Measurement and Control Systems for an Imaging Electromagnetic. Flow Meter

Transcription

1 Measurement and Control Systems for an Imaging Electromagnetic Abstract-Electromagnetic flow meters based on e principles of Faraday s laws of induction have been used successfully in many industries. The conventional electromagnetic flow meter can measure e mean liquid velocity in axisymmetric single phase flows. However, in order to achieve velocity profile measurements in single phase flows wi non-uniform velocity profiles, a novel Imaging Electromagnetic Flow meter (IEF) has been developed which is described in is paper. The novel electromagnetic flow meter which is based on e weight value eory to reconstruct velocity profiles is interfaced wi a Microrobotics VM1 microcontroller as a stand-alone unit. The work undertaken in e paper demonstrates at an imaging electromagnetic flow meter for liquid velocity profile measurement is an instrument at is highly suited for control via a microcontroller. Helmholtz coil, induced voltage, weight value, microcontroller I. INTRODUCTION Electromagnetic flow meters have been used for several decades, wi e basic principles being derived from Faraday s laws of induction. Conventional -electrode electromagnetic flow meters (EMFMs) have been used successfully in a variety of industries for measuring volumetric flow rates of conducting fluids in single phase pipe flows. At present, a conventional -electrode EMFM can measure e volumetric flow rate of a single phase flow wi relatively high accuracy (about 0.5% of reading) provided at e velocity profile is axisymmetric [1]. However highly non-uniform velocity profiles are often encountered, e.g. ust downstream of partially open valves. The axial flow velocity ust downstream of a gate valve varies principally in e direction of e valve stem, wi e maximum velocities occurring behind e open part of e valve and e minimum velocities behind e closed part of e valve. In such non-uniform velocity profiles e accuracy of e conventional EMFM can be seriously affected [-3]. One meod for improving e accuracy of e volumetric flow rate estimate is to measure e axial velocity profile wi e Imaging Electromagnetic Flowmetering (IEF) technique described in is paper and en to use is profile to determine e mean flow velocity in e cross section. Previous researchers e.g. [4], [5], [6] and [7] have proposed techniques to obtain velocity profiles in e flow cross section but few practical devices have emerged. In view of e above, e main obective of is paper is to describe a new non-intrusive electromagnetic flow metering technique for measuring e axial velocity profile of single phase flows of conducting fluids. In Section III of is paper e mechanical and electrical designs of an IEF device are described, as well as e relevant signal detection and processing meods. In Section IV of e paper, a microcontroller is introduced as e processing core of e IEF to achieve e functions of 1 School of Computing and Engineering, University of Huddersfield, Huddersfield HD1 3DH, UK Tianin Key Laboratory of Process Measurement and Control, School of Electrical Engineering and Automation, Tianin University, Tianin 30007, People s Republic of China Flow Meter Y. Zhao 1,, G. Lucas 1, T. Leeungculsatien 1 and T.Zhang 1 driving e magnetic field, acquiring voltage data from e electrode array, matrix inversion to calculate e velocity profile and data display. Section V presents experimental results of local axial velocity distributions obtained from e IEF device under a variety of different flow conditions and includes comparisons wi reference local axial velocity measurements obtained from a Pitot-static tube. II. BACKGROUND THEORY An alternative approach to accurate volumetric flow rate measurement in highly non-uniform single phase flows was proposed by auors such as Horner [8] who described a six electrode electromagnetic flow meter which is insensitive to e flow velocity profile. However, is type of flow meter cannot provide information on e local axial velocity distribution in e flow cross section unlike e IEF device presented in is paper. The essential eory of EMFMs states at charged particles in a conducting material which move in a magnetic field experience a Lorentz force acting in a direction perpendicular to bo e material s motion and e applied magnetic field. Williams [9] applied a uniform transverse magnetic field perpendicular to e line oining e electrodes and e fluid motion and his experiments revealed at for a uniform velocity profile e flow rate is directly proportional to e voltage measured between e two electrodes. Subsequently Shercliff [10] showed at e local current density in e fluid is governed by Ohm s law in e form ( E v B) (1) where is e local fluid conductivity, v is e local fluid velocity, and B is e local magnetic flux density. The expression ( v B) represents e local electric field induced by e fluid motion, whereas E is e electric field due to charges distributed in and around e fluid. For fluids where e conductivity is constant (such as e single phase flows under consideration in is paper) Shercliff [10] simplified equation (1) to show at e distribution of e electrical potential in e flow cross section can be obtained by solving ( v B) () For a circular cross section flow channel bounded by a number of electrodes, wi a uniform magnetic field of flux density B normal to e axial flow direction, it can shown wi reference to [10] at, in a steady flow, a solution to equation () which gives e potential difference U between e pair of electrodes is of e form B U v( x, W( x, dxdy a where v ( x, is e steady local axial flow velocity at e point ( x, in e flow cross section, W ( x, is a (3)

2 so-called weight value relating e contribution of v ( x, to U and a is e internal radius of e flow channel. Let us now assume at e flow cross section is divided into N large regions (fig. 1(c)) and at e axial flow velocity in e i such region is constant and equal to v i (i.e. for a given region e axial flow velocity does not vary wiin at region). Let us furer suppose at N potential difference measurements U are made between independent pairs of electrodes on e boundary. From ese assumptions, and by discretising equation (3), e following relationship is obtained between e potential difference measurement U and e i steady axial velocity v. i N B U vi wi Ai a i1 Here A i represents e cross sectional area of e i region and e term w i is e weight value which relates e steady flow velocity in e i region to e potential difference measurement. Provided at e required N weight values are known [11] equation (4) can be manipulated to enable e steady axial flow velocity v i in each of e N regions to be determined from e N potential difference measurements U ( 1to N ) made on e boundary of e flow cross section. This process for calculating e velocity in each of e regions can be expressed by e matrix equation a 1 V [ WA] U B where V is an N 1 matrix containing e required velocities, W is an N N matrix containing e weight values w i, A is a diagonal matrix containing e cross sectional areas of e regions and U is an N 1 matrix containing e N boundary potential difference measurements. Since many pipe flows are turbulent e question now arises as to what is meant by a steady axial velocity v i in a given region in turbulent flow. Texts on fluid mechanics e.g. [1] state at in a turbulent flow, when e velocity over a given averaging time remains constant, e flow is termed steady. For e flows relevant to e present investigation is averaging time is approximately 7 seconds (see Sections III-D and IV-B). Consequently, when using e techniques described in is paper e measured potential differences U must be averaged over at least is time period in order for repeatable velocities v i to be obtained from one averaging period to e next. Note at equation (4) is strictly only valid if e steady local velocity in each of e N large regions is e same everywhere in a given region. However results presented in [11] show at e techniques outlined above can be used to estimate e mean axial flow velocity in a given region even when e local velocity wiin at region varies by as much as ±10% of e mean value for at region. In order to calculate e weight values w i (in Equations (4) and (5)) a finite element (F.E.) package, COMSOL, which can numerically solve equation () for complex geometries was used [13]. Using is F.E. package a simulated Helmholtz coil was used to produce a magnetic field wi uniform magnetic flux density B in e y direction [11]. The condition of e simulation was at e flow channel is divided into N regions and e fluid in e i region has an imposed velocity v i in e z direction (4) (5) while e fluid in e remaining regions is at rest. From e potential distribution obtained from is simulation, N potential differences U ( 1to N ) between N electrode pairs were calculated, allowing all of e weight values w i associated wi e i region to be calculated according to equation (6) (wi 1to N ). wi a 1 U B vi Ai (6) The process was en repeated for each of e oer ( N 1) regions in succession until all relevant N weight values were calculated. The cross section of e electromagnetic flow meter relevant to is paper is divided into 7 regions as shown in Fig. (1c) and hence N 7. Helmholtz Coil (a) 3D Model B e9 e8 e10 e7 e11 (b) View on x-y plane e6 e1 e5 i 1 i i 3 i 4 i 5 i 6 i 7 e13 Flow channel (c) Schematic diagram of e flow regions Index i denotes region number Fig. 1. Model of Finite Element Simulation. (1(c) shows e 7 regions and e boundary electrodes denoted e1 to e16) Table 1 shows e electrode pairs between which e potential difference measurements U ( 1to 7 ) are made. The calculated weight values for a given region (index i ) and for a given electrode pair (index ) are shown graphically in Fig. (). Note at for e case of electrode pair e1 - e9 (for which 4 ) e system geometry is identical to at analysed eoretically in [10]. For is geometry e local weight value W ( x, at point ( x, is given by e4 e14 a y x y x y x 4 a W ( x, (7) 4 a a By calculating e area weighted mean value of W ( x, for each of e seven regions shown in Fig. (1) e weight values w i4 ( i 1to 7 ) can be computed and compared wi e values obtained using e numerical meod described above. Fig. (3) shows e values of w i4 obtained using e eoretical meod (equation 7) and e numerical meod. The good agreement between e two techniques indicates e veracity of e numerical meod used in is paper for determining w i. This agreement has also previously been reported in [14]. (Note at e value of W ( x, tends to infinity for x a, y 0 and so, when calculating w 44, very small regions in e immediate vicinity of ese two coordinates must be excluded from e calculation). e3 e15 e e1 e16

3 Table 1: Electrode pairs between which e N potential difference measurements were made U Electrode pair =1 e4 e6 = e3 e7 =3 e e8 =4 e1 e9 =5 e16 e10 =6 e15 e11 =7 e14 e1 A D B C E A- Meter Body; B- Helmholtz Coil; C- Flanges; D- Electrode Array; E- Cable Supports (a) Mechanical design of EMFM Coil 1 Y X Flow Pipe Coil R ref Rref SSRN (b) Schematic diagram of EMFM Upsu 0V dc PSU Fig. 4. The IEF device used in e experiments Fig.. Weight values for e different regions (index i) and different electrode pairs (index ). Fig. 3. Comparison of weight values w i4 (associated wi electrode pair e1 e9) obtained numerically and eoretically III. THE ELECTROMAGNETIC FLOW METER A. Electromagnetic Flow Meter Geometry A real imaging electromagnetic flow meter (see Fig. (4a)) was constructed wi e same geometry at had been modelled in e F.E. simulation described above. The non-conducting flow meter body, wi an internal radius of 80mm, was made from Delrin. Four grooves on e flow meter body were accurately machined by a Computed Numerically Controlled (CNC) machine to accommodate two circular coils which formed a Helmholtz coil configuration. The Helmholtz coil consisted of a parallel pair of identical circular coils which each had e same number of turns n. The electrical resistances for coil1 and coil were each measured and bo were found to be equal to 34.98Ω. At any instant in time e electrical current in each coil had e same magnitude and direction. Driving e coils in parallel (see Figs. 4 and 6) raer an in series means at, for a given supply voltage U psu, twice e coil current and hence twice e magnetic flux density in e flow cross section is achieved. Provided at e coils are well matched, driving em in parallel has minimal implications for e uniformity of e magnetic field. The mean spacing between e two coils was equivalent to R, e mean radius of each coil, and so, at any instant in time, a near-uniform magnetic field in e y direction (see Figs. 1 and 4) existed in e flow cross section. At e plane of e electrode array ( z 0 ) e components of e magnetic field in e x and z directions were always negligible. The magnitude B of e magnetic flux density of e Helmholtz coil in e y direction can be approximated by nic B 0.5 (8) 5 R where 0 is e permeability of free space and i c is e total coil current as shown in Fig. 6. Thus B is proportional to e total coil current i c and so we may write B Ki c (9) where K n R (10) For e IEF device described in is paper e mean radius R of each coil was 115mm and e number of turns n was 104 so at when e total coil current was A, e magnitude of e magnetic flux density at e midpoint of e line oining e centres of e two coils was predicted to be 80 gauss. Measurements obtained using a gaussmeter showed at e actual magnetic flux density (in e y direction) at is position was gauss. The distribution of e y component of e magnetic flux density in e flow cross-section at e plane z 0 measured using e gaussmeter is presented in Fig. 5. The maximum and minimum values of magnetic flux density were gauss and gauss respectively. The area weighted mean value was gauss. This meant at e maximum variation of e magnetic flux density from e mean value was +0.76% to -0.5%. The standard deviation of e magnetic flux density in e flow cross section was 0.18 gauss. Such values are typical for uniform field electromagnetic flow metering devices. The electrode array contains 16 electrodes for measuring flow induced potential differences as described above, wi each electrode being made from 316L stainless steel. Stainless steel was chosen for e electrode material because (i) it has high corrosion resistance and (ii) it has a low relative permeability ( r 1 ). If a corrosive material were used for e electrodes, rust could form which would reduce e electrical conductivity of e electrodes or even completely insulate em. This would create a maor problem in accurately measuring e potential differences U. The low relative permeability of e electrodes also 3

4 SSR 1 SSR SSR 3 SSR 4 Microcontroller meant at ey did not significantly affect e uniformity of e magnetic field in e flow cross section produced by e Helmholtz coil. Supports ( E in Fig. 4(a)) were used to position e cables which run between e electrodes and e detection circuitry. These cables were mounted in such a way at ey were always parallel to e local magnetic field. This meant at any cable loops were not cut by e time varying magnetic field, us preventing non-flow-related potentials from being induced in e cables. Fig. 5. Distribution of e y component of e magnetic flux density in e flow cross-section B. Application of a Time Dependent Magnetic Field to e Flow Cross Section A dc power supply unit, dc PSU in Fig. 6, was connected to a solid state relay network (SSRN). The solid state relays were connected to form an H-bridge configuration and two outputs from e microcontroller were used as logic inputs to e SSRN in such a way at at any instant in time e voltages applied at points a and b in Fig. 6 were as per e table below. DAC0 DAC1 Fig. 6. Schematic diagram of coil excitation and temperature compensation circuits Table : Relay State and Voltage across Helmholtz Coil Relay State Voltage at a Voltage at b RP1 SSRN dc PSU 0 V Upsu ic U psu 0 RP 0 U psu RP3 0 0 When e voltage at a was U psu and e voltage at b was 0 en, after all transients had died away, e maximum total coil current i c, max flowed in e coils (see Fig. 7(a)). When e voltage at a was 0 and e voltage at b was U psu en, after all transients had died away, e minimum coil current i c, min flowed in e coils (where ic, min ic,max ). When e voltages at a and b were bo 0, no current flowed in e coils. Thus, e variation of i c wi time was e hybrid square wave pattern shown in Fig. 7(a). The resultant time dependent magnetic flux density in e y direction in e flow tube at z 0 (e plane of e electrode arra is shown in Fig. 7(b). The reason for setting e magnetic flux density as a time dependent hybrid square a R ref i c i c + - DA U r Rc1 Rc Coil 1 Lc1 Lc Coil b 4 wave was (i) to reduce electrochemical effects at e electrodes and (ii) to enable e flow induced potential differences U to be distinguished from time dependent, non flow induced bias voltages as described in detail in Section III-D. The two coils were closely matched and e resistance R c of each coil had a known value of R c, 15 when e coils were at a temperature of 15 C. However ambient temperature variations, and heating of e coils due to e coil current, caused e value of R c to vary wi time. The flow induced voltages U from which e flow velocity profile was reconstructed were proportional to B max e maximum value of e time dependent magnetic field. In turn, B max was proportional to i c, max as indicated by equations (9) and (10). Accurate velocity profile reconstruction relies upon knowing B max at all times and so it was necessary to know i c,max at all times. As can be seen from Fig. 6 e total coil current i c was passed rough a precision reference resistor wi known resistance R ref of 0.1Ω and a very low temperature coefficient of 0ppm/ C. A voltage U r appeared across R ref and was fed to e microcontroller via a differential amplifier wi a gain of 10 ( DA in Fig. 6). U r was measured by e analogue to digital converter wiin e microcontroller. The maximum value of U r was U r,max where U r, max Rref ic,max (11) Since R ref was known and U r, max was measured by e microcontroller, i c, max could be calculated from equation (11), enabling B max to be calculated from equations (9) and (10) - ereby enabling e true value of e maximum magnetic field streng to be known at all times and used in e velocity reconstruction calculations. i c,max i c,min B max 0 B max i c B c c S1 S S3 S4 S1 S S3 S4 (a) (b) Time (S) Time (S) Fig. 7. (a) Variation of coil current wi time over one excitation cycle and (b) variation of e magnetic flux density wi time (as measured by a gauss meter) over one excitation cycle The transients appearing in e coil current cycle (Fig. 7(a)) were due to e RL time-constant of e Helmholtz coil. When e relays in e SSRN were put into states RP1 or RP (Table ) e current flowing rough e coils could not change instantaneously. The time c required for e current to make a change from 0 to e maximum value i c,max was determined by e RL time-constant of e circuit comprising Rref and e resistances and inductances of e two coils (see Fig. 6). The value of c was found to be s, after which e coil current i c and magnetic flux density B were bo steady (refer to Fig. 7(b)). After e microcontroller sent

5 control signals to e relays to change e coil current i c, e controller would wait for 0.15s to allow completion of e magnetic field transient before starting acquisition of e flow induced potential differences. This ensured at e flow induced potential differences were collected during at part of e cycle when e magnetic flux density was constant. C. Electronic Circuit Design for Measuring e Boundary Potential Differences A time dependent flow induced potential difference U appeared between e electrode pair caused by e interaction of e flowing fluid and e imposed magnetic field. A voltage U necessary for reconstructing e velocity profile must be extracted from U using appropriate signal processing techniques, as described later in is section. Each pair of electrodes between which it was necessary to obtain a value of U was connected to e inputs of a separate Voltage Measurement and Control Circuit as shown in Fig. 8. VF Electrode Pair VF HPF U x, Measurement Point ( U x, AU Usp) U ref Feedback U sp SPA - DA 1 + U0 U HGA LPF 1 LPF x + - y C I R HPF I e(t) Hz and a pass band gain of 1 and is used to eliminate any high frequency noise on e output from HGA]. The purpose of e control circuit in Fig. 8 was to compensate for e effects of U 0 by continually applying a suitable control voltage U ref to e offset input y of e HGA in such a way as to ensure at e measured output voltage U x, was always of e form U x, AU Usp, where U sp is a desired set-point dc voltage provided by e set-point adust unit (SPA in Fig. 8). [Note at e HGA does not amplify signals applied at e offset input y ]. A suitable value for U sp could, if required, be zero. The appropriate value for e control voltage U ref was achieved in e following way. U x, was low pass filtered by LPF (a second order filter wi a -3dB frequency of 0.8Hz and a pass band gain of 1) to remove e flow induced component AU so at only a slowly varying non flow induced component remained. The set point voltage U sp was subtracted from is slowly varying component at e differential amplifier DA1 (Fig. 8) to give an error signal e (t) which was en fed to e inverting input of an integrator wi a time-constant of 1 second (Fig. 8). The output voltage from e integrator was U ref, e control voltage applied to HGA. Voltage Measurement Circuit Integrator GND Control Circuit Fig. 8. Schematic diagram of voltage measurement and control circuit Because e applied magnetic field varies wi time (as described in e previous section) U also varied wi time. Typically e amplitude of U was only a few millivolts and so before being sampled by e ADC (analogue to digital convertor) in e microcontroller it had to be amplified by a high gain differential amplifier (HGA in Fig. 8) wi gain A (equal to 996 in e present investigation). A voltage follower and a first order high pass filter (VF and HPF respectively in Fig. 8) were used to condition e signals from each electrode prior to being passed to e HGA. The high pass filters had a -3dB frequency of Hz and a pass band gain of 1 and were used to help eliminate e very large dc offset voltages which appeared on each electrode due to e effects of e electrode/electrolyte interaction and due to e accumulation of charge on e non-conducting pipe wall. However, despite e high pass filters, e differential voltage at e input to HGA consisted of e sum of U and a residual, unwanted, time dependent bias voltage U 0 (Fig. 8). [Note at bo U and U 0 were differential voltages appearing across e inputs to HGA]. U 0 arose as a result of electrochemical interaction between e electrodes and e process fluid (water) [15]. The magnitude of U 0 was generally much larger an e amplitude of U. D. Compensating for e effects of e bias voltage U 0 If e effects of U 0 were not eliminated en e voltage U x, measured (for e electrode pair) at point x in Fig. 8, would be given by U x, A( U0 U ) and e resultant (slowly varying) component AU 0 would make e value of U x, lie well outside of e range of e analogue to digital converters on e microcontroller [note at LPF1 in Fig. 8 is a second order low pass filter wi a -3dB frequency of 5 Fig. 9. Measured time dependent voltage U x, (when U sp 0 ) For e integrator time constant of 1 second, e mean value of U x, could be maintained steady at approximately e set-point value U sp, irrespective of e value of U 0. The variation of U x, wi time for a given electrode pair over a single magnetic field excitation cycle is shown in Fig. 9. For clarity in Fig 9 U sp is shown as zero. Unfortunately, despite e presence of e control circuit, experimental observation showed at a small time dependent offset voltage U (typically of e order of a few millivolts) was present in e signal U x,. U almost certainly arose from e fact at e control circuit could not always fully restore e mean value of U x, to e set point voltage before e relevant samples of U x, were taken (as described below). The influence of U was eliminated as described below. It can be seen at for a single excitation cycle U x, can be split into four segments (or stages) denoted S1 to S4 in Fig. 9. For stage S1, which is of leng 0.3s and which corresponds to relay state RP1 in Table, e value of U x, after transient time is denoted ( U x, ) 1 where c U x, ) 1 AU U sp U ( (1) and where U is e maximum value of e flow induced voltage during e excitation cycle. During e time interval of 0.175s denoted t 1 in Fig. 9, e microcontroller is used to obtain an average value ( U x, ) 1 from 10 samples of ( U x, ) 1. Note at is process is repeated for 1to 7.

6 For stage S of e excitation cycle (which is of leng 0.4s and which corresponds to relay state RP3 in Table ), after e transient in U x, is completed, e value of U x, is denoted ( U x, ) where ( U x, ) Usp U (13) During a time interval of 0.75s, denoted t in Fig. 9, e microcontroller is used to calculate an average value ( U x, ) from 15 samples of ( U x, ) for each value of ( 1to 7 ). For stage S3 of e excitation cycle (which is of leng 0.3s and which corresponds to relay state RP in Table ) e value of U x, after transient time c is denoted ( U x, ) 3 where Ux, ) 3 AU Usp U ( (14) and where U is e minimum value of e flow induced voltage during e excitation cycle. During a time interval of 0.175s denoted 3 in Fig. 9, e microcontroller is used to obtain an average value ( U x, ) 3 from 10 samples of ( U x, ) 3 for each value of ( 1to 7 ). Finally, for stage S4 of e excitation cycle (which is again of leng 0.4s and which again corresponds to relay state RP3 in Table ) and after e transient in U x, is completed, e value of U x, is denoted ( U x, ) 4 where ( U x, ) 4 U sp U (15) During a time interval of 0.75s denoted t 4 in Fig. 9 e microcontroller is used to calculate an average value ( U x, ) 4 from 15 samples of ( U x, ) 4 for each value of ( 1to 7 ). For e given excitation cycle e values of U ( 1to 7 ) required for calculating e velocities (see section II) are given by ( U x, ) 1 ( U x, ) ( U x, ) 3 ( U x, ) 4 U (16) A Examination of equation (16) shows at e influence of U on e values of U is effectively eliminated. Furermore, subtraction of ( U x, ) from ( U x, ) 1 and subtraction of ( U x, ) 4 from ( U x, ) 3 in equation (16) helps to minimise e influence of e time dependent changes in U on U. From equations (1)-(15) it is apparent at equation (16) is also equivalent to e following expression U ( U U ) / (17) where U and U are respectively e mean values of e maximum and minimum flow induced voltages during e excitation cycle. Note at time intervals t and t 4 (see Fig. 9) were longer an time intervals t 1 and t 3. This is because experimental observation showed at more noise was present on U x, during excitation stages S and S4 and so a larger number of samples were taken to average out is noise. Note at furer experimental work may be necessary to optimise e durations of stages S1 to S4 for flow conditions different to ose discussed later in is paper. Finally in is section, it is instructive to discuss e signal 0 U U appearing at e input to e high gain differential amplifier HGA in Fig. 8 for an improperly designed IEF flow meter and for non-optimised voltage measurement and control circuitry. Under such circumstances e signal 0 U U can appear as shown in Fig. 10. The large spikes in Fig. 10 are non flow induced voltages arising from changes in e magnetic flux rough e loop formed by e cables connecting e electrodes to e measurement circuitry (note at e loop is completed by e conducting fluid between e relevant electrode pair). Large voltage spikes such as ese can be eliminated by ensuring at e plane of each cable loop is always parallel to e local direction of e magnetic field as described in section III-A. In Fig. 10, during stages S1 and S3 of e excitation cycle, it can be seen at e flow induced voltage component may decay slightly wi time. This decay can be eliminated by ensuring at e time constants of e high pass filters shown in Fig. 8 are adequately large. Two oer features of Fig. 10 are wory of comment. (i) Alough e magnitude of e random, slowly varying, bias voltage U 0 is shown in Fig. 10 as being of e same order of size as e amplitude of e flow induced component U, in reality e magnitude of U 0 could be many times greater an e amplitude of U. (ii) Some high frequency noise was always present in e flow induced signal U, possibly due to flow turbulence generated at e electrodes. This high frequency noise was eliminated by e low pass filter LPF1 placed between e high gain differential amplifier HGA and e measurement point x (as shown in Fig. 8). U 0 U0 U Fig. 10. Voltage 0 (7.1) U U S1 S S3 S4 U 0 U from a non-optimised system IV. AN ON-LINE CONTROL SYSTEM FOR THE IEF DEVICE In contrast to e earliest meods employed by e auors of implementing an IEF device by processing e acquired data off-line using a PC, is section describes e use of e IEF device combined wi a microcontroller as a processing core, enabling e system to work independently and to calculate and display velocity profiles on-line in real time. A. Hardware Specification of VM1 Microcontroller The VM1 [16] is an embedded controller which, in its use wi e IEF device, is interfaced to e flow meter via an analogue I/O module as shown in Fig. 11. This Analogue Module was used to acquire e voltages U x, ( 1to 7 ) as described in section III and e voltage U r appearing across e reference resistance R ref (see Fig. 6) using a 1 bit analogue to digital convertor. The analogue I/O module was also connected to e SSRN so at e outputs DAC0 and DAC1 were used to control e switching of e relays SSR1 to SSR4 as shown in Fig. 6. A display panel on e VM1 enabled display of e imaged velocity profile. The (7.) Time 6

7 QVGA Module VM1 Microcontroller ADC DAC Helmholtz coil LCD display was also used for display of numerical results such as totalised flow rate. electrode array Meter Body 7 measurements Voltage Measurement U x, Circuit 7 Control Circuit 7 Temperature Compensation SSRN wi Driver Circuit Fig. 11. Schematic diagram of IEF microcontroller processing module B. Procedure for Controlling Operation of e IEF Device U r DAC0 DAC1 8 inputs outputs In e embodiment of e IEF device shown in Fig. 11, before e flow meter starts running, e number of magnetic field excitation cycles G (where G 5 in e present investigation) over which it is required to find e mean velocity in each region is input to e microcontroller. After each G excitation cycles e graphical and numerical displays on e LCD panel are updated (note: a single excitation cycle consists of e magnetic field undergoing stages S1 to S4 as shown in Fig. 7). Once e virtual key Start on e touchscreen is pressed e IEF device starts working continuously. At e beginning of each stage of e excitation cycle, e VM1 sends control signals via its outputs DAC0 and DAC1 to e solid state relay network SSRN in order to generate e appropriate magnetic field. [Note at alough e DAC outputs were used to operate e relay network, two of e digital I/O lines on e VM1 would have been equally satisfactory]. Measurements of U x, ( 1to 7 ) are made by e microcontroller using e analogue to digital converters. At e first stage (S1) of each excitation cycle e SSRN is set to state RP1 (see Table ). After e appropriate time delay, 10 samples of e induced voltages ( U x, ) 1 ( 1to 7 ) and 10 samples of e voltage ( U r ) 1 across e high-precision resistance R ref are obtained. Mean values ( U x, ) 1 ( 1to 7 ) of e induced voltages and a mean value ( U r ) 1 of e voltage across e precision resistance are calculated as follows: q 10 (, ) 1 q U x ( U x, ) 1 /10 (18) q1 q 10 ( ) 1 q U r ( U r ) 1 /10 (19) q1 This process is repeated for steps S, S3 and S4 of each excitation cycle to generate values for ( U x, ), ( U x, ) 3 and ( U x, ) 4 ( 1to 7 ) (where for ( U x, ) and ( U x, ) 4 equation (18) is modified to account for e fact at e averages were taken from 15, raer an 10, samples). The process is also repeated to obtain values for ( U r ), ( U r ) 3 and ( U r ) 4. The index for a given excitation cycle is denoted g. After each excitation cycle, mean flow induced potential differences U, g ( 1to 7 ) are calculated using ( U x, ) 1 ( U x, ) ( U x, ) 3 ( U x, ) 4 U, g (0) A Analogue Module Processing Core of IEF Image Keypad Furermore, a mean value ( U r, max ) g for e maximum voltage drop across e precision resistance is calculated using ( Ur ) 1 ( Ur ) ( Ur ) 3 ( Ur ) 4 ( Ur,max ) g (1) Note at in equation (0), A is e gain of high gain differential amplifier (HGA) shown in Fig. 8. After G excitation cycles, e potential differences U ( 1to 7 ), from which e velocities are reconstructed (see section II), are calculated using G U U, g / G () g1 U r, max Furermore, after G excitation cycles, e value of e voltage appearing across e reference resistance (which is used in determining e magnetic flux density B, using equations (9),( 10) and (11)) is calculated from max G U r, max ( U r,max ) g / G (3) g1 By setting G 5, since each excitation cycle was 1.4 seconds, e axial velocity in each region was calculated from data obtained over a 7 second period. A 7 second period was experimentally found to be sufficient to enable repeatable flow velocity profile measurements to be obtained at a constant value of e reference water flow rate obtained from a turbine flow meter (see section V). Using e weight values w i ( 1to 7, i 1to7 ) stored in e microcontroller in array W, e cross sectional areas of e regions stored in array A, e measured potential differences U ( 1to 7 ) and by setting B Bmax (where B max is obtained as described above) e velocities v i ( i 1to 7 ) can be calculated by solving matrix equation (5). Next, in a single phase flow, e liquid volumetric flow rate Q w can be calculated from e velocities v i by using equation (4) below 7 Q w vi Ai (4) i1 Finally, e velocity in each region is displayed on e LCD screen in bar chart form to give a graphical representation of e velocity profile. Q w can also be displayed on e LCD screen in numerical format. V. EXPERIMENTAL RESULTS A series of experiments was carried out on e IEF flow meter controlled by e VM1 microcontroller. When using e VM1 device, velocity profile reconstruction was performed on-line (in real time). The IEF flow meter was mounted in e 80mm internal diameter working section of a flow loop flowing single phase water of conductivity 153µScm -1. A turbine meter was placed in series wi e working section of e flow loop to enable a reference measurement Q w, ref of e water volumetric flow rate to be made. Several flow conditions were investigated, for which e IEF device was used to measure e water velocity profile, as described below. (i) For e first flow condition e water velocity profile at e IEF flow meter was a fully developed turbulent velocity 7

8 profile. The reference water flow rate obtained from e turbine meter was 17.46m 3 hr -1. The velocity profiles reconstructed using e on-line VM1 system are shown in Fig. 1(a). From Fig. 1(a) it is clear at e reconstructed velocity is approximately e same for all of e regions a result which is to be expected from e IEF device due to e relative flatness of e fully developed, single phase, turbulent velocity profile. Note at Fig. 1 also shows results obtained from an off-line system comprising a PC and a National Instruments data acquisition card. It is clear from Fig. 1 at e results from is off-line system are virtually identical to e results from e on-line VM1 system. This result is important because most systems for imaging industrial processes require e computing power of a PC to process and display e data, whereas e techniques outlined in is paper can be performed ust as well using a simple microcontroller. A comparison was made between e total water volumetric flow rate Q w, IEF obtained from IEF device by integration of e water velocity profile in e flow cross section (see equation 4) and reference water volumetric flow rate Q w, ref obtained from e turbine meter. The mean integrated value of Q w, IEF obtained from e IEF device was 17.54m 3 hr -1 whilst e mean value of Q w, ref was 17.46m 3 hr -1. This represents an error of 0.45% in e flow rate obtained from e IEF device. This error is of e same order of size as e quoted accuracy of e reference turbine meter and erefore suggests at e IEF device is indeed capable of accurately measuring e total water volumetric flow rate by integration of e velocities v i in e flow cross section (equation (4)). (ii) For e second flow condition, a gate valve was mounted ust upstream of e IEF device. By partially opening e valve a velocity profile was created in which e local flow velocity increased from a minimum value at e position of electrode e13 (see Fig. 1) to a maximum value at e position of electrode e5. The velocity profile reconstructed using e VM1 system for is second flow condition is shown in Fig. 1(b) from which it is clear at e reconstructed water velocity increases from a minimum value in region 7 (adacent to electrode e13) to a maximum value in region 1 (adacent to e5). Regions Fig. 1. Velocity profiles obtained using e VM1 microcontroller wi on-line reconstruction and a PC/NI system wi off-line reconstruction Regions 1 (a) Valve is fully open and reference flow rate is 17.46m 3 1 hr (b) Valve is partially open and reference flow rate is 17.3m 3 hr (iii) In a final experiment a flow profile conditioner comprising a bundle of tubes of different diameters was installed 00mm upstream of e IEF device to generate a velocity profile at varied from a minimum to a maximum value in e direction of increasing y. Three flow conditions f1, f and f3, wi reference water flow rates of 16.17m 3 h -1, m 3 h -1 and 6.93 m 3 h -1 (as measured by e 8 turbine meter), were used. The reconstructed local axial velocity distributions, at each flow condition, obtained using e IEF device ( v IEF in Fig. 13) were compared wi local axial velocity distributions obtained using a Pitot-static tube ( v Pitot in Fig. 13). [Note at e Pitot-static tube is a differential pressure device used for making reference measurements of e local fluid velocity, see for example [1]]. In is experiment e Pitot-static tube was traversed to 18 different points in e flow cross section at each flow condition, allowing estimates of e mean flow velocity in each of e 7 regions (Fig. 1(c)) to be made). The magnitude of e maximum difference between v IEF and v Pitot (for all 7 regions) was 7.56%, 7% and 6.9% for flow conditions f1, f and f3 respectively. Note at because e Pitot-static tube is an intrusive device, e measurements of v Pitot are likely to contain some error. More accurate measurements, for example using Laser Doppler Anemometry, may be necessary in e future to obtain a better understanding of e true accuracy of e measurements of v IEF. The error in e total volumetric flow rate from e IEF device (obtained using equation (4)) wi respect to e reference value from e turbine meter was -0.65%, 0.90% and -0.68% for flow conditions f1, f and f3 respectively. This level of accuracy is sufficient for many practical flow metering applications. Fig. 13. Comparison between measurements of e velocity downstream of a flow profile conditioner made using e IEF device and a Pitot-static tube. f3 f VI. CONCLUSIONS This paper describes a new multi-electrode electromagnetic flow meter (IEF) for imaging velocity profiles in single phase flow. A microcontroller is used as e processing core of e IEF to achieve e functions of driving e magnetic field, acquiring boundary voltage data from e electrode array, performing matrix inversion to calculate e velocity profile and displaying e calculated results in bo alphanumerical and graphical format. The paper goes on to show how e IEF device can be used to map velocity profiles of bo uniform and non-uniform single phase flows - such as flows behind partially open valves and at e arrangement of e regions in which e flow velocity is measured (see Fig. 1(c)) is particularly suited to flows in which e axial flow velocity varies principally in a single direction. It has also been shown at for a fully developed turbulent flow, when e reconstructed velocities are integrated in e flow cross section to give e total liquid volumetric flow rate, e result agrees to wiin f1

9 0.45% wi a reference measurement of e liquid volumetric flow rate obtained using a conventional turbine flow meter. For highly disturbed flows ust downstream of a flow profile conditioner e error of is volumetric flow rate measurement can increase to as much as 0.9% for e range of flow conditions investigated. Measurements of local velocities obtained by e IEF device were found to agree wi reference local velocity measurements obtained using a Pitot-static tube to 7.56% or better alough due to its intrusive nature measurements from e Pitot-static tube were likely to contain some error. The work presented in e paper demonstrates at a practical imaging electromagnetic flow meter for liquid velocity profile measurement is feasible. [14] J Z Wang, G P Lucas and G Y Tian A numerical approach to e determination of electromagnetic flow meter weight functions, Meas. Sci. Technol., vol. 18, no. 3, pp , Mar [15] A. C. Fisher Electrode Dynamics, Oxford University Press, ISBN [16] Micro Robotics, VM1 Microcontroller Datasheet, 003. REFERENCES [1] H. Kanai, The effects upon electromagnetic flowmeter sensitivity of non-uniform field and velocity profiles, Med. Biol. Eng., vol. 7, no.7, pp , [] K. W. Lim, M. K. Chung, Numerical investigation on e installation effects of electromagnetic flowmeter downstream of a 90 elbow laminar flow case, Flow Meas. Instrum., vol. 10, pp , Dec [3] A.Ono, N. Kimura, H. Kamide and A. Tobita, Influence of elbow curvature on flow structure at elbow outlet under high Reynolds number condition, J. Nucl. Eng. Desi., vol. 41, pp , Nov [4] T. Katoh and S. Honda, 3-D flow tomography rough electromagnetic induction, SICE annual conference. vol., pp , Aug. 004 [5] A. Traechtler, B. Horner, and D. Schupp, Tomographic meods in electromagnetic flow measurement for determining flow profiles and parameters, Technisches Messen, vol. 64, no. 10, pp , [6] L. Xu, Y. Wang, and F. Dong, On-Line Monitoring of Nonaxisymmetric Flow Profile Wi a Multielectrode Inductance Flowmeter, IEEE Trans. Instrum. Meas., vol. 53, no. 4, pp , Aug [7] B Horner and F Mesch An induction flowmeter insensitive to asymmetric flow profiles, European concerted action on process tomography conf. (Bergen, Norwa, ISBN , pp , Oct [8] B. Horner, A Novel profile-insensitive multi-electrode induction flowmeter suitable for industrial use, Flow Meas. Instrum., vol. 4, no.3, pp , Oct [9] E. J. Williams, The introduction of electromotive forces in a moving liquid by a magnetic field, and its application to an investigation of e flow of liquids, Proc. Phys. Soc. (London), vol. A4, pp , [10] J. A. Shercliff, The Theory of Electromagnetic Flow Measurement, Cambridge, U.K.: Cambridge Univ. Press, 196. [11] T. Leeungculsatien and G P Lucas Continuous phase velocity profile measurement in multiphase flow using a non-invasive multi-electrode electromagnetic flow meter, AIP Conf. Proc. 148, pp , Aug. 011 (ISBN ). [1] B.S. Massey., Mechanics of Fluids. 4 ed., Van Nostrand Reinhold, New York, 1979 [13] COMSOL, COMSOL Corporation Femlab 3.3 user s guide, 006 9