A comparison of turbulence models and two and three dimensional meshes for unsteady CFD ash deposition tools

This is a e sion o a publica ion in Please ci e he publica ion as ollows: DOI: Copy igh o he o iginal publica ion: This is a pa allel published e sion o an o iginal publica ion. This e sion can di e om he o iginal published a icle. published by A compa ison o u bulence models and wo and h ee dimensional meshes o uns eady CFD ash deposi ion ools Ga cia Pe ez Manuel, Vakkilainen Esa Ga cía Pé ez, M., Vakkilainen, E. (2019). A compa ison o u bulence models and wo and h ee dimensional meshes o uns eady CFD ash deposi ion ools. Fuel, Vol. 237, Issue 1 Feb ua y 2019, p. 806–811. DOI: 10.1016/j. uel.2018.10.066 Publishe 's e sion Else ie Fuel 10.1016/j. uel.2018.10.066 © Else ie 2019 Con en s lis s a ailable a ScienceDi ec Fuel jou nal homepage: www.else ie .com/loca e/ uel Full Leng h A icle A compa ison o u bulence models and wo and h ee dimensional meshes o uns eady CFD ash deposi ion ools Manuel Ga cía Pé ez ⁎ , Esa Vakkilainen Lappeen an a Uni e si y o Technology, Ene gy Technology, P.O. Box 20, FIN-53851 Lappeen an a, Finland ARTICLE INFO Keywo ds: Fouling Combus ion Ash deposi ion Compu a ional fluid dynamics Tu bulence model ABSTRACT This wo k aims o assess he adequacy o he o en made wo dimensional mesh simplifica ion in ash deposi ion models. Li le in o ma ion is a ailable ega ding i s alidi y due o he hea y compu a ional cos s ha a p ope h ee-dimensional g id model would en ail. We ha e implemen ed a case s udy (a deposi ion p obe in a k a eco e y u nace) wi h 2D and 3D mesh models in o de o compa e hei esul s ega ding he ash deposi ion and he fluid flow. An addi ional simula ion has been ca ied ou o compa e he esul s be ween URANS and DES u bulence models. Fo he pa icula case s udied in his a icle, he wo-dimensional simplifica ion is jus ified as he esul s did no a y no ably whe eas en ailing ema kably smalle compu a ional cos s. None heless, he usage o DES u bulence model yielded mode a ely diffe en esul s, quali a i ely close o deposi obse a ions, jus i ying pe haps he h ee-dimensional app oach when accu acy is needed o he deposi ion o fine pa icles on he lee edges o he ubes. 1. In oduc ion Fly ash impac ion and deposi ion on boile ubes en ail e osion and co osion o he hea exchange su aces, as well as down imes and o e all pe o mance penal ies in boile s o any kind, up o a poin ha hese may ha e an impac on he o e all design [1]. The physical and chemical phenomena in ol ing ash gene a ion, g ow h, anspo , and deposi ion is hus o a majo conce n [1,2]. A conside able effo is being made o a be e knowledge o hese phenomena, CFD modeling being a pa icula ly popula and affo dable app oach. Un o una ely hese ools a e s ill a an ea ly s age [3] and would ideally be enhanced wi h g id-independency s udies (as, e.g., [4]) and/o empi ical alida ions (as, e.g., [5,6]), o en omi ed due o hei challenging na u e [1]. In he wo k o Li e al. [7] he deposi ion on a hombic hea ans e ube a ay was modeled and alida ed sa- is ac o ily. Ma idou e al. [8] analyzed he effec o he usage o ubes o diffe en diame e wi hin a ow. Han e al. [9] compa ed he de- posi ion on ci cula e sus ellip ical ube a ays. All he s udies men ioned in he p e ious pa ag aph used 2D meshes o hei models. No ably ewe h ee-dimensional simula ions a e y- pically ound in li e a u e. Fo ins ance, Wang e al. [10] s udied he flow pa e ns and deposi ion o e a andem o wo H- ype finned ubes. The deposi ion and e osion on a supe hea e co ne was modeled by Li e al. [11]. Leppänen e al. [12] p edic ed he ume ash o ma ion and deposi ion on o he supe hea e su ace wi h a 3D mesh comp ising he en i e u nace and he backpass o a k a eco e y boile . All hese wo ks conside ed s udy domains wi h geome ies which we e no amenable o a wo-dimensional app oach, esul ing in o conside ably hea y 3D meshes. Mo e o en han no , he wo ks which used a 3D app oach e iewed by he au ho s o he p esen s udy did no a emp o pe o m an uns eady flow simula ion o a g id con e gence analysis. Typically, he wo-dimensional app oach is execu ed when he modeled domain shows an app op ia e pe iodici y and/o symme y [7]. This way, he calcula ion ime may be educed by a ew o de s o magni ude. F equen ly, o long uns eady calcula ions wi hin a pa a- me ic s udy, his may be he only easonable way o simula ing. Howe e , he adequacy o his e y common simplifica ion has seldom been assessed o e en conside ed. Many deposi ion su aces unde s udy a e ube a ays which expe ience h ee-dimensional u bulence eddies [13,14] which could be affec ing pa icle ajec o ies. G ei zu e al. [15] obse ed diffe ences be ween he acked pa icle ajec o ies o a 2D and a 3D mesh o he same domain; a ibu ing he bes fi o he 3D case o he expe imen al esul s o a be e simula ion o he h ee dimensional pa icle dispe sion caused by he u bulen eddies. Li e al. [13] compa ed he deposi ion modeled o e a ube wi h bo h 2D and 3D meshes. I was concluded ha he 3D app oach yielded h ps://doi.o g/10.1016/j. uel.2018.10.066 Recei ed 23 Janua y 2018; Recei ed in e ised o m 27 Sep embe 2018; Accep ed 10 Oc obe 2018 ⁎ Co esponding au ho . E-mail add ess: manuel.ga cia.pe ez@lu .fi(M. Ga cía Pé ez). Fuel 237 (2019) 806–811 0016-2361/ © 2018 The Au ho (s). Published by Else ie L d. This is an open access a icle unde he CC BY-NC-ND license (h p://c ea i ecommons.o g/licenses/BY-NC-ND/4.0/). T mode a ely be e esul s acco ding o empi ical measu emen s, al- hough a a he coa se mesh was used, possibly esul ing in o an o e es ima ion o he on deposi s o he smalles pa icles [3]. Un- o una ely, bo h he simula ion and he expe imen al se -up we e poo ly de ailed [13].Wefind fi ing o conside how, in gene al, esul s on ash deposi ion could be affec ed by he 2D mesh simplifica ion. The p esen s udy aims o confi m he alidi y o his 2D assump ion by modeling a case s udy in bo h wo- and h ee-dimensional meshes. The case s udy selec ed o he uns eady pa icle deposi ion was a wa e -cooled deposi ion p obe inse ed in he las supe hea e a ea o a k a eco e y boile . The simula ions we e ca ied ou in Ansys FLUENT 18.0 enhanced wi h he disc e e phase model and use -defined unc ions. Diffe en mesh esolu ions, dimensions (in he sense o spa- ial coo dina es), ash pa icle diame e s and u bulence models a e es ed and compa ed. 2. Model desc ip ion The ash deposi ion a ound a 4-cm (ou e diame e ) wa e -cooled p obe wi h an ou e wall empe a u e o 39 °C inse ed in k a eco e y boile is simula ed wi h FLUENT. Typical k a eco e y alues and gas pa ame e s ha e been selec ed [16–18] o ma ch he ones o he su- pe hea e egion. The ups eam gas comes a 686 °C wi h a eloci y o 3.5 m/s and a a p essu e o 92 kPa (ou le ). The flue gas has a dynamic iscosi y o − 3.82·10 5 kg/(m s), a he mal conduc i i y o 0.0663 W/(m K), a specific hea o 1248 J/(kg K) and a molecula weigh o 28.97 kg/ kmol. Diffe en meshes o he same case s udy a e implemen ed in o de o compa e hei esul s. The g id esolu ion is a ied o ensu e ha he nume ical con e gence is eached. In addi ion, o one o he 3D me- shes, he u bulence models URANS −k ω SST and DES a e compa ed. Conclusions ega ding he alidi y o he 2D simplifica ion and u bu- lence models shall be d awn. In his s udy, he di ec ion along he p obe is o en e e ed o as he hi d coo dina e, which is he simplified one in he 2D simula ions. The loca ions on he pe ime e o e he ci cula p obe a e de e mined wi h he angula coo dina e θ, whe e =θ0 co esponds o he p obe lee and =±θ π co esponds o he p obe wind. 2.1. Compu a ional domain and meshes The simula ions execu ed in his s udy use a o al o ou diffe en meshes o he same case s udy. The wo-dimensional domains consis o a ec angle wi h a ci cula hole (4 cm diame e ) which ep esen s he p obe. The flue gas comes om le o igh , hus he le edge is se as a eloci y inle (loca ed 0.2 m, o 5 imes he p obe diame e ups eam he p obe cen e ) and he igh edge is se as a p essu e ou le (loca ed 0.4 m, o 10 imes he p obe diame e downs eam he p obe cen e ). The uppe and lowe edges a e se as pe iodical bounda ies so as no o cons ain he flow (loca ed each one a a dis ance om he p obe o 0.14 m o 3.5 imes he p obe diame e ). These 2D domains a e meshed wi h iangula -pa ed schemes ollowing wo diffe en esolu ion e- qui emen s o ensu e he g id independency o he esul s. The coa se (fine) 2D meshing o he domain p oceeds as ollows. Fi s ly, he p obe pe ime e is di ided in 600 (800) elemen s, ac- coun ing o he nume ic accu acy guidelines p oposed by Webe e al. [3,19]. A size unc ion is hen implemen ed o con ol he size o he iangula cells as hey a e pa ed u he away om he p obe pe i- me e wi h a g owing a io o 1.40 (1.03). The maximum allowed cell size a ea 35 mm 2 o bo h meshes. The esul ing 2D g id is composed o 25256 (62246) cells. Fig. 1 shows he esul ing fine mesh. The h ee dimensional meshes a e buil based on he co esponding wo-dimensional ones by ’s acking’o eplica ing slices o hem along he hi d coo dina e. The hickness o he 3D domain is wice he p obe diame e , i.e., 8 cm. The calcula ion ime o he 3D mesh inc eases mo e han p opo ionally wi h he hi d dimension, and i is hus p ohibi i e o inc ease i much u he . The coa se (fine) mesh is composed o 50 (70) slices o he wo-dimensional mesh, esul ing in o a slice hickness o 1.60 (1.14) mm and a o al o 1.26 (4.24) million cells. These a e ema kably hea y meshes o a ansien s udy. Fig. 2 illus a es he h ee dimensional coa se mesh. 2.2. Ashes and disc e e pa icle acking The disc e e phase model a ailable in he so wa e package is im- plemen ed o ack and calcula e he mo ion and ajec o ies o k a ash pa icle pa cels. I a pa cel impac s on o he p obe su ace, he use - define ou ine DEFINE_DPM_EROSION [20] is called o pe o m he s icking- ebound submodel b iefly desc ibed below. Th ee diffe en ash pa icle size diame e s a e injec ed in he do- main h ough he gas inle and a e calcula ed independen ly. The pa - icle diame e s unde conside a ion a e 0.7, 4.0 and 40 μ m. Wi h his aim, mul iple independen injec ions a e se up. The dus concen a ion in he flue gas is 8 g/m 3 o each pa icle diame e , acco ding o ypical alues [21]. By injec ing mul iple pa icle pa cels pe each inle ace (pppi ) i is possible o ha e a sufficien ly la ge numbe o pa cels being acked, and hus, o ob ain a mo e s a is ically obus and less biased esul a e simula ing he flow du ing a limi ed numbe o on Ká mán oscilla ions [22]. Consequen ly, 10 pppi we e injec ed a each ime-s ep o all he simula ions excep o he DES case, which was ins ead limi ed o 3 pppi ( hus, each indi idual pa cel ep esen s a la ge numbe o pa icles acco dingly o he same gas ash concen a ion) due o he pa icula ly longe DES simula ion ime and he hea y calcula- ion cos o he ajec o ies o o e 25 million pa cels in he domain (once educed o 3 pppi ). The s icking model app oach used in his wo k is based on he mechanis ic model o an Beek [23] o egula pa icle impac ions, which has been implemen ed by a numbe o au ho s wi h sa is ac o y esul s, some o which ha e al eady been ci ed [4,9,10,24]. In addi ion, he Kons andopoulos c i e ion o oblique impac s [25] has been con- side ed wi h he use o he empi ical ebound co ela ions o B ach, Dunn and Li [26,27]. This combina ion o app oaches has been used in p e ious simula ions by he p esen au ho s. A ull desc ip ion o he s icking- ebound ou ines implemen ed in his s udy is somewha long and ully de ailed elsewhe e [6]. Fig. 1. Two dimensional domain wi h he fine mesh esolu ion. Fig. 2. Th ee dimensional domain wi h he coa se mesh esolu ion. M. Ga cía Pé ez, E. Vakkilainen Fuel 237 (2019) 806–811 807 K a fine ash is made mainly o ine alkali sul a es [21,28] and i has been se o he ollowing p ope ies: densi y 2664 kg/m 3 , specific hea 902 J/kg K, and he mal conduc i i y 0.0608 W/mK. Rega ding he mechanical p ope ies o he mechanis ic s ick- ebound ou ines, he p ope ies o K 2 SO 4 deposi s ha e been selec ed [6,23]: Young modulus 3·1010 Pa, Poisson’s a io 0.3, Yield s ess 4 .10·108Pa, ic ion coefficien 0.7, and su ace ene gy 0.15 J/m 2 . The pa icle pa cels a e acked wi h a cus omized d ag law which accoun s o he spa ial a iabili y o he pa icle Knudsen numbe Kn and he Cunningham co ec ion ac o C c [29,30] =μ ρd M RT Kn 2.533 p w (1) =+ ⎡ ⎣⎛ ⎝ −⎞ ⎠+⎛ ⎝ −⎞ ⎠ ⎤ ⎦ C1 Kn 1.205exp 0.0026 Kn 0.425exp 0.74 Kn c(2) whe e μ ρM,, wand Ta e espec i ely he gas iscosi y, densi y, mo- lecula weigh and empe a u e. dp is he pa icle diame e , and = R 8.31 4 J/(mol · K). The d ag coefficien in his s udy is hus compu ed as − CC Dc 1 , whe e C D is he d ag coefficien yielded by he law o Mo si and Alexand e [31]. In addi ion, he mopho esis simula ion is enabled [32] as i has been obse ed o be a majo deposi ion mechanism o he smalles ypes o pa icles [5,22,33]. 2.3. Cases unde s udy Fi e diffe en simula ions a e ca ied ou in his s udy. Fou o hem a e iden ical excep o hei mesh, in o de o pe o m a p ope com- pa ison among hei esul s. Due o he low u bulence ( = R e 122 5 )an URANS −k ω SST model is sugges ed [34,33]. Addi ionally, a fi h case is execu ed using he coa se 3D mesh bu wi h a De ached-Eddy Simula- ion (DES) u bulence model whe e he nea -wall egion u bulence is simula ed wi h he −k ω SST. The inle u bulence in ensi y is 7%, and he iscosi y a io is 10. Fo he DES case, a spec al syn hesize which akes in o accoun he inle u bulen in ensi y has been enabled o gene a e adequa ely fluc ua ing eloci y componen s in he inle o a mo e ealis ic simula ion. The simula ion pa ame e s a e summed up in Table 1. The simu- la ed flow ime o he DES case needs o be pa icula ly longe in o de o cap u e a less biased pa icle impac ion sample, since he flow was no s ic ly pe iodic as i could be app ecia ed in Fig. 3. The o he cases may be pe o med wi h a ela i ely low in ege numbe o flow oscil- la ions due o hei pe iodici y and he la ge quan i y o independen pa icle injec ions implemen ed. 2.4. Sol e and ou line o he model execu ion The model is execu ed in ANSYS Fluen 18.0. The double-p ecision sol e wi h de aul disc e iza ion schemes a e used. The ime-s ep chosen o all simula ions is − 1 0 4 s, calcula ing 35 i e a ions pe ime s ep. The li o ce o e he p obe is moni o ed as he flow wi h he pa icles is simula ed o he poin whe e i s oscilla ions become quasi- s able. Only om ha poin onwa ds, da a abou each pa icle pa cel impac ion (such as geome ic coo dina es o he impac ion poin , im- pac ion eloci ies and ebound eloci ies i applicable) on he p obe is collec ed and egis e ed du ing a ime span o (see Table 1) o ul e io pos p ocessing. This s a egy has been ollowed in p e ious wo k [22,33]. 3. Resul s and discussion 3.1. On he compu a ional cos s Fig. 4 highligh s he wall-clock ime needed o compu e one ime- s ep o flow, o ack he pa icle pa cels, and o calcula e he ebound o ones ha equi e i . All he ime-s eps execu ions o his figu e we e ca ied ou in he same machine, an HP P olian SL230s G8 wi h wo p ocesso s In el Xeon E5-2660 (se ing up Pa allel Fluen wi h 16 h eads, no hype h eading was used), unning wi h Linux Cen OS 7. I should be no ed ha he la ge numbe o pa cels being acked (o e 167 million pa cels o he 3DF case, 89 million o he 3DC case and 26 million o he DES) equi e a la ge amoun o a ailable RAM memo y, which is g ea e han 128 GiB o he 3DF case. The du a ion o a ime s ep calcula ion highligh s he somewha high imp ac icabili y o using 3D models in his kind o cases due o he usually la ge amoun o ime s eps o calcula e. A highe flow eloci ies, he ime s ep du a ion migh ha e o be dec eased e en u he , en ailing an e en la ge numbe o s eps o compu e. 3.2. Deposi ion a ound he p obe pe ime e Figs. 5–7show he collec ed deposi ion a es o e he p obe pe i- me e (a e aged along he hi d coo dina es o he cases using a 3D mesh). I can be no ed how o he fi s ou cases he deposi ion is, a leas quali a i ely, equi alen . Thus, i URANS u bulence models a e Table 1 Summa y o execu ed simula ions. Tis he flow oscilla ion pe iod. s ands o he flow ime o pa icle impac ion logging a e he flow s abiliza ion. Sim. Mesh T[ms] [s] Tu bulence 2DC 2D, coa se 53.87 =T 5 0.2675 s URANS 2DF 2D, fine 53.62 =T 5 0.268 1 s URANS 3DC 3D, coa se 53.87 =T 5 0.2693 s URANS 3DF 3D, fine 54.03 =T 5 0.270 1 s URANS DES 3D, coa se 49.84 =T25 1.24 6 sDES Fig. 3. Tempo a y e olu ion o he ae odynamic li o ce on he p obe su ace. Fig. 4. A e age calcula ion ime equi ed pe ime-s ep (20 ime-s eps we e measu ed o each case), in seconds. M. Ga cía Pé ez, E. Vakkilainen Fuel 237 (2019) 806–811 808 used, he use o 3D meshes may no be jus ified. Howe e , he DES u bulence model seems o show in ui i ely be e esul s as he deposi ion in he leewa d side o he p obe is somewha mo e uni o m han in he o he cases. Al hough he lee de- posi s a e less known and unde s ood han he wind deposi s ( ypically less effo has been pu on measu ing hose [1]), quali a i e obse a- ions and models ha e epo ed ha he ea deposi s acqui e a ela- i ely uni o m o fla shape [20,35]. The e o e when accu acy is needed o small pa icle deposi ion in he ea sides o ubes, he usage o 3D meshes enhanced wi h DES u bulence modeling migh be necessa y. This diffe ence in he esul s o DES e sus he URANS cases is ul- ima ely caused by he flow field phenomena occu ing in he p obe lee. All hese 0.7 and 4.0 μ m pa icles showed an impac ion efficiency o e a 99.9% consis en ly a ound he en i e pe ime e , meaning ha he DES case is b inging ewe pa icles o he lee su ace. The mopho esis should be disca ded as an explana ion o his phenomenon, since i s p opensi y (as p oposed in p e ious s udies [33,35]) was showed o be ma ginally la ge o he DES case han i was o he URANS case used o compa ison (3DC). Mo eo e , i he mopho esis happened o be significan ly less in ense in he DES case, hen he deposi ion diffe - ences be ween he DES e sus he URANS cases would be, agains ob- se a ions (Figs. 5 and 6), smalle o he 4.0 μ m pa icles han wha hey we e wi h he 0.7 μ m pa icles. The e o e he easons behind smalle a i al a es is explained by a smalle dus concen a ion in he p obe wake o he DES case as a consequence o he diffe en flow fields and o ex pa e ns obse ed when compa ing he wo cases a he peak o a flow oscilla ion, as obse ed in Fig. 8: in he DES case he pa icle- ca ying flow is ea aching he wake a u he loca ion downs eam o m he p obe and no su ounding lee-nea by o ices, no u ning away owa ds he p obe su ace. As i can be deduced also om he flow li s in Fig. 3, he DES case p esen s a smalle ans e sal componen o he flow eloci y, implying again ha ewe pa icles a e d agged o he o ex- egion o be hen d i en he mopho e ically o deposi ion. Obse e hose peaks o deposi ion appea ing a angles o ≈± απ 0.55 o he bigges pa icles es ed in his s udy. Those peaks a e a consequence o he uppe and lowe pe iodic bounda y condi ions selec ed: as hese la ge pa icles expe ience a ebound a e impac ing in he lee o he p obe, hey s ill possess an impo an ine ia and hus hey a e no much d agged by he flow as hey a el nea ly pe pen- dicula ly o i . A e hey each he uppe (lowe ) domain bounda y, due o he pe iodical configu a ion o he model, hey impac again he p obe on i s lowe (uppe ) side. Such an effec may no be obse ed o he smalle pa icles since mos o hem do no ebound (o e 99% o s icking p obabili y has been compu ed o he wo smalle pa icle diame e s), and s ill hose which do ebound a e hen effec i ely d agged and ca ied by he gas, no eaching hose domain bounda ies. 3.3. Deposi ion along he hi d coo dina e I is illus a i e o analyze he pa icle a i al obse ed along he hi d coo dina e (only applicable o he cases wi h 3D meshes). As an example, obse e Fig. 9 which highligh s he numbe o 4.0 μ m pa cel impac ions on o he p obe su ace. I can be no ed ha he dependency wi h he hi d coo dina e is negligible. Howe e , i should be s essed ha his ac would no cons i u e a sufficien condi ion by i sel o wa an y ha ash deposi ion may be p ope ly modeled wi h wo-di- mensional app oaches. None heless i is a condi ion ha should be ulfilled. Fo all he o he possible cases and pa icle diame e s, an iden ical independency on he hi d coo dina e was also obse ed. 3.4. Final commen s on he limi a ion o he s udy The Fini e Volume Me hod o en implemen ed in CFD makes use o a disc e iza ion scheme o sol e he uns eady Na ie –S okes equa ion sys em. A each i e a ion, hese equa ions a e applied using he dis- c e iza ion schemes in o de o build an algeb aic sys em o equa ions. The size o his sys em is di ec ly ela ed o he numbe o mesh cells. Thus, quali a i ely, he cos o sol ing a mesh may g ow app oxima ely wi h he cube o i s size. On he o he hand, his size o a 3D mesh may be ypically a ound a couple o o de s o magni ude la ge han ha o a 2D mesh. Conside ing also ha he calcula ions mus be uns eady o a p ope de e mina ion o he smalles pa icle ajec o ies, he o en- made 2D assump ion is equen ly ega ded as necessa y in li e a u e, especially wi h limi ed compu ing esou ces. Howe e some s udies migh be aking his decision in cases whe e i is no alid. The simula ions o his s udy could be execu ed in a clus e o compu e s wi h a easonably good pe o mance. S ill, i ook se e al mon hs o calcula ion o comple e due o he e y high compu a ional demand o he 3D cases. We would ha e p e e ed o conduc a mo e comple e s udy wi h a sensi i i y analysis on he numbe o ubes in a ow, he dep h o he domain along he hi d coo dina e, and he inle Fig. 5. Deposi ion a es o e he p obe pe ime e o 0.7 μm pa icles. Fig. 6. Deposi ion a es o e he p obe pe ime e o 4.0 μm pa icles. Fig. 7. Deposi ion a es o e he p obe pe ime e o 40 μm pa icles. M. Ga cía Pé ez, E. Vakkilainen Fuel 237 (2019) 806–811 809 fluid eloci y. Un o una ely i is ye no easonable o pe o m a s udy which would comp ise all hese analyses wi h he compu a ional cap- abili y a ailable in a ypical esea ch o ganiza ion. The conclusions d awn in his s udy a e alid o he pa icula implemen ed scena io. I would be desi able, o ins ance, o compa e he 2D and 3D cases wi h highe gas eloci ies; bu as he eloci y inc eases, bo h he equi ed mesh and he ime-s ep esolu ion mus become e en fine [19] en- ailing an inc ease on he compu a ional cos s p opo ionally, ap- p oxima ely, o he gas eloci y aised o he fi h powe . Addi ional wo k should be ca ied on o es he alidi y o his assump ion in a a ie y o ypically encoun e ed cases o ha e a mo e p ope scien ific confidence on he alidi y o he 2D o URANS simplifica ions. 4. Conclusions The 2D mesh simplifica ion o he ash deposi ion CFD models is ound equen ly in li e a u e. This s udy has made an a emp o assess i s alidi y by pe o ming CFD models o e he same case. The con- ibu ion o his wo k is unde lined by: •compa ing 2D and 3D esul s o e he same case s udy, •pe o ming uns eady flow simula ions, •using fine g ids and confi ming he g id-independency o he esul s, and •implemen ing a mechanis ic pa icle s ick– ebound ou ine; The e is a lack o s udies in li e a u e wi h models analyzing he ash deposi ion wi h his combina ion o ea u es. Un o una ely we did no ha e any empi ical da a a disposal o his pa icula p obe o con as he esul s. None heless his wo k was aimed mo e owa ds highligh ing he possible diffe ences among modeling app oaches han owa ds he de elopmen o a new one. Fig. 8. Ins an aneous gas eloci y fields and ec o s o a peak o an oscilla ion wi h minimum (peak) li o he 3DC ( op) and DES (bo om) simula ions, in he domain middle plane o he hi d coo dina e. No e how o he 3DC case, he gas s eam expe iences a mo e sudden di ec ion change owa ds he wake o he p obe ca ying pa icles in o he o ices; whe eas o he DES simula ion his wake en ainmen occu s u he downs eam, wi h a lowe eloci y and so e o ices. Fig. 9. Numbe o pa icle pa cel impac s on he h ee-dimensional p obe su ace as a unc ion o he p obe angle and he hi d coo dina e (along he p obe). Case 3DF, 4 μ m pa icles. The mass o each impac ion pa icle pa cel o his case and diame e is − 1 .776·10 12 kg. M. Ga cía Pé ez, E. Vakkilainen Fuel 237 (2019) 806–811 810 Fo he pa icula case s udy o a deposi ion p obe in a k a e- co e y u nace, i has been ound ha he wo-dimensional simplifi- ca ion i sel did no yield impo an diffe ences in he esul s, bu he usage o a mo e elabo a ed, h ee-dimensional u bulence model (DES e sus URANS) did ha e an effec on he leewa d side o he deposi . I is hus possible ha he 2D simplifica ion is jus ified o cases wi h big pa icles (a leas 10 μ m) and/o in ense u bulence. Howe e , i p ecise accu acy is essen ial, a 3D g id wi h a DES u bulence model may be equi ed o ume ash pa icles and mild u bulence. The e o e i is o high in e es o ca y ou addi ional wo k co obo a ing he alidi y o he 2D simplifica ion wi hin a a ie y o geome ies, inle flow elo- ci ies and u bulence in ensi ies. Re e ences [1] Li MJ, Tang SZ, Wang FL, Zhao QX, Tao WQ. Gas-side ouling, e osion and co osion o hea exchange s o middle/ low empe a u e was e hea u iliza ion: a e iew on simula ion and expe imen . Appl. The . Eng. 2017;126:737–61. [2] Bax e LL. Ash deposi o ma ion and deposi p ope ies. A comp ehensi e summa y o esea ch conduc ed a Sandia’s combus ion esea ch acili y, ech. ep., Sandia Na ional Labs., Albuque que, NM (US); Sandia Na ional Labs., Li e mo e, CA (US), Li e mo e, Cali o nia; 2000. [3] Webe R, Mancini M, Schaffel-Mancini N, Kupka T. 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