Studies on the drag and shape of gas bubbles rising through a stagnant liquid

Aybers, N.; Tapucu, A.

doi:10.1007/bf00751164

Cited by 56 publications

(34 citation statements)

References 4 publications

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“…The test showed that the ultrasound velocity measurements are consistent within 2% of the camera data. We measure top speeds of our bubbles typically about 36 cm/s, which is consistent with other experimental measurements [2,9,30]. The relative accuracy of our velocity measurements is more precise, typically ±1 mm/s, or about 0.2% accuracy.…”

Section: Experimental Apparatus and Methodssupporting

confidence: 88%

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Force measurements on rising bubbles

Shew¹,

Poncet²,

Pinton³

2006

J. Fluid Mech.

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The dynamics of millimeter sized air bubbles rising through still water are investigated using precise ultrasound velocity measurements combined with high speed video. From measurements of speed and three dimensional trajectories we deduce the forces on the bubble which give rise to planar zigzag and spiraling motion. I. BACKGROUNDAn understanding of bubble-fluid interactions is important in a broad range of natural, engineering, and medical settings. Air-sea gas transfer, bubble column reactors, oil/natural gas transport, boiling heat transfer, ship hydrodynamics, ink-jet printing and medical ultrasound imaging are just a few examples where the dynamics of bubbles play a role (e.g [6,16,26]).We narrow our focus to a single air bubble rising through still water. The buoyant force which drives the bubble's rise does work resulting in an increase in kinetic energy of the surrounding fluid. This induced flow, in turn, gives rise to hydrodynamic forces on the bubble and hence changes in the bubble trajectory. The measurement of these forces is the aim of the experimental work presented here Our study includes a range of bubble sizes between 0.84 and 1.2 mm in radius. At the small end of this range the bubble's path is rectilinear. As the bubble size is increased, one observes a transition to a planar zigzag path [8,23]. A second instability, often preceded by the zigzag, results in a spiraling path [5,8,15,23]. For even larger bubbles, a third type of oscillating path occurs, which has similarities to the zigzag, sometimes called "rocking". We do not address this state and emphasize that it is different than the zigzag mentioned above. Unlike the zigzag state that we study, the rocking bubble undergoes dramatic shape oscillations and the frequency of path oscillation is several times higher than the zigzag or spiral [5,15]. Our approach is to use well resolved measurements of three-dimensional bubble trajectories to calculate the hydrodynamic forces on the bubbles. Other recent studies have investigated path instabilities with special attention paid to the role of the bubble's wake. Lunde and Perkins [15] used dye to observe the wake of ascending bubbles and solid particles. Brücker [5] used particle image velocimetry to study the wake of large spiraling and rocking bubbles. Mougin and Magnaudet [22,23] These studies have revealed a wake consisting of two long, thin, parallel vortices aligned with the bubble's path. One vortex rotates clockwise and the other counter-clockwise. For a spiraling bubble the wake vortices are continuously generated, while they are interrupted twice per period of path oscillation for the zigzag. Mougin and Magnaudet [22,23] observed a nearly identical wake structure in their numerical simulations (see also [24]). It is believed that the wake vortices play a critical role in generating hydrodynamic forces on the bubble.In the next section we describe the experimental apparatus and measurement techniques, as well a typical bubble trajectory. In section III, we present a method for extracti...

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Section: Experimental Apparatus and Methodssupporting

confidence: 88%

“…Aybers and Tapucu [1,2]used photographic techniques to measure bubble speed, drag coefficients, size, shape, and path. Mercier, Lyrio, and Forslund [17] used a stroboscope and several cameras to measure short sections of bubble trajectories.…”

Section: Introductionmentioning

confidence: 99%

Force measurements on rising bubbles

Shew¹,

Poncet²,

Pinton³

2006

J. Fluid Mech.

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“…This agrees with findings of other authors (Luther et al 2004;Guet et al 2005): spherical shapes are typical for bubbles up to r eq = 0.4 mm, ellipsoidal up to r eq = 1.0 mm, while bubbles of r eq > 1.0 mm can have rather complex shapes (Fig. 5) because they experience surface oscillations upon ascent due to instabilities in the wake (Saffman 1956;Aybers and Tapucu 1969a;Aybers and Tapucu 1969b;Jamialahmadi et al 1994;Leifer et al 2000). An increase in oscillation and deformation of the echo-reflecting surface of bubbles also justifies the observed increase in σ bs variability with bubble volume.…”

Section: Assessmentsupporting

confidence: 91%

“…This postulation is suitable for spherical bubbles. Still, because bubbles escaping from the sediment are large enough and thus have nonspherical shapes (Saffman 1956;Aybers and Tapucu 1969b;Clift et al 1978;Jamialahmadi et al 1994), the relation between geometric and acoustic sizes can be obtained if sizespecific patterns of bubble scatter are known. In this paper, we determined an empirical relationship between the volume of "non-resonant" bubbles and σ bs measured with a down-looking 120 kHz echosounder.…”

Section: Discussionmentioning

confidence: 99%

Quantifying gas ebullition with echosounder: the role of methane transport by bubbles in a medium‐sized lake

Ostrovsky

Mcginnis

Lapidus

et al. 2008

Limnology & Ocean Methods

159

165

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In lakes and reservoirs with variable water level, gas ebullition can play a substantial role in methane transport in the water column and to the atmosphere. However, measuring methane ebullition from sediment is difficult as releases are highly heterogeneous and intermittent on macro- and micro-scales. In contrast to conventional gas traps and optical methods, hydroacoustic technology allows rapid scanning over large volumes of the water column synoptically to quantify gas bubble abundance. A 120-kHz dual beam downward-looking echosounder was used to measure the size distributions of bubbles that do not resonate at the sonar frequency. Data obtained with this sonar permit accurate calculation and evaluation of ebullition flux from the bottom. A robust relationship was established between gas volumes and backscattering cross-section of individual bubbles in experimental conditions, and rise velocities of bubbles were precisely measured. The volume backscattering coefficient was shown to be a good gauge of the total volume of bubbles per cubic meter of water, allowing the use of a single-beam sonar for measuring volumetric bubble concentrations. Data obtained from hydroacoustic surveys on Lake Kinneret, where gaseous methane is emitted from randomly dispersed sediment sources, indicated that ~90% of bubbles escaping from soft sediments ranged from 1.3 mm to 4.5 mm and ~50% ranged from 2.0 mm to 3.2 mm in equivalent radius. In summer-fall 2001, the gaseous methane fluxes from hypolimnetic sediments was ~10 mmol m-2 d-1, accounting for one-third of the observed methane accumulation in the hypolimnion. This relatively high ebullition rate could be attributed to the gradual decreasing of the mean water level in preceding years

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“…[25][26][27] The density ratio of air to water is 1 : 997. The shapes of the air bubbles are characterised by the Eötvös number, Eo, the Morton number M, and the bubble Reynolds number, Re, defined as ) where d e is the equivalent bubble diameter, s is the surface tension, m is the liquid viscosity, and u T is the terminal velocity.…”

Section: Air Bubbles In Watermentioning

confidence: 99%

A Volume of Fluid (VOF) Method for the Simulation of Metallurgical Flows

2001

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A finite difference numerical method, based on the VOF approach for tracking interface distortions, is presented. It is capable of accurately simulating the fluid flow of multiple immiscible fluids for metallurgical applications. This volume tracking method is based on piecewise linear reconstructions of interfaces, density distributions based on a shifted grid approach, and a fully kernel-based CSF method for surface force modelling. Second order temporal and spatial accuracy are achieved using improved Euler time-stepping enhancement of a two-step projection algorithm, supported by a multigrid-preconditioned GMRES solver that enabled large density ratios (1 : 30 000) between the fluids and fine scale flow phenomena to be resolved. The code was used to simulate the rise of an air bubble in water and in liquid pig iron and was able to capture the time dependent oscillation of the bubble. The bubble velocity varied with the instantaneous shape of the bubble. The averaged terminal velocity of the gas bubble in water was in good agreement with published experimental data. Splash formation from a top submerged gas injection lance was simulated to illustrate the capability of the code in resolving the break up and fragmentation of liquid drops for possible use in the study of bath smelting processes.

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Studies on the drag and shape of gas bubbles rising through a stagnant liquid

Cited by 56 publications

References 4 publications

Force measurements on rising bubbles

Force measurements on rising bubbles

Quantifying gas ebullition with echosounder: the role of methane transport by bubbles in a medium‐sized lake

A Volume of Fluid (VOF) Method for the Simulation of Metallurgical Flows

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