Flow Measurement and Instrumentation 16 (2005) 199–204

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Simulation study of the sensing fieldin electromagnetic tomography fotwo-phase flow measurement

Ze Liua,∗, Min Heb, Hanliang Xiongc

aDepartment of Automation, Beijing Jiaotong University, Beijing, PR ChinabCollege of Engineering, Shanghai Maritime University, Shanghai, PR China

cDepartment of Automation, Tianjin University, Tianjin, PR China

Received 10 October 2004; received in revised form 30 January 2005; accepted 15 February 2005

Abstract

The sensing field in the electromagnetic tomography (EMT) system has been studied based on a novel parallel excitation which usflexible circuit strips array. The principle of parallel excitation is analyzed. To find out the interaction between the excitation fieldobject field which is produced by conductive and/or ferromagnetic materials in the measured space, both empty sensing field asensing field are simulated using the finite element method (FEM). The simulation result shows that this kind of parallel excitateffective solution of an EMT excitation system. A discussion of the dual mode imaging in EMT is also included.© 2005 Elsevier Ltd. All rights reserved.

Keywords: Process tomography; Electromagnetic tomography; Parallel excitation; FEM

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1. Introduction

Electromagnetic tomography (EMT) can provide a rsonable way to measure the solid–gas flow and solid–liqflow which contain magnetic material by reconstructingimages of the flow process. EMT, which was proposedyears ago [1], is one of the electrical tomography technogies. It combines electromagnetic theory with compuized tomography technology. EMT also has another namagnetic induction tomography (MIT) [2,3]. This technol-ogy can reconstruct the spatiotemporal distribution imaof conductive and/or ferromagnetic materials by detecthe boundary magnetic flux density of the space beingsearched. In addition, the sensor of an EMT system hasadvantages of being non-invasive, non-contacting andhazardous. So it can be used in the fields of industrial mphase flow measurement, chemical abstraction, foreign material monitoring, geologic exploration and biomedical r

∗ Corresponding author.E-mail addresses:zliu@center.njtu.edu.cn (Z. Liu), hemin@eyou.com

(M. He), hanliang@public.tpt.tj.cn (H. Xiong).

0955-5986/$ - see front matter © 2005 Elsevier Ltd. All rights reserved.doi:10.1016/j.flowmeasinst.2005.02.008

be

:

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search. Furthermore, EMT can be used to develop advamulti-phase flow measurement instruments, in combinawith other electrical tomographies.

Three different electromagnetic tomography systewere reviewed by Peyton in 1996 [4]. The main difference othe threekinds of systems is the excitation mode. This pafocuses on the parallel excitation mode [5] and presents akind of novel parallel excitation structure using a flexicircuit strips array. Based on this kind of novel excitatstructure, the excitation sensing field is simulated usingfinite element method (FEM). In order to investigateinteraction between the alternative excitation field andmaterial measured, the object fields to be simulated contathree test poles respectively, including a copper polferrite pole and a special pole, which are conductiveferromagnetic. Finally, the characteristics of thedual modeimaging are discussed according to the simulation result.

2. Principle of parallel excitation

To construct a rotatable parallel excitation field, thecurrent distributed around the measured pipe shouldcontrolled according to the following rules. A parallel

200 Z. Liu et al. / Flow Measurement and Instrumentation 16 (2005) 199–204

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Nomenclature

B magnetic flux density, TI excitation current, AID excitation current ofpoint D in Eq. (2.5), AIE excitation current ofpoint E in Eq. (2.5), AK0 surface current density, A/mR radius, mmσ conductivity, S/mµr relative permeability

Fig. 1. Magnetic flux density of an infinite current board.

magnetic field can be generated by using an infinite curboard.Fig. 1 shows the theory model of the magnetic fluxdensity generated by an infinite current board. Considean arbitrary pointP above the infinite current board, imagnetic flux density dB which is generated by the twcurrent lines L1 and L2 distributed on theX O Z plane,is enhanced in theX direction and counteracted in theYdirection. So the magnetic flux density distribution besidethe infinite current board can be calculated from Eq. (2.1):

B = BXi =[−

∫ ∞

−∞µK0 sinα

2π(x2 + y2)1/2dx

]i

=[−µK0y

2π

∫ +∞

−∞dx

x2 + y2

]i

=[−µK0

2πarctan

x

y

∣∣∣∣+∞

−∞

]i

=

−µK0

2i, y > 0

+µK0

2i, y < 0,

(2.1)

whereB is the magnetic flux density generated by the infincurrent board. In Eq. (2.1), BX is the magnetic flux densitin the X direction; K0 is the surface current density of theinfinite board with unit thickness. Eq. (2.1) shows that themagnetic flux densities (above and below the board)equal in magnitude and opposite in direction.

If a parallel infinite current board, in which the curredirection is opposite, is fixed above the former board,magnetic flux density distributions of these two boards w

t

Fig. 2. Magnetic flux density of two infinite current boards.

be as shown inFig. 2. So the magnetic flux density generatedby boards I and II can be induced by Eq. (2.1) and bedescribed by Eqs. (2.2) and (2.3):

BI =

+µK0

2i, y > −R

−µK0

2i, y < −R

(2.2)

BII =

+µK0

2i, y < R

−µK0

2i, y > R.

(2.3)

Combining Eqs. (2.2) and (2.3) and using the superpositioprinciple, the magnetic flux density between boards I andcan be obtained by Eq. (2.4):

B = +µK0i, −R < y < R. (2.4)

As shown inFig. 2, suppose the current distributed alothe circle between boards I and II can generate the smagnetic flux density in the center as that of the two paralboards. The magnetic flux density generated byID and IEshould be equal in the center of the circle. They are shin Eq. (2.5):

BD = µID

2π LBE = µIE

2π R. (2.5)

So the excitation current of point E,IE, can be calculated bEq. (2.6):

IE = ID sinθ. (2.6)

Furthermore, by using the integral method along the currdistribution path and the Biot–Savart law, the magnetic fldensity of an arbitrary point among the circle excited bycurrent distribution along the circle can be proved to be eto that excited by the two infinite boards. So, if the excitatcurrent along the circle satisfies Eq. (2.6), thenthe magneticflux density among the circle will be parallel and even [5].Moreover, the excitation field rotation can be realizedcontrolling the distribution of the excitation currents in tflexible circuit strips array along the excitation circle.

Z. Liu et al. / Flow Measurement and Instrumentation 16 (2005) 199–204 201

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3. Sensing field simulation of a novel parallel excitation

3.1. Realization of aparallel excitation

In the actual exciting system of EMT, the distributiof exciting current along the excitation layer cannot becontinuously. A novel excitation structure using a flexicurrent strips array has been designed and applied inexperimental system. The system can reconstruct iniimages of test poles [6]. Its excitation system uses 32 flexibcurrent strips which are arranged uniformly aroundexcitation circle. The current distribution on each stripgiven by Eq. (3.1):

Ii = I sin(ϕi − pθ0) sin(ωt + φ0), (3.1)

where i denotes the excitation strip number, p is theexcitation projection sequence number,ϕi is the angle ofexcitation strip i , and θ0 is the angle difference of thetwo adjacent excitation projections.I · sin(ωt + φ0) is thenotation of the excitation signal. The maximum current othe strips is 10 mA. Compared with the parallel excitatimplementation using two orthogonal excitation coils [4,5],the advantage of this kind of excitation is that the excitcurrent of every exciting strip around the circle cancontrolled flexibly and independently.

3.2. Simulation of theempty excitation field

Bias error will appear if the parallel excitationconstructed by using finite flexible circuit strips becauthe strips cannot be fixed infinitely. For analyzing thexcitation sensing field of the nonideal excitation structuthe magnetic flux density distribution is simulated by usan FEM based on the actual sensor structure. The simulconditions are as follows. The radius of the measuredis 35 mm. The material of thepipe is organic glassesThe radius of electromagnetic shield layer is 60 mm.the actual EMT system, the electromagnetic shield layemade up of ferrite rings and a permalloy cylinder. Insimulation model, the magnetic vector potential of the shlayer is constrained as equal to emulate the conditiothe actual structure. The radius of the excitation laye55 mm. 32 flexible excitation strips are arranged uniformaround the excitation layer. The excitation currents onstrips are distributed around the pipe according to Eq. (3.1).Under these conditions, the simulated magnetic fluxdistribution of the empty measured pipe is shown inFig. 3.

In Fig. 3, the outer layer is the electromagnetic shielayer. The inner layers are the excitation layer, deteclayer, outer wall of the measured pipe and inner wallmeasured pipe in turn.Fig. 3 shows that the magnetic fluxlines in the measured pipe are parallel and even.Fig. 4 isthe simulated magnetic flux density distribution of the emfield. TheX–Y plane denotes the cross section of the senthe Z-axis is the magnitude of the magnetic flux densAs shown inFig. 4, themagnetic flux densities in the cros

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n

f

;

Fig. 3. Distribution of magnetic flux lines in empty field.

Fig. 4. Distribution of magnetic flux density in empty field.

section of the measured pipe (R = 35 mm) are equal, anits magnitude is 1.0985× 10−7 T. According to the formertheoretical analysis, the magnetic flux density in the crsection of the pipe can be calculated; it is 1.01467×10−7 T.So the simulation result of the sensing field is similar toresult of the theoretical analysis.

3.3. Simulation of sensing fields

Sensing fields of detectors in the parallel excitation EMsystem are simulated by electromagnetic FEM. Sensifield diagramsof detectors are shown asFig. 5 partly. Theexcitation direction is the first projection. The sensing fieof detectors in other directions are similar to these. It shthat as the position to detectors goes nearer the sensitivithigher. The last sensing field inFig. 5 is the general sensinfield of the total eight detectors. It is the sum of the eigdetectors’ sensing fields. As shown inFig. 5, the sensitivityin the center is the lowest. And the detectors, whichvertical to the excitation direction, have higher sensitivthan parallel ones. This is the individual feature of a paralleexcitation system.

4. Simulation of interaction between excitation field andobject

To analyze the interaction between the excitation fieand the measured object, the sensing fields with condu

202 Z. Liu et al. / Flow Measurement and Instrumentation 16 (2005) 199–204

Fig. 5. Sensing fields of detectors in first projection.

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and/or ferromagnetic object are simulated by usingFEM. Test objects are as follows: a copper pole whoconductivity is 5.87× 107 S/m, a ferrite pole whose relativpermeability is 200, and a special pole whose conductivit5.87× 107 S/m and relative permeability is 200. The radiuof these poles is 10 mm. The frequency of the excitatsignals is200 kHz. The simulated distributions of magneflux lines and magnetic flux density are shown inFig. 6.Fig. 6(a) shows the distributions of magnetic flux lines anflux density distribution with the copper pole in the centof the measured pipe, (b) withthe ferrite pole, (c) with thespecial pole. In the graphs in the right column, theX–Yplane is the cross section of the measured pipe and thZ-axis is the magnitude of the magnetic flux density.

The simulation result shows that the conductive objexcludes the magnetic flux lines, but the ferromagneobject attracts the magnetic flux lines. In Fig. 6(c), thespecial pole generates a complex interaction with theexcitation field.

To analyze the distributions more obviously, magneflux density distributions along X-axis, Y-axis and thedetection layer(R = 38.4 mm) are shown inFig. 7. Thefour lines in the graphs denote the magnetic flux dendistributions of the empty field, field with the copper pofield with the ferrite pole, and field with the special poThe line styles of the three graphs are shown in the legof graph 7(c). The X-axis is the direction of excitationprojection. As shown in (a) and (b), ferromagnetic mateevidently reinforces the magnetic flux density, and ininner area the magnetic flux density reaches a maxim

value; but conductive material weakens the magneticdensity, and inits inner area the magnetic flux density almodecreases to zero. The result coincides with the theoreticalanalysis that a conductive object in the alternative excitafield can generate an eddy current and a ferromagnetic objecan be magnetized. The direction of magnetic flux dengenerated by the eddy current is opposite to the excitadirection, whereas the direction of magnetic flux densitygenerated by a ferromagneticmaterial is the same as thexcitation direction.Fig. 7also shows that the magnetic fludensities modulated by the conductive and ferromagnmaterial are coupled to each other. Obviously this kindcoupling is nonlinear.

5. Conclusion and discussion

Parallel excitation in an EMT system can be obtainedusing alternative excitation currents which are distributalong the excitation layer outside the measured pipe.controlling the current distribution, the magnetic excitatprojection can be rotated. A novel structure of paraexcitation, which uses a flexible current strip array, ispresented and its sensing field is simulated based oactual sensor system. The simulation results showthis kind of excitation structure can generate an eand parallel magnetic excitation field in the measupipe. Conductive and ferromagnetic materials have evidinteraction with the excitation field. So this kind of excitatistructure can be used to reconstruct images of conduc

Z. Liu et al. / Flow Measurement and Instrumentation 16 (2005) 199–204 203

(a) Copper pole(R = 10 mm, σ = 5.87× 107 S/m) in the center of the pipe.

(b) Ferrite pole(R = 10 mm, µr = 200) in the center of the pipe.

(c) Special pole(R = 10 mm, σ = 5.87× 107 S/m,µr = 200) in the center of the pipe.

Fig. 6. Distribution of magneticflux lines and flux density of a parallel excitation field with objects.

(a) Along theX-axis. (b) Along theY-axis. (c) Along a circle of the detection layer.

Fig. 7. Magnetic flux density distribution in a parallel excitation field along different paths.

204 Z. Liu et al. / Flow Measurement and Instrumentation 16 (2005) 199–204

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or ferromagnetic materials. But investigations are stneeded for reconstructing images of both conductiveferromagnetic material at the same time. The reason is ththe interaction of conductive and ferromagnetic materialcoupled to each other nonlinearly. This phenomenon bringa challenge to the realization of dual mode imaging inEMT system. Some technologies, such as complex siexcitation and demodulation, sensitivity decoupling, amulti-frequency excitation, may provide solutions to thedifficulties.

Acknowledgements

The authors would like to thank the National NatuScience Foundation of the People’s Republic of Chinasupport through grant number 60302011.

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