2nd Sino-German Workshop on EPM (Dresden)
Experimental studies of bubble-driven liquid metal flows
in a static magnetic field
C. Zhang, S. Eckert, G. Gerbeth
Forschungszentrum Rossendorf, Dresden - Germany
MHD Department
Institute of Safety Research
Background & Motivation
• Numerous applications of bubble-driven flows
and magnetic fields in metallurgical engineering
• Combination of gas bubble injections and
magnetic fields
• Comprehensive understandings of such MHD
two-phase flows
MHD Department
Institute of Safety Research
Scalar quantity transportations in MHD flows
• A static magnetic field might both increase and
decrease the heat transfer rate in enclosed thermal
convections
–
T. Tagawa & H.Ozoe, J. Heat Transfer 120, 1027-1032
–
U. Burr & Mueller, 2002. J. Fluid Mech 453, 345-369
–
G. Authie, et al., 2003, Eur. J. Mech. B/Fluids 22, 203-220
• Flow field information are highly desirable
• How about bubble-driven flow in a magnetic field?
Single bubble motion; bubble plume flow
MHD Department
Institute of Safety Research
Bubble-driven flow: experimental setup
• Cylindrical container aspect ratio=2.5
• Liquid metal – GaInSn
• Single Ar bubble or bubble plume
Qmax=8cm3/s
• A vertical longitudinal magnetic field
or a horizontal transverse magnetic
field, B=0 - 0.2T
• UDV measurements of the vertical and
radial component velocity
MHD Department
Institute of Safety Research
Single bubble rising in a longitudinal magnetic field
Rising bubble
Bubble wake
US transducer
MHD Department
Institute of Safety Research
Bubble wake modified by the longitudinal magnetic field
B=0
B0
MHD Department
Institute of Safety Research
Bubble drag coefficient modified by the longitudinal magnetic field
1.2
Magnetic interaction number:
ratio between electromagnetic
and inertial force (N = 0 ... 1.3)
Bubble Eötvös number
gd e 2
Eo 

1.1
CD / CD(N=0)
N  el B2 L /(u T )
Eo=2.2
Eo=2.5
Eo=3.4
Eo=4.9
Eo=6.6
1.0
0.9
0.8
0.7
0.01
0.1
1
10
N
MHD Department
Institute of Safety Research
Bubble velocity oscillation frequency and amplitude modified
by the longitudinal magnetic field
1.1
1.1
St = fde/uT
1.0
A/A(N=0)
St / St(N=0)
1.0
0.9
0.8
0.7
0.02
Eo=2.2
Eo=2.5
Eo=3.4
Eo=4.9
Eo=6.6
0.9
0.8
0.7
0.6
0.1
1
N
3
0.02
Eo=2.2
Eo=2.5
Eo=3.4
Eo=4.9
Eo=6.6
0.1
1
3
N
MHD Department
Institute of Safety Research
Bubble plume-driven flow in the transverse magnetic field
- Spatial properties (Q=0.37cm3/s)
B=0
B=0.06T
MHD Department
Institute of Safety Research
Bubble plume-driven flow in the transverse magnetic field
- Spatial properties (Q=0.37cm3/s)
B=0.11T
B=0.17T
MHD Department
Institute of Safety Research
Bubble plume-driven flow in the transverse magnetic field
- Spatial properties (Q=3.7cm3/s)
B=0
B=0.06T
MHD Department
Institute of Safety Research
Bubble plume-driven flow in the transverse magnetic field
- Spatial properties (Q=3.7cm3/s)
B=0.11T
B=0.17T
MHD Department
Institute of Safety Research
Bubble plume-driven flow in the transverse magnetic field
-Radial component void fraction distribution measurements
0.05
B=0 radius perpendicular to B
B=0 radius parallel to B
B=0.13T radius perpendicular to B
B=0.13T radius parallel to B
B
void fraction
0.04
0.03
0.02
0.01
0.00
Container cross-section view
0.0
0.2
0.6
0.4
0.8
1.0
R
Q=7cm3/s
MHD Department
Institute of Safety Research
Bubble plume-driven flow in the transverse magnetic field
- Temporal properties (Q=4.0cm3/s)
Q=5cm3/s R=0.87
MHD Department
Institute of Safety Research
Bubble plume-driven flow in the transverse magnetic field
- Temporal properties (Q=4.0cm3/s)
Q=5cm3/s R=0.87
MHD Department
Institute of Safety Research
Summary
•
The non-intrusive UDV measuring technique allows us to look into
the opaque liquid metal flows
•
A DC transverse magnetic field modifies both the spatial and
temporal properties of the ordinary bubble-driven flow
•
DC magnetic field may enforce flow instabilities!
(Continuous casting + EMBR)
•
Potential tools for controlling liquid metal flows in metallurgical
engineering
MHD Department
Institute of Safety Research
Perspectives for future research projects
Potential topics of interest:
– Liquid metal mixing enhancement
(control of heat and mass transfer in bubble plumes)
– Gas phase distributions
– Free surface stabilization
– Continuous casting
– …
FZR: Capacity of EPM model experiments in metallurgical
engineering
– Liquid metal model experiments
– Magnetic fields (tailored fields  MULTIMAG facility)
– Measuring techniques
MHD Department
Institute of Safety Research
Acknowledgement
The research is supported by the Deutsche
Forschungsgemeinschaft (DFG) in the form of the SFB
609 “Electromagnetic Flow Control in Metallurgy,
Crystal Growth and Electrochemistry”.
This support is gratefully acknowledged by the authors.
MHD Department
Institute of Safety Research
Height [mm]
Magnetic field influence on the liquid velocity distribution
in the container meridional plane
200
200
150
150
100
100
50
50
0
-50
-25
0
25
50
0
-50
Radius [mm]
65.0
60.0
55.0
50.0
45.0
40.0
35.0
30.0
25.0
20.0
15.0
10.0
5.00
0
-5.00
-10.0
-15.0
-20.0
-25.0
-30.0
-35.0
-25
0
25
50
Radius [mm]
Q=20sccm
MHD Department
Institute of Safety Research
Vortex structure evolution in a static magnetic field
P. Davidson. 1995, JFM, 299, 153-186
MHD Department
Institute of Safety Research

 
j   el (  u  B)
by taking the curl of both sides and using the equation


 
 
 
 
  (u  B)  ( B  )u  (u  ) B  (  B)u  (  u ) B



  j   el ( B0  )u
when the velocity is uniform in the direction of the magnetic field, then
current density is a potential, namely

j  
 2  0

u wall  0

 j  0
jy
wall
   / y wall  0
  const
so there is no Joule dissipation in such case. Accordingly, the Joule
dissipation can be reduced by forming the two-dimensional vortical
structures along the magnetic field line direction.
D. Lee & H. Choi, JFM, 2001, 439. 367-394
MHD Department
Institute of Safety Research
Bubble drag coefficient modified by the longitudinal magnetic field
1.2
CD(N) / CD(N=0)
1.1
1.0
0.9
0.8
0.7
0.1
Eo=2.7
Eo=4.1
Eo=4.4
Eo=5.9
Eo=6.4
Eo=6.9
0.2
CD 
0.4
4  d e g
3 uT2  l
0.6
0.8 1
2
N
MHD Department
Institute of Safety Research
Bubble velocity oscillation frequency and amplitude modified
by the longitudinal magnetic field
1.4
1.2
1.0
A(n) / A(N=0)
St(N) / St(N=0)
1.3
1.2
Eo=2.7
Eo=4.1
Eo=4.4
Eo=5.9
Eo=6.4
Eo=6.9
1.1
1.0
0.9
0.1
0.8
0.6
0.4
0.2
0.2
0.4
N
0.6
0.8
1
2
0.0
0.1
Eo=2.7
Eo=4.1
Eo=4.4
Eo=5.9
Eo=6.4
Eo=6.9
0.2
0.4
0.6
0.8
1
2
N
MHD Department
Institute of Safety Research