Bubble behavior in a Taylor vortex

Deng, Rensheng; Wang, Chi-Hwa; Smith, Kenneth A.

doi:10.1103/physreve.73.036306

Cited by 23 publications

(11 citation statements)

References 9 publications

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“…In the grand-canonical ensemble, the fit yields C 2,0 = 0.039 446 (4) and c g = 0.105 5 (7); the former is consistent with the existing result C 2,0 = 0.039 44(4) [28], the latter agrees well with the exactly known value c = 0.105 436 634 [19]. In the canonical ensemble, the result is C 2,0 = 0.039 446 (6) and c c = −0.33 (5).…”

Section: Numerical Resultssupporting

confidence: 89%

Percolation in the canonical ensemble

Hu¹,

Blöte²,

Deng³

2012

J. Phys. A: Math. Theor.

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We study the bond percolation problem under the constraint that the total number of occupied bonds is fixed, so that the canonical ensemble applies. We show via an analytical approach that at criticality, the constraint can induce new finite-size corrections with exponent y can = 2y t − d both in energy-like and magnetic quantities, where y t = 1/ν is the thermal renormalization exponent and d is the spatial dimension. Furthermore, we find that while most of universal parameters remain unchanged, some universal amplitudes, like the excess cluster number, can be modified and become non-universal. We confirm these predictions by extensive Monte Carlo simulations of the two-dimensional percolation problem which has y can = −1/2.

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Section: Numerical Resultssupporting

confidence: 89%

Percolation in the canonical ensemble

Hu¹,

Blöte²,

Deng³

2012

J. Phys. A: Math. Theor.

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“…The almost linear relationship between the maximum radial velocity and Re agrees with the theoretical analysis provided by Czarny et al24 Moreover, the relationship can explain the profile of maximum bubble size that can be captured in a Taylor vortex at various Re 19. However, this is different from Davey's nonlinear correlation between axial (or radial) velocity and reduced Re in an infinitely long liquid column 25.…”

Section: Resultssupporting

confidence: 85%

“…A schematic diagram of the experimental apparatus is shown in Figure 1, which is similar to the system used by Deng et al19 A Newtonian mineral oil (with a density ρ of 0.86 g/cm 3 and a viscosity μ of 0.0297 Pa s) was used as the working fluid between a rotating inner cylinder ( R i = 18.4 mm, H = 60 mm) and a stationary outer cylinder ( R o = 30 mm, L = 200 mm). This gives a gap width d of 11.6 mm, a radius ratio η = R i / R o of 0.613, and an aspect ratio Γ of 5.17.…”

Section: Methodsmentioning

confidence: 99%

Characterization of Taylor vortex flow in a short liquid column

et al. 2009

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in Wiley InterScience (www.interscience.wiley.com).We present a study on Taylor vortex flow in the annulus between a rotating inner cylinder and a stationary outer cylinder, featured with a wide gap (radius ratio is 0.613) and a short column (aspect ratio is 5.17). A particle image velocimetry (PIV) system was used to determine the position, shape, and velocity distribution of the vortices, by which the flow was also confirmed to lie in the nonwavy Taylor vortex regime for all operating conditions explored in this study. Our results suggest that end boundary effects are important, in which the vortex number decreases with decreasing column length. For a system with an aspect ratio of 5.17, six vortices appear in the gap with their position, size, and shape varying at different Reynolds numbers. The fluid velocities show an asymmetric feature with respect to the vortex centers, while the maximum axial and radial velocities increase almost linearly with the increasing reduced Reynolds number (Re À Re c ). In addition, computational fluid dynamics study was employed under the same conditions, and its results agree well with the PIV measurements. Overall, this study provides a quantitative understanding of the formation of Taylor vortices in a constrained space. V V C 2009 American Institute of Chemical Engineers AIChE J, 55: 3056-3065, 2009

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“…They concluded that bubble accumulation on the downward side of vortices was primarily due to the lift force, in what is known as the preferential sweeping mechanism. Deng, Wang & Smith (2006) experimentally investigated the behaviour of bubbles in a Taylor vortex wherein the drag and buoyancy forces are in balance, in line with later observation in this work. Lohse & Prosperetti (2003) studied the equilibrium position of a bubble in a horizontally rotating cylinder and suggested the need for future studies investigating different lift models.…”

Section: Vortex-bubble Interactionsupporting

confidence: 60%

Volume displacement effects during bubble entrainment in a travelling vortex ring

2013

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When a few bubbles are entrained in a travelling vortex ring, it has been shown that, even at extremely low volume loadings, their presence can significantly affect the structure of the vortex core (Sridhar & Katz, J. Fluid Mech., vol. 397, 1999, pp. 171–202). A typical Euler–Lagrange point-particle model with two-way coupling for this dilute system, wherein the bubbles are assumed subgrid and momentum point sources are used to model their effect on the flow, is shown to be unable to capture accurately the experimental trends of bubble settling location, bubble escape and vortex distortion for a range of bubble parameters and vortex strengths. The bubbles experience significant amounts of drag, lift, added mass, pressure and gravity forces. However, these forces are in balance with each other as the bubbles reach a mean settling location away from the vortex core. The reaction force on the fluid due to the net summation of these forces alone is thus very small and is unable to affect the vortex core. By accounting for fluid volume displacement due to bubble motion, experimental trends on vortex distortion and bubble settling location are captured accurately. The fluid displacement effects are studied by computing various contributions to an effective volume displacement force and are found to be important even at low volume loadings. As the bubble size and hence bubble Reynolds number increase, the bubbles settle further away from the vortex centre and have strong potential for vortex distortion. The net volume displacement force depends on the radial pressure force, the radial settling location of the bubble, as well as the vortex Reynolds number. The resultant of the volume displacement force is found to be roughly at $4{5}^{\circ } $ with the vortex travel direction, resulting in wakes directed towards the vortex centre. Finally, a simple modification to the standard point-particle two-way coupling approach is developed wherein the interphase reaction source terms are consistently altered to account for the fluid displacement effects and reactions due to bubble accelerations.

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Bubble behavior in a Taylor vortex

Cited by 23 publications

References 9 publications

Percolation in the canonical ensemble

Percolation in the canonical ensemble

Characterization of Taylor vortex flow in a short liquid column

Volume displacement effects during bubble entrainment in a travelling vortex ring

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