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Media type:
E-Article
Title:
Direct numerical simulations of bubbly flows.
Part 1. Low Reynolds number arrays
Contributor:
ESMAEELI, ASGHAR;
TRYGGVASON, GRÉTAR
imprint:
Cambridge University Press (CUP), 1998
Published in:Journal of Fluid Mechanics
Language:
English
DOI:
10.1017/s0022112098003176
ISSN:
0022-1120;
1469-7645
Origination:
Footnote:
Description:
<jats:p>Direct numerical simulations of the motion of two- and three-dimensional
buoyant
bubbles in periodic domains are presented. The full Navier–Stokes
equations are
solved by a finite difference/front tracking method that allows a fully
deformable
interface between the bubbles and the ambient fluid and the inclusion of
surface
tension. The governing parameters are selected such that the average rise
Reynolds
number is <jats:italic>O</jats:italic>(1) and deformations of the bubbles are small. The
rise velocity of a
regular array of three-dimensional bubbles at different volume fractions
agrees
relatively well with the prediction of Sangani (1988) for Stokes flow.
A regular array of
two- and three-dimensional bubbles, however, is an unstable configuration
and the
breakup, and the subsequent bubble–bubble interactions take place
by ‘drafting, kissing,
and tumbling’. A comparison between a finite Reynolds number two-dimensional
simulation with sixteen bubbles and a Stokes flow simulation shows that
the finite
Reynolds number array breaks up much faster. It is found that a freely
evolving
array of two-dimensional bubbles rises faster than a regular array and
simulations
with different numbers of two-dimensional bubbles (1–49) show that
the rise velocity
increases slowly with the size of the system. Computations of four and
eight three-dimensional bubbles per period also show a slight increase in the average
rise velocity
compared to a regular array. The difference between two- and three-dimensional
bubbles is discussed.</jats:p>