Empirical correlation for spray half cone angle in plain-jet airblast atomizers

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 Empi ical co ela ion o sp ay hal cone angle in plain-je ai blas a omize s And ás U bán a , Bálin Ka ona a , Milan Malý b , Jan Jedelský b , Vik o Józsa a,⁎ a Budapes Uni e si y o Technology and Economics, Facul y o Mechanical Enginee ing, Depa men o Ene gy Enginee ing, 1111, Budapes , Műegye em kp. 3., Hunga y b Facul y o Mechanical Enginee ing, B no Uni e si y o Technology, Technicka 2896/2, 616 69 B no, Czech Republic ARTICLE INFO Keywo ds: Ai blas Rapeseed oil Sp ay cone angle Image p ocessing Th eshold A omiza ion ABSTRACT Plain-je ai blas a omize s a e widely used in indus ial applica ions. The li e a u e con ains nume ous pape s on Sau e mean diame e , howe e , he e is no es ima ion me hod a ailable o sp ay cone angle, SCA, which de i a ion is he p ima y goal o his s udy. Fou dis inc , p ac ical model liquids we e analyzed: dis illed wa e , diesel oil, ligh hea ing oil, and c ude apeseed oil. The a omizing p essu e and liquid p ehea ing empe a u e we e a ied in he ange o 0.3–2.4 ba and 25–85 °C, espec i ely. This la e pa ame e enabled a wide and con inuous liquid kinema ic iscosi y in es iga ion ange o 0.33–44.2 mm 2 /s. The esul ing sp ays we e imaged a a ious shu e speeds o p ope edge de ec ion. An adap i e h esholding algo i hm was de eloped in Ma lab so wa e en i onmen o calcula e SCA. The me hodology is discussed in de ail o acili a e he e-im- plemen a ion o his echnique since he e is no gene ally accep ed me hod o SCA measu emen . SCA in e sely a ied wi h liquid densi y and ollowed a powe law wi h he ai - o-liquid mass low a io; howe e , he de i ed exp ession also pe o med well by eplacing ai - o-liquid mass low a io by ei he Mach numbe o momen um lux a io. A simple empi ical equa ion was de i ed, which allows he es ima ion o SCA o ai blas a omiza ion in a wide pa ame e ange wi hin a 3.5% de ia ion. The measu ed esul s we e e alua ed in he ligh o high- speed came a images in he icini y o he nozzle; i was ound ha inc eased liquid je b eakup leng h dec eases SCA while in ense ligamen o ma ion inc eases i . 1. In oduc ion The mos impo an pa ame e o a liquid sp ay is i s mean d ople size, which de e mines he a e age e apo a ion/solidi ica ion ime, impingemen , and he gene al in e ac ion wi h he su ounding gas low. The second highligh ed pa ame e is he Sp ay Cone Angle, SCA, which cha ac e izes sp ay sp eading. I bea s an emphasized ole in nume ous applica ions, including cooling [1], me allu gy [2], and combus ion sys ems [3]. While he e a e a ew in e na ionally accep ed and used mean d ople diame e de ini ions – depending on he appli- ca ion and ocus –, he e is no gene al de ini ion o SCA [4]. A eason o i is he wide a ie y o exis ing a omize geome ies and ope a ing condi ions. P ac ical a omize s wo k in a u bulen low ield ha couples wi h he d ople mo emen [5].SCA de e mina ion o swi l a omize s shows a high sensi i i y on he a omize cons an [6], and analy ical app oxima ions a e a ailable o in iscid low [7]. The li - e a u e is signi ican ly hinne o o he a omize ypes in which SCA is de e mined by he esul ing sp ay ins ead o a well-localized liquid shee . Hence, he d ople - u bulence in e ac ion makes sp ay edge de- ec ion a non i ial ask [8]. Upon de ining he edges, SCA can be easily es ima ed. A gene al ecommenda ion o SCA measu emen o gasoline uel injec o s was made by Hung e al. [9], including sp ay edge de e mi- na ion. They ha e highligh ed ha he sp ay can be cu ed, hence a well-de ined dis ance om he nozzle should be se . Ne e heless, hei esul s canno be gene alized o ai blas a omize s, which is he subjec o his pape due o he well-es ablished geome y anges and speci i- ca ions in ecip oca ing engine applica ions. As a consequence, 60 imes he liquid o i ice diame e was chosen o he p esen analysis ha is used o p essu e a omize s [4] and lies in he sel -simila egion o annula je s [10]. The sp ay edge de ec ion can be pe o med by ei he imaging [11] o non-imaging op ical echniques [12]. The image e- solu ion o cu en comme cial came as is high enough o pe o m ac- cu a e measu emen s, also used in he cu en s udy. Ma ínez-Gal án e al. [1] and Bizjan e al. [13] simila ly aced he blu y sp ay edge p oblem and used a h esholding echnique. Thei idea was imp o ed in he p esen s udy, i.e., by using an adap i e app oach, discussed in Subsec ion 2.2. A simila algo i hm was success ully applied in pa icle de ec ion in mic oscopy [14] and X- ay image p ocessing [15]. Since a sp ay image is an ins an aneous map o d ople s, a e aging is necessa y o elimina e his a ia ion. I can be done by a e aging a ce ain numbe o images [1] o using a p ope exposu e ime. In he p esen h ps://doi.o g/10.1016/j. uel.2020.118197 Recei ed 29 Feb ua y 2020; Recei ed in e ised o m 14 Ap il 2020; Accep ed 22 May 2020 ⁎ Co esponding au ho . E-mail add ess: [email p o ec ed] (V. Józsa). Fuel 277 (2020) 118197 A ailable online 31 May 2020 0016-2361/ © 2020 The Au ho (s). Published by Else ie L d. This is an open access a icle unde he CC BY license (h p://c ea i ecommons.o g/licenses/BY/4.0/). T pape , his la e me hod was used, wi h an ex ension o e alua ing he SCA a ia ion wi h he shu e speed. Ai blas a omize s we e de eloped o eplace p essu e swi l a omi- ze s, which ha e low lexibili y in he liquid low a e [16]. Tu ndown a io o 50:1 was made a ailable h ough go e ning he a omiza ion p ocess by he high- eloci y ai low; he liquid is injec ed a a ew m/s wi hou lowe limi a ion. This a omize ype belongs o he win- luid amily and elies on he a ailable high-p essu e gas, which blows o e he liquid su ace, leading o ligamen hen d ople o ma ion; he go e ning physics was e iewed by Lashe as and Hop inge [17]. The p esen ly in es iga ed plain-je ai blas a omize has a simple pipe-in- pipe design ha makes i s manu ac u ing and main enance easy. Sp ay cha ac e is ics o ai blas a omiza ion we e in es iga ed by Ma e al. [18] and Gad e al. [19]; ne e heless, hey did no aim o de i e an empi ical co ela ion be ween he ope a ing pa ame e s and SCA which is he p ima y goal o his s udy. Ta eq e al. [20] in es iga ed he SCA o a p e ilming ai blas a omize , and, simila ly, hey did no de i e any co ela ion o his pa ame e . The liquid b eakup p ocess go e ns SCA, hence, he liquid disin- eg a ion in he icini y o he nozzle g ea ly a ec s he inal esul . Wa anawanyoo e al. [21] in es iga ed a win- luid a omize in a si- mila ai - o-liquid pa ame e ange, which is analyzed p esen ly, de- ailed in Subsec ion 2.1. They iden i ied a ious b eakup modes and es ima ed only he d ople size dis ibu ion 100 mm downs eam o he nozzle wi hou SCA e alua ion. Cha alampous e al. [22] analyzed he liquid je b eakup leng h by h ee di e en echniques, concluding ha e en a simple elec ical connec i i y echnique can lead o signi ican esul s; howe e , i equi es an in usi e p obe. The liquid je b eakup leng h a ec s he sp ay sp eading since he high- eloci y ai je quickly decays as i in e ac s wi h he low- eloci y liquid je . Hence, g ea e liquid je b eakup leng h leads so smalle SCA. A no el, dual-angle pa icle acking elocime y echnique o sp ay and d ople b eakup measu emen was p oposed by Pham e al. [23], which enables highly de ailed acking o he d ople b eakup p ocess. I nume ous pa ame e s in luence a quan i y, he use o he Buckingham π heo em helps in inding he p ope co ela ion h ough de i ing non-dimensional quan i ies [24]. The absence o such an in- es iga ion o SCA o ai blas a omize s s a s wi h he analysis o he possible pa ame e s a ec ing a omiza ion, which a e discussed in de ail o , e.g., de e mining he Sau e Mean Diame e , SMD [25]. An ea ly wo k by Ab amo ich [26] on p essu e a omiza ion concluded ha SCA depends on he densi y a io o ai and liquid. Ul ima ely, i was ound ha Ohneso ge and Webe numbe s de e mine he a omiza ion mode, hence SCA is also a ec ed by hem [4]. This pape is a successo o ou p e ious wo k in which he SMD o he sp ay was deeply in es iga ed [27]. The p esen ly in es iga ed liquids a e he same o consis ency: dis illed wa e (W), s anda d diesel oil (D, EN 590), ligh hea ing oil (LHO), and c ude apeseed oil (RO). The no el y o he p esen pape is p incipally illing a scien i ic gap by de i ing an empi ical co ela ion o SCA o a plain-je ai blas a omize . Since he d ople o ma ion is la gely depending on he nea - nozzle egime o he sp ay, he liquid s uc u es o he p ima y b eakup a e isually e alua ed. The hi d goal is o p o ide a gene al SCA de- e mining amewo k o make his p ocedu e anspa en and easy o implemen o p ac ical applica ions whe e measu emen echniques beyond a comme cial digi al came a a e seldom a ailable. 2. Ma e ials and me hods Fi s ly, he expe imen al se up is de ailed, along wi h he discussion o he measu emen unce ain ies. Then he image p ocessing me ho- dology is desc ibed o p o ide a gene al amewo k o SCA analysis o a possible e-implemen a ion o his echnique. Las ly, he de i a ion o he non-dimensional quan i ies and he empi ical co ela ion o SCA a e de ailed. 2.1. Expe imen al se up The schema ic d awing o he a omiza ion es ig shown in Fig. 1a, ea u ing he nozzle ip. The liquid je was in oduced o he plain-je ai blas a omize ia a cen al pipe wi h 0.4 mm inne diame e while inne and ou e diame e s o he annula a omizing ai o i ice we e 0.8 mm and 1.6 mm, espec i ely. The gauge p essu e o he a omizing ai , p g , was se by a egula o al e in he ange o 0.3 and 2.4 ba in 5 s eps wi h 1 kPa accu acy. The ai was also used o p essu ize he liquid ank o main ain a low ye smoo h liquid low a e which was 0.35 g/s o all he ou liquids: D, LHO, RO, and W. The liquid olume low a e was measu ed by an Omega FPD3202 low me e which has < 2.7% Nomencla u e La in le e s A[deg] cons an in he SCA co ela ion a[m/s] speed o sound =ALR m m/ A L [–] ai - o-liquid mass low a io B[–] cons an in he SCA co ela ion d 0 [mm] liquid pipe inne diame e o he a omize m [kg/s] mass low a e =w aMa / [–] Mach numbe =MFR w w· / · AALL 2 2 [–] momen um lux a io N 1 ,N 2 [–] non-dimensional numbe s =Oh We /Re [–] Ohneso ge numbe p[ba ] p essu e R[J/(kg·K)] speci ic gas cons an R 2 [–] coe icien o de e mina ion =w dRe · / R0 [–] Reynolds numbe S ,A [–] ela i e s anda d de ia ion o Acons an SCA [deg] sp ay cone angle SMD [μm] Sau e mean diame e T[°C] empe a u e w[m/s] eloci y =w dWe · · / R 2 0 [–] Webe numbe G eek le e s κ[–] speci ic hea a io μ[kg/(m·s)] dynamic iscosi y ν[m 2 /s] kinema ic iscosi y ρ[kg/m 3 ] densi y σ[N/m] su ace ension 0 ambien 25 °C a 25 °C Aa omizing ai ga omizing ai gauge Lliquid R ela i e Abb e ia ions D diesel oil LHO ligh hea ing oil RO c ude apeseed oil SSE sum o squa ed es ima e o e o s W dis illed wa e . Tilde deno es non-dimensional numbe s de i ed om a single physical quan i y. A. U bán, e al. Fuel 277 (2020) 118197 2 unce ain y a 95% le el o signi icance. The calib a ion was pe o med a six poin s a ound he desi ed low a e, using he se up p esen ed in Fig. 1. An elec ic hea e was ins alled o he liquid line o se he p ehea ing empe a u e, T L , be ween 25 and 85 °C in i e 15 °C s eps. The liquid empe a u e was con olled by a PID con olle , using a B class P 100 esis ance he mome e wi h an accu acy o < 0.8 °C. The condi ions lis ed abo e esul ed in 100 di e en condi ions in o al wi h a wide pa ame e ange in su ace ension (20.7–32.1 and 62.3–72.1 mN/m), kinema ic iscosi y (0.33–44.2 mm 2 /s), and liquid densi y (808–997 kg/m 3 ), which a e cha ac e is ic o liquid uels in combus- ion. No e ha he gap in su ace ension is p esen due o he sig- ni ican ly highe alues o wa e han o he hyd oca bon liquids. Ne e heless, he p incipal aim in selec ing he liquids was o ensu e a con inuous ange in iscosi y. The measu ed ma e ial p ope ies, along wi h hei co esponding unce ain ies, a e discussed in ou p e ious wo k [27]. A an was used o emo e he mis o enable he acquisi ion o clea images wi hou a ec ing he SCA. I did no wo k lawlessly a high p g when e y ine sp ay was gene a ed, discussed in Subsec ion 2.2. The ange o he key non-dimensional numbe s is summa ized in Table 1 in Subsec ion 2.3. The shu e speed was expec ed o a ec SCA as longe exposu e ime allows mo e in o ma ion o be collec ed in he pe iphe al egime whe e he d ople mass lux is low he e. Hence, 1/60 s, 1/80 s, and 1/ 100 s shu e speeds we e used o ge ela i ely sha p images. Fi e pic u es we e eco ded wi h all h ee se ings, which means 1500 images in o al o be p ocessed. The con e sion ac o in hese images was 15.5 pixels/mm. The sp ay was imaged in on o a black pla e by a Panasonic DMC-TZ80 comme cial digi al came a and illumina ed om he on in a small angle by a comme cial 50 W LED spo ligh , shown in Fig. 1b. The image esolu ion was 18 MP, while he ocal a io was se o 4.3. Since ai blas a omiza ion gene a es dilu e sp ay, he posi ion o he LED ligh had no no able in luence on he calcula ed SCA alues, which was ca e ully checked. In o de o unde s and he d ople o ma ion and SCA a ia ion be e , a high-speed came a, a FASTCAM SA-Z ype 2100 K-M−16 GB (Pho on, Japan) wi h long-dis ance mic oscope 12X Zoom lens (NAVITAR, USA) composed o 2X F-moun adap e ( ype 1–62922), 12 mm F.F zoom lens ( ype 1–50486) and a ached 0.25X lens ( ype 1–50011), was used o cap u e he b eakup o he liquid je in he i- cini y o he a omize nozzle; he op ical se up is shown in Fig. 1c. The sp ay was illumina ed om he backg ound by an HPLS-36DD18B (Ligh speed Technologies, Inc., USA) pulsed LED ligh sou ce. The ligh pulse du a ion was 100 ns. No e ha he eco ding o hese images was pe o med ea lie , along wi h he Phase Dopple measu emen s in e [27], using he same a omize and liquid p ehea e appa a us. The di e ence was ha he maximum T L was highe han he p esen ly se 85 °C alue. Hence, T L was 90 °C o W and 100 °C o he h ee o he liquids o high-speed imaging esul s. The shu e speed was 1/ 630,000 s o 159 s, and he ame a e was 160,000 ames/second. The image esolu ion was 256 × 256 pixels, which is equi alen o 3.2 × 3.2 mm physical size wi h a con e sion ac o o 80 pixels/mm. The high ame a e was necessa y o cap u e he mo emen o he luid packe s while he a omizing discha ge eloci y was in he ange o 208–420 m/s, acco ding o p g = 0.3–2.4 ba . Since he high-speed came a was ocused on he icini y o he nozzle, SCA canno be de- duced om hese esul s. Ne e heless, he d ople o ma ion and hei mo ion due o u bulence allow a be e unde s anding o he a ia ion o SCA. 2.2. Image p ocessing To p ocess a la ge numbe o images wi hou he bias o manual e alua ion, a Ma lab code was de eloped o his pu pose. I s low cha is shown in Fig. 2. Since he elemen a y p ocesses a e simple manip- ula ion algo i hms, he un ime is in he ange o one second. The i s s ep is eading he image o be p ocessed. Then he image has o be cu o a uni o m shape, which is c ucial o he e alua ion, shown in Fig. 3a. P e-calib a ion is equi ed o c opping, i.e., he pixels a e con e ed o physical dimensions. The ou le diame e o he liquid je is 400 µm, being equal o he inne diame e o he uel pipe. I was conside ed as a e e ence o image calib a ion, also suppo ed by he high-speed images ocusing on he p ima y b eakup egion, discussed in Subsec ion 3.2. Nex , he esul ing image was subjec ed o gamma co ec ion and g ayscale con e sion, shown in Fig. 3b. Gamma be ween 0 and 1 makes he image ligh e while alues exceeding one shi s i owa ds black. A cons an alue o 1.1 was used in he p esen s udy o emo e a po ion o he isible ine mis and image noise, based on he ollowing obse a ions. Gene ally, excessi e gamma alues a ec SCA, Fig. 1. Schema ic o a) liquid and a omizing ai piping and hei ins umen a- ion and op ical se up o b) SCA and c) p ima y b eakup measu emen . Table 1 The main non-dimensional ange o he liquids. D LHO RO W p g [ba ] min. 0.3 0.3 0.3 0.3 max. 2.4 2.4 2.4 2.4 ALR [-] min. 0.78 0.78 0.78 0.78 max. 2.07 2.07 2.07 2.07 Re A [-] min. 9166 9173 9178 9192 max. 30,712 30,723 30,734 30,751 Re L /10 6 [-] min. 22.7 5.04 1.57 91.2 max. 115.4 51.8 21.0 380 We A [-] min. 824.7 711.4 659.2 294.4 max. 5582 5080 4375 1859 Oh L [-] min. 0.014 0.0309 0.072 0.00274 max. 0.0325 0.140 0.442 0.00528 Ma [-] min. 0.62 0.62 0.62 0.62 max. 1.45 1.45 1.45 1.45 MFR [-] min. 5.71 5.96 6.19 6.86 max. 30.73 32.05 32.31 36.9 A. U bán, e al. Fuel 277 (2020) 118197 3 which should be a oided. This e ec was obse ed a , e.g., p g = 2.4 ba when ine sp ay was gene a ed and he mis became dense, making he edge de ec ion cumbe some. Highe iscosi y cases also caused biased esul s when excessi e gamma co ec ion was applied. Then he image was subjec ed o bina y con e sion whe e 1 is he whi e an 0 is he black. This p ocedu e was necessa y o p epa e he h esholding algo- i hm o calcula e he bounda ies o he sp ay. Final smoo hing was pe o med o ill he inne gaps, shown in Fig. 3c. By sea ching o he i s and las whi e pixels in a ow, he sp ay bounda ies can be de- e mined, esul ing in wo cu es. Fig. 3d shows he i ed lines o he le and igh edge o he sp ay bounda y, which in e sec ion angle gi es he SCA ul ima ely. Besides he shu e speed selec ion, inapp op ia e h eshold alue leads o biased esul s. Hence, sweeping wi h he h eshold le el was pe o med i s , shown in Fig. 4, o adap i ely ind he app op ia e h eshold. Ini ially, a small alue does no a ec he numbe o whi e pixels. Abo e 0.8 he e, only black pixels emain since he e was no ully whi e pixel. E en hough a black backg ound was used, he co e- sponding pa o he image was da k g ey in he images. Hence, he ini ial apid dec ease is due o he con e sion o he backg ound o black. Then smalle , ligh e pa ches o he image u n o black ha p ecedes he disappea ing o he subs an ial pa s o he sp ay, shown in Fig. 4b, as a local minimum be o e he jump o ze o. To ind he sp ay edges, his minimum was calcula ed, which adap i ely p o ided he app op ia e h eshold alue o SCA de e mina ion. Hence, no single h eshold alue was used in he p esen s udy, unlike in he case o Gamma. E en hough he e was a di e ence in he shu e speeds, he applied p ocedu e esul ed in highly simila esul s, and he discussed SCA alue in Subsec ion 3.1 was he a e age o hem. No e ha he a ia ion o he SCA alues was e y low, hence he a e aging ma - ginally a ec ed he inal esul . High p g esul ed in d ople s below 5 µm, which we e less p one o lea e he es sec ion due o hei low ine ia, shown in Fig. 5. To a oid biased SCA de e mina ion, excessi e mis suc ion should be a oided ha ine i ably esul s in coa se image quali y. As a consequence, a manual e iew o he il e ing p ocedu e was necessa y a a ew ope - a ing poin s. 2.3. Empi ical equa ion o mula ion By pe o ming he Buckingham π heo em on he ele an pa a- me e s in he p esen measu emen se ies and, he ollowing non-di- mensional numbe s we e de i ed. Fi s ly, he single physical quan i y a ios – and also hei ecip ocals – can be conside ed: = + +T T T ~( 273. 15)/( 273. 15) A A L (1) =° T T ~ 25 C/ L L (2) = ~/ A A L (3) =° ~/ LLL ,25 C (4) = ~/ A A L (5) =° ~/ LLL ,25 C (6) = =µ µ µ ~/ · /( · ) AA L AALL (7) = = ° ° ° µ µ µ ~/ · /( · ) LL C LL L LL ,25 ,25 C ,25 C (8) =° ~/ 25 C (9) Fig. 2. The image p ocessing low cha . Fig. 3. The s eps o image p ocessing and SCA de e mina ion. The axes show he numbe o pixels. Fig. 4. Image h esholding. a) pe cen age o whi e pixels and b) de i a i e o a). A. U bán, e al. Fuel 277 (2020) 118197 4 =ALR m m/ A L (10) =w aMa / A (11) whe e Tis he empe a u e, ρis he densi y, νis he kinema ic iscosi y, μis he dynamic iscosi y, σis he su ace ension, ALR is he ai - o- liquid mass low a io, m is he mass low a e, Ma is he Mach numbe , ais he local speed o sound, and w A is he ai eloci y a e adiaba ic expansion [27]. Tilde deno es non-dimensional numbe s de i ed om a single physical quan i y. Subsc ip 25 °C e e s o a 25 °C. a,w A , and ρ A a e calcula ed by Eqs. (12)–(14): = +a R T· ·( 273. 15) A (12) = + + w R T p p p 2· 1· ·( 273. 15)· 1 A A A A g ,0 1 (13) = + + + p p R T p p p·( 273. 15) · A A g A A A g ,0 1 (14) whe e R= 287 J/(kg·K) is he speci ic gas cons an o ai , κ= 1.4 is he Fig. 5. Raw images o D a omiza ion a T L = 25 °C and p g = a) 0.3 ba , b) 0.9 ba , c) 2.4 ba . No e he coa sening image quali y. Fig. 6. SCA as a unc ion o T L a a ious p g o all liquids. A. U bán, e al. Fuel 277 (2020) 118197 5 speci ic hea a io, p A is he ambien p essu e, which is also he a o- mizing ai p essu e a e he adiaba ic expansion. T A,0 is he a omizing ai empe a u e be o e eaching he nozzle. Subsc ip A e e s o a o- mizing ai – a e he expansion –, Ldeno es liquid, and T A,0 is he a omizing ai empe a u e be o e he nozzle. Equa ions (2),(4),(6), and (8) we e in oduced o allow he isola ed inclusion o liquid empe a- u e wi hou a ec ing he quan i ies which con ain he p ope ies o a omizing ai . Besides he single quan i y a ios, h ee u he highly ele an non-dimensional numbe s in sp ays we e also e alua ed, shown by Eqs. (15)–(18): =w dRe · / R0 (15) =w dWe · · / R 2 0 (16) = = µ dOh We /Re / · · 0 (17) =MFR w w· / · AALL 2 2 (18) whe e Re is he Reynolds numbe , We is he Webe numbe , Oh is he Ohneso ge numbe , and MFR is he momen um lux a io. w R =w A -w L is he ela i e eloci y be ween he wo s eams and σis he su ace ension. Since bo h densi y and iscosi y can be unde s ood as he Fig. 7. High-speed images in he icini y o he nozzle o all liquids and a ious p g and T L . No e ha he uppe limi o T L was 90 °C in he case o W ins ead o 100 °C. The physical size o he images is 3.2 × 3.2 mm. The numbe s in he op igh co ne a e We A and Oh. A. U bán, e al. Fuel 277 (2020) 118197 6 ma e ial p ope y o ei he he a omizing ai o he liquid, he i s h ee o hese numbe s also ea u e Ao Lsubsc ip in he ollowing o cla i ica ion. The main non-dimensional pa ame e s o he p esen in- es iga ion a e lis ed in Table 1.p g ,ALR, Re A , Ma, and MFR a e iden- ical o simila o all liquids. Since he su ace ension o W is abou he iple o ha o he o he liquids, leading o di e ences in We A . Re L and Oh include he liquid iscosi y, which was ca e ully selec ed o allow he in es iga ion o a con inuous ange. Hence, he ange o hese p ope ies is unique o all liquids. Based on all he non-dimensional numbe s, i is e iden ha keeping all o hem simila is impossible. To o e come his issue and allow he compa ison o a ious a omize s and liquid sp ays, Ohneso ge in- oduced he Oh-Re L diag am [4] in which all o he poin s lie in he ‘a omiza ion’ ange. Fae h e al. [28] in es iga ed he b eakup egimes o d ople s and in oduced a We A -Oh diag am o classi ica ion. P e- sen ly, all he poin s all in o he ‘shea b eakup’ egime since We A > 200 and Oh < 0.5. Consequen ly, i can be s a ed ha he d ople o ma ion is go e ned by he same physical mechanisms in all o he abo e cases, hence liquid b eakup and SCA o di e en liquids a di e en condi ions can be compa ed. 3. Resul s and discussion Fi s ly, he SCA measu emen esul s a e p esen ed, e alua ing he e ec o all p g ,T L , and liquids. Since he je b eakup has a signi ican impac on SCA, he p ima y b eakup is analyzed nex a wo empe a- u es and h ee p essu e o all liquids o be e unde s and he abo e esul s. Las ly, he de i a ion o he empi ical co ela ion is de ailed, using an op imiza ion algo i hm. Since he pa ame e i ing easily e- sul s in high R 2 alues, he i ed coe icien s we e pe u bed by 1% o see hei e ec on he sum o he squa ed es ima e o e o s, SSE, o ind he esul s wi h low sensi i i y and hence po en ially applicable o SCA es ima ion. 3.1. SCA measu emen esul s The de e mined SCA as a unc ion o p g and T L o all liquids is shown in Fig. 6. The esul s show a dec easing end p incipally wi h inc easing p g in all he cases. I can be explained by he e ec o con- inuously inc easing he axial momen um o he a omizing ai ha in- ensi ies d ople con ec ion. Tu bulence acili a es he adial p opaga- ion o d ople s and coun e ac s wi h his phenomenon, which is becoming mo e in ense wi h he inc eased p g . Howe e , he o me e ec is no ably s onge , leading o ul ima ely smalle SCA a highe Table 2 Pe o mance o a ious non-dimensional numbe s a N 2 while =N~ L 1 was used. No e ha he conside ed da ase o W was limi ed o T L = 70 °C. N 2 Liquid R 2 SSE S ,A ALR D 0.920 8.24 0.0225 LHO 0.950 4.24 0.00760 RO 0.951 5.9 0.0198 W 0.881 7.46 0.0185 Ma D 0.912 8.08 0.0183 LHO 0.941 13.4 0.00378 RO 0.961 14.3 0.0117 W 0.864 13.5 0.0203 MFR D 0.912 9.06 0.0633 LHO 0.937 15.6 0.0309 RO 0.948 16.2 0.0779 W 0.848 12.7 0.0443 ~ A D 0.933 17.7 1.099 LHO 0.960 48.1 0.447 RO 0.937 68.1 0.958 W 0.895 52.4 0.553 We L D 0.899 11.9 0.155 LHO 0.926 11.2 0 RO 0.945 193 0.363 W 0.835 61.9 0.260 Re A D 0.930 9.47 0.228 LHO 0.951 4.29 0.0729 RO 0.949 8.33 0.151 W 0.862 37.3 0.231 Re L D 0.903 856 0 LHO 0.930 117 0.000134 RO 0.946 150 0 W 0.836 15.4 0 T ~ A D 0.943 27.1 0.0492 LHO 0.960 221 0.0465 RO 0.937 180 0.0269 W 0.894 13.9 0.0339 Table 3 Poo ly pe o med combina ions in he case o D. N 1 N 2 R 2 SSE S ,A ~ L ~ A 0.873 2.3 × 10 9 0.641 ~ L µ ~ A 0.570 214,415 1.86 ~ L We A 0.915 1128 0.154 Oh L ALR 0.749 995 0.294 Oh L Ma 0.915 995 0.293 Oh L MFR 0.913 991 0.298 T ~ L ALR 0.546 2598 0.521 T ~ L Ma 0.556 2599 0.517 T ~ L MFR 0.589 1980 0.540 ~ L ALR 0.922 1463 0.390 ~ L Ma 0.911 9017 0.0183 ~ L MFR 0.911 9695 0.0633 µ ~ L ALR 0.922 8028 0.0225 µ ~ L Ma 0.911 8067 0.0183 µ ~ L MFR 0.911 8691 0.0633 ~ ALR 0.922 71.7 0.092 ~ Ma 0.911 191 0.0183 ~ MFR 0.911 244 0.063 Table 4 Inc ease o SSE in pe cen age compa ed o he o iginal alue by pe u bing only Aand Bby ± 1% while he o he cons an was unchanged. N 2 Liquid A+ 1%/-1% B+ 1%/-1% ALR D 15.1/8.80 0.635/0.469 ALR LHO 45.2/24.3 1.14/1.59 ALR RO 33.4/17.5 0.82/1.13 ALR W 9.70/40.8 0.079/0.09 Ma D 6.05/30.0 0.61/0.491 Ma LHO 29.4/50.5 0.618/0.707 Ma RO 35.7/55.7 0.654/0.732 Ma W 21.2/38.0 0.338/0.348 MFR D 38.5/16.3 6.47/8.60 MFR LHO 31.3/39.2 12.6/11.0 MFR RO 34.3/52.0 13.2/11.7 MFR W 18.1/36.2 2.87/2.63 T ~ A D 37.9/30.1 4.59/4.77 T ~ A LHO 19.0/17.3 1.49/1.50 T ~ A RO 20.8/18.7 1.52/1.55 T ~ A W 52.3/34.5 1.61/1.63 Table 5 Cons an o Eq. (20) o he in es iga ed liquids. N 2 Cons . D LHO RO W ALR A 20.7 25.0 25.1 24.3 B−0.20 −0.19 −0.18 −0.07 Ma A19.5 23.6 23.8 23.8 B−0.23 −0.22 −0.21 −0.08 MFR A 27.2 32.0 32.0 26.8 B−0.11 −0.11 −0.11 −0.04 A. U bán, e al. Fuel 277 (2020) 118197 7 p g . Inc eased T L ea u es sligh ly inc eased SCA o p incipally LHO and RO. I s e ec on D and W is signi ican ly lowe , complying wi h he limi ing iscosi y e m, de ined in ou p e ious wo k [27]. I is a ki- nema ic iscosi y alue below which he liquid p ehea ing has no ad- di ional physical e ec on he We-con aining e m o SMD es ima ion beyond he empe a u e-dependen ma e ial p ope ies, and i was ound o be 4.2 mm 2 /s ha was no eached by RO a any in es iga ed T L and eached by LHO a T L = 55 °C. The SCA esul s show ha he a ia ion in he in es iga ed anges is ela i ely small. D and LHO showed 5.27° and 5.38°, espec i ely, while i was 6.22° o RO, which is ela ed o he signi ican d op in i s iscosi y wi h p ehea ing, discussed in Subsec ion 3.2. The a ia ion o SCA o W was only 3.6°. The measu emen esul s o W a 85 °C show a dec ease a all p g, which is agains he o he ends, and he ma e ial p ope ies do no jus i y his phenomenon. Also, his T L is well below he boiling empe a u e; hence, local s eam o ma ion in he p ehea ing chambe can be excluded. Mo eo e , SCA a ied ma ginally wi h p g unlike in he case o he o he liquids and lowe T L o W a omiza ion. Since his obse a ion equi es signi ican ly deepe , highly ocused u he in es iga ions, he measu emen esul s o W we e e alua ed only up o 70 °C. 3.2. P ima y je b eakup isualiza ion The p ima y b eakup o liquid je s is shown in Fig. 7 a T L = 25 and 100 °C – excep o W whe e he uppe limi was 90 °C, and a p g = 0.3, 0.9, and 2.4 ba . The p omp ly expanding a omizing ai is esponsible o he dispe sion o he d ople s in he adial di ec ion, which e ec is g ea ly enhanced by he highly u bulen ai je ha b ings chao ic mo ion ha also sp eads he d ople s in all di ec ions. The o al disin- eg a ion leng h o D je is he g ea es a all condi ions, which is no accompanied by no able ligamen o ma ion. This seems he mos sig- ni ican di e ence be ween his and o he liquid ypes and being he eason o smalle SCA, shown in Fig. 6. Since he icini y o he nozzle has a lowe d ople popula ion, he iny d ople s a e less likely o sp ead a a la ge angle. A p g = 2.4 ba and T L = 100 °C, D disin eg a ion is apid, and he ansi ion be ween he liquid je co e and he ine d o- ple s is no isible. The b eakup o liquid packe s is he ca as ophic ype o all liquids unde hese condi ions. Rega ding liquid iscosi y, densi y, and su ace ension, LHO lies be ween D and RO. Mo e speci ically, i s ma e ial p ope ies a T L = 100 °C closely ma ch ha o D a 25 °C, and LHO a 25 °C beha es simila ly as RO a 100 °C [27] which is also obse able in he co e- sponding images as he b eakup mode closely ma ches. The di e ence in Oh o D a 25 °C and LHO a 100 °C is 5% while i is 12.5% in We A ha also sugges s a simila beha io . By compa ing LHO a 25 °C and RO a 100 °C, Oh is hal ed and he 12.5% di e ence in We A emains. This esul complies wi h he Oh-We A simila i y condi ion p oposed by Fae h e al. [28], men ioned ea lie . By e alua ing LHO a iden ical condi ions o D and RO, i is cha ac e ized by mode a e ligamen o - ma ion, and he liquid je b eakup leng h also lies be ween he wo liquids. The ligamen o ma ion is mos spec acula in he case o RO a p g = 0.3 ba and T L = 25 °C, whe e he liquid iscosi y is he highes . This p ocess is also obse able a ele a ed p essu es. Ne e heless, a T L = 100 °C, he ligamen s a e only isible a p g = 0.3 ba wi h sig- ni ican ly smalle sizes. The liquid sp eading is high due o he in ense ligamen o ma ion, leading o he highes SCA alues in he Fig. 8. The ela i e de ia ion o Eq. (20) in pe cen age a each measu emen poin . A. U bán, e al. Fuel 277 (2020) 118197 8 in es iga ed pa ame e ange. The high iscosi y o RO is clea ly isible since all he o ming liquid ac ions a e signi ican ly la ge han in he case o o he liquids. The ca as ophic je b eakup p ocess is bes isualized in he case o W, which also shows e y small ligamen s a all condi ions due o he high su ace ension alue while iscosi y is low, also meaning low Oh. The liquid packe s a e la ge in he wake o he liquid je , which un- de goes u he b eakup downs eam. The wa e d ople s show mo e in ense sp eading in he icini y o he nozzle, and he e ec o T L is low, as i was shown in Fig. 6. E en hough We o W a ele a ed p g ma ches ha wi h he o he liquids, Oh is one magni ude lowe han ha o D and wo magni udes lowe han ha o RO. This answe s why i s p ima y b eakup signi ican ly di e s om ha o o he liquids. SCA es ima ion based on he high-speed came a images is no pos- sible since he sp eading o he sp ay is delayed a highe p g ; only a sligh ly dis u bed s aigh wo-phase je is isible. E en hough he gene a ed iny d ople s a e isible, hei sp eading is only obse able a a highe downs eam dis ance. The images show only 8 d 0 , while i was concluded based on he global sp ay images ha 60 d 0 is a su icien dis ance o ha e a ully de eloped SCA. 3.3. De i ing an empi ical co ela ion o SCA Upon de e mining he ele an non-dimensional numbe s, discussed in Subsec ion 2.3, he o mula ion o he empi ical co ela ion is he nex ask. Since wo p incipal pa ame e s we e a ied, p g and T L , he inal SCA o mula is abou o be de e mined in he o m o Eq. (19): =SCA A N N· · B 12 (19) whe e Aand Ba e cons an s, and N 1 and N 2 a e wildca d non-dimen- sional numbe s. This o m was de i ed by analyzing he SCA co ela- ions o o he a omize ypes [4] and conside ing he powe law e ec o p g on SCA, which is ep esen ed by N 2 .N 1 s ands o he inclusion o he e ec o liquid p ehea ing. Since he numbe o cons an s is equal o he numbe o a ying pa ame e s, o he o mulae wi h mo e deg ee o eedom would lead o o e i ing. This ex ension is only could be done i he numbe o pa ame e s is inc easing, e.g., by adjus ing he a o- mize geome y, liquid mass low a e, e c., which would lead o an excessi e numbe o measu emen poin s. To o e come his issue, he design o expe imen s me hod can be used, which was success ully applied by Chen e al. [29] o SMD de e mina ion. Howe e , his echnique only can wo k e icien ly i he shape o he equa ion is well- es ablished; hence his pape only aims o p o ide an adequa ely shaped o mula, and i s ex ension is he nex s ep in his esea ch. Fi s ly, an R 2 analysis was pe o med, subs i u ing N 1 wi h T ~ L , ~ L , ~ L , µ ~ L , ~ , and Oh and N 2 wi h T ~ A , ~ A , ~ A , µ ~ A ,ALR, Ma, Re, We, and MFR. The Aand Bcoe icien s we e de e mined simul aneously by using he GlobalSea ch algo i hm in Ma lab, based on he SCA–p g e- sul s a a ious T L and liquids. Since ~ L was he bes -pe o ming non- dimensional numbe o N 1 , he candida es o N 2 a e p esen ed in Table 2 by ixing N 1 a ~ L . In addi ion o R 2 ,SSE, and ela i e s anda d de ia ion o he A cons an , S ,A , a e also p esen ed. Since S o B was al eady low in all he cases, his pa ame e was omi ed om Table 2. By conside ing only R 2 , T ~ A is he bes non-dimensional numbe can- dida e o N 2 , closely ollowed by ~ A . Howe e , bo h o hem a e cha ac e ized by high SSE and S ,A . Conside ing all he pa ame e s, ALR is he bes choice, ollowed by Ma and MFR. The es o he non-di- mensional numbe s showed high SSE o S ,A , hence hey a e disca ded. This la e pa ame e e e s o ha e en hough he i ing o Eq. (19) can be pe o med by achie ing high R 2 alues, A a ies signi ican ly wi h he ope a ing condi ion. Table 3 summa izes some o he es combina ions which did no wo k, p esen ing he esul s only o D. =N~ L 1 was ixed in he i s h ee cases, and hen he emaining non-dimensional pa ame e s o N 1 we e e alua ed wi h all ALR, Ma, and MFR, which we e pe o med excellen ly o N 2 , shown in Table 2. E en hough high R 2 alues could be achie ed in se e al cases, SSE and S ,A show ha hese pai s a e inapp op ia e o SCA es ima ion. To e alua e he app op ia eness o he concluded N 1 and N 2 non- dimensional numbe s in Eq. (19), bo h Aand B alues we e pe u bed by 1% in bo h posi i e and nega i e di ec ions while he o he one was ixed. The eason behind his was he ollowing. Equa ion (19), he model, has wo a iables, while wo pa ame e s, T L and p g , we e a ied. Hence, a wide ange o N 1 and N 2 can be used wi h an accep able i quali y. Howe e , i is expec ed ha he p esen ly app oxima ed and unknown equa ion o SCA de e mina ion should no a y much when ei he Ao Bcons an is sligh ly al e ed due o, e.g., measu emen e o . In o he wo ds, a good app oxima ion o SCA es ima ion should show low sensi i i y o he model and measu emen unce ain ies. To quan- i y his sensi i i y, he esul ing SSE is compa ed o he o iginal alue in pe cen age, shown in Table 4. The less he inc ease, he mo e obus he gi en o m o Eq. (19) is. I can be concluded ha he a ia ion o Bhas a signi ican ly lowe impac on he inal esul han A. Besides he excellen ly pe o ming ALR, Ma, and MFR, T ~ A was also included since i s pe o mance app oach ha o he o he h ee non-dimensional numbe s, e en hough i s o i- ginal SSE was no ably highe , shown in Table 2. Following he ul ima e goal o his pape , i.e., de e mining an em- pi ical co ela ion ha adequa ely es ima es SCA o plain-je ai blas a omiza ion in a wide ange o condi ions, he liquid densi y a io, and ALR p o ided he bes i , shown by Eq. (20): =SCA A ALR· · L B (20) He e, ALR is p ima ily esponsible o desc ibing he a ia ion in p g . ~ L inco po a es he e ec o liquid p ehea ing and is ee om he e ec o he a omizing ai . The liquid-dependen cons an s in Eq. (20) a e summa ized in Table 5 o bo h Ma and MFR besides ALR. These o he wo non-dimensional numbe s can be used i a ellow esea che would like o ex end he alidi y o Eq. (20) and ALR ails o pe o m well. I Eq. (20) would be he pe ec model o SCA es ima ion, hen all cons an s would ma ch. No e ha a uni ied model was es ed; howe e , i was omi ed due o he excessi e de ia ion exceeding 100%. The ma ching o he cons an s is ul illed in he case o LHO and RO, which o he wise showed simila beha io in all he p e ious in es iga ions. Howe e , he exponen o W is la gely di e en , p obably due o he e y low Oh numbe s, which we e no achie able by he o he liquids. In ligh o his condi ion, i is an unexpec ed esul ha i s SCA a ied in a simila ange han ha o LHO and RO. This migh change i , e.g., he ambien p essu e a ies. The physical p ope ies o LHO a e close o hose o D; howe e , he gene ally smalle SCA o D esul ed in 20% lowe A alues while Bis close o ha o LHO and RO. Consequen ly, he p esen physical model is no liquid-independen bu can be ex- ended by u he sys ema ic s udies. Fig. 8 shows he de ia ion be ween he measu ed and es ima ed SCA o all liquids, using Eq. (20). The de e mined 3.5% maximum de ia ion is an accep able esul , meaning 1° in SCA. The de ia ion in he ex- pe imen s o Gi en and Mu aszew [30] o a p essu e-swi l a omize was 5%, which is o en conside ed as a e e ence in he li e a u e o SCA es ima ion. E en hough hese alues could be u he educed by using ad anced measu emen and e alua ion echniques, conside ing he manu ac u ing ole ances and he sligh ly a ying condi ions in p ac- ical sys ems, his esul mee s he equi emen s o common indus ial p ac ice. 4. Conclusions Plain-je ai blas a omiza ion o wa e (W), diesel oil (D), ligh hea ing oil (LHO), and c ude apeseed oil (RO) was in es iga ed in an a mosphe ic es ig a a ious a omizing gauge p essu es, p g , and liquid p ehea ing empe a u es, T L . The inal goal o his pape was o de i e A. U bán, e al. Fuel 277 (2020) 118197 9