Drag Reduction in Aerated Chute Flow: Role of Bottom Air Concentration

Abstract

Wall shear stress modification in self-aerated flows has been observed in boundary layer type flows mainly in the form of drag reduction. Due to its complexity, drag reduction has predominantly been studied using experimental techniques and empirical analyses, whereas the development of conceptual approaches is limited. In this study, two-phase open channel flow equations with variable density are revisited and bottom air concentration is identified as a key parameter for drag reduction in air-water flows. The application of this new theory to smooth and stepped chute flows is introduced and implications for the determination of friction factors are discussed. A modified version of the Manning-Strickler formula is proposed to model friction factors across a wide range of roughness and bottom air concentration levels.

Linking turbulent waves and bubble diffusion in self-aerated open-channel flows: two-state air concentration

“…Air–water multiphase flows are of key interest because entrained air affects flow properties, thereby leading to (i) flow bulking, which may compromise overtopping safety of spillways (Straub & Anderson 1958; Hager 1991; Boes 2000), (ii) drag reduction, which can lead to flow velocities of twice or thrice the counter-part single-phase flow (Wood 1984; Chanson 1994; Kramer et al. 2021), (iii) cavitation protection of solid surfaces (Falvey 1990; Frizell, Renna & Matos 2013), (iv) enhanced gas transfer (Gulliver, Thene & Rindels 1990; Bung 2009) and (v) total dissolved gas super-saturation, that can mortally affect fish (Pleizier et al. 2020).…”

“…This process is called self-aeration (figure 1a), and the location of the so-called inception point of air entrainment has been associated with the interaction of a developing boundary layer with the free surface (Lane 1939;Straub & Anderson 1958;Wood 1984), as well as with an unstable state of free-surface perturbations (Brocchini & Peregrine 2001;Valero & Bung 2018). Air-water multiphase flows are of key interest because entrained air affects flow properties, thereby leading to (i) flow bulking, which may compromise overtopping safety of spillways (Straub & Anderson 1958;Hager 1991;Boes 2000), (ii) drag reduction, which can lead to flow velocities of twice or thrice the counter-part single-phase flow (Wood 1984;Chanson 1994;Kramer et al 2021), (iii) cavitation protection of solid surfaces (Falvey 1990;Frizell, Renna & Matos 2013), (iv) enhanced gas transfer (Gulliver, Thene & Rindels 1990;Bung 2009) and (v) total dissolved gas super-saturation, that can mortally affect fish (Pleizier et al 2020). Therefore, the accurate description of the air concentration distribution has been a topic of sustained research interest since the second half of the twentieth century, and two different schools of thought can be distinguished (figure 1b).…”

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

“…a pure TWL, and it was combined with the two-state convolution (2.10) to account for flows where the air bubble diffusion layer protrudes to the channel bottom, see § 2.3. Therefore, the bottom air concentration c0 , defined as the air concentration in the vicinity of the solid invert (Hager 1991;Kramer et al 2021), is a natural choice to exemplify the application range of proposed equations. Figure 7 shows a plot of c0 versus c , illustrating that (2.7) is valid for c 0.25, while (2.10) is valid for c 0.25.…”

“…These bubbles subsequently break down into a wide range of bubble sizes (Lamarre & Melville 1991;Deane & Stokes 2002;Deike, Melville & Popinet 2016;Chan, Johnson & Moin 2021), and eventually penetrate towards the channel bottom through turbulent diffusion. It is known that entrained air can significantly alter flow properties, thereby † Email address for correspondence: m.kramer@unsw.edu.au leading to flow bulking, drag reduction, cavitation protection and enhanced gas transfer (Straub & Anderson 1958;Falvey 1990;Gulliver, Thene & Rindels 1990;Kramer et al 2021).…”

“…It is known that entrained air can significantly alter flow properties, thereby leading to flow bulking, drag reduction, cavitation protection and enhanced gas transfer (Straub & Anderson 1958; Falvey 1990; Gulliver, Thene & Rindels 1990; Kramer et al. 2021).

Figure 1.Self-aeration in high-Froude-number flows: ( a ) the TWL of a flow over a microrough channel bed at the Water Research Laboratory, UNSW Sydney, Australia; specific water flow rate m s; chute angle ; streamwise distance from invert to m; image courtesy of Armaghan Severi, adapted with permission; ( b ) schematic of the TWL of a self-aerated flow down a smooth chute, including a differentiation between entrapped, entrained and total conveyed air.

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