On the breakup of an air bubble injected into a 
fully developed turbulent flow. 
Part 1. Breakup frequency

Martı́nez-Bazán, C.; Montañés, J. L.; Lasheras, Juan C.

doi:10.1017/s0022112099006680

Cited by 384 publications

(356 citation statements)

References 22 publications

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“…where γ is the surface tension, ρ the water density and C is a dimensionless constant which has a value of approximately 0.5 (Martinez-Bazan et al 1999;Garrett et al 2000;Deane & Stokes 2002). Several experimental studies (Loewen et al 1996;Terrill et al 2001;Deane & Stokes 2002;Leifer & de Leeuw 2006;Rojas & Loewen 2007;Blenkinsopp & Chaplin 2010) have identified a bubble size distribution following a power law of the bubble radius N (r) ∝ r −m with m ∈ [2.5 : 3.5], roughly compatible with Eq.…”

Section: Bubble Size Distribution Models and Observationssupporting

confidence: 52%

“…the time to fragment bubbles from the largest bubbles in the system r m to bubbles close to the Hinze scale. The fragmentation time, or lifetime of a bubble of radius r, τ (r) is given by the ratio of the size of the bubble r and the turbulent velocity fluctuations at this scale ∆v ∼ (εr) 1/3 (Martinez-Bazan et al 1999;Garrett et al 2000) τ (r) ∼ r(εr) −1/3 ∼ r 2/3 ε −1/3 .…”

Section: Adapting the Dimensional Analysis From Garrett Et Al (2000)mentioning

confidence: 99%

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Air entrainment and bubble statistics in breaking waves

2016

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We investigate air entrainment and bubble statistics in three-dimensional breaking waves through novel direct numerical simulations of the two-phase air-water flow, resolving the length scales relevant for the bubble formation problem, the capillary length and the Hinze scale. The dissipation due to breaking is found to be in good agreement with previous experimental observations and inertial-scaling arguments. The air-entrainment properties and bubble-size statistics are investigated for various initial characteristic wave slopes. For radii larger than the Hinze scale, the bubble size distribution, can be described by N (r, t) = B(V 0 /2π)(ε(t − ∆τ )/W g)r −10/3 r −2/3 m during the active breaking stages, where ε(t − ∆τ ) is the time dependent turbulent dissipation rate, with ∆τ the collapse time of the initial air pocket entrained by the breaking wave, W a weighted vertical velocity of the bubble plume, r m the maximum bubble radius, g gravity, V 0 the initial volume of air entrained, r the bubble radius and B a dimensionless constant. The active breaking time-averaged bubble size distribution is described bȳ N (r) = B(1/2π)( l L c /W gρ)r −10/3 r −2/3 m , where l is the wave dissipation rate per unit length of breaking crest, ρ the water density and L c the length of breaking crest. Finally, the averaged total volume of entrained air,V , per breaking event can be simply related to l byV = B( l L c /W gρ), which leads to a relationship to a characteristic slope, S, of V ∝ S 5/2 . We propose a phenomenological turbulent bubble break-up model, based on earlier models and the balance between mechanical dissipation and work done against buoyancy forces. The model is consistent with the numerical results and existing experimental results.

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Section: Bubble Size Distribution Models and Observationssupporting

confidence: 52%

Section: Adapting the Dimensional Analysis From Garrett Et Al (2000)mentioning

confidence: 99%

Air entrainment and bubble statistics in breaking waves

2016

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“…Hinze [26] used the definition that 95% of the air is contained in bubbles with a diameter less than d c and the calculated turbulent energy dissipation rate ε for Deane's [18] data was much smaller. Garrett et al [24] used the results of Martínez-Bazán et al [30,31] and established a one-to-one relationship between the local dissipation rate and bubble size.…”

Section: Bottom Turbulent Dissipation Ratementioning

confidence: 99%

Development of Bubble Characteristics on Chute Spillway Bottom

Bai¹,

Liu²,

Feng³

et al. 2018

Water

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Chute aerators introduce a large air discharge through air supply ducts to prevent cavitation erosion on spillways. There is not much information on the microcosmic air bubble characteristics near the chute bottom. This study was focused on examining the bottom air-water flow properties by performing a series of model tests that eliminated the upper aeration and illustrated the potential for bubble variation processes on the chute bottom. In comparison with the strong air detrainment in the impact zone, the bottom air bubble frequency decreased slightly. Observations showed that range of probability of the bubble chord length tended to decrease sharply in the impact zone and by a lesser extent in the equilibrium zone. A distinct mechanism to control the bubble size distribution, depending on bubble diameter, was proposed. For bubbles larger than about 1-2 mm, the bubble size distribution followed a-5/3 power-law scaling with diameter. Using the relationship between the local dissipation rate and bubble size, the bottom dissipation rate was found to increase along the chute bottom, and the corresponding Hinze scale showed a good agreement with the observations.

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“…The breakup model by Luo is able to describe the BSD in stirred tanks correctly but, because of its sensitivity to the size of the smallest bubble group, the model must be adjusted using experimental data and its general applicability is thus limited. Therefore, although the breakup model by Luo is the most widely used model and has been adopted by numerous authors, the use of different breakup models with DSD functions that contain the capillary constraint (Lehr et al, 2002) or prefer the equal-sized breakup (Alopaeus et al, 2002;Martínez-Bazán et al, 1999) should be considered. Besides, modifications of the Luo model that restrict the formation of small bubbles have been proposed (Hagesaether et al, 2002;Wang et al, 2003).…”

Section: Bubble Size Distributionmentioning

confidence: 99%

CFD Prediction of Gas-Liquid Flow in an Aerated Stirred Vessel Using the Population Balance Model

Kálal¹,

Jahoda²,

Fořt³

2014

Chemical and Process Engineering

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The main topic of this study is the experimental measurement and mathematical modelling of global gas hold-up and bubble size distribution in an aerated stirred vessel using the population balance method. The air-water system consisted of a mixing tank of diameter T = 0.29 m, which was equipped with a six-bladed Rushton turbine. Calculations were performed with CFD software CFX 14.5. Turbulent quantities were predicted using the standard k-ε turbulence model. Coalescence and breakup of bubbles were modelled using the homogeneous MUSIG method with 24 bubble size groups. To achieve a better prediction of the turbulent quantities, simulations were performed with much finer meshes than those that have been adopted so far for bubble size distribution modelling. Several different drag coefficient correlations were implemented in the solver, and their influence on the results was studied. Turbulent drag correction to reduce the bubble slip velocity proved to be essential to achieve agreement of the simulated gas distribution with experiments. To model the disintegration of bubbles, the widely adopted breakup model by Luo & Svendsen was used. However, its applicability was questioned.

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On the breakup of an air bubble injected into a fully developed turbulent flow. Part 1. Breakup frequency

Cited by 384 publications

References 22 publications

Air entrainment and bubble statistics in breaking waves

Air entrainment and bubble statistics in breaking waves

Development of Bubble Characteristics on Chute Spillway Bottom

CFD Prediction of Gas-Liquid Flow in an Aerated Stirred Vessel Using the Population Balance Model

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