flume tilting) and (2) sediment overloading. Tilt‐induced aggradation resulted in rapid deposition in the downstream half of the flume of a cross‐stratified deposit with downstream dipping pebbles (pseudo‐imbricated). and caused a slight decrease in the equilibrium mean water surface slope and total bedload transport rate. These differences between pre‐ and post‐aggradation equilibrium flow conditions are due to a decrease in the local grain roughness of the bed. Sediment overloading produced a downstream fining and thinning wedge of sediment with upstream dipping pebbles (imbricated), whereas the equilibrium flow and sediment transport conditions remained relatively unchanged. Degradation was induced by (1) decreasing the downstream flow depth (flume tilting) and (2) cutting off the sediment feed. Tilt‐induced degradation produced rapid downstream erosion and upstream deposition due to flow convergence with little change to the equilibrium flow and sediment transport conditions. The cessation of sediment feed produced degradation and armour development, a reduction in the mean water surface slope and flow velocity, an increase in flow depth, and an exponential decrease in bedload transport rate as erosion proceeded. A bedload transport model predicted total and fractional transport rates extremely well when the coarse‐grained (or bedform trough) areas of the bed are used to define the sediment available to be transported. A sediment routing model, MIDAS, also reproduced the equilibrium and non‐equilibrium flow conditions, total and fractional bedload transport rates and changes in bed topography and texture very well.

Minimization of Frazil‐Ice Production by River‐Flow Regulation

Excessive production of frazil ice in rivers may lead to the occurrence of ice jams and attendant flooding during winter. An often‐discussed means of minimizing frazil‐ice production, and thereby for mitigating frazil jams, is regulation of river flow in order to facilitate rapid ice‐cover formation. A numerical model of ice‐cover formation by frazil‐ice accumulation over stage‐regulated pools is exercised to assess the durations of flow‐discharge regulation that would be required for ice covers to form over river pools of diverse length, regulated downstream depth, and channel slope. The numerical model indicates that for a given navigation pool, there exists an optimum river discharge that corresponds to a minimum time required for an ice cover to form. Optimal discharge is a function of pool length, channel slope, and downstream flow depth, but is invariant with air temperature.