On the Cause of the Maximum Velocity of Water Flowing in Open Channels being below the Surface

Francis, James B.

doi:10.1061/taceat.0000315

Cited by 29 publications

(6 citation statements)

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“…A characterizing feature of turbulent flows in open ducts is the so called ‘velocity dip’ phenomenon, namely the fact that, differently from laminar flows, the maximum streamwise velocity does not occur at the free surface, but below it. This phenomenon was already observed by hydraulic engineers in the 19th century (Francis 1878; Stearns 1883), and it has been reported in numerous experiments (Nezu, Nakagawa & Tominaga 1985; Kirkgöz & Ardiçlioğlu 1997; Yang, Tan & Lim 2004; Knight et al. 2018) and more recently also in numerical simulations (Sakai 2016).…”

Section: Introductionsupporting

confidence: 53%

“…For the open duct cases with (figure 7 d – f ), the presence of the free surface breaks the symmetry, making the velocity isocontours no longer closed, and shifting the maximum velocity farther from the bottom wall. In laminar open duct flows, the maximum streamwise velocity is located at the free surface, whereas in the turbulent case it dips below it, as first observed by Francis (1878) and Stearns (1883). The mean streamwise velocity in open ducts with , shows similar velocity dip as in the case (figure 7 g – i ).…”

Section: Mean Flow Structurementioning

confidence: 58%

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Direct numerical simulation of flow in open rectangular ducts

Yu,

Modesti,

Pirozzoli

2023

J. Fluid Mech.

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We study turbulent flow in open channels with a free surface and rectangular cross-section, for various Reynolds numbers and duct aspect ratios. Direct numerical simulations are used to obtain accurate characterization of the secondary motions, which are found to be more intense than in closed ducts, and to scale with the bulk, rather than with the friction velocity. A notable feature of open-duct flows is the presence of a velocity dip, namely the peak velocity is achieved at some depth underneath the free surface. We find that the depth of the velocity peak increases with the Reynolds number, and correspondingly the flow becomes more symmetric with respect to the horizontal midplane. This is also confirmed from the change of the topology of the secondary motions, which exhibit a strong corner circulation at the free-surface/wall corners at low Reynolds number, which, however, weakens at higher $Re$ . The structure of the mean velocity field is such that the log law applies with good approximation in the direction normal to the nearest wall, which allows us to explain why predictive friction formulae based on the hydraulic diameter concept are successful. Additional analysis shows that the secondary motions account for a large fraction of the frictional drag (up to $15$ %).

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Section: Introductionsupporting

confidence: 53%

Section: Mean Flow Structurementioning

confidence: 58%

Direct numerical simulation of flow in open rectangular ducts

Yu,

Modesti,

Pirozzoli

2023

J. Fluid Mech.

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“…However, in narrow open-channels involving an aspect ratio Ar < 5, where Ar = b/h is the ratio of the channel width b to flow depth, and near side walls or corner zones even for wide open-channels (Vanoni 1941), the maximum velocity appears below the free surface producing the velocity-dip-phenomenon, involving a deviation from the log-wake law. This phenomenon, which was reported more than a century ago (Francis 1878, Stearns 1883, was observed both in open-channels and rivers. It is related to secondary currents generated in three-dimensional (3D) open-channel flows (Imamoto andIshigaki 1988, Wang andCheng 2005).…”

Section: Introductionmentioning

confidence: 64%

An ordinary differential equation for velocity distribution and dip-phenomenon in open channel flows

Absi¹

2011

Journal of Hydraulic Research

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International audienceAn ordinary differential equation for velocity distribution in open channel flows is presented based on an analysis of the Reynolds-Averaged Navier-Stokes equations and a log-wake modified eddy viscosity distribution. This proposed equation allows to predict the velocity-dip-phenomenon, i.e. the maximum velocity below the free surface. Two different degrees of approximations are presented, a semi-analytical solution of the proposed ordinary differential equation, i.e. the full dip-modified-log-wake law and a simple dip-modified-log-wake law. Velocity profiles of the two laws and the numerical solution of the ordinary differential equation are compared with experimental data. This study shows that the dip correction is not efficient for a small Coles' parameter, accurate predictions require larger values. The simple dip-modified-log-wake law shows reasonable agreement and seems to be an interesting tool of intermediate accuracy. The full dip-modified-log-wake law, with a parameter for dip-correction obtained from an estimation of dip positions, provides accurate velocity profiles

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“…The shape of the cross section, the roughness of the channel walls, and the presence of bends or a small disturbance at the entrance were proposed as possible causes of unequalized shear stresses on both sides of the channel and of the maximum velocity below the surface. 36 This has also been observed in open water systems such as rivers and streams, where the maximum flow velocity often occurs at ∼ 1 / 3 depth below the water surface, 37,38 with a typical flow profile similar to that in Figure 5b.…”

Section: Langmuirmentioning

confidence: 71%

Role of Mixed Boundaries on Flow in Open Capillary Channels with Curved Air–Water Interfaces

Zheng

Wang²,

et al. 2012

Langmuir

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Flow in unsaturated porous media or in engineered microfluidic systems is dominated by capillary and viscous forces. Consequently, flow regimes may differ markedly from conventional flows, reflecting strong interfacial influences on small bodies of flowing liquids. In this work, we visualized liquid transport patterns in open capillary channels with a range of opening sizes from 0.6 to 5.0 mm using laser scanning confocal microscopy combined with fluorescent latex particles (1.0 μm) as tracers at a mean velocity of ∼0.50 mm s(-1). The observed velocity profiles indicate limited mobility at the air-water interface. The application of the Stokes equation with mixed boundary conditions (i.e., no slip on the channel walls and partial slip or shear stress at the air-water interface) clearly illustrates the increasing importance of interfacial shear stress with decreasing channel size. Interfacial shear stress emerges from the velocity gradient from the adjoining no-slip walls to the center where flow is trapped in a region in which capillary forces dominate. In addition, the increased contribution of capillary forces (relative to viscous forces) to flow on the microscale leads to increased interfacial curvature, which, together with interfacial shear stress, affects the velocity distribution and flow pattern (e.g., reverse flow in the contact line region). We found that partial slip, rather than the commonly used stress-free condition, provided a more accurate description of the boundary condition at the confined air-water interface, reflecting the key role that surface/interface effects play in controlling flow behavior on the nanoscale and microscale.

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On the Cause of the Maximum Velocity of Water Flowing in Open Channels being below the Surface

Cited by 29 publications

References 0 publications

Direct numerical simulation of flow in open rectangular ducts

Direct numerical simulation of flow in open rectangular ducts

An ordinary differential equation for velocity distribution and dip-phenomenon in open channel flows

Role of Mixed Boundaries on Flow in Open Capillary Channels with Curved Air–Water Interfaces

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