Transcript Project B-1 Interface reconstruction from magnetic field

2D Measurements of Magnetic Field near
the Interface between Two Fluids Carrying
an Electrical Current
S. Men, C. Resagk, H. Brauer,
M. Ziolkowski, M. Kuilekov
Ilmenau University of Technology
Outline
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
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Motivation
Theoretical Model
Experimental Setup
Results and Discussion
Summary and outlook
Motivation
Several MHD applications in processing of materials: Aluminum reduction,
steel/iron making, glass melting, crystal growth, etc. require deep knowledge of
behaviors of the surface/interface of electrically conducting fluids.
the use of probes is difficult or even
impossible (limited access and hostile
environment).
necessary to develop
methods for cell diagnosis.
appropriate
Magnetic Field Tomography (MFT)
Construct a highly
simplified aluminium
reduction cell to
investigate a MFT
system
•
•
•
Build up a magnetic sensor system to detect
weak magnetic field (~nT);
Develop optical techniques to observe interface
displacement;
Identify the main interface shape features by
means of MFT.
Theoretical Model
 r,    A
M
N
 
m   M n 1
mn
J m kmn r   cosm 
 
 
 
o
J r  r  r
Br  
dV 
 3


V
4
r  r
Experimental Setup
CCD
camera
Light
sheet
laser
Two-fluid cell:
KOH+
GaInSn
Pneumatic
shaker
2D fluxgate sensor
-FXM 205
Specifications:
Measuring range: ±100µT
Output voltage: ±18.5mV/µT
Noise:
30pT/Hz
Bandwidth(-3dB): DC to 1.25kHz
Linearity:
 0.25%
Orthogonality: 1°
Operating temp: -40~+85°C
Zero drift:
100nT/K
Supply voltage: 5V ±0.1V DC
Supply current: 5mA eff
Output impedance: <1k
Dimensions— sensor: 2mm15mm
electronics: 26mm
Results and discussion
Optical measurement of interface oscillation
Mode 11 : fshaker=7.2-7.6Hz
Mode 21 : fshaker=9.3-9.6Hz
fshaker=7.3Hz, Idc=1.0A, A=10.17mm
fshaker=9.4Hz, Idc=1.0A, A=8.28mm
Simulation of interface oscillation
J0
mode 11, A=10mm
electrolyte
k1
Bz
Br
liquid metal
k2
Simulation of interface oscillation
mode 21, A=8.0mm
Schematic of data acquisition and processing
Magnetic field measurements
Signals of eight Bz and Br at fshaker=7.3Hz, z=57.5mm
Peak at 3.65Hz  Subharmonic at interface
Contour line of mode 11 at 1.0A, fshaker=7.3Hz
Measurements
Bz
Br
A=9.5-10.5mm
Forward calculation
Bz
Br
A=10.0mm
Mode 21 at fshaker=9.4Hz, Idc=1.0A
Measurement
A=7.5-8.5mm
Forward calculation
A=8.0mm
Flow chart of interface reconstruction
Interface mode
mn, A
FEM3D
Magnetid flux density
In sensor positions
Extract current
density
Biot-Savart
law
Reconstructed interface
mode 11
mode 21
10
-10
 B
Nsensor
CF12%
CF 
i 1
zi
 Bzimeas   Bri  Brimeas 
2
2
 B   B  
Nsensor
i 1
meas 2
zi
meas 2
ri

 100%
CF 16%
Summary and outlook
1.
A sensor ring consisting of eight 2D sensors is suitable to
measure the magnetic field near the oscillating interface
between two electrically conducting fluids for modes m2, n3.
2.
Forward calculation by FEM3D based on the optical
measurement is consistent well with the experimental results.
3.
Evolutionary algorithm is effective for the magnetic field
tomography to reconstruct a non-axisymmetric interface of a
low mode.
4.
Better experimental results (smaller reconstruction error) can
be expected when more sensors in one ring and/or more sensor
rings are applied.
5.
A rectangular cell whose shape is similar to an aluminium
reduction cell will be investigated a little later.
Thank you for your attention!