Water Surface Profile along Different Side Weirs in Subcritical Flow Regime

Introduction: Side weir structures are extensively used in hydraulic engineering, irrigation and environmental engineering, and it usually consists of a main weir and a lateral channel. Side weirs are also used as an emergency structure. This structure is installed on one side or both sides of the main channel to divert the flow from the main channel to the side channel. Lateral outflow takes place when the water surface in the main channel rises above the weir sill. Flow over a side weir is a typical case of spatially varied flow with decreasing discharge. There have been extensive studies on side weir overflows. Most of the previous theoretical analysis and experimental research works are related to the flow over rectangular side weirs in rectangular main channels. In the current study, the flow conditions over a trapezoidal side weir located in a rectangular main channel in subcritical flow regime is considered. Materials and Methods: The experiments were performed in a rectangular open channel having provisions for a side weir at one side of the channel. The main channel was horizontal with 12 m length, 0.25 m width, and 0.5 m height, and it was installed on a frame; lateral channel that has a length of 6 m, width of 0.25 m, and height of 1 m. It was set up parallel to the main channel; walls and its bed were made up of Plexiglas plates. The side weir was positioned at a distance of 6 m from the channel’s entrance. A total of 121 experiments on trapezoidal side weirs were carried out. Results and Discussion: For trapezoidal side weir, effective non-dimensionnal parameters were identified using dimensional analysis and Buckingham's Pi-Theorem. Finally, the following non-dimensional parameters were considered as the most effective ones on the discharge coefficient of the trapezoidal side weir flow. in which Fr1= upstream Froude number, P= hight of the trapezoidal side weir, y1= upstream water depth, z=side slope of the trapezoidal side weir and T=top flow width of the trapezoidal side weir. Water surface profiles were measured along the weir crest, the main channel centerline, and far from the weir section. Different elevations in water surface profile depend on the upstream Froude number in the main channel; depth differences in low Froude numbers are at minimum values, and in high Froude numbers are at maximum amounts. The water surface level along the crest drops at the entrance of the side weir to the first half of the side weir; and it has been attributed to the side weir entrance effect at the upstream. Afterwards, the water level rises towards the downstream of the weir. According to the experimental results, measurements of the water in the centerline of the main channel are reliable and water surface drop is negligible. According to the parameters affecting the discharge coefficient for each value of z, discharge coefficient equations were developed with acceptable accuracy such that the effects of this parameter were shown separately. Finally, the general equation was proposed. The general functional form for discharge coefficient is presented as follows where the effect of the side slope parameter, z, is also considered. The mean and maximum percentage errors of the discharge coefficient computed using the proposed equation are as 2.6% and 11.5% , respectively. Conclusion: In this study, the characteristics of trapezoidal side weir overflows in subcritical flow regime were discussed. For this purpose, experimental data related to the water surface profile of the side weir and discharge coefficient were collected and analyzed. The results showed that the most efficient section for measuring water surface profile is located at the center line of the main channel. It was found that for trapezoidal side weir, the discharge coefficient depends on the Froude number, the ratio of crest height to initial depth, the overflow length to initial depth, and the side slope of the weir. In this study, conventional trapezoidal weir theory has been used in order to evaluate the discharge coefficient and provide side weir discharge equation. For this purpose, three reference depths were considered for conventional weir, and for each depth an equation was developed for the discharge coefficient. Comparison between predicted values and experimental data showed that average flow depth results in accurate outcomes for assessing the discharge coefficient. The average value of error for discharge coefficient estimation by the proposed equation is 2.6%. Thus this equation is proposed for use in practice by water engineers. Keywords: Control structure, Conventional weir, Discharge coefficient, Spatially varied flow, Trapezoidal side weir, Water surface profile

Side weirs or lateral weirs are widely used for water level control in water treatment plants and irrigation and drainage systems. The side weir is a fixed structure installed at one side of a channel to divert flow laterally. Computation of the water surface profile along the side weir is essential in determination of the discharge over the side weir. An analytical solution of the dynamic equation for spatially varied flow with decreasing discharge, in prismatic channels with a side weir, is available in the technical literature only for the special case of a rectangular channel based on the constant specific energy assumption. However, in irrigation networks, the most common irrigation channels are of trapezoidal cross-section. This paper presents an elegant analytical solution for establishing the water surface profile along a side weir in a trapezoidal channel. Since triangular and rectangular cross-sections are special cases of the trapezoidal cross-section, the proposed analytical solution is also applicable to these cross-sections. The solution, which yields a direct computation of the flow profile in subcritical and supercritical flow regimes, should be a useful engineering tool for the evaluation and design of side weirs in open channels.

If the operation of existing vortex drop shafts should be verified, then it is essential to know the hydraulic performance of these special structures under both subcritical and supercritical flow regimes. The purpose of the present research consisted of providing practical guidelines and recommendations for managing the hydraulic design and verification of subcritical and supercritical vortex drop shafts. The examination of various experimental results from physical model investigations allowed to show that the inlet channel and the spiral inlet behaved differently depending on the energy approach flow content. The main dissimilarity lay, however, in the functioning of the vertical shaft and the dissipation chamber. The rotation of the falling flow along the vertical shaft was more evident for approaching supercritical flows. Severe flow conditions in terms of water depths and bottom pressures could be observed in the dissipation chamber under a supercritical flow regime. The design of this special component must be carried with prudence compared with the subcritical flow regime because failure events as the chamber submergence and the crash of the bottom surface just under the shaft outlet may occur for approaching supercritical flows.

The 3D flow over side weirs is investigated using Computational Fluid Dynamic (CFD). The study aims to assess the capability of ANSYS CFX code for modeling flow characteristics in a circular channel with side weir for subcritical flow condition. Twelve models were studied for some ranges of variables such as discharge, length and height of side weir. The numerical simulation was based on the solution of continuity and momentum equations for three dimensional, incompressible, steady and turbulent flow. The volume of fluid (VOF) method was used to predict the free surface changes and the RNG k-e model was employed for simulating the flow field. The experimental data of Uyumaz and Muslu (1985) were used for verification. For all models, the specific energy is obtained and the average energy difference at the upstream and downstream side of the weir was very small and the assumption of constant energy in the circular channel was acceptable. The numerical results predicted the changes in the water surface profile at the main channel central axis and indicated that the water level rises from upstream to downstream end of the weir. The discharge coefficient (Cd) variation with the upstream Froude number (Fr1) for different weir height and length were studied and it was found that the value of (Cd) decreased with the increase of (Fr1) value. For each side weir length, the variation of (Cd) with the ratio of the weir height to channel diameter (P/D) were studied and it was observed that with the increase of (P/D) ratio the value of the (Cd) increased. The relation between the (Cd) and the ratio of the side weir length to channel diameter (L/D) for different weir height were also investigated. It was noticed that the (Cd) value increased gradually as the (L/D) ratio increased. The combined effects of (Fr1), (P/D) and (L/D) on the (Cd) were studied for all models and an empirical expressions for describing this relation was obtained and it was found that (Cd) was a function of all the above parameter.

An experimental investigation of the flow over sharp edged side-weirs in rectangular channels is reported. The experiments cover subcritical and supercritical flow regimes with weirs of zero as well as finite height. The subcritical flow experimental data agree well with the derived analytical expression for the variation of the De Marchi coefficient with the Froude number of the main channel flow. The De Marchi coefficient for the side weirs of finite height has been found to be essentially the same as for the corresponding side-weir of zero height.

Prediction and modeling of hydraulic phenomenon is an important part of hydraulic engineering activities. One of the applications of prediction and modeling is estimating the discharge coefficient for hydraulic structures. Side weirs are widely used for allocating and removing excess flow in water engineering projects. The governing equation on side weir hydraulic characteristics is spatially varied flow (SVF). Computer modeling of hydraulic characteristics this structure includes the calculation of water surface profiles and estimating the discharge coefficient (Cdsw). The numerical method was used to calculate the water surface profile and there are several ways to estimate the Cdsw, such as experimental formulas and computational intelligence techniques. In this paper, the Fourth Runge Kutta method is used for numerical solution of SVF and firstly to estimate Cdsw, some famous empirical equations are assessed. Among the empirical formulas, the Borghei is the most accurate one. To increase the accuracy of computer modeling, the Multilayer Neural network (MLP) is developed to estimate Cdsw. The result shows that using neural network to estimate Cdswincreases the accuracy of the final model about 16 %.

Interaction of side weir overflow with bed-load transport and bed morphology in a channel

This article presents the results of a study on an axisymmetric gravity-driven slender free-surface flow down a cone by deriving depth-averaged conservation equations on a cone-adapted coordinate system and obtaining a backwater-type differential equation for steady, axisymmetric films with prescribed apex discharge. Analysis of this equation reveals a location-dependent critical condition separating supercritical and subcritical regimes and shows that a classical constant normal depth does not exist; instead, the flow approaches an equilibrium between gravity and resistance forces as it develops downstream. Asymptotic expansions for the flow and critical depths recover previously established results for the laminar leading-order and first-order corrections under consistent velocity shape coefficients, confirming that capillarity affects only first-order terms. The framework predicts a critical length beyond which the flow must be subcritical, Reynolds number decays inversely with the distance, leading to inevitable relaminarization on sufficiently long cones, and the potential need for hydraulic jumps to compatibilize supercritical and subcritical flow regimes, paralleling open-channel hydraulics on mild slopes. Numerical solutions of the backwater equation agree with existing measurements where the slender-film assumptions hold, providing a practical basis to compute flow depth and regime transitions on conical surfaces.

This paper presents a Large Eddy Simulation (LES) of an elliptic cylinder with an aspect ratio of 2, using the WALE sub-grid scale model in OpenFOAM. The simulation is conducted in the subcritical flow regime at a Reynolds number of 3900, utilizing a modified filtered linear discretization technique for the divergence terms that ensures a balance between accuracy and stability, while providing a better representation of the energy spectrum. The results are compared with those of previous studies on circular cylinders. The findings indicate that the elliptic cylinder exhibits higher mean drag, primarily due to increased pressure drag on the frontal area, with lower pressure drag on the rear side compared to the circular cylinder, while the temporal lift exhibited sinusoidal behavior with a single distinct frequency. No significant variation is observed in the separation point or recirculation zone length. Time-averaged turbulent flow parameters reveal elevated levels of normalized Reynolds stresses, suggesting earlier shear-layer roll-up and transition, which are influenced by the elliptic cylinder's reduced afterbody.

In the present study a Dynamic Grid Adaptation (DGA) algorithm is used for predicting flow around a circular cylinder in sub-critical flow regime at a Reynolds number of 1.4·105. The reason for adopting a DGA algorithm is to use the flow field as a driving criteria for mesh refinement rather then the geometry of the computational domain or the judgment of the CFD user as common in conventional mesh. It is demonstrated how DGA reduces the mesh size significantly and also makes time consuming mesh testing unnecessary. The concept being adopted is to concentrate mesh refinement in regions with high gradients and high turbulent viscosity, while in the region further downstream where the flow is fully developed a coarser mesh will develop and turbulence is modeled with the Large Eddy Simulation (LES) turbulence model. The aim of the study is to present an appropriate variable for mesh refinement, which accomplishes a high rate of mesh refinement in the region with high gradients. The new variable is a product of the local mesh cell size and the rate of strain and includes two additional variables to allow control over the refinement behaviour.

Lateral intakes are used for water transmission and distribution on farms and irrigation networks. In present study, the flow field within a rectangular lateral intake in subcritical flow regime is numerically simulated in a three-dimensional. In this analysis of CFD, turbulence of flow field is simulated using standard $$k - \varepsilon$$ , and RNG $$k - \varepsilon$$ turbulence models, and changes of free surface is simulated by volume of fluid scheme. Comparison between CFD and experimental results showed that the numerical model simulated the free surface and velocity field with high accuracy. Root mean square error for longitudinal and transverse profiles of the flow free surface in the main channel is respectively calculated as 0.132% and 0.094%. Based on simulation results, with the flow progress towards the downstream diversion channel, the secondary circulation cell is developed. A relation is presented for calculating strength of the secondary flow with a nonlinear regression method and using Minitab software. Also, a relation is proposed for calculating the flow energy head within the downstream channel and lateral channel (E3, E2) compared to the flow energy head in the upstream intake (E1).

Study of flow at side weir in narrow flume using visualization techniques

Water surface profiles (WSPs) are among the most valuable information in artificial and natural open channels. Most of the conventional methods for computing the WSPs in compound channels are based on the water surface calculated by the divided channel method (DCM) which is used by HEC-RAS. However, this approach cannot predict the water surface with good accuracy when dealing with compound channels. Therefore a new approach is implemented to calculate the WSP. This approach consists of two steps. In the first step, the rating curve is computed based on the newly proposed method by Maghrebi et al. In the second step, based on the governing equations for gradually varied flow including energy equation, the WSP is computed. The experimental results reported for three sets of measured WSPs in compound channels and WSP measurements of the Main River are used to evaluate the accuracy of the proposed method. The results show that the proposed technique can predict the WSP with better accuracy in comparison to the HEC-RAS and CES models.

Discussion of “Discharge Coefficient of Symmetrical Stepped and Triangular Labyrinth Side Weirs in a Subcritical Flow Regime”

The effect of water surface slope in the lateral direction on flow over side weirs was studied. Water surface elevation on the weir plane was expressed by a parameter ψ based upon the hydraulic profile on the channel axis. Two different relationships of ψ as a function of the Froude number were used to calculate side weir discharges. Results were compared with the experimental data. It was shown that better results are obtained when transition conditions of ψ=1 at the ends of the side weirs with no lateral surface slope are taken into account. However the effect of water surface slope in lateral direction is of secondary importance as compared to the angle of the deflected water jet along the side weir.