Weir Type Research Articles

Effect of the shape and type of piano key weirs on the flow efficiency

This study evaluates the effect of the piano key weir’s (PKW) shape and type on the flow efficiency for different inlet and outlet keys width ratios (W i /W o ). The study is performed experimentally and numerically using a CFD model. Three PKW shapes are studied (rectangular, trapezoidal, and triangular). First, three Type-A shapes were studied experimentally considering W i /W o = 0.8. The trapezoidal shape had the highest efficiency, while the triangular had the least. The experimental results were used to verify the numerical model, then, the rectangular and trapezoidal shapes were studied numerically for W i /W o = 1.25. The trapezoidal Type-A PKW with W i /W o = 1.25 showed the highest flow efficiency of all shapes and W i /W o ratios. The rectangular and trapezoidal Type-B PKWs were also studied for W i /W o = 1.25 and compared to Type-A. The Type-B PKW showed higher efficiency. The ratio W i /W o is the most studied effective parameter on the PKW flow efficiency, followed by the weir’s shape, then its type.

Accurate discharge coefficient prediction of streamlined weirs by coupling linear regression and deep convolutional gated recurrent unit

ABSTRACT Streamlined weirs, which are a nature-inspired type of weir, have gained tremendous attention among hydraulic engineers, mainly owing to their established performance with high discharge coefficients. Computational fluid dynamics (CFD) is considered as a robust tool to predict the discharge coefficient. To bypass the computational cost of CFD-based assessment, the present study proposes data-driven modeling techniques, as an alternative to CFD simulation, to predict the discharge coefficient based on an experimental dataset. To this end, after splitting the dataset using a k-fold cross-validation technique, the performance assessment of classical and hybrid machine learning–deep learning (ML-DL) algorithms is undertaken. Among ML techniques, linear regression (LR), random forest (RF), support vector machine (SVM), k-nearest neighbor (KNN) and decision tree (DT) algorithms are studied. In the context of DL, long short-term memory (LSTM), convolutional neural network (CNN) and gated recurrent unit (GRU), and their hybrid forms, such as LSTM-GRU, CNN-LSTM and CNN-GRU techniques, are compared using different error metrics. It is found that the proposed three-layer hierarchical DL algorithm, consisting of a convolutional layer coupled with two subsequent GRU levels, which is also hybridized with the LR method (i.e. LR-CGRU), leads to lower error metrics. This paper paves the way for data-driven modeling of streamlined weirs.

Study on aeration performance of different types of piano key weir

Abstract Aeration is the process of increasing the dissolved oxygen (DO) content of water, which is an important water quality parameter for the survival of aquatic life. In this process, large amounts of air bubbles develop; as a result, contact surface area increases, and hence the water-air-mass transfer accelerates. There are numerous methods for increasing DO concentration in water, including self-aeration, mechanical aeration, chemical aeration, and hydraulic structures. The hydraulic structures are an economical and efficient way of enhancing stream/river water aeration. Even though the water only comes into contact with the structure for a short while, it increases the amount of DO in a river system. In this study, an experimental investigation has been carried out to determine the aeration performance of different types of piano key weir (PKW). To this end, three different types (type-A, type-B, and type-C) of PKW laboratory-scaled models were tested. The results demonstrated that the type-A PKW created maximum oxygen transfer efficiency of the three PKW types. In addition, the results show that the aeration efficiency of all PKW models increases with drop height but decreases with increasing discharge over the weirs.

Application of AI Approaches to Estimate Discharge Coefficient of Novel Kind of Sharp-Crested V-Notch Weirs

In this study, the hydraulic features of the SCVW (a novel type of sharp-crested V-notch weirs) were scrutinized in the popular vertex angles θ, i.e., 30°, 45°, 60°, 90°, 120°, 128°, and 150°, under aerated, steady and free overflow conditions in an open channel for large physical models. To assess the changes of the discharge coefficient of the SCVW (i.e., CdSCVW) versus weir height and θ, widespread laboratory works were performed by measuring the water head over the crest of the weir and the discharge. Special formulas for the CdSCVW in the θ=60° were checked, and an appropriate empirical equation was recommended. The calculated CdSCVW by the proposed equation was within 0%–10% of the measured values. Three types of nonparametric artificial intelligence (AI) methods, namely, support vector regression (SVR), gene expression programming (GEP), and a robust hybrid model entitled hybrid (SVR-ACO) were developed to estimate the CdSCVW. For the sake of modeling, 196 experimental datasets were applied in the mentioned methods to evaluate the CdSCVW by taking into consideration the dimensionless variables which impact the determining procedure of the CdSCVW. In this modeling, by varying the architecture and core factors of the aforementioned methods, several scenarios were defined. The generated mathematical equation of CdSCVW by the best scenario of the GEP was compared with the corresponding measured values in which the results were in 0%–10%. According to the attained statistical indices, scatter plots, and the values of the total grade (TG) technique, the hybrid SVR(RBF)-ACO model was determined as the superior and optimal method to estimate the CdSCVW with high performance and accuracy.

Experimental Study of Scour Downstream Piano Key Weir Type C with Changing Height of Weir Width of Keys and Apron Solid

To find out mechanism scour downstream weirs and study effect changing ratio width of keys Wi/Wo , length of Apron solid and studying effect of changing the lateral length B on depth and length of the maximum scour by passing different discharge and using homogeneous soil. A laboratory study was conducted to measure depth of scour downstream piano key weir type C and to show effect height weir, ratio width of keys and length of apron solid. Three heights of weir (25,30,35) cm , three ratios of width keys (1,1.25,1.5) and two distances were used For apron solid (90,120) by passing four different discharges (15, 22, 29, 36)) l/s in experiments, where number of models used nine models, on which (72) experiments were conducted. The depth of scour for all experiments that by reducing height weir , maintaining ratio width of the keys and discharge, scour decreases for all experiments. The results also showed that by increasing length of apron solid by 33.33%, the scour depth will be decreased by a rate ranging between (2.17-28.75)%. and that by increasing the percentage of the width keys from ratio (1) ) to ratio (1.5) scour depth decreases by a rate ranging between (13.04-47.38%) for all experiments, decreasing height of weirs from 35 cm to 25 cm, the percentage decrease scour depth ranged (20-40.2)%. To arrive at a positional equation in terms of variables and a coefficient of determination of R2 = 0.958 .

Flow Characteristics Investigation On Trapezoidal Weir Using FLOW 3D

Weir is a building that is formed to change the nature of river flow to accommodate irrigation needs. The main purpose of a weir is to raise the river water level, drain the channel through the intake channel, allow water to be tapped, control all flow, etc. If a flow experiences a large shock, it will cause a hydraulic jump resulting in a transition of flow from supercritical to subcritical. The analysis can be performed, it was done using the Computational Fluids Dynamics (CFD) software, FLOW-3D. To model the 3-D weir used in this FLOW-3d, AutoCAD is used and finally, Flow Sight will be used to display visualization results such as graphics and videos. This paper investigates the Froude number and depth-averaged velocity on the trapezoidal weir. Moreover, the numerical modelling of trapezoidal weirs has been compared with the experimental result and numerical modelling of other types of weirs. The results show that the Froude number is proportional to the average velocity of this depth because the Froude number increases with the increase in the average velocity. There is a difference with the flow that flows after the weir, in a trapezoidal weir the Froude number decrease slightly but after that, it increases again downstream.

On approximate quasi Pareto solutions in nonsmooth semi-infinite interval-valued vector optimization problems

This paper deals with approximate solutions of a nonsmooth semi-infinite programming with multiple interval-valued objective functions. We first introduce four types of approximate quasi Pareto solutions of the considered problem by considering the lower-upper interval order relation and then apply some advanced tools of variational analysis and generalized differentiation to establish necessary optimality conditions for these approximate solutions. Sufficient conditions for approximate quasi Pareto solutions of such a problem are also provided by means of introducing the concepts of approximate (strictly) pseudo-quasi generalized convex functions defined in terms of the limiting subdifferential of locally Lipschitz functions. Finally, a Mond–Weir type dual model in approximate form is formulated, and weak, strong and converse-like duality relations are proposed.

An iterative hydraulic design methodology based on numerical modeling for piano key weirs

Piano Key Weir (PKW) is a special type of overflow weir which provides an improved discharge capacity with its increased crest length. Increased discharge capacity makes this weir an attractive alternative in the rehabilitation of existing spillways. After the introduction of this new weir type, many experimental and numerical studies are conducted to understand the effect of the numerous geometrical parameters on the discharge capacity. However, empirical discharge formulas suggested by different researchers are not conforming to a unique expression mostly due to dependence on the experimental conditions from which they are derived. A numerical approach is used in the present study to investigate the dependence of discharge capacity of a PKW unit on several geometric parameters. Numerical models are developed and three-dimensional velocity fields are computed using FLOW-3D® software. Discharge efficiency of a PKW over an equivalent linear sharp-crested weir is evaluated within the practical range of parameters from 145 numerical solutions for 29 different PKW models. Numerically obtained data is used to form dimensionless expressions for the weir height and length as function of discharge efficiency which are proposed to facilitate an iterative numerical solution to meet the design requirements of a given project. This approach allows cost optimization while dimensioning the PKW for the required hydraulic capacity. The design procedure based on iterative numerical solutions is described and exemplified.

A Sensitivity Analysis of Piano Key Weir Overhang Crest Length

In the scope of dam rehabilitation to manage floods increase or to increase storage, the Piano Key Weir is a good solution for concrete dams. The efficiency of Piano Key Weirs is now well demonstrated through various experimental studies. Until now most of the Piano Key Weir prototypes close to the Piano Key Weir Type A using symmetrical up- and downstream overhangs for structural reasons. The position of the overhangs influences the inlet and outlet key slopes and cross section as well as the side crest length influenced by these slopes and cross sections. On this paper, the influence of these main parameters has been studied on several models considering variation of the overhang lengths.

Determination of Discharge Coefficient for both Semicircular and Triangular Labyrinth Weirs

A Labyrinth weir is a type of nonlinear weir folded in plan-view, with the ability to pass a large flow at low heads due to an increase in the effective length of the weir crest for a given channel width. The discharge coefficients (Cd) were experimentally determined for both semicircular and triangular labyrinth weirs of varying sidewall angles (α) under free-flow conditions using eight physical models. Dimensional analyses are conducted using the Buckingham π theorem to find the dependent and non-dependent variables. A nonlinear empirical equation was developed using (Statistical Package for the Social Sciences 22) software. The findings show that the discharge coefficient decreases with the increase of headwater to (Ht/P) for both types of labyrinth weir with different plan forms. It is found that the efficiency of the semicircular and triangular labyrinth is higher than linear weir for (Ht/P ≤ 0.45) and decreases with increasing the value of (Ht/P) due to interference of flow between the layers in downstream. The obtained results revealed that the discharge coefficient (Cd) values obtained empirically using multivariable power regression and 5th degree polynomial equations considerably agree with the experimental data, for both of the semicircular and triangular labyrinth weirs. Furthermore, the correlation coefficient R2was (0.9951) and (0.9637) using 5th degree polynomial equation, and their values were (0.9643) and (0.9274) using multivariable power regression equation for both semicircular and triangular labyrinth weir models, respectively. The results in the present study compared quite well with the predicted results of the proposed equations obtained by other investigators.

Using CFD modelling to study hydraulic flow over labyrinth weirs

Abstract The compound labyrinth weir is a new type of labyrinth weir that is considered a good applicable choice for increasing the capacity of discharge. The flow over a compound labyrinth weir is a complex problem because the flow behavior is three-dimensional. The present study aims to simulate the flow over the compound labyrinth weir into the critical regions that cannot be observed when using an experimental test. The computational fluid dynamics (CFD) programme was utilised to implement a sensitive analysis for this purpose and under different flow conditions. The MAPE and RMSE indices were utilised to verify the CFD results with experimental work. The statistical indices of the maximum error ME, RMSE and MAPE were 4.7%, 0.033 and 3.9 respectively. Therefore, the findings showed that there is a good matching between the experimental and CFD results. The CFD results demonstrated that the hydraulics behaviour of the compound labyrinth weir was similar to the oblique and linear weirs in high discharges. The results also confirmed that air cavities and bubbles existed behind the nappe flow in addition to the negative pressure that may occur beneath the nappe when the flow is aerated. Furthermore, the flow was divided into two parts and most streamlines were concentrated over the notches. Moreover, the flow velocity passing through the notches was greater than the flow velocity over the high crest of the compound labyrinth weir.

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 (HT), weir discharge (Q), and head to weir height (HT/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 (HT, Q, and HT/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.

Comparative Study of Nonsymmetrical Trapezoidal and Rectangular Piano Key Weirs with Varying Key Width Ratios

Rectangular piano key weirs (RPKW) have been introduced as an innovative type of labyrinth weir with a smaller footprint and high hydraulic performance. To date, limited attention has been paid to PKWs with other planforms. In this study, experiments and numerical simulations were conducted to investigate and compare the discharge capacity of unsymmetrical trapezoidal piano key weirs (TPKW) and classical rectangular PKWs with varying inlet/outlet key width ratios. Results indicate that, even if all other parameters are held constant, the discharge capacity of a trapezoidal PKW can still be further improved by up to 10% through optimizing the key width ratio. Relative to RPKWs, TPKWs were proven to be more efficient, especially for high relative heads because of the larger outlet cross section, and less efficient for low relative heads due to the relative lack of total crest length. For the specific geometric configurations considered in this study, the optimal range of key width ratio for TPKW and RPKW is likely to be within 1.30 to 1.57 and 1.50 to 1.77, respectively. At the end of this study, a new PKW configuration is introduced, which combines the advantages of both geometries (rectangular and trapezoidal) and improves the overall weir efficiency up to 8%.

Morphodynamic processes in rivers with cascade movable weirs – A case study of the middle Fen River

Cascade movable weirs have been increasingly widely used for river landscaping, water storage and ecological wellbeing. The weirs disturb the prior equilibrium in line with fluvial hydrology, sediment transport and geomorphology, and may lead to profound changes in the river, of which, however, the understanding has so far remained poor. Here, the first of its kind, a computational modelling study is presented on the morphodynamic processes under the impact of cascade hydraulic lifting dams, a type of movable weirs, as to the middle Fen River, China. A two-dimensional shallow water hydro-sediment-morphodynamic model is applied to resolve the fluvial processes, which is physically coupled and computationally efficient based on Finite Volume Method, unstructured mesh, local time stepping and parallel computing. Computational results show that the cascade dams alter the flow and sediment transport locally and on the reach scale in a distinct manner under different operation schemes, which in turn incur disparate morphological changes. Collapse of all the dams all year round would lead to net degradation in the study reach, with the floodplains aggrading and the main channel degrading. Operation of all the dams all year round may induce an overall aggradation both on the floodplains and in the main channel. If all the dams collapse in flood seasons and operate in dry seasons (CF), degradation occurs in the main channel whereas the floodplains experience aggradation, with a net degradation. When only the dams in the main channel operate all year round (OM), the floodplains degrade while the main channel aggrades, resulting in a net aggradation in the study reach. Either aggradation or degradation may prevail locally on floodplains, in main channel and individual subreaches. The present findings lead us to propose a complex operation scheme of annually alternating CF and OM to constrain significant morphological changes.

Predicting the discharge coefficient of oblique cylindrical weir using neural network techniques

Cylindrical weir shapes offer a steady-state overflow pattern, where the type of weirs can offer a simple design and provide the ease-to-pass floating debris. This study considers a coefficient of discharge (Cd) prediction for oblique cylindrical weir using three diameters, the first is of D1 = 0.11 m, the second is of D2 = 0.09 m, and the third is of D3 = 0.06.5 m, and three inclination angles with respect to channel axis, the first is of θ1 = 90 ͦ, the second is of θ2 = 45 ͦ, and the third is of θ3 = 30 ͦ. The Cd values for total of 56 experiments are estimated by using the radial basis function network (RBFN), in addition of comparing that with the back-propagation neural network (BPNN) and cascade-forward neural network (CFNN). Root mean square error (RMSE), mean square error (MSE), and correlation coefficient (CC) statics are used as metrics measurements. The RBFN attained superior performance comparing to the other neural networks of BPNN and CFNN. It is found that, for the training stage, the RBFN network benchmarked very small RMSE and MSE values of 1.35E-12 and 1.83E-24, respectively and for the testing stage, it also could benchmark very small RMSE and MSE values of 0.0082 and 6.80E-05, respectively.

Detention and Release in Rectangular Gabion Weir

The present paper aims to study the mechanization of detention and release processes when a rectangular gabion weir is used in lined irrigation canals as the preliminary solution to treat the problem of lowering water levels generally during the summer season. At this study a laboratory flume canal with dimensions of 10.0 m long by 0.3 m wide and 0.5 m high was used to carry out the weir experiments. The used hydraulic model constructed with dimensions of 0.3 m width by 0.4 m height, and five different lengths of 0.4, 0.6, 0.8, 1.0, and 1.2 m respectively. Whereas the used gravel samples, as filling material, were of monosized gravel with diameters ranged between 9.5-14.0, 14.0-19.0, 19.0-25.0, 25.0-37.5, and 37.5-50 mm respectively. While the measured discharge values during the experiments were in the range of 0.0007-0.015.0 m3/s, they reached a total of 194 test runs. The results showed that the upstream water depth, as Detention depth, is directly proportional to both of the discharge and the length of the weir, and inversely proportional to the diameter of the used gravel sample, the downstream water depth, as Release depth, is directly proportional with discharge, simultaneously there is no clear effect for both the length weirs length and the used gravel sample on it‘s value. Finally, both values of detention and release depths are directly proportional to each other. A series of empirical formulas were made for designers to manage detention and release processes for this type of weirs.

Using a hybrid artificial intelligence approach to estimate length of the hydraulic jump caused by novel kind of Sharp-Crested V-notch weirs

In this study, the SCVW (a novel type of Sharp-Crested V-notch weirs) is employed for more experimentally and theoretically investigations. The length of the hydraulic jump at downstream of the SCVW (LjSCVW) is measured via new supplementary experimental datasets via most popular vertex angles θ (128° and 60°). The experiments are conducted under aerated, steady, and free overflow conditions in an open channel for large physical models. To assess the variations of LjSCVW versus the θ, extensive laboratory work is performed at different discharges (Q), diverse triangular segments number (Nst) in the SCVW, and various tailgate angles (ɸ). Via dimensional analysis and pre-processing method, most effectual parameters on the LjSCVW were obtained as Fr1 (approaching Froude number), Re1 (incoming Reynolds number), and (relative sequent depths). Based on the experimental results, by increasing the values of Fr1 and Re1, the values of LjSCVW noticeably increased. Three types of data-driven models (DDMs), namely, support vector regression (SVR), gene expression programming (GEP), and a robust hybrid model entitled hybrid (SVR-ACO) are developed to estimate the LjSCVW. The suggested hybrid model is a coupled form of SVR with ant colony optimization (ACO) algorithm, which is used to enhance the estimation precision of the LjSCVW. According to the attained statistical indices (determination coefficient (R2) = 0.98, root mean square error (RMSE) = 0.191, and value of total grade (TG) = 19.78) and scatter plots, the hybrid SVR-ACO model was determined as the most superior method to estimate the LjSCVW with high accuracy.

Effect of Different Channels on Discharge Coefficient of Labyrinth Weirs

In this study, the effect of channel-bed slope and non-prismatic converging channel on the discharge coefficient of labyrinth weirs is numerically investigated utilizing FLOW-3D model. Numerical simulation results show that modifying the labyrinth weir channel through both methods improves the discharge coefficient. Among the selected bed slopes and converging channel wall, the slope of β=4% and angle of θ=10° yielded the highest discharge coefficient. For a ratio HT/P=0.1, (HT: flow height, P: weir height) the discharge coefficient and discharge rate for bed slope and convergence angle case were 19.22%, 23.9% and 22.28%, 25.91% higher than for a conventional labyrinth weir in prismatic channel, respectively. Simultaneous application of a bed slope and convergence angle significantly increases the discharge coefficient and discharge value case were 28.64% and 30.42% higher than compared to the conventional case. Therefore, changing the bed slope and wall angle of the weir channel increases the discharge coefficient and in this type of weir and these design alterations should be considered in weir design.

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.

On optimality and duality in interval-valued variational problem withB-(p,r)-invexity

In this paper, we consider a class of interval-valued variational optimization problem. We extend the definition ofB-(p,r)-invexity which was originally defined for scalar optimization problem to the interval-valued variational problem. The necessary and sufficient optimality conditions for the problem have been established underB-(p,r)-invexity assumptions. An application, showing utility of the sufficiency theorem in real-world problem, has also been provided. In addition to this, for the interval-optimization problem Mond–Weir and Wolfe type duals are presented and related duality theorems have been proved. Non-trivial examples verifying the results have also been presented throughout the paper.