flow velocimetry for weakly conducting electrolytes based ... · pdf fileuids like salt water...

July 12, 2013 17:21 WSPC/INSTRUCTION FILEAPMF*2013*Ebert*Vasilyan*Wiederhold

International Journal of Modern Physics: Conference Seriesc© World Scientific Publishing Company

FLOW VELOCIMETRY FOR WEAKLY CONDUCTING

ELECTROLYTES BASED ON HIGH RESOLUTION

LORENTZFORCE MEASUREMENT

R. Ebert

Department of Mechanical Engineering, Ilmenau University of Technology, P.O. Box 100565Ilmenau, D-98693, Germany

[email protected]

S. Vasilyan

Department of Mechanical Engineering, Ilmenau University of Technology, P.O. Box 100565

Ilmenau, D-98693, Germany

[email protected]

A. Wiederhold

Department of Mechanical Engineering, Ilmenau University of Technology, P.O. Box 100565

Ilmenau, D-98693, Germany

[email protected]

Received Day Month YearRevised Day Month Year

We demonstrate that a flow velocity measurement can be transformed into a non-invasive

force measurement by metering the dragforce acting on a system of magnets that is

arranged around a flow channel. This method is called Lorentzforce velocimetry andhas been developed in the last years in our institute. It is a highly feasible principle for

materials with large conductivity like liquid metals.

To evolve this method for weakly conducting fluids like salt water or molten glass thedragforce measurement is the challenging bottleneck. Here forces of 10−8 and less of the

weightforce of the magnet system have to be resolved in the rather noisy environment of

the flow channel.In this paper different force measurement techniques get tested and compared. In

the first setup the drag-force is acting on the magnets that are hanging as a pendulumwith 0.5 m long wires on a mounting. Here the displacement in the range of a few µm canbe detected with a laser interferometer and another optical positioning sensor. For the

second setup the magnet system is attached to a state of the art electromagnetic forcecompensation balance. The balance is used in an unusual orientation: It is turned by 90

degrees to measure the horizontally acting Lorentzforce. Different ways of getting the

correct force signal out of the two measurement setups will be presented and discussed.For generalization of the measurement principle the Lorentzforce is determined for

different fluid profiles. In addition to that we have developed new systematic noise re-

duction methods to increase the resolution of both force measurement techniques by afactor of ten or larger which we will present here.

Keywords: Lorentzforce; flow measurement technique; EFC balance; interferometer.

1


2 R. Ebert, S. Vasilyan, A. Wiederhold

1. Introduction

Espacially for very hot, aggressive or hygienically sensible mediums the conventional

flow velocity measurement methods are just inadequate techniques. The demand for

a propper technology can be satisfied by the so called Lorentzforce velocimetry -

a non-invasive measurement principle - that has been developed in our institute in

the last years.

Here, a system of permanent magnets arranged around the flow channel causes

eddy currents in the liquid due to the relative motion of the magnetic field and

the medium in the channel (Faraday’s law of induction). Those eddy currents will

generate a secondary magnetic field which leads - according to the magnetic field

transport equation - to a force acting back on the system of permanent magnets.

We will call this force Lorentzforce. This force between the permanent magnets and

the moving conductor (in our case: the fluid) is used for many applications like

eddy current brakes. Measuring the force acting on the magnet system allows to

determine the flow velocity respectively the volume flow rate.

The Lorentzforce velocimetry was further developed for industrial applications

like continuous steel casting. But for weakly conducting fluids such as glass melts

and salt melts or even less conducting mediums in food and pharma industries it

was not yet established due to the tiny Lorentzforces that need to be resolved:

FL ∝ σ · v ·B2 (1)

(FL: Lorentzforce, σ: conductivity, v: velocity, B: magnetic flux density)

The conductivity of those substances are in the range of 1..100 Sm−1 in contrast

to liquid metals with 106 Sm−1. Therefore the Lorentzforces are in the range of 1

µN for a system of magnets with a weightforce of about 10 N . Such a high relative

resolution requires state of the art force measurement techniques.

2. Experimental setup

At first a channel was built out of glass to demonstrate the versatility of the Lorentz-

force velocimetry even for weakly conducting fluids. Here the system of magnets is

mounted like a pendulum at four wires (fig. 1). The Lorentzforce can be measured

by the displacement of a pendulum. Therefore we use a Laser interferometer and

an optical positioning sensor. This setup was presented in Ref. 1.

Based on results measured at this setup a second channel has been built as fig.

2 shows. It has an optimized geometry to produce a well defined fluid profile in the

duct. The length of the test section is about 1.5 m. This allows us to measure at

different positions and hence different velocity profiles. The Lorentzforce is measured

in this setup with an electromagnetic force compensation balance in a 90 degree

tilted orientation to measure the horizontal component of the force. It uses an

optical positioning sensor and a software control loop to reach and to retain the

zero-position. For mechanical decoupling of environmental noise from the building

(e. g. vibrations from the pump) the force measurement system is mounted at a


Flow velocimetry for weakly conducting electrolytes based on high resolution Lorentzforce measurement 3

Fig. 1. Schematic illustration of channel 1 with flow channel (a), system of magnets (b), laser

interferometer (c), mounting and wires (d) and massive granite table (e).

massive granite block that stands on a separate fundation and is not coupled with

the building’s one.

3. Measurement results

3.1. Fist channel

Faucet water has been used as working fluid because its electrical conductivity

can be easily adjusted by adding salt (NaCl). Depending from the conductivity

(varied from 0.03 Sm−1 up to 14 Sm−1) Lorentzforces up to about 80 µN have

been measured. The force signal was proportional to the fluid velocity. For detailed

informations see ref. 1.

Fig. 2. Schematic illustration of channel 2 with pump (a), nozzle (b), test section / duct (c),mounting for Lorentzforce velocimeter (d), mechanical decoupling (e) and relax vessel (f).



Fig. 3. Side view of the Halbach magnet array and the EFC balance positioned around the duct

to detect Lorentzforces.

3.2. Second channel

For different electrical conductivities (varied from 0.03 Sm−1 up to 20 Sm−1)and

different fluid velocities the resulting Lorentzforces have been measured. Addition-

ally the position of the force measurement system was varied (five equidistant places

along the full duct length). We will call them position 1 to 5 in flow direction. As

a fluid we have used salt water again. Fig. 4 shows the force signal for the different

sensor positions. To remove long term drifts (e. g. temperature changes) the force

signal has been detrended. Averaging over 1200 samples with a sampling rate of 20

Hz allows to reduce the standard deviation to a minimum. The optimal intervall

length of this moving average filter was determined before numerically with some

test-measurements. Equation 1 predicts a proportionality not just between FL and

v but also between FL and σ. Therefore fig. 5 shows the slope of the linear regres-

sion functions from fig. 4 over the conductivity. There is an overlap of the graphs

of every position recognizable - except position 2 (further investigations necessary).

The distributions have just a small deviation relative to their linear fit and intersect

the vertical axis near zero.

3.2.1. Environmental influences: Temperature

As an example of environmental noise we present the correlation between force

signal and temperature here. During the heating period in the cold seasons we

measured a long period oscillations of the force with an amplitude of about 2.5 µN



Fig. 4. Lorentzforce over fluid velocity for different electrical conductivities and different positionsof the force sensor. The five positions are equidistant from the inlet nozzle (position 1) until the

outlet (position 5).

and a period of 75 minutes. In the end a distribution of a dozen temperature sensors

unveiled the source of this oscillations finally: It comes from the room heaters (see

fig. 6). Those room heaters are part of a large heating circuit of the building with a

water warm up perdiod of the same duration. The sign of the force scale is a matter



0 5 1 0 1 5 2 00

2 0

4 0

6 0

8 0

1 0 0

1 2 0

p o s i t i o n 5 p o s i t i o n 4 p o s i t i o n 3 p o s i t i o n 2 p o s i t i o n 1 l i n e a r f i t o f p o s i t i o n 5 l i n e a r f i t o f p o s i t i o n 4 l i n e a r f i t o f p o s i t i o n 3 l i n e a r f i t o f p o s i t i o n 2 l i n e a r f i t o f p o s i t i o n 1Slo

pes o

f linea

r regre

ssion

s (fig

. 4) [k

g/s]

E l e c t r i c a l c o n d u c t i v i t y [ S / m ]

Fig. 5. Slope of the linear regression functions in fig. 4 over the conductivity. The proportionality

as predicted by theory (eq. 1) is clearly recognizeable.

Fig. 6. Raw Lorentzforce signal (broad curve) shows a periodic oscillation that is strongly cor-

related to the temperature (narrow curve). Only relative temperatures are important here. Thisallows the high relative temperature resolution.

of definition of the measurement coordinate system - so with opposite sign both

curves have nearly identically shape but with a time difference of a few minutes.

The reason of the mentioned correlation will be discussed in the following section.

4. Discussion

Both force measurement techniques can be used to detect Lorentzforces in the range

of µN . The response time of the pendulum setup is larger due to a small attenuation

coefficient. The step-response oscillation is damped by e in about 30 seconds. The

EFC balance is at least ten times faster. Hence it is feasible for faster changes in the



flow rate but it also is more sensible to environmental noise. For use in industrial

applications the commercial EFC balance is the superior choice due to its faster

operation. In terms of sensitivity our in-house indirect force measurement technique

- the pendulum setup with the laser interferometer - is on par with the commercial

solution and it is a highly feasible and in comparison a simple construction if only

slow flow accelerations need to be resolved.

The proportionality between the electrical conductivity and the Lorentzforce has

been verified experimentally just as the proportionality between Lorentzforce and

flow velocity.

With respect to the flow profile (implemented by different sensor positions along

flow channel) no significant change has been detected. This means this flow profile

sensitive measurement method is feasible at least for typical fluid velocity profiles

that occur in a pipe and in a duct.

Both measurement systems are quite sensible to environmental disturbances.

The explained correlation of a long term drift in the force signal and the room

temperature can be explained by thermal expansion due to an oscillating room

heater temperature that heats the setup only from one side. This causes a (small)

tilting of the aluminum frame on which the force sensor is mounted. Due to the

large ratio of the weight force of the magnets (about 10 N) and the Lorentzforces

(µN range) even very small tilting angles effect a recognizable change in the force

signal.

5. Outlook

For decreasing the sensitivity to temperature fluctuations we plan to use a frame

material with a smaller expansion coefficient.

Obstacles in the flow channel will allow to measure at very different flow profiles.

By that we plan to develope the measurement method for more general industrial

applications.

Acknowledgements

The authors are grateful to the German Science Foundation (Deutsche Forschungs-

gemeinschaft) for financial support of this work in the framework of the Research

Training Group Lorentz force velocimetry and Lorentz force eddy current testing.

Further the authors are grateful to Andr Wegfrass who has constructed both chan-

nels and hence he has built up the fundamentels of this research.

Appendix A. References

References

1. A. Wegfrass, C. Diethold, M. Werner, C. Resagk, T. Froehlich, B. Halbedel and A.Thess, Measurement Science and Technology 23, 6 (2012)

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