A labyrinth spillway is an overflow spillway to regulate and control flow in canals, rivers and reservoirs. The main hypothesis for the development of such a spillway is to increase the discharge per unit width of structure for a given headwater. This type of structure is often an efficient alternative to a gated-spillway type where either the increase of the flood-passage capacity or the control of the water surface upstream is concerned. This study was aimed to investigate the hydraulic performance of labyrinth spillways of general trapezoidal plan form with simple curved apexes.In the experimental work, twelve spillway models with double cycles were considered using three different curved apexes (R/w=0.15, 0.2, 0.25), each with four different crest heights (w/P=1.5, 2, 3, 4). Based on the cited recommendations, the length magnification was set to a constant ratio of (l/w=3); the crest shape was to be of a semicircular form with simple radius (r=15 mm); and the spillway walls were vertical with the thickness of T=2r. An intensive experiment was carried out over a wide range of flows, providing 720 flow data ranging from free flow to submerged flow conditions. 1D flow equation was presented using combined mathematical and dimensional analysis. A coefficient of discharge, Cd, was introduced to represent the influence of the effective geometric and hydraulic parameters on the flow capacity over the spillway. Modular limit was also controlled to see whether the flow over the spillway would be submerged. The results of the study indicate that the modified curved plan form of the spillway apexes with consistent divergence in the downstream channel introduces a significant improvement in the flow efficiency over the labyrinth spillways. Spillways with narrower curved apexes (i.e. R/w4 0.2), and with the vertical aspect ratio of (24w/P<3) provide more stable and higher hydraulic performance than any other labyrinth plan forms over a wide range of flows (i.e. 0.1<H0/P<0.6). In terms of the flow capacity, the proposed spillway model is shown to be more efficient than other zigzag plan forms (i.e. triangular and trapezoidal shapes) with an identical crest length.

A ‘ spillway’ is a structure used to provide the controlled release of flood water from upstream into downstream area of a dam. As an important component of every dam, a spillway should be constructed strongly, reliably and efficiently to be used at any moment. Labyrinth and stepped spillways are presented as appropriate modifications to those spillways hardly capable of managing the maximum potential discharge. Owing to their nonlinear crests for a given width, labyrinth and stepped spillways have a larger discharge rate than linear-crest spillways at an identical height. Compared to other energy dissipaters, the combination of stepped and labyrinth spillways is known as a very strong energy dissipater. In the following part, the combination of these two structures and their dimensional change for increasing the water-energy dissipation are addressed. To conduct this study, an experimental flume with a 90-degree bend in the Islamic Azad University of Ahwaz was used. In total, 90 experiments were conducted on three different labyrinth-shape stepped spillway models with two different lengths, three different widths, and five different discharges. Analysis of the results showed a greater energy loss reduction in triangular rather than rectangular or trapezoidal labyrinth-shape stepped spillways. In addition, energy loss was greater in labyrinth spillways with two cycles than those with one cycle. Energy loss was increased by raising the Froude number from 0. 05 to 0. 1; in contrast, energy loss was decreased with increasing the Froude number from 0. 1 to 1. 0, which was due to the submergence of steps, a decrease in the roughness of steps and an increase in the intensity of aeration.

Labyrinth spillways are considered as suitable and economic structures because, firstly, their discharge flow rate, under low hydraulic heads, is high, and secondly, they occupy less space. The flow over these spillways is three-dimensional and is influenced by several parameters. This study endeavors to offer a new equation for the calculation of the discharge flow of triangular labyrinth spillways by using the Buckingham Theory, Genetic Algorithm, the equations offered by other researchers and non-dimensional laboratory parameters. To do so, several experiments were carried out in the hydraulic laboratory of the Department of water science at BuAli Sina University in Hamedan. These experiments were done on triangular labyrinth spillways in a straight condition in certain flumes which were 10 meters long, 0.83 meters wide, and 0.5 meters height. To verify the recommended equation, the authors used the information related to the labyrinth spillway design of Bartletts Ferry dam in the US and the equation for triangular spillways suggested by previous researcher. The results indicated that the equation recommended in this study is far more accurate than the previous one.

Introduction: In designing spillways, chutes and stilling basins the dimension of stilling basin will reduce if the energy of the flow dissipates along the chute or spillway. One of the most characteristics of stepped spillways is dissipation of energy along the spillway. Stepped spillways are able to increase the energy dissipation according to their form and geometry. The main problem is to increase the effectivity of the steps on energy dissipation. The aim of this research is to introduce and propose a new form of stepped spillways in order to achieve a higher level of flow energy dissipation during its transport to the downstream. Methodology: In this research hydraulic of the passing flow over stepped spillway is investigated under effect of geometric alteration and change of steps shape to some triangular, trapezoidal and rectangular labyrinths with equal ratio of LT/W=1. 85 (effective length to the spillway width) utilizing FLOW-3D for a skimming flow of the range of 0. 84≤ yc/h≤ 1. 69. All the models utilized in this paper are sketched using AutoCAD® and transmitted into FLOW-3D for simulation. According to using CFD technic, the governing equations are Navier-Stokes equations and continuity equation. This CFD package solves the incompressible Reynolds Navier-Stokes equations using finite volume technic on a meshed domain in order to threedimensional analysis of the flow. The VOF method was used to simulate the free surface of the flow and the RNG k-ε model was used for the turbulence modeling. The VOF is a finite volume method in which the desired region is divided into finer elements and/or control volumes. When the flow has a free surface, some elements are not filled with fluid and some of these cells are partially filled. An appropriate method for defining the condition of the cells is to introduce a parameter (F) that shows part of the element that is filled with fluid. This quantity is named the function of fluid volume. The RNG k-ε model is a two-equation model in which the first equation declares the energy in turbulence (k is turbulent kinetic energy) and the second equation defines the dissipation of turbulent kinetic energy (ε is dissipation in turbulence). The RNG k-ε turbulence model is used because of its ability in the simulation of high computational mesh flows and less dependence to empirical constants in the related equations and also its good performance in flow separation regions. Results and discussion: The results of velocity distribution achieved from FLOW-3D is compared and validated with experimental results of Felder et al. (2012) for steps no. 8, 9 and 10. Also, different models are performed and simulated to select an appropriate and optimal mesh. According to mesh sensitivity analysis and optimum mesh size selection, finally the coarser mesh was selected to be 1. 9 cm (868, 271 mesh elements) and the finer mesh was selected to be 0. 8 cm (1, 336, 622 mesh elements). Totally 2, 204, 893 mesh elements with a relative error of 6. 07% were utilized for simulation and modeling. At the first stage, the results showed that the maximum error of velocity distribution between experimental data of Felder et al. (2012) and numerical simulation of FLOW-3D for the step no. 8 is 8. 58% that indicated good accordance between the numerical and experimental results. At the second stage, it was seen that interference of flow blades because of passing over labyrinth shape of the steps is the superiority of this type of labyrinth stepped spillways. Also, the trapezoidal labyrinth shape shows a better performance in achieving the highest energy dissipation. Conclusion: In the same flow conditions, the rectangular, triangular and trapezoidal shape labyrinth spillway were more effective in velocity reduction by 4. 62%, 12. 21%, and 23. 76% and in energy dissipation by 5. 6%, 13. 1% and 17% than standard stepped spillways respectively. This is because of flow interference and increasing the resistance against the flow in these types of stepped spillways. The water in the skimming flow regime passes over the spillway as a continuous later. In this state, the steps act as some excrescences against the flow. So, the most part of the flow energy in this regime will be dissipated via some rotary flows beneath the false bed. Reshaping the steps as labyrinths, will increase the recirculating region and will produce more rotating flows than the standard stepped spillways. These types of spillways have fewer amounts of the residual head than that for flat stepped spillways. The residual head ratio in these spillways is Hres/yc≈ 2. 57 and in standard stepped spillways is Hres/yc≈ 4. 32. Finally, these types of spillways can be introduced as the next generation of stepped spillways in increasing their efficiency and hydraulic performance.

Labyrinth Spillways are one of the hydraulic structures to regulate and control the flow of water in canals, rivers and reservoirs. In some situations, there is no enough space for increasing the length of the weir to increase the discharge. Therefore, labyrinth spillways are one of the solutions for this problem. If the cycle of linear labyrinth spillway is located on the curve, then the crest length increases, and as a result the inlet flow condition is improved and the hydraulic coefficient increases. In this laboratory study, the discharge coefficient for different downstream wall slopes is studied.2 different spillways with side-wall angle (6o and 11/25o) and 4 downstream wall slope are studied. The results indicate that downstream wall sloping reduces the hydraulic coefficient. Discharge coefficient variations with downstream slope and flow height on spillway crest were studied. Different equations were presented to estimate the discharge coefficient of the spillway by considering the downstream slope.

In this research, optimal design of trapezoidal labyrinth spillway has been investigated using Gray Wolf Optimization (GWO) algorithm with respect to hydraulic conditions. By choosing the assumed volume of spillway concrete as the objective function, after several running the model and trial & error, parameters of the algorithm such as iteration, number of wolves and the penalty coefficient were determined to be 1000, 30 and 1011, respectively and by five times of testing, at the 996th iteration, the optimal response of objective function was achieved. The obtained value from the proposed algorithm was compared to the real value and also the results of the Cuckoo Search (CS) algorithm, Genetic Algorithm (GA) and Differential Evolution (DE) in previous studies. Using GWO algorithm for designing the considered dam's spillway, made reduction of 40. 928% in amount of assumed concrete volume and increase the rate of discharge to 10. 71% than to real value, which showed a better performance compared to above algorithms. Significant reduction of the consumed concrete volume in the proposed spillway by using GWO algorithm indicates ability and necessity of using this algorithm to solve optimization problems in the field of spillways.

Considering the importance of designing the dam spillways in order to provide optimal dimensions while maintaining their optimal performance, an approach using weed algorithms (IWO) and water cycle (WCA) suggested to multi objective optimization of the trapezoidal labyrinth spillways. In designing the labyrinth spillways, the optimal model is to achieve a model with the highest possible flow passing through the spillway (efficiency) during flood times and the smallest possible volume, which represents the least amount of concreting and construction costs. In this regard, the effectiveness of two algorithms on the labyrinth spillway of the UTE dam investigated, and three different scenarios considered to evaluate the effect of different parameters on the results of optimization. The GD’s value for the IWO algorithm is lower than the WCA ones; on the other hand, the WCA algorithm has the most value of standard deviation and average repetition based on the GD criteria. This shows that IWO algorithm has high accuracy. Based on the S criteria, the average value in IWO equals 0.102 and in WCA is 0.367, so, regarding to the criteria’s values, IWA algorithm has more accuracy and convergence ratio comparing to the WCA algorithm in multi objective optimization of the labyrinth spillways. Applying the multi objective optimization method can provide a set of optimized answers for designers So that they would be able to select a suitable design in every condition and based on the defined values of costs and efficiency. In evaluating the proposed scenarios, the third one provides better optimal solutions than the second scenario by examining the optimal value for more variables. As a result, the variables of the discharge coefficient and the wall thickness have a significant effect on the optimization of the labyrinth spillways.

Morning glory spillway is one of the spillways that used to passing of flood from high to low level. This spillway is used in the reservoir dams that are placed in narrow valleys and in many locations with high slope in reservoir walls. In the Morning glory spillways, the vortex flow can reduce discharge, discharge coefficient and the performance of spillway. The zigzag spillway, as another type, is introduced as a proper option for compensating the problem of passing maximum possible flow rate, usually encountered by spillways. In the present study, the experimental results of a physical model were used to develop a hydraulic design with squire and circle inlet and analysis method for Labyrinth Morning Glory Spillway. The analysis of experimental data in circle and square inlet showed, that increase in length of spillway and zigzag, causes decrease in the discharge coefficient. Finally the result of effect spillway inlet on flow rate demonstrate that discharge coefficient in square inlet is more than circle, whereas without vortex breaker.

Introduction: Spillways are important hydraulic structures that are constructed to release flood discharge in the dam reservoirs. Spillways must have sufficient capacity, efficiency and safety in the passage of floods, and in addition it must have economic justification. One of the effective and economical solutions to increase the discharge capacity within a certain width of the spillways is to use labyrinth spillways. In most cases, it is observed that it is not possible to increase the length of the spillway due to the site conditions. In this case, using a labyrinth spillway to increase the length of the crest can be a good solution. As the result, it increases the efficiency and discharge capacity. In equal congress type of spillway, the overlap of the falling flows and the resulting compression of the flow during the spillway, reduces the efficiency and discharge coefficient. In this study, the reduction of falling flows interference, and the congressional spillways with the length of unequal congresses have been studied and compared. Methodology: In this study, the labyrinth spillways with the length of unequal congresses in two types A and B in the flume of the hydraulic laboratory of Bu Ali Sina University have been investigated. All models includes of 5 cycles. The effective length of heights are equal to 336 cm and 10 cm, respectively. Thus, the effect of these two parameters on all models are the same. In this research, two type of congress weirs have been considered. The first type (A) consists of 5 congressional weirs with different congress lengths, so that the closer we get to the center of the weir, the length of congress increases, and the second type (B) consists of 5 congressional weirs with different congress lengths. So, the closer we get to the center of the weir, the length of congress decreases, and the longest congress in this type is the first and last congress. To measure the water depth a point depth gauge with an accuracy of 0. 1 mm has been used. To conduct this research, 10 laboratory models of labyrinth weirs with different congress lengths and one laboratory model of labyrinth weir with the equal length of congresses have been constructed for comparison with other models. In each type, the flow rate and water depth on the labyrinth crest were carefully monitored. This operation was repeated 3 times for each type to minimize the errors caused by the test and the average data of each type was used for analysis. Results and Discussion: The results of this study in all labyrinth spillways with unequal congress lengths, show that by increasing the Ht/P ratio, the value of C decreases and in each weir for the lowest value of Ht/P has the highest discharge coefficient or C and with the beginning of falling flows and their interference and subsequent submergence, the overflow discharge coefficient is drastically reduced. This reduction occurs with greater intensity for labyrinth weirs with unequal congress lengths than for labyrinth weir with equal congress lengths. It was found that, the discharge coefficients of the labyrinth weirs with different congress lengths in high discharges are not much different from each other and shows the same performance. According to the results of this study, in general, the efficiency and discharge coefficient of the spillways of congresses of type A is better than type B. It is also observed that the discharge coefficient of labyrinth weirs with different congresses lengths in high discharges are not much different from each other and show the same performance. Conclusions: The results show that if the total length of that part of the congresses which is higher than the adjacent congress and there is no flow in front of it reaches 25% of the total effective length, it will increase the efficiency and improve the discharge coefficient. If it is more than 25%, the spillway efficiency will be reduced and the discharge coefficient will fall. Also, in the best type in this research, the discharge coefficient in the spillways of unequal congresses has increased by 40. 7% compared to equal congresses.

Labyrinth weirs can be used to increase outlet capacity for a given spillway crest elevation and length or to increase storage by raising the crest while maintaining spillway capacity. Downstream scour dimensions of spillway are important parameters in designing of this structures. By combining the spillway and the gate, two major problems of sedimentation on upstream of spillway and the accumulation of waste materials can be solved. In this study, totally 12 experiments were carried out in 3 different discharges, 10, 15 and 20 liters per second. In this study overflow and flow simultaneously from top of weir and gate for two linear and labyrinth spillway were explored. A layer sand with d50=1 mm and thickness of 15 cm were covered at downstream apron to make a mobile bed. Results showed that by increasing the particle Froude for a constant depth, the maximum scour depth and scour hole length increased. Also it was found that when the flow passed through the spillway and gate simultaneously, in both labyrinth and linear spillway, the maximum scour depth and scour hole length increased with respect to discharge. Transverse profiles at the maximum scour depth also showed that there was a relative symmetry in the case of a linear spillway without a gate, and in this case the bottom profile could be considered as two-dimensional. The maximum scour depth and scour hole length increased with increasing discharge, and its magnitude in labyrinth spillways, was less than that in linear spillways.