Influence of the Semicircular Cycle in a Labyrinth Weir on the Discharge Coefficient

Labyrinth weirs are particularly well suited for spillway rehabilitation where dam safety concerns, freeboard limitations, and a revised and larger probable maximum flow have required replacement or modification of the spillway. Labyrinth weirs with multiple crest elevations can be used in spillway design to confine base flows to a section of the crest and/or satisfy discharge hydrograph requirements. Labyrinth weirs provide higher discharge capacity than conventional weirs, with the ability to pass large flows at comparatively low heads. Over past 50 years many research investigations have considered the hydraulic performance of labyrinth weirs, particularly as dependent on the geometric features. The previous work has improved the design basis for such weirs. In the present study, discharge coefficients were experimentally determined for both sharp crested semi-circular labyrinth weirs and trapezoidal labyrinth weirs of side wall angle ( α =37 0 ). A comprehensive laboratory study including 9 models was conducted to determine the discharge coefficient of the semi-circular labyrinth weirs. It was found that from this experimental study the discharge coefficient of the circular labyrinth weir is higher than that of the linear weir, but lower than that of the trapezoidal weir.

Labyrinth weirs provide higher discharge capacity than conventional weirs, with the ability to pass large flows at comparatively low heads. Labyrinth weirs are primarily used as spillways for dams where the spillway width is restricted. In recent years, many research investigations have considered the hydraulic performance of labyrinth weirs, particularly as dependent on the geometric features. The previous work has improved the design basis for such weirs. However, their design still requires experimentally derived and generalized performance curves. It is especially important to observe the behavior of the weir nappe to ensure the design provides hydraulic optimization and to account for pressure fluctuations, possible vibrations, resonance effect, noise and flow surging. In the present study, discharge coefficients were experimentally determined for both circular labyrinth weirs and sharp crested trapezoidal labyrinth weirs of varying side wall angle (α). Additional studies were completed with nappe breakers included to reduce the impact of vibration on the labyrinth weirs. In general, the test data indicated that nappe breakers placed on the trapezoidal labyrinth weirs and circular labyrinth weirs reduced the discharge coefficient by up to 4% of the un-amended weir.

The discusser would like to thank the authors for presenting discharge coefficient data for nonvented trapezoidal labyrinth weirs with quarter-round and half-round crest shapes for sidewall angles of 6, 8, 10, 12, 15, 20, and 35°. Different sets of weir models having weir height P 1⁄4 15.24 cm and P 1⁄4 30.48 cm are studied by the authors. The work by the authors in accomplishing the regression equations applicable to discharge coefficients is really appreciated. These accurate equations are applicable to the trapezoidal labyrinth weirs that have sidewall angles of 6, 8, 10, 12, 15, 20, and 35° with head to weir height ratio of 0.05 ≤ Ht=P ≤ ∼0.8 − 0.9. The regression equations presented by the authors are selected over polynomial relationships because of their improved data representation (R ≥ 0.99) and extrapolation performance (they remain well behaved up to Ht=P ≤ 2.0). It worth noting that for other wall angles between 6 and 35°, the interpolation procedure should be employed to obtain the discharge coefficients. The application of the linear interpolation technique for determining the values of the discharge coefficients for intermediate values of the sidewall angle seems to be inappropriate because of the nonlinearity of the discharge coefficient curves. However, in practice it is very suitable to have a single equation applicable to any sidewall angle between 6 and 35°. Thus, the discusser would like to introduce unified regressionbased equations for discharge coefficients (based on experimental data presented in original paper), which are valid for any sidewall angles between 6 and 35°. For this, the head to weir height ratio (Ht=P) and sidewall angle (α) are considered as independent variables in the proposed equations for discharge coefficients. It should be noted that the thickness and the crest curvature of the weirs may influence the flow pattern and cause different values of the discharge coefficient (Azimi 2013). This investigation attempts to find a generalized and unified equation for the discharge coefficient of the labyrinth weir. The proposed equation renders the authors’ study more valuable and will be accurate and easy to use in practical situations.

Conclusions To conclude, this discussion provides unified equations for the coefficient of discharge of labyrinth weirs, which can be applied across a spectrum of sidewall angles (α ¼ 8–30°) for the prediction of discharge. The proposed equations render the authors’ work more valuable and complete from a practitioner’s perspective. Thus, they can be directly used for the predictions of discharge by real prototype dams. The discussion also reveals that a labyrinth weir with a smaller side wall angle achieves its maximum flow capacity at a relatively lower water head above the crest than a labyrinth weir with a higher side wall angle. Because the occurrences of nappe interference and local submergence (Crookston and Tullis 2012) in labyrinth weirs with low side wall angles cause a reduction in the discharge capacity, it can be inferred that labyrinth weirs are suitable for the low water head conditions above the crest; hence, they need to be designed for the same condition to achieve economy. However, it is suggested to find a suitable modification in the upstream apex of the labyrinth weirs that can avoid or delay the occurrence of the nappe interference phenomenon to preserve the ability of delivering increased discharge with increasing Ht=P value over a relatively wider range of water head above the weir crest.

Most of the studies on labyrinth weir were carried out in the laboratory, and regression models have been developed for discharge coefficient in terms of pertinent independent parameters. It is difficult to obtain an exact analytical solution to the head discharge relationship due to the existence of 3D flow. Consequently, various forms of soft computing techniques are used as an appropriate alternative to achieve greater accuracy in developing a discharge prediction model. In the present study, support vector regression (SVR) has, therefore, been implemented to develop a discharge coefficient prediction model for a triangular labyrinth (TL) weir using a sizeable amount of laboratory data available in the literature. An attempt has also been made to obtain a simple discharge coefficient equation using the same data based on the non-linear regression (NLR) approach for field application. A comparative study has been carried out to assess the accuracy of the discharge coefficient models obtained in the present study and those reported in the literature. Sensitivity analysis has been made to study the influence of individual parameters on the discharge coefficient. The accuracy of different discharge coefficient prediction models was also tested for the data of prototype labyrinth weir and appropriate models were recommended for the field application.

A labyrinth weir is a polygonal overflow weir that is characterized by its hydraulic performance and distinct geometric shape (triangular, trapezoidal or rectangular cycles). The present study provides new knowledge and design information on the performance and operation of adaptive neuro-fuzzy inference system (ANFIS) and gene expression programming (GEP) techniques for predicting discharge coefficient of labyrinth weirs in a flume. Discharge coefficient, Cd, was considered as a function of headwater ratio, upstream Froude number, magnification ratio, sidewall angle, apex ratio, and cycle width ratio (dimensionless parameters). The records obtained through 300 laboratory data sets were used to determine the Cd of labyrinth weirs. The results showed that the best GEP model determined the Cd values of the normal and inverted orientation labyrinth weir with a RMSE of 0.0139, 0.590, DC of 0.977, 0.852 and R of 0.996, 0.923, respectively by using the four dimensionless parameters of Fr, HT/P, Lc/W and A/w as input variables. The best ANFIS model determined the Cd value of the normal orientation labyrinth weir by using all six dimensionless parameters (RMSE = 0.0110, DC = 0.964, R = 0.987) and inverted orientation labyrinth weir by using three dimensionless parameters of HT/P, α, and w/p as input variables (RMSE = 0.0290, DC = 0.952, R = 0.987). The results of sensitivity analysis showed that Fr in the GEP model and Fr and HT/P in the ANFIS model are the most effective variables for determining Cd for normal and inverted orientation labyrinth weirs, respectively. It was found that when low headwater ratios were eliminated from analysis, performance accuracy of the models was improved.

A trapezoidal labyrinth weir is a general transverse hydro-structure typically placed across rivers that causes longitudinal sediment discontinuity and affects riparian ecological system. A sediment exclusion labyrinth (SEL) weir is a modification designed to increase sediment exclusion from upstream to downstream over or through it. Hydraulic model experiments were carried out in straight rectangular cross-sectional open channel (15 m in length and 0.82 m in width). Four different shapes of weirs were examined. type 1 was a general labyrinth weir, whereas types 2–4 were SEL weirs with an inclined bottom slope (type 2), open slots (type 3), and reversed-wedge type holes (type 4). Standard sand (Jumunjin, Korea, d50 = 0.56 mm, σg = 1.48, SG = 2.65) was uniformly supplied upstream using an in-house grooved drum, and sediment exclusion efficiency was calculated from the ratio of sediment amount to excluded sediment yield for each type of weir. Higher efficiencies were founded in all SEL weirs compared with the sediment exclusion efficiency of the type 1 weir. In particular, type 2 and type 4 weirs were easy to construct and their flow patterns and hydraulic performance were similar to those of type 1. Finally, their sediment exclusion efficiencies were higher under a normal water level (Fr ≤ 0.2), whereas the type 3 weir was the pattern favorable for a high water level (Fr > 0.2) because its discharge capacity was significantly higher. Sediment exclusion characteristics were analyzed in terms of flow rate based on the decomposition analysis of residual sediment particle size distribution. It is expected that the results from this study will be used to design SEL weirs as basic materials if more hydrodynamic parameters are studied and combined with field monitoring.

Labyrinth Weir (LW) is a popular control structure that passes a significantly higher flow rate compared to the linear weirs. In order to approach the optimal design of a trapezoidal LW, a multi-objective problem is defined to concurrently minimize the LW consumed concrete volume and maximize its discharge capacity. Simultaneously, a Radial Basis function Neural Networks (RBFNN) is designed and used for estimating LW discharge coefficient (Cd) according to the existing experimental results. An improved multi-objective particle swarm optimization (MOPSO) algorithm named TOPSIS Fuzzy MOPSO (TFMOPSO) is proposed to solve the LW optimization problem. This algorithm utilizes the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) to rank the solutions, while a fuzzy inference system is developed to select the algorithm strategy for finding two leaders among the non-dominated solutions. The performance of the proposed TFMOPSO has been tested on the optimization problem of the LW of the Ute dam. The results of TFMOPSO, along with three other state-of-the-art multi-objective algorithms, are explored in terms of hypervolume, coverage, and spacing metrics. It is demonstrated that the TFMOPSO outperforms other algorithms and studies for solving the LW multi-objective optimization problem for the case of Ute dam. Also, RBFNN is found to be one of the most appropriate approaches among studied algorithms in estimating the discharge coefficient of LW, while Pareto optimal solutions from TFMOPSO exhibit a significant improvement compared to the original design of Ute dam LW.

The discharge capacity and hydraulic efficiency of a labyrinth weir can be increased with an Arced cycle configuration. An Arced geometric layout for labyrinth weirs is presented, including nomenclature for arc-specific geometric variables. Discharge coefficients as a function of HT/P for half-round trapezoidal Arced labyrinth weirs with 6 and 12° sidewall angles are also presented. The hydraulic performance of the tested Arced labyrinth weir geometries is compared to Projecting and in-channel labyrinth configurations and to an arced weir (horseshoe weir) with a half-round crest, including the effects of approaching flow conditions and local submergence. Differences between geometrically similar and geometrically comparable Arced labyrinth weirs are identified and discussed.

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

Recently, many research studies have focused on labyrinth weirs' hydraulic performance, especially as dependent on engineering features. In the current study, the hydraulic properties of flow over labyrinth triangular weirs models (from the upper perspective) with sharp crest have been experimentally studied and compare their efficiency with suppressed rectangular weirs (conventional weirs). Twelve fiberglass models are developed for this reason and tested in a 6m in length, 30cm in width, and 40cm height in laboratory flume, nine models were constructed for triangular labyrinth weirs and three models were constructed for suppressed rectangular weirs, Three alternative heights (p=15, 20, and 25cm) were employed in this research, for each height, the vertex angle (θ) changed three times (60օ, 90օ, 120օ), and for each one of these weirs was used, seven different discharge were approved. The overall tests in this study were 84. The dimensionless parameters on which the discharge coefficient (Cd) is dependent were obtained using dimensional analysis. parameters were plotted. According to this experimental present study, as compared to linear weirs, labyrinth triangular weirs shown to be more hydraulically efficient. Also, the height of the weir (P) has effects on the discharge coefficient, where (Cd) increased with decreasing (P). Also, the vertex angle of triangular labyrinth weirs(θ) has a major influence on discharge coefficient and on weir performance, where the discharge coefficient raises when decreases the value of angle(θ), in another means, when the angle decreases gave an increase in the path of the flow, where it gave the triangular labyrinth weir with an angle of 60o the discharge coefficient reached its greatest value (2.55), followed by the weir with an angle of 90o and 120o respectively. In other words (a small vertex angle gives more length effective (Le) to the weir) and this leads to an increase in flow capacity or performance for the weir.

A performance comparison of the meta model methods for discharge coefficient prediction of labyrinth weirs

The spillway capacity can be adjusted to increase the crest of spillway length, or increasing the coefficient discharge or effective head, or any others permutation of these approaches. In a standing spillway, a labyrinth weir constructing is a case of an active technique for increasing the length of spillway crest and as resultant increase the capacity of discharge (up to 3-4 times) for the identical effective head. Therefore, labyrinth weirs are well-matched to the sites. There are many effective factors such as width to the height of the weir which is called a vertical aspect ratio (w/p), head of water to height of crest ratio (Ht/p), angle of the side wall (α), and conditions of channel that effect on the weir capacity and labyrinth weir hydraulic design of. In this paper four different geometric variations applied to a two cycle of sharp crested trapezoidal labyrinth weir under free flow condition which include changing of vertical aspect ratio (w/P) (width to height ratio) that have effects on the hydraulic efficiency of the labyrinth weir and state the effect of the hydraulic parameter Ht/P on the coefficient of discharge (Cdw ) over weir. It was concluded that decreasing w/P has affirmative effect on the discharge capacity. On adverse it has influence of decreasing the discharge coefficient by about 20% (when increasing w/P to 1.5), while increasing it to 2.0 and 2.5 will cause more reduction to Cdw ranging from 32% to 25% for w/P=2.0 & 40% to 35 for w/P=2.5. The smaller values of the head Ht provide more discharge coefficient.

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

Labyrinth weirs are complex hydraulic structures. They have been widely used as a water regulator and to increase discharge in channels and spillway dams. Labyrinth weirs are an economical and effective method to pass large floods. In addition, they are used to reduce the requirements of the structural footprint. These features make them an interesting and appropriate choice to increase the capacity of discharge. Several factors affect the discharge capacity and the hydraulic performance of labyrinth weirs, including water level to crest height ratio, angle of sidewalls, apex width, conveyance channel conditions, and vertical aspect ratio. The present paper aims to summarise the most relevant knowledge of the hydraulic characteristics of the labyrinth weirs reported in previous articles. The importance of the present study is to provide a better understanding of how these weirs operate, in addition to which future studies deserve further investigation. The results demonstrated that some parameters still need further investigation. Also, energy dissipation over the labyrinth weir needs further investigation with different weir geometry. Furthermore, the results showed that common design equations did not take into account all parameters affecting labyrinth weir performance, including geometries, flow conditions, site conditions, and scale effect. In addition, machine learning techniques need further study.