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Keywords = Froude number similarity

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15 pages, 1382 KiB  
Article
Wave Run-Up Distance Prediction Combined Data-Driven Method and Physical Experiments
by Peng Qin, Hangwei Zhu, Fan Jin, Wangtao Lu, Zhenzhu Meng, Chunmei Ding, Xian Liu and Chunmei Cheng
J. Mar. Sci. Eng. 2025, 13(7), 1298; https://doi.org/10.3390/jmse13071298 - 1 Jul 2025
Viewed by 267
Abstract
Predicting wave run-up on seawalls is essential for assessing coastal flood risk and guiding resilient design. In this study, we combine physical model experiments with a hybrid data driven method to forecast wave run-up distance. Laboratory tests generated a nonlinear data set spanning [...] Read more.
Predicting wave run-up on seawalls is essential for assessing coastal flood risk and guiding resilient design. In this study, we combine physical model experiments with a hybrid data driven method to forecast wave run-up distance. Laboratory tests generated a nonlinear data set spanning a wide range of wave amplitudes, wavelengths, Froude numbers. To capture the underlying physical regimes, the records were first classified using a Gaussian Mixture Model (GMM), which automatically grouped waves of similar hydrodynamic character. Within each cluster a Gradient Boosting Regressor (GBR) was then trained, allowing the model to learn tailored input–output relationships instead of forcing a single global fit. Results demonstrate that the GMM-GBR combined model achieves a coefficient of determination R2 greater than 0.91, outperforming a conventional, non-clustered GBR model. This approach offers a reliable tool for predicting seawall performance under varying wave conditions, contributing to better coastal management and resilience strategies. Full article
(This article belongs to the Special Issue Wave Hydrodynamics in Coastal Areas)
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27 pages, 10029 KiB  
Article
Hydrodynamic and Morphological Effects of Non-Powered Floating Objects on Sediment Resuspension: A CFD and Regression Analysis
by Nuray Gedik, Onur Bora, Mehmet Sedat Kabdaşlı and Emel İrtem
Appl. Sci. 2025, 15(5), 2717; https://doi.org/10.3390/app15052717 - 4 Mar 2025
Cited by 1 | Viewed by 753
Abstract
This study investigates the hydrodynamic and morphological effects caused by non-powered floating objects (e.g., barges, pontoons, and floating or moored platforms) that are towed by external forces (such as tugboats) across flat, shallow seabeds. This study employs an integrated approach combining advanced computational [...] Read more.
This study investigates the hydrodynamic and morphological effects caused by non-powered floating objects (e.g., barges, pontoons, and floating or moored platforms) that are towed by external forces (such as tugboats) across flat, shallow seabeds. This study employs an integrated approach combining advanced computational fluid dynamics (CFD) simulations with multivariate polynomial regression analysis to systematically investigate the hydrodynamic and morphological effects of non-powered floating objects on sediment resuspension. A total of 96 simulation scenarios were conducted, of which 84 significant cases (where the floating object did not touch the seabed) were analyzed. Variations included bow geometries (blunt and raked), towing speeds, and operational parameters. The results indicate that, under similar towing speeds and clearance heights, blunt bows increase the suspended sediment concentration by approximately 90–190% compared to raked bows. The regression model, attaining an R-squared value of 0.9647, identified the Froude number, squat ratio, squared towing time, and object type as critical predictors of suspended sediment concentration. Furthermore, the interaction terms between the Froude number and object type were significant, enhancing the model’s predictive accuracy. These results underscore the importance of optimized design and operational strategies in minimizing the environmental impact of floating structures, especially in shallow marine environments where sediment dynamics play a crucial role in ecological balance. Careful consideration of towing speed, object geometry, and operational parameters can significantly reduce sediment resuspension, mitigating ecological consequences. Full article
(This article belongs to the Section Civil Engineering)
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24 pages, 7772 KiB  
Review
A Review of Experiment Methods, Simulation Approaches and Wake Characteristics of Floating Offshore Wind Turbines
by Xiaoxu Chen, Tengyuan Wang, Chang Cai, Jianshuang Liu, Xiaoxia Gao, Naizhi Guo and Qingan Li
J. Mar. Sci. Eng. 2025, 13(2), 208; https://doi.org/10.3390/jmse13020208 - 22 Jan 2025
Viewed by 2058
Abstract
With the urgent demand for net-zero emissions, renewable energy is taking the lead and wind power is becoming increasingly important. Among the most promising sources, offshore wind energy located in deep water has gained significant attention. This review focuses on the experimental methods, [...] Read more.
With the urgent demand for net-zero emissions, renewable energy is taking the lead and wind power is becoming increasingly important. Among the most promising sources, offshore wind energy located in deep water has gained significant attention. This review focuses on the experimental methods, simulation approaches, and wake characteristics of floating offshore wind turbines (FOWTs). The hydrodynamics and aerodynamics of FOWTs are not isolated and they interact with each other. Under the environmental load and mooring force, the floating platform has six degrees of freedom motions, which bring the changes in the relative wind speed to the turbine rotor, and furthermore, to the turbine aerodynamics. Then, the platform’s movements lead to a complex FOWT wake evolution, including wake recovery acceleration, velocity deficit fluctuations, wake deformation and wake meandering. In scale FOWT tests, it is challenging to simultaneously satisfy Reynolds number and Froude number similarity, resulting in gaps between scale model experiments and field measurements. Recently, progress has been made in scale model experiments; furthermore, a “Hardware in the loop” technique has been developed as an effective solution to the above contradiction. In numerical simulations, the coupling of hydrodynamics and aerodynamics is the concern and a typical numerical simulation of multi-body and multi-physical coupling is reviewed in this paper. Furthermore, recent advancements have been made in the analysis of wake characteristics, such as the application of instability theory and modal decomposition techniques in the study of FOWT wake evolution. These studies have revealed the formation of vortex rings and leapfrogging behavior in adjacent helical vortices, which deepens the understanding of the FOWT wake. Overall, this paper provides a comprehensive review of recent research on FOWT wake dynamics. Full article
(This article belongs to the Section Marine Energy)
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14 pages, 1586 KiB  
Article
Dimensionless Number Group Analysis of Surface-Treated Powders
by Bellamarie Ludwig
Powders 2023, 2(4), 749-762; https://doi.org/10.3390/powders2040047 - 13 Dec 2023
Viewed by 1571
Abstract
Modeling powder properties remains a complex and difficult area of study because particulate materials can behave differently under variable conditions based on their bulk and surface-level properties. The research presented in this manuscript was designed to support the fundamental understanding of powder systems [...] Read more.
Modeling powder properties remains a complex and difficult area of study because particulate materials can behave differently under variable conditions based on their bulk and surface-level properties. The research presented in this manuscript was designed to support the fundamental understanding of powder systems by joining experimental and theoretical calculations of dimensionless numbers groups for design purposes. In order to do so, this work focused on two critical variables to better understand fluidization design: physical and chemical surface properties. To better resolve the influence of surface properties, surface-treated powders were used. Five different powder samples of varying particle size distribution were characterized using physical property measurements, including pressure drop profiles to obtain the minimum fluidization velocity, density measurements, and particle sizing. Using theoretical equations, the minimum fluidization velocity was also calculated to compare with those obtained experimentally and determine typical dimensionless number groups used in bulk handling system design. The results showed that the theoretically determined values were lower than those calculated using the experimentally umf. In the case of the Reynolds number, the experimental values were 3–20% higher than the theoretical values, which is an important distinction for designing conveying systems and pipeline flow. Similar results were observed for the theoretical and experimental Froude numbers, indicating an important dependence on the cohesive properties of the particle interactions. Additional dimensionless number groups were considered, including the granular bond number and flow factors. To investigate the influence of surface forces, Hamaker constants were utilized for alumina and polydimethylsiloxane in the calculation of the granular bond number. A lower granular bond was observed with a decrease in the Hamaker constant for PDMS, suggesting that the surface forces would be lower for our surface-treated powders. Full article
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20 pages, 5801 KiB  
Article
An Experimental Study of Different Stratified Water Intake Structures in a Deep-Water Reservoir
by Haitao Liu, Shuangke Sun, Guangning Li, Tiegang Zheng and Kai Shi
Water 2023, 15(24), 4251; https://doi.org/10.3390/w15244251 - 12 Dec 2023
Cited by 1 | Viewed by 1943
Abstract
For water temperature stratified reservoirs, stratified water intake structures are used to extract surface warm water to reduce the adverse effects of low-temperature discharge on river habitats and agricultural irrigation. A physical simulation method has been explored and used to conduct the comparative [...] Read more.
For water temperature stratified reservoirs, stratified water intake structures are used to extract surface warm water to reduce the adverse effects of low-temperature discharge on river habitats and agricultural irrigation. A physical simulation method has been explored and used to conduct the comparative experimental study on the efficiency of the three types of intake structures: a traditional stoplog gate intake, a stoplog gate with a horizontal curtain and a vertical curtain upstream of the intake. In order to extend the laboratory results to the prototype, a similarity relationship for water temperature stratification was derived based on the principle of equal density stratification Froude number between the model and the prototype, as well as the functional relationship between water density and temperature. The similarity relationship makes it possible to simulate the same prototype density flow under different laboratory water temperature conditions, and this was confirmed through experiments conducted in several months with different water temperatures. Under constant water flow conditions, a stable target water temperature distribution can be formed in the experimental model through continuous stratified heating and real-time power regulation, to simulate the density flow generated by various intake operation in water temperature stratified reservoir. The relationships between the intake water temperature and the reference water temperature at intake depth in reservoir were analyzed to distinguish the difference of water intake efficiency. The experimental results showed that, the traditional stoplog gate has a relatively lower efficiency in extracting warm water affected by the lower edge expansion of the drag layer into the cold water zone below the intake elevation; by setting horizontal curtain to prevent the cold water from climbing below, it is helpful to improve the water intake efficiency; by setting vertical curtain in the upstream area of the intake, the velocity of warm water in the upper part of the drag layer increases, and the intake efficiency has been significantly improved. The above research provides a scientific approach for mechanism research and mathematical model validation of thermal density flow. Full article
(This article belongs to the Section Hydraulics and Hydrodynamics)
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36 pages, 2677 KiB  
Article
Dimensionless Groups by Entropic Similarity: II—Wave Phenomena and Information-Theoretic Flow Regimes
by Robert K. Niven
Entropy 2023, 25(11), 1538; https://doi.org/10.3390/e25111538 - 11 Nov 2023
Cited by 1 | Viewed by 1673
Abstract
The aim of this study is to explore the insights of the information-theoretic definition of similarity for a multitude of flow systems with wave propagation. This provides dimensionless groups of the form Πinfo=U/c, where U is a [...] Read more.
The aim of this study is to explore the insights of the information-theoretic definition of similarity for a multitude of flow systems with wave propagation. This provides dimensionless groups of the form Πinfo=U/c, where U is a characteristic flow velocity and c is a signal velocity or wave celerity, to distinguish different information-theoretic flow regimes. Traditionally, dimensionless groups in science and engineering are defined by geometric similarity, based on ratios of length scales; kinematic similarity, based on ratios of velocities or accelerations; and dynamic similarity, based on ratios of forces. In Part I, an additional category of entropic similarity was proposed based on ratios of (i) entropy production terms; (ii) entropy flow rates or fluxes; or (iii) information flow rates or fluxes. In this Part II, the information-theoretic definition is applied to a number of flow systems with wave phenomena, including acoustic waves, blast waves, pressure waves, surface or internal gravity waves, capillary waves, inertial waves and electromagnetic waves. These are used to define the appropriate Mach, Euler, Froude, Rossby or other dimensionless number(s)—including new groups for internal gravity, inertial and electromagnetic waves—to classify their flow regimes. For flows with wave dispersion, the coexistence of different celerities for individual waves and wave groups—each with a distinct information-theoretic group—is shown to imply the existence of more than two information-theoretic flow regimes, including for some acoustic wave systems (subsonic/mesosonic/supersonic flow) and most systems with gravity, capillary or inertial waves (subcritical/mesocritical/supercritical flow). For electromagnetic wave systems, the additional vacuum celerity implies the existence of four regimes (subluminal/mesoluminal/transluminal/superluminal flow). In addition, entropic analyses are shown to provide a more complete understanding of frictional behavior and sharp transitions in compressible and open channel flows, as well as the transport of entropy by electromagnetic radiation. The analyses significantly extend the applications of entropic similarity for the analysis of flow systems with wave propagation. Full article
(This article belongs to the Section Multidisciplinary Applications)
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14 pages, 3492 KiB  
Article
Local Scour around Side-by-Side Double Piers in Channel Bends under Ice-Covered Conditions—An Experimental Study
by Feihu Song, Jun Wang, Zhenhua Zhang, Tiejie Cheng, Guowei Li and Jueyi Sui
Water 2023, 15(13), 2317; https://doi.org/10.3390/w15132317 - 21 Jun 2023
Cited by 3 | Viewed by 1868
Abstract
The pier scour process is normally intensified in the presence of an ice cover, which poses risks to the longevity and safety of bridges. In the present study, the impact of the densimetric Froude number, locations, and pier spacing of side-by-side piers on [...] Read more.
The pier scour process is normally intensified in the presence of an ice cover, which poses risks to the longevity and safety of bridges. In the present study, the impact of the densimetric Froude number, locations, and pier spacing of side-by-side piers on the local scour depth under ice-covered flow conditions were investigated based on clear water scour experiments in an S-shaped laboratory flume. The results demonstrated that the local scour at piers along the convex bank was more substantial than that along the concave bank when other factors stayed identical. The densimetric Froude number clearly has more impact on local scour at piers along the convex bank than that along the concave bank. Different from the mechanism of the pier scour in a straight channel, the scour depth around a pier along the convex bank in the S-shaped flume increases as the distance between two piers (or pier spacing) increases, while it decreases around the piers along the concave bank. Similar scour patterns were observed when the side-by-side piers were installed at different bend apex cross-sections. The maximum local scour depths at piers along the convex bank measured at different bend apex cross-sections were relatively unchanged when other influencing factors were held constant. However, the maximum scour depth around piers along the concave bank decreased as the bends increased toward downstream. Full article
(This article belongs to the Special Issue Cold Region Hydrology and Hydraulics)
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16 pages, 6212 KiB  
Article
Laboratory Study of the Hydraulic Performance of the A-Type Triangular Piano Key Weir
by Forough Alizadeh Sanami, Amir Ghaderi, Fardin Alizadeh Sanami, Parisa Mirkhorli and Silvia Di Francesco
Water 2023, 15(11), 2124; https://doi.org/10.3390/w15112124 - 2 Jun 2023
Cited by 4 | Viewed by 2254
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Section Hydraulics and Hydrodynamics)
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23 pages, 9997 KiB  
Article
Application of Physical and Numerical Modeling for Determination of Waterway Safety under the Bridge in Kaunas City, Lithuania
by Tomasz Dysarz, Tomasz Kałuża, Karolis Mickevičius, Jonas Veigneris, Paweł Zawadzki, Sebastian Kujawiak, Stanisław Zaborowski, Joanna Wicher-Dysarz, Natalia Walczak, Jakub Nieć and Raimundas Baublys
Water 2023, 15(4), 731; https://doi.org/10.3390/w15040731 - 12 Feb 2023
Cited by 5 | Viewed by 3550
Abstract
The main problem presented in this paper is the safety inlet navigation of the waterway below the bridge in the city of Kaunas in Lithuania. The analyzed reach is located in the Nemunas river downstream of the Kaunas dam. It is a part [...] Read more.
The main problem presented in this paper is the safety inlet navigation of the waterway below the bridge in the city of Kaunas in Lithuania. The analyzed reach is located in the Nemunas river downstream of the Kaunas dam. It is a part of the waterway E–41 leading to the Klaipeda harbor on the southern coast of the Baltic Sea. The work was initiated by the Lithuanian company UAB “Inžinerinis projektavimas” with funds from the project called European Union Trans-European Transport Network (EU TEN-T). The main requirement imposed along this reach is to keep sufficient depth even in the range of the lowest flows. The depth is sufficient if it is not lower than 1.15 m for minimum flows such as Q95% and Q95% with ice. The hydraulic conditions for maximum flow Q50%, Q5%, and Q1% are also taken into account for control because the threat of hydraulic jump generation was also noticed. The research is based on georeferenced data from public and non-public sources. The hydrologic data were received from the Lithuanian Hydrometeorological Service. The physical model was created in the Water Laboratory of the Department of Hydraulic and Sanitary Engineering at Poznan University of Life Sciences, Poland. The preprocessing of spatial data in ArcGIS 10.8.2 and rules of hydraulic similarity were implemented in the process of physical model preparation. Three experiments were conducted in the laboratory with scaled values of Q95%, Q5%, and Q1%. The measurements of the water surface and evaluations of the average velocity were used to validate the 2D numerical model prepared in HEC-RAS 6.3.1. The basic layers of the HEC-RAS model were preprocessed in ArcGIS 10.8.2 by ESRI company. The numerical model was implemented to test different values of unknown roughness of the channel bottom. The simulations were conducted for the real values of Q95% and Q95% with ice and Q50%. The results of the simulations were depth and Froude number maps. These maps were classified into zones of no risk, middle risk, and high risk. ArcGIS in the post-processing phase was applied to identify the locations of the hazards. The magnitude of risk was expressed in terms of minimum depth achieved, maximum Froude number, as well as the length of the reaches with high risk related to these two factors. The threat of hydraulic jump formation below the bridge was also noticed. Conducted results confirmed that the combination of hydrodynamic simulations and geoprocessing in the pre- and post-processing stages could be a powerful tool in hydraulic engineering analyses. Additionally, it is worth noting that numerical modeling enables a wider analysis of potential conditions than could be possible with a physical model only. Full article
(This article belongs to the Special Issue Harbor, Waterway and Marinas Hydrodynamics)
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18 pages, 2601 KiB  
Article
Waved-Shape Accumulation of Ice Jam—Analysis and Experimental Study
by Pangpang Chen, Jueyi Sui, Guangxue Cao and Tiejie Cheng
Water 2022, 14(23), 3945; https://doi.org/10.3390/w14233945 - 4 Dec 2022
Cited by 4 | Viewed by 2051
Abstract
Ice jam is a unique hydrological phenomenon in rivers in cold regions. The appearance of an ice jam in a river results in an increase in the wetted perimeter of the flow cross-section, and thus an increase in flow resistance as well as [...] Read more.
Ice jam is a unique hydrological phenomenon in rivers in cold regions. The appearance of an ice jam in a river results in an increase in the wetted perimeter of the flow cross-section, and thus an increase in flow resistance as well as water level. It may cause ice flooding sometimes. Similar to the “sand wave” phenomenon in riverbed, it has been observed in laboratory experiments that the waved-shape accumulation of ice particles (termed as “ice wave”) under an ice jam occurred. In this study, an Equation for describing the relationship between the approaching flow Froude number (Fr) and the ratio of ice jam thickness to flow depth (t/H) has been proposed. Taking the inflection point value of the equation under different flow depths, a characteristic curve has been developed to judge whether ice waves under an ice jam occurs. When the flow Froude number in front of an ice jam is below the value at the inflection point of the curve, the ice jam can maintain a mechanical stability within the ice jam thickness in a range from the lower limiting value to the upper limiting value, which were close to the ice wave trough thickness and the ice wave crest thickness, respectively. An Equation for calculating the ice wavelength has been derived and verified by using results of laboratory experiments. The relationship between the migration speed of ice wave and the ratio of ice discharge to water flow rate (Qi/Q) has been also analyzed. At last, case studies have been conducted with respect to ice accumulation in the St. Lawrence River, the Beauharnois Canal and the La Grande River. Results of case studies show that the shoving and ice dam have been dominated by mechanical factors, which would be accompanied by the ice wave phenomenon during the ice jam accumulation process. Results of case studies about ice accumulation in natural rivers also show that the relative thickness of an ice jam (t/H) of 0.4 is the criterion for assessing whether an ice jam in a river belongs to an ice dam. Full article
(This article belongs to the Special Issue Fluvial Hydraulics Affected by River Ice and Hydraulic Structures)
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15 pages, 4349 KiB  
Article
Hydrodynamics of the Instream Flow Environment of a Gravel-Bed River
by Agnieszka Woś and Leszek Książek
Sustainability 2022, 14(22), 15330; https://doi.org/10.3390/su142215330 - 18 Nov 2022
Cited by 3 | Viewed by 1801
Abstract
This work was aimed at comparing the instream flow environment of four basic hydromorphological units of a mountain gravel-bed river: pools, runs, riffles and rapids. A survey was performed during the average flow stage on the Skawa River in southern Poland. In the [...] Read more.
This work was aimed at comparing the instream flow environment of four basic hydromorphological units of a mountain gravel-bed river: pools, runs, riffles and rapids. A survey was performed during the average flow stage on the Skawa River in southern Poland. In the 3.5 km long reach, 31 physical habitats were surveyed: eight pools, eight runs, nine riffles and seven rapids. Using Micro ADV Sontek equipment, instantaneous velocity time series components were measured at eight locations in three positions—z/h = 0.2, 0.4 and 0.6—in each unit. Turbulence descriptors—the mean components of velocity, turbulence intensities calculated as the root mean square of velocity component time series, turbulent kinetic energy TKE, Reynolds shear stresses and standard hydraulic attribute, i.e., Froude number—were estimated. Although there was a wide dispersion of the turbulence variable distributions, a standard tendency of decreased mean velocity and increased turbulence towards the bottom was observed. Most turbulence parameters—streamwise velocity, turbulence intensities, TKE and streamwise-vertical Reynolds shear stresses—reveal differences of instream flow environment between the pools, runs and riffles. In addition, the mean turbulence intensities suggested a 1:2:3:3 proportion of turbulence intensity in pools, runs, riffles and rapids, respectively. Riffles and rapids, in general, have similar turbulence values, whereas rapids are deeper and visually more energetic. Full article
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31 pages, 10956 KiB  
Article
Study of Two Ships Approaching Process and Towing Motion under Wave Action
by Shengtao Chen, Han Zou, Guocai Qi, Dongju Li and Zhouyuan Xu
J. Mar. Sci. Eng. 2022, 10(9), 1209; https://doi.org/10.3390/jmse10091209 - 29 Aug 2022
Cited by 1 | Viewed by 5056
Abstract
The rescue of ships in distress at sea relies mainly on rescue vessels, which includes the approaching process and the towing motion of the two ships. Ship rescue can be reduced to a two-ship problem, primarily involving the relative motion between ships during [...] Read more.
The rescue of ships in distress at sea relies mainly on rescue vessels, which includes the approaching process and the towing motion of the two ships. Ship rescue can be reduced to a two-ship problem, primarily involving the relative motion between ships during rescue. We established a mathematical model of ship motion based on the viscous fluid N-S equation, and the approaching process of two Wigley ships under waves was simulated in a two-dimensional plane. Then, according to three-dimensional potential flow theory, the coupled motion response model of the ships under six degrees of freedom was constructed, and calculation models of wind, waves, currents and other environmental disturbance factors were established to numerically calculate the towing motion. The results show that the upstream vessel has a lower heave motion amplitude and higher roll motion amplitude during the approaching process; A ratio of 1.5 times the width of the ship is the critical area where the motion of the two ships interacts with each other; For the berthing process, the faster the motion of the active vessel is, the lower the motion amplitude will be for both upstream and downstream vessels. When towing under rough sea conditions, changes in wave height and towing velocity have a large influence on the coupling effect of the towing system. When towing, head-on waves and low sea conditions are preferred, and the velocity should be sufficiently high to reduce the influence of cable self-weight on the towed ship. According to the simulations, the recommended velocity range is 3–5 m/s. Finally, a ship model scaling model was developed based on the similar quasi-Froude number of the ship model test, and the simulation results were verified by conducting parallel and towing tests of the model in a basin with a spherical wave-maker device. Full article
(This article belongs to the Special Issue Seakeeping and Performance in Waves of Marine Vessels)
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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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18 pages, 5971 KiB  
Article
Numerical Analysis of Pressure Profiles and Energy Dissipation across Stepped Spillways Having Curved Risers
by Najam us Saqib, Muhammad Akbar, Huali Pan, Guoqiang Ou, Muhammad Mohsin, Assad Ali and Azka Amin
Appl. Sci. 2022, 12(1), 448; https://doi.org/10.3390/app12010448 - 4 Jan 2022
Cited by 8 | Viewed by 3055
Abstract
In this study, curved risers stepped spillways models based on the increasing angle of suspension were tested to check for improvement in energy dissipation and pressure distributions. Four fourteen-steps stepped spillway models with a slope 1:0.84 were selected, using Froude’s number non-dimensional similarity. [...] Read more.
In this study, curved risers stepped spillways models based on the increasing angle of suspension were tested to check for improvement in energy dissipation and pressure distributions. Four fourteen-steps stepped spillway models with a slope 1:0.84 were selected, using Froude’s number non-dimensional similarity. The risers of steps were made curved, based on three angles of suspensions, i.e., 30°, 60°, and 90°. The simulations were performed by FLOW 3D software and by the turbulence model Renormalization Group (RNG) for discharges between 0.020 and 0.068 m3/s followed by the model calibration. The 3D Reynolds-averaged Navier–Stokes equations were solved, which included sub-grid models for air entrainment, density evaluation, and drift–flux, to capture free-surface flow over the stepped spillway. It was estimated that curving the risers increases the energy dissipation up to three percent for lower flow rates, whereas it has no significant impact on energy dissipation for higher flow rates. It was found that in simply stepped spillway lower steps dissipate more energy as compared to curved risers stepped where energy dissipation is shifted to higher steps. On the other hand, curved risers stepped spillways showed lower values of negative pressures as compared to the simply stepped spillway. It was seen that a higher energy dissipating step as experienced more negative pressures as compared to the lower energy dissipating step. Full article
(This article belongs to the Special Issue New Frontiers in Sustainable Geotechnics)
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23 pages, 5288 KiB  
Article
Drag on a Square-Cylinder Array Placed in the Mixing Layer of a Compound Channel
by Rui M. L. Ferreira, Miltiadis Gymnopoulos, Panayotis Prinos, Elsa Alves and Ana M. Ricardo
Water 2021, 13(22), 3225; https://doi.org/10.3390/w13223225 - 14 Nov 2021
Cited by 3 | Viewed by 2530
Abstract
There are no studies specifically aimed at characterizing and quantifying drag forces on finite cylinder arrays in the mixing layer of compound channel flows. Addressing this research gap, the current study is aimed at characterizing experimentally drag forces and drag coefficients on a [...] Read more.
There are no studies specifically aimed at characterizing and quantifying drag forces on finite cylinder arrays in the mixing layer of compound channel flows. Addressing this research gap, the current study is aimed at characterizing experimentally drag forces and drag coefficients on a square-cylinder array placed near the main-channel/floodplain interface, where a mixing layer develops. Testing conditions comprise two values of relative submergence of the floodplain and similar ranges of Froude and bulk Reynolds numbers. Time-averaged hydrodynamic drag forces are calculated from an integral analysis: the Reynolds-averaged integral momentum (RAIM) conservation equations are applied to a control volume to compute the drag force, with all other terms in the RAIM equations directly estimated from velocity or depth measurements. This investigation revealed that, for both tested conditions, the values of the array-averaged drag coefficient are smaller than those of cylinders in tandem or side by side. It is argued that momentum exchanges between the flow in the main channel and the flow in front of the array contributes to reduce the pressure difference on cylinders closer to the interface. The observed drag reduction does not scale with the normalized shear rate or the relative submersion. It is proposed that the value of the drag coefficient is inversely proportional to a Reynolds number based on the velocity difference between the main-channel and the array and on cylinder spacing. Full article
(This article belongs to the Section Hydraulics and Hydrodynamics)
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