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17 pages, 273 KiB  
Article
Secularization, Profanation, and Knowledge of the Heart in Contemporary French Fiction
by Roy Peachey
Religions 2025, 16(5), 642; https://doi.org/10.3390/rel16050642 - 19 May 2025
Viewed by 289
Abstract
Given the highly contested nature of the debate over secularization in modern literature, this paper examines the ways in which four contemporary French novelists address questions of human and divine absence in their fiction, focusing on Joël Egloff’s J’enquête, Gaspard-Marie Janvier’s Le [...] Read more.
Given the highly contested nature of the debate over secularization in modern literature, this paper examines the ways in which four contemporary French novelists address questions of human and divine absence in their fiction, focusing on Joël Egloff’s J’enquête, Gaspard-Marie Janvier’s Le dernier dimanche, Jérôme Ferrari’s Le sermon sur la chute de Rome, and Sylvie Germain’s Tobie des marais. It argues that some of the most pressing questions of our secular age—including questions of intersubjectivity and human and divine absence—are addressed in these competing narratives of secularization. It then examines Jean-Louis Chrétien’s notion of cardiognosie, or knowledge of the heart, and his argument that profanation, rather than secularization as such, is of central importance in the modern novel’s construction of meaning before concluding with a close reading of Jérôme Ferrari’s Le sermon sur la chute de Rome and a consideration of the heart in Sylvie Germain’s Tobie des marais as a first step toward establishing the means by which profanation has been faced and overcome in recent fictional texts. Full article
(This article belongs to the Special Issue Catholic Theologies of Culture)
20 pages, 11233 KiB  
Article
Capturing Free Surface Dynamics of Flows over a Stepped Spillway Using a Depth Camera
by Megh Raj K C, Brian M. Crookston and Daniel B. Bung
Sensors 2025, 25(8), 2525; https://doi.org/10.3390/s25082525 - 17 Apr 2025
Viewed by 486
Abstract
Spatio-temporal measurements of turbulent free surface flows remain challenging with in situ point methods. This study explores the application of an inexpensive depth-sensing RGB-D camera, the Intel® RealSense™ D455, to capture detailed water surface measurements of a highly turbulent, self-aerated flow in [...] Read more.
Spatio-temporal measurements of turbulent free surface flows remain challenging with in situ point methods. This study explores the application of an inexpensive depth-sensing RGB-D camera, the Intel® RealSense™ D455, to capture detailed water surface measurements of a highly turbulent, self-aerated flow in the case of a stepped spillway. Ambient lighting conditions and various sensor settings, including configurations and parameters affecting data capture and quality, were assessed. A free surface profile was extracted from the 3D measurements and compared against phase detection conductivity probe (PDCP) and ultrasonic sensor (USS) measurements. Measurements in the non-aerated region were influenced by water transparency and a lack of detectable surface features, with flow depths consistently smaller than USS measurements (up to 32.5% less). Measurements in the clear water region also resulted in a “no data” region with holes in the depth map due to shiny reflections. In the aerated flow region, the camera effectively detected the dynamic water surface, with mean surface profiles close to characteristic depths measured with PDCP and within one standard deviation of the mean USS flow depths. The flow depths were within 10% of the USS depths and corresponded to depths with 80–90% air concentration levels obtained with the PDCP. Additionally, the depth camera successfully captured temporal fluctuations, allowing for the calculation of time-averaged entrapped air concentration profiles and dimensionless interface frequency distributions. This facilitated a direct comparison with PDCP and USS sensors, demonstrating that this camera sensor is a practical and cost-effective option for detecting free surfaces of high velocity, aerated, and dynamic flows in a stepped chute. Full article
(This article belongs to the Special Issue 3D Reconstruction with RGB-D Cameras and Multi-sensors)
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12 pages, 2707 KiB  
Article
A New Type of Pre-Aeration Stepped Spillway
by Yu Zhou, Fangyong Xin, Ke Xu, Jiakai Mei, Siwei Jia, Haodong Qiu and Yuanyuan Wang
Water 2024, 16(22), 3213; https://doi.org/10.3390/w16223213 - 8 Nov 2024
Cited by 1 | Viewed by 1296
Abstract
Aiming to increase energy dissipation and prevent the cavitation potential of a traditional stepped spillway (TSS) at large unit discharges, a kind of pre-aeration stepped spillway, called a hydraulic-jump-stepped spillway (HJSS), is introduced in this paper. Unlike a TSS, a basin added upstream [...] Read more.
Aiming to increase energy dissipation and prevent the cavitation potential of a traditional stepped spillway (TSS) at large unit discharges, a kind of pre-aeration stepped spillway, called a hydraulic-jump-stepped spillway (HJSS), is introduced in this paper. Unlike a TSS, a basin added upstream of the stepped chute in the HJSS plays a vital role in the hydraulic performance owing to the formation of a hydraulic jump in the basin. This paper presents experimental research on the hydraulic performance of the HJSS in comparison to a TSS with the same chute slope (θ = 39.3°) for a wide range of unit discharges, including the flow pattern, energy dissipation, pre-aeration effect, and maximum splash height. The results showed that the HJSS corresponded to a large energy dissipation rate, the air was effectively entrained at the inlet of the stepped chute, and there was an observation of splash formation in the foregoing and downstream steps. Under large unit discharges, the HJSS maintained an energy dissipation rate exceeding 80%. Additionally, at the inlet, the air concentrations reached 4.5% on the bottom and 11.2% on the sidewall. The findings of this research could be used as a general guideline for stepped spillway design with large unit discharges. Full article
(This article belongs to the Special Issue Hydraulic Engineering and Numerical Simulation of Two-Phase Flows)
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28 pages, 5606 KiB  
Article
Modifying the Refuse Chute Design to Prevent Infection Spread: Engineering Analysis and Optimization
by Kursat Tanriver and Mustafa Ay
Appl. Sci. 2024, 14(21), 9638; https://doi.org/10.3390/app14219638 - 22 Oct 2024
Cited by 2 | Viewed by 2306
Abstract
Considering the presence of airborne viruses, there is a need for renovation in refuse chutes, regarded as the first step in recycling household waste in buildings. This study aimed to revise the design of existing refuse chutes in light of the challenging experiences [...] Read more.
Considering the presence of airborne viruses, there is a need for renovation in refuse chutes, regarded as the first step in recycling household waste in buildings. This study aimed to revise the design of existing refuse chutes in light of the challenging experiences in waste management and public health during the coronavirus pandemic. This research primarily focused on the risks posed by various types of coronaviruses, such as the novel coronavirus (COVID-19) and acute respiratory syndrome (SARS and SARS-CoV), on stainless steel surfaces, with evidence of their survival under certain conditions. Refuse chutes are manufactured from stainless steel to resist the corrosive effects of waste. In examining the existing studies, it was observed that Casanova et al. and Chowdhury et al. found that the survival time of coronaviruses on stainless steel surfaces decreases as the temperature increases. Based on these studies, mechanical revisions have been made to the sanitation system of the refuse chute, thus increasing the washing water temperature. Additionally, through mechanical improvements, an automatic solution spray entry is provided before the intake doors are opened. Furthermore, to understand airflow and clarify flow parameters related to airborne infection transmission on residential floors in buildings equipped with refuse chutes, a computational fluid dynamics (CFD) analysis was conducted using a sample three-story refuse chute system. Based on the simulation results, a fan motor was integrated into the system to prevent pathogens from affecting users on other floors through airflow. Thus, airborne pathogens were periodically expelled into the atmosphere via a fan shortly before the intake doors were opened, supported by a PLC unit. Additionally, the intake doors were electronically interlocked, ensuring that all other intake doors remained locked while any single door was in use, thereby ensuring user safety. In a sample refuse chute, numerical calculations were performed to evaluate parameters such as the static suitability of the chute body thickness, static compliance of the chute support dimensions, chute diameter, chute thickness, fan airflow rate, ventilation duct diameter, minimum rock wool thickness for human contact safety, and the required number of spare containers. Additionally, a MATLAB code was developed to facilitate these numerical calculations, with values optimized using the Fmincon function. This allowed for the easy calculation of outputs for the new refuse chute systems and enabled the conversion of existing systems, evaluating compatibility with the new design for cost-effective upgrades. This refuse chute design aims to serve as a resource for readers in case of infection risks and contribute to the literature. The new refuse chute design supports the global circular economy (CE) model by enabling waste disinfection under pandemic conditions and ensuring cleaner source separation and collection for recycling. Due to its adaptability to different pandemic conditions including pathogens beyond coronavirus and potential new virus strains, the designed system is intended to contribute to the global health framework. In addition to the health measures described, this study calls for future research on how evolving global health conditions might impact refuse chute design. Full article
(This article belongs to the Section Materials Science and Engineering)
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23 pages, 7508 KiB  
Article
Numerical Analysis of Flow Characteristics and Energy Dissipation on Flat and Pooled Stepped Spillways
by Umar Farooq, Shicheng Li and James Yang
Water 2024, 16(18), 2600; https://doi.org/10.3390/w16182600 - 13 Sep 2024
Cited by 3 | Viewed by 2187
Abstract
The hydraulic performance of pooled stepped spillways has received less recognition compared to the traditional stepped spillways. Regarding the effectiveness of pooled stepped spillways in managing flow dynamics, previous studies have focused on investigating how different step configurations and varying chute angles can [...] Read more.
The hydraulic performance of pooled stepped spillways has received less recognition compared to the traditional stepped spillways. Regarding the effectiveness of pooled stepped spillways in managing flow dynamics, previous studies have focused on investigating how different step configurations and varying chute angles can enhance energy dissipation in gravity flow over the chute. However, the potential for optimal performance and the importance of proper design have not been thoroughly explored in the existing literature. This study aims to explore new configurations of pooled stepped spillways and compare them to traditional stepped spillway designs to enhance hydraulic efficiency and maximize energy dissipation. The study examines two types of configurations of stepped spillways—two flat and two pooled configurations, each with ten steps. Using the computational Fluid Dynamics (CFD) technique, such as Volume of Fluid Method (VOF) and the realizable k-ε turbulence model for two-phase flow analysis with a 26.6° chute slope. Initially, the model was validated with experimental data by comparing various hydraulic parameters. These parameters include water depth, roller length, jump length, ratio of critical depth, and sequent depth. The hydraulic performance of both stepped geometric configurations was evaluated through numerical simulations to examine how the geometries of flat and pooled stepped spillways influence flow characteristics, energy dissipation, velocity, pressure distribution, and the Froude number at the downstream. The study analyzed downstream flow characteristics, maximum energy dissipation rates, depth-averaged velocity, static pressure, and pressure contours at the lateral direction under six different flow rates in flat and pooled stepped spillways. The findings indicate that flat-step configurations exhibit lower energy dissipation compared to pooled configurations. The relative energy loss of flow on pooled steps dissipates more energy than on flat steps. Furthermore, it is observed that the pooled configurations performed better for energy dissipation and flow stability compared to the flat configurations. The energy dissipation increased in pooled stepped spillways by 34.68% and 25.81%, respectively. Additionally, the depth-averaged flow velocity and pressure distribution decreased in case 2 and case 4 compared to the flat-step configurations. Full article
(This article belongs to the Special Issue Hydraulic Engineering and Numerical Simulation of Two-Phase Flows)
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23 pages, 4708 KiB  
Article
Numerical Investigation of Different Stepped Spillway Geometries over a Mild Slope for Safe Operation Using Multi-Phase Model
by Binaya Raj Pandey, Megh Raj K C, Brian Crookston and Gerald Zenz
Water 2024, 16(11), 1635; https://doi.org/10.3390/w16111635 - 6 Jun 2024
Cited by 5 | Viewed by 2479
Abstract
The appropriate design and operation of spillways are critical for dam safety. To enhance design practices and gain insights into flow hydraulics, both experimental and numerical modeling are commonly employed. In this study, we conducted a numerical investigation of flow over a mildly [...] Read more.
The appropriate design and operation of spillways are critical for dam safety. To enhance design practices and gain insights into flow hydraulics, both experimental and numerical modeling are commonly employed. In this study, we conducted a numerical investigation of flow over a mildly sloping (1V:3H) stepped spillway with various step geometries using a multi-phase mixture model with dispersed interface tracking in ANSYS Fluent. The model was validated against experimental data from Utah State University, focusing on water surface profiles over the crest, velocities, and air concentrations. The validated numerical model was used to simulate flow over different step geometries (i.e., 0.2 m H uniform Step, 0.1 m H uniform step, non-uniform steps, adverse slope steps, and stepped pool) for a range of discharges from 0.285 m3/s/m to 1.265 m3/s/m. While flow depths over the crest and velocities in the chute compared well with experimental results, air concentrations exhibited some deviation, indicating numerical limitations of the solver. The shift in the location of the inception point was found to be mainly influenced by a higher flow rate than the different design configurations over an identical mild slope. The downstream non-linear flow velocity curve with different flow rates indicated less effectiveness of the step roughness over a high flow rate as a result of the reduction in relative roughness. The theoretical velocity ratio indicated the least reduction in downstream velocity with the stepped pooled spillway due to the formation of a “stagnant pool”. A higher negative-pressure region due to flow separation at the vertical face of the steps was obtained by adverse slope steps, which shows that the risk of cavitation is higher over the adverse slope step spillway. Turbulent kinetic energy (TKE) was found to be higher for uniform 0.2 m H steps due to the strong mixing of flow over the steps. The least TKE was found at the steps of the stepped pool spillway due to the formation of a “stagnant pool”. Uniform 0.2 m H steps achieved the maximum energy dissipation efficiency, whereas the stepped pool spillway obtained the least energy dissipation efficiency, introducing higher flow velocity at the stilling basin with a higher residual head. The adverse slope and non-uniform steps were found to be more effective than the uniform 0.1 m H steps and stepped pool spillway. The application of uniform steps of higher drop height and length could achieve higher TKE over the steps, reducing the directional flow velocity, which reduces the risk of potential damage. Full article
(This article belongs to the Special Issue CFD Modelling of Turbulent Free Surface Flows)
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18 pages, 4385 KiB  
Article
Hydrodynamic Loads in a Stilling Basin of a Converging Stepped Spillway: An Experimental Study
by Bojan Milovanovic, Predrag Vojt, Budo Zindovic, Vladan Kuzmanovic and Ljubodrag Savic
Water 2024, 16(1), 140; https://doi.org/10.3390/w16010140 - 29 Dec 2023
Cited by 1 | Viewed by 1556
Abstract
This paper presents a methodology for estimation of hydrodynamic loads acting on the bottom and at the walls of a stilling basin of a stepped chute with converging walls, based on the pressure measurements at the selected points of a scale model. This [...] Read more.
This paper presents a methodology for estimation of hydrodynamic loads acting on the bottom and at the walls of a stilling basin of a stepped chute with converging walls, based on the pressure measurements at the selected points of a scale model. This is the first study of hydrodynamic loads for this type of structure, and the first one of the loads on the stilling basin walls in general. For selected flow discharges, step heights and hydraulic jump submergence ratio, the hydrodynamic pressures were measured at a significant number of points, providing the spatio-temporal distribution of relevant hydrodynamic loads. The most influential effect proved to be a convergence angle of the chute walls. Based on these measurements, appropriate regression expressions were proposed for predicting hydrodynamic loads. These expressions show good agreement with measurements, offering a reliable tool for the structural design of stepped spillway stilling basins. Full article
(This article belongs to the Section Hydraulics and Hydrodynamics)
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10 pages, 254 KiB  
Editorial
Advances in Spillway Hydraulics: From Theory to Practice
by Anton J. Schleiss, Sebastien Erpicum and Jorge Matos
Water 2023, 15(12), 2161; https://doi.org/10.3390/w15122161 - 7 Jun 2023
Cited by 12 | Viewed by 6639
Abstract
Over the past decades, significant advances have been achieved in hydraulic structures for dams, namely in water release structures such as spillway weirs, chutes, and energy dissipators. This editorial presents a brief overview of the eleven papers in this Special Issue, Advances in [...] Read more.
Over the past decades, significant advances have been achieved in hydraulic structures for dams, namely in water release structures such as spillway weirs, chutes, and energy dissipators. This editorial presents a brief overview of the eleven papers in this Special Issue, Advances in Spillway Hydraulics: From Theory to Practice, and frames them in current research trends. This Special Issue explores the following topics: spillway inlet structures, spillway transport structures, and spillway outlet structures. For the first topic of spillway inlet structures, this collection includes one paper on the hydrodynamics and free-flow characteristics of piano key weirs with different plan shapes and another that presents a theoretical model for the flow at an ogee crest axis for a wide range of head ratios. Most of the contributions address the second topic of spillway transport structures as follows: a physical modeling of a beveled-face stepped chute; the description and recent developments of the generalized, energy-based, water surface profile calculation tool SpillwayPro; an application of the SPH method on non-aerated flow over smooth and stepped converging spillways; a physical model study of the effect of stepped chute slope reduction on the bottom-pressure development; an assessment of a spillway offset aerator with a comparison of the two-phase volume of fluid and complete two-phase Euler models included in the OpenFOAM® toolbox; an evaluation of the performance and design of a stepped spillway aerator based on a physical model study. For the third topic of spillway outlet structures, physical model studies are presented on air–water flow in rectangular free-falling jets, the performance of a plain stilling basin downstream of 30° and 50° inclined smooth and stepped chutes, and scour protection for piano key weirs with apron and cutoff wall. Finally, we include a brief discussion about some research challenges and practice-oriented questions. Full article
(This article belongs to the Special Issue Advances in Spillway Hydraulics: From Theory to Practice)
23 pages, 5819 KiB  
Article
Plain Stilling Basin Performance below 30° and 50° Inclined Smooth and Stepped Chutes
by Ivan Stojnic, Michael Pfister, Jorge Matos and Anton J. Schleiss
Water 2022, 14(23), 3976; https://doi.org/10.3390/w14233976 - 6 Dec 2022
Cited by 4 | Viewed by 4376
Abstract
Energy dissipators, such as stilling basins, are usually required at the toe of stepped chutes to achieve adequate and safe operation of the spillway. Stepped chute hydraulics has been extensively studied in last several decades, however, only limited knowledge is available on the [...] Read more.
Energy dissipators, such as stilling basins, are usually required at the toe of stepped chutes to achieve adequate and safe operation of the spillway. Stepped chute hydraulics has been extensively studied in last several decades, however, only limited knowledge is available on the stilling basin performance below stepped chutes. In particular, the effect of the chute slope remains unknown, despite being a central design issue. Therefore, an experimental campaign was performed using a 30° or 50° inclined smooth or stepped chute with an adjacent conventional plain stilling basin. The experimental results indicated that, within the stilling basin, the surface characteristics and the roller as well as hydraulic jump lengths are practically independent of the chute slope. This further strengthens the previous findings that stepped chutes require 17% longer dimensionless jump lengths and consequently stilling basin lengths. The experimental results also confirmed that stepped chutes generated increased extreme and fluctuating bottom pressure characteristics at the stilling basin entrance area. With increasing chute slope, the latter were found to significantly magnify. However, such increased magnitudes were not expected to provoke cavitation damage as stepped chute inflows induced bottom aeration at the basin entrance, irrespective of the chute slope. Full article
(This article belongs to the Special Issue Advances in Spillway Hydraulics: From Theory to Practice)
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27 pages, 9279 KiB  
Article
Smooth and Stepped Converging Spillway Modeling Using the SPH Method
by Juliana D. Nóbrega, Jorge Matos, Harry E. Schulz and Ricardo B. Canelas
Water 2022, 14(19), 3103; https://doi.org/10.3390/w14193103 - 2 Oct 2022
Cited by 6 | Viewed by 3132
Abstract
Three-dimensional (3D) simulations using the smoothed particle hydrodynamics (SPH) method were performed for smooth and stepped spillways with converging walls, in order to evaluate the influence of the wall deflection and the step macro-roughness on the main non-aerated flow properties. The simulations encompassed [...] Read more.
Three-dimensional (3D) simulations using the smoothed particle hydrodynamics (SPH) method were performed for smooth and stepped spillways with converging walls, in order to evaluate the influence of the wall deflection and the step macro-roughness on the main non-aerated flow properties. The simulations encompassed a 1V:2H sloping spillway, wall convergence angles of 9.9° and 19.3°, and discharges corresponding to skimming flow regime, in the stepped chute. The overall development of the experimental data on flow depths, velocity profiles, and standing wave widths was generally well predicted by the numerical simulations. However, larger deviations in flow depths and velocities were observed close to the upstream end of the chute and close to the pseudo-bottom of the stepped invert, respectively. The results showed that the height and width of the standing waves were significantly influenced by the wall convergence angle and by the macro-roughness of the invert, increasing with a larger wall deflection, and attenuated on the stepped chute. The numerical velocity and vorticity fields, along with the 3D recirculating vortices on the stepped invert, were in line with recent findings on constant width chutes. Full article
(This article belongs to the Special Issue Advances in Spillway Hydraulics: From Theory to Practice)
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17 pages, 9284 KiB  
Article
Velocity Measurements in Highly Aerated Flow on a Stepped Chute without Sidewall Constraint Using a BIV Technique
by Martí Sánchez-Juny, Soledad Estrella, Jorge Matos, Ernest Bladé, Eduardo Martínez-Gomariz and Enrique Bonet Gil
Water 2022, 14(16), 2587; https://doi.org/10.3390/w14162587 - 22 Aug 2022
Cited by 2 | Viewed by 2771
Abstract
The lack of sidewalls in a spillway leads to lateral expansion of the flow and, consequently, a non-uniform transversal flow rate distribution along the chute. The present work shows the velocity field measured in a physical model of a 1 V:0.8 H steeply [...] Read more.
The lack of sidewalls in a spillway leads to lateral expansion of the flow and, consequently, a non-uniform transversal flow rate distribution along the chute. The present work shows the velocity field measured in a physical model of a 1 V:0.8 H steeply sloping stepped spillway without sidewalls. An application of a Bubble Image Velocimetry (BIV) technique in the self-aerated region is shown, using air bubbles entrained into the flow downstream of the inception point as tracers. The results indicate that, for small dimensionless discharges and sufficiently downstream of the point of inception, the free-surface velocity compares relatively well with the corresponding air–water interfacial velocity previously obtained with a double-tip fiber optical probe in the same facility. In turn, the velocity profiles along the normal to the pseudo-bottom, far downstream of the inception point, are reasonably in agreement with the air–water interfacial velocity profiles in the inner part of the skimming flow, with the largest differences being verified in the upper skimming flow region near the free-surface. Full article
(This article belongs to the Special Issue Advances in Experimental Hydraulics, Coast and Ocean Hydrodynamics)
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20 pages, 2556 KiB  
Article
SpillwayPro: Integrated Water Surface Profile, Cavitation, and Aerated Flow Analysis for Smooth and Stepped Chutes
by Tony L. Wahl and Henry T. Falvey
Water 2022, 14(8), 1256; https://doi.org/10.3390/w14081256 - 13 Apr 2022
Cited by 8 | Viewed by 4486
Abstract
Spillways of large and small dams experience flow conditions that exceed the capabilities of common water surface profile computer programs. Unique channel geometries, steep slopes, and streamline curvature demand rigorous mathematics, while phenomena associated with aerated flow and potential cavitation require special analyses, [...] Read more.
Spillways of large and small dams experience flow conditions that exceed the capabilities of common water surface profile computer programs. Unique channel geometries, steep slopes, and streamline curvature demand rigorous mathematics, while phenomena associated with aerated flow and potential cavitation require special analyses, especially for stepped chutes. SpillwayPro is a generalized, energy-based, water surface profile calculation tool for both smooth and stepped chutes that integrates cavitation analysis and aerated flow effects, with separate modules supporting aerator design and the development of optimized structure profiles that meet cavitation parameter objectives. Simultaneous calculation of smooth and stepped-chute flow profiles enables the rapid assessment of the energy dissipation benefits of steps, as well as their unique aerated flow and cavitation issues. SpillwayPro’s technical basis is presented, and its results are compared to the data from prototype case studies and empirical methods developed from large-scale laboratory studies. SpillwayPro’s fundamental energy-based methods are useful for cases that differ from idealized empirical approaches and would benefit from a more rapid analysis than can be accomplished with physical or computational fluid dynamics (CFD) modeling. Full article
(This article belongs to the Special Issue Advances in Spillway Hydraulics: From Theory to Practice)
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13 pages, 16500 KiB  
Article
Physical Modeling of Beveled-Face Stepped Chute
by Sherry L. Hunt, Kem C. Kadavy, Tony L. Wahl and Dana W. Moses
Water 2022, 14(3), 365; https://doi.org/10.3390/w14030365 - 26 Jan 2022
Cited by 7 | Viewed by 2949
Abstract
New construction practices for roller compacted concrete (RCC) overlays and stepped chutes are changing the step geometry from a traditional square-edge, vertical face to a 45° beveled face. A large-scale 3(H):1(V) (i.e., θ = 18.4°) stepped chute model was tested with a 45° [...] Read more.
New construction practices for roller compacted concrete (RCC) overlays and stepped chutes are changing the step geometry from a traditional square-edge, vertical face to a 45° beveled face. A large-scale 3(H):1(V) (i.e., θ = 18.4°) stepped chute model was tested with a 45° beveled face step with a height (h) of 152 mm. Results were compared to data on square-edge, vertical face steps previously obtained. The distance to the inception point of free-surface aeration normalized by the surface roughness was reduced approximately 25% for the same Froude number defined in terms of roughness height. An existing inception point relationship for vertical face steps was adjusted with a best fit correction factor to predict the free-surface inception point for this chute slope and beveled face angle. Relative flow depths, mean air concentration, and energy loss data showed similar general trends for vertical face and beveled face steps, but the depths and air concentrations for beveled face steps were slightly higher for equal values of relative free-surface inception point, Li/L, and relative step height (e.g., h/dc). Energy loss at the free-surface inception point ranged from approximately 20 to 40% of total head for both step types. Additional research is needed to determine the generalized effects of the bevel angle and the chute slope on flow properties. This research is expected to be used by field engineers for the design of stepped chutes with beveled face steps. Full article
(This article belongs to the Special Issue Advances in Spillway Hydraulics: From Theory to Practice)
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24 pages, 16320 KiB  
Article
Extreme Pressures and Risk of Cavitation in Steeply Sloping Stepped Spillways of Large Dams
by Jorge Matos, Carolina Kuhn Novakoski, Rute Ferla, Marcelo Giulian Marques, Mauricio Dai Prá, Alba Valéria Brandão Canellas and Eder Daniel Teixeira
Water 2022, 14(3), 306; https://doi.org/10.3390/w14030306 - 20 Jan 2022
Cited by 14 | Viewed by 3992
Abstract
Stepped spillways have been increasingly used to handle flood releases from large dams associated with hydropower plants, and it is important to evaluate the fluctuating pressure field on the steps. Hydraulic model investigations were conducted on three 53° (1V:0.75H) sloping and relatively large-stepped [...] Read more.
Stepped spillways have been increasingly used to handle flood releases from large dams associated with hydropower plants, and it is important to evaluate the fluctuating pressure field on the steps. Hydraulic model investigations were conducted on three 53° (1V:0.75H) sloping and relatively large-stepped chutes to characterize the mean, fluctuating, and extreme pressures acting on the most critical regions of the step faces, near their outer edges. The pressure development along the chutes is presented, generally indicating an increase of the modulus of pressure coefficients up to the vicinity of the point of inception of air entrainment, and a decrease further downstream. The extreme pressure coefficients along the spillway are fitted by an empirical formula, and the critical conditions potentially leading to cavitation on prototypes are calculated. The correlation between the cavitation index and the friction factor is also applied for predicting the onset of cavitation on prototypes, and the results are compared with the pressure data-based method. Generally, the results obtained from those methods yield typical values for the cavitation index in the vicinity of the point of inception, varying approximately from 0.8 to 0.6, respectively. In light of these results, maximum unit discharges of about 15–20 m2/s are considered advisable on 53° sloping large-stepped spillways without artificial aeration, for step heights ranging from 0.6 to 1.2 m. For much higher unit discharges, a considerable reach of the spillway may potentially be prone to the risk of cavitation damage. Full article
(This article belongs to the Special Issue Advances and Challenges in Hydropower)
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22 pages, 5487 KiB  
Article
Performance and Design of a Stepped Spillway Aerator
by Stéphane Terrier, Michael Pfister and Anton J. Schleiss
Water 2022, 14(2), 153; https://doi.org/10.3390/w14020153 - 7 Jan 2022
Cited by 8 | Viewed by 3680
Abstract
Stepped spillways are frequently limited to specific discharges under around 30 m2/s due to concerns about potential cavitation damages. A small air concentration can prevent such damages and the design of bottom aerators is well established for smooth chutes. The purpose [...] Read more.
Stepped spillways are frequently limited to specific discharges under around 30 m2/s due to concerns about potential cavitation damages. A small air concentration can prevent such damages and the design of bottom aerators is well established for smooth chutes. The purpose of this study is to systematically investigate the performance of a deflector aerator at the beginning of stepped chutes. Six parameters (chute angle, step height, approach flow depth, approach flow Froude number, deflector angle and deflector height) are varied in a physical model. The spatial air concentration distribution downstream of the aerator, the cavity sub-pressure, water discharge and air discharges are measured. The results describe the commonly used air entrainment coefficient, the jet length, as well as the average and bottom air concentration development to design an aerator. The lowest bottom air concentration measured in all tests is higher than the air concentration recommended in literature to protect against cavitation damages. And, unlike smooth chutes, there appears to be no significant air detrainment downstream of the jet impact. One deflector aerator seems therefore sufficient to provide protection of a stepped spillway. Full article
(This article belongs to the Special Issue Advances in Spillway Hydraulics: From Theory to Practice)
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