Weir Type Research Articles

A Performance Comparison of Machine Learning Algorithms for Arced Labyrinth Spillways

Labyrinth weirs provide an economic option for flow control structures in a variety of applications, including as spillways at dams. The cycles of labyrinth weirs are typically placed in a linear configuration. However, numerous projects place labyrinth cycles along an arc to take advantage of reservoir conditions and dam alignment, and to reduce construction costs such as narrowing the spillway chute. Practitioners must optimize more than 10 geometric variables when developing a head–discharge relationship. This is typically done using the following tools: empirical relationships, numerical modeling, and physical modeling. This study applied a new tool, machine learning, to the analysis of the geometrically complex arced labyrinth weirs. In this work, both neural networks (NN) and random forests (RF) were employed to estimate the discharge coefficient for this specific type of weir with the results of physical modeling experiments used for training. Machine learning results are critiqued in terms of accuracy, robustness, interpolation, applicability, and new insights into the hydraulic performance of arced labyrinth weirs. Results demonstrate that NN and RF algorithms can be used as a unique expression for curve fitting, although neural networks outperformed random forest when interpolating among the tested geometries.

Mean velocity and turbulent characteristics of flow over half-cycle cosine sharp-crested weirs

The classical sharp-crested weirs are not suitable to implement in irrigation canals with high suspended sediment flow. Over the time, sediment deposition occurs in the upstream of sharp-crested weirs and causes a time variant water level raise in the upstream and consequently variable discharge coefficients. A series of laboratory experiments was carried out to test the hypothesis of strong turbulent formation and three-dimensional flow in the upstream of half-cosine sharp-crested weirs to prevent sediment deposition. To verify this hypothesis, a series of laboratory experiment was carried out for different weir heights and top widths in free and submerged flow conditions. Mean flow structure and turbulent characteristics of half-cosine and rectangular sharp-crested weirs were measured using a micro-Acoustic Doppler Velocimeter (ADV) probe. It was found that the streamwise velocities of half-cosine weirs were higher than the corresponding rectangular weirs, however, the velocity fluctuations in this direction were similar for both types of weirs. Velocity fluctuations in vertical and transverse directions were found to be significant in half-cosine weirs. The results showed higher turbulent kinetic energy below the crest level for half-cosine weirs which made them capable of sediment resuspension and sediment removal. In was found that the introduced weir model are suitable structures for passage of small floating debris and sediments. A head-discharge formulation was also developed based on the geometry of half-cosine weir in free flow and a constant discharge coefficient was obtained by solving the Fresnel integrals. For practical purposes, semi-empirical formulations were also developed to estimate flow discharge in both free and submerged flow conditions.

Effect of Deploying the Flow Guide Vane in Upstream of Triangular Duckbill Weirs on the Efficiency of this Type of Weir in Laboratory Conditions

One of the effective ways for the flow of water in low head water conditions is using triangular duckbill weirs. Regarding the high efficiency of these weirs in higher rate of flow discharge in constant head water conditions, the investigation about this type of weirs is greatly required. The present study is done on triangular duckbill weir with two different vertex angle, installed in the laboratory straight channel. In the upstream of the installation place of the triangular duckbill weir, some flow guide vanes with different specifications are installed and the required tests were done in three different groups. The discharge coefficient was calculated by obtaining the required laboratory parameters, such as upstream water level and upstream velocity in free flow conditions. The ration of the flow discharge over triangular duckbill weir to the flow discharge of straight weir was calculated and the graphs relative to the total water head were drawn. The results show that the flow guide vane with smaller width has more effects on the efficiency of the triangular duckbill weir. Moreover, in all wall angle of located vane, the efficiency of weir with larger vertex angle is less than that with smaller vertex angle. Since the flow interference is increased by increasing the flow discharge in the triangular duckbill weir with low vertex angle, then, the presence of the flow guide vanes can reduce the horizontal component and increase the vertical component of upstream velocity over the weir. Thus, the flow passes with more velocity over the weir crest at the same time and the flow discharge rate is increased and therefore the efficiency of this weir is increased.

Caraş River Gorge Aspects of Salmonids’ Communities Management – Technical Solutions

Abstract There are many obstacles in rivers that prevent or hinder passage of fish past barriers. Here, we present a specially designed solution for juvenile and adult brown trout so that they may to swim past discharge-regulating weirs in the upper Caraş River in both the upstream and downstream directions. The proposed solution relies on gravity flow and will have current velocities that will not inhibit weak swimmers swimming upstream to pass the weirs. Corrosion-resistant materials and the absence of components that could potentially injure the fish will be used in the construction of these technical solutions. Although testing of the functionality of this solutions for upstream - downstream and downstream - upstream passage of weirs is needed, we believe that if implemented, it should improve connectivity especially for brown trout and consequently conserve within-stream genetic diversity in the Caraş River and where appropriate in alike other Carpathian lotic systems with similar types of weirs.

Numerical Investigation on the Hydraulic Properties of the Skimming Flow over Pooled Stepped Spillway

Pooled stepped spillway is known for high aeration efficiency and energy dissipation, but the understanding for the effects of pool weir configuration on the flow properties and energy loss is relatively limited, so RNG k − ε εturbulence model with VOF method was employed to simulate the hydraulic characteristics of the stepped spillways with four types of pool weirs. The calculated results suggested the flow in the stepped spillway with staggered configuration of` two-sided pooled and central pooled steps (TP-CP) was highly three dimensional and created more flow instabilities and vortex structures, leading to 1.5 times higher energy dissipation rate than the fully pooled configuration (FP-FP). In FP-FP configuration, the stepped spillway with fully pooled and two-sided pooled steps (FP-TP) and the spillway with fully pooled and central pooled steps (FP-CP), the pressure on the horizontal step surfaces presented U-shaped variation, and TP-CP showed the greatest pressure fluctuation. For FP-TP and FP-CP, the vortex development in the transverse direction presented the opposite phenomenon, and the maximum vortex intensity in TP-CP occurred at Z/W = 0.25, while FP-FP illustrated no significant change in the transverse direction. The overlaying flow velocity distribution in the spanwise direction demonstrated no obvious difference among FP-FP, FP-TP, and FP-CP, while the velocity in TP-CP increased from the axial plane to the sidewalls, but the maximum velocity for all cases were approximately the same.

Laboratory investigation of the Discharge Coefficient of flow in arced labyrinth weirs with triangular plans

Weirs play a decisive role in the safety of dams. There are different types of weirs including labyrinth, linear, arced, piano key, etc. Arced weir is an arc of a circle which makes possible an increase in the effective length of the weir crest at a specific width, and thus enabling a greater discharge to pass through the weir for a specific hydraulic load. This study attempted to investigate the Discharge Coefficient and the discharge which passes through direct and arced weirs in linear and triangular labyrinth modes in the laboratory. The Discharge Coefficient of these weirs, which is a function of the ratio of the total hydraulic load to the weir crest height (Hd/P), is compared given the effect of the weir shape and their hydraulic performance. The results show that the increased (Hd/P) value leads to a decreased Discharge Coefficient in all weirs. The amount of the aforesaid decrease varies depending on weir type reaching up to 20% and 51% in the linear weir and the labyrinth weir respectively. Moreover, the increased effective length of the weir as a result of its arced shape resulted in improved efficiency of linear arced weirs and labyrinth arced weirs up to 21% and 57% respectively. With hydraulic load increasing, the height of standing wave at the downstream of arced weirs increased leading to a decreased efficiency of arced weirs.

ϵ-Efficient solutions in semi-infinite multiobjective optimization

In this paper we apply some tools of nonsmooth analysis and scalarization method due to Chankong–Haimes to find ϵ-efficient solutions of semi-infinite multiobjective optimization problems (MP). We establish ϵ-optimality conditions of Karush–Kuhn–Tucker (KKT) type under Farkas–Minkowski (FM) constraint qualification by using ϵ-subdifferential concept. In addition we propose mixed type dual problem (including dual problems of Wolfe and Mond–Weir types as special cases) for ϵ-efficient solutions and investigate relationship between mentioned (MP) and its dual problem as well as establish several ϵ-duality theorems.

Experimental investigation on local scour at the downstream of grade control structures with labyrinth planform

ABSTRACT Grade control structures are commonly used to prevent degradation, increase bank and bed of rivers stability and prevent cross structures failure in rivers. To safe design grade control structures, estimation of local scour depth downstream of these structures is crucial. In this study, the effects of different parameters on local scour at the downstream of grade control structures with labyrinth planform were investigated experimentally. Different types of rectangular and trapezoidal labyrinth planform weirs were studied. Experimental results showed that the labyrinth planform has a high effect on reducing scour depth. It was found that decreasing the length of cycles in the trapezoidal labyrinth weirs and increasing width of cycles in rectangular weirs causes reduction of the maximum scour depth. Experimental observations and comparison of results showed that trapezoidal labyrinth weirs effectively reduce scouring with an average of 19 percent in comparison with linear weir; moreover, the rectangular labyrinth weir reduces to 10 percent. Furthermore, dimensional equation for prediction of scour depth is derived.

Discharge capacity evaluation and hydraulic design of a piano key weir

Abstract A piano key weir (PKW) is a new type of labyrinth weir that increases the unit discharge at the unregulated spillway inlet of the weir. It is considered to be an important structure in water supply and drainage systems. However, its complex geometry makes it difficult to achieve an optimal hydraulic design, and only a few design equations and criteria are available. This study investigates the discharge capacity of a PKW and evaluates the characteristics of its discharge using various sources of experimental data from a database. First, previously proposed discharge capacity formulas are summarized and analyzed. Then, a new formula that integrates the existing test data with the results of dimensional analysis and multiparameter optimization is proposed. The weir characteristics are evaluated using the proposed formula and a mathematical model. The results show that both the proposed formula and numerical model are promising approaches to evaluate the discharge capacity of an A-type PKW and can guide its design.

Development of an evaluation method for velocity distribution over cylindrical weirs using doublet concept

The cylindrical weir is one of the common types of weirs. It can be used for flow measurement, flow diversion and water level control in open channels. Simple design and large discharge coefficient are the main advantages of cylindrical weirs. In present study, flow around cylindrical weirs is simulated by combination of uniform potential flow with two doublets and crest velocity distribution and discharge coefficient of the weir are then obtained. To evaluate the obtained equations, experiments are conducted on three models of cylindrical weirs. A reasonable good agreement is observed between the measured experimental data and the obtained equations.

Vector optimization with generalized cone locally connected functions

In this paper properties of generalized cone locally (strictly) connected functions are studied. The concepts of cone locally (strictly) Pseudo connected and cone locally (naturally) quasi connected functions are introduced. Various interrelations between these function are discussed with the help of an example. Necessary optimality conditions are obtained for an approximate weak quasi efficient solution of a vector optimization problem over cones. Sufficient optimality conditions are also established using the above mentioned functions. Approximate Wolfe type and Mond–Weir type duals are formulated and duality theorems are proved.

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.

Optimality and duality in constrained interval-valued optimization

Fritz John and Karush–Kuhn–Tucker necessary conditions for local LU-optimal solutions of the constrained interval-valued optimization problems involving inequality, equality and set constraints in Banach spaces in terms of convexificators are established. Under suitable assumptions on the generalized convexity of objective and constraint functions, sufficient conditions for LU-optimal solutions are given. The dual problems of Mond–Weir and Wolfe types are studied together with weak and strong duality theorems for them.

Analysis of various parameters affecting weir design and fabrication of Weirs: An Overview

Several geometric parameters influence weir discharge and it is explained in our present study. The PK weir is more efficient than rectangular labyrinth weir due to reduction in entrance losses of PK weir inlet key geometry. PK weir is a type of labyrinth weir with variation in angle. Therefore, in this paper we also discuss about labyrinth weir. PKW are compatible for constructing on existing or new spillway with lesser space requirement and structural stability. PKW are installed in order to increase the discharge capacity for a given footprint area. PKW is used to increase the overflow capacity of existing dams such as, Hazelmare dam (South Africa), Dartmouth dam (Australia). Trapezoidal piano key weirs have higher discharge efficiency than rectangular weirs and it is due to interference wedge. Cd of TPKW is influenced by L/W but Wi/Wo has least effect.

Analysis of various parameters affecting weir design and fabrication of Weirs: An Overview

Several geometric parameters influence weir discharge and it is explained in our present study. The PK weir is more efficient than rectangular labyrinth weir due to reduction in entrance losses of PK weir inlet key geometry. PK weir is a type of labyrinth weir with variation in angle. Therefore, in this paper we also discuss about labyrinth weir. PKW are compatible for constructing on existing or new spillway with lesser space requirement and structural stability. PKW are installed in order to increase the discharge capacity for a given footprint area. PKW is used to increase the overflow capacity of existing dams such as, Hazelmare dam (South Africa), Dartmouth dam (Australia). Trapezoidal piano key weirs have higher discharge efficiency than rectangular weirs and it is due to interference wedge. Cd of TPKW is influenced by L/W but Wi/Wo has least effect.

A Non-Hydrostatic Depth-Averaged Model for Hydraulically Steep Free-Surface Flows

This study describes the results of a numerical investigation aimed at developing and validating a non-hydrostatic depth-averaged model for flow problems where the horizontal length scales close to flow depth. For such types of problems, the steep-slope shallow-water equations are inadequate to describe the two-dimensional structure of the curvilinear flow field. In the derivation of these equations, the restrictive assumptions of negligible bed-normal acceleration and bed curvature were employed, thus limiting their applicability to shallow flow situations. Herein, a Boussinesq-type model is deduced from the depth-averaged energy equation by relaxing the weakly-curved flow approximation to deal with the non-hydrostatic steep flow problems. The proposed model is solved with an implicit finite difference scheme and then applied to simulate steady free-surface flow problems with strong curvilinear effects. The numerical results are compared to experimental data, resulting in a reasonable overall agreement. Further, it is shown that the discharge characteristics of free flow over a round-crested weir are accurately described by using a Boussinesq-type approximation, and the drawbacks arising from a standard hydrostatic approach are overcome. The suggested numerical method to determine the discharge coefficient can be extended and adopted for other types of short-crested weirs.

Calibration of weirs using unsteady flow

This paper presents a method for unsteady calibration of rectangular and triangular weirs using height measurement instead of another flow measurement device as a standard. The theoretical equation of the dependence of the flow with the head for that weir, as long as the covered area, must be known. The method is theoretically developed and applied to a rectangular and to a triangular type of weir obtaining very good results when compared to other studies. In both cases the coefficients of discharge values were 0.617 and 0.587, respectively, which is very well within the values obtained by other researchers. In those analysis, the coefficient of determination of was as high as 0.998.

On nonsmooth robust multiobjective optimization under generalized convexity with applications to portfolio optimization

We introduce a new concept of generalized convexity at a given point for a family of real-valued functions and deduce nonsmooth sufficient optimality conditions for robust (weakly) efficient solutions. In addition, we present a robust duality theory and Mond–Weir type duality for an uncertain multiobjective optimization problem. Furthermore, some nonsmooth saddle-point theorems are obtained under our generalized convexity assumption. Finally we show the viability of our new concept of generalized convexity for robust optimization and portfolio optimization.

Bendung Bertangga sebagai Alternatif pada Perencanaan Bangunan Irigasi

Bendung bertangga merupakan modifikasi dari profil standar untuk bendung tipe ogee. Aliran yang melimpas pada bendung bertangga diklasifikasikan menjadi tiga tipe, yaitu aliran bebas, aliran transisi dan aliran tenggelam. Aliran tenggelam ini lebih banyak digunakan dalam perencanaan bendung dikarenakan hampir semua pengoperasian bendung adalah untuk perhitungan debit besar. Penelitian ini bertujuan untuk menguji dan mengetahui keunggulan bendung bertangga dengan melakukan variasi perlakuan model meliputi sudut kemiringan, jumlah anak tangga dan nilai bilangan Froude. Penelitian ini dilakukan pengujian terhadap dua model tipe bendung yakni bendung ogee dan bendung bertangga pada kondisi aliran tenggelam. Untuk variasi sudut kemiringan pelimpah (θ) yang digunakan 30˚ dan 45˚, jumlah anak tangga (N) 40 dan 20 serta kedalaman kritis terhadap tinggi tangga (yc/h) berkisar 0,70 < yc/h < 3,00. Model penelitian ini menggunakan bilangan Froude (Fr) < 10. Hasil penelitian menunjukkan bahwa faktor gesekan Darcy Weisbach (f) untuk bendung bertangga adalah 0,311 yang mempengaruhi terhadap nilai kehilangan energi. Kadar oksigen terlarut pada aliran bendung bertangga meningkat sebesar 2,011% - 2,846%. Sedangkan nilai kehilangan energi relatif (∆E1/E0) pada bendung bertangga adalah 86,129% dan bendung ogee adalah 72,466%. Peningkatan nilai kehilangan energi relatif akan mempengaruhi terhadap panjang kolam olak di hilir bendung

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