VIII International Scientific Colloquium

Modelling for Materials Processing

Riga, September 21 - 22, 2017

Lorentz Force Velocimetry Applied to Liquid Metal Two-phase

Flow

Z. Lyu, Ch. Karcher, A. Thess

Abstract

Lorentz force velocimetry (LFV) is a non-contact electromagnetic flow measurement

technique for electrically conductive liquids. We aim to extend LFV to liquid metal two-phase

flow measurement. In a previous test we consider the free rising of non-conductive

bubbles/particles in a thin tube of liquid metal (GaInSn) initially at rest. Here the measured

force is due to the displacement flow induced by the rising bubble/particle. We observe that

the Lorentz force strongly depends on the size of the bubble/particle and the local position at

which it travels through the applied magnetic field. However, the free rising velocity cannot

be controlled, which is problematic for the statistics of LFV measurement. Therefore, in this

paper we present experimental results obtained in an improved setup of controllable particle

motions in liquid metal. In this experiment the particle rises with a straight fishing line, which

suppresses any lateral motion and is pulled by a linear driver at controllable velocity. We

observe the scaling laws of Lorentz force depending on particle velocity and distance between

magnet and liquid.

Introduction

Two-phase flow in electrically conductive liquid occur in a number of metallurgical

processes [1]. For example in continuous casting of steel, argon bubbles are injected in order

to prevent clogging of the submerged entry nozzle, to mix the melt in the mold, and to remove

slug particles via the free surface. How bubbly liquid metal flows behave under magnetic

fields and how to measure them is therefore not only of fundamental interest but also of

practical importance.

One promising candidate for liquid metal two-phase flow measurements is Lorentz

Force Velocimetry (LFV) [2,3]. It is based on measuring the flow-induced force acting on an

externally arranged permanent magnet. This force is the counter-force to the Lorentz force,

which is induced in the melt due to electromagnetic interactions between the moving

conductive liquid and the applied magnetic field. Earlier work has demonstrated the capability

of LFV to reconstruct even complex flow fields [4] and to detect bubble/particle free rising in

a thin tube of liquid metal [5]. However, the free-rising velocity cannot be controlled, which is

problematic for the statistics of LFV measurement. The aim of this work is to investigate LFV

measurement in an updated setup with particle fixed on a fishing line, which is pulled by a

linear driver. In this experiment the particle rises along the straight fishing line that suppresses

any lateral motions. Moreover, the vessel is much larger than the particle and particles are

injected at the position close to one side-wall. Therefore the effects of the other three side-

walls can be neglected. Thus we can control the velocity of the particle, and investigate the

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doi:10.22364/mmp2017.33

measurement technique in different flow regimes. In this paper we investigate the effects of

particle velocity, and distance between particle and magnet on Lorentz force signals.

The paper is organized as follows. In section 1 we describe the experimental setup.

Results are discussed in section 2. Finally, we shall summarize the main findings.

1. Experimental setup

As shown in Fig. 1, the experimental setup consists of a plastic vessel

(60×60×400mm3) filled with liquid metal GaInSn. The spherical particle made of plastic

(6mm diameter) is electrically non-conducting and fixed on the fishing line, which is pulled

through the top and bottom holes of the vessel and moves in 10mm distance parallelly to the

left side-wall. The velocity of the sphere is controlled by an additional linear driver, which

provides speeds in the range of 0 to 200mm/s. The effect of fishing line’s motion is neglected

because of its small size (0.1mm in diameter). Our LFV consists of a 12×12×12mm3

permanent magnet (NdFeB 42) which is installed in 10mm distance on the side of the liquid

and an Interference-Optical-Force-Sensor (IOFS) [6], which measures the z-component of

Lorentz forces induced by the displacement flow of liquid melt around the particle.

Fig. 1. Schematic of experimental setup (1 LFV; 2 spherical particle; 3 fishing line; 4 O-ring)

Fig. 2. Magnetic flux density Bx of the 12×12×12 mm3 permanent

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The magnetic flux density Bx of the 12×12×12 mm3 permanent magnet is measured at

certain positions by a Gauss meter, and the results are shown in Fig. 2. Obviously, the main

contributions to the Lorentz force result from the flow induced by the moving particle in the

region between the particle and the side-wall. Within this region, the magnetic flux density

drops from 81.7 to 19.3mT.

2. Results and discussion

The particle moving through the near-magnet region causes perturbations on the

Lorentz force signals due to the displacement flow of the liquid metal around the particle. The

repeatability of LFV measurement is shown in Fig. 3. Twenty samples of Lorentz force

signals at 50mm/s of particle velocity and 10mm of gap between magnet and liquid boundary

are presented. The peak values of Lorentz forces appear at t = 2.5s, when the particle moves

through the near magnet region, and vary from 12µN to 24µN. The variation results from the

systematic errors of the experimental configuration, namely the length change of the fishing

line due to stress and the small lateral motions of it.

Fig. 3. Samples of Lorentz forces at particle velocity 50 mm/s.

The effects of particle velocities have been investigated in the cases of 10mm gap

between magnet surface and liquid side-wall (Fig. 4). The particle velocities are 50, 75, 100,

125, 150mm/s, respectively. The mean value of Lorentz force peaks increases with particle

velocity, because Lorentz force density f = kσB2u [N/m3] [2] is proportional to liquid velocity,

which is in turn affected by particle velocity. Here is the electrical conductivity of the liquid

metal, B is the magnetic flux density, u is the liquid velocity, and k is the proportionality

coefficient. In addition, upon increasing particle velocity, the standard deviation of the peak

values of Lorentz forces likewise increases. This finding can be explained by the fact that the

wake structures become more unsteady in time and space under high Reynolds numbers [7,8].

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The effect of the distance between particle and magnet on peak values of Lorentz force

signals is shown in Fig. 5. The peak values decrease by larger distance, because the magnetic

flux density in the liquid becomes lower (Fig. 2). Additionally, the standard deviation of

Lorentz force decreases. One reason is that the magnetic field generated by the permanent

magnet is spatially localized. By that, the larger the distance, the lower the magnetic flux

density (Fig. 2). The lower magnetic flux density causes less shear and thus the displacement

flow becomes more stable. Another reason is that at larger distance, the effective volume of

Lorentz force is larger, and the product of total Lorentz forces becomes less variable.

Fig. 4. Lorentz force statistics vs. particle velocity.

Fig. 5. Lorentz force statistics vs. distance between magnet surface and liquid boundary.

3. Conclusion

To shortly summarise, Lorentz forces of particle rising in liquid metal under a

permanent magnet are investigated. We observe the scaling laws of Lorentz force depending

on particle velocity and distance between magnet and liquid. However, a strong deviation of

Lorentz force exists when particle velocity is high due to the unsteady wake structures. The

standard deviation of Lorentz force decreases at larger distance between magnet and liquid,

because the effective volume is larger and the integral product of total Lorentz force becomes

less variable.

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Acknowledgement

The authors acknowledge financial support from Deutsche Forschungsgemeinschaft

within the Research Training Group Lorentz force velocimetry and Lorentz force eddy current

testing under grant GRK 1567 and from Helmholtz Alliance LIMTECH within the seed grant

program in the Young Investigator Group. We are also thankful to Erik Nestler for

experimental support.

Reference [1] Davidson, P. A.: An introduction to Magnetohydrodynamics. Cambridg University Press, 2001.

[2] Thess, A., Votyakov, E., Kolesnikov, Y.: Lorentz force velocimetry. Physical Review Letters, Vol. 96, 2006,

No. 16, pp. 164501.

[3] Thess, A., Votyakov, E., Knaepen, B., et al.: Theory of the Lorentz force flowmeter. New Journal of Physics,

Vol. 9, 2007, No. 8, pp. 299.

[4] Heinicke, C., Wondrak, T.: Spatial and temporal resolution of a local Lorentz force flowmeter. Measurement

Science and Technology, Vol. 25, 2014, No. 5, pp. 055302.

[5] Lyu, Z., Karcher, Ch.: Non-contact electromagnetic flow measurement in liquid metal two-phase flow using

Lorentz force velocimetry. Magnetohydrodynamics, Vol. 53, 2017, No. 1, pp. 67-78.

[6] Füßl, R., Jäger, G.: The influence of the force feed-in system on high-accuracy low force measurement.

Proceedings of the XIX IMEKO World Congress—Fundamental and Applied Metrology, Lisbon, Portugal,

2009.

[7] Fröhlich, J., Schwarz, S., Heitkam, S., et al.: Influence of magnetic fields on the behavior of bubbles in liquid

metals. The European Physical Journal Special Topics, Vol. 220, 2013, No. 1, pp. 167-183.

[8] Zhang, J., Ni, M. J., Moreau, R.: Rising motion of a single bubble through a liquid metal in the presence of a

horizontal magnetic field. Physics of Fluids, Vol. 28, 2016, No. 3, pp. 032101.

Authors M. Sc. Lyu, Ze Dr.-Ing. Karcher, Christian

Institute of Thermodynamics and Fluid Mechanics Institute of Thermodynamics and Fluid Mechanics

Technische Universität Ilmenau Technische Universität Ilmenau

P.O. Box 10 05 65 P.O. Box 10 05 65

D-98684 Ilmenau, Germany D-98684 Ilmenau, Germany

E-mail: Ze.Lyu@tu-ilmenau.de E-mail: Christian.Karcher@tu-ilmenau.de

Dr. Thess, André

Institute of Engineering Thermodynamics

German Aerospace Center

Am Pfaffenwaldring 38-40

70569 Stuttgart

E-mail: Andre.Thess@dlr.de

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