This full text version, available on TeesRep, is the post-print (final version prior to publication) of:

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1 This full text vesion, available on TeesRep, is the post-pint (final vesion pio to publication) of: Zhang, J., Coultha, J., Cheng, R. an Amstong Bian, (003) 'Theoetical an expeimental stuies of the spatial sensitivity of cicula electostatic F metes', oceeings of 5th intenational symposium on coal combustion, Nanjing, China, 3-6 Novembe pp When citing this souce, please use the final publishe vesion as above. This ocument was ownloae fom lease o not use this vesion fo citation puposes. All items in TeesRep ae potecte by copyight, with all ights eseve, unless othewise inicate. TeesRep: Teessie Univesity's Reseach Repositoy

2 THEORETICAL AND EXERIMENTAL STUDIES OF THE SATIAL SENSITIVITY OF AN ELECTROSTATIC ULVERISED FUEL METER D. Jianyong Zhang, Emeitus ofesso John Coultha School of Science an Technology, Univesity of Teessie, Milesbough, UK Abstact: In coal-fie powe plants, the coal is pulveise an pneumatically conveye to the bunes. It is essential to measue an contol pulveise fuel (F) to impove combustion efficiency; euce pollution an lowe opeating costs. Unlike single-phase flow, whee flow ensity is geneally consiee to be unifom, ai-solis two-phase flow in pneumatic conveying systems can unego inhomogeneous concentation istibutions acoss a given pipe coss-sectional aea, especially aoun bens an bifucatos o tifucatos. The oping flow egime is an exteme example of inhomogeneous solis istibution, whee highly concentate solis fom a column-like (ope-like) flow. Fo such complex flow egimes, solis concentation o solis mass flow metes will give iffeent outputs when inhomogeneous flow occus at locations whee these metes ae installe if they ae sensitive to the flow pattens. This poblem can be solve in two ways. The fist an simplest appoach is to estict the mete s installation to locations whee solis ae elatively unifomly istibute ove the coss-sectional aea of the pipe. Altenatively, it can be solve by using a mete having unifom spatial sensitivity, so that the measuement woul not be affecte by the flow egimes. Because the installation locations of F metes must suit othe equiements, such as accessibility fo the convenience of maintenance, it is ieal if the metes have unifom spatial sensitivities. Electostatic mass-flow metes ae typically use to give a measue of the fuel mass flow ate. One esign employs ing-shape electoes which have non-unifom sensitivity, esulting in vaiations in mete output fo the same flow steam passing though the sensing volume at the iffeent aii elative to the mete s cental line. This pape pesents a theoetical analysis of the spatial sensitivity of the electostatic mete with

3 ing-shape electoes in the time an fequency omains. One goal of the stuy is to impove its pefomance an to achieve unifom sensitivity. The expeimental ata pesente in this pape suppot the oveall mathematic moeling, base on electostatic fiel theoy, using the finite element metho (FEM). Although the FEM analysis povies useful esults, a moe igoous investigation is ecommene fo futue wok. Keywos: Electostatic pulveise fuel mete spatial sensitivity. Intouction In coal-fie powe plants, the fuel is pulveise, mixe with ai an pneumatically conveye to the funace bunes. Upon leaving the pulveising mill, the mixtue of solis an ai is split into seveal iffeent pipes, each feeing an iniviual bune. The typical mill can fee up to eight sepaate bunes. Usually, the fuel an ai ae metee pio to thei enty into the mill, so that thei atio can be set accuately. Diffeences in outing of the conveyos injecting the pulveise fuel (F) into the funace, as well as unequal istibution at the points whee the incoming steam is split into sepaate pathways, can cause an uneven fee of pulveize coal to the bunes. Consequently, the combustion stoichiomety at the bunes is istube, esulting in localize, fuel-ich egions whee thee is insufficient ai to bun the coal an ash with a high-cabon content. Convesely, fuel-lean egions will also occu causing high NOx levels to appea. It is theefoe esiable to measue an contol the flow ate of pulveise coal supplie to each bune so as to optimise combustion. The typical 500-MW boile might have foty to sixty 500mm iamete bunes. The volume concentation of solis, i.e. the atio of solis volume to the volume of the mixtue of ai an solis fe to these bunes, is vey low (typically about 0.%), hence the metes must have high sensitivity. At a conveyance velocity of about 5 m/s, the mixtue becomes highly abasive, so that no estiction to the flow can be toleate. The F mete escibe in this pape is compise of a shot steel pipe section into which ing-shape electoes ae fitte flush with, an insulate fom, the conucting pipe wall, theeby offeing no estiction to the flow. Signals geneate in these electoes ue to

4 the flowing chage paticles ae use to povie a measue of the solis concentation an the solis velocity, so that the massflow ate of the fuel to each bune can be infee fom these two paametes. The istibution of solis ove the coss section of a pneumatic conveying pipe has been investigate by Hube [], Bena J Bay et al [], Yilmaz et al [3], an Fank [4]. Fom Fig. An Example of oping Flow aoun a Bifucato thei stuies, it was conclue that the solis can unego inhomogeneous concentation istibutions acoss a given pipe coss-sectional aea. Such istibutions ae affecte by the conveyance velocity, paticle size, humiity, an conveyo geomety. The so-calle oping flow egime is an exteme example of inhomogeneous istibution whee insie the ope, the highly concentate solis flow is fome, as illustate in Fig.. Ieally, if the mete is esigne to measue the solis mass flow ate, it shoul have the same output in esponse to the solis steam caying ientical solis mass flow wheeve it passes though within the mete s sensing volume. In othe wos, the mete shoul have a unifom spatial sensitivity which is efine in this pape as the atio of the oot- mean-squae value of the signal pouce by the mete to the mass flow ate of a oping flow in paallel with the pipe cente line measue at iffeent axial positions at a given flow velocity. Howeve the chages inuce in the electoes an the ms value of the output of the mete epen on the solis steam position elative to the pipe cente line. Although the passive electostatic pulveise-fuel mete has a numbe of avantages ove othe metes, it oes not have a unifom spatial sensitivity as o simila techniques such as the capacitive pulveise fuel mete [5] o electostatic pobe [6] an pobes base on lase systems [7]. Impoving of the pefomance of the F mete involves seveal issues, some of which ae still the subject of ongoing investigations [8-]. One pimay issue is

5 iecte to achieving unifom spatial sensitivity hence it is necessay to stuy the spatial sensing chaacteistics of this type of mete to achieve that goal. Velocity measuement The velocity of the flowing solis is measue using two ing-shape electoes place a known istance apat. These electoes etect vaiations in inuce chage signals. The latte ae coss-coelate to measue the flow tansit time between the two electoes. Suppose that x(t) an y(t) ae the signals fom the upsteam an ownsteam electoes, espectively. The coss coelation of these signals R xy ()is given by; T R xy ( ) lim x( t y t t T T ) ( ) () 0 The coss coelation function is chaacteise by a peak occuing at a time elay m that escibes the tansit time of the soli paticles between the two electoes. If the electoe spacing is L, then the solis velocity V is given by V=L/ m () The measuement of paticle velocity V in Eq. () is absolute, having imensions of istance ivie by time. Solis concentation measuement In pneumatic conveying, electical chaging of the conveye solis occus. The pimay souces of electification ae fictional contact chaging between paticles, chage tansfe fom one paticle to anothe an fiction between paticles an the conucting pipe wall. The fluctuation level in the net chages caie by solis is popotional to the solis concentation une the lean-phase conition. The electostatic pulveise fuel mete escibe in this pape was esigne to measue this fluctuation to inicate solis concentation an solis mass flow ate. These can be calculate if the solis velocity is known. Figue shows a simplifie, schematic view of the signal-etecting system stuie in this pape. The ing-shape metallic electoe is installe flush with the inne suface of the

6 eathe conveyo. The electoe is insulate fom the conucting conveyo wall but expose to the flowing ai-soli mixtue an is ac couple to an amplifie. R x Electically Conucting ipe Insulato Ring-shape Electoe W To eamplifie aticle with unity point chage Flow Diection x: Co-oinate along pipeline : aial Cooinate R: ipe inne iamete W: Electoe With Fig. Schematic of a Ring Shape Electoe Fitte into neumatic Conveyo This aangement ensues that the electoe oes not estict the flow an is sensitive to the chages caie by the fuel paticles. It also minimises the electoe wea that can occu with intusive pobes [6]. The chages ae inuce on the electoe when chage paticles pass within its vicinity. The oot mean squae (ms) value of the anom vaiations in the chages inuce on the electoe is popotional to the vaiation in the net chages caie by flowing paticles an is use as the inication of the solis concentation. It is obvious that this is not an absolute measuement of solis concentation, because the chage vaiation in the electoe is epenent on many popeties, such as moistue content an the chemical composition of the solis. If the mete is calibate une a given set of conitions (fo example, humiity, chemical

7 composition of the solis, paticle size istibution, etc.), the measue value cannot give tue mass flow ate o concentation when the conitions change. The inication becomes only a elative measuement une conitions which ae iffeent fom that of the calibation. Fo contol an fuel-balancing puposes, it is sufficient to measue the atio of solis mass flow ate in each conveyo to the total mass flow ate emanating fom the mill. This atio is known as split. ovie that the mass flow ate measue by the mete is popotional to the tue mass flow ate of the fuel flowing simultaneously though each conveyo the tue split can be calculate by using the elative mass flow ate in each conveyo. Because the flow measue in each conveyo is fe fom a single mill pocessing the same fuel, an because flow passes though each conveyo by successive ivision to the bunes, we can expect the solis in each conveyo to have simila popeties. The absolute o tue solis mass-flow ate to each bune nee not necessaily be known. Example: Split measuement system Figue 3 povies an example showing a tifucating junction, though which solis fom the mill pass though an ae split into thee pneumatic conveyos to which thee pulveise fuel metes ae fitte. The split can be infee fom the atio of measue solis mass flow ate on the coesponing metes. The pulveise fuel measuement system uses one compute to acquie an pocess all signals eive fom the electoes an to isplay instantaneous values of pulveise fuel velocity, elative solis concentation, elative solis mass flow ate, an solis split fo each conveyo. Ai Coal Mill F metes Fan Boile Fig. 3 An Example of Fuel Distibution

8 The spatial esponse of a ing-shape electoe The chage inuce on a ing-shape electoe fom a single paticle having unity chage has been moele mathematically by Gajewski [] an Cheng [3]. Cheng s moel was base on electostatic theoy an calculate using the finite element metho (FEM). The FEM technique is a vey poweful tool fo obtaining the numeical solution of a wie ange of engineeing poblems such as stess, stain, tempeatue istibution, flow velocity o electic fiel stength [4]. As shown in Fig., the chage Q inuce on the inne suface of the electoe ue to a paticle of unity point chage insie the pipe was calculate using following expession; Q s s (3) Hee is the suface ensity of the chage inuce on the electoe, an S is entie inne suface aea of the electoe. Fom electostatic theoy, one can show that the chage ensity on the suface of a conucto is equal to the electical flux ensity D. = D (4) The following expessions also apply in the analysis, D=p (5) D=E (6) E=- (7) Whee p is the volume space chage, hee efee to as the souce chage, E is the electic fiel stength, efes to the elative pemittivity of the meium, is the gaient opeato an is the electical potential. Combining the above equations gives ()=-p (8) The following bounay conitions of potential on each pat of the bounay of the egion consiee wee assume; ( p )=0( i )=0 ( t ) =0 (9)

9 whee p, i, t ae the bounaies of the pipe, the insulato an the electoe espectively. The insulato s potential was assume to be zeo, but it may not have been so. Howeve using othe low potentials ( Volts o 3 Volts) fo the insulato with the finite element metho pouce simila esults fo the electic fiel within the senso seems, hence the assumption seems justifie. The equivalent esistance an capacitance of the electoe wee not taken into account in this moel. They will be consiee togethe with the peamplifie. The FEM analysis esults wee cuve fitte to the following equation. k Q=Ae x (0) whee A an k ae two constants that ae functions of the with W of the electoe an the aius fom the cente line of the electoe towas the pipe wall. The vaiable x enotes the istance along the pipeline fom the cente of the electoe coss section as illustate in Figs. an 4. The quantity Q is the chage inuce fom a paticle caying unity point chage. The esponse of the ing-shape electoe to oping flow When pulveise flow, athe than a single point chage, is consiee, the paticle size an suface aea must be taken into account. In aition, bipola chaging of the paticles is possible. The inuce signal in this case will be ue to the net chage on the paticles. Theefoe, some assumptions must be mae to pemit a theoetical analysis that can be compae with expeimental esults. The paticles ae assume to be spheical an to have unifom paticle iamete D p, an each paticle is assume to have the same suface chage ensity p. It is also assume that the paticles ae evenly istibute within a given incemental volume, i.e. the numbe of solis paticles within a unit volume can be escibe by a single vaiable N. The chages caie by the paticles ae theefoe assume to have the same polaity an value. This assumption ignoes the iffeence between the net chage an the total negative o positive chages. In the iscussions to follow, the input to the electoe is efine as the net chage caie by solis, an the output of the electoe is the chage inuce on the electoe.

10 The ing-shape electoe has axial symmety; hence, fo any oping flow that occus in paallel with the pipeline ove the electoe sensing volume, thee will always be a ing-shape. flow steam which pouces the same chage on the electoe. In tems of the chage Roping flow Electoe x Flow iection Equivalent ingshape steam x x (x,)=(0,0) ipe inne A: Hypothetic Roping flow in paallel with pipeline B: Equivalent ing-shape flow Fig. 4 A oping Flow an Its Ring-Shape Equivalent Steam inuce on the electoe, this ing-shape steam is theefoe the equivalent of columnshape (oping) flow. Figue. 4B shows a ing-shape steam having inne aius an oute aius + which is the equivalent of the oping flow shown in Fig.4A. In this case, A an k ae functions of the electoe with W an the aial position of the chage paticles. They thus ae expesse in the following equations as A(W) an k(w).

11 Base on the pinciple of supeposition of electostatic fiels an Eq. 0, the inuce chage Q mic ue to a hypothetical ing *x of a mico volume within the sensing volume, shown at position (x) in Fig. 4, can be expesse as follows. p k( W ) x Q mic = D N A( W) e x () p Let appoach zeo, exten x towas the sensing length of the electoe, an ivie both sies of Eq. by * so as to guaantee that the ing contains the same amount of chage wheeve the oping steam appeas. The esponse of the electoe to the net chage caie by this hypothetical ing thus epesents the spatial esponse at the aius. The latte can be expesse as follows: Q NET k( W ) x D N A( W ) e x () p L x Hee L x is the imension of the electoe sensing volume along the pipeline, an Q is NET the chage inuce on the electoe ue to the net chage in this ing-shape paticle-aimixtue steam with istance elative to the cental pipe axis. This oping paticle steam can be egae as a taveling wave of velocity V oiginating fom the outlet of a conveyo splitting junction. In oe to stuy the esponse of the electoe to a unit impulse of net chage, it is assume that the chage caie by the soli paticles is as follows: Q NET x p D N( t) ( t ) (3) V Hee Q NET is the net chage caie by the paticles of a unit impulse wavefom taveling along the pipeline at aial istance elative to the cente line of the pipe. Because time vaiations must be consiee, the paticle numbe ensity N is e-expesse hee as the time vaying N(t) in the above equation. It is clea that at any given time, only one point along the x iection exists whee becomes Q NET, o N(t) is not equal to zeo. This point is equal to V t. Hence Eq.

12 Q NET k(, W ) V t h ( t) A( W) e (4) This equation escibes the ynamic spatial esponse of a ing-shape electoe to a ingshape unit impulse of net chage caie by soli paticles. The vaiable h (t) also epesents the impulse esponse of the ing-shape electoe to the mass flow ate of the solis, since it was assume that the solis concentation is popotional to the net chage caie by solis at a given velocity. Spatial fequency esponse of an electoe Applying Fouie tansfomation to Eq. 4, the spatial fequency-esponse chaacteistic of a ing-shape electoe to a unit impulse of net chage caie by paticles is as follows jt k( W ) V t jt A W ) H ( ) h ( t) e t A( W ) e e t = e V k( W ) ( 4V k( W ) (5) Spatial fequency esponse of a ing-shape electostatic pulveise fuel mete In pactice, the electoe must be connecte to measuing equipment o to a peamplifie. An ac-couple (iffeential) cicuit is usually esigne to etect the oot mean squae (ms) value of the ac signal components on the electoe, coesponing to the fluctuation in the net chage caie by paticles. In this pape the combination of the electoe an the electonics compise the F mete. A simplifie epesentation of an ac-couple cicuit is shown in Fig. 5. Hee Q epesents the chage inuce on the electoe; the equivalent esistance R n an capacitance C n of the electoe to the eathe conveying pipe ae also consiee. The input esistance an capacitance Q C U o C n n Fig. 5 ac-couple Voltage Amplifie

13 Relative amplitue of the pe-amplifie ae ignoe. A geneal tansfe function of ac-couple peamplifie is as follows, U o ( ) C n ( ) ( ) (6) Q( ) ( j ( C C C ) C C ) n n Taking the net chage caie by the solis as the input an U o as the output of the pulveise fuel mete the tansfe function T() of the mete is the pouct of both the electoe an the peamplifie tansfe functions. The mete s fequency spatial sensitivity theefoe can be expesse as T () = H ()*(), i.e., n n n U T ( ) Q o NET ( ) A( W ) e ( ) V k( W ) 4V k( W ) * ( j ( C n n C C ( ) n C ) C C ) n n n (7) The values of R n an C n of a given electoe epen on its geomety an the insulation between the pipe wall an the electoe. Assuming that the electonics ae esigne to etect chage vaiations on the electoe that coespon only to fluctuations in the net paticle chage, the powe spectal function of the mete output is as follows o NET U ( ) T ( ) Q ( ) o NET U ( ) T ( ) q ( ) (8) (9) whee Q ( ) is the fequency NET tansfe function of the net chage of the oping steam of paticles at aial position, an q ( ) is NET the fluctuation in the net chage. The flow noise is usually egae as a ban-limite white noise, as is the fluctuation in net chage q ( ). Figue 6 shows the peicte NET /R=0.8 /R=0.5 /R= Fequency (Hz) Fig.6 eicte Fequency spatial sensitivity of the mete Hz

14 Nomalize amplitue powe spectum of the mete at a velocity of 5m/s base on Eq. 9, whee the fluctuation in net chage is assume to be ban-limite white noise having a constant powe ensity spectum ove the effective fequency ange. Typical paametes fo the cicuit of Fig. 5 ae the following: R n = M, C n =.47 nf, R = 0. M, an C = µf. Spatial sensitivity expesse in the time omain Accoing to aseval s fomula [5], a stochastic pocess is elate to its powe spectal ensity function. Fom Eq. 9, it thus follows that U oms T 0 T ( ) q net ( ) (0) whee U oms is the ms F mete output, an T is the effective uppe cut-off fequency. If q ( ) is white noise of value A 0 up to fequency T, then the spatial sensitivity of NET the ing-shape, pulveise fuel mete can be calculate using the following equation: U ms A 0 T T ( ) 0 () Figue 7 shows the spatial sensitivity in the time omain calculate fom Eq Relative istance fom the pipe cente /R Fig. 7 Mete s Spatial Sensitivity in the Time Domain Expeimental valiation The expeiments escibe in this section wee caie out at the laboatoies of Casella CRE Enegy, Stoke Ocha, Cheltenham in the Unite Kingom. A 4-inch ( cm) iamete electostatic mete was installe in a test facility, as epicte in Fig. 8. The

15 oping ai-solis flowing in paallel with the pipeline wee povie using a one inch (.54-cm) iamete jet connecte to the solis ispense. A Ventui tube was locate beneath the ispense whee compesse ai an solis wee mixe an conveye to the test section. The jet position in the conveyo coul be ajuste both hoizontally an vetically, so that the oping flow coul be injecte at iffeent aii. Jet Hole Jet position ajuste Roping Flow Ring-shape F Mete To Daft Fan, filteing an Collecting Facility One inch (.54cm) Diamete Jet ulveise Coal Dispense Compesse ai Flexible hose latfom fitte with loa cells Fig.8 Spatial Sensitivity Test Facility The flow ates of the solis an conveying ai mass wee monitoe by compute an logge into files. Thei values an thei fast Fouie tansfoms (FFT) wee calculate using National Instument s Labview softwae. The sampling ate of ata collection was 0kHz, an 048 ata points wee collecte fo each measue paamete. The solis oping flow ate was about 300 kg/h an the conveying ai-mass flow ate in the jet was about 60 kg/h. The velocity of the oping flow was kept at about 5 m/s with the help of a aft fan at the en of the ig. Both theoetical analysis an expeimental esults wee nomalise by setting thei espective maximum values to unity. The expeimental esults can theefoe be compae to those peicte fom Eqs. 9 an, because the net chage caie by the paticles an its fluctuation level ae assume to be popotional to the solis concentation.

16 Nomalize mete's output ms Nomalize Value Nomalize Value Fo the pupose of compaison, Fig. 6 is eawn besie Fig. 9 which is base on /R= /R=0.5 /R= Fequency (Hz) Fequency (Hz) Fig.9 Test Results of fequency Response Fig.6 eicte Fequency spatial Sensitivity of the Mete expeimental esults. The shapes of the coesponing cuves ae simila in these two figues, except that the peak positions an the geometical means of the cuves in Fig. 9 ae both shifte ownwa in fequency. This may have been cause by the jet vibation which woul have contibute low fequency components to the flow steam. The solis moving ajacent to the pipewall contibute highe fequency components an have highe-level oveall esponse, because the sensing length of the electoe along the pipeline eceases with elative aial position (/R) [3]. incease Relative istance to the pipe cente /R Fig. 0 Spatial sensitivity test esults

17 Nomalize Value Nomalize Value The oveall shape of the measue spatial esponse shown in Fig. 0 is simila to the calculate esponse shown Fig. 7. In pactice, it is ifficult to obtain eliable expeimental spatial esponse esults nea the pipe wall whee the oping flow iveges. In pactice, it was vey ifficult to keep the oping flow pefectly constant, because the flow ate of the conveying ai as well as the pessue at the Ventui tube, change anomly. Thus, although the cuve in Fig. 0 is compise of about 000 ata points, it is not smooth. Veification of the assumptions use in the theoetical analysis We assume in ou theoetical analysis that the fluctuation in the chage caie by the solis is ban-limite white noise. This assumption was veifie by compaing the measue powe spectum of the mete with the theoetically peicte esponse. The measue powe spectum shown in Fig., cause by flow noise fom pulveise fuel, compaes well with the theoetical esponse shown in Fig., although the actual Fequency (Hz) Fig. Mete s owe Spectal Chaacteistics Base on Theoetic Analysis Fequency (Hz) Fig. Mete's owe Spectal Response Test Results spectum banwith is naowe. Howeve the similaity between the two figues is appaent, geneally confiming the above assumptions. Conclusions A compaison of Figs. 6, 7, an with Figs. 9, 0 an confims that the mathematical moel fo the esponse of the pulveize fuel mete is consistent with the expeimental esults, although a moe igoous investigation is neee. Lowe fequency components ominate the mete output even though wie-ban amplifies wee use. The solis

18 moving nea the pipe wall contibute highe fequency components an have highe amplitues than o the solis flowing nea the cente of the pipe. Refeences [] Hube N., Sommefiel M., Chaacteization of the Coss-Sectional aticle Concentation in neumatic Conveying System, owe Technology, Vol.79,994 pp9-0 [] Bena J. Bay et al, Concentation Vaiations within ipe Coss-Sections in a Dilute hase neumatic Conveying System, IENZ Tansactions, Vol. 4, No /EMCh, 997, pp- [3] Yilmaz Ali et al, Roping henomena in pulveize Coal Conveying Lines, owe Technology, Vol.93, 998, pp [4] Fank Thomas, et al, Aspects of efficient paallelization of ispese gas-paticle flow peiction using Euleian-Lagangian Appoach, oceeings of ICMF-00, 4 th Intenational Confeence on Multiphase Flow, May -June, 00 New Oleans LA, USA ape 3 [5] Hamme E. A., Geen R. G., The spatial filteing effect of a capacitance tansuce electoe, J. hys.e: Sci.Instu., Vol.6, 983, pp [6] S. Laux, J Gusha, T. Rosin, J.D. Kesch, ECT: Moe than just coal-flow monitoing, Moen powe systems, Mach 00, pp -9. [7] Wang Shimin, et al, Avance Measuement an Diagnosis Technology Applie in Coal-Fie Utility Boiles, oceeings of 5 th Intenational Symposium on Coal Combustion, Nanjing, China, Novembe 3-6, 003, pape No. 4 [8] DTI oject Summay 330( ulveise Fuel Measuement with Split Contol, Clean Coal Technology ogamme, July 00 [9] ECSC 70-R 050 Final Repot, Measuement & Contol Techniques fo Impoving Combustion Efficiency an Reucing Emissions fom Coal Fie lant, Apil 00. [0] ECSC Coal Technical Reseach ogamme, On-Line Measuement of aticle Size in Fine Coal Tanspot system, Contact Numbe: 70-R-05, oject Commence, Nov 000. [] Zhang J., Coultha J., Amstong B., Lean hase Solis Contol Using inch Valves an Mass Flowmetes fo ulveise Fuel, Bulk Solis Hanling, Tans Tech

19 ublications ISSN /003, pp [] Gajewski J. B., Mathematical moel of non-contact measuements of chages while moving, Jounal of Electostatics, Vol. 5, 984, pp8-9. [3] Cheng R., A stuy of electostatic pulveise fuel metes, h.d. thesis, Univesity of Teessie, U.K [4] Dattaay Jagish Rao, GE Enegy, [5] Calson A. Buce, Communication Systems, An Intouction to Signal an Noise in Electical Communication, Secon Eition, McGaw Hill inc. 975, USA pp3 Nomenclatue Symbol Definition Symbol Definition A Systematic constant, esistances of a ing-shape electoe A 0 amplitue of banlimite white noise aius of a single paticle, o solis-ai mixtue steam line o ing shape steam line to the C isolating (iffeential) capacitance C n equivalent capacitance of a ing-shape electoe to the eathe pipe D electical flux ensity D p iamete of a spheical paticle E electical fiel stength pipe cental line R xy () coss coelation function S entie electoe inne suface T () U o, U o () tansfe function of the electostatic ing-shape mete when a oping flow is a aius output of pulveise fuel mete an its tansfe function

20 H () spatial fequency esponse of a ingshape electoe to a net unit impulse chage caie by solis paticles k systematic constant of a ing-shape electoe L spacing between upsteam an own steam electoes fo velocity measuement L x electoe sensing length along pipeline (cooinate x) N paticle numbe in unit volume of aisolis mixtue at position N(t) paticle numbe time vaiable in unit volume of ai-solis mixtue () tansfe function of ac-couple peamplifie p souce chage Q, Q() chage inuce on the ing-shape electoe an its tansfe function Q mic inuce chages on the ing-shape electoe ue to a mico volume of aisolis mixtue *x at position (x) U oms V oot mean squae value of pulveise fuel mete output solis velocity x co-oinate along the pipeline x(t) y(t) signal eive on the mete installe at up steam fo the solis velocity measuement signal eive on the mete installe at own steam fo the solis velocity measuement electical potential i bounay of the insulato p bounay of the pipe t bounay of the ing-shape electoe

21 Q inuce chage on NET the electoe ue to net chages in a ing-shape solis steam appeae at aius to the pipe cental line Q NET, Q NET ( ) solis net chage oping steam at aius to the pipe cental line an its tansfe function q NET, q NET ( ) fluctuation in the net chage caie by solis paticles an its tansfe function R n inne aius of the pipe an ingshape electoe iffeence esistance equivalent esistance of the electoe to the eathe pipe p solis paticle suface chage ensity (t) unit impulse function (t-x/v) unit impulse wavefom taveling at velocity V along the pipeline elative pemittivity of the meium time elay T effective uppe cutoff m solis tansient time fequency fom upsteam measuing point to the own steam measuing point gaient opeato Angula fequency