Explicit equations for critical depth in open channels with complex compound cross sections. A discussion

In open channel hydraulics, the notion of critical flow conditions and critical depth are not restricted to open channel flows with hydrostatic pressure distributions. This contribution shows an extension of the concept of critical flow conditions linked with the minimum specific energy, as introduced by Bakhmeteff [1] and extended by Liggett [9] and Chanson [5]. It demonstrated that the critical depth may be defined more broadly including when the pressure field is not hydrostatic

Comment on "Critical Flow Constrains Flow Hydraulics in Mobile-Bed Streams: A New Hypothesis" by G. E. Grant

The writer discusses the challenging ideas proposed by GRANT (1997) on steep movable bed channel flows. First the definition of critical flow are revisited. Then, the calculation of bed shear stress in near-critical flows are discussed. New experimental data are presented, and they highlight the three-dimensional variations of boundary shear stress. It is believed further that the applicability of GRANT's (1997) hypothesis is restricted because of the confusion between critical and near-critical flows

Discussion of "transcritical flow due to channel contraction" by O. Castro-Orgaz, J. V. Giraldez, and J. L. Ayuso

The design of channel contraction is not obvious when transcritical or near-critical flows take place. The concept of critical flow conditions was first developed by Bélanger (1828) and later expanded by Bakhmeteff (1912, 1932). Bélanger and Bakhmeteff both defined the concept of critical flow in relation to the singularity of the backwater equation. Herein further applications of transcritical flow in channel contraction are discussed and a solution of the critical flow singularity is presented

Minimum Specific Energy and Critical Flow Conditions in Open Channels

In open channels, the relationship between the specific energy and the flow depth exhibits a minimum, and the corresponding flow conditions are called critical flow conditions. Herein they are re-analysed on the basis of the depth-averaged Bernoulli equation. At critical flow, there is only one possible flow depth, and a new analytical expression of that characteristic depth is developed for ideal-fluid flow situations with non-hydrostatic pressure distribution and non-uniform velocity distribution. The results are applied to relevant critical flow conditions : e.g., at the crest of a spillway. The finding may be applied to predict more accurately the discharge on weir and spillway crests

Experimental Characterization of the Hydraulic Jump Profile and Velocity Distribution in a Stilling Basin Physical Model

[EN] The study of the hydraulic jump developed in stilling basins is complex to a high degree due to the intense velocity and pressure fluctuations and the significant air entrainment. It is this complexity, bound to the practical interest in stilling basins for energy dissipation purposes, which brings the importance of physical modeling into the spotlight. However, despite the importance of stilling basins in engineering, bibliographic studies have traditionally focused on the classical hydraulic jump. Therefore, the objective of this research was to study the characteristics of the hydraulic jump in a typified USBR II stilling basin, through a physical model. The free surface profile and the velocity distribution of the hydraulic jump developed within this structure were analyzed in the model. To this end, an experimental campaign was carried out, assessing the performance of both, innovative techniques such as the time-of-flight camera and traditional instrumentation like the Pitot tube. The results showed a satisfactory representation of the free surface profile and the velocity distribution, despite some discussed limitations. Furthermore, the instrumentation employed revealed the important influence of the energy dissipation devices on the flow properties. In particular, relevant di erences were found for the hydraulic jump shape and the maximum velocity positions within the measured vertical profiles, when compared to classical hydraulic jumps.This research was funded by 'Generalitat Valenciana predoctoral grants (Grant number [2015/7521])', in collaboration with the European Social Funds and by the research project: 'La aireacion del flujo y su implementacion en prototipo para la mejora de la disipacion de energia de la lamina vertiente por resalto hidraulico en distintos tipos de presas' (BIA2017-85412-C2-1-R), funded by the Spanish Ministry of Economy.Macián Pérez, JF.; Vallés-Morán, FJ.; Sánchez Gómez, S.; De-Rossi-Estrada, M.; García-Bartual, R. (2020). Experimental Characterization of the Hydraulic Jump Profile and Velocity Distribution in a Stilling Basin Physical Model. Water. 12(6):1-20. https://doi.org/10.3390/w12061758S120126Valero, D., Viti, N., & Gualtieri, C. (2018). Numerical Simulation of Hydraulic Jumps. Part 1: Experimental Data for Modelling Performance Assessment. Water, 11(1), 36. doi:10.3390/w11010036Bayon, A., Valero, D., García-Bartual, R., Vallés-Morán, F. ​José, & López-Jiménez, P. A. (2016). Performance assessment of OpenFOAM and FLOW-3D in the numerical modeling of a low Reynolds number hydraulic jump. Environmental Modelling & Software, 80, 322-335. doi:10.1016/j.envsoft.2016.02.018Wang, H., & Chanson, H. (2015). Experimental Study of Turbulent Fluctuations in Hydraulic Jumps. Journal of Hydraulic Engineering, 141(7), 04015010. doi:10.1061/(asce)hy.1943-7900.0001010Padulano, R., Fecarotta, O., Del Giudice, G., & Carravetta, A. (2017). Hydraulic Design of a USBR Type II Stilling Basin. Journal of Irrigation and Drainage Engineering, 143(5), 04017001. doi:10.1061/(asce)ir.1943-4774.0001150Macián-Pérez, J. F., García-Bartual, R., Huber, B., Bayon, A., & Vallés-Morán, F. J. (2020). Analysis of the Flow in a Typified USBR II Stilling Basin through a Numerical and Physical Modeling Approach. Water, 12(1), 227. doi:10.3390/w12010227Montes, J. S., & Chanson, H. (1998). Characteristics of Undular Hydraulic Jumps: Experiments and Analysis. Journal of Hydraulic Engineering, 124(2), 192-205. doi:10.1061/(asce)0733-9429(1998)124:2(192)Ohtsu, I., Yasuda, Y., & Gotoh, H. (2001). Hydraulic condition for undular-jump formations. Journal of Hydraulic Research, 39(2), 203-209. doi:10.1080/00221680109499821Ohtsu, I., Yasuda, Y., & Gotoh, H. (2003). Flow Conditions of Undular Hydraulic Jumps in Horizontal Rectangular Channels. Journal of Hydraulic Engineering, 129(12), 948-955. doi:10.1061/(asce)0733-9429(2003)129:12(948)Bakhmeteff, B. A., & Matzke, A. E. (1936). The Hydraulic Jump in Terms of Dynamic Similarity. Transactions of the American Society of Civil Engineers, 101(1), 630-647. doi:10.1061/taceat.0004708Chachereau, Y., & Chanson, H. (2011). Free-surface fluctuations and turbulence in hydraulic jumps. Experimental Thermal and Fluid Science, 35(6), 896-909. doi:10.1016/j.expthermflusci.2011.01.009Zhang, G., Wang, H., & Chanson, H. (2012). Turbulence and aeration in hydraulic jumps: free-surface fluctuation and integral turbulent scale measurements. Environmental Fluid Mechanics, 13(2), 189-204. doi:10.1007/s10652-012-9254-3Montano, L., Li, R., & Felder, S. (2018). Continuous measurements of time-varying free-surface profiles in aerated hydraulic jumps with a LIDAR. Experimental Thermal and Fluid Science, 93, 379-397. doi:10.1016/j.expthermflusci.2018.01.016Montano, L., & Felder, S. (2020). LIDAR Observations of Free-Surface Time and Length Scales in Hydraulic Jumps. Journal of Hydraulic Engineering, 146(4), 04020007. doi:10.1061/(asce)hy.1943-7900.0001706Rajaratnam, N. (1965). The Hydraulic Jump as a Well Jet. Journal of the Hydraulics Division, 91(5), 107-132. doi:10.1061/jyceaj.0001299McCorquodale, J. A., & Khalifa, A. (1983). Internal Flow in Hydraulic Jumps. Journal of Hydraulic Engineering, 109(5), 684-701. doi:10.1061/(asce)0733-9429(1983)109:5(684)Viti, N., Valero, D., & Gualtieri, C. (2018). Numerical Simulation of Hydraulic Jumps. Part 2: Recent Results and Future Outlook. Water, 11(1), 28. doi:10.3390/w11010028Blocken, B., & Gualtieri, C. (2012). Ten iterative steps for model development and evaluation applied to Computational Fluid Dynamics for Environmental Fluid Mechanics. Environmental Modelling & Software, 33, 1-22. doi:10.1016/j.envsoft.2012.02.001Carrillo, J. M., Castillo, L. G., Marco, F., & García, J. T. (2020). Experimental and Numerical Analysis of Two-Phase Flows in Plunge Pools. Journal of Hydraulic Engineering, 146(6), 04020044. doi:10.1061/(asce)hy.1943-7900.0001763Heller, V. (2011). Scale effects in physical hydraulic engineering models. Journal of Hydraulic Research, 49(3), 293-306. doi:10.1080/00221686.2011.578914Chanson, H. (2006). Bubble entrainment, spray and splashing at hydraulic jumps. Journal of Zhejiang University-SCIENCE A, 7(8), 1396-1405. doi:10.1631/jzus.2006.a1396Hager, W. H., & Bremen, R. (1989). Classical hydraulic jump: sequent depths. Journal of Hydraulic Research, 27(5), 565-585. doi:10.1080/00221688909499111Meftah, M. B., De Serio, F., Mossa, M., & Pollio, A. (2008). Experimental study of recirculating flows generated by lateral shock waves in very large channels. Environmental Fluid Mechanics, 8(3), 215-238. doi:10.1007/s10652-008-9057-8Ben Meftah, M., Mossa, M., & Pollio, A. (2010). Considerations on shock wave/boundary layer interaction in undular hydraulic jumps in horizontal channels with a very high aspect ratio. European Journal of Mechanics - B/Fluids, 29(6), 415-429. doi:10.1016/j.euromechflu.2010.07.002Hager, W. H., Bremen, R., & Kawagoshi, N. (1990). Classical hydraulic jump: length of roller. Journal of Hydraulic Research, 28(5), 591-608. doi:10.1080/00221689009499048Kirkgöz, M. S., & Ardiçlioğlu, M. (1997). Velocity Profiles of Developing and Developed Open Channel Flow. Journal of Hydraulic Engineering, 123(12), 1099-1105. doi:10.1061/(asce)0733-9429(1997)123:12(1099

Bubbly flow measurements in hydraulic jumps with small inflow Froude numbers

The transition from supercritical to subcritical open channel flow is characterised by a strong dissipative mechanism called a hydraulic jump. A hydraulic jump is turbulent and associated with the development of large-scale turbulence and air entrainment. In the present study, some new physical experiments were conducted to characterise the bubbly flow region of hydraulic jumps with relatively small Froude numbers (2.4 < Fr(1) < 5.1) and relatively large Reynolds numbers (6.6 x 10(4) < Re < 1.3 x 10(5)). The shape of the time-averaged free-surface profiles was well defined and the longitudinal profiles were in agreement with visual observations. The turbulent free-surface fluctuation profiles exhibited a peak of maximum intensity in the first half of the hydraulic jump roller, and the fluctuations exhibited some characteristic frequencies typically below 3 Hz. The air-water flow properties showed two characteristic regions: the shear layer region in the lower part of the flow and an upper free-surface region above. The air-water shear layer region was characterised by local maxima in terms of void fraction and bubble count rate. Other air-water flow characteristics were documented including the distributions of interfacial velocity and turbulence intensity. The probability distribution functions (PDF) of bubble chord time showed that the bubble chord times exhibited a broad spectrum, with a majority of bubble chord times between 0.5 and 2 ms. An analysis of the longitudinal air-water structure highlighted a significant proportion of bubbles travelling within a cluster structure. (C) 2011 Elsevier Ltd. All rights reserved

Hydraulic jumps: Turbulence and air bubble entrainment

A free-surface flow can change from a supercritical to subcritical flow with a strong dissipative phenomenon called a hydraulic jump. Herein the progress and development in turbulent hydraulic jumps are reviewed with a focus on hydraulic jumps operating at large Reynolds numbers typically encountered in natural streams and hydraulic structures. The key features of the turbulent hydraulic jumps are the highly turbulent flow motion associated with some intense air bubble entrainment at the jump toe. The state-of-the-art on the topic is discussed based upon recent theoretical analyses and physical data

Free-surface profiles, velocity and pressure distributions on a broad-crested weir: a physical study

Basic experiments were conducted on a large-size broad-crested weir with a rounded corner. Detailed free-surface, velocity, and pressure measurements were performed for a range of flow conditions. The results showed the rapid flow distribution at the upstream end of the weir and next to the weir brink at large flow rates. The flow properties above the crest were analyzed taking into account the nonuniform velocity and nonhydrostatic pressure distributions. Introducing some velocity and pressure correction coefficients, it is shown that critical flow conditions were achieved above the weir crest for 0.1 < x/L-crest < 1. The velocity measurements highlighted a developing boundary layer. The data differed from the smooth turbulent boundary layer theory, although the present results were consistent with earlier studies. On average, the boundary stress was approximately tau(o)/(rho x g x H-1) 0.0015-0.0025. DOI: 10.1061/(ASCE)IR.1943-4774.0000515. (C) 2012 American Society of Civil Engineers

Bernoulli theorem, minimum specific energy and water wave celerity in open channel flow

One basic principle of fluid mechanics used to resolve practical problems in hydraulic engineering is the Bernoulli theorem along a streamline, deduced from the work-energy form of the Euler equation along a streamline. Some confusion exists about the applicability of the Bernoulli theorem and its generalization to open-channel hydraulics. In the present work, a detailed analysis of the Bernoulli theorem and its extension to flow in open channels are developed. The generalized depth-averaged Bernoulli theorem is proposed and it has been proved that the depth-averaged specific energy reaches a minimum in converging accelerating free surface flow over weirs and flumes. Further, in general, a channel control with minimum specific energy in curvilinear flow is not isolated from water waves, as customary state in open-channel hydraulics

Development of the Bélanger Equation and Backwater Equation by Jean-Baptiste Bélanger (1828)

A hydraulic jump is the sudden transition from a high-velocity to a low-velocity open channel flow. The application of the momentum principle to the hydraulic jump is commonly called the Bélanger equation, but few know that Bélanger's (1828) treatise was focused on the study of gradually varied open channel flows. Further, although Bélanger understood the rapidly-varied nature of the jump flow, he applied incorrectly the Bernoulli principle in 1828, and corrected his approach 10 years later. In 1828, his true originality lay in the successful development of the backwater equation for steady, one-dimensional gradually-varied flows in an open channel, together with the introduction of the step method, distance calculated from depth, and the concept of critical flow conditions