Experimental and numerical studies of the hydrodynamics in a bubble column

Abstract. In this paper, we quantify and discuss the physical and surface chemical processes leading to the formation, temporal evolution and sedimentation of dust grains in brown dwarf and giant gas planet atmospheres: nucleation, growth, evaporation and gravitational settling. Considering dust particles of arbitrary sizes in the different hydrodynamical regimes (free molecular flow, laminar flow, turbulent flow), we evaluate the equilibrium drift velocities (final fall speeds) and the growth rates of the particles due to accretion of molecules. We show that a depth-dependent maximum size of the order of a max ≈ 1 µm (upper regions) . . . 100 µm (lower regions) exists, which depends on the condensate and the stellar parameters, beyond which gravitational settling is faster than growth. Larger particles can probably not be formed and sustained in brown dwarf atmospheres. We furthermore argue that the acceleration towards equilibrium drift is always very fast and that the temperature increase of the grains due to the release of latent heat during the growth process is negligible. Based on these findings, we formulate the problem of dust formation coupled to the local element depletion/enrichment of the gas in brown dwarf atmospheres by means of a system of partial differential equations. These equations state an extension of the moment method developed by Gail & Sedlmayr (1988) with an additional advective term to account for the effect of size-dependent drift velocities of the grains. A dimensionless analysis of the new equations reveals a hierarchy of nucleation → growth → drift → evaporation, which characterises the life cycle of dust grains in brown dwarf atmospheres. The developed moment equations can be included into hydrodynamics or classical stellar atmosphere models. Applications of this description will be presented in a forthcoming paper of this series.

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“…Lain et al (1999), carrying out experimental studies on bubbly flows, arrive at the following empirical expression for the drag force…”

Section: Force Of Frictionmentioning

confidence: 99%

Dust in brown dwarfs

Woitke

Helling

2003

A&A

175

239

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“…Clearly, bubble deformation needs to be considered when dealing with the flow in bubble columns. Lain et al (1999) made an unexpected observation concerning the slip velocity of bubbles in a bubble column. They studied the flow properties of a bubble column at rather low gas fractions up to 3%.…”

mentioning

confidence: 99%

“…This low gas fraction, combined with a column diameter of 140 mm, allowed the authors to use Phase Doppler Anemometry [see also Broder & Sommerfeld (1998)], a technique that not only nonintrusively measures the particle velocity but also the size of spherical particles. Lain et al (1999) used small bubbles to satisfy the need for spherical bubbles. In their experiment the bubble size distribution had a narrow peak around a bubble diameter of 800 µm that contained the majority of bubbles, but also a second, smaller peak with a bubble diameter of 1300 µm.…”

mentioning

confidence: 99%

Gravity-Driven Bubbly Flows

Mudde

2005

Annu. Rev. Fluid Mech.

163

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■ Abstract Gravity-driven bubbly flows are a specific class of flows, where all action is provided by gravity. An industrial example is formed by the so-called bubble column: a vertical cylinder filled with liquid through which bubbles flow that are introduced at the bottom of the cylinder. On the bubble scale, gravity gives rise to buoyancy of individual bubbles. On larger scales, gravity acts on nonuniformities in the spatial bubble distribution present in the bubbly mixture. The gravity-induced flow and flow structures can increase the inhomogeneity of the bubble distribution, leading to a turbulent flow. In this flow, specific scales are identified: a large-scale circulation with the liquid flowing upward in the center of the column and downward close to the wall. On the intermediate scale there are vortical structures; eddies of liquid, with a size on the order of the diameter of the column, that stir the liquid and radially transport the bubbles. On the small scale there is the local stirring of the bubbles. We describe the ideas developed over time and identify some open questions. We discuss the experimental findings on the turbulence generated, the stability of the flow, axial dispersion, and the similarities between bubble columns and air lifts. Especially for higher gas fractions, many questions still lack accurate answers. The lateral lift force in bubble swarms and the structure of the turbulence in the bubbly mixture are important examples of inadequately understood physical phenomena, providing many challenges for fundamental and applied research on bubbly flows.

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“…with the drag modeled using the empirical correlations for a fluid sphere of Laín et al [27], virtual mass as Drew and Lahey [28], lift as Tomiyama et al [29] and wall lubrication force as Antal et al [30].…”

Section: Governing Equationsmentioning

confidence: 99%

Development of a multiscale solver with sphere partitioning tracking

Peña-Monferrer¹,

Muñoz-Cobo²,

Monrós-Andreu³

et al. 2015

Computational Methods in Multiphase Flow VIII

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A new method to compute the dispersed phase in a Lagrangian framework is shown in this contribution for computing incompressible bubbly flows. Each bubble is divided dynamically in equivolumetric elements and tracked into the Eulerian mesh for an appropriate assignment of the effect of the bubble in the cell. The coupling between phases is done considering in the momentum equation the interfacial forces along the bubble path during an Eulerian time step. The bouncing of the bubbles between themselves and the wall is modeled with a dynamic soft sphere model. The computational results obtained for different flow conditions are validated with the recently released experimental data on upward pipe flow. The test section used is a 52 mm pipe of 5500 mm of length maintained under adiabatic conditions with air and water circulating fluids. Time-averaged results of radial distribution for void fraction, chord length, number of bubbles detected, turbulence kinetic energy, dispersed and continuous velocity profiles show a good agreement.

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Experimental and numerical studies of the hydrodynamics in a bubble column

Cited by 127 publications

References 0 publications

Dust in brown dwarfs

Dust in brown dwarfs

Gravity-Driven Bubbly Flows

Development of a multiscale solver with sphere partitioning tracking

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