Rising velocity of a swarm of spherical bubbles in power law fluids at high reynolds numbers

1998 ◽  
Vol 76 (1) ◽  
pp. 137-140 ◽  
Author(s):  
R. P. Chhabra
2001 ◽  
Vol 5 (2) ◽  
pp. 65-73 ◽  
Author(s):  
John F. Harper

Over many years the author and others have given theories for bubbles rising in line in a liquid. Theory has usually suggested that the bubbles will tend towards a stable distance apart, but experiments have often showed them pairing off and sometimes coalescing. However, existing theory seems not to deal adequately with the case of bubbles growing as they rise, which they do if the liquid is boiling, or is a supersaturated solution of a gas, or simply because the pressure decreases with height. That omission is now addressed, for spherical bubbles rising at high Reynolds numbers. As the flow is then nearly irrotational, Lagrange's equations can be used with Rayleigh's dissipation function. The theory also works for bubbles shrinking as they rise because they dissolve.


Author(s):  
Pooja Thakur ◽  
Naveen Tiwari ◽  
Raj P. Chhabra

Abstract In this study, a rotating cylinder is placed in a stream of shear-thinning fluids, flowing with an uniform velocity. Detailed investigations are performed for the following range of conditions: Reynolds number 100 ? Re ? 500, power-law index 0.2 ? n ? 1 and rotational velocity 0 ? ? ? 5. Flow transitions are observed from steady to unsteady at critical values of the Reynolds number, the rotational velocity, and the power-law index. Critical values of the Reynolds number Re^c have been obtained for varying levels of the rotational velocity, and the power-law index. Re^c varies non-monotonically with the rotational velocity. At a particular Reynolds number, an increase of the rotational velocity acts as a vortex suppression technique. For shear-thinning ?uids considered here, the vortex suppression occurs at a larger value of the critical rotational velocity ?^c, relative to Newtonian ?uids. For the unsteady ?ow, lift coef?cient versus time curve exhibits oscillatory behavior, and this has been used to delineate the ?ow regime as steady or unsteady ?ow. For unsteady ?ow regimes, both the amplitude of the lift coef?cient and the Strouhal number increase with increasing Reynolds numbers. The results presented in this work for such high Reynolds numbers elucidate the possible complex interplay between the kinematic and rheological parameters of non-Newtonian ?uids. This investigation also complements the currently available low Reynolds number results up to ? Re = 140.


2012 ◽  
Vol 43 (5) ◽  
pp. 589-613
Author(s):  
Vyacheslav Antonovich Bashkin ◽  
Ivan Vladimirovich Egorov ◽  
Ivan Valeryevich Ezhov ◽  
Sergey Vladimirovich Utyuzhnikov

AIAA Journal ◽  
1999 ◽  
Vol 37 ◽  
pp. 1062-1071 ◽  
Author(s):  
A. Seifert ◽  
L. G. Pack

AIAA Journal ◽  
2000 ◽  
Vol 38 ◽  
pp. 825-834
Author(s):  
F. Novak ◽  
T. Sarpkaya

2004 ◽  
Author(s):  
William L. Keith ◽  
Kimberly M. Cipolla ◽  
David R. Hart ◽  
Deborah A. Furey

Author(s):  
Michael Maurer ◽  
Jens von Wolfersdorf ◽  
Michael Gritsch

An experimental and numerical study was conducted to determine the thermal performance of V-shaped ribs in a rectangular channel with an aspect ratio of 2:1. Local heat transfer coefficients were measured using the steady state thermochromic liquid crystal technique. Periodic pressure losses were obtained with pressure taps along the smooth channel sidewall. Reynolds numbers from 95,000 to 500,000 were investigated with V-shaped ribs located on one side or on both sides of the test channel. The rib height-to-hydraulic diameter ratios (e/Dh) were 0.0625 and 0.02, and the rib pitch-to-height ratio (P/e) was 10. In addition, all test cases were investigated numerically. The commercial software FLUENT™ was used with a two-layer k-ε turbulence model. Numerically and experimentally obtained data were compared. It was determined that the heat transfer enhancement based on the heat transfer of a smooth wall levels off for Reynolds numbers over 200,000. The introduction of a second ribbed sidewall slightly increased the heat transfer enhancement whereas the pressure penalty was approximately doubled. Diminishing the rib height at high Reynolds numbers had the disadvantage of a slightly decreased heat transfer enhancement, but benefits in a significantly reduced pressure loss. At high Reynolds numbers small-scale ribs in a one-sided ribbed channel were shown to have the best thermal performance.


Sign in / Sign up

Export Citation Format

Share Document