Discharge Coefficient Of Weirs Research Articles

A novel approach using CFD and neuro-fuzzy-firefly algorithm in predicting labyrinth weir discharge coefficient

In this paper, for the first time, to model the discharge coefficient of labyrinth weirs, the evolutionary firefly algorithm (FFA) is used for optimizing the membership functions of the adaptive neuro-fuzzy inference system (ANFIS). Also, to enhance the performance of the ANFIS and ANFIS-FFA models, the Monte Carlo simulations (MCs) are employed. Additionally, the k-fold cross-validation is utilized for training and testing the methods. Next, some input dimensionless parameters including the Froude number (Fr), the ratio of the head above the weir to the weir height (HT/P), cycle sidewall angle (α), the ratio of length of the weir crest to the channel width (Lc/W), the ratio of length of apex geometry to the width of a single cycle (A/w) and the ratio of the width of a single cycle to the weir height (w/P) are determined. After that, seven different models are developed for ANFIS and ANFIS-FFA. Then, by conducting a sensitivity analysis, the superior models (ANFIS-FFA 5 and ANFIS 5) and the most effective input parameter (Froude number) are identified. Moreover, the error distribution results exhibit that about 70% of the superior model results have errors less than 5%. Subsequently, the discharge coefficient is simulated by means of a computational fluid dynamics (CFD) model. Furthermore, a comparison of the CFD model with the ANFIS and ANFIS-FFA models reveals that the ANFIS-FFA model is significantly more accurate. Also, an uncertainty analysis is performed for the CFD, ANFIS and ANFIS-FFA models. Finally, a very simple code calculating the discharge coefficient of labyrinth wires is presented. This code can be easily employed without any knowledge on ANFIS, FFA and prior information about MATLAB.

Investigation of trapezoidal sharp-crested side weir discharge coefficients under subcritical flow regimes using CFD

Side weirs are utilized to regulate water surface and to control discharge and water elevation in rivers and channels. Here, the discharge coefficient for trapezoidal sharp-crested side weirs (TSCSW) and their affecting parameters are numerically investigated. To simulate the hydraulic and geometric characteristics of TSCSWs, three weir crest lengths of 15 cm, 20 cm and 30 cm with lengths of 20 cm, 30 cm and 40 cm and with two different sidewall slopes are utilized. The results show that for constant P/B (P: weir height, B: main channel width), the depth of flow along the channel and weir decreases as the crest length increases. Also, with increasing P/y1 ratio (P: weir height, y1: upstream flow depth), the discharge coefficient decreases for small crest lengths and increases for large crest lengths. The results show that for constant T/L ratio (T: passing flow width, L: side weir crest length), increasing the length, height and sidewall slope of a side weir will increase the discharge coefficient. It is observed that as the upstream Froude number increases for side weirs with longer crest lengths, the intensity of deviating flow and kinetic energy over the TSCSW will increase. Finally, some relations with high correlation factors are proposed for obtaining discharge coefficients using the dimensionless parameters of P/y1, T/L and Fr1. Based on proposed relations and sensitivity analysis, it is shown that T/L and P/y1 are the most effective parameters for reducing the discharge coefficient reduction.

Discharge coefficient of hydrofoil weirs based on potential flow theory around a symmetric Joukowsky hydrofoil

A hydrofoil weir is a special type of weir that is designed on the basis of aerofoil theory. These weirs have the merits of a higher discharge coefficient, more stability, and fewer fluctuations for a water-free surface compared to sharp-, broad and long-crested weirs. Hydrofoil weirs with an incidence angle of potential flow look like ogee weirs and can be used as dam spillways. In the present study, a conformal mapping technique is applied to investigate the flow around a hydrofoil weir and compare it to the flow around a circular cylinder, where the potential and free vortex flows are combined. The discharge coefficient and velocity distribution are obtained using the Joukowsky transformation and fundamental theories of hydraulics. The analytical results are calibrated using an extensive set of former experimental data. The results indicate that the present approximate analytical model predicts the discharge coefficient and velocity distribution with an acceptable precision compared to the available developed empirical relationships for these weirs, and is a good tool for the design of hydrofoil weirs.

Performance of a shallow-water model for simulating flow over trapezoidal broad-crested weirs

Abstract Shallow-water models are standard for simulating flow in river systems during floods, including in the near-field of sudden changes in the topography, where vertical flow contraction occurs such as in case of channel overbanking, side spillways or levee overtopping. In the case of stagnant inundation and for frontal flow, the flow configurations are close to the flow over a broad-crested weir with the trapezoidal profile in the flow direction (i.e. inclined upstream and downstream slopes). In this study, results of shallow-water numerical modelling were compared with seven sets of previous experimental observations of flow over a frontal broad-crested weir, to assess the effect of vertical contraction and surface roughness on the accuracy of the computational results. Three different upstream slopes of the broad-crested weir (V:H = 1:Z 1 = 1:1, 1:2, 1:3) and three roughness scenarios were tested. The results indicate that, for smooth surface, numerical simulations overestimate by about 2 to 5% the weir discharge coefficient. In case of a rough surface, the difference between computations and observations reach up to 10%, for high relative roughness. When taking into account mentioned the differences, the shallow-water model may be applied for a range of engineering purposes.

Application of Gaussian Process Regression Model to Predict Discharge Coefficient of Gated Piano Key Weir

The Piano Key (PK) weir is a new type of long crested weirs. This study was involved the addition of a gate to PK weir inlet keys. It was conducted by the Department of Water Engineering, University of Tabriz, Iran to determine if the gate increased hydraulic performance. A Gated Piano Key (GPK) weir was constructed and tested for discharge ranges of between 10 and 130 l per second. To this end, 156 experimental tests were performed and the effective parameters on the GPK weir discharge coefficient (Cd), such as gate dimensions (b and d), gate insertion depth in the inlet key (Hgate), the ratio of the inlet key width to the outlet key width (Wi/Wo) and the head over the GPK weir crest (H) were investigated. In addition, application of soft computing to estimate of Cd was carried out using MLP, GPR, SVM, GRNN, multiple linear and non-linear regressions methods using MATLAB 2018 software. This study suggests the relation for Cd with non-dimension parameters. The results of this study showed that H, Wi/Wo, Hgate and b and d, had the greatest effect on the GPK weir discharge coefficient, respectively. The GPR method was introduced as a new effective method for predicting discharge coefficient of weirs with RMSE = 0.011, R2 = 0.992 and MAPE = 1.167% and provided the best results when compared with other methods.

Investigation of discharge coefficient of trapezoidal labyrinth weirs using artificial neural networks and support vector machines

Weirs are a commonly used system to adjust water surface level and to control the flow in canals and hydraulic structures. Labyrinth weirs are a type of weirs that can pass through a certain amount of flow which has a lower upstream water level than the linear weirs, by increasing the effective length. In the present study, the performance of multilayer perceptron (MLP) networks, radial basis function networks and support vector machines with different kernel functions were investigated in order to estimate the discharge coefficient (Cd) of labyrinth weirs with quarter-round crests. For this purpose, 454 laboratory data were used. The non-dimensional parameters of L/W, a, W/P, and Ht/P were considered as the input, and the non-dimensional parameter of Cd was regarded as the output in the models. In comparison with the other models, the performance of the MLP model with RMSE, R, and DC of 0.019, 0.985, and 0.971, respectively, was more acceptable and closer to the experimental data. Also, the data density plot and the violin plot showed that the dispersion and distribution of the probability of the estimated data to the MLP model with the data obtained from the laboratory have a very close and similar adaptation.

Experimental study on flow over sinusoidal and semicircular labyrinth weirs

ABSTRACT For a given width, a labyrinth weir has a developed crest length, thereby increasing the flow capacity for a given upstream headwater. This paper experimentally studies the flow over labyrinth weirs with semicircular and sinusoidal configurations in a rectangular channel under a wide range of flow discharges. The effects of headwater ratio (HT/P), length of weir (L/P), arc radius ratio (R/P) and the number of cycles (N) on the discharge coefficient of semicircular and sinusoidal labyrinth weirs are investigated. Experimental results indicated the decreasing trend of Cd for HT/P>0.35 which is probably related to the progressive development of local submergence. Despite the effects of local submergence, the labyrinth weirs have nearly the same discharge coefficient as broad-crested weirs, and the flow discharge exceeded the linear weirs efficiency by ∼30. Additionally, reliable equations for estimating the discharge coefficient of labyrinth weirs with semicircular and sinusoidal configurations are presented.

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.

Design of radial basis function-based support vector regression in predicting the discharge coefficient of a side weir in a trapezoidal channel

In general, trapezoidal channels are used in irrigation and drainage networks. When installing a side weir on the side wall of a trapezoidal channel, as excess water reaches the side weir plane, additional flow from the crest of the side weir is driven into the side channel. The main aim of this study is to predict the discharge coefficient of rectangular side weirs located on trapezoidal channels using support vector machines (SVMs). Based on the effective parameters on the discharge coefficient of side weirs in trapezoidal channels, six different models (SVM 1–SVM 6) are introduced. According to the analysis results of SVM 1–SVM 6 models, the superior model is introduced as a function of the Froude number (Fr), ratio of side weir length to the bottom width of a trapezoidal channel (L/b), ratio of side weir length to the flow depth upstream of the weir (L/y1), side slope of the trapezoidal channel (m) and ratio of flow depth upstream of the weir to the trapezoidal channel bottom width (y1/b). Based on the simulation results, the superior model has a reasonable accuracy. For example, the root mean square error, mean absolute relative error and correlation coefficient (R2) values calculated for the superior training model are 0.0156, 0.0327 and 0.884, respectively. Furthermore, the ratio of side weir length to trapezoidal channel bottom width (L/b) is identified as the most effective input parameter for modeling discharge coefficient. Additionally, a matrix is presented for superior model to estimate discharge coefficient of the side weirs.

Perspective of Water Distribution Based on the Performance of Hydraulic Structures in the Varamin Irrigation Scheme (Iran)

AbstractDespite the extensive application of check and offtake structures in irrigation canals, their periodic assessment is generally not included in water management plans, especially in Iran. This issue would be more important when there are many problems in water distribution in irrigation projects. In this study the performance and operating status of different hydraulic structures in the Varamin irrigation scheme were evaluated using a precise flowmeter. Results show that Neyrpic modules have an error in range of −8 to 83% and these structures, on average, delivered 22% more water. The discharge coefficient of duckbill weirs has changed considerably as well and they are not able to regulate the water level appropriately, because of ageing and physical destruction. The results showed that to achieve an acceptable performance of Neyrpic modules in this scheme it is essential to perform some physical modifications, such as cleaning and sealing the gates, removing sediment around the gates, replacing old gates and continuous inspection of infrastructure. A series of measurements to estimate water losses during the conveyance process show that the conveyance efficiency for each 1000 m length of main, secondary and tertiary canals are respectively 95.0, 91.5 and 89.3%. Consequently to achieve a suitable water distribution pattern, preventive maintenance should be considered. © 2018 John Wiley & Sons, Ltd.

The evaluation of the effect of nappe breakers on the discharge capacity of trapezoidal labyrinth weirs by ELM and SVR approaches

The labyrinth weir is one type of overflow design used to direct and transfer water in open channels and to provide both routine flow and flood passage over dam spillways. Labyrinth weirs are primarily used at sites where the available spillway width is limited. Due to the increase in crest length, a labyrinth weir provides an increase in discharge capacity relative to conventional weir structures. It is important that the discharge coefficient be accurately represented to ensure appropriate and economical design. The discharge coefficient of trapezoidal labyrinth weirs (TLW) is estimated by using extreme learning machines (ELM) and support vector regression (SVR) techniques in this study. Additional discharge coefficient prediction models have been developed for applications that include the use of nappe breakers (NB). These are frequently included in the design as a mechanism to reduce the impact of vibrations and oscillations on these weirs. A total of 1128 test runs for discharge coefficient measurements of TLW with/without NB were performed in the present study. The statistical criteria used for the evaluation of the performance of models are Mean Absolute Error (MAE), Root Mean Square Error (RMSE), Root Relative Squared Error (RRSE), Mean Absolute Percentage Error (MAPE) and Determination Coefficient (R2). Results of this investigation suggest that the models using Extreme Learning Machines (ELM) and Support Vector Regression (SVR) methods are successful in modeling the discharge coefficient of TLW with/without NB. The best correspondence between model and observation occurred using the ELM model; this resulted in an RMSE for the TLW with/without NB of 0.0188 and 0.0158, respectively.

Surface to sewer flow exchange through circular inlets during urban flood conditions

Abstract Accurately quantifying the capacity of sewer inlets (such as manhole lids and gullies) to transfer water is important for many hydraulic flood modelling tools. The large range of inlet types and grate designs used in practice makes the representation of flow through and around such inlets challenging. This study uses a physical scale model to quantify flow conditions through a circular inlet during shallow steady state surface flow conditions. Ten different inlet grate designs have been tested over a range of surface flow depths. The resulting datasets have been used (i) to quantify weir and orifice discharge coefficients for commonly used flood modelling surface–sewer linking equations and (ii) to validate a 2D finite difference model in terms of simulated water depths around the inlet. Calibrated weir and orifice coefficients were observed to be in the range 0.115–0.372 and 0.349–2.038, respectively, and a relationship with grate geometrical parameters was observed. The results show an agreement between experimentally observed and numerically modelled flow depths but with larger discrepancies at higher flow exchange rates. Despite some discrepancies, the results provide improved confidence regarding the reliability of the numerical method to model surface to sewer flow under steady state hydraulic conditions.

Numerical Investigation of Geometric Parameters Effect of the Labyrinth Weir on the Discharge Coefficient

Weirs, as overflow structures, are extensively applied for the measurement of flow, its diversion, and control in the open canals. Labyrinth weir as a result of more effective length than conventional weirs allows passing more discharge in narrow canals. Determination of the design criteria for the practical application of these weirs needs more examination. Weir angle and its position relative to the flow direction are the most effective parameters on the discharge coefficient. In this article, Fluent software was applied as a virtual laboratory, and extensive experiments were carried out to survey the effect of geometry on the labyrinth weir discharge coefficient. The variables were the height of weir, the angle of the weir, and the discharge. The discharge coefficients acquired from these experiments were then compared with the corresponding values obtained from the usual rectangular sharp-crested weir experiments. Comparison of the results indicated that in all cases with different vertex angle, flow discharge coefficients are in a satisfactory range for relative effective head less than 0.3. The discharge coefficient is reduced for relative effective head more than 0.3 due to the collision of water napes. It revealed that the higher the weir, the more discharge capacity. As a result, the labyrinth weirs have a better performance in comparison with the common sharp-crested.

New type side weir discharge coefficient simulation using three novel hybrid adaptive neuro-fuzzy inference systems

In many hydraulic structures, side weirs have a critical role. Accurately predicting the discharge coefficient is one of the most important stages in the side weir design process. In the present paper, a new high efficient side weir is investigated. To simulate the discharge coefficient of these side weirs, three novel soft computing methods are used. The process includes modeling the discharge coefficient with the hybrid Adaptive Neuro-Fuzzy Interface System (ANFIS) and three optimization algorithms, namely Differential Evaluation (ANFIS-DE), Genetic Algorithm (ANFIS-GA) and Particle Swarm Optimization (ANFIS-PSO). In addition, sensitivity analysis is done to find the most efficient input variables for modeling the discharge coefficient of these types of side weirs. According to the results, the ANFIS method has higher performance when using simpler input variables. In addition, the ANFIS-DE with RMSE of 0.077 has higher performance than the ANFIS-GA and ANFIS-PSO methods with RMSE of 0.079 and 0.096, respectively.

Prediction of side weir discharge coefficient by radial basis function neural network

Prediction of side weir discharge coefficient by radial basis function neural network

Sharp-crested weir located at the end of a circular channel

Sharp-crested weirs are frequently used for discharge measurements in open channels. They offer a simple, reliable and accurate flow measurement approach if they are properly installed and maintained. Suppressed weirs can be installed in channels with different shapes. The standard suppressed rectangular weir is well documented in the literature. The current research is conducted to achieve an accurate and simple formula for flow through the suppressed, sharp-crested weir located at the end of circular, open channels. The discharge equation of a suppressed, circular weir ends up as incomplete elliptic integrals of the first and second kinds, which are not very suitable for practical purposes owing to their complexity. In this study, a simple and accurate theoretical discharge equation has been presented for this weir. A series of laboratory experiments (244 runs) are also performed to investigate the discharge coefficient of sharp-crested weirs located at the end of two horizontal, circular, open channels. Using the data collected from two pipes of diameters 19·1 and 30·1 cm, a suitable discharge coefficient equation with an average relative error of less than 2·3% is presented; thus actual discharge through the channel can be simply estimated using the proposed equations.

Derivation of discharge coefficient of a pivot weir under free and submergence flow conditions

A pivot weir is a measuring and regulating structure that benefits fixed weirs and can be used to set the level of water from long distances in modern irrigation networks utilizing a mechanical lift. Earlier studies have shown that the discharge coefficient of a pivot weir is mostly based on experimental results and few studies have used theoretical approaches to estimate this coefficient. In this paper, analytical equations are proposed to estimate the discharge coefficient of a pivot weir and the results are compared with those of experimental approaches. The equations proposed in this study are based on the Bernoulli and momentum equations for both free and submerged flow conditions. The correction coefficients in the proposed equations have been determined using experimental data. The results show that the proposed equations offer less complexity and higher accuracy when estimating the pivot weir discharge coefficient than the results of earlier studies. Furthermore, these equations can be used as full range standard equations because of their theoretical basis.

Development of more accurate discharge coefficient prediction equations for rectangular side weirs using adaptive neuro-fuzzy inference system and generalized group method of data handling

A rectangular side weir is a hydraulic structure commonly utilized all around the world in urban stormwater and wastewater sewer networks and in irrigation drainage systems to deviate excessive flow passing through the main channel. In this study, a genetic algorithm (GA) is employed to identify the best selection of adaptive neuro-fuzzy inference system (ANFIS) membership functions and the evolutionary design of a generalized group method of data handling (GMDH) structure for prediction of the side weir discharge coefficient. Moreover, the Singular Value Decomposition (SVD) method is applied to calculate the linear parameters of the ANFIS results and linear coefficient vectors in GMDH (ANFIS-GA/SVD and GMDH-GA/SVD). The side weir dimensionless length, Froude number, the ratio of weir height to upstream flow depth, and the ratio of weir length to upstream flow depth serve as inputs to the ANFIS-GA/SVD and GMDH-GA/SVD models to forecast the discharge coefficient. We compared the results of these multi-objective methods with the single-objective methods and found that the multi-objective methods are superior regarding accuracy. Sensitivity analysis is also carried out to determine the impact of each parameter on discharge coefficient estimation. ANFIS-GA/SVD outperformed ANFIS-GA, GMDH-GA/SVD, GMDH-GA and existing regression-based and machine learning-based equations. The uncertainty analysis is also carried out to assess the quantitative performance of all models. The results indicate that the uncertainty width for the best model (ANFIS-GA/SVD) is ±0.0067.

Improvement of extreme learning machine using self-adaptive evolutionary algorithm for estimating discharge capacity of sharp-crested weirs located on the end of circular channels

Weirs are used in different shapes such as rectangular, triangular and circular to control and measure the flow in open channels. To design a weir properly, determining its discharge coefficient is very important. In this study, the discharge coefficient of sharp-crested weirs located on circular channels is modeled by the self-adaptive optimization of extreme learning algorithm using the differential evolutionary algorithm (SaDE-ELM). Also, Monte Carlo simulations (MCs) are used to study the compatibilities of SaDE-ELM models. However, the k-fold cross validation method (k=5) is used to investigate the abilities of the used numerical models. According to the input parameters, four models of SaDE-ELM are introduced. Study of the numerical results shows that the superior model simulates the discharge coefficient as a function of the Froude number (Fr) and the ratio of the circular channel diameter to the weir crest height (D/P) and a relationship is provided for the superior model. The values of mean absolute relative error (MARE), root mean square error (RMSE) and correlation coefficient (R2) for the superior model are calculated 0.184, 0.002 and 0.997, respectively. However, the maximum error value for this model is less than 3%. Also, the results of the uncertainty analysis show that the superior model has an underestimated performance which its 95% prediction error interval is simulated between 0.000314 and −0.000314. In other words, the width of uncertainty band for the superior model is calculated equal to −0.000314.

Discharge coefficient of semi-circular labyrinth side weir in subcritical flow

Side weirs are flow diversion or intake devices that are widely used in irrigation and drainage networks and urban sewage systems. Labyrinth weirs have a proven hydraulic advantage due to their increased discharge rate at the same head for a given design condition. A labyrinth weir is defined as a weir crest that is not straight in plan-form. The increased sill length provided by labyrinth weirs effectively reduces upstream head to the particular discharge. In this study, a comprehensive laboratory study was conducted in a physical model of a semi-circular labyrinth side weir and the model is evaluated for three heights and three radii. In this particular study, the hydraulic effects of this shape of side weir in increasing discharge capacity was investigated. The discharge coefficient of semi-circular labyrinth side weirs was determined and the results were analysed to find the influence of the dimensionless parameters of weir height ( w/b ), weir length ( r/b ), nape height (( y 1 −w)/r ), and upstream Froude number ( Fr 1 ) on discharge coefficient ( Cd ), based on the experimental conditions and previous studies. It was found that the discharge coefficient of the semi-circular labyrinth side weir gives a relatively high discharge coefficient value compared to other types of classic side weir positioned on a straight channel. Additionally, reliable equations for calculating the discharge coefficient ( Cd ) of semi-circular labyrinth side weirs are proposed. According to the proposed equation, Cd depends on dimensionless parameters, which are the ratios of r/b, r/w , ( y 1 −w ) /r , ( y 2 −w )/ r and Fr 1 . Keywords: side-weir, discharge coefficient, semi-circular labyrinth side weir, subcritical flow