2D and 3D numerical modelling of internal flow of Pressure-swirl atomizer

2D and 3D nume ical modelling o in e nal low o P essu e-swi l a omize Milan Maly1, Ja osla Slama2, Ma cel Sapik1 and Jan Jedelsky1 1B no Uni e si y o Technology, Technicka 2, 616 69 B no, Czech Republic 2P o yko s. .o, Vina ska 3a, 603 00 B no, Czech Republic Abs ac . This pape compa es 2D axisymme ic and 3D nume ical models used o p edic he in e nal low o a p essu e-swi l a omize using a comme cial so wa e Ansys Fluen 18.1. The compu ed esul s a e compa ed wi h expe imen al da a in e ms o sp ay cone angle (SCA), discha ge coe icien (CD), in e nal ai - co e dimensions and swi l eloci y p o ile. The swi l eloci y was expe imen ally s udied using a Lase Dopple Anemome y in a scaled anspa en model o he a omize . The in e nal ai -co e was isualized a high empo al and spa ial esolu ion by a high-speed came a wi h backli illumina ion. The in e nal low was nume ically ea ed as ansien wo-phase low. The gas-liquid in e ace was cap u ed wi h Volume o Fluid scheme. The nume ical sol e used bo h lamina and u bulen app oach. Tu bulence was modelled using k- ε, k-ω, Reynolds S ess model (RSM) and coa se La ge Eddy Simula ion (LES). The lamina sol e was capable o p edic all he pa ame e s wi h an e o less han 5% compa ed wi h he expe imen al esul s in bo h 2D and 3D simula ion. Howe e , i o e p edic ed he eloci y o he discha ged liquid shee . The LES model pe o med simila ly o he lamina sol e , bu he liquid shee eloci y was 10% lowe . The wo- equa ion models k-ε and k-ω o e p edic ed he u bulence iscosi y and he in e nal ai -co e was no p edic ed. 1 In oduc ion The P essu e swi l a omize s (PS) ha e an i eplaceable ole in many indus ial applica ions including combus ion, sp ay cooling, sp ay d ying e c. In a ypical PS a omize , he pumped liquid is ed ia angen ial po s in o a swi l chambe whe e i gains high angula eloci y and c ea es a low-p essu e zone along a cen e line o he swi l chambe . Subsequen ly, he ai is pulled inside he low-p essu e zone, so an ai -co e is o med. The swi ling liquid is discha ged om he exi o i ice in a o m o a conical liquid shee a a ce ain sp ay cone angle (SCA) and consequen ly disin eg a es due o ae odynamical o ces in o ilamen s and ligamen s. Veloci y and hickness o he liquid shee , as well as he SCA, a ec he size o esul ing d ople s. Despi e he simple geome y, he in e nal low beha iou is complex, mainly due o he dominan swi ling eloci y componen and he induced in e nal ai - co e which blocks a po ion o he exi o i ice. The in e nal o ex beha es as a Rankine o ex as he swi l eloci y has i s maximum loca ed a he ai -co e su ace [1]. Seconda y low e ec as Gö le o ices could be also p esen ed in a bounda y laye inside he swi l chambe [2, 3]. In open li e a u e, many co ela ions a e a ailable ( o a gene al o e iew see [4]), which allows us o es ima e he a omize pe o mance such as d ople sizes, SCA, liquid shee hickness, discha ge coe icien , e c. Howe e , he mos o hose co ela ions we e made by i ing he expe imen al esul s and hey we e de eloped o limi ed geome y a ia ions and ope a ing condi ions. To be e unde s and he link be ween he a omize pe o mance and design, he in e nal low mus be examined. Some au ho s s udied he in e nal low analy ically. Simple non- iscous ea men , e iewed in [5, 6], can be used o a basic insigh in o he low beha iou , bu i is no accu a e enough o p edic he discha ge pa ame e s. The be e ag eemen can be achie ed when he iscous low is assumed [7, 8], bu some aspec s like a empo al s abili y o seconda y low e ec s a e unable o be esol ed. The numbe o pape s ela ed o he nume ical simula ion o he PS a omize s had a isen in ecen yea s due o an inc ease in a compu a ional pe o mance. One o he i s nume ical s udies o he PS a omize was conduc ed in 1997 by Yule and Chinn [9]. They used a 2D axisymme ic model wi h he lamina sol e and epo ed a de ia ion om he expe imen al da a o be less han 3%. Simila nume ical se up was used by Amini [7] and showed be e ag eemen wi h he expe imen al da a han he analy ical iscous models. He compa ed hose models a Reynolds numbe inside he inle po s in a ange o Rep = 11,000–122,000. The di e ence be ween 2D and 3D compu a ional models was examined by Sume e al [10]. They used he lamina sol e and ound ha he ai - co e diame e was abou 5% smalle in he case o he 3D model. Howe e , he equency o wa es on he ai -co e su ace was p edic ed by bo h models closely and wi h good ag eemen o he expe imen al da a. A compa ison © The Au ho s, published by EDP Sciences. This is an open access a icle dis ibu ed unde he e ms o he C ea i e Commons A ibu ion License 4.0 (h p://c ea i ecommons.o g/licenses/by/4.0/). EPJ Web o Con e ences 213, 02055 (2019) h ps://doi.o g/10.1051/epjcon /201921302055 EFM 2018 o La ge Eddy Simula ion (LES) and he lamina models was pe o med by Madsen e al. [11]. They used a scaled a omize and ope a ed i in ange o Rep = 12,000–41,000. A hose ope a ing egimes, he lamina model had a sligh ly be e ag eemen o he expe imen al da a han LES. The au ho s also examined simple u bulence models ep esen ed by he RNG and ealizable k-ε models. Howe e , hese models we e unable o p edic he in e nal ai -co e. Galbia i e al. [12] compa ed he LES simula ion wi h RNG k-ε and RSM models. They ound ha he a ia ion among used models was insigni ican when compa ed o de ia ion in esul s om he empi ical co ela ions. They also no ed ha he low ield was consis en o he LES and k-ε model, while RSM had some disc epancies. Baha anchi e al. [13] examined se e al schemes o cap u e he liquid-ai in e ace using a 2D simula ion wi h he RNG k-ε u bulence model. A geo- econs uc scheme was ound o be he mos sui able o cap u ing he ai -co e. They also discussed i i is necessa y o model a su ace ension and ound ha he su ace ension had e ec only i he Webe numbe is smalle han 204. F om a p ac ical poin o iew, i had a negligible e ec on he de eloped low. In his pape , 2D and 3D nume ical models o he PS a omize a e compa ed. The nume ical sol e used bo h lamina and u bulen app oach. The nume ical esul s a e also compa ed wi h expe imen al da a om [1]. 2 Expe imen al se up The expe imen s we e pe o med on a cold es bench a he B no Uni e si y o Technology. 2.1. The A omize A small-sized Simplex a omize used in a combus ion chambe o a u boje ai c a engine was in es iga ed. Due o small p opo ions, see he dimension in Fig. 1, he op ical measu emen inside he a omize would be di icul . To o e come his issue he anspa en scaled model was manu ac u ed. The scaled model was 10 imes la ge han he o iginal a omize and i was made om cas PMMA. To main ain he same low beha iou , dimensionless numbe s such as Reynolds numbe , Swi l numbe , Webe numbe and F oude numbe mus be kep he same. Reynolds numbe ela ed o he inle po s is de ined: = , (1) whe e dp is he hyd aulic diame e o he inle po , wp is he mean eloci y inside he po and  is he liquid kinema ic iscosi y. The swi l numbe S0 is he a io o swi l momen um o he axial momen um, and o he Simplex a omize s i can be de ined as [14]: = , (2) whe e o = do/2, do and s a e in Fig. 1 and Ai is he o al a ea o he inle po s. The S0 is iden ical o bo h he o iginal and he scaled a omize . Fig. 1. A ske ch o he o iginal a omize wi h he main dimensions in mm. The anspa en a omize had all dimensions 10 imes la ge . F oude numbe , F , compa es he e ec o g a i y wi h he ene gy o he bulk low and can be calcula ed as:  =2(− )  (3) whe e oa is he adius o ai -co e in he exi o i ice, Q is he olume low a e. To minimalize he e ec o g a i y, i is necessa y o keep F >> 1. Webe numbe , We, is de ined as he a io o ine ia and he su ace ension o ce. The su ace ension o ce usually has negligible e ec inside he swi l chambe . Acco ding o [13] and [14], ma ching he Webe numbe can be sa ely igno ed. Simila ly, no e ec o su ace ension was obse ed in ou ini ial CFD simula ions. Bo h he o iginal and scaled a omize s we e ope a ed a oom empe a u e o 23 °C using JET A1 wi h physical p ope ies: σ = 0.029 kg/s2, μl = 0.0016 kg/(m·s) and ρl = 795 kg/m3. The o iginal a omize was ope a ed a he inle p essu e Δpi = 1 MPa, he inle mass low a e was  = 7.3 kg/h. The mean eloci y inside he inle po s was wi = 5.16 m/s, which esul ed in Rep = 1021. The scaled a omize was ope a ed a he same Rep hus he inle p essu e had o be educed o 10 kPa. The F o o iginal a omize was 293 bu i dec eased o 9.3 o he scaled a omize . 2.2. Expe imen al se up The high-speed came a Pho on SA-Z was used o documen he spa ial and empo al beha iou o he ai - co e inside he scaled anspa en model o he a omize . The came a was se o 4,000 ames pe second wi h a ame esolu ion o 1024×1024 px. The came a was used a backli illumina ion wi h backg ound LED panel. The ypical esul is shown in Fig. 2. 2 EPJ Web o Con e ences 213, 02055 (2019) h ps://doi.o g/10.1051/epjcon /201921302055 EFM 2018 Fig. 2. High-speed isualiza ion wi h LDA measu emen axis. The Lase Dopple Anemome e (LDA), a 2D FlowExplo e made by Dan ec Dynamics A/S was used o measu e he swi l eloci y p o ile. The measu emen s we e pe o med in he h ee axial dis ances o 2.5, 8 and 13 mm om he op o he swi l chambe . Howe e , only he esul s om 8 mm axis a e p esen ed he e. The loca ion o he measu emen axis is shown in Fig. 2. The esul s we e co ec ed acco ding o Zhang [15] due o he di e en e ac i e index o he liquid and a omize body. Fo de ailed desc ip ion o he expe imen al se up see [1]. 3 Nume ical se ups The ansien CFD simula ions we e made using comme cial so wa e Ansys Fluen 18.1. A 2D axisymme ic model wi h a swi l, shown in Fig. 3, and a h ee-dimensional 3D model wi h pe iodic bounda y condi ions, as shown in Fig. 4, we e used. As he a omize had h ee inle po s, a 120° sec ion was modelled. P essu e- eloci y coupling was done using PISO scheme. The liquid-ai in e ac ion was cap u ed by a Volume o Fluid model wi h a geo- econs uc scheme o Comp essi e scheme was used in he case o LES. The inle bounda y was se o he eloci y inle wi h wi = 5.16 m/s. In he case o he 2D model, i was se o conse e he mass low a e in he adial di ec ion and conse e he angula momen um in he angen ial di ec ion. The p essu e ou le was se o he ou e bounda ies. The no-slip condi ion was used on he in e nal wall bounda ies. The ai was ea ed as bo h wi h cons an densi y and as an ideal gas wi h ene gy equa ion. Va iable ime s epping was used wi h a Cou an numbe 0.5. A ypical ime s ep size was app oxima ely 2×10-8 s. As he low was ea ed as ansien , a e eaching a quasi-s a ic solu ion, ime a e aging was applied. Se e al u bulence models based on a Reynolds- a e aged Na ie -S okes (RANS) equa ion, LES and lamina sol e we e used and compa ed o achie e esul s compa able wi h he expe imen . De ailed ma hema ical desc ip ion o he used models can be ound in [16]. Simple wo-equa ion models ep esen ed by k-ε and k- ω we e chosen o hei good accu acy o indus ial applica ions. Those models de e mine a u bulen leng h scale and a ime scale by sol ing wo sepa a e anspo equa ions. The k-ε model is based on a anspo equa ion o kine ic ene gy k and dissipa ion a e ε. In his pape , he RNG k-ε model o swi l dominan lows was used as i designed o swi ling lows. The k-ω SST model wi h low-Re co ec ion was chosen as he second wo-equa ion model. This model combines he s anda d k-ω model o nea wall ea men and he k-ε model in he ee s eam low. Reynolds S ess model (RSM) is he mos ad anced RANS model o he swi l dominan lows as i sol es all he anspo equa ions o he Reynolds s esses. This model was used wi h a low-Re and shea low co ec ion. La ge Eddy Simula ion (LES) was ep esen ed by Wall-Adap ing Local Eddy Viscosi y model (WALE). Howe e , i was pe o med on he same mesh as he RANS models, hus i is e e ed he e as a Coa se LES. The e we e se no pe u ba ions in he eloci y inle . 3.1. Mesh independence es The all quad/hex s uc u al meshes we e c ea ed in Ansys Meshing o bo h 2D and 3D models. The 3D mesh used ma ch con ol on he pe iodic bounda ies. An a e age skewness o 2D mesh was 0.058 and an a e age aspec a io o 1.18. The mesh independency es was made o he 2D model. The inle p essu e was ound o be he mos sensi i e pa ame e o he numbe o cells. As he in e nal ai -co e blocks pa o he exi o i ice, i is necessa y o cap u e he ai -co e bounda y wi h high accu acy. Thus, he mesh needed o be ine nea he in e ace. The e ec o mesh esolu ion h ough he adius o he exi o i ice is shown in Fig. 5. The e o in he p edic ion o he inle p essu e is apidly inc easing i he numbe o cells is lowe han 20. Fo he 3D simula ion, a comp omise be ween calcula ion speed and accu acy was chosen as he mesh wi h a esolu ion o 25 cells h ough he adius o he exi o i ice was used. This 3D mesh had a o al o 459,591 cells while he inal 2D mesh con ained 30 cells h ough he adius o he exi o i ice wi h a o al o 46,645 cells. Fig. 3. 2D mesh wi h bounda y condi ions. 3 EPJ Web o Con e ences 213, 02055 (2019) h ps://doi.o g/10.1051/epjcon /201921302055 EFM 2018 Fig. 4. 3D mesh wi h bounda y condi ions. Fig. 5. Mesh independency s udy. 4 Resul s and discussion In his chap e , he CFD simula ions a e compa ed wi h he expe imen al da a in e ms o he discha ge pa ame e s such as he discha ge coe icien CD, SCA and a omize e iciency , he ai -co e dimensions and he eloci y p o iles inside he swi l chambe . In he inle po , he lamina low can be assumed as Rep = 1021. Howe e , i may change o ansien o e en u bulen low inside he exi o i ice as he eloci y inc eases. Ne e heless, Chinn [14] o e old he lamina low e en o e y high Rep as he swi l dominan low ends o lamina ise he low i sel and he a omize is oo small o de elop a ully u bulen low. Ini ial CFD simula ions we e pe o med o bo h, he o iginal and scaled a omize . The dimensionless ai -co e diame e s, dimensionless eloci y p o iles, SCA and CD we e iden ical o bo h a omize s, he e o e in his pape , he esul s a e shown he e in a dimensionless o m and hey a e based on he CFD simula ions o he o iginally sized a omize . The di e ence be ween incomp essible and comp essible gas phase was also in es iga ed bu no e iden e ec was ound. This is in ag eemen wi h [17], whe e Mach numbe smalle han 0.3 ensu es ha he ai phase can be sa ely handled as incomp essible. Conside ing he maximal ai eloci y in ou simula ions, Mach numbe was much smalle han 0.1; hus, in his pape , he simula ions a e done wi h he cons an ai densi y. 4.1. Discha ge pa ame e s An accu a e p edic ion o he ai -co e dimensions is he c ucial aspec as i signi ican ly a ec s he discha ge pa ame e s. The discha ge coe icien CD is an impo an discha ge pa ame e de ined as a a io o he inle mass low o he heo e ical mass low a e: = 2Δ, (4) whe e Ao is he c oss-sec ional a ea o he exi o i ice. Fo he PS a omize s, he CD is ela i ely low as a po ion o he exi o i ice c oss sec ion is occupied by he ai -co e. The e iciency o con e sion o he inle p essu e ene gy in o kine ic ene gy a he a omize exi is called he a omize e iciency, and i is de ined as: =  2Δ, (5) whe e o is he eloci y o he liquid shee a he a omize discha ge. I was no possible o measu e o di ec ly, hus he liquid shee eloci y had o be es ima ed om he high-speed eco ds and i is measu ed app oxima ely 1 mm downs eam om he a omize exi o i ice. PIVlab so wa e was used o es ima e he eloci y o he liquid shee as i is shown in Fig. 6. The o was ob ained om he simula ions in he same downs eam dis ance as in he expe imen . The swi l eloci y componen was neglec ed in bo h cases, only he axial and adial eloci y componen s we e conside ed. Fig. 6. Veloci y ec o s om PIVlab so wa e. 0.80 0.85 0.90 0.95 1.00 1.05 1.10 0 10 20 30 40 50 Inle p essu e [MPa] Cell coun [–] 4 EPJ Web o Con e ences 213, 02055 (2019) h ps://doi.o g/10.1051/epjcon /201921302055 EFM 2018 Table 1. The discha ge pa ame e s and ai -co e dimensions. Δpi CD das/do dao/do SCA o ηn [MPa] [-] [-] [-] [deg] [m/s] [%] Expe imen al da a 1.00 0.37 0.47 0.71 72 36 0.51 LES 3D 1.03 0.36 0.31 0.67 75 41 0.63 RSM 3D 0.91 0.38 0.31 0.65 72 41 0.73 Lamina 3D 1.00 0.37 0.32 0.67 73 42 0.71 RSM 2D 0.82 0.41 0.23 0.65 72 40 0.77 Lamina 2D 1.01 0.37 0.37 0.7 74 46 0.83 k-ω SST 2D 0.39 0.59 – – – 17 0.29 RNG k-ε 2D 0.28 0.70 – – – 25 0.91 Fig. 7. Phases, ed = ai , blue = liquid. Top: 2D k-ω model, bo om: 2D lamina model In he expe imen , he in e nal ai -co e had an almos cons an diame e along he swi l chambe and ex ends in diame e in he exi o i ice. The wo-equa ion u bulence models k-ε and k-ω we e unable o p edic he ai -co e inside he swi l chambe . The ypical low pa e n om hose models is shown in Fig. 7. As he ai -co e is no p esen ed, all he discha ge pa ame e s a e p edic ed wi h eno mous e o – see able 1. These models p obably o e p edic ed he u bulen eddy iscosi y which esul s in a dec ease in he swi l eloci y and consequen ly he ai -co e decayed. We exclude hose models om u he e alua ions. The RSM model was able o cap u e he ai -co e shape co ec ly. Howe e , i unde es ima es i s dimension. The smalle ai -co e leads o he highe CD as he smalle ai - co e block a smalle po ion o he exi o i ice. In he case o 2D RSM simula ion, he ai -co e diame e was unde es ima ed by 20% and by 10% in he case o he 3D model. Bo h 2D and 3D lamina models and LES model we e able o p edic he inle p essu e, CD and he ai -co e dimensions closely. Howe e , he 2D lamina model signi ican ly o e p edic ed he eloci y o he discha ged liquid shee o and he a omize e iciency. The LES p edic ed he a omize e iciency mos closely bu i was s ill o e p edic ed abou 20%. The eason may be ha he CFD model neglec ed he su ace oughness o he eal a omize . 4.2. Veloci y p o iles The swi l eloci y p o iles a e shown in Fig. 8. The wo- equa ion models a e excluded. The swi l eloci y eaches i s maximum a he ai -co e su ace, which is ypical o a Rankine o ex. In he expe imen , i was six imes g ea e han he mean eloci y inside he inle po . All he nume ical models we e able o p edic he posi ion o eloci y maximum. Ne e heless, he 2D models we e unable o cap u e he magni ude o he eloci y peak accu a ely as he lamina 2D model o e p edic ed he swi l eloci y maximum o abou 15% while he 2D RSM unde p edic ed i abou 15%. This co ela es well wi h he dimension o he ai -co e om Table 1 whe e he 2D lamina model showed he la ges dimensions o he in e nal ai -co e, while he 2D RSM pe o med opposi e. Only small a ia ions in he swi l eloci y p o iles we e ound a di e en axial dis ances om he op o he swi l chambe as i was shown in [1]. The adial and axial eloci y p o iles a e shown in Fig 8 and Fig 9 espec i ely. The adial eloci y is e y low compa ed o he o he eloci y componen s. The 3D RMS and 3D lamina models p edic ed a posi i e local maximum inside he ai -co e while o he models no . The 2D RSM, on he o he hand, showed a nega i e local maximum in he posi ion o / s = 0.2. The axial eloci y was almos ze o up o he posi ion o / s = 0.2 whe e i s a s apidly g ow and eaches a maximum o 4×wi a / s = 0.05. Simila ly, as in he case o swi l eloci y, he 2D lamina model o e p edic ed he axial eloci y magni ude while 2D RSM unde p edic ed i compa ed o 3D models. 5 EPJ Web o Con e ences 213, 02055 (2019) h ps://doi.o g/10.1051/epjcon /201921302055 EFM 2018 Fig. 8. Swi l eloci y. Fig. 9. Radial eloci y. Fig. 10. Axial eloci y. 5 Conclusions The a omize discha ge pa ame e s and he eloci y p o iles we e p edic ed using a ious CFD models and he esul s we e compa ed wi h he expe imen al da a. The su ace ension and gas comp essibili y we e neglec ed as hey ha e no p ac ical impac on he esul s. The simple wo-equa ion models k-ε and k-ω we e unable o p edic he ai -co e and he esul s a e wo hless. The 2D lamina model was able o closely p edic CD and SCA bu o e es ima ed swi l eloci y, liquid shee eloci y o and ηn. The bes esul s we e ob ained using he 3D lamina and 3D LES model, which gi e he same CD and SCA, bu he LES model had a be e p edic ion o ηn in compa ison wi h he expe imen . Fu he wo k will be ela ed o he alida ion o ime- dependen a iables as ai -co e ins abili ies and su ace wa es and also ull 3D simula ion will be included as he pe iodic bounda y condi ions assume ha he cen e o he ai -co e is ixed along he cen eline o he swi l chambe . This wo k has been suppo ed by he p ojec No. GA18-15839S unded by he Czech Science Founda ion, he p ojec “Compu e Simula ions o E ec i e Low-Emission Ene gy” unded as p ojec No. CZ.02.1.01/0.0/0.0/16_026/0008392 by Ope a ional P og amme Resea ch, De elopmen and Educa ion, P io i y axis 1: S eng hening capaci y o high-quali y esea ch and p ojec No. RV9080000313 ounded by Facul y o Mechanical Enginee ing, B no Uni e si y o Technology. Re e ences 1. M. Maly, J. Jedelsky, J. Slama, L. Janacko a, M. Sapik, G. Wigley, and M. Jicha, 123, 10, (2018) 2. D. Coope , A. Yule, and J. J. Chinn, ILASS, (1999) 3. W. Qian, X. Hui, C. Zhang, Q. Xu, Y. Lin, and C. J.Sung, CFaE, 074A, (2017) 4. A. H. Le eb e and V. G. McDonell, A omiza ion and sp ays, (2017) 5. J. J. Chinn., AaS, 19(3), (pa 1), (2009) 6. J. J. Chinn., AaS, 19(3), (pa 2), (2009) 7. G. Amini., 2016, " 79, 11 (2016) 8. E. Wimme , and G. B enn, IJMF, (2013) 9. A. Yule, and J. J. Chinn, ILASS, (1997) 10. B. Sume , N.E kan, O. Uzol, and I. Tunce , ICLASS, (2012) 11. J. Madsen, B. H. Hje age , and T. Solbe g, ILASS, 6, (2004) 12. C. Galbia i, S. Tonini, P. Con i, and G. E. Cossali, JPP, 6 (2016) 13. A. Abbasi Baha anchi, A. No din Da us, Ansa i, M., and E. Abbasi Baha anchi, IMECE, 12 (2012) 14. J. J. Chinn, ILASS, (2008) 15. Z. Zhang, LDA Applica ion Me hods: Lase Dopple Anemome y o Fluid Dynamics, (2010) 16. Ansys®, Fluen Theo y Guide, Release 18.2. (2017) 17. J. D. Ande son, Fundamen als o Ae odynamics, (2001) 0 1 2 3 4 5 6 7 8 0 0.2 0.4 0.6 0.8 1 w/wi[–] / s [–] 3D Lamina 3D LES 3D RSM 2D lamina 2D RSM expe imen -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0 0.2 0.4 0.6 0.8 1 /wi[–] / s[–] 3D Lamina 3D LES 3D RSM 2D lamina 2D RSM -8 -6 -4 -2 0 2 4 6 0 0.2 0.4 0.6 0.8 1 u/wi[–] / s [–] 3D Lamina 3D LES 3D RSM 2D lamina 2D RSM 6 EPJ Web o Con e ences 213, 02055 (2019) h ps://doi.o g/10.1051/epjcon /201921302055 EFM 2018