Piano Key Research Articles

Hydraulic assessment of different types of piano key weirs

ABSTRACT Piano Key Weir (PKW) is a non-linear weir with a small foundation footprint that allows large discharges through a narrow channel. The presence of overhangs classifies it into A, B, C, and D. For different PKW types, this study aims to assess the discharge, hydraulic characteristics (flow regimes, water surface profile, and nappes interference), and energy dispersion. This study employs the FLOW-3D software and validated by comparing experimental types A and D PKW with numerical simulations. Experimental and simulation results agreed well, with lower MAPE values for both types. After that, eight simulations for each PKW type were run, with headwater ratios (H t /P) from 0.13 to 0.85 (H t : total upstream head above crest, P: PKW height). Regarding discharge performance, type-B was superior to all other PKW types at lower heads (H t /P ≤0.40) due to longer upstream overhangs. While at higher heads (H t /P > 0.40), type-A became the highest PKW type. Since PKWs disperse energy more effectively than linear weirs, they acquire new performance as energy dissipators. Type-C had the highest energy dispersion rate, followed by type-A, type-D, and type-B. Finally, an empirical equation was provided to predict energy dispersion rates over PKW types as a function of discharge coefficient.

Hydraulic performance analysis of piano key weirs with curvilinear keys: a numerical and experimental study

ABSTRACT A significant number of dams worldwide are very old and thus require a reassessment of maximum flood discharges due to siltation and climate change effects. The Piano Key Weir (PKW) is a relatively new labyrinth-type weir that has emerged as a viable solution for dam rehabilitation and new projects with space constraints. While various studies have been conducted in the past to investigate the influence of geometrical parameters of PKW, there is a lack of information regarding the effect of non-linear slope profile of keys on the discharge efficiency. In this paper, ogee profiles have been introduced in the outlet keys to study their influence on the discharge coefficient. The experiments were performed at the Hydraulics Laboratory, IIT Roorkee, India, using a flume 15 m long, 0.39 m wide and 0.52 m deep. These experiments involved four PKW models with different slope profiles in the outlet key. The results of the laboratory studies and RANS model simulations indicate that the PKW models with ogee shaped outlet keys are more efficient than the linear shaped counterpart for heads higher than their design head. The maximum increase in discharge coefficient for the PKW models with curvilinear outlet keys was 9%.

Investigating the Energy Dissipation Mechanism of Piano Key Weir: An Integrated Approach Using Physical and Numerical Modeling

The enormous energy carried by discharged water poses a serious threat to the Piano Key Weir (PKW) and its downstream hydraulic structures. However, previous research on energy dissipation in PKWs has mainly focused downstream effects, and the research methods have been largely limited to physical model experiments. To deeply investigate the discharge capacity and hydraulic characteristics of PKW, this study established a PKW model with universally applicable geometric parameters. By combining physical model experiments and numerical simulations, the flow pattern of the PKW, the discharge at the overflow edges, and the variation in the energy dissipation were revealed for different water heads. The results showed that the discharge of the side wall constitutes the majority of the total discharge at low water heads, resulting in a relatively high overall discharge efficiency. As the water head increases, the proportion of discharge from the inlet and outlet keys increases, while the proportion from the side wall decreases. This change results in less discharge from the side wall and a consequent reduction in the overall discharge efficiency. The PKW exhibits superior energy dissipation efficiency under low water heads. However, this efficiency exhibits an inverse relationship with an increasing water head. The overall energy dissipation efficiency can reach 40% to 70%. Additionally, the collision of the water flows inside the outlet chamber and the mixing of the overflow jet play a primary role in energy dissipation. The findings of this study have significant implications for hydraulic engineering construction and PKW operational safety.

Experimental investigation of flow splitters' impact on the hydraulics of Piano Key Weirs

Piano Key Weirs (PKWs) have gained significant attention due to due to challenges associated with nappe oscillation in their flow dynamics. This experimental study explores the effectiveness of flow splitters—specifically circular, square, and rectangular designs—in enhancing the hydraulic performance of various PKW shapes: triangular, rectangular, and trapezoidal, under a range of hydraulic conditions, including both free and submerged flow. Experiments were conducted in a dedicated channel, 10 m long, 0.75 m wide, and 0.80 m high. The results indicate that under submerged flow conditions, discharge coefficients decreased by 61 % for rectangular, 59 % for triangular, and 55 % for trapezoidal PKWs compared to free flow, reflecting a reduction in efficiency. Notably, the trapezoidal PKWs maintained the highest discharge coefficient, improving efficiency by 2 % over triangular PKWs and by 12 % over rectangular PKWs. Flow splitters facilitate flow separation by linking entrapped air beneath the flow to the free surface, thereby mitigating nappe oscillation. In free flow conditions, rectangular and square splitters are more effective than circular ones for flow separation and energy dissipation, although geometric variations did not significantly influence the upstream water head in submerged flow scenarios. While flow splitters did not affect the discharge coefficient or efficiency of the various weir shapes under submerged conditions, they were found to decrease discharge by 10 % for triangular PKWs in free flow conditions. Overall, flow splitters demonstrated greater efficiency in submerged flow scenarios. In free flow, triangular PKWs were observed to dissipate approximately 4.4 % more energy than rectangular PKWs and 6 % more than trapezoidal shapes, with minimal differences in energy dissipation during submerged flow. This research also introduces a new equation for estimating the discharge coefficient in free flow, incorporating a correction factor yielding R2 = 0.967, RMSE = 0.217, and MRPE = 5.94 %, expanding upon the work of Zarei et al. [19] for submerged flows. The study enhances understanding of hydraulic behaviors and discharge coefficients of PKWs equipped with flow splitters, contributing to improved aeration performance.

Prediction of inlet-to-outlet width ratio of type-A piano key weir using fuzzy neural network (FNN)

ABSTRACT A Piano Key Weir (PKW) is a nonlinear (labyrinth-type) weir with a small spillway footprint and a large discharge carrying capacity. It (PKW) enables water bodies to continue functioning at elevated supply levels while causing no damage to dam structures, resulting in increased storage. PKW's geometrical structure is extremely complex, and geometrical aspects have a significant impact on its efficiency and on energy dissipation. Among them relative width ratio (Wi/Wo) (i.e., inlet to outlet key width ratio) is a critical parameter that affects the PKW's discharge efficiency, and energy dissipation across the weir significantly. This study predicts the PKW's inlet to the outlet key ratio and understands the resulting hydraulic behaviours based on a Fuzzy Neural Network (FNN). The dataset used in this study was collected experimentally, which adds to the study's authenticity because it is not a conventional dataset. The model's performance is evaluated by the Root Mean Square Error (RMSE) and Mean Absolute Error (MAE); both values are 0.0305 and 0.0222, respectively. According to the dataset, these scores tell the model's reliability as it is in the ideal range. The FNN approach can be applied in a variety of fields to predict or solve different problems erent problems.

Baffle-Enhanced Scour Mitigation in Rectangular and Trapezoidal Piano Key Weirs: An Experimental and Machine Learning Investigation

The assessment of scour depth downstream of weirs holds paramount importance in ensuring the structural stability of these hydraulic structures. This study presents groundbreaking experimental investigations highlighting the innovative use of baffles to enhance energy dissipation and mitigate scour in the downstream beds of rectangular piano key weirs (RPKWs) and trapezoidal piano key weirs (TPKWs). By leveraging three state-of-the-art supervised machine learning algorithms—multi-layer perceptron (MLP), extreme gradient boosting (XGBoost), and support vector regression (SVR)—to estimate scour hole parameters, this research showcases significant advancements in predictive modeling for scour analysis. Experimental results reveal that the incorporation of baffles leads to a remarkable 18–22% increase in energy dissipation and an 11–14% reduction in scour depth for both RPKWs and TPKWs. Specifically, introducing baffles in RPKWs resulted in a noteworthy 26.7% reduction in scour hole area and a 30.3% decrease in scour volume compared to RPKWs without baffles. Moreover, novel empirical equations were developed to estimate scour parameters, achieving impressive performance metrics with an average R2 = 0.951, RMSE = 0.145, and MRPE = 4.429%. The MLP models demonstrate superior performance in predicting maximum scour depth across all scenarios with an average R2 = 0.988, RMSE = 0.035, and MRPE = 1.036%. However, the predictive capabilities varied when estimating weir toe scour depth under diverse circumstances, with the XGBoost model proving more accurate in scenarios involving baffled TPKWs with R2 = 0.965, RMSE = 0.048, and MRPE = 2.798% than the MLP and SVR models. This research underscores the significant role of baffles in minimizing scouring effects in TPKWs compared to RPKWs, showcasing the potential for improved design and efficiency in water-management systems.

Self-Cleaning Ability of the Piano Key Weir with Driftwood Blockages

Self-Cleaning Ability of the Piano Key Weir with Driftwood Blockages

Submerged flow over various shapes of piano key weir

The weir, an essential element of dams utilized for floodwater management, plays a crucial role in human life. Over the years, nonlinear weirs have advanced into Piano Key Weirs (PKWs). These PKWs provide enhanced discharge efficiency, a reduced structural footprint, and heightened cost-effectiveness. PKWs possess a sophisticated structure defined by numerous geometric parameters. The impact of these parameters on the discharge capacity is of paramount significance. This study aims to experimentally investigate the hydraulic of submerged PKWs with different plan shapes, including triangular, trapezoidal, and rectangular, with apex width to cycle width ratio of (A/w) of 0, 0.25, and 0.5, and magnification ratio (B/w) of 1, 2, and 3, respectively. The results indicate that submergence depends on the shape and size of the PKW. Furthermore, the efficiency of the PKW increases as the ratio of approach flow head to weir height (Ho⁄P) decreases and B⁄w increases. The influence of the shape of the PKW on the performance of the weir is more pronounced at higher values of B/w. Additionally, the order of the highest discharge coefficient values follows a pattern from the trapezoidal to triangular and rectangular PKWs. Specifically, for B⁄w = 2, the trapezoidal PKW exhibits an approximate improvement of 6 and 15 % in the discharge efficiency compared to the triangular and rectangular PKWs, respectively. A new equation was developed to predict the discharge coefficient for different shapes of PKWs under various hydraulic conditions. Based on the experimental data, this study offers valuable insights into the hydraulic behavior and discharge coefficient of PKWs. This research significantly contributes to enhancing our understanding and optimizing the performance of submerged PKWs in water management systems.

Discussion of “A Reformed Empirical Equation for the Discharge Coefficient of Free-Flowing Type-A Piano Key Weirs”

Discussion of “A Reformed Empirical Equation for the Discharge Coefficient of Free-Flowing Type-A Piano Key Weirs”

Seeing the piano sound Exploration on utilizing finite element analysis to visualize piano sound

The study aims to provide a way for impaired people to learn music better through music visualization. We established a relationship between piano key frequencies and Chladni patterns. Firstly, we performed modal analysis simulations using ANSYS, covering the full range of excitable modes in the frequency range of the piano keys. However, since the natural frequencies of the simulation results were slightly different from experimental results, we used the hammering method to validate the simulation results and to demonstrate that the finite element modal analysis was able to simulate the dynamic properties of the circular plate well. Subsequent studies have found that different excitation frequencies in the lower frequency range may also affect the generation of Chladni patterns. Using harmonic analysis in ANSYS, we confirmed that tones of similar frequency on the same plate can produce different Chladni patterns, thus greatly simplifying the previous problem of having to use multiple plates of different shapes and sizes in order to visualize most of the piano keys. Based on the graphical simulation of a single tone, we have successfully extended it to a melody. This result provides strong support for effectively helping the hearing impaired to learn to play musical instruments, makes it possible to present music in a visual form, and opens up new possibilities for the wider use of music education tools in the hearing-impaired community.

Effect of Variation in Key Slope Ratios and Key Width Ratios on Energy Dissipation Over a Piano Key Weir

Effect of Variation in Key Slope Ratios and Key Width Ratios on Energy Dissipation Over a Piano Key Weir

EXPERIMENTAL COMPARISON OF FLOW ENERGY LOSS IN TYPE-B AND -C TRAPEZOIDAL PIANO KEY WEIRS (PKWS)

As non-linear weirs with a high flow rate, Piano Key Weirs (PKWs) have attracted the attention of water engineers in recent years. Given the limited information available on the energy losses of these weirs, it is important to investigate the energy losses and discharge capacity of these weirs. In this research, two trapezoidal PKWs, i.e., type-B and -C, with a height of 0.2 m were used. The studied flow rates were 0.025, 0.03, 0.035, and 0.04 m3/s. The results showed that energy loss decreased by increasing the flow velocity and upstream depth. The average energy loss in the type-B trapezoidal PKW was about 10.9% lower than that in the type-C PKW. The type-B weir had a higher discharge coefficient of about 5.6% compared to that of the type-C weir. Finally, an equation was presented to calculate the energy loss of these two weirs with a correlation coefficient of 97.42%.

Experimental Study of the Effect of Geometric Dimensions of Rectangular Piano Key Overflow Crest on the Flow Intensity Coefficient

Experimental Study of the Effect of Geometric Dimensions of Rectangular Piano Key Overflow Crest on the Flow Intensity Coefficient

Geometric Modification of Piano Key Weirs to Enhance Hydraulic Performance and Discharge Capacity

The piano key (PK) weir is a cost-effective structure for flood discharge. Its typical layout comprises a rectangularly cranked crest in planform with up- and downstream overhangs. With the intention to enhance its hydraulic efficiency, the conventional weir is improved. The sloping floor of each key is modified with a downward semi-circle in the cross-section; each overhanging apex is thus assigned an elliptical crest. Thus, the developed crest length of the resulting weir becomes considerably extended. Experiments are performed to compare the hydraulic behaviors of the improved weir with a reference one. The models are 3D-printed to attain high manufacture precision. For the model dimensions chosen in the study, the developed crest is ~36% longer. The study demonstrates that the improvements in geometry lead to appreciably enhanced flow discharge capacity. Within the hydraulic range examined, the augment in flow discharge varies within a range from 30% to 53%. In terms of both discharge capacity and flow patterns, the improved weir clearly outperforms the conventional one. The elliptical overhang apexes noticeably extend the developed crest length. The streamlined upstream overhang without singularity and the lowered inlet key floor reduce the entrance energy loss and improve the inflow to the inlet key and the flow over the crest. The lowered floor also gives rise to extra water volume, which administers to the flow motion towards the crest. For the outlet key, its lowered floor facilitates the outflow and alleviates the liableness of local submergence at high discharges. If the footprint for spillway construction is limited or the increase in the reservoir water stage must be controlled, the use of a more effective PK weir for flood discharge has significant engineering implications.

Hydromechanics of the Asymmetric Trapezoidal Piano Key and Labyrinth Weirs

Hydromechanics of the Asymmetric Trapezoidal Piano Key and Labyrinth Weirs

Novel Techniques to Study the Effect of Parapet Wall Geometry on the Performance of Piano Key Weirs

Piano key weirs (PKWs) with crown parapet walls effectively manage water levels and maximize storage. However, their efficiency is compromised by interactions between water flow and submerged outlets during rising water levels. This study investigates novel parapet wall designs to improve PKW performance and reduce submergence effects. The experiment focuses on a PKW with a fixed 12.6 cm weir height. Three parapet wall configurations are tested: Mode 1 (walls on all apex), Mode 2 (walls fixed on sides and inlet), and Mode 3 (walls along the sides). Each mode includes three parapet wall profiles: rectangular (consistent form), triangular, and trapezoidal (varying characteristics). Results indicate that parapet wall design significantly affects water level variations with increasing wall height. Mode 3, featuring triangular and trapezoidal parapet walls, demonstrates the highest discharge capacity among the examined profiles. The discharge coefficient correlates with parapet wall height and form. Notably, the triangular wall in Mode 3 outperforms Modes 1 and 2 when parapet walls maintain an R/P ratio of 0.36. This study introduces innovative parapet wall designs to enhance PKW efficiency. By implementing advanced configurations, significant improvements in water control and discharge capacity can be achieved. These findings contribute to the state-of-the-art in PKW technology and offer valuable insights for practical engineering applications.

Laboratory Study of the Hydraulic Performance of the A-Type Triangular Piano Key Weir

A piano key weir (PKW), a new type of weir aiming to increase the discharge capacity of an existing dam, was recently designed. Despite a large body of research in this field, only a few studies were conducted on A-type triangular piano key weirs (TPKW) in straight channels. In this context, this present research sought to study the flow regime, stage–discharge relationship, and discharge coefficient. Experiments were carried out using nine TPKW models and three linear weirs (LW) as the control weirs. The results indicated that the triangular piano key weirs are capable of passing a higher discharge in similar laboratory conditions compared to linear key weirs due to their longer length. For a given h/P ratio (h is the water head over the weir crest, and P is the weir height) and constant length (Le), an increase in the weir height from 0.07 m to 0.15 m decreases the discharge coefficient by approximately 20%. From sensitivity analysis, the most influential parameters for the tested TPKW models are the h/Le dimensionless ratio, followed by the P/Le and Fr. Moreover, the discharge coefficient has a reverse trend when the dimensionless parameters h/P, h/Le, and Froude number are increased. However, with decreasing h/Le, the discharge coefficient of TPKW tends to that of a broad-crested weir because of local submergence. It is expected that the results obtained will be a reference for researchers who work in this field.

Influence of Piano Key Weir Crest Shapes on Flow Characteristics, Scale Effects, and Energy Dissipation for In-Channel Application

Influence of Piano Key Weir Crest Shapes on Flow Characteristics, Scale Effects, and Energy Dissipation for In-Channel Application

A Reformed Empirical Equation for the Discharge Coefficient of Free-Flowing Type-A Piano Key Weirs

The existing equations for the discharge coefficient of Piano key weirs (PKWs) use a limited range of experimental data, which means that they are inappropriate for wide parametric ranges that might lead to significant errors. This study aimed to propose a reformed empirical equation using a wide range of data points gathered from previous experimental studies. Further, the appropriateness to use the existing equations for the collected data points, and the related errors, were investigated in detail using graphical and statistical analyses. The proposed equation predicted the discharge coefficients with <5% absolute errors for 83.5% data points and with <10% absolute errors for 100% data points, and the mean absolute error was 2.9%. Such variations may be attributed to the differences in experimental conditions that exist among the previous studies. The correlation indices were higher for the proposed equation as compared to the same for the existing equations, whereas the error indices were lowest for the proposed one. For some very specific parametric ranges, the existing equations still hold better accuracy. Overall, the proposed equation can precisely estimate the discharge coefficient of the basic geometry of Type-A PKWs for a wide parametric range and will be handy in the hydraulic design of such PKWs.

Effect of the inlet-to-outlet key width ratio of Piano Key Weir on its hydraulic behaviour

The Piano Key Weir (PKW) is an ungated type of spillway, i.e., a novel evolution over the traditional labyrinth weir. It allows the reservoirs to operate with elevated supply levels without causing any damage to the dam structures, thereby providing additional storage. It is designed to improve the hydraulic performance of linear weirs by increasing pass discharge and energy dissipation. In this study, an experimental investigation has been carried out to assess the effect of the inlet-to-outlet width ratio (Wi/Wo) on PKW hydraulic behaviours viz hydraulic efficiency and energy dissipation. To this end, nine different width proportions (1 ≤ Wi/Wo ≤ 2) type-A PKW models were tested and examined. The findings revealed that the Wi/Wo ratio significantly impacts the hydraulic performance of PKW, and the results indicate that the efficiency of the PKW increases as the width ratio increases at a certain limit and then starts decreasing. The discharge coefficient was the highest for the given discharge and head, resulting in the best hydraulic performance with a Wi/Wo ratio between 1.25 and 1.30. However, the energy dissipation across the PKW decreases as the width ratio increases. Moreover, the discharge coefficient of different width ratios (Wi/Wo) ranging between 1.28 and 1.30 is 7–17% higher than Wi/Wo = 1 and 8–13% higher than Wi/Wo = 2.0. However, the energy dissipation across the weir for Wi/Wo = 2.0 indicates 15–29% less energy dissipation than Wi/Wo = 1. It means the energy dissipation across the weir decreases as the Wi/Wo ratio increases.