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The roughness Froude number is a relatively new dimensionless parameter that began appearing in the hydraulic engineering literature in the late 1970s, first for the analysis of aeration inception in smooth chutes, and then later in connection with stepped chutes. This article reviews its foundations, historical development, alternative forms, present-day applications, and physical significance, which has received little attention previously. In addition to its empirically demonstrated connection to aeration inception, this paper shows that one form of a roughness Froude number has a strong relation to the transition between nappe and skimming flow regimes of stepped chutes, while another combines the dimensionless flow friction factor and the relative submergence of roughness elements. [ABSTRACT FROM AUTHOR]

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Air entrainment and self-aeration flow are phenomena that can generate fluctuation in pressure and induce disadvantages in piping systems. In this study, the mechanism of air bubble formation in Partially Filled Pipe Flow (PFPF) is investigated through a series of experiments on a butterfly valve with flow visualization and pressure measurement. This paper provides a description of the formation of bubbles induced by a butterfly valve and analyzes the characteristics of the pressure and flow coefficient of the valve. The pressures at various locations on the pipeline adjacent to the valve were measured to compare with the positions recommended by the International Society of Automation standard. The results indicated that in PFPF, the differences in the pressure between measured points downstream are noticeable, notably at valve openings less than 50°. The bubbles created at the valve, which lead to the highly-disordered aerated flow downstream, might induce the differences. The pressure drop and the flow rate across the butterfly valve in 100% water fraction flow are respectively 3–7.5 and 2–9 times higher than those in 90% WF. The flow coefficient of the 3-inch butterfly valve was found to increase linearly with the Reynolds number before leveling off when the Reynolds number exceeds 6×104. Besides, the flow coefficients in 100% water fraction flow are double those in 90% water fraction flow.

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. [ABSTRACT FROM AUTHOR]

Copyright of China Rural Water & Hydropower is the property of China Rural Water & Hydropower Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

ABSTRACT The operation of stepped spillways is limited by a range of discharges due to the risk of occurrence of the cavitation phenomenon and erosion on its steps. Since there is a demand for spillways with the possibility of overflow of greater discharges, the designs seek to increase the air concentration of the flow, which can occur through the installation of piers in the spillway in order to protect the structure from the above mentioned damage. The aim of this work is to analyze flow characteristics and extreme minimum and maximum pressures with non-exceedance probability of 0.1% and 99.9% acting next to the step edges of the spillway with aeration induced by piers through an experimental analysis in a physical model. Based on the results obtained, flow behavior was defined and equations for predicting the extreme pressures that occur along the stepped spillway with aeration induced by piers were proposed.

Aerated flows pose both challenges and opportunities in the measurement of free water surface. In this study, an amplitude-modulated continuous wave scanning LIDAR device was used to measure a distance from the device sensor to the water column surface subjected to different degrees of aeration, while reference measurements were performed by high-speed imaging. Different aeration conditions were generated by variation of the air flow rate supplied to the liquid and by using perforated plates with different hole arrangements. The LIDAR device was shown to produce level readings consistently below visible water levels. The measurement error of the LIDAR method is largely determined by the volume fraction of air in water and was lowest at about 0.1 air volume fraction. The error increases linearly until a very high air volume fraction (i.e., above 0.55), while the LIDAR method also performs poorly in unaerated water. Although the measurement uncertainty of LIDAR in the range of aerated water is by at least an order of magnitude higher than in the case of measuring dry solid surfaces, the method is viable for free surface measurement under low to moderate aeration conditions that don't produce excessive foaming. • Laser ranging measurements of aerated free water surface were performed. • Reference water surface measurements by high-speed imaging. • Slight aeration significantly improves the accuracy of the LIDAR method. • Minimum error around 0.1 air volume fraction, increases linearly after that. • Low effect of air bubble size on measurement error. [ABSTRACT FROM AUTHOR]

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.

The energy dissipation in plunge pools is often related to air entrainment in the plunging jet. Recent experimental work showed that the void fractions below the impinging jet are significantly smaller than outside the jet impact. This was attributed to the compression of the entrained air bubbles. In this paper, the thermodynamics of air bubble compression is introduced as a novel energy dissipation mechanism in civil engineering hydraulics. For the analysis of reported experimental data, isothermal conditions were applied as a lower bound approximation. It was found that the energy dissipation rates range from 2.7–9.7% for a jet velocity of 10 m s−2 and void fractions of 0.11 and 0.31, to 15.9–36.0% for a jet velocity of 24.5 m s−1 and void fractions of 0.35–0.55. The results may explain the difference between energy dissipation rates in plunge pools at model and full scale. [ABSTRACT FROM AUTHOR]

Circular drop manholes are widely implemented for steep catchments in urban drainage networks. Poor downstream hydraulic transition processes of a manhole system, i.e., the formation of hydraulic jump near the outlet entrance, and the sudden transition from free surface to pressurized flow with bursts of air in the outflow pipe can severely constraint the capacity of water conveyance. In this paper, we defined four basic hydraulic stages that indicate where hydraulic transition processes begin and end. The measurements of typical manhole models with different drop heights were conducted under different inflow and outflow conditions. Three types of transition processes covering all flow patterns have resulted into a graphical visualization by analyzing two pairs of dimensionless parameters. The flow inside a circular drop manhole was considered to reach its discharge capacity when the abrupt drop of manhole water level is visible in the fully aerated flow pattern. Four empirical equations revealing the water level filling ratio and discharge efficiency at different hydraulic stages were also presented for further predictions of choking risks.

A numerical model, based on the open source code OpenFOAM, was developed to predict jet regimes and total dissolved gas downstream of spillways. The model utilizes the volume of fluid method to track the interface between air and water. A detached eddy simulation model is used for turbulence closure. Transport and dissolution of bubbles are predicted using an Eulerian approach. A bubble number density equation was implemented to predict bubble size changes caused by dissolution and compression. Total dissolved gas was computed using a transport equation that includes the mass transfer between bubbles and water. The model simultaneously captured spillway jet regimes and distribution of total dissolved gas in a spillway sectional model of McNary Dam. Model parameters, gas volume fraction and bubble size at the entrainment region, were calibrated to match total dissolved gas measured in the field under different dam operations. [ABSTRACT FROM AUTHOR]

The presence of air in open channel flows will increase the bulk of the flow, and is of great importance in the design of spillway and chute sidewalls. Hydraulics in the developed region is investigated in this paper systematically by a series of model and prototype investigations. It is verified that the velocity in the aeration region is the dominant factor. For the flow with an identical velocity but a different flow depth, the air concentration distributions are nearly the same. From the theory based on the formation of drops on the surface by the turbulent liquid jets and the vortex deformation, a formula to calculate the incremental depth is obtained by best correlating the model and prototype investigations. The formula is reasonable with less mean error than those obtained by other methods, which could recommended for the use in engineering designs. [ABSTRACT FROM AUTHOR]

There is a lack of knowledge on the air concentration distribution in plunge pools affected by aerated jets. A set of physical experiments was performed on vertical submerged aerated jet flows impinging a plunge pool. The air concentration distribution in the plunge pool was analyzed under different inflow air concentrations, flow velocities, and discharge rate conditions. The experimental results show that the air concentration distribution follows a power-law along the jet axis, and it is independent of the initial flow conditions. A new hypothetical analysis model was proposed for air diffusion in the plunge pool, that is, the air concentration distribution in the plunge pool is superposed by the lateral diffusion of three stages of the aerated jet motion. A set of formulas was proposed to predict the air concentration distribution in the plunge pool, the results of which showed good agreement with the experimental data.

Measuring the topography of water surfaces with conventional measurement methods is, particularly in the case of turbulent flow with strong vertical and longitudinal dynamics, a very demanding and challenging task. Channel confluences are important elements in river engineering, as they appear in natural and regulated river channels, torrents, as well as in numerous hydraulic structures. At confluences, especially in the case of incoming supercritical flow, turbulent three-dimensional flows occur, and a time-varying structure of waters surface. Laser scanning enables data capture with high spatial and temporal resolution, and this method is widely used nowadays. This article discusses laser scanning as a measurement method for acquiring the agitated shape of a water surface. The application of a commercial two-dimensional LIDAR device for free-water-surface acquisition is presented for two cases. In the first case the measurements were performed in a glass tank where it was possible to determine the precise reference water level. In the second case we used LIDAR with turbulent aerated flow for fluctuating free-water surface measurement. Measurements were taken in the model of supercritical confluence, where the development of standing waves leads to the phenomenon of self-aerated flow. The measurements presented in the paper were conducted for a selected discharge rates and the Froude numbers of the main and side flow channels. Measurement results are shown as surface profiles at several selected locations of confluence. This measurement method has proven to be very promising. [ABSTRACT FROM AUTHOR]

Thin-plate weirs are the simplest and least expensive devices, which frequently have been employed in many water projects. In this research, a unique type of Sharp-Crested V-notch weir, entitled SCVW, has been introduced. The hydraulic characteristics of the present weir were investigated theoretically and experimentally under free aerated and non-aerated flow conditions in an open channel for large physical models. To investigate the variations of the discharge coefficient of SCVW versus weir height and vertex angle, a comprehensive laboratory experiments were conducted by measuring the discharge and the water head over the crest of weir. Possibility of different formulations for the head- discharge relationship of SCVW was examined and suitable analytical equation was proposed. The computed discharge using the suggested equation was within 0–10% of the observed ones. According to the experimental observations, the SCVW showed better performance in comparison with normal wire. [ABSTRACT FROM AUTHOR]

The large deformations associated with air and water interactions are critical factors that affect the hydrodynamic characteristics of hydraulic structures. As a type of Lagrange meshless particle method, smoothed particle hydrodynamics (SPH) has been shown to have many advantages when modeling the interface flow and tracing the free surface because the particles inherit the velocity, mass, and density properties. Significant theoretical and numerical studies have been performed recently in this area. In the present study, a two-phase SPH framework was developed based on these previous studies and we explored its capacity to capture the main features of large density ratio aerated flows. The cohesive pressure was included only in the momentum equation of the air phase for additional amendments to ensure the stability and accuracy of the two-phase SPH model. Three case studies were performed to test the performance of the two-phase SPH model. A convergence study demonstrated the need to balance the CPU time consumption and the real-time requirements. A dam-break simulation based on pressure variation in the air pocket showed the superior analytical performance of the two-phase model compared with the single-phase model. The results of a hydraulic jump simulation were compared with the theoretical results in order to understand the collision between the solid and liquid using the SPH method more clearly. Thus, the consistency between the simulation and the theoretical and experimental results demonstrated the feasibility and stability of the two-phase SPH framework. [ABSTRACT FROM AUTHOR]

Optical flow estimation is known from Computer Vision where it is used to determine obstacle movements through a sequence of images following an assumption of brightness conservation. This paper presents the first study on application of the optical flow method to aerated stepped spillway flows. For this purpose, the flow is captured with a high-speed camera and illuminated with a synchronized LED light source. The flow velocities, obtained using a basic Horn-Schunck method for estimation of the optical flow coupled with an image pyramid multi-resolution approach for image filtering, compare well with data from intrusive conductivity probe measurements. Application of the Horn-Schunck method yields densely populated flow field data sets with velocity information for every pixel. It is found that the image pyramid approach has the most significant effect on the accuracy compared to other image processing techniques. However, the final results show some dependency on the pixel intensity distribution, with better accuracy found for grey values between 100 and 150. [ABSTRACT FROM AUTHOR]

The free flow on the step surfaces has received much attention for its representative body type, flow structure, water-air two phase flow, cavitation, and many complex issues. The experiments about the time-averaged pressure and aeration concentration distribution on the step surface show that the vertical plane of steps will inevitably experience negative pressure, which must rely on adequate aeration concentration to avoid cavitation damage. However, the self-aerated flow at the head section has a relatively low aeration concentration, and the concentration of the entire steps decreases with the increasing of weir head, the minimum appears in the vicinity of the corner, and the location is close to the minimum pressure. Thus, it is necessary to set aerator in the upstream end of the step surfaces to avoid cavitation damage. [ABSTRACT FROM AUTHOR]

Stepped chutes effectively dissipate the energy of supercritical flow of steep channels. In general, stepped chute flows are characterized by self-aeration. For their hydraulic design, it is important to know the aerated flow depth, the aerated flow velocity, the air concentration, and the specific energy. Herein, quasi-uniform aerated skimming flow is systematically investigated over a range of chute angles from 19° to 55° for a wide range of step heights and discharges. Air concentration and aerated flow velocity profiles are presented, and the depth-averaged air concentration and the friction factor are determined. The specific energy is determined based on the aerated flow characteristics, revealing the effects of chute angle and step height on the specific energy of aerated skimming flow. This quantity was compared with the conventional specific energy of clear-water flows. [ABSTRACT FROM AUTHOR]

Abstract: Setting aeration facilities on the discharge structure in the dam to make the gas in the flow, is a common used method to reduce erosion damage to the building today. Based on the feature of the discharge structure and considering the types of the ventilation facilities and air-intake system, this paper simplified a model for project to analyze and established the corresponding mathematical model. With ICEM/CFD software the finite element model was generated. Using the commercial software FLUENT to do the flow state analysis, it obtained the velocity of the aerated flow and the pressure distribution. On the basis of the simulation of the single characteristic diameter bubble flow, it gave a contrast and analysis to the range of application and the differences of accuracy between the SIMPLE and PISO methods. [Copyright &y& Elsevier]

Abstract: Sharp bends in drainage channels are sometimes engineered to suit local topography, especially in densely populated cities where land is limited. A hydraulic model study of a steep urban drainage channel is carried out to investigate the causes of an overflow incident in Hong Kong urban area, and to develop the drainage improvement measures to prevent flooding. The stepped drainage channel has a sharp bend in the middle and several trash racks are located along the channel. Experiments are performed on a 1:16 Froude scale model. In the first phase, experiments on a purposely built straight channel model are performed to study the bottom roughness of the stepped channel flow isolating the effect of the bend. After the straight channel experiments, four trash rack scenarios are tested in the exact model with detailed channel features. The flow in the drainage channel is supercritical and highly aerated. Based on the theory of skimming flow in stepped channels, a hydraulic assessment suggests that the bend and trash racks may be dominant causes of the overflow. The experiments show that sharp bend causes a spiral flow leading to significant lateral overflow. The trash racks are observed to generate a serious ski-jump type overshooting flow. It is found that the stormwater overshoot and flooding can be prevented by the repositioning of appropriately sized trash racks and the containment of the spiral flow. The proposed channel improvement design has been implemented on site and found to work successfully in heavy rainstorms after installation. The present study offers novel insights into the design of urban drainage works. [Copyright &y& Elsevier]

In connection with the specific features of high velocity aerated flow generated by hydraulic engineering structures, the mathematical model is developed for high turbulence air-water two-phase flow with the use of twin flow theoretical model in this paper. Furthermore the numerical method is proposed to treat bubbled flows. In addition, on the basis of air-water stratified twin flow model, the new calculation methods and free surface tracking technique are proposed to describe complicated movements of the free surface. Finally, the proposed model is used to calculate artificial aerated flows. The computed results coincide quite well with experimental results. This means that the proposed method can provide solid basis for practical engineering design. [ABSTRACT FROM AUTHOR]

ABSTRACT: The effect of reducing cavitation damage in high-speed flow structure not only relate with entrained air concentration, but also relate with air bubble density has been discovered in recent research. The air bubbles in aerated flow with diameter below then 0.2mm or 0.5mm plays important role in reducing cavitation damage. May be very little air concentration can protect construction free from cavitation erosion. Thereby, measuring bubble size must be emphasized in study of reducing cavitation damage. Measuring bubble size can use probe of needle-type and image usually. By analyses and application experience of velocimeter of air concentration probe of needle-type, suggesting of the median size of bubble d50 adopt measuring data by probe directly, and calculate space distance and density of bubble. Although, the d50 and space distance would be big then real size, and density small then real value. The measuring results have importance value for studying mechanism and establishing a new criterion on entrained air to reduce cavitation damage. [Copyright &y& Elsevier]

Circular drop manholes are widely implemented for steep catchments in urban drainage networks. Poor downstream hydraulic transition processes of a manhole system, i.e., the formation of hydraulic jump near the outlet entrance, and the sudden transition from free surface to pressurized flow with bursts of air in the outflow pipe can severely constraint the capacity of water conveyance. In this paper, we defined four basic hydraulic stages that indicate where hydraulic transition processes begin and end. The measurements of typical manhole models with different drop heights were conducted under different inflow and outflow conditions. Three types of transition processes covering all flow patterns have resulted into a graphical visualization by analyzing two pairs of dimensionless parameters. The flow inside a circular drop manhole was considered to reach its discharge capacity when the abrupt drop of manhole water level is visible in the fully aerated flow pattern. Four empirical equations revealing the water level filling ratio and discharge efficiency at different hydraulic stages were also presented for further predictions of choking risks. [ABSTRACT FROM AUTHOR]

• In a two-phase breaking bore roller, air entrainment takes place in the form of air entrapment at the roller toe, air-water exchange across the roller 'free-surface', spray and splashing with dynamic water drop ejection and reattachment, roll up and roll down of water 'tongues' engulfing air pockets. • All experimental measurements indicated a relatively short and thin air-water flow region. The number of air bubbles within the roller was limited, chord lengths spanned over several orders of magnitude, with increasing chord size with increasing vertical elevation within the roller. • Large proportion of clustered bubbles were observed and the clustering characteristics were similar to those in stationary hydraulic jumps. • Results could serve as a validation frame for computational fluid dynamics (CFD) modelling, as the modelling of air-water interactions in breaking rollers of hydraulic jumps and tidal bores remain a huge challenge for numerical modeller. A tidal bore is an unsteady rapidly-varied open channel flow characterised by a rise in water surface elevation in estuarine zones, under spring tidal conditions. After formation, the bore is traditionally analysed as a hydraulic jump in translation and its leading edge is characterised by a breaking roller for Froude number Fr 1 > 1.3–1.5. The roller is a key flow feature characterised by intense turbulence and air bubble entrainment. Detailed unsteady air-water flow measurements were conducted in a breaking bore propagating in a large-size channel, using an array of three dual-tip phase detection probes and photographic camera. The data showed a relatively steep roller, with a short and dynamic bubbly flow region. Air entrainment took place in the form of air entrapment at the roller toe, air-water exchange across the roller 'free-surface', spray and splashing with dynamic water drop ejection and re-attachment, roll up and roll down of water 'tongues' engulfing air pockets. The roller free-surface profile and characteristics were comparable to observations in stationary hydraulic jumps and steady breaker, for similar flow conditions. Within the roller, the amount of entrained air was quantitatively small for Froude number Fr 1 = 2.2. The number of air bubbles was limited, with between 5 and 20 bubbles per phase-detection probe sensor detected at each vertical elevation. The entrained air bubble chord lengths spanned over several orders of magnitude, with a large proportion of clustered bubbles. Overall, the study highlighted the three-dimensional nature of the air-water roller motion and strong evidence of the in-homogeneity of the turbulent air-water mixture. [ABSTRACT FROM AUTHOR]

There is a lack of knowledge on the air concentration distribution in plunge pools affected by aerated jets. A set of physical experiments was performed on vertical submerged aerated jet flows impinging a plunge pool. The air concentration distribution in the plunge pool was analyzed under different inflow air concentrations, flow velocities, and discharge rate conditions. The experimental results show that the air concentration distribution follows a power-law along the jet axis, and it is independent of the initial flow conditions. A new hypothetical analysis model was proposed for air diffusion in the plunge pool, that is, the air concentration distribution in the plunge pool is superposed by the lateral diffusion of three stages of the aerated jet motion. A set of formulas was proposed to predict the air concentration distribution in the plunge pool, the results of which showed good agreement with the experimental data. [ABSTRACT FROM AUTHOR]