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Turbulent free-surface in self-aerated flows: superposition of entrapped and entrained air

Published online by Cambridge University Press:  01 February 2024

Matthias Kramer Open the ORCID record for Matthias Kramer [Opens in a new window]
Matthias Kramer*
Affiliation:
School of Engineering and Technology (SET), UNSW Canberra, Canberra, ACT 2610, Australia
*
†Email address for correspondence: m.kramer@unsw.edu.au
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Abstract

The characterisation and the modelling of air concentration distributions in self-aerated free-surface flows has been subject to sustained research interest since the 1970s. Recently, a novel two-state formulation of the structure of a self-aerated flow was proposed by Kramer & Valero (J. Fluid Mech., vol. 966, 2023, A37), which physically explains the air concentration through the weak interaction of two canonical flow momentum layers, comprising a turbulent boundary layer and a turbulent wavy layer (TWL). The TWL was modelled using a Gaussian error function, assuming that the most dominant contribution are wave troughs. Here, it is shown that air bubbles form an integral part of the TWL, and its formulation is expanded by adopting a superposition principle of entrapped air (waves) and entrained air (bubbles). Combining the superposition principle with the two-state formulation, an expression for the depth-averaged (mean) air concentration is derived, which allows us to quantify the contribution of different physical mechanisms to the mean air concentration. Overall, the presented concepts help to uncover new flow physics, thereby contributing fundamentally to our understanding of self-aerated flows.

JFM classification

Multiphase and Particle-laden Flows: Gas/liquid flow Waves/Free-surface Flows: Channel flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 980 , 10 February 2024 , A25
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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References

Blenkinsopp, C.E. & Chaplin, D.H. 2007 Void fraction measurements in breaking waves. Proc. R. Soc. A 463, 3151–3170.CrossRefGoogle Scholar
Brocchini, M. & Peregrine, D.H. 2022 The dynamics of strong turbulence at free surfaces. Part 1. Description. J. Fluid Mech. 449, 225–254.CrossRefGoogle Scholar
Bung, D. 2009 Zur selbstbelüfteten Gerinneströmung auf Kaskaden mit gemäßigter Neigung (in German). PhD thesis, University of Wuppertal.Google Scholar
Bung, D.B. & Valero, D. 2018 Re-aeration on stepped spillways with special consideration of entrained and entrapped air. Geoscience 8, 333.CrossRefGoogle Scholar
Chan, W.R.C., Johnson, P.L. & Moin, P. 2021 The turbulent bubble break-up cascade. Part 1. Theoretical development. J. Fluid Mech. 912, A42.CrossRefGoogle Scholar
Chanson, H. 1996 Air Bubble-Entrainment in Free Surface Turbulent Shear Flows. Academic.Google Scholar
Chanson, H. & Toombes, L. 2001 Experimental investigations of air entrainment in transition and skimming flows down a stepped chute. Application to embankment overflow stepped spillways. Research Rep. CE158. Dept. of Civil Engineering, The University of Queensland.Google Scholar
Cui, H., Felder, S. & Kramer, M. 2022 Non-intrusive measurements of air-water flow properties in supercritical flows down grass-lined spillways. In Proceedings of the 9th IAHR International Symposium on Hydraulic Structures (ed. M. Palermo, Z. Ahmad, B. Crookston & S. Erpicum), 24–27 October 2022, IIT Roorkee, Roorkee, India.Google Scholar
Deane, G.B. & Stokes, M.D. 2002 Scale dependence of bubble creation mechanisms in breaking waves. Nature 418 (6900), 839–844.CrossRefGoogle ScholarPubMed
Deike, L., Melville, K. & Popinet, S. 2016 Air entrainment and bubble statistics in breaking waves. J. Fluid Mech. 801, 91–129.CrossRefGoogle Scholar
Falvey, H.T. 1990 Cavitation in chutes and spillways, Engineering Monograph, vol. 42. United States Department of the Interior, Bureau of Reclamation.Google Scholar
Felder, S., Severi, A. & Kramer, M. 2022 Self-aeration and flow resistance in high-velocity flows down spillways with micro-rough inverts. J. Hydraul. Engng 149 (6), 04023011.CrossRefGoogle Scholar
Gulliver, J.S., Thene, J.R. & Rindels, A.J. 1990 Indexing gas transfer in self-aerated flows. J. Environ. Engng 116 (3), 503–523.CrossRefGoogle Scholar
Hager, W.H. 1991 Uniform aerated chute flow. J. Hydraul. Engng 117 (4), 528–533.CrossRefGoogle Scholar
Killen, J.M. 1968 The surface characteristics of self aerated flow in steep channels. PhD thesis, University of Minnesota.Google Scholar
Kramer, M. 2020 Air-water flows at hydraulic structures: experimental investigations of interfacial characteristics and air-water mass transfer. Tech. Rep. KR 4872/2-1. DFG Research Fellowship.Google Scholar
Kramer, M., Felder, S., Hohermuth, B. & Valero, D. 2021 Drag reduction in aerated chute flow: role of bottom air concentration. J. Hydraul. Engng 147 (11), 04021041.CrossRefGoogle Scholar
Kramer, M. & Valero, D. 2023 Linking turbulent waves and bubble diffusion in self-aerated open-channel flows: two-state air concentration. J. Fluid Mech. 966, A37.CrossRefGoogle Scholar
Krug, D., Philip, J. & Marusic, I. 2017 Revisiting the law of the wake in wall turbulence. J. Fluid Mech. 811, 421–435.CrossRefGoogle Scholar
Lamarre, E. & Melville, W.K. 1991 Air entrainment and dissipation in breaking waves. Nature 351, 469–472.CrossRefGoogle Scholar
Matos, J. 1995 Discussion of “Air concentration distribution in self-aerated flow” by N.R. Afshar, G.L. Asawa and K.G. Ranga Raju. J. Hydraul. Res. 33, 589–592.CrossRefGoogle Scholar
Muraro, F., Dolcetti, G., Nichols, A., Tait, S.J. & Horoshenkov, V.K. 2021 Free-surface behaviour of shallow turbulent flows. J. Hydraul. Res. 59, 1–20.CrossRefGoogle Scholar
Rao, N.S.L. & Gangadharaiah, T. 1971 Distribution characteristics of self-aerated flows. In Characteristics of Self-Aerated Free-Surface Flows. Water and Waste Water/Current Research and Practice (ed. R.S.L. Rao & H. Kobus), vol. 10, pp. 119–161. Eric Schmidt Verlag.Google Scholar
Severi, A. 2018 Aeration performance and flow resistance in high-Velocity flows over moderately sloped spillways with micro-rough bed. PhD thesis, Water Research Laboratory, School of Civil and Environmental Engineering.Google Scholar
Straub, L. & Anderson, A.G. 1958 Experiments on self-aerated flow in open channels. J. Hydraul. Div. 84 (7), 1–35.CrossRefGoogle Scholar
Valero, D. & Bung, D. 2016 Development of the interfacial air layer in the non-aerated region of high-velocity spillway flows. Instabilities growth, entrapped air and influence on the self-aeration onset. Intl J. Multiphase Flow 84, 66–74.CrossRefGoogle Scholar
Valero, D. & Bung, D. 2018 Reformulating self-aeration in hydraulic structures: turbulent growth of free surface perturbations leading to air entrainment. Intl J. Multiphase Flow 100, 127–142.CrossRefGoogle Scholar
Wei, W. & Deng, J. 2022 Free surface aeration and development dependence in chute flows. Sci. Rep. 12, 1477.CrossRefGoogle ScholarPubMed
Wei, W., Xu, W., Deng, J. & Guo, Y. 2022 Self-aeration development and fully cross-sectional air diffusion in high-speed open channel flows. J. Hydraul. Res. 60 (3), 445–459.CrossRefGoogle Scholar
Whutrich, D., Shi, R. & Chanson, H. 2022 Ensemble-statistical approach in the measurement of air–water flow properties in highly unsteady breaking bores. Rev. Sci. Instrum. 93, 054502.CrossRefGoogle Scholar
Wilhelms, S. & Gulliver, J.S. 1994 Self-aerated flows on corps of engineers spillways. Tech. Rep. W-94-2. US Army Corps of Engineers, Waterways Experiment Station.Google Scholar
Wilhelms, S. & Gulliver, J.S. 2005 Bubbles and waves description of self-aerated spillway flow. J. Hydraul. Res. 43 (5), 522–531.CrossRefGoogle Scholar
Wood, I. 1985 Air water flows. In Proceedings of the 21st IAHR Congress, Melbourne, Australia. Keynote address, pp. 18–29.Google Scholar
Wood, I. 1991 Free-surface air entrainment on spillways. In Air Entrainment in Free-Surface Flows - IAHR Hydraulic Structures Design Manual (ed. I. Wood). CRC Press.Google Scholar
Zhang, G. & Chanson, H. 2017 Self-aeration in the rapidly- and gradually-varying flow regions of steep smooth and stepped spillways. Environ. Fluid Mech. 17, 27–46.CrossRefGoogle Scholar