Experiments on the breakdown of laminar flow in a parallel-plate channel

Beavers, G. S.; Sparrow, E. M.; Magnuson, R.

doi:10.1016/0017-9310(70)90127-4

Cited by 19 publications

(5 citation statements)

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“…whereū is the gap-averaged velocity. This is consistent with our calculation ρ w v i (2h)/µ w = 1134, which reveals the flow to be laminar (Beavers, Sparrow & Magnuson 1970). We derive a coupled set of gap-averaged equations by integrating equations (3.1)-(3.3) along the z direction (Roig et al 2012):…”

Section: Gap-averaging Processsupporting

confidence: 87%

“…First, we set the pipe diameter to be D = 0.137 m, the air-to-water inflow rate ratio to be q a /q w = 1/4 and the superficial inflow velocity to be v i = 0.162 m s −1 . We varied the gap thickness h from 0.001 to 0.005 m, for which the flow remained to be laminar (Beavers et al 1970) and cross-gap gravity effect was not significant. As shown in figure 11(a), when h = 0.001 m (i.e.…”

Section: Effects Of Gap Thickness and Pipe Diametermentioning

confidence: 99%

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The shape and motion of gas bubbles in a liquid flowing through a thin annulus

et al. 2018

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We study the shape and motion of gas bubbles in a liquid flowing through a horizontal or slightly inclined thin annulus. Experimental data show that in the horizontal annulus, bubbles develop a unique ‘tadpole-like’ shape with a semi-circular cap and a highly stretched tail. As the annulus is inclined, the bubble tail tends to vanish, resulting in a significant decrease of bubble length. To model the bubble evolution, the thin annulus is conceptualised as a ‘Hele-Shaw’ cell in a curvilinear space. The three-dimensional flow within the cell is represented by a gap-averaged, two-dimensional model, which achieved a close match to the experimental data. The numerical model is further used to investigate the effects of gap thickness and pipe diameter on the bubble behaviour. The mechanism for the semi-circular cap formation is interpreted based on an analogous irrotational flow field around a circular cylinder, based on which a theoretical solution to the bubble velocity is derived. The bubble motion and cap geometry is mainly controlled by the gravitational component perpendicular to the flow direction. The bubble elongation in the horizontal annulus is caused by the buoyancy that moves the bubble to the top of the annulus. However, as the annulus is inclined, the gravitational component parallel to the flow direction becomes important, causing bubble separation at the tail and reduction in bubble length.

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Section: Gap-averaging Processsupporting

confidence: 87%

Section: Effects Of Gap Thickness and Pipe Diametermentioning

confidence: 99%

The shape and motion of gas bubbles in a liquid flowing through a thin annulus

et al. 2018

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“…In our experiment, ultrapure water was used and the glass plates were washed with Piranha solution, so the effects of contamination can be neglected and the drag force due to total wetting is assumed to be zero. As for the assumption (2), Beavers et al 26 concluded that transition to turbulent flow only occurs when the cell Reynolds number Re = ρuh/µ (the characteristic length is gap thickness h) exceeds 2200, so the laminar flow can be preserved safely in all cases once the velocity remains below 0.2 m/s and the cell thickness is below 9 mm simultaneously. When the flow is far away from the bubble interface, the velocity distribution is parabolic due to Poiseuille flow (regions I and V in Figure 1(c)).…”

Section: Numerical Simulationmentioning

confidence: 99%

Experimental and numerical study of buoyancy-driven single bubble dynamics in a vertical Hele-Shaw cell

et al. 2014

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Buoyancy-driven single bubble behaviour in a vertical Hele-Shaw cell with various gap Reynolds numbers Re(h/d)2 has been studied. Two gap thicknesses, h = 0.5 mm (Re(h/d)2 = 1.0–8.5) and 1 mm (Re(h/d)2 = 6.0–50) were used to represent low and high gap Reynolds number flow. Periodic shape oscillation and path vibration were observed once the gap Reynolds number exceeds the critical value of 8.5. The bubble behaviour was also numerically simulated by taking a two-dimensional volume of fluid method coupled with a continuum surface force model and a wall friction model in the commercial computational fluid dynamics package Fluent. By adjusting the viscous resistance values, the bubble dynamics in the two gap thicknesses can be simulated. For the main flow properties including shape, path, terminal velocity, horizontal vibration, and shape oscillation, good agreement is obtained between experiment and simulation. The estimated terminal velocity is 10%–50% higher than the observed one when the bubble diameter d ≤ 5 mm, h = 0.5 mm and 9% higher when d ≤ 18 mm, h = 1.0 mm. The estimated oscillation frequency is 50% higher than the observed value. Three-dimensional effects and spurious vortices are most likely the reason for this inaccuracy. The simulation confirms that the thin liquid films between gas bubbles and the cell walls have a limited effect on the bubble dynamics.

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“…Goh and Ooi [11] reported that the laminar-to-turbulent region for an annular microchannel of r * = 0.97 to be between 2200 to 3400, which coincides with that of parallel plate configuration reported by Beavers et al [38]. Gnielinski [39] identified 2300 Re 10000  to be in the transition region for this channel configuration.…”

Section: Forced Internal Convection In Concentric Annulussupporting

confidence: 81%

Convective heat transfer in microchannels with varying flow cross-section

Cheng¹

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Experiments on the breakdown of laminar flow in a parallel-plate channel

Cited by 19 publications

References 1 publication

The shape and motion of gas bubbles in a liquid flowing through a thin annulus

The shape and motion of gas bubbles in a liquid flowing through a thin annulus

Experimental and numerical study of buoyancy-driven single bubble dynamics in a vertical Hele-Shaw cell

Convective heat transfer in microchannels with varying flow cross-section

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