Piano Key Weirs Research Articles

Temporal evolution of scouring downstream of a trapezoidal piano key weir

ABSTRACT This study experimentally investigated the temporal evolution of the scour parameters downstream of a trapezoidal piano key weir. The densimetric Froude number (Fr d50) in the range of 0.39–0.57 and the relative vertical distance of the sediment bed level to the weir toe (Δz/P) in the range of 0.025–0.5 were taken into consideration. In general, with an increase in Fr d50, the scouring rate, maximum scour depth, scour hole area and scour hole volume enhanced over time. The increases in the scour parameters were greater at the initial stages of the tests. About 87, 80, 65 and 70% of the maximum scour depth, weir toe scour, scour hole area and scour hole volume occurred within the first 20% of the durations of the tests, respectively. Any increase in Fr d50 and Δz/P augmented the scour depth at the weir toe. The results also indicated that the distance of maximum scour depth from the weir increased for greater values of Δz/P and Fr d50. The amounts of scour downstream of the outlet keys were greater than those downstream of the inlet keys. The trend of variations of the longitudinal bed profiles remained nearly unchanged over time. New equations were developed to predict the temporal variations of scour parameters, with acceptable accuracy.

Experimental and Simulation Studies on Water Discharge Coefficients of Rectangular Piano Key Weirs

The piano key weir (PKW) is a developed type of labyrinth spillway with the ability to transfer large amounts of discharge by keeping executive costs constant. In this study, the parameters affecting the discharge coefficient of nine models were evaluated using physical models and simulations by Flow-3D software. The PKW models included: PK1.0, PK1.1, PK1.2, PK1.3, PK1.4, PK1.5, and PK1.6 representing the width ratios of the inlet (Wi) to outlet (Wo) keys of 1.0, 1.1, 1.2, 1.3, 1.4, 1.5 and 1.6 respectively and the other two models were PKT (PK1.1 with a thicker wall) and PKTP (PK1.1 with a thicker wall and an enhanced crown). According to the results of experimental and simulation evaluations, the model of PK1.4 was selected as the optimal model, which increased the discharge rate by 30% compared to the control weir. Moreover, increasing

Discharge Estimation over Piano Key Weirs: A Review of Recent Developments

The piano key (PK) weir has advanced over the labyrinth weir to increase the discharge capacity. Piano key weirs exhibit nonlinear flow behavior and are easy to place on the existing spillway or newly constructed dam with less base area. Various investigators are given equations to calculate the discharge coefficient for free and submerged flow conditions. The study focuses on reviewing the impacts of the PK weir geometry on the weir flow discharge coefficient, including weir length and height, upstream and downstream key widths, and apex overhangs. In this study, all possible aspects of PK weirs were briefly reviewed. From sensitivity analysis, it is observed that the discharge coefficient of the PK weir is more sensitive for the L/W dimensionless ratio followed by the B/P ratio. L is total length of the weir crest, W is width of the weir, B is total width of PK weir and P is height of the weir. This review paper is intended to serve as an accessible resource for hydraulic structures researchers and hydraulic engineering professionals alike interested in the hydraulics of PK weirs.

Numerical and experimental analysis of scour downstream of piano key weirs

Numerical and experimental analysis of scour downstream of piano key weirs

Application of a multi-objective optimization model for the design of Piano Key Weirs with a fixed dam height

Piano Key Weirs (PKWs) have recently been used as new or rehabilitation options in the world because of their advantages in hydraulic performance and construction costs. However, designing an efficient PKW is challenging due to a large and complex set of geometric and hydraulic parameters. Therefore, reaching an optimal PKW design depends on the examination of various geometric combinations and hydraulic parameters. In this study, we applied a multi-objective optimization model known as Non-dominated Sorting Genetic Algorithm-II to determine an optimal design by maximizing hydraulic discharge while minimizing the volume of the concrete. Here, we evaluated the capability of our approach in two separate case studies, one which represented as a rehabilitated weir and other as a new design. Both studies show that the developed approach could significantly reduce the concrete volume per unit of discharge. Moreover, the results show similar patterns in terms of the hydro-economic behavior of the model, which were discussed in three distinguished regions. The unique characteristics of these regions were elaborated, and their most cost-effective values of design parameters were identified. Finally, we discussed how the proposed model and findings of this study could be used for improving the preliminary design of PKWs in practice.

Experimental and Numerical Study of the Effect of Zigzag Crests with Various Geometries on the Performance of A-type Piano Key Weirs

Experimental and Numerical Study of the Effect of Zigzag Crests with Various Geometries on the Performance of A-type Piano Key Weirs

Study of hydraulic characteristics of trapezoidal piano key side weir using different approaches

Abstract Side weirs are widely used in hydraulic engineering applications. The studies on the subject have been generally focused on classical and labyrinth side weirs. However, the same is not true for piano key side weirs (PKSW) in a straight channel. The piano key weir (PKW) has high discharge capacity compared with classical weirs. In this study, the hydraulic characteristics of a trapezoidal piano key side weir (TPKSW) in straight channels were investigated experimentally. In all experiments, the hydraulic characteristics of nine TPKSW models were studied extensively using the De Marchi, Domínguez and Schmidt approaches in the subcritical flow regime, with Froude number range 0.12 < F1 < 0.87. The results show that a TPKSW provides better performance compared to traditional rectangular and triangular labyrinth side weirs. Specifically, for the 0.12 < F1 < 0.4 condition, the efficiencies of a TPKSW and trapezoidal labyrinth side weir are close to each other. A trapezoidal labyrinth side weir is more efficient than a TPKSW at larger Froude numbers. The discharge capacity of the TPKSW is 2.9 to 12 times higher than that of the rectangular side weir. Scatter diagrams were obtained for CPW and F1 numbers using various approaches available in the literature. The diagram generated by the De Marchi approach has much less scattering, compared to the diagrams generated by the Domínguez and Schmidt approaches. It has been determined that TPKSWs are an effective type of side weir in lateral flows. Lastly, an empirical equation was obtained for the discharge coefficient, which is in good agreement with the experimental data.

Computation of energy dissipation across the type-A piano key weir by using gene expression programming technique

Abstract Energy dissipation across the weir and dam structures is a vital economic and technical solution for designing the downstream morphology of any hydraulic system. Accurately estimating the energy over any hydraulic system using traditional empirical formulas is tedious and challenging. Consequently, employing new and precise techniques still in high demand is crucial. In this study, the authors developed an empirical model for estimating the residual energy downstream of the type-A piano key weir (PKW) using gene expression programming (GEP) by considering six non-dimensional parameters: headwater ratio, magnification ratio, inlet to outlet width ratio, inlet to outlet key bottom slopes, inlet to outlet overhang portions and the number of cycles. The performance of the proposed models has been compared to empirical equations using the statistical factors coefficient of determination (R2), concordance coefficient (CC), and root mean square error (RMSE). The computed relative residual energy values using the proposed models are within ±10% of the observed ones. The proposed GEP model predicted the relative residual energy satisfactorily, with coefficients of determination of R2 = 0.978 for training, 0.980 for testing and root mean square errors (RMSE) of 0.032 and 0.029 for the training and testing datasets, respectively.

The influence of inlet to outlet width ratio on The hydraulic performance of piano key weir (PKW-type A)

Abstract A piano key weir (PKW) is a modified version of non-linear weirs and it can be obtained via amending the centerline length of the weir by a small footprint. It is developed to increase the hydraulic performance of the linear weirs via increasing the pass discharge and the energy dissipation. A laboratory investigation is conducted on five physical PKW (Type A) models to investigate the effect of inlet to outlet width ratio (Wi/Wo) on the hydraulic performance of PKWs. The results showed that the (Wi/Wo) ratio has a predominant influence on the hydraulic performance of PKW. It was found out that the best hydraulic performance was obtained with Wi/Wo ratio equal to 1.25 among other investigated Wi/Wo ratios because the discharge coefficient was the highest for the given discharge and head. Further, the results revealed that the variation of Wi/Wo ratio from 1.25 had a negative impact on both discharge coefficient and efficiency. It was found out that the percentages of reduction in discharge coefficient when Wi/Wo=0.8, 1, 1.5% and 2 were 11%, 6%, 2% and 8%, respectively in comparison with the Wi/Wo=1.25. Similarly, for these Wi/Wo ratios, the percentages of reduction in discharge decrease by 11%, 6.5%, 2.35% and 9%, respectively, relatively to Wi/Wo=1.25. The linear regression equations' coefficients for the PKW models varied from 0.983 to 0.994, which means the performance of the models are good for the given Wi/Wo ratios.

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.

Gene expression programming for computing energy dissipation over type-B piano key weir

Computation of energy dissipation over weir (or spillway) structures is vital to solving numerous engineering problems, notably during floods. Therefore, an accurate estimation of the energy dissipation at the base of the spillway is essential. The spillways must be designed to spill large amounts of water at high efficiency with high structural performances without causing any damage to the structure or its surroundings. Energy dissipation over weir structures is difficult to predict using conventional formulas based on empirical methods. Consequently, new and accurate techniques are still highly demanded. In this study, Gene Expression Programs (GEP) were used to estimate the relative energy dissipation at the base of type-B Piano Key Weirs (PKWs) by taking three non-dimensional parameters into account: headwater ratio, magnification ratio, and the number of cycles. The performances of the GEP model were compared with empirical equations based on statistical factors coefficient of determination (R2), and root mean square error (RMSE). The computed values of the relative residual energy using the proposed models are within ±5% of the observed ones. Results indicate that the proposed GEP model predicted the relative residual energy satisfactorily with the coefficient of determination (R2 = 0.9979 for training, 0.9980 for testing) and root mean square error (RMSE) of 0.0099, 0.0092 for training and testing datasets, respectively.

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.

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 .

Evolution of local scour downstream of Type A PK weir in non-cohesive sediments

Abstract A large-scale piano key weir laboratory study was conducted to investigate the evolution of the scour process occurring in the downstream basin for two non-cohesive granular bed materials, including the analysis of scour-hole geometry and patterns at equilibrium. It was observed that hydraulic conditions, particularly tailwater level, significantly affect the scour mechanisms and equilibrium morphology, eventually resulting in scour depths that exceeded the weir height. Unprecedented insights on the scour dynamics are also provided, along with tools to estimate the time evolution and maximum scour depth, its location in the streamwise direction, and the maximum scour length.

Hydraulic Design and Analysis of Piano Key Weirs: A Review

Hydraulic Design and Analysis of Piano Key Weirs: A Review

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.

Energy dissipation of flow over the type-B Piano Key Weir

Piano Key Weir (PKW) is an evolution with an efficient implementation over conventional labyrinth weir, especially at low heads. It is used as the crest of spillways and specific flow regulation applications for overflow control structures. The effects of a PKW on the downstream flood regime have not yet been thoroughly studied; only a few studies have focused so far on the downstream characteristics of the PKWs. The consideration of energy-dissipation is the main component of downstream elements for all hydraulic structures. Therefore, there is a need to log and assess details on the energy dissipation of the PKWs. This paper presents the results of the experimental study to investigate the energy dissipation at the base of type-B PKW under free-flow conditions in a rectangular channel. According to the current study's findings, the type-B PKWs show a higher energy dissipation efficiency at low heads than other nonlinear or ordinary weirs, but dissipation efficiency decreases as the discharge or head over the weir increases. The energy dissipation was found to decrease with the increasing magnification ratio and relative width ratio; however, the energy dissipation was found to increase with increasing cycle number (for a constant-width channel). In addition, the sensitivity of the weir, i.e., using the steps at the outlet key instead of the slopping floor, increases the efficiency of energy dissipation for low head discharges about 6.43% while decreasing by 2.05% for higher head discharges.

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%.

Erratum for “Sediment Movement over Type A Piano Key Weirs” by Binit Kumar, Subhojit Kadia, and Zulfequar Ahmad

Erratum for “Sediment Movement over Type A Piano Key Weirs” by Binit Kumar, Subhojit Kadia, and Zulfequar Ahmad