APPLICATION OF NUMERICAL SIMULATION IN THE DESIGN OFTWIN-PLANE TOMOGRAPHIC CAPACITANCE SENSORS FOR FLOW

IMAGING

Arko*

ABSTRAK

PENERAPAN SIMULASI NUMERIK DALAM PERANCANGAN SENSOR TOMOGRAFI KAPASITIF BERDAMPINGAN GANDA UNTUK PENCITRAAN PROSES ALIRAN.Makalah ini membahas pentingnya sinulasi medan listrik secara numerik dalam perancangan sensortomografi kapasitif dengan banyak elektroda untuk pencitraan proses aliran di industri. Untuk sensortomografi berpenampang ganda, jarak antar penampang haruslah tepat dan perlu adanya tambahangrounding diantara kedua penampang. Sebaran medan listrik disekitar elektroda yang berdekatannamun dari penampang yang berbeda ketika diaktifkan secara simultan perlu dipelajari, karena sebarantersebut akan mempengaruhi zona sensor. Selain itu, tingkat material yang disensor juga perludiperhatikan. Untuk mendapatkan disain sensor yang optimal dan untuk memahami perilaku medanlistrik dalam zona sensor, simulasi dengan komputer memberikan solusi yang ideal.

Kata kunci: simulasi medan, disain sensor, tomografi kapasitif

ABSTRACT

APPLICATION OF NUMERICAL SIMULATION IN THE DESIGN OF TWIN-PLANETOMOGRAPHIC CAPACITANCE SENSORS FOR FLOW IMAGING. This paper addresses theneed for field simulation in the design of multi electrode capacitance sensors for tomographic flowimaging. For twin-plane sensors, the distance between planes should be well spaced and additionalgrounding between them may be necessary. The fringing effects when two adjacent electrodes fromdifferent planes are driven simultaneously need to be studied, as it will affect the sensing zones. Thelevel of solids loading in the sensing area is another issue that requires attention. To obtain optimalsensor design and to understand the behavior of electric potential fields within the sensing zones,computer simulation offers an excellent solution.

Index Terms: field simulation, sensor design, tomography, cross correlation, flow measurement

* Pusat Pengembangan Teknologi Informatika dan Komputasi – BATAN

INTRODUCTION

Tomographic imaging offers a unique opportunity to unravel the complexityof internal structures without invasive measurements [1]. The basic idea is to mountan array of sensors around the pipe or vessel to be imaged. In the case of ElectricalCapacitance Tomography (ECT) [2,3,4], sensor output signals depend on thepermittivity distribution of the material within the sensing zones. A range ofapplications of tomography has been identified [1,3]. The most attractive feature ofelectrical tomography is its suitability for real time imaging in industrial processesbecause of its inherent simplicity and high-speed capability, compared to radiation-based tomography. Furthermore, since the sensors are non-intrusive, there is nodisturbance to the processes being investigated.

Applications of ECT in the field of flow imaging demand a fast system, whichcan capture images at a rate of 100 frames/second or more, depending on the flowvelocity. The sensor design requires the most stringent consideration as the materialto be imaged is no longer a static object, but moves at various velocities and in anon-uniform distribution. Therefore, the effects of sensor dimensioning, sensorsshielding and spacing between planes need to be studied carefully. The effect ofsolids level in the sensing zones needs to be investigated too. If these factors areinadequately addressed, the measurement results may render incorrect or even beuseless.

SIMULATION PROCEDURE

Electrostatic field simulation offers an excellent solution to understand thebehavior of capacitance sensors under various sensor configurations and materialsbeing sensed. The resultant optimum sensor configuration is then adopted toconstruct the physical sensors. There are two ways to perform an electrostatic fieldsimulation:• Using commercially available software packages such as Maxwell Field

Simulator[5] and PC Opera,• Writing code from scratch using a programming language such as C or Pascal.

The first way is more appropriate for complex or 3D simulations since mostpackages provide pre-processing, main and post-processing modules to ease thesimulation process. The cost of the software package is sometimes prohibitive,especially if the simulation is just for occasional study. The second way certainlyneeds more elaborate work, but for one or two-dimensional simulation, this is moreattractive and cheaper. An excellent reference for this method can be found in books

by Versteeg et al [6] and Smith [7]. In either way, the simulation tries to solvenumerically Laplace’s equation of the form [8]:

0) =∇∇ φεε 0.( r

Here φ(x,y,z) is the electric potential,εr(x,y,z) is the relative permittivity, andε0 is the permittivity of free space (8.854x10-12 Fm-1).

In our study, both the commercial package (Maxwell Field Simulator) andcode using C++ language have been used, and the actual twin-plane 8-electrodesensors of the same configuration have been employed for flow measurement in anindustrial pneumatic conveying system.

Basically, the sensor simulation starts by drawing the geometry, assigningmaterial properties, giving the boundary condition, solving Laplace’s equation, andthen plotting and examining the equipotential lines. By simulating various electrodelengths, plane spacing, grounding between planes, pipe wall and materialpermittivities, an optimum configuration can be selected. Results from 2Dsimulation already give a very good indication of sensor behavior by examining theequipotential spreading in the sensing zones. The general procedure of simulation isdepicted in a flow chart of Figure 1.

Draw geometric model

Generate grid

Assign material property, permittivity

Assign boundary condition, voltages

Generate field solution

Display plot of fields and inspectparameter

Figure 1. Simplified flow chart of field simulation

Only field simulation using a programming language is illustrated here,although it is partly still applicable when using commercial software packages. Anexample is given below of applying this technique to a horizontal perspex pipe,containing plastic beads. The pipe is fitted with twin planes of copper sheetelectrodes.

Draw geometric model

First a geometric model of the simulation domain is drawn to get a clearpicture of what to simulate. In our case, the twin-plane ECT sensors are modeled intwo dimensions because of their inherent symmetry. Figure 2 below shows the axialcut of the sensor pipe.

electrodes

grounded copper shielding

pipe wallspacerelectrodes

flow

250mm

70mm

Figure 2. Sensor structure (axial section)

Generate grid

Next, we need to generate a grid. Since the domain is a rectangle, the finitedifference method (FDM) is chosen to solve the field problem. The actual size of thedomain under simulation is 250mmx70mm, where the internal and external pipediameters are 50mm and 60mm, respectively. For convenient, using a grid size of1mmx1mm allows us to discretise the domain into 250x70 grid points. The resultantgrids are depicted in the following Figure 3.

Assign material property, permittivity

The relative permittivities of the air, plastic beads and perspex pipe wall arethen assigned values of 1.0, 2.8 and 3.0, respectively. The thin copper electrodes,spacer and shielding are assigned permittivity of 1.0. Increasing or decreasing thelevel of plastic beads in the geometric model simulates the effect of different solidsloading within the pipe.

Assign boundary condition, voltages

As we want to simulate the electric potential field when two adjacent drivenelectrodes from different planes are energized while the other two adjacent detectionelectrodes of corresponding planes are left floating, the two driven electrodes areassigned a fixed voltage level of 15 Volts. The copper shields are set to a fixedpotential of 0 Volt. The potential of a copper spacer is set to either a fixed potentialof 0 Volt for grounded spacer, or left unassigned for floating spacer.

Generate field solution

After all simulation parameters and boundary values have been setup, the nextimportant step is to generate the field solution based on the given conditions. In aniterative, line by line manner a Three Diagonal Matrix Algorithm (TDMA) is appliedto solve partial different equations until solution converges. Although a TDMAalgorithm is used generally for one dimensional problems, it proves very elegant andapplicable for solving a system of equations for our discretised, two dimensionalfield problem. The advantages of the TDMA algorithm are that it is computationallyinexpensive and requires a minimum amount of storage as small as the number ofgrid points. The algorithm is readily translated into a program in a PC.

i

j

South

North

X: known boundary values : points at which values are calculated : points at which values are considered to be temporarily known

Figure 3. Line by line application of TDMA method on a discretised domain.

To solve the equations, TDMA is applied along a chosen line (marked withcircular dots in Figure 3), for example south-north lines. All values to the left andright of the current line are assumed to known temporarily. The calculation issubsequently continued to the next south-north line until the last line is completed.The sequence in which lines are selected for calculation is known as the sweepdirection. If we choose to sweep from west to east (along the i-line), the electricpotential values to the west of points at which values are calculated are known fromthe calculations on the previous line. Values to the east are, however, still unknownand are initialised to a certain values (e.g . zero) during the very first sweep.Therefore the solution process must be iterative and at the end of each iteration cyclethe electric potential is taken to have its value at the end of the previous iteration.The iteration is repeated until the required accuracy is reached.

Display plot of fields and inspect parameter

At the end of calculation, a generated solution is available, for example, in afile or memory. In our case, the solution is a matrix of 250x70 elements; eachelement being a value of an electric potential at the respective point. Contour plot,mesh and surface commands of MATLAB Software are very easy to use in order toview and examine the solution graphically.

The steps explained above give a general overview on how to tackle a fieldsimulation problem; a very useful tool and valuable expertise for engineeringresearch. By now, it should not be too difficult to use commercially availablesoftware packages to do more complex simulation problems.

SIMULATION RESULTS

The contour plots simulate capacitance sensors mounted around a pipe wallhaving internal and outer diameter of 50mm and 60mm, respectively. Each electrodeis of 75mm length. The spacing between planes is 50mm.

a.

b.

Figure 4. Contour plots of axial equipotential lines due to the excitation voltages atlower electrodes for an empty pipe: a) spacer is grounded, b) spacer isfloating

a. b.

Figure 5. 3D plots of electric potential fields of Figure 4 above show that groundedspacer reduces potentials and fringing between planes.

a.

b.

Figure 6. As in figure 4, except that the potentials are plotted along the pipe. a)spacer is grounded, b) spacer is floating. The maximum potentialbetween planes suppressed up to around .5 Volt due to a grounded spacer.

a. b.

Figure 7. As in figure 4, except that the pipe is 30% full of plastic beads. Theequipotential lines show ‘breaking’ at the air-solids interface

a.

b.

Figure 8. As in figure 7, except that the potentials are plotted along the pipe. a)spacer is grounded, b) spacer is floating. The maximum potentialbetween plane is suppressed up to a round 2.5 Volt due to a groundedspacer.

a.

b.Figure 9. As in figure 4, except that the pipe is 70% full of plastic beads. The

equipotential lines show ‘breaking’ at the air-solids interface. a) spacer isgrounded, b) spacer is floating.

DISCUSSION

This preliminary work seems to offer a good opportunity to exploit numericalsimulation in conjunction with experimental work to gain better understanding offield behavior for a certain sensor configuration and driving strategy. Wherepowerful commercial software for field simulation is available, this should beutilised. The steps explained and results presented in this paper should encourageresearchers to familiarize themselves with simulation tools, regardless theavailability of such commercial simulation packages.

REFERENCES

1. ALONSO, M., FINN, E. J., Fundamental university Physics vol 2: Fields andwaves, 2nd edition, Addison Wesley, (1983)

2. BECK, M.S., WILLIAMS, R. A, “Process Tomography: a European innovationand its applications”, Meas Science and Tech., 7 (March 1996), p. 215-224

3. GAMIO, J. C., YANG, W. Q., WATERFALL, R. C., BECK, M. S., “A highsignal-to-noise ratio capacitance transducer for use in a multiple-excitationtomography system”, Frontiers in Industrial Process Tomography II ,Engineering Foundation Proceeding, Delft, (1997), p.229-234

4. Maxwell 3D Field Simulator, User’s Manual, Ansoft, (1993)

5. PLASKOWSKI, A., BECK, M. S., THORN, R. DYAKOWSKI, T., ImagingIndustrial Flows, applications of electrical process tomography, Institute ofPhysics (1995)

6. SMITH, G. D., Numerical solution of partial differential equations: Finitedifference methods, 3rd edition, Clarendon Press, Oxford, (1985)

7. VERSTEEG, H.K., MALALASEKERA, W., An introduction to computationalfluid dynamics, the finite volume method, Longman Scientific and Technical,(1995)

8. YANG, W.Q., “Hardware design of electrical capacitance tomography system”,Meas Science and Tech., 7 (March 1996), p.225-232

DISKUSI

UTAJA

Dalam hal makalah penyaji, pipa digambarkan sebagai ruang antara 2 pelat.Seberapa jauh penyimpangan dengan adanya pengandaian di atas?

ARKO

Sebenarnya untuk mendapatkan hasil yang lebih detail, simulasi 3-D perludilakukan, yang tentunya akan memerlukan program yang lebih kompleks dankomputer yang lebih besar. Dalam studi ini yang menjadi masalah adalah inteferensiantara plane-1 dengan plane-2. Bila 2 elektrode dari plane yang berbeda diaktifkan(diberi tegangan 15 Volt) pada saat yang sama, inteferensi antar plane akan terjadidan perlu diperkecil dengan penambahan plat tembaga yang di-ground-kan (0 Volt).Dalam satu plane yang sama, hanya ada satu elektrode sensor dan eletrode driveryang aktif, sementara elektrode yang lain selalu di-ground-kan. Jadi pengabaianpengaruh oleh elektrode yang di-ground-kan ini masih diterima pada studi saat ini.

DAFTAR RIWAYAT HIDUP

1. Nama : ARKO

2. Tempat/Tanggal Lahir : Magelang, 6 Agustus 1967

3. Instansi : P2TIK - BATAN

4. Pekerjaan / Jabatan : Staf Bidang Sistem Jaringan Komputer

5. Riwayat Pendidikan : (setelah SMA sampai sekarang)

• Tenchnische Universiteit Delpt, Electrical Engin. (1987-1992) (S1/S2)

• UMIST-Manchester, Electrical Engineering (1996-1999) (S3)

6. Pengalaman Kerja : 1986 – sekarang : Staf P2TIK - BATAN

7. Organisasi Professional : The Institution of Electrical Engineer (IEE)