Prediction of particle sticking efficiency for fly ash deposition at high temperatures

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Proceedings of the Combustion Institute 37 (2019) 2995–3003

www.elsevier.com/locate/proci

Prediction

of

particle

sticking

efficiency

for

fly

ash

deposition

at

high

temperatures

Xin

Yang

a

,

Derek

Ingham

a

,

Lin

Ma

a ,∗

,

Maurizio

Troiano

b

,

Mohamed

Pourkashanian

a

a_Energy_2050,_Department_of_Mechanical_Engineering,_University_of_Sheffield,_Sheffield_S10_2TN,_UK b_Dipartimento_di_Ingegneria_Chimica,_dei_Materiali_e_della_Produzione_Industriale,_{Università degli}_Studi_di_Napoli

FedericoII,PiazzaleVincenzoTecchio80,80125Napoli,Italy

Received28November2017;accepted3June2018 Availableonline25June2018

Abstract

Thetendencyofashparticlestostickunderhightemperaturesisdictatedbytheashchemistry,particle physicalproperties,depositsurfacepropertiesandfurnaceoperationconditions.Amodelhasbeen devel-opedinordertopredicttheparticlestickingefficiencyforflyashdepositionathightemperatures.Themodel incorporatestheparticlepropertiesrelevanttotheashchemistry,particlekineticenergyandfurnace oper-ationconditionsandtakesintoconsiderationthepartialstickingbehaviourandthedepositlayer.Totest themodel,thestickingbehavioursof syntheticashinadroptubefurnaceareevaluatedandtheslagging formationfromcoalcombustioninadown-firedfurnaceismodelled.Comparedwiththemeasurements,the proposedmodelpresentsreasonablepredictionperformanceontheparticlestickingbehaviourandtheash depositionformation.Throughasensitivityanalysis,furnaceoperationconditions(velocityand tempera-ture),contactangleandparticlesizehavebeenfoundtobethesignificantfactorsincontrollingthesticking behavioursforthesyntheticashparticles.Theashchemistryandfurnacetemperaturedictatethewetting potentialoftheashparticlesandthemeltingabilityofthedepositsurface;particlesizeanddensitynotonly controltheparticlekineticenergy,butalsoaffecttheparticletemperature.Thefurnacevelocityconditionhas beenidentifiedasbeingabletoinfluencetheselectivedepositionbehaviour,wherethemaximumdeposition efficiencymovestosmallerparticleswhenincreasingthegasvelocity.Inaddition,thethermophoresiseffect onthearrivalrateof theparticlesreduceswithincreasingthegasvelocity.Further,increasingthemelting degreeof thedepositlayercouldgreatlyenhancethepredicteddepositionformation,inparticularforthe highfurnacevelocitycondition.

ThisisanopenaccessarticleundertheCCBYlicense.(http://creativecommons.org/licenses/by/4.0/ )

Keywords: Ashdeposition;Particlesticking;Slagging;Furnaceoperationcondition;CFD

∗_{Corresponding}_author.

E-mailaddress:lin.ma@sheffield.ac.uk (L.Ma). https://doi.org/10.1016/j.proci.2018.06.038

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1. Introduction

Prediction of ash deposition formation is of greatimportanceintheefficientutilisationof vari-oussolidfuelsandthedevelopmentofcombustion technologies[1–4] .Predictingtheparticlesticking efficiencyisacriticalstepinmodellingtheash de-positionformation, which isdictated bythe ash chemistry,particleproperties,depositsurface prop-erties,andfurnaceoperationconditions.Ash chem-istry dictates the melting potential and the rhe-ology of ash particles, which controls how the molten/partiallymoltenashparticlesbehavewhen impactingontheheatexchanger surfaces.In ad-dition,ashchemistryisimportantindictatingthe degreeof sinteringof thedeposits,whichis rele-vanttotheremovalofdeposits[5] .Depositsurface propertiesareimportantincontrollingthe spread-ingbehaviourandtheenergydissipationoftheash particles impacting on the surfaces.Further, the surfacescouldgraduallybecomestickyduetothe formationoftheliquidphaseonthedepositlayer [6 ,7 ].Highfurnacetemperaturepromotesthe melt-ingofashparticlesandtheformationofthesticky depositlayer.Thedecreaseinthefurnacevelocity conditionunderoxy-coalcombustionconditionin asmallscalefurnacecouldincreasethedeposit ac-cumulationcomparedtotheair-firedcombustion condition[8] .Withoutenoughairtransportedinto thecombustionchamberincursadelayinthe com-bustionandthiscanaggravatethepyrite-induced slaggingformationinthefurnace[9] .

Manyresearcheshavebeenperformedto pre-dicttheparticlestickinessinordertocalculatethe ashdepositionrate.Walshetal.[6] proposedthe particlestickingmodel,wherethestickinessis in-verselyproportionaltoashviscositybasedonthe assumption that the sticking efficiency increases withan increaseinthecontact area betweenthe ash droplets and the deposit surface. The other widely used model is based on the melting be-haviourproposedbyTranetal.[10] ,whichassumes thatonlywhenashparticlesordepositedsurface hasacertain liquidphasecontentthenit is pos-sibleforparticles tobe sticky. Both twoparticle stickingmodelsattempttotakeintoconsideration theashchemistryandfurnacetemperature. How-ever,thereexistlargediscrepanciesinthecriterion valuesduetothenegligenceoftheparticlekinetic energyinthesetwomodels[11–13] .Ontheother hand,Maoetal.[14] developedasemi-empirical dropletsticking/reboundingmodelthroughan en-ergy conservationanalysis of thespread and re-bound of liquid droplets. The model takes into consideration the main parameters (contact an-gle, viscosity, surface tension, droplet size and density)in controllingthesticking behavioursof liquiddroplets.Muelleretal.[15] predictedthe re-boundingbehaviourof largeparticlesfortheash depositionformationinanentrainedflowreactor

byemployingtheenergyconservationbasedmodel [14 ,16 ]. Ni et al. [17] evaluated the sticking po-tentialof slagdropletsthroughusing thesimilar particlesticking/reboundingmodel. Itwasfound thatunderhighvelocityconditions(3-20m/s),the sticking potentials of slagdroplets increase with increasingthe particle velocity andparticle size, which isinconsistent with thepredicted sticking behaviourof slagdroplets byBalakrishnanetal.

[18] ,whereslagdropletshavehighersticking po-tentialwiththelowerparticlesizeandimpact ve-locity.Recently,Kleinhansetal.[19] explainedthe deposition phenomenon of the small aluminum silicateparticles and thelarge iron-rich particles throughemploying a similarenergy based parti-clesticking/reboundingmodel.Theprediction per-formanceoftheenergyconservationbasedmodel isdependent on theprediction of the maximum spreadfactorduringtheimpactionprocess,which wasderivedfromthespreadingof waterdroplets withparticleReynoldsnumbermuchhigherthan thatfortheash droplets[14 ,16 ]. Inaddition,the partialstickingphenomenonhasbeenfoundinthe experimentalinvestigationsofstickingbehaviours ofthedropletswhichhavesmallexcessenergyafter impaction[20–22] ,whichisneglectedintheenergy conservationbasedparticlestickingmodels[14,17– 19] .It is clear thatthe current energy conserva-tionbasedparticlesticking/reboundingmodelstill needsfurtherdevelopment.

Thispaperaimstodevelopanimproved parti-clestickingmodelbasedontheenergyconservation analysisduringtheparticleimpactionprocessesfor ashdroplets.Theproposedmodelconsiderstheash chemistry,particlephysicalproperties,deposit sur-facepropertiesandfurnaceoperationconditions. Inaddition,asensitivityanalysisofthemajor pa-rametersin controlling the particle sticking effi-ciencyhasbeeninvestigatedusingthenewmodel developed.Twodifferentpreviousexperimental re-sultsonparticlestickingbehaviourshavebeenused tovalidatetheproposedparticlestickingmodel, in-cluding(i)thesoda-limeglassparticlessticking ex-perimentsbySrinivasacharetal.[23] ,and(ii)the ash deposition experimentsduring coal combus-tioninadown-fired furnacebyBeckmannet al. [13] .

2. Particlestickingmodel

Slagging of ash droplets on heat exchanger tubes can be described by the spreadand stick-ing of droplets impacting on a target surface [14,24] ,asshownin Fig. 1 .Fornormalimpacts, at stage 1, just before impaction, ash droplets possess kinetic energy, EKE1,andsurface energy,

ESE1. During impaction, ash droplets spread on the tube surface due to the inertial and viscous forces.Thekineticenergyistransferredtothe sur-face energy and partially dissipated in

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overcom-Fig.1.Sticking/reboundingprocessaftertheimpaction ofashdropletsontheheatexchangertubesurface (mod-ifiedfrom[14,24 ]).

ingtheviscous force duetothedeformation. At stage2,onreachingthemaximumspread diame-ter,theflattenedash dropletshavenokinetic en-ergy and possess the maximum surface energy,

ESE2. After that, the splats gradually recoil up-wards.Atstage3,onreachingthemaximumrecoil, theflattened ashdropletshavenokineticenergy, andpossesssurfaceenergy,ESE3,andpotential en-ergy,EPE3.Atstage4,theexcessenergyisdissipated andthedropletsreachequilibriumandsticktothe heatexchangertubesurfaces.Itisassumedthat,if ashdropletshaveenoughenergytoprovidetheash dropletstodetachfromthesurfaceswiththe orig-inalsphericalshape(surfaceenergyequaltoESE1), thereboundoftheashdropletsuponimpactingon thetubesurfacesoccurs[14] .Atthereboundstage, thepotential energyis neglecteddueto itssmall valuecomparedtosurfaceenergy.Therefore,the re-boundcriterioncanbeformulatedasfollows: E∗= 1 ESE 1 [(ESE 3+EPE 3)− ESE 1] = 1 ESE 1 [(ESE 2− EDiss2→3)− ESE 1] (1)

where,E∗istheexcess energy normalizedbythe surfaceenergy(ESE1)instage1,andEDiss2→3isthe energydissipatedbetweenstages2and3.ESE1and

ESE2canbeexpressedas:

ESE 1=πD20γLV (2) ESE 2=ESE_LV+ESE_SL− ESESV = πD2 0γLV 1 4d 2 m(1− cosθ )+ 2 3dm (3) where, D0 is the particle size of the ash droplets; ESE_LV, ESE_SL and ESE_SV are the

liquid-vapoursurfaceenergy,thesolid-liquid sur-faceenergy, andthesolid-vapoursurfaceenergy, respectively;γLV istheliquid-vapoursurface

ten-sion;dm isthemaximumspreadratio,definedas

theratioof themaximumspreaddiametertothe original droplet size, D0; θ is the contact angle. Thecontact anglecoulddecreasewithincreasing thefurnacetemperatureandthemeltingpotential of the ash particles (relevant to ash chemistry) [19 ,25 ]. In addition, the apparent contact angle shouldbeusedwhenthesurfaceroughnessof the

Fig.2. Comparisonofthepredictedandmeasuredvalue forthemaximumspreadingratio(R2₌_0.67)_and_energy dissipation(R2₌_0.92)_by_using_the_derived_{correlations.}

heatexchanger tube istaken intoaccount inthe spreadandimpactionoftheashdroplets[14 ,20 ]. Themaximumspreadratioof theashdropletsis assumed to be dependent on the particle Weber numberunderhightemperaturesandtheparticle Reynoldnumberisnotdirectlyconsidered.Dueto thelimitationinobtainingthespreading dataof ash droplets, theexperimentalspreading data of thesucroseand inkdroplets from[14 ,26 ], which havemuch lower particle Reynolds number (ap-proximately30–1000)thanwaterdroplets(higher than 4000) [14 ,26 ], is employed to obtain the empiricalcorrelationofthemaximumspreadratio using the linearregression analysis (as shownin Fig. 2 ):

dm=1+0.259∗ We0.317 (4)

where,We=(ρpUp2D0)/γLV istheparticleWeber

number,ρp isthedensityof theashdroplets;Up

isthenormalcomponentoftheimpactvelocityof theashdroplets.Basedontheassumptionthatthe energy dissipation(EDiss2→3) isafunctionof the maximumspreadratioandthecontactangle[14] ,

EDiss2→3canbeobtainedbasedontheexperimental data[14 ,20 ,23 ]usingpartialleastsquareregression (asshowninFig. 2 ):

EDiss2→3= πD20γLV

0.00536∗ dm4.70∗ (1− cosθ )0.591

(5) SubstitutingEqs. (2) ,(3 )and(5 )intoEq. (1) ,the excessenergyratio(E∗)canbeexpressedas: E∗= 1 4d 2 m(1− cosθ )+ 2 3dm −0.00536∗ dm4.70∗ (1− cosθ )0.591− 1 (6)

For E∗≤ 0, the sticking efficiency, Estick,

equals tounity. Byconsideringthe partial stick-ing/reboundphenomenonofthedropletswiththe excessenergyslightlylargerthanzero,thesticking efficiencyisassumedtobeafunctionoftheexcess energy ratio, E∗. It is assumed that the sticking efficiency of droplets is not significantwhen the droplets lose more than half of the incoming surfaceenergy [27] ,whichrepresents thesticking

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Table1

Propertiesofthesoda-limeglassparticles.

Glassproperties,Trepresentstemperaturein°C Ashcomposition,% Contactangle,o ₁₈₀_/₍₁₊_eT−930₁₀₀ ₎ _SiO

2 72

Surfacetension,N/m 0.66− 0.0003∗ T Na2O 15

Viscosity,Pas 10(−2.92+T4700−218.76.13) _CaO ₈

Density,kg/m3 ₂₅₃₅_{− 0}_.₁₄₃_{∗ T} _MgO ₅

efficiency, Estick,being negligible when theexcess

energy ratio islarger than 0.5.The sticking effi-ciency,Estick,canbe expressedbyan exponential

formulationas:

Estick=exp(a∗ E∗), ifE∗>0 (7)

where,a=−9.21tosatisfytheaboveassumption thatEstick=0.01(asmallvaluefortheexponential

formulation)whenE∗=0.5.Sincethestickinessof themolten/partiallymoltendepositlayercouldbe attributedtotheliquidphasecontent[28 ,29 ],itis assumedthattheformationofthedepositlayercan reducetheexcessenergyratiobyafactorrelatedto itsmeltingdegree.Therefore,thestickingefficiency,

Estick∗ ,canbefurtherexpressedasfollows:

Estick∗ =exp[−9.21∗ E∗(1− fmelt)], ifE∗>0 (8)

where,fmelt istheliquidphasecontent(ortermed

asthemeltfraction)ofthedepositsurface,whichis estimatedbythedepositcompositionand temper-aturethroughthechemicalequilibriummethod.

3. Casedescriptions

3.1. Case1:stickingbehaviourofsyntheticash particles

Syntheticashparticles(soda-limeglass)with di-ametersrangingfrom53μmto74μmwereused toinvestigatethesticking behaviourunder differ-entfurnace temperatures (ranging from approxi-mately890Kto1225K).Moredetailsof the de-positionexperimentscanbefoundintheworkof Srinivasacharetal.[23] .Theproperties(ash com-position,contactangle,surfacetension,viscosity, anddensity)of theusedsoda-lime-glassparticles areshown in Table 1 [19 ,23 ]. Deposition experi-mentalresultsshowthat:(i)glassparticlesstartto stickontheprobeat1075Kandthesticking effi-ciencysharplyincreasetounityatatemperatureof 1225Kwhentheparticlevelocityis4m/sand(ii) ashdepositionoccursatlowertemperaturewhen reducingtheparticlekineticenergy.

3.2. Case2:slaggingformationfromcoal combustion

TheSouthAfricanMiddelburgcoalwasusedto investigatetheashdepositionbehaviourinadrop

tubefurnace.Moredetailsofthedeposition exper-imentscanbefoundintheworkofBeckmannetal.

[13] .Theflyashdepositionresultsatthelower lo-cationinthefurnace,wherethecharburnoutis ap-proximately99.4%andtheeffectoftheunburned charontheashdepositionisassumedtobe negli-gible,aremodelledinthisstudy.Theflyash prop-erties(ashcomposition,particlesize,andparticle loading)andthefurnaceconditionsarefromthe workof Beckmannet al.[13] ,andother proper-ties(particledensity,particlespecificcapacity,and surface tension) are estimated basedon the ash composition,asshowninTable 2 [17,30–32] .Since thereisnoexperimentaldataon thecontact an-gle,a valueof 135° isusedin thecurrent study, whichproducesagoodcorrelationwiththe mea-surementsof thedepositionrate.Anuncertainty studyof thecontact angle rangingfrom120° to 160° indicatesthatthevalueofthedepositionrate rangesfrom0.59to1.54g/hfortheuncooledprobe and0.66to2.03g/hforthecooledprobe.

CFD modelling is carried out to predict the flyash depositionbehaviour.ANSYSFluent ver-sion 16.1 has been employed to perform the basiccalculations,incorporating theuser-defined routine DEFINE_DPM_EROSION in order to predicttheashdepositionformation[12 ,33 ]. Math-ematical submodels, such as the Realizable k-ε model with the enhanced wall treatment, Dis-crete Ordinatemodel andDiscrete Phase Model (DPM), were used formodelling the turbulence, radiation heat transfer and particle trajectories, respectively.Both the gravitationalforce andthe thermophoreticforcebyTalbotetal.[34] are con-sideredforpredictingtheparticletrajectories.The computational domainis considered to be a2D geometry(0.3m∗0.6m)withadepositiontubeof outerdiameter22mmplacedinthecentralregion. Afinemesh,whichmeetsthesizerequirementsfor predictingtheparticleimpactionbehaviour[35] ,is distributedaroundthedepositionprobe.Itshould benotedthat, intheCFDsimulations,the parti-clediameters(rangingfrom1μmto150μm)with 50 intervals are used since the difference in the predictedparticlearrivalrateisapproximately5% comparedtotheresultswith150intervals.In addi-tion,the"steadystate"assumptionisusedforboth thecooled(600°C)anduncooledprobessincethis studyfocusesontheash depositionformationat theearlystageinasmalltimeinterval.However,a dynamicmodelisrequiredforpredictingthewhole

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Table2

FlyashpropertiesandfurnaceconditionsusedintheCFDsimulations.

Flyashproperties,Trepresentstemperaturein°C Ashcomposition,% Sizedistribution,μm Rosin-Rammler,Dmean(21),spreadparameter(0.76) SiO2 38.6

Particleloading,kg/h 1.983∗10−2 Al2O3 32.3

Density,kg/m3 ₃₃₃₃ _Fe

2O3 5.8 Specificcapacity,J/(kgK) 975.65+0.23∗ (T+273.15)+0.24/(T+273.15)2 CaO 12.3 Surfacetension,N/m 0.415+0.004∗ (T− 1400)/100 MgO 2.0 Viscosity,Pas 10(−8.07+T14100+273.72.15) TiO2 1.9 Furnaceconditions Na2O 0.9 Gastemperature,°C 1125 K2O 1.1 Gasvelocity,m/s 0.357 P2O5 2.0 O2,vol%(dry) 3.68 SO3 3.1 CO2,vol%(dry) 15.7

Fig. 3.Comparison of thesticking efficiency(ST) be-tweenthestickingmodelsandmeasurementsasa func-tion of temperature. (For moredetails of theparticle stickingmodelsused,pleaserefertothesupplemental ma-terial.Thesameusageoftheparticlestickingmodelsis appliedtoCase2,asshowninFig. 5 ).

ashdepositiongrowthprocessinordertoconsider theeffectsofthedepositsurfaceconditions (sur-facetemperature,depositshape,etc.)[32 ,33 ,36 ]. 4. Resultsanddiscussion

4.1. Case1:evaluationofstickingefficiencyfor syntheticash

Figure 3 showsthestickingefficiencyasa func-tionof temperatureamong thedifferent sticking models. Comparedto the viscosity based model (criterion value, 105_Pa.s _[23]_), _the _melt _fraction basedmodel(criterionvalue,15%[10] ),theother energy conservationbasedparticlesticking mod-els proposed by Mao et al. [14] and Kleinhans etal.[19] ,andtheempiricalcorrelationproposed byKleinhansetal.[19] ,thepredictedsticking effi-ciencyonlywhenusingthepresentmodelismore consistent withthe experimentaldata,where the sticking efficiency rapidly increases fromzero to unity in the temperature range from 1050K to 1200K.Figure 4 showsthesensitivityanalysisof themainfactorsonthestickingbehaviourof the soda-limeglassparticleswhilevaryingthe temper-ature.First,thefactors(includingparticlevelocity,

Fig. 4.Sensitivityanalysisof the mainfactorsonthe stickingefficiencyforthesoda-limeglassparticle (size-63.5μm and velocity-4m/s). (For more details of the sensitivityanalysis,pleaserefertothesupplemental ma-terial.).

contactangle,size,anddensity)havenegative sen-sitivitycoefficients,whichrepresentthaton increas-ingthevaluesofthesefactorsreducesthesticking propensities,whilethetemperature,surfacetension andmelt fraction havean oppositetrend. These predictedresultsareinaccordancewiththe previ-ousexperimentalobservations:(i)soda-limeglass particles with less kinetic energy being easierto stickontheprobe[23] ,(ii)dropletsimpactionon thesubstrateswithahighercontactanglebeingless sticky[14 ,37 ,38 ],and(iii)ashslagwithhigher sur-facetensionhavingthelargeradhesionofworkand bondstrength[39] .Second,thevelocity, tempera-ture,contactangleandparticlesizehavethehigher sensitivitycoefficient totheother factors investi-gated,whichisduetothesignificantrolein deter-miningthemaximumsurfaceenergyandtheenergy dissipation.

4.2. Case2:evaluationofdepositionrateforcoal combustion

Figure 5 showstheslagging ratebetween the experimental andpredicted results bythe differ-entparticlestickingmodels.Thepredictedslagging ratesfromthepresentmodelandthepredicted re-sultsfromBeckmannetal.[13] obtainedbyusing theviscositybasedmodel(criterionvalue,25Pa.s) areclosetothemeasurements.Figure 6 presentsthe

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Fig.5. Comparisonofthedepositionratesbetweenthe stickingmodelsandthemeasurements.

Fig.6.Predicteddepositionbehavioursoftheflyash par-ticles:T,KE,IE,andSEarethemassaveragedparticle temperature,log10(kineticenergy),impactionefficiency andstickingefficiency,respectively.

detaileddepositionbehavioursasafunctionofthe particlesizethroughthepresentmodel.First, ther-mophoresisincreases the impactionefficiency of thesmallashparticlesonthecooledprobe,which resultsinahigherslaggingrateforthecooledprobe asobservedinboththepredictedresultsand mea-surements.Second,thepredictedparticlesticking efficiencyisslightlyhigher (by 0.05–0.10)forthe uncooledprobein thisstudy. Third,small parti-cleshaveamuchhigherstickingefficiencythanthe coarse particles andthisis because of thelower kineticenergyinthesmallparticles.However,the viscositybasedparticlestickingmodelmayleadto anoppositerelationshipbetweenthesticking effi-ciencyandtheparticlesizeforthecooledprobeas thesmallerparticleshavelowertemperaturethan thelargerparticlesatthecoolingstage.Inaddition, fortheuncooledprobe,theparticle sticking effi-ciencieswhenusingtheviscositybasedmodelcould besimilarforashparticleswithdifferentsizes.

The furnacevelocity conditionisquite differ-ent among the combustors (lab-scale, pilot-scale and utility boiler) although the smaller scale combustors are carefully designed to match the

Fig.7.Predicteddepositionbehaviourswithincreasing thegasvelocity:IET,SET,andDETrepresenttheoverall impactionefficiency,overallstickingefficiencyandoverall depositionefficiency,respectively.

Fig.8.Predicteddepositionefficiencyasafunctionof particlesizeunderdifferentgasvelocityconditions.

time-temperature history of the particles within utility boilers [40] . A further analysis is carried outbygraduallyincreasingthegasvelocityofthe baselineCFDcaseswiththeoriginalgasvelocity (0.357m/s).Figure 7 presentsthepredicted depo-sitionbehaviours of thecurrent fly ash particles at different gas velocity conditions. The overall particleimpactionefficiency(forallparticlesinthe projected surface) increases from approximately 10%to40%andtheoverallstickingefficiency(for allarrivalparticlesontheprobesurface)decreases fromapproximately45%to4%withincreasingthe gasvelocityupto15m/s,whichresultsinthe de-creaseintheoveralldepositionefficiency(defined as the impaction efficiency∗sticking efficiency) fromapproximately6.1%to1.5%.Inaddition, un-derahighergasvelocity,thedepositionefficiency fortheuncooledprobe couldbehigher thanthe cooledprobe.Thisisbecausethethermophoretic effectontheflyashdepositionbehaviourgradually reduceswithincreasingthegasvelocity.The cool-ingeffectfromthecooleddepositionprobereduces withincreasingthegasvelocity.Figure 8 showsthe depositionefficiencyasafunctionof particlesize underdifferentgasvelocityconditions.The maxi-mumdepositionefficiencygraduallychangesfrom thecoarseparticlesizeregion(100μm)inthelow gasvelocityconditiontothemedium/smallparticle sizeregion(10–30μm)inthehighgasvelocity con-ditions.Thisindicatesthattheselectivedeposition behaviourisrelevanttothegasvelocityconditions in combustors. Barrosoet al. [41 ,42 ] experimen-tallyfoundthatincreasingtheparticlesizecould increase the ash deposition potential in an en-trained flow reactor (≈ 0.5m/s) while Raask

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Fig.9. Predictedoveralldepositionefficiencyasa func-tionofthemeltfractioninthedepositlayer:the enhance-ment factor, FDET=DET/DET0; DET0 is the overall depositionefficiencyforthebaselinecase.

[39] presentedthatsmallparticles(around10μm) depositeasierthanlargerparticlesinutilityboilers (≈ 10–25m/s).Anotherfurtheranalysisiscarried out by gradually increasing the melting degree of thedepositlayer.Figure 9 showstheeffectof increasingthemeltingdegreeofthedepositlayer onthepredictedoveralldepositionefficiency. In-terestingly,theenhancementfactor(8timeswhen usingthemeltfractionwith80%)forthecasewith the highest gas velocity is muchlarger than the othertwocases.Thisindicatesagainthatsticking anddepositionbehaviourarestrictlyrelatedtothe globalandlocalvelocityconditions.

4.3. Remarksonthecurrentparticlestickingmodel

In this paper, an improved particle sticking methodisdevelopedbasedontheenergy conser-vationanalysis.Comparedwiththeexperimental results in the particle sticking behaviour of the sodalimeglassparticlesandtheslaggingformation fromcoalcombustion,theproposedmodel hasa goodpredictionperformance.Thesensitivity anal-ysisshowsthesignificantroleofparticlevelocity, temperature,contactangleandparticlesizein de-terminingtheparticlestickingefficiencyofthe syn-theticashparticles.Furtheranalysisindicatesthat theselectivedepositionbehaviourisrelevanttothe gasvelocityconditionsinthefurnaces.Inaddition, increasingthemeltingdegreeofthedepositsurface couldsignificantlyincreasethestickingefficiency andenhancethedepositionformation,especially forthelargegasvelocityconditions.Highfurnace temperatureandtubesurfacetemperaturecould in-creasetheparticlestickinessandpromotethe for-mationofthestickydepositlayer,whichresultsin therapiddepositaccumulation.Inaddition, con-trollingthegasvelocitycouldalleviatethedeposit accumulationonthestickydepositlayersincefewer particlesareabletoimpact onthetubesunder a lower velocity.Also,increasingthecontact angle betweentheashdropletsandthetubesurfacecould reducetheashdepositionrate,whichisin

accor-dancewiththefindingsbyNaganumaetal.[37 ,38 ], where the surface coatings are used to increase thecontact angleandcontrolthe ashdeposition formation.

The main assumption of thecurrent sticking modelisthatthestickingbehaviourofflyash depo-sitionunderhightemperaturescouldbedescribed bythespreadandstickingof thedroplets. How-ever,impactingashparticlesmaynotbecompletely molten,especiallyinthesuperheaterregionwhere thefluegastemperatureispossiblylowerthanthe ash fusiontemperatures.Inthe proposedmodel, thepresenceofthesolidphaseintheashparticles isindirectly consideredbyitseffectonthe parti-cle wettingproperties (contactangle andsurface tension),which isdependent on thetemperature andashchemistry.Thisconsiderationisconsistent with theresultsreportedby Songet al.[25] and Kleinhans et al. [19] , where it was shown that, withdecreasingtemperatureofash,thecontact an-gleincreasesalongwiththedecreaseinthe melt-ingpotential.Itshouldbenotedthatash viscos-ityisnotdirectlyconsideredinthepresentmodel. Inthework of BennettandPoulikakos [43] ,the surfacetensionissignificanttothespreadfactor evenwellintotheviscousdissipationdomain,while theeffectofviscousdissipationrapidlydisappears inthesurfacetensiondomain.Thisoutcome con-firmstheimportantroleofthecontactangle dur-ingthespreadingofparticles.Viscositycontributes topartof theenergy dissipation[14] ,butthe en-ergycouldnotbehugelydissipatedbyanincrease in the viscosity because ash particles are easier toreboundwiththedecreaseinthetemperature. Inaddition, thespreading data of relatively vis-cousdropletswerechosentodevelopthecurrent model.Accuratetreatmentoftheviscosityinthe predictionofthespreadingbehaviourandthe en-ergydissipationforcoalashrequiresthedetailed knowledgeof theroleof viscosityinthe spread-ingbehaviourduringcoalashdropletimpactionon thesurface,whichneedsfurtherinvestigation.Also, thedetailedunderstandingof thespreadand im-pactionbehaviourof ashparticlesonthedeposit layer(porous/sinteredlayer)needsfurtherstudyin ordertorigorouslytreattheeffectof thedeposit layeronthestickingbehaviour.Inaddition,the in-fluenceoftheresidualcarbonontheenergy dissi-pationduringtheparticlespreadingandimpaction shouldbeinvestigatedinordertoimprovethe pro-posedmodel.Also,theeffectoftheimpactangleon theenergy dissipation requires investigations un-deratemperature-velocityconditionclosetoreal combustors/gasifiers[44] ,whichcouldbeanother aspect for improving the proposed model. Note thatthebulkashcompositionisusedfor predict-ingthestickingbehaviouroftheCase2wherethe coalburnedwasalow-alkalibituminous.This ap-proximation could be less accurate when the fly ash is highly heterogeneous in ash composition,

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especially for fuels with high alkali/pyrite con-tent,whichneedstheparticlebasedash composi-tionbeingusedinpredictingtheparticlesticking behaviour.

5. Conclusions

(i)Animprovedparticlestickingmodel,based ontheenergyconservationanalysisand con-sidering the ash chemistry, particle physi-calproperties,depositsurfacepropertiesand furnaceoperationconditions,hasbeen devel-opedforflyashdepositionathigh tempera-tures.Theproposedparticlesticking model hasbeenvalidatedbythestickingbehaviour of the synthetic ash in a drop tube fur-nace andtheslaggingformationfromcoal combustioninadown-firedfurnacethrough CFDmodelling.

(ii) The sensitivityanalysisshowsthatthe pro-posed model is able to consider the main factors indictatingtheparticlesticking be-havioursof thesyntheticashparticles. Fur-naceoperationconditions(velocityand tem-perature),contactangleandparticlesizeare foundtobesensitiveparametersin determin-ingtheparticlestickingefficiency.

(iii) Furnacevelocityconditionaffectsthe selec-tive depositionbehaviours of fly ash parti-cles. Increasing thegasvelocitycan reduce the particle size which has the maximum deposition efficiency. This implies that the coarseflyashparticlesareeasiertodeposit in smaller scale furnaces while the small-mediumflyashparticlesareeasiertodeposit inutilityboilers.Increasingthemelting de-greeofthedepositlayergreatlyenhancesthe depositionformation,especiallyforlargegas velocityconditions.

(iv) Tubesurfacetemperatureaffectsthe deposi-tionbehaviourviaitsinfluenceonthe parti-clearrivalrateandtheformationofadeposit layer. Underthelowtubesurface tempera-tureandthelowgasvelocitycondition, ther-mophoresisgreatlyincreasesthearrivalrate of smallparticles.Withoutformingasticky deposit layer, the deposition rate could be higherforthecooledtubethantheuncooled tube.However,ifforminganeffectivedeposit layer,thedepositionrateislikelytobehigher fortheuncooledtubethanthecooledtube, especiallyunderhighvelocityconditions.

Acknowledgement

Theauthorsacknowledgethesupportfromthe EPSRC grants(EP/M015351/1 ,OpeningNew Fu-els for UK Generation; EP/K02115X/1, Devel-opmentandEvaluationof Sustainable

Technolo-giesforFlexibleOperationofConventionalPower Plants).

Supplementarymaterials

Supplementarymaterialassociatedwiththis ar-ticlecan be found, inthe online version,at doi: 10.1016/j.proci.2018.06.038 .

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