Experimental study of effect of creating an additional cycle along the lateral crest of the labyrinth weirs

One of the practical and economical ways to enhance the discharge capacity is to use labyrinth weirs. The longer crest length in labyrinth weirs than in linear weirs has caused these weirs to have both a higher discharge coefficient and water discharge capacity than a linear weir. In the present study, the discharge coefficient of trapezoidal and triangular labyrinth weirs was investigated by creating an additional cycle along the lateral crest of the weir. By constructing 10 physical models of labyrinth weirs, tests were performed in the hydraulic and sediment laboratory of the Khuzestan Water and Power Authority (KWPA). Dimensional analysis by the Buckingham method revealed the discharge coefficient (Cd) as a function of variable parameters such as the total hydraulic head to weir height ratio (Ht/P) and weir shape factor (Sf). The results of experimental tests showed that at the hydraulic head ratio (Ht/P) of 0.1, the TP weir had a higher discharge coefficient of 3.5% than the TPTPO weir and 2.5% than the TPTRO weir. However, at a hydraulic head ratio of 0.12, the TR weir had a lower discharge coefficient of 4.6% than the TRTPO weir and 6.9% compared to the TRTRO weir. For the hydraulic head ratio of 0.14, the TRTPI weir was 5.8% and the TRTRI weir was 9.4% higher than the TR weir. Statistical analysis using SPSS indicated that TRTPO and TPTRO weirs had the highest correlation with the cubic model.     

Evaluation of flow characteristics in labyrinth weirs using response surface methodology

Labyrinth weirs can increase the flow discharge capacity for a specific head and width by increasing the weir length. This paper studies the flow behavior of labyrinth weirs using Flow-3D® software. The main goal is to evaluate the capability of the response surface methodology (RSM), especially central composite design (CCD), to describe the performance of labyrinth weirs. Traditional and RSM-CCD methodologies are applied using experimental data of previous researchers and numerical data of the present study, respectively. Results show that RSM-CCD can produce an acceptably accurate model for the discharge coefficient of labyrinth weirs with only a small fraction of the data required for the traditional model. In addition, the discharge coefficient of a labyrinth weir decreases by increasing head and decreasing sidewall angle due to the inflow contraction and nappe interference in inlet and outlet cycles, respectively. The discharge efficiency can be up to 4.5 times higher for a labyrinth weir compared to a linear weir. Finally, a new method is introduced for designing labyrinth weirs.     

Radial Basis Neural Network and Particle Swarm Optimization-based equations for predicting the discharge capacity of triangular labyrinth weirs

Conventional weirs are utilized for controlling, measuring and adjusting the flow depth in hydraulic structures, such as those found in irrigation and drainage networks. Various weirs with modified shapes are utilized to increase the discharge capacity. The main goal of this study is to investigate the discharge coefficient (C_d) of triangular labyrinth weirs using soft computing methods. The performance of the Radial Basis Neural Network (RBNN) is compared with that of Multiple Nonlinear and Multiple Linear Particle Swarm Optimization (MNLPSO and MLPSO). Models developments are conducted using published experimental data from the literature. Comparing the RBNN, MLPSO and MNLPSO results obtained through these soft computing techniques with experimental data shows that all models perform well in predicting the discharge coefficient of a triangular labyrinth weir. Performance of the proposed approaches which demonstrated explicit equation given by MNLPSO model provided the discharge capacity with lower error (RMSE=0.0223) is compared with the MLPSO (RMSE=0.0346) and RBNN (RMSE=0.045) approaches.     

Investigation of flow characteristics and energy dissipation over new shape of the trapezoidal labyrinth weirs

Labyrinth weirs are mainly used to increase the discharge capacity. The current study adds a new performance to labyrinth weirs as an energy dissipator. The labyrinth weirs' zigzag shape and flow behaviour could benefit energy dissipation. Therefore, the present study aims to investigate the hydraulic characteristics and energy dissipation of the compound labyrinth weir. Sixteen models were used for different sidewall angles (α°) of 6–35 and 90 (linear weir for comparison). The results demonstrated the highest values of the compound coefficient of discharge, C_dc, for a sidewall angle of 35°, and the lowest value of the compound coefficient of discharge for a sidewall angle of 6°. The C_dc increased initially at low H՛_t/P՛ values, and the C_dc showed a decreasing trend for higher values of H՛_t/P՛. For sidewall angles (α°) ranging from 6 to 35, the compound coefficient of discharge C_dc does not significantly change as it approaches a value of H՛_t/P՛ = 1.0. Furthermore, for the range of the relative critical head (y_c/P՛) between 0.07 and 0.95, the results showed that the compound labyrinth weirs could dissipate the energy of flow by 93%, 92%, 89%, 85%, 83%, 79%, and 75% for α° = 6, 8, 10, 12, 15, 20°, and 35, respectively. The amount of improvement in energy dissipation over a compound labyrinth weir was better than a linear weir by 17%, 15%, 14%, 12%, 11%, 10%, and 8% for α° = 6, 8, 10, 12, 15, 20, and 35, respectively. The residual energy (E₁/E_min) at the base of downstream compound labyrinth weirs was closer to the minimum potential amount of residual energy as y_c/P՛ increased. For a given value of y_c/P՛, the relative residual energy at the base of compound labyrinth weirs increased as the sidewall angle (α) increased. An empirical equation has been provided to predict the compound coefficient of discharge when relative energy dissipation data is available.     

Studying the relationship between the hydraulic and geometry characteristics of labyrinth weirs based on the historical memory of reported data

One of the effective ways to increase the efficiency of weirs is to use nonlinear weirs, such as labyrinth weir, which increases the flow capacity by increasing the length of the weir at a fixed width. Given the importance of precisely estimating the flow discharge coefficient of this type of weir and its impact on supplying the safety of water structures, in the present study, the flow coefficient of labyrinth weirs was estimated using data-driven models of Extreme Learning Machine (ELM), Classification And Regression Tree (CART), Chi-square Automatic Interaction Detector (CHAID), and Multiple Linear Regression (MLR). After the modeling process, the predicted results were compared with the observed values using statistical measures and diagnostic analysis. In this study, three input combinations of hydraulic parameters, including the total upstream hydraulic head of weir (H_T), weir discharge (Q), and head to weir height (H_T/P) were used as input vectors. In order to evaluate the accuracy of the models, the statistical indicators of Coefficient of Efficiency (CE), RMSE, MDE, and RSD were employed. The final results showed that the ELM method created with all potential input parameters (H_T, Q, and H_T/P) was highly accurate in determining flow discharge coefficient. Due to having the lowest error (CE = 0.8815, RMSE = 0.0370), it was selected as the superior model.     

Flow characteristics over asymmetric triangular labyrinth side weirs

Side weir is placed at the channel bank as a head regulator or a diversion device. Flow over a side weir has been the subject of many research studies considering its three dimensional and complicated characteristics. However, the labyrinth side weirs warrant further research due to their higher efficiency compared to linear side weirs. In this paper, subcritical flow characteristics and discharge coefficient for both symmetric and asymmetric triangular labyrinth side weirs were studied experimentally. The results show that asymmetric labyrinth side weirs have higher discharge coefficient compared to symmetric labyrinth side weirs; since a larger portion of the crest is orthogonal to the flow. Using the present laboratory data, general equations were proposed for the estimation of discharge coefficient of both symmetric and asymmetric triangular labyrinth side weirs. The results of this study can be useful to design side weirs with high hydraulic performance.     

A review of studies on estimating the discharge coefficient of flow control structures based on the soft computing models

The discharge coefficient (Cd) plays a vital role in the accurate design and safety of weirs, spillways, and dams. In the last decade, Soft Computing(SC) models, which showed excellent capabilities for non-linear mapping between parameters, were widely used to estimate the discharge coefficient of flow control structures. This study provides a comprehensive review of the application of SC models for estimating Cd of different flow control structures such as ogee spillways, orifices, side weirs, etc. In addition, the most common empirical relations which are obtained from laboratory experiments are discussed briefly. The findings revealed that weir length/flow depth ratio, weir length/channel width ratio, weir height/flow depth, and Froude number are widely used to estimate Cd in the side weirs. Besides, the ratio of orifice crest height to height of side orifice, the ratio of main channel width to length of side orifice, ratio of main channel width to height of side orifice, and ratio of the height of side orifice to upstream flow depth were extensively employed to calculate Cd of orifice structures. The common parameters for measuring Cd of labyrinth weirs are, discharge over a labyrinth cycle, weir height, channel width, apex constant, upstream head, discharge over the weir, effective length, convergence constant, sidewall angle, and Froude number. In the weir-gate structure, some factors such as contraction coefficient of the gate, head loss, and weir height are key parameters for the accurate evaluation of Cd. The trends of SC models, features of popular models, and the background of models are discussed briefly in this paper. Also, research gaps and possible directions for new studies are suggested.     

Experimental analysis of flow characteristics over hydrofoil weirs

The rounded crested weirs are commonly used for discharge measurements and this overflow structures have advantages such as stable overflow pattern and good accuracy. Hydrofoil weirs with streamlined properties are similar to the ogee weirs and can be used as a spillway profile. The hydraulic features of flow over hydrofoil weirs created by the NACA0018, NACA0021 and NACA0024 hydrofoil geometry placed in an open channel are investigated experimentally under free-flow conditions. The velocity field of hydrofoil weir flows are measured by one-dimensional Laser Doppler Anemometer. Experimental velocity profiles are measured along the middle section of the channel, especially around the weir structure, to determine the boundary layer separation. According to the determination of optimum weir structure the free surface profiles, pressure distributions on weir surfaces, experimental discharge coefficients and head losses over weir structures are determined for different structure and flow conditions. Pressure distributions over the hydrofoil weir are presented. In addition, the relationships between discharge coefficient (C_d) and flow rate (Q), specific total head (H/R), relative weir height (P/H), relative total head (H/P) and dimensionless total energy head upstream of the weir (H/L) are investigated.     

Experimental investigation of flow characteristics over asymmetric Joukowsky hydrofoil weirs for free and submerged flow

Weirs are one of the most common hydraulic structures used to regulate the upstream approach flow depth and measure the flow discharge. The hydrofoil weirs are a type of short-crested weirs that are designed based on the airfoil theory. These weirs have some merits compared to other types, such as a higher discharge coefficient, more stability, better submergence limiting condition, and lower fluctuations of the pressure and the free-surface profile. In the present study, experimental models of hydrofoil weirs with different relative eccentricities, cambers, angles of attack, and upstream slope angles are applied to investigate their hydraulic characteristics under free and submerged flow conditions. The longitudinal profiles of static pressure over different hydrofoil weirs are compared to circular-crested and ogee weirs. The results indicate that the maximum bed negative pressure belongs to the circular-crested weir, and the lowest bed pressure over the hydrofoil and ogee weirs are approximately the same. Applying a hydrofoil weir with an appropriate curvature and angle of attack instead of a circular-crested weir not only increases the structural weir height as well as the upstream water depth but also results in the lowest values of bed negative pressure, thereby reduces the potential of cavitation over the weir body, being safer hydraulic structures. The results also show that the discharge coefficient of hydrofoil weirs is greater than that of the broad- and short-crested weirs for the upstream approach flow depth relative to the weir crest to weir length h₁/L > 0.12 and is greater than that of the ogee weirs for 0.35 < h₁/L < 0.45. Furthermore, the derived relationships for the discharge coefficient, threshold submergence, and the discharge reduction factor due to submergence accurately predict the hydraulic characteristics of hydrofoil weirs compared to the available developed empirical relationships for these weirs and can be used efficiently for design purposes.     

Discharge characteristics and structure of flow in labyrinth weirs with a downstream pool

A new design of a labyrinth weir is introduced in this study by adding a square pool to the vertex of a one-cycle triangular labyrinth weir with a sidewall angle of 45°. The addition of the square pool increased weir length without causing an excessive nappe interaction, and as a result, reduced the head water over the weir with the same discharge. Laboratory experiments were carried out to investigate the hydraulic performance of the new design with a potential application in pool-weir fishways. Mean and turbulence characteristics of flow for different weir geometries and in both free and submerged flow regimes were measured to be used for prediction of fish behaviour in the upstream of the proposed weir models. Discharge coefficients based on channel width and weir length were calculated. It was found that the new design can significantly increase the capacity of triangular labyrinth weirs and provide financial advantages in construction over triangular labyrinth weirs without pools in low discharges. In submerged flow conditions, the proposed model performed better than sharp-crested linear weirs in low discharges. Contour plots of the three-dimensional velocity components showed a region of strong mean flow around the neck of the new weir model. Turbulent characteristics such as turbulent kinetic energy, power spectra, exuberance ratio, and joint probability distribution functions of velocity fluctuations were extracted from instantaneous three dimensional velocities for different weir depths and flow regimes. Two vertical planes were identified based on the highest turbulent mixing in free and submerged flow regimes. The depths contributing the most to turbulent mixing were identified; active depths decreased as the flow regime changed from free to submerge flow regime.     

Influence of crest geometric on discharge coefficient efficiency of labyrinth weirs

Labyrinth type weirs are structures that, due to their geometry, allow the discharge capacity to be increased compared to linear weirs. They are a favorable option for dam rehabilitation and upstream level control. There are various geometries of labyrinth type weirs such as trapezoidal, triangular or piano key as well as different types of crest profiles. Geometric changes are directly related to hydraulic efficiency. The objective of this work was to analyze the hydraulic performance of a labyrinth type weir, by simulating several geometries of the apex and of the crest using Computational Fluid Dynamics (CFD). For model validation, experimental studies reported in the literature were used. Tests were carried out with trapezoidal and circular apexes and four types of crest profiles: sharp-crest, half-round, quarter-round and Waterways Experiment Station (WES). The results revealed a determination coefficient of R² = 0.984 between experimental and simulated data with CFD, which provides statistical agreement. Simulations showed that circular-apex weirs are more efficient than those with trapezoidal apex, because they have a higher discharge coefficient (4.7% higher). Of the four types of crest profiles analyzed, the half-round and the WES crest profiles had similar discharge coefficients and were generally greater than those of the sharp-crest and the quarter-round (5.26% y 8.5% higher) profiles. Nevertheless, to facilitate a practical construction process, it is recommended to use a half-round profile. For hydraulic heads with H_T/P > 0.5 ratio, all profiles generated sub-atmospheric pressures on the side walls of the weir. However, when H_T/P ≈ 0.8 ratio the half-round crest generated a higher negative pressure (−1500 Pa), while the sharp-crest profile managed to increase the pressure by 76% (−350 Pa), but with a greater area of negative pressure. On the other hand, the WES profile reduced the negative-pressure area by 50%.     

Sensitivity analysis of the factors affecting the discharge capacity of side weirs in trapezoidal channels using extreme learning machines

Side weirs are installed on the side walls of main channels to control and regulate flow. In this study, sensitivity analysis is planned using Extreme Learning Machines (ELM) to recognize the factors affecting the discharge coefficient in trapezoidal channels. A total of 31 models with 1 to 5 parameters are developed. The input parameters are ratio of side weir length to trapezoidal channel bottom width (L/b), Froude number (Fr), ratio of side weir length to flow depth upstream of the side weir (L/y₁), ratio of flow depth upstream of the side weir to the main channel bottom width (y₁/b) and trapezoid channel side wall slope (m). Among the models with one input parameter, the model including Froude number modeled the discharge coefficient more accurately (MAPE=4.118, R²=0.835). Between models with two input parameters, the model using Fr and L/b produced MAPE and R² values of 2.607 and 0.913 respectively. Moreover, among the models with four input parameters, the model containing Fr, L/b, L/y₁ and y₁/b was the most accurate (MAPE=2.916, R²=0.925).     

Flow velocity pattern around trapezoidal piano key side weirs

In general, the side weirs are the structures installed along a channel or river. When the flow depth rises above the weir crest, the overflow passes through these weirs and enters the lateral canal. Nowadays, piano key weirs are considered as an important alternative to labyrinth weirs to modify the weirs encountering with difficulty to pass the maximum flow discharges. The present study investigates the hydrodynamic performance and the effect of the uniformity of velocity field on the resultant kinetic energy in the trapezoidal piano key side weirs with 90° installed laterally in the main channel wall. These weirs are classified as A-Type piano key weirs and two approaches (main: Mode 1 and adverse: Mode 2) were used to investigate the effect of the weirs' placement on their performance. The results showed that for velocity vectors in both modes, on average, the maximum flow discharge through the side weir occurred in the x and y directions (V_x and V_y) at Z*<0.2 and 0.2<Y*<0.7. The results also showed that at the control surface of X* = 1, the maximum values of α occur due to existing the inverse flow and increasing the deflection angle of the velocity vectors. The performance of the weir in Mode 2 was more appropriate Mode 1 due to the lack of weir base at the flow inlet, which is an obstacle for the deflection angle of the velocity vectors.     

A new approach for oblique weir discharge coefficient prediction based on hybrid inclusive multiple model

One type of long-crested weir is oblique weir. Oblique weirs are longer than standard weirs. Therefore, they can pass more discharge capacity than weirs at the given channel width. The main objective of the present study was to investigate the efficacy of several intelligent models including multiple linear regression (MLR), Gaussian process regression (GPR), artificial neural network (ANN) and multiple models driven by ANN (MM-ANN) methods in estimating oblique weir discharge coefficient (C_d). Different input combinations were predicted using the variables of H/P, P/L_e, and W/L_e and the output coefficient of discharge. Prediction models were analyzed by statistical index, including root mean square error (RMSE), correlation coefficient (R), error percentage chart, relative error (RE%) plot, Kling-Gupta efficiency (KGE), probability density function (PDF) plot, scatter plot, scatter plot of error residuals and Taylor's diagram. Obtained results showed that the ANN model performed best by combining the inputs of the three variables (i.e., H/P, P/L_e, and W/L_e) with R = 0.746 and RMSE = 0.065 among the standalone models. Eventually, the proposed hybrid model MM-ANN was most accurate in estimating the oblique weir C_d by improving the prediction results of the implemented models.     

Discharge characteristics of a modified oblique side weir in subcritical flow

Side weirs are frequently used in many water projects. Due to their position with respect to the flow direction, side weirs are categorized as plain, oblique and labyrinth. One of the advantages of an oblique side weir is the increase in the effective length of the weir for overflowing and, therefore, diverting more discharge with the same channel opening, weir height and flow properties (i.e., upstream discharge, upstream Froude number and so on). In this paper, an experimental set-up of a new design of an oblique side weir with asymmetric geometry has been studied. The hydraulic behavior of this kind of oblique side weir, with a constant opening length, different weir heights and asymmetric oblique angle, has been investigated in a subcritical situation. The results from over 200 test measurements show that this kind of weir is up to 2.33 times more efficient with respect to the conventional side weir in a rectangular channel among the tested conditions. Finally, the discharge coefficient as a function of geometrical and flow variables are presented for design engineers. In addition, a more precise relation has been obtained for flow with Froude numbers less than 0.4.     

An experimental study of the effects of the parapet walls geometry on the discharge coefficient of trapezoidal piano key weirs

Parapet walls on the crown of piano key weirs (PKW) are employed in the channels to regulate or increase water levels of the upstream. They are also used in the reservoirs to increase water storage. Most recent surveys concerning discharge coefficient and parapet walls have been conducted on the rectangular piano key weirs (RPKW) while not many of them devoted to trapezoidal piano key weirs (TPKW). Also, the effects of its parapet wall and crest shape are rarely investigated in this regard. The aim of this research was to study the impacts of height (R), installation arrangements (S), and crest shape of parapet walls (flat, triangular, and semicircular) on changes of the upstream water level and discharge coefficient of TPKW. The weir height (P) was 15 cm. The parapet walls were installed on the crest of weir with three different arrangements: S₁ (on the crest overall), S₂ (on the sidewalls and inlet key), and S₃ (on the sidewalls). The results indicated that the influence of installation arrangement on changes of water level increased with the growth of parapet walls height. In the case of a flat parapet walls, maximum and minimum increase rates of total head were recorded for S₁ and S₃ arrangements, respectively. There was also a direct relationship between discharge coefficient (C) and the heights of parapet walls in a constant water level at upstream. When installing flat parapet walls with R/P = 0.3, the value of C for S₂ exceeded those for S₁ and S₃.     

Effect of anti-vortex structures installed on stepped labyrinth side weirs on discharge capacity

Side weirs are essential structural elements commonly used to control water levels in rivers and canals. If the length of the opening is limited, a labyrinth side weir can be used to increase the amount of water diverted out of the channel and the effective length. This research studied the influence of installing an antivortex structure in stepped labyrinth side weirs on discharge capacity. It has four types of antivortex installed in different hydraulic conditions at different Froude numbers, dimensionless crest height, dimensionless weir opening length, step number, and head angle. Using data from 168 experimental runs without antivortex to allow comparison and 672 experimental runs to determine the best performance of antivortex structures that improved discharge capacity, and 528 runs measured velocity to investigate the intensity of secondary currents generated by lateral flow and other hydraulic conditions, including water surface profiles. According to the research results, installing antivortices regulated the flow, significantly improved the efficiency of the single-cycle stepped labyrinth side weir, and lowered secondary flows caused by interaction with the vertical axis. Finally, the discharge coefficient improves to 18% after analyzing the best type of antivortex, considering shape and height.     

Experimental and numerical simulation of arced trapezoidal piano key weirs

Piano key weirs are high performance labyrinth weirs particularly at lower heads (water height over the weir). These weirs are considered a recent development in terms of application and research. This study was conducted to numerically and experimentally investigate the hydraulic performance of arced trapezoidal piano key weirs ATPKW under different hydraulic and geometric conditions. The main purpose was to investigate the effect of the planform arc angle on the weir's hydraulic performance. To this end, four LRPKW models as well as four ATPKW models were studied. Due to the complexities associated with flow over piano key weirs, numerical models were used to simulate the flow pattern over the weir. Comparison of the results obtained for the ATPKW and LRPKW models indicated that, at upper heads, the ATPKW models offered a higher hydraulic performance than the LRPKW models. On the other hand, LRPKW model indicated better performance at lower heads. In addition, it was found that reducing the planform arc angle from 90° to 45° caused an initial reduction in the discharge coefficient, after which it dramatically increased. Also, LRPKW models indicated a more effective length and a more appropriate performance.     

Discharge formula for rectangular sharp-crested weirs

Sharp-crested rectangular weirs used for discharge measurement in channels and laboratories are experimentally investigated. Height and width of weir plate are the two parameters characterizing the head-discharge relationship. Laboratory experiments are conducted by measuring the discharge and the head over the weir for variable weir heights and widths. Applicability of various formulations for the discharge coefficient are investigated. Experiments indicate that discharge is independent of weir height, when the weir is operated within an appropriate discharge range. Average velocity over the weir plotted against the weir head displays universal characteristics such that it can be used in the expression of discharge over the weir, eliminating the need for a discharge coefficient. The head-discharge relationship for a rectangular weir has distinct features for the partially contracted weirs and for the fully contracted slit weirs.