2 nd Sino-German Workshop on EPM (Dresden)

MHD DepartmentInstitute of Safety Research

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


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


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


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


Single bubble rising in a longitudinal magnetic field

Rising bubble

Bubble wake

US transducer


Bubble wake modified by the longitudinal magnetic field

B=0 B0


Bubble drag coefficient modified by the longitudinal magnetic field

0.01 0.1 1 100.7

0.8

0.9

1.0

1.1

1.2

CD /

CD(N

=0)

N

Eo=2.2 Eo=2.5 Eo=3.4 Eo=4.9 Eo=6.62

el TN B L /( u )

Magnetic interaction number:

ratio between electromagnetic and inertial force (N = 0 ... 1.3)

2egd

Eo

Bubble Eötvös number


Bubble velocity oscillation frequency and amplitude modified by the longitudinal magnetic field

0.02 0.1 1 30.7

0.8

0.9

1.0

1.1

St /

St(

N=

0)

N

Eo=2.2 Eo=2.5 Eo=3.4 Eo=4.9 Eo=6.6

0.02 0.1 1 3

0.6

0.7

0.8

0.9

1.0

1.1

A/A

(N=

0)

N

Eo=2.2 Eo=2.5 Eo=3.4 Eo=4.9 Eo=6.6

St = fde/uT


Bubble plume-driven flow in the transverse magnetic field- Spatial properties (Q=0.37cm3/s)

B=0 B=0.06T



B=0.11T B=0.17T



B=0 B=0.06T



B=0.11T B=0.17T


Bubble plume-driven flow in the transverse magnetic field-Radial component void fraction distribution measurements

B

Container cross-section view 0.0 0.2 0.4 0.6 0.8 1.0

0.00

0.01

0.02

0.03

0.04

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

void

frac

tion

R

Q=7cm3/s


Bubble plume-driven flow in the transverse magnetic field- Temporal properties (Q=4.0cm3/s)

Q=5cm3/s R=0.87


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


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


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.


Magnetic field influence on the liquid velocity distribution in the container meridional plane

-50 -25 0 25 500

50

100

150

200

Radius [mm]

He

igh

t [m

m]

-50 -25 0 25 500

50

100

150

200

-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

40.0

45.0

50.055.0

60.0

65.0

Radius [mm]

Q=20sccm


Vortex structure evolution in a static magnetic field

P. Davidson. 1995, JFM, 299, 153-186


)( Buj el

BuuBBuuBBu

)()()()()(

uBj el

)( 0

j

0 j

02

0wallu

0/ wallwally yj

const

when the velocity is uniform in the direction of the magnetic field, then

current density is a potential, namely

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

by taking the curl of both sides and using the equation


Bubble drag coefficient modified by the longitudinal magnetic field

lT

eD

u

gdC

23

4

0.1 0.2 0.4 0.6 0.8 1 20.7

0.8

0.9

1.0

1.1

1.2C

D(N

) / C

D(N

=0)

N

Eo=2.7 Eo=4.1 Eo=4.4 Eo=5.9 Eo=6.4 Eo=6.9


Bubble velocity oscillation frequency and amplitude modified by the longitudinal magnetic field

0.1 0.2 0.4 0.6 0.8 1 20.9

1.0

1.1

1.2

1.3

1.4

St(

N)

/ St(

N=

0)

N

Eo=2.7 Eo=4.1 Eo=4.4 Eo=5.9 Eo=6.4 Eo=6.9

0.1 0.2 0.4 0.6 0.8 1 20.0

0.2

0.4

0.6

0.8

1.0

1.2

A(n

) / A

(N=

0)

N

Eo=2.7 Eo=4.1 Eo=4.4 Eo=5.9 Eo=6.4 Eo=6.9

2 nd Sino-German Workshop on EPM (Dresden)

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