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International Scientific Colloquium
Modelling for Electromagnetic Processing
Hannover, September 16-19, 2014
Small-size permanent magnet system for contactless local velocity
measurement in liquid metals
D. Hernández, C. Karcher, A. Thess
Abstract
Lorentz force velocimetry (LFV) is a contactless velocity measurement technique of
liquid metals. In LFV, the interaction between the magnetic field of a permanent magnet
system and a flowing liquid melt gives rise to eddy currents and a Lorentz force inside the
fluid. Due to Newton’s third law, there is an opposite force of the same magnitude acting on
the magnet systems which is connected to a force sensor. According to the principles of
magnetohydrodynamics, the measured force is proportional to the flow rate or to the velocity.
In the case of local LFV, the magnets are significantly smaller in comparison with the crosssection of the flow. This last technique has already been proved to identify small mechanical
obstacles submerged in liquid metal flow [2]. The main objective of this paper is to extend the
resolution of the model experiments by using an arrangement of smaller permanent magnets.
Introduction
Local velocity or even volumetric flow rate measurements of liquid metals is still an
unsolved problem. The commercial classical measurement techniques (fly-wheel, Pitot tube,
hot wire probes, etc.) require direct contact with the fluid and cannot be used for chemical
aggressive and high-temperature melts like liquid steel in the steel industry. Even contactless
measuring techniques such as Ultrasonic Doppler probe or Particle Image velocimetry fail due
to its opaqueness. Fortunately, there is a recently developed electromagnet technique called
Lorentz force velocimetry (LFV) [1]. In this technique, the flowing liquid metal interacts with
a static magnetic field produced by permanent magnets. According to the principles of
magnetohydrodynamics, this interaction generates eddy currents, and therefore, a total Lorentz
force inside the melt which its direction is opposite to the flow. Owing to Newton’s third law,
there is a counter force of the same magnitude that acts on the magnet system which is
connected to a force sensor. The magnitude of this flow-braking Lorentz force FL depends on
the electrical conductivity σ, the volumetric flow rate Q or velocity V, and the strength of the
imposed magnetic field B0 according to the scaling relation [1]
FL ~ σ Q B02
or
FL ~ σ V B02
(1, 2)
If the magnetic field lines penetrate the entire cross-section of the flow, the Lorentz
force FL is proportional to the mass flow rate Q of the metal melt (Equation 1). On the other
hand in Local Lorentz force velocimetry, where the permanent magnets are relative smaller
than the cross-section of the flow, the Lorentz force FL is proportional to the local velocity of
the liquid metal (Equation 2). With this last technique, Heinicke in [2] was able to identify
obstacles in liquid metal flow and the awake behind them in a rectangular duct. These model
experiments are made in the liquid metal loop GALINKA, see figure below, using as a test
melt the low-melting alloy GaInSn in eutectic composition. The goal of this paper is to extend
the resolution and sensitivity of the model experiments by using a novel arrangement of smaller
permanent magnets.
Inductive
flow meter
Electromagnetic
pump
Plexiglass
test section
Liquid loop
tion
direc
Flow
Permanent
magnet
Heat exchanger
Force sensor
Fig.1. Experimental facility GALINKA. GaInSn in eutectic composition is pumped by a an
electromagnetic pump and circulates in a loop made of stainless steel and a 50 mm x 50 mm plexiglass
rectangular test section. Aside the test section, a permanent magnet is arranged and fixed to a force
sensor.
1. Presentation of the problem
As explained before, local Lorentz force velocimetry works with permanent magnets
which size is considerably small in comparison with the cross-section of the flow. In this way,
it is possible to identify locally obstacles in the flow as Heinicke performed in [2] with a 10 mm
cubic magnet achieving a spatial resolution of 3cm. The main goal of the present paper is to
extend the spatial resolution and the sensitivity of this model experiments by using smaller
magnets, in this case, 5 mm cubic magnets.
However, by reducing the size of the
5mm
permanent magnet for increasing the spatial
resolution, the total Lorentz force reduces as
10mm
well, making its measurement a hard task to
be successfully achieved by the current
measurement techniques. Heinicke in [3]
was not able to have a clear measurement
with a 5mm cubic magnet and an
interference optical force measurement
system. In order to be able to increase the
spatial resolution and at the same time
maintain a measurable force, arrangements
of 5 mm cubic magnets are proposed instead
of using the old 10 mm cubic magnet (Fig.
Fig.2. Principle of replacement of one 10mm 2).
cubic permanent magnet (green) to magnet
systems composed by three (top), five (middle)
and nine (bottom) 5mm permanent magnets.
In this way, it is possible to change the magnetization direction, the position and the number of
the cubic magnets, in order to increase the magnitude of the Lorentz force while improving its
spatial resolution for local velocity measurements.
2. Results
We start the analysis of the problem by comparing the magnitude of the magnetic field
distribution between the old 10 mm cubic magnet and the new permanent magnet
arrangements in the 50 mm x 50 mm rectangular duct of the GALINKA (Fig. 3). In all
simulations, the magnetization direction is perpendicular to the duct, the material of the
magnets is N42 and all magnets are at a distance of 5 mm away from the liquid metal. Fig. 3
(b) illustrates an oval-shaped magnetic field distribution in the rectangular duct which implies
an increase on the spatial resolution of the force, and therefore, of the velocity in the direction
of the flow x. However, the ratio between the maximum of the magnitude of the magnetic
field of the old set up (10 mm cubic magnet) and the new permanent magnet arrangement
(three 5 mm cubic magnets) is 1.8.
(a)
(b)
(c)
(d)
Fig.3. Magnitude of the magnetic field produced by a 10 mm N42 cubic magnet (a) and an
arrangement of three (b), five (c) and nine (d) 5 mm N42 cubic magnets inside a 50 mm x 50 mm
rectangular duct. The distance between the surface of the magnet arrangement and the liquid is 5 mm
and the magnetization direction is perpendicular to the flow in each case. In the magnetic field
simulations (a) and (b), we can see that the magnetic field of the proposed magnetic arrangement has an
oval-type distribution providing a higher spatial resolution of the force in the flow direction x with a
decay of a factor 1.8 of the maximum value in comparison with the 10 mm permanent magnet. The
simulations were performed using the electromagnetic field simulation software Maxwell 2014.
Conclusions
The oval-shape distribution of the magnitude of the magnetic field using an
arrangement of smaller magnets illustrates the possibility of increasing the spatial resolution of
the measured force, and therefore, the velocity, which is the main goal of local Lorentz force
velocimetry. Nevertheless of these partial results, it is not enough to compere de maximum
magnitude of the magnetic field but its distribution in the liquid metal, due to the fact that the
Lorentz force is a body force acting on the volume subset of the flow exposed to the external
magnetic field. Experiments with the GALINKA are currently been prepared for the validation
of these results.
References
[1] Thess, A., Votyakov, E., Knaepen, E., Zikanov, O.: Theory of Lorentz force velocimetry. New Journal of
Physics, 9, 2007.
[2] Heinicke, C.: Spatially resolved measurements in a liquid metal flow with Lorentz force velocimetry. Exp
Fluids, 54, 2013, pp. 29-39.
[3] Heinicke, C.: Local Lorentz force velocimetry for liquid metal duct flows. PhD thesis, Technische
Universität Ilmenau, 2013, 60-68 pp.
Authors
Hernández, Daniel
Institute of Thermodynamics and Fluid Mechanics
Technische Universität Ilmenau
Helmholzring 1
D-98684 Ilmenau, Germany
E-mail: [email protected]
Prof. Dr. Thess, André
Institute of Thermodynamics and Fluid Mechanics
Technische Universität Ilmenau
Helmholzring 1
D-98684 Ilmenau, Germany
E-mail: [email protected]
Dr.-Ing. Karcher, Christian
Institute of Thermodynamics and Fluid Mechanics
Technische Universität Ilmenau
Helmholzring 1
D-98684 Ilmenau, Germany
E-mail: [email protected]