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A numerical study of bubbly flow in a curved duct using front tracking method
Mohamad Taghi Mehrabani, Mohamad Reza Heyrani Nobari
*Department of Mechanical Engineering, Amirkabir University of Technology, Tehran, Iran
* P.O.B. 15875-4413 Tehran, Iran, [email protected]
A
RTICLEI
NFORMATIONA
BSTRACTOriginal Research Paper Received 08 November 2015 Accepted 04 January 2016 Available Online 14 February 2016
In this article bubbly flow under the specified axial pressure gradient in a curved channel is studied numerically. To do so, a second order parallelized front-tracking/finite-difference method based on the projection algorithm is implemented to solve the governing equations including the full Navier-Stokes and continuity equations in the cylindrical coordinates system using a uniform staggered grid well-fitted to the geometry concerned. In the absence of gravity the mid-plane parallel to the curved duct plane, which is the symmetry plane in the single fluid flow inside the curved duct, separates the bubbly flow into two different flow regions not interacting with each other. Twelve bubbles with diameters of 0.125 wall units are distributed in equally spaced distances from each other. The numerical results obtained indicate that for the cases studied here, the bubbles reach the statistical steady state with an almost constant final orbital motion path due to the strong secondary field. Furthermore, the effects of different physical parameters such as Reynolds number, and curvature ratio on the flow field at the no-slip boundary conditions, are investigated in detail.
Keywords:
Curved duct Multiphase Flow Bubble
Incompressible Flow Finite Difference
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Fig. 1 Geometry of the physical domain
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90×90×90
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percentage during the simulation
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Fig.4 Grid independency test in three different mesh sizes of
50×50×50, 70×70×70, and 90×90×90
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vertical channel[8]
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[ Downloaded from mme.modares.ac.ir on 2023-12-10 ]
1
Table
Parameters used in the simulation
=
1
=
3
/ 1
=
6
/ 1
80
× 80
× 80
0.2
0.2
1.2
1
0.125
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/ 3 1
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2.
Re =
.
Fig.8 secondary flow (left) and axial main flow velocity (right)
in R-Z plane of the duct
( ) ( )
8R-Z
Fig.9 3D stream line with bubbles (left) and secondary flow
field (right) in R-Z plane of the duct
( )
9( )
R-Z 2- Flow plane
Fig. 7 initial bubble distribution in three different curved
duct
7
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Fig. 10 Steady state bubble trajectory project on the cross-
section of the curved duct in R-Z plane
10 R-Z
.
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Fig. 11 Statistical steady state bubble trajectory in the curved
duct (inner wall view)
)
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R-Z Z
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Fig. 12 Statistical steady state bubble trajectory in the curved
duct (top wall view)
)
12[ Downloaded from mme.modares.ac.ir on 2023-12-10 ]
Fig.13 Development of bubble motion projected to the curved
duct cross-section to its steady state orbit
13
Fig.14 R & Z Spiral motion of bubble inside the curved duct
by indicating the r and z coordinates of bubble centroid versus time for = 1
14
R
Z
= 1/3
.
.
17
Fig.15 R & Z Spiral motion of bubble inside the curved duct
by indicating the r and z coordinates of bubble centroid versus time for = 1/3
15
R
Z
= 1/3
Fig.16 R & Z Spiral motion of bubble inside the curved duct by
indicating the r and z coordinates of bubble centroid versus time for = 1/6
16
R
Z
= 1/6
z
.
10[ Downloaded from mme.modares.ac.ir on 2023-12-10 ]
Fig.17 axial velocity contour for channels
17
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We =
We
ijk
z
(m)
=
(Pa.s)
(m2/s)
(kg/m3)
l (kg/m3)
(kg/m3)
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10 -
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