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.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics,Applied Mathematics
Reference35 articles.
1. 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.
2. Free surface aeration and development dependence in chute flows;Wei;Sci. Rep.,2022
3. Self-aeration development and fully cross-sectional air diffusion in high-speed open channel flows;Wei;J. Hydraul. Res.,2022
4. Air entrainment and bubble statistics in breaking waves;Deike;J. Fluid Mech.,2016
5. 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.