Study and characterization of the instabilities generated in expanding spherical flames of hydrogen/methane/air mixtures

S udy and cha ac e iza ion o he ins abili ies gene a ed in expanding sphe ical lames o hyd ogen/me hane/ai mix u es M. Reyes a,* , R. Sas e a , F.V. Tinau b , J. Rod ı ´guez-Fe n andez c a Depa men o Ene gy and Fluid Mechanics Enginee ing, Uni e si y o Valladolid, Paseo del Cauce s/n, 47011, Valladolid, Spain b CMT-Mo o es T e micos, Uni e si a Poli  ecnica de Val encia, 46022, Valencia, Spain c Uni e sidad de Cas illa la Mancha. ETS Ingenie ı´a Indus ial (Edi icio Poli  ecnico), A da. Camilo Jos e Cela,3, 10371, Ciudad Real, Spain highligh s O igin and na u e o ins abili ies de eloped in sphe ical hyd ogen/me hane lames. Di e en ia e ins abili ies o hyd odynamic and he mal-di usi e o igin. Ins abili y peninsulas calcula ed o es ablish s abili y limi s in each mix u e. Lewis e ec i e numbe de e mines he shape and loca ion o ins abili y peninsulas. a icle in o A icle his o y: Recei ed 11 Ma ch 2022 Recei ed in e ised o m 3 May 2022 Accep ed 8 May 2022 A ailable online xxx Keywo ds: Combus ion ins abili ies The mal-di usi e and hyd odynamic e ec Peninsula o ins abili y Cellula i y G ow h a e o ins abili ies Schlie en pho og aphy abs ac In he p esen wo k an analysis o he o igin and na u e o in insic ins abili ies in com- bus ion p ocesses wi h di e en hyd ogen/me hane mix u es is de eloped. These expanding sphe ical lame on expe imen s ha e been de eloped in a cylind ical con- s an olume combus ion bomb, which allows eco ding he p ocess h ough Schlie en pho og aphy me hod. The s abili y s udy in combus ion p ocesses has a g ea impo ance o assu e hei secu i y and con ol, since he unde s anding o lame ins abili ies is necessa y o imp o ing he in e nal combus ion engines pe o mance. To ca y ou his men ioned s udy, a e iew o he concep s and pa ame e s used in sphe ical lame on ins abili ies esea ch is i s p oposed, as well as a physical expla- na ion o each concep and he ela ions among hem. Addi ionally, a me hodology ha aims o de e mine he in luence o he uel mix u es in he o igin and de elopmen o he lame on ins abili ies is sugges ed. Mo eo e , he in insic e ec s o he combus ion p ocess, such as he he mal-di usi e and he hyd o- dynamic e ec , a e sepa a ely s udied, including hei indi idual con ibu ions o he g ow h a e o ins abili ies which allows o de e mine combus ion na u e and o ob ain he ins abili y peninsula o each uel mix u e. *Co esponding au ho . E-mail add ess: [email p o ec ed] (M. Reyes). A ailable online a www.sciencedi ec .com ScienceDi ec jou nal homepage: www.else ie .com/loca e/he in e na ional jou nal o hyd ogen ene gy xxx (xxxx) xxx h ps://doi.o g/10.1016/j.ijhydene.2022.05.063 0360-3199/©2022 The Au ho (s). Published by Else ie L d on behal o Hyd ogen Ene gy Publica ions LLC. 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/). Please ci e his a icle as: Reyes M e al., S udy and cha ac e iza ion o he ins abili ies gene a ed in expanding sphe ical lames o hyd ogen/me hane/ai mix u es, In e na ional Jou nal o Hyd ogen Ene gy, h ps://doi.o g/10.1016/j.ijhydene.2022.05.063 Finally, his me hodology includes a quali a i e s udy o he cellula i y phenomenon (when he ins abili ies de elop all o e he lame on ), conside ing he pa ame e s which in luence on his phenomenon. ©2022 The Au ho (s). Published by Else ie L d on behal o Hyd ogen Ene gy Publica ions LLC. 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/). In oduc ion Nowadays, he e is an ene gy p oblem wo ldwide based on he one hand, on a p ac ically exclusi e dependence on ossil uels de i ed om pe oleum, and, on he o he hand, on he e ec ha hei use has on he en i onmen due o he emissions gene a ed in hei combus ion p ocess. I is es i- ma ed ha he anspo sec o is esponsible o almos 30% o o al CO 2 emissions in he Eu opean Union (EU), wi h his gas being he main cause o he g eenhouse e ec . A possible solu ion is he eplacemen o hese CO 2 -p oducing uels wi h o he s wi h low o no ca bon con en such as hyd ogen (H 2 )o ammonia (NH 3 ), being mo e sus ainable om he en i on- men al poin o iew. P io o he in oduc ion o any uel mix u e in a con en- ional engine, i s beha io mus be s udied by isola ing i om o he ex e nal ac o s ha may a ec he pe o mance o combus ion, such as he u bulence ha occu s in an engine due o he mo emen o he pis ons. Cons an olume com- bus ion bombs (CVCB) allow he analysis o mix u es in lamina egime, hus acili a ing he s udy o hei na u e. The abo e app oach is a he base o his esea ch wo k, in which lamina combus ion o sphe ical lames o mix u es o H 2 / CH 4 /ai wi h di e en pe cen ages o hyd ogen (H 2 ) a e cha - ac e ized in a CVCB wi h cylind ical geome y. A undamen al aspec in he cha ac e iza ion o uel combus ion is he s udy o i s s abili y, which consis s o he analysis o he de elopmen o he ins abili ies inhe en o he combus ion p ocess: o igin, na u e ( he mo-di usi e o hy- d odynamic, mainly), g ow h, e c. These can al e he mo phology o he lame and a ec he bu ning eloci y. The e is a g owing in e es in unde s anding and con olling he uns able beha io o cellula lames [1] and he ansi ion o cellula i y in expanding sphe ical lames [2e4]. The e a e se e al ways o cha ac e ize a combus ion p o- cess depending on he me hod and esou ces used, bu all o hem aim o de e mine he mos signi ican pa ame e s ha de ine how a combus ion is de eloping: he modynamic condi ions, bu ning eloci y, ins abili ies, and lame mo phology among o he s. The Schlie en echnique is used in his wo k o eco d he lame on de elopmen . This ech- nique is based on he ligh de lec ion caused by densi y g a- dien s [5]. I was i s employed by Toeple in 1864 [6]. The Schlie en me hod is widely used o he s udy o lames in a combus ion p ocess since i allows hei eco ding wi h a g ea cla i y [7]. Thanks o he use o his echnique, i is possible o s udy he mo phology [8,9], ins abili ies and cellula i y o he lame on , as well as i s bu ning eloci y [4,5,8,10] and, he e o e, cha ac e ize he uel mix u e conside ed [11,12]. Spon aneous pe u ba ions appea in lames due o a ious phenomena such as acous ic ib a ions o p essu e wa es [4]. In insic combus ion e ec s cause ha he ampli ude o he wa es on he lame on dec eases o inc eases depending on he dominan ac ion o hose e ec s. The esul o each e ec in he lame on is he ins abili y, independen ly o hei s abilizing o des abilizing cha ac e [13,14]. The phenomena ha can p oduce ins abili ies in he lame on (in a lamina egime) o a p emixed combus ion a e h ee: olume o ces, hyd odynamic e ec s and he mo-di usi e e ec s [15]. Volume o ces a e ele an when a less dense luid mo es owa ds a dense one in he opposi e di ec ion o ha o a olume o ce ( o example, g a i y). Then, he e appea s an ins abili y due o olume o ces (also known as Rayleigh- Taylo [16]). In a lame, his occu s when he combus ion p oduc s (wi h lowe densi y) ad ance owa ds he esh mix u e (highe densi y) upwa ds (con a y o g a i y); he lame on is hen conside ed as a discon inui y o densi ies. This ins abili y ype, compa ed wi h he o he wo, has he lowe in luence on he de elopmen o he lame. The second ins abili y conside ed is he hyd odynamic one (Da ieus-Landau, DL), which is associa ed wi h he he mal expansion o densi y di e ence be ween he unbu n and bu n gases in a combus ion p ocess, delimi ed by he lame on [13,14]. The hyd odynamic e ec gene a es des abilizing ins abili ies since hey end o in ensi y all o he lame on pe u ba ions signi ican ly la ge han he lame on hick- ness (d l )[15,17]. Hyd odynamic ins abili y can also be s imu- la ed by educed lame hickness and high p essu es [18]. In addi ion, u bulen p opaga ion speed can be enhanced by he onse o he hyd odynamic ins abili y [19,20]. The he mal-di usi e e ec is he cause o he hi d ins abili y ype ha a ec s he combus ion p ocess in a sig- ni ican way. This ins abili y does no ha e a unique s able o uns able cha ac e since i in ol es he mal and molecula di usi i ies, ha ha e opposi e esul s [15,21e24]. The mo- lecula di usi i y a ec s he pe u ba ions in such a way ha i inc eases hem (des abilizing con ibu ion); on he con a y, he he mal di usi i y ends o a enua e he lame on (s abilizing con ibu ion). This e ec can be ep esen ed quan i a i ely by he dimensionless Lewis numbe (Le), which is he a io be ween he mal di usi i y (a) and molecula di usi i y (D). Des abilizing he mal-di usi e ins abili y occu s when he Le is smalle han a c i ical alue (when he molecula di u- si i y domina es he p ocess), and c acks and cells de elop in e na ional jou nal o hyd ogen ene gy xxx (xxxx) xxx2 Please ci e his a icle as: Reyes M e al., S udy and cha ac e iza ion o he ins abili ies gene a ed in expanding sphe ical lames o hyd ogen/me hane/ai mix u es, In e na ional Jou nal o Hyd ogen Ene gy, h ps://doi.o g/10.1016/j.ijhydene.2022.05.063 om he beginning on he lame on su ace; o he wise, he lame should be unw inkled a i s , al hough a e a ce ain ime, needed o he hyd odynamic ins abili y o appea , w inkles can be isible [25]. In addi ion o he la e , he in- luence o he lame s e ch mus be conside ed in sphe ical lames. This pa ame e includes s ain and cu a u e e ec s due o he lame geome y and always ends o a enua e he ins abili ies in he combus ion beginning (in insically s able cha ac e ). I should be s udied oge he wi h he na u e o he mix u e and, speci ically, he he mo-di usi e e ec [24,26] ep esen ed by he Lewis numbe (Le) o be e , he e ec i e Lewis numbe (Le e ), see Re s. [21,24,27,28], which is a weigh ed a e age o he eac an s Lewis numbe s. The c i ical adius and he cellula adius a e s udied in li e a u e o cha ac e ize he onse o ins abili y on lames and he cellula phenomenon, espec i ely [24,29e33]. The dimensionless lame adius is he Pecle numbe (Pe), which is he a io be ween he ins an aneous adius and he lame hickness. Many de ini ions o c i ical adius can be ob ained in li e a u e, B adley e al. [34] de ined he c i ical adius a he ins an o he appea ance o he i s c acks in he lame on . Bech old and Ma alon [2] iden i ied he c i ical adius, o lames wi h e ec i e Lewis numbe bigge han a c i ical alue, as he adius beyond which he lame is uns able due o he dominance o he hyd odynamic e ec when ins abili ies a e no longe dampened, al hough isually i is no app e- ciable. This is he de ini ion o c i ical adius adop ed in his wo k, associa ed wi h he c i ical Pecle numbe (Pe c ). Ano he de ini ion e e s o he lame adius when he lame is isibly uns able due o he de elopmen o cellula i y. This adius can be called c i ical cellula adius, also u ilized by B adley e al. [34]. F om his adius, he cellula i y inc eases he lame on su ace, which p oduces an augmen a ion in he appa en combus ion bu ning eloci y (o be e , combus ion a e). In he wo ks o Jiang e al. [35] and Tinau e al. [5] his de ini ion o he c i ical adius is applied. The unde s anding o hyd ogen/me hane combus ion and lame ins abili ies is necessa y o imp o ing in e nal com- bus ion engines pe o mance. P e ious wo ks ha e been ocused on he bu ning eloci y s udy o hyd ogen/me hane mix u es [36e42]. O he s udies ha e ocused on he engine combus ion [43e45]. Va ious esea che s ha e in es iga ed he cell o ma ion in hyd ogen/ai lames and in mix u es o hyd ogen wi h o he hyd oca bons lames [46e49], indica ing ha hyd ogen addi ion inc eased hyd odynamic and he mal- di usi e ins abili ies. Addi ionally, an unde s anding o he o ma ion and o igin o cellula ins abili ies in hyd ogen/ me hane-ai lames should be conside ed u he . Jiang e al. [50] s udied he cellula s uc u e o me hane/hyd ogen/ai lames in a sphe ical combus o , o a ious equi alence a- ios and hyd ogen ac ions, and s udied a co ela ion be- ween he cellula s uc u e and p essu e. Kim e al. [51] s udied cellula ins abili ies on expanding sphe ical p opa- ga ion hyd ogen/ai e, me hane/ai and p opane/ai lames. They cha ac e ized he size o he cell, obse ing bigge cells due o hyd odynamic ins abili y han he gene a ed by he he mal-di usi e. The c i ical Pecle numbe is also a ec ed by he ini ial p essu e, dec easing wi h he inc emen o p essu e. Zhang e al. [52] made a lame dynamics analysis o na u al gas en iched wi h hyd ogen in p emixed u bulen combus ion, ob aining an inc emen o he w inkled s uc u e wi h he u bulence in ensi y and wi h he hyd ogen a io. Cellula ins abili ies enhance he global p opaga ion a e o lamina lames and ha e also been s udied by many e- sea che s [30,47,53e55]. Kwon e al. [56] s udied hyd ogen lames a ele a ed p essu es o iden i y he e ec s o he mal expansion a io, lame hickness, Lewis numbe , and s e ch a e on he gene a ion o hyd odynamic and di usional- he mal ins abili ies in he lame on . Jiang e al. [50] in es- iga ed cell o ma ion in hyd ogen/me hane p emixed lames and ob ained a co ela ion be ween cellula s uc u e o he lame on and p essu e. Sun e al. [30] s udied he cellula ins abili ies o hyd ogen-ai p emixed lames a di e en ini ial condi ions, showing ha , o lean hyd ogen/ai lames, he cellula ins abili ies a e domina ed by he he mal- di usi e ins abili y, and o s oichiome ic and ich hyd ogen/ai lames, he cellula s uc u e is in luenced by he hyd odynamic ins abili y. Oka o e al. [57] ha e de eloped an expe imen al and heo e ical in es iga ion o cellula in- s abili ies in lean hyd ogen/me hane mix u es in a cons an olume combus ion chambe , ob aining an inc emen o he cellula ins abili y and sel -accele a ion wi h he inc emen o he hyd ogen con en and mix u e p essu e. Hu e al. [47] obse ed ha he inc emen o hyd ogen in me hane/ hyd ogen/ai mix u es p omo es cellula i y in lean lames. Law e al. [58] s udied he ou wa d p opaga ion and de elop- men o su ace cellula ins abili y o spa k-igni ed sphe ical p emixed lames o mix u es o hyd ogen, hyd oca bon, and ai , showing ha p opane subs i u ion mode a es cell o - ma ion due o bo h di usionale he mal as well hyd ody- namic ins abili ies. Smallbone e al. [59] ca ied ou s udies o lame ins abili y, lamina and u bulen eloci y o hyd ogen/ ai mix u es in a an s i ed combus ion bomb. Wang e al. [60,61] in es iga ed he lame on s uc u e o syngas p e- mixed lames. Vu e al. [1] in es iga e he cell o ma ion in hyd ogen/me hane/monoxide eai p emixed lames. Jiang e al. [50] s udied he in luence o p essu e in he de elopmen o a cellula s uc u e. In p esen wo k an analysis o he o igin and na u e o in insic ins abili ies in sphe ical expanding lames o hyd ogen/me hane blends is de eloped, because he e is a lack o da a in li e a u e. These sphe ical lame on expe i- men s ha e been pe o med in a cylind ical cons an olume combus ion bomb (CylCVCB), which allows image eco ding h ough Schlie en pho og aphy me hod and eco ding he ins an aneous p essu e. Wi h he me hodology p esen ed in his esea ch, i is possible o ob ain he s abili y maps o di e en combus ion mix u es, which co esponds wi h he images di ec ly ob ained. To ca y ou his esea ch, a e iew o he concep s and pa ame e s used in he s udy o in- s abili ies in sphe ical lames is i s p oposed, as well as a physical explana ion o each concep and he ela ions among hem. A e ha , he expe imen al ins alla ion and me hod- ology a e explained, and inally expe imen al esul s a e p e- sen ed o mix u es o me hane/hyd ogen wi h di e en pe cen age o hyd ogen ( om 0 o 100%), o wo di e en uel/ai equi alence a ios, and ini ial p essu e and empe a- u e cons an in all he expe imen s. in e na ional jou nal o hyd ogen ene gy xxx (xxxx) xxx 3 Please ci e his a icle as: Reyes M e al., S udy and cha ac e iza ion o he ins abili ies gene a ed in expanding sphe ical lames o hyd ogen/me hane/ai mix u es, In e na ional Jou nal o Hyd ogen Ene gy, h ps://doi.o g/10.1016/j.ijhydene.2022.05.063 S abili y analysis in sphe ical lames To cha ac e ize an uns able sphe ical lame, i is impo an o di e en ia e be ween he ins an a which ins abili ies a e o igina ed (a he i s s ages o he combus ion o in he subsequen ins an s o he de elopmen o he combus ion p ocess) and whe he o no he e olu ion o he ins abili y leads o he de elopmen o a cellula lame on . The g ow h a e o sphe ical lame ins abili ies is de ined as he inc ease in ime o he ela i e ampli ude o he pe u ba ion ( a io be ween he ampli ude and he ins an a- neous adius o he sphe e) o med on he su ace o he lame [14] as he join e ec o he hyd odynamic and he mal- di usi e ins abili ies. When he lame adius has eached a ce ain alue 0 (signi ican ly g ea e han he hickness o he lame, dl) he ampli ude Ao he pe u ba ion can be non-dimensionalised wi h o gi e a. Once pe u bed a iables a e expanded in a sphe ical ha monic se ies, a akes he ollowing o m (adap ed om Re . [4] o cohe ence wi h he subsequen exp essions o he e ms appea ing in i ): a¼a0RuþdlU ,ln R(1) whe e a0is he ini ial dimensionless ampli ude when ¼ 0 ; R¼ / 0 is he dimensionless lame adius; dlis he lame on hickness (dl¼a=Sl, whe e ais he he mal di usi i y o he mix u e and Sl he lamina eloci y [10]). uis associa ed wi h hyd odynamic ins abili y [4,21,29,32]; i is a dimensionless pa ame e (usually deno ed as uDL in i s equi alen in la lames), ha only depends on he he mal expansion sand he dimensionless wa enumbe n.Uis associa ed wi h he mal- di usi e ins abili y [29]; i is also dimensionless and de- pends on he he mal expansion, Lewis numbe and Zeldo ich numbe (b) (see below). The dimensionless wa enumbe n quan i ies he numbe o wa es, wi h a lwa eleng h, ha i in a ci cum e ence o adius n¼2p l, as illus a ed in Fig. 1. The g ow h a e o an ins abili y is 1 =aðda =d Þ[4,21], he e- ina e iden i ied by he le e S, will adop di e en o ms depending on he case. The gene al unc ion o Sð Þis aken om he esea ch o Addabbo, Bech old and Ma alon [21,32], collec ed in he s udy o Lapalme e al. [24] and ep esen ed in equa ion (2). Sð Þ¼1 a da d ¼1 d d udl U¼1 d d uU Pe(2) In equa ion (2) i is possible o see he con ibu ions o he ins abili y g own a e due o he hyd odynamic (u) and he mo-di usi e ( U Pe) e ec s [29]. Hyd odynamic e ec is always posi i e (con ibu ing o ins abili y), bu he he mo- di usi e e ec can inc ease o educe he i s , depending on he alue o U: U¼Q1þbLee 1 s1Q2þP Q3(3) No e ha Uconsis s o h ee con ibu ions, each accom- panied by a Qicoe icien . The physical meaning o each o hem is as ollows: he e m Q1b ings he in luence o he he mal conduc i i y (s able cha ac e ); he second e m bLee 1 s1Q2 ep esen s he e ec o he molecula di usion (s able o uns able) and he e m P Q 3 (P is he P and l num- be ) b ings he e ec o he iscosi y (s able) [62]. The co- e icien s Q 1 ,Q 2 and Q 3 a e gi en in Eqs. (4)e(6). Q1¼g1 sDn4ðsþ1Þþsn3ð2uþ5Þþn2us 2s2þs1 þnsðs73usuÞ2sð1þuÞ(4) Q2¼g2ðs1Þ 2D2n4þn3ð2us þ2uþ10s3Þþn22su2þð5s1Þu þ3s2s22þnsu2ð14sÞ14s2þ1uþ39s8s2 2su2þ4uþ3 (5) Q3¼2nðn21Þðs1Þ sD½ðnþ2Þð ~ kðxÞg3Þ3ð ~ lðxÞ1Þ (6) whe e D¼2auþb2a. The de ini ions o coe icien s g1;g2 and g3appea in he second column o Table 1. I can be seen ha he h ee gidepend on he expansion a io sand a unc ion ~ kðxÞwhich ep esen s he he mal conduc i i y exp essed in e ms o he dimensionless empe a u e T=Tu (i.e., he lame empe a u e To e he unbu ned gas empe - a u e Tu) and scaled by i s alue in he unbu ned gas. In o de o ob ain explici exp essions o gi ha s ill e ain he main dependence on s, di e en possibili ies o he a ia ion o ~ kðxÞ can be conside ed: cons an (o de o 1), a iable as ffiffiffi T p, and a iable as T. The exp essions o gi o he h ee possible de- pendences o ~ kðxÞappea in he addi ional columns o Table 1. In he i s case ( ~ k(x)¼1), wi h he hypo hesis o cons an anspo p ope ies, he mal conduc i i y is a cons an and he in luence o iscosi y on he s abili y o he lame is min- imal [21]. I is wo h men ioning he o mula ion made by B adley and Ha pe in 1994 [4] wi h he assump ion o con- s an p ope ies. Coe icien s Q i a e also de ailed in B adley [3] which desc ibes ou s ages in he p opaga ion o a lamina sphe ical lame, hese a e: (1) s able lamina p opaga ion, (2) c acking o he lame on and cell o ma ion, (3) p opaga ion o he cellula lame, (4) u bulen p opaga ion. Fig. 1 eFlame adius, wa e ampli ude and wa eleng h. in e na ional jou nal o hyd ogen ene gy xxx (xxxx) xxx4 Please ci e his a icle as: Reyes M e al., S udy and cha ac e iza ion o he ins abili ies gene a ed in expanding sphe ical lames o hyd ogen/me hane/ai mix u es, In e na ional Jou nal o Hyd ogen Ene gy, h ps://doi.o g/10.1016/j.ijhydene.2022.05.063 The e ec o he s e ch canno be s udied sepa a ely because he na u e o he mix u e mus be conside ed and, speci ically, he he mo-di usi e e ec e lec ed in he a io be ween he e ec i e Lewis numbe Le e in a mix u e, and he c i ical Lewis numbe o he combus ion (Le e * ). Equa ion (7) shows his la e pa ame e , whe e bis he Zeldo ich num- be ; as o Q 1 and Q 3 , hey mus be e alua ed o he c i ical adius o Pecle numbe acco ding o equa ions (4) and (6). Lee *¼1s1 bQ2ðQ1þQ3P Þ(7) As i was explained be o e, i in a uel mix u e Le e <Le e * ,i means ha he he mo-di usi e e ec is des abilizing, and ins abili ies g ow om he beginning. On he con a y, in combus ions wi h Le e >Le e * he he mo-di usi e e ec is s abilizing and, he e o e, he only e ec capable o inc easing ins abili ies is he hyd odynamic one. I is possible o ob ain he cu es o he g ow h a e o he ins abili y Swhen he alues o Eq. (2) a e ep esen ed e sus he wa enumbe no al e na i ely he wa eleng h o he pe u ba ions l o a pa icula lame on adius o ime [2,4,64], as can be seen in Fig. 2, whe e i is possible o see wo egions: s able and uns able. Bo h zones a e sepa a ed by he alue o S¼0, he s abili y limi o a sphe ical lame. The do ed line co esponds wi h he c i ical adius c om which he e a e ce ain wa eleng hs whose g ow h a e is posi i e (uns able lame). Expe imen al appa a us and p ocedu e Expe imen al se up In his esea ch wo k, expe imen s we e conduc ed in a cy- lind ical cons an olume combus ion essel (CylCVCB) [5], wi h he ollowing dimensions: diame e 114 mm and heigh 135 mm, o in es iga e he combus ion de elopmen and in pa icula , ins abili ies and he onse o cells in he lame su ace, see Fig. 3. The combus ion chambe was designed wi h wo op ical windows made o used silica on he side- walls o he cylinde . The ins alla ion is ins umen ed o measu e ins an aneous p essu e du ing he combus ion (piezoelec ic p essu e ansduce Kis le ype 7063) and o egis e he lame de elopmen wi h a high-speed Schlie en pho og aphy sys em: lame images we e eco ded using a high-speed came a Phan om V210 a 7000 ames pe second ( esolu ion 832 800 and exposu e ime o 10 ms). Hyd ogen, me hane and ai a e indi idually in oduced om p essu e anks using a pa ial p essu e me hod, and an igni ion sys em s a s he combus ion a he cen e o he combus ion chambe ( o mo e in o ma ion abou he expe - imen al ins alla ion see Re . [5]). An algo i hm is used o p ocess he images ob ained wi h he Schlie en echnique (high-speed came a), o ob ain he ime e olu ion o he lame adius and o s udy he cellula s uc u e which appea s as a w inkling o he lame su ace. Radius e olu ion is ob ained h ough ame by ame p o- cessing, a e backg ound emo al, bina iza ion and hinning ans o ma ion o highligh he bo de s be ween cells, as i is explained in de ail in Re . [5], ob aining he ins an aneous posi ion o he lame on (wi h a andom sample consensus algo i hm p og ammed in Ma lab) and iden i ying he cells ha appea in he lame du ing de combus ion de elopmen . Ins an aneous p essu e is egis e ed inside he combus ion chambe , and i is analyzed by means o a wo-zone diagnosis model, wi h he aim o ob aining bu ning eloci y, Lewis numbe and e ec i e Lewis numbe (Le and Le e ), he mal expansion s, ins abili y g ow h a e S, and he es o he pa- ame e s necessa y o s udy he ins abili y g own a e and hei coe icien s, explained in de ail in p e ious sec ions. Table 1 eAnaly ical exp essions ha de ine he coe icien s g i and p ac ical as a unc ion o he he mal conduc i i y [21,63]. ~ kðxÞ¼1 ~ kðxÞ¼ ffiffiffiffi T p~ kðxÞ¼T g1s s1Z s 1 ~ kðxÞ xdx s s1ln s2s ffiffiffi s pþ1 s g21 s1Z s 1 ~ ~ kðxÞ xlns1 x1dx 1 s1Z0 ∞ ln½1þðs1Þezdz 4 s1 ffiffiffi s p1ln½0:5ðffiffiffi s pþ1Þg 1 g31 s1Z s 1 ~ kðxÞdx 12ðs3=21Þ 3ðs1Þ sþ1 2 Fig. 2 eIns abili y g ow h a e cu es o a gi en lame adius as a unc ion o he pe u ba ion wa eleng h. in e na ional jou nal o hyd ogen ene gy xxx (xxxx) xxx 5 Please ci e his a icle as: Reyes M e al., S udy and cha ac e iza ion o he ins abili ies gene a ed in expanding sphe ical lames o hyd ogen/me hane/ai mix u es, In e na ional Jou nal o Hyd ogen Ene gy, h ps://doi.o g/10.1016/j.ijhydene.2022.05.063 Me hodology In his esea ch wo k, mix u es o H 2 /CH 4 wi h di e en pe - cen ages o hyd ogen ( a ying om 0, 20, 50, 80 and 100%) a e analyzed o de e mine he in luence o hyd ogen addi ion on he s abili y o a lame, speci ically on he o igin and na u e o he ins abili ies in insic o a combus ion p ocess. To isola e he e ec o hyd ogen om o he possible in luencing a i- ables, wo g oups o expe imen s wi h s oichiome ic and lean uel/ai a io (F¼1 and F¼0.7) ha e been selec ed; wi h an ini ial p essu e o 0.1 MPa, and an ini ial empe a u e o 323 K. The i s g oup (F¼1) has been s udied o iden i y he in lu- ence o he hyd ogen in he lame s abili y analysis (s abili y limi s, combus ion na u e, ins abili ies, and cellula i y). The aim o he second g oup is o s udy he impac o lean equi alence a io on he s abili y analysis, as well as he e ec o he hyd ogen con en , by compa ing he esul s wi h hose o s oichiome ic equi alence a io. The s abili y s udy in lames o H 2 /CH 4 eai mix u es is made by examining ou undamen al cha ac e is ics o a sphe ical lame: s abili y limi s ela ed o pe u ba ions wa eleng h l, lame na u e, ins abili ies g ow h a e Sand he cellula i y phenomenon. In his sec ion, i is b ie ly explained he meaning o each one o hem and hei main goals. These ou cha ac e is ics a e de eloped and applied o he selec ed expe imen s in he sec ion co esponding o esul s. S abili y limi s ela ed o pe u ba ions wa eleng h (l) To s udy he s abili y limi s ela ed o he wa eleng h o he pe u ba ions (l) i is use ul he g aphical ep esen a ion o he s abili y limi s o a lame, which is called s abili y cu e o ins abili y peninsula [13]. Fig. 4i shows an example o his cha whe e he wa enumbe s o which ins abili ies g ow h a e is ze o (S¼0) a e plo ed e sus he Pecle numbe . Simila ly, ins ead o he Pecle numbe , he lame adius could also be u ilized ( his is employed in he esul s sec ion o his pape ). These alues con o m a egion ha con ains he wa e- numbe s o all he pe u ba ions ha expe ience an inc e- men o hei ampli ude a a ce ain lame Pecle numbe (o adius) since hei g ow h a e is posi i e (S>0); he e o e, i is called he uns able egion ( he blue one). The o he a ea is he s able egion, in which he g ow h a e o he pe u ba ions is nega i e (S<0) and consequen ly he wa es a e a enua ed. I should be no ed ha he nose o he peninsula co esponds o he c i ical Pecle numbe (o c i ical lame adius) om which he lame en e s in he uns able egion. Fo a Pecle numbe la ge han he c i ical alue, he e is a se ies o g owing pe u ba ions de ined by hei wa enumbe s (wa eleng hs) be ween n max (o l min ) and n min (o l max ), while all hose which a e ou side his ange a e dec easing. Fig. 4ii shows a g ow h a e cu e o a gi en Pecle numbe in which hese limi s a e ma ked. These maximum and minimum alues ul ill he ollowing condi ion o each Pecle numbe (and associa ed lame adius): S¼0¼1 a da d ¼1 d d udl U0uU Pe ¼00Pe ¼U u(8) Fig. 4iii con ains a join ep esen a ion o he in o ma ion o he ins abili y g ow h a e cu e o a gi en Pecle numbe and he ins abili y peninsula. Fig. 3 eSchema ics o he expe imen al se up. in e na ional jou nal o hyd ogen ene gy xxx (xxxx) xxx6 Please ci e his a icle as: Reyes M e al., S udy and cha ac e iza ion o he ins abili ies gene a ed in expanding sphe ical lames o hyd ogen/me hane/ai mix u es, In e na ional Jou nal o Hyd ogen Ene gy, h ps://doi.o g/10.1016/j.ijhydene.2022.05.063 Flame s abili y na u e. A combus ion is conside ed in insically uns able when he lame on ins abili ies appea and g ow al eady om he beginning o he p ocess, i.e., i he ins abili y g ow h a e is posi i e (S>0) a he i s s a es o he combus ion. On he con a y, i he ins abili ies begin o g ow only a e he lame adius has eached a ce ain alue (e en i i is small), a combus ion is conside ed s able. The e o e, he combus ion s abili y cha ac e is de ined by he ins abili ies g ow h a e in he i s s ages o he p ocess. As men ioned be o e, he hy- d odynamic e ec has always a des abilizing cha ac e . Howe e , he he mal-di usi e e ec could be s abilizing (coun e ac ing he hyd odynamic e ec oge he wi h he lame s e ch) o des abilizing (inc easing he hyd odynamic e ec ), meaning ha he combus ion s abili y na u e is s ongly dependen on his second e ec . This sec ion aims o cha ac e ize he combus ion na u e and he mo phology o a s abili y cu e de i ed om an un- s able combus ion. Wi h he objec i e o iden i ying he s abili y na u e o a lame, he alue o i s e ec i e Lewis numbe mus be compa ed wi h he alue o i s c i ical e ec i e Lewis numbe . I he e ec i e Lewis numbe alue is g ea e han he c i ical one (Le e >Le e * ) he combus ion is s able a he beginning, i s ins abili y peninsula is loca ed o he igh o he e ical axis, he ins abili ies ha e a hyd odynamic sou ce and s a o g ow only once he Pecle numbe has a alue highe han 0. O he wise, when Le e ;<Le e * , he combus ion has an uns able na u e, he ins abili ies a ise om he he mal-di usi e e ec al eady om he beginning (in addi ion o he hyd odynamic con ibu ion. Following he p e ious app oach, he limi be ween he s able and uns able combus ion is well ma ked by he e ec- i e Lewis numbe whose c i ical alue is, in gene al, close o 1. In Fig. 5 wo ins abili y peninsulas o di e en Lewis e ec i e numbe s a e p esen ed. When he Lewis numbe is equal o i s c i ical alue (Le e ¼Le e * ), he peninsula nose ouches he e ical axis, i.e., he c i ical Pecle numbe o he combus ion is equal o ze o (b oken line in Fig. 5). When he Lewis numbe is lowe han i s c i ical alue (Le e >Le e * ), he peninsula is displaced o he igh in he igu e. Ins abili ies g ow h a e and ela i e con ibu ions o hy- d odynamic and he mal-di usi e e ec s. As p e iously men ioned, he in luences o hyd odynamic and he mal-di usi e con ibu ions a e e lec ed on he in- s abili ies g ow h a e (see Eq. (2) and Eq. (3)). The he mal- di usi e e ec has mo e in luence a he p ima y s ages o he combus ion p ocess, since i is in e sely p opo ional o he Pecle numbe ( U Pe). When he lame adius inc eases, his e ec loses impo ance, and he g ow h a e is domina ed by he hyd odynamic e ec (u). Consequen ly, he mo e s a- bilizing powe he he mal-di usi e con ibu ion has, he la e he ins abili ies due o he hyd odynamic con ibu ion appea . Acco ding o he abo e, ega dless o he combus ion Fig. 4 eSchemes o he s abili y cu e. Fig. 5 eIns abili y peninsulas o wo mix u es wi h di e en alues o Le e . in e na ional jou nal o hyd ogen ene gy xxx (xxxx) xxx 7 Please ci e his a icle as: Reyes M e al., S udy and cha ac e iza ion o he ins abili ies gene a ed in expanding sphe ical lames o hyd ogen/me hane/ai mix u es, In e na ional Jou nal o Hyd ogen Ene gy, h ps://doi.o g/10.1016/j.ijhydene.2022.05.063 na u e, all he lames would isibly de elop ins abili ies in a combus ion chambe wi h an in ini e size. Cellula i y de elopmen . The cellula i y phenomenon is he isible consequence o he ull de elopmen o he ins abili ies in a lame on . A a ce ain adius, he wa es ampli udes a e so big ha hey ins an ly b eak down he lame on s uc u e in such a way ha cells a e sp ead all o e he lame su ace in a pe cep ible way, which can be eco ded by he pho og aphic schlie en echnique. A quali a i e analysis o he lames can be ca ied ou h ough he s udy o hose images in o de o es ablish he mo e- and less-de e minan pa ame e s on he appa i ion and de elopmen o he cellula i y phenomenon. Resul s o he s abili y o hyd ogen/me hane lames In his sec ion esul s o he s abili y o hyd ogen-me hane lames a e p esen ed o di e en pe cen ages o hyd ogen in he lame mix u e and o wo di e en uel/ai equi alence a ios: s oichiome ic and lean mix u e (F¼0.7). Fo all cases, he alues o he expansion a io sa e calcula ed o each ime. The alues o each mix u e e ec i e Fig. 6 eIns abili y peninsulas. in e na ional jou nal o hyd ogen ene gy xxx (xxxx) xxx8 Please ci e his a icle as: Reyes M e al., S udy and cha ac e iza ion o he ins abili ies gene a ed in expanding sphe ical lames o hyd ogen/me hane/ai mix u es, In e na ional Jou nal o Hyd ogen Ene gy, h ps://doi.o g/10.1016/j.ijhydene.2022.05.063 Lewis numbe a e he co esponding o he c i ical adius o he s able ones and o he ini ial adius o hose uns able, always in he unbu ned side. The c i ical Lewis numbe is calcula ed acco ding o Eq. (7). S abili y limi s In Fig. 6 he s abili y maps e sus he Pecle numbe (le ) and he lame adius ( igh ) a e p esen ed o all he expe imen s de eloped. Compa ing hese wo ep esen a ions, i can be emo ed he lame hickness in luence. In Fig. 6i and 6ii s a- bili y cu es a e p esen ed o he expe imen s de eloped a s oichiome ic uel/ai equi alence a io o di e en hyd ogen con en (0%, 20%, 50%, 80% and 100%). I can be seen ha bo h peninsulas o he mix u es wi h 50% H 2 o F¼1a e a he le o he cha wi h he lowes alue o he c i ical Pecle numbe o lame adius (co esponding o hei noses). Acco ding o he abo e men ioned, his means ha he in- s abili ies g ow almos om he combus ion beginning bu his does no co espond necessa ily wi h an ea lie appa i- ion o a cellula lame, as explained la e . The peninsulas ob ained o he es o uel composi ions a e di e en depending on i hey a e plo ed e sus he Pecle numbe o lame adius. I can be seen in Fig. 6i and 6ii ha he pe cen age o hyd ogen a ec s signi ican ly o he s abili y limi s bu no in a p opo ional way. Compa ing he maps plo ed e sus he Pecle numbe and e sus he lame adius (Fig. 6i and 6ii) i is possible o see he in luence o he lame on hickness, especially o he combus ions wi h 80% and 100% o hyd ogen, since hey ha e bigge Pecle numbe s o he same adii ( hinne lame on hickness). In Fig. 6ii i can be obse ed ha he de elopmen o ins abili ies occu s a smalle adii o he medium and high hyd ogen con en mix- u es (50, 80 and 100% o H 2 ) han o hose wi h high me hane con en (20 and 0% o H 2 ). Con as ing Fig. 6i and 6ii shows ha he lame hickness dec eases wi h inc easing hyd ogen con- en : o he same Pecle numbe a smalle adius is ob ained. Ins abili y peninsulas e sus Pecle numbe o combus- ions unde lean- uel condi ions a e p esen ed in Fig. 6iii, 6 . Fi s hing o no ice is ha he expe imen s wi h low hyd ogen con en a e sligh ly displaced o he le compa ed o hose wi h s oichiome ic- uel condi ions (i.e., sligh ly smalle alues o he c i ic Pecle numbe ). As o he medium and highe hyd ogen con en mix u es, hei peninsulas a e comple ely di e en since now hey a e uns able combus ions om hei o igin. The mo phology o his cu es is jus a line, meaning ha he g ow h a e cu es (S¼ ðnÞ) only ha e one oo , i.e., only one alue o he wa enumbe (n) ul ils S¼0 (ins ead o he wo ha he s able combus ions ha e wi h a peninsula shape); he uns able egion co esponds, conse- quen ly, wi h he uppe pa o he g aph shown in Fig. 6 and he s able egion is he in e io pa . When he ins abili y peninsulas a e ep esen ed e sus he lame adius (Fig. 6i and 6 i) he peninsulas o he lowe hyd ogen con en mix u es a e displaced o he igh , i.e., hei c i ical adius a e bigge compa ed o hose o he s oichiome ic case. This sugges ha mix u es wi h 0 and 20% o H 2 (i.e., me hane is dominan ) a e mo e s able a lean condi ions han a s oichiome ic condi ions. Fo high and medium hyd ogen con en s (dominan hyd ogen) he endency is he same, independen ly o i he ins abili y cu es a e ep esen ed e sus he Pecle numbe o lame adius (see Fig. 6 and 6 i). Flame s abili y na u e The compa ison o he e ec i e Lewis numbe , Le e , (calcu- la ed wi h mix u e p ope ies) wi h he c i ical alue Le e * (calcula ed by means o Eq. (7)) p o ides he key o know i a mix u e is in insically s able o no . Fo his eason, he alues o hese wo pa ame e s, in each combus ion p ocess, a e plo ed oge he in Fig. 7. All he s oichiome ic mix u es s udied in his esea ch wo k a e s able in hei o igin, since all he Lewis numbe s ep esen ed in Fig. 7 (i) a e bigge han i s c i ical alue (Le e >Le e * ). Compa ing his Figu e wi h he ins abili y peninsulas (Fig. 6) i can be said ha he close he wo Lewis numbe a e, he mo e o he le he peninsula is and he less s abilizing capabili y he he mal-di usi e e - ec has. The e olu ion o he Lewis numbe and i s c i ical alue based on he hyd ogen con en can be ela ed o he dominan uel in each case. T adi ionally, o mix u es o me hane/ hyd ogen/ai , has been accep ed ha hyd ogen is dominan when i s con en is 50% and highe , while in case o a lowe hyd ogen con en me hane is dominan . This can be seen in he esea ch o bu ning eloci ies o his ypes o mix u es ca ied ou by Reyes e al. [36]. These esul s a e compa ible wi h he expe imen al beha io obse ed o s oichiome ic mix u es in his s udy. I can be seen in he s abili y maps (Fig. 6), especially in hose ep esen ed e sus he lame adius (Fig. 6ii and 6i ) o in he Lewis numbe s (Fig. 7i), ha he shape o Fig. 7 eLe e and Le e * e sus he pe cen age o hyd ogen in he uel mix u e. in e na ional jou nal o hyd ogen ene gy xxx (xxxx) xxx 9 Please ci e his a icle as: Reyes M e al., S udy and cha ac e iza ion o he ins abili ies gene a ed in expanding sphe ical lames o hyd ogen/me hane/ai mix u es, In e na ional Jou nal o Hyd ogen Ene gy, h ps://doi.o g/10.1016/j.ijhydene.2022.05.063 giCoe icien s o Eqs. (4)-6) lWa eleng h FFuel/ai equi alence a io: uel/ai mass a io o e he s oichiome ic uel/ai mass a io: F¼m =ma m =mas oich Densi y sExpansion a io SG ow h a e o an ins abili y uPa ame e associa ed wi h hyd odynamic ins abili y UPa ame e associa ed wi h he he mal-di usi e ins abili y Subsc ip s 0 Re e ence condi ions b Bu ned c C i ical i Ini ial ub Unbu ned e e ences [1] Vu TM, Pa k J, Kim JS, Kwon OB, Yun JH, Keel SI. Expe imen al s udy on cellula ins abili ies in hyd oca bon/ hyd ogen/ca bon monoxideeai p emixed lames. In J Hyd ogen Ene gy 2011;36(11):6914e24. [2] Bech old JK, Ma alon M. Hyd odynamic and di usion e ec s on he s abili y o sphe ically expanding lames. Combus Flame 1987;67(1):77e90. [3] B adley D. Ins abili ies and lame speeds in la ge-scale p emixed gaseous explosions. Philos T ans R Soc London, Se A: Ma h Phys Eng Sci 1999;357(1764):3567e81. [4] B adley D, Ha pe CM. The de elopmen o ins abili ies in lamina explosion lames. Combus Flame 1994;99(3):562e72. [5] Tinau F, Reyes M, Melga A, Gim enez B. Op ical cha ac e iza ion o hyd ogen-ai lamina combus ion unde cellula i y condi ions. In J Hyd ogen Ene gy 2019;44(25):12857e71. [6] Gaydon AG, Wol ha d HG. Flames, hei s uc u e, adia ion, and empe a u e. Chapman &Hall; 1979. [7] Se les G. Schlie en and shadowg aph echniques: isualizing phenomena in anspa en media. 2002. [8] Reyes M, Tinau FV, Gim enez B, Cama~ no A. Combus ion and lame on mo phology cha ac e iza ion o H2eCO syngas blends in cons an olume combus ion bombs. Ene gy Fuels 2021;35(4):3497e511. [9] Gu G, Huang J, Han W, Wang C. P opaga ion o hyd ogeneoxygen lames in Hele-Shaw cells. In J Hyd ogen Ene gy 2021;46(21):12009e15. [10] Cao Y, Daha i M, Tlili I, Raise A. In es iga ion on he lamina lame speed o CH4/CO2/ai mix u e a a mosphe ic and high p essu es using Schlie en pho og aphy. In J Hyd ogen Ene gy 2020;45(55):31151e61. [11] Li F, Lee C- , Wang Z, Wu H, Lu G. Schlie en in es iga ion on impac s o duc size on mac oscopic sp ay cha ac e is ics o duc ed uel injec ion. Appl The m Eng 2020;176:115440. [12] Yu Y. Expe imen al s udy on e ec s o e hanol-diesel uel blended on sp ay cha ac e is ics unde ul a-high injec ion p essu e up o 350 MPa. Ene gy 2019;186:115768. [13] Ma alon M. In insic lame ins abili ies in p emixed and nonp emixed combus ion. Annu Re Fluid Mech 2007;39:163e91. [14] Is a o A, Lib o ich V. On he s abili y o p opaga ion o sphe ical lames. J Appl Mech Tech Phys 1966;7(1):43e50. [15] Williams FA. Combus ion heo y. 1985. [16] Bychko V, Libe man MA. Dynamics and s abili y o p emixed lames. Phys Rep 2000;325(4e5):115e237. [17] Ma alon M. The Da ieuseLandau ins abili y o p emixed lames. Fluid Dynam Res 2018;50(5):051412. [18] Fogla N, C e a F, Ma alon M. In luence o he Da ieus- Landau ins abili y on he p opaga ion o plana u bulen lames. P oc Combus Ins 2013;34(1):1509e17. [19] T oiani G, C e a F, Ma alon M. Expe imen al in es iga ion o Da ieuseLandau ins abili y e ec s on u bulen p emixed lames. P oc Combus Ins 2015;35(2):1451e9. [20] Reyes M, Tinau F, Gim enez B, Cama~ no A. Combus ion and lame on mo phology cha ac e iza ion o H2eCO syngas blends in cons an olume combus ion bombs. Ene gy Fuels 2021;35(4):3497e511. [21] Addabbo R, Bech old J, Ma alon M. W inkling o sphe ically expanding lames. P oc Combus Ins 2002;29(2):1527e35. [22] Law C. P opaga ion, s uc u e, and limi phenomena o lamina lames a ele a ed p essu es. Combus Sci Technol 2006;178(1e3):335e60. [23] Cla in P, Williams F. E ec s o molecula di usion and o he mal expansion on he s uc u e and dynamics o p emixed lames in u bulen lows o la ge scale and low in ensi y. J Fluid Mech 1982;116:251e82. [24] LapalmeD,Hal e F,Mounaı ¨m-Rousselle C, See s P. Cha ac e iza ion o he modi usi e and hyd odynamic mechanisms on he cellula ins abili y o syngas uel blended wi h CH4 o CO2. Combus Flame 2018;193:481e90. [25] Zhang N, Zhang F, Zhong S, Peng Z, Yu J, Liu H, e al. Nume ical and heo e ical in es iga ion o e hanol/ai lame ins abili y. Combus Theo Model 2020;24(6):1108e29. [26] Kim W, Sa o Y, Johzaki T, Endo T. Expe imen al s udy on he onse o lame accele a ion due o cellula ins abili ies. J Loss P e P ocess Ind 2019;60:264e8. [27] Kim WK, Mogi T, Kuwana K, Dobashi R. Sel -simila p opaga ion o expanding sphe ical lames in la ge scale gas explosions. P oc Combus Ins 2015;35(2):2051e8. [28] Bell JB, Cheng RK, Day MS, Shephe d IG. Nume ical simula ion o Lewis numbe e ec s on lean p emixed u bulen lames. P oc Combus Ins 2007;31(1):1309e17. [29] Oppong F, Zhongyang L, Li X, Xu C. Inhe en ins abili ies in e hyl ace a e p emixed lames. Fuel 2021;290:120000. [30] Sun Z-Y, Liu F-S, Bao X-C, Liu X-H. Resea ch on cellula ins abili ies in ou wa dly p opaga ing sphe ical hyd ogen-ai lames. In J Hyd ogen Ene gy 2012;37(9):7889e99. [31] Huang S, Zhang Y, Huang R, Xu S, Ma Y, Wang Z, e al. Quan i a i e cha ac e iza ion o c ack and cell's mo phological e olu ion in p emixed expanding sphe ical lames. Ene gy 2019;171:161e9. [32] Addabbo R. The s uc u e and s abili y o expanding and con e ging nea -s oichiome ic lames. New Je sey Ins i u e o Technology; 2001. [33] Kelley AP, Jomaas G, Law CK. C i ical adius o sus ained p opaga ion o spa k-igni ed sphe ical lames. Combus Flame 2009;156(5):1006e13. [34] B adley D, Sheppa CGW, Woolley R, G eenhalgh DA, Locke RD. The de elopmen and s uc u e o lame ins abili ies and cellula i y a low Ma ks ein numbe s in explosions. Combus Flame 2000;122(1e2):195e209. [35] Jiang Y-H, Li G-X, Li H-M, Li L, Tian L-L. S udy on he in luence o lame inhe en ins abili ies on c ack p opaga ion o expanding p emixed lame. Fuel 2018;233:504e12. [36] Reyes M, Tinau FV, Ho illo A, La uen e A. Expe imen al cha ac e iza ion o bu ning eloci ies o p emixed me hane- ai and hyd ogen-ai mix u es in a cons an olume combus ion bomb a mode a e p essu e and empe a u e. Appl The m Eng 2018;130:684e97. in e na ional jou nal o hyd ogen ene gy xxx (xxxx) xxx16 Please ci e his a icle as: Reyes M e al., S udy and cha ac e iza ion o he ins abili ies gene a ed in expanding sphe ical lames o hyd ogen/me hane/ai mix u es, In e na ional Jou nal o Hyd ogen Ene gy, h ps://doi.o g/10.1016/j.ijhydene.2022.05.063 [37] Reyes M, Tinau FV, Gim enez B, Pas o JV. E ec o hyd ogen addi ion on he OH*and CH*chemiluminescence emissions o p emixed combus ion o me hane-ai mix u es. In J Hyd ogen Ene gy 2018;43(42):19778e91. [38] Miao H, Ji M, Jiao Q, Huang Q, Huang Z. Lamina bu ning eloci y and Ma ks ein leng h o ni ogen dilu ed na u al gas/hyd ogen/ai mix u es a no mal, educed and ele a ed p essu es. In J Hyd ogen Ene gy 2009;34(7):3145e55. [39] Miao H, Jiao Q, Huang Z, Jiang D. Measu emen o lamina bu ning eloci ies and Ma ks ein leng hs o dilu ed hyd ogen- en iched na u al gas. In J Hyd ogen Ene gy 2009;34(1):507e18. [40] Hu E, Huang Z, He J, Miao H. Expe imen al and nume ical s udy on lamina bu ning eloci ies and lame ins abili ies o hyd ogeneai mix u es a ele a ed p essu es and empe a u es. In J Hyd ogen Ene gy 2009;34(20):8741e55. [41] Hu E, Huang Z, He J, Miao H. Expe imen al and nume ical s udy on lean p emixed me haneehyd ogeneai lames a ele a ed p essu es and empe a u es. In J Hyd ogen Ene gy 2009;34(16):6951e60. [42] Ge ke U, S eu s K, Rebecchi P, Boulouchos K. De i a ion o bu ning eloci ies o p emixed hyd ogen/ai lames a engine- ele an condi ions using a single-cylinde comp ession machine wi h op ical access. In J Hyd ogen Ene gy 2010;35(6):2566e77. [43] Reyes M, Tinau F, Melga A, P e ez A. Cha ac e iza ion o he combus ion p ocess and cycle- o-cycle a ia ions in a spa k igni ion engine uelled wi h na u al gas/hyd ogen mix u es. In J Hyd ogen Ene gy 2016;41(3):2064e74. [44] Ve hels S, Wallne T. Hyd ogen- ueled in e nal combus ion engines. P og Ene gy Combus Sci 2009;35(6):490e527. [45] Wang J, Huang Z, Miao H, Wang X, Jiang D. S udy o cyclic a ia ions o di ec -injec ion combus ion ueled wi h na u al gasehyd ogen blends using a cons an olume essel. In J Hyd ogen Ene gy 2008;33(24):7580e91. [46] Tse SD, Zhu DL, Law CK. Mo phology and bu ning a es o expanding sphe ical lames in H2/O2/ine mix u es up o 60 a mosphe es. P oc Combus Ins 2000;28(2):1793e800. [47] Hu E, Huang Z, He J, Zheng J, Miao H. Measu emen s o lamina bu ning eloci ies and onse o cellula ins abili ies o me haneehyd ogeneai lames a ele a ed p essu es and empe a u es. In J Hyd ogen Ene gy 2009;34(13):5574e84. [48] Tang C, He J, Huang Z, Jin C, Wang J, Wang X, e al. Measu emen s o lamina bu ning eloci ies and Ma ks ein leng hs o p opaneehyd ogeneai mix u es a ele a ed p essu es and empe a u es. In J Hyd ogen Ene gy 2008;33(23):7274e85. [49] Law CK, Jomaas G, Bech old JK. Cellula ins abili ies o expanding hyd ogen/p opane sphe ical lames a ele a ed p essu es: heo y and expe imen . P oc Combus Ins 2005;30(1):159e67. [50] Jiang Y-H, Li G-X, Li F-S, Sun Z-Y, Li H-M. Expe imen al in es iga ion o co ela ion be ween cellula s uc u e o he lame on and p essu e. Fuel 2017;199:65e75. [51] Kim W, Imamu a T, Mogi T, Dobashi R. Expe imen al in es iga ion on he onse o cellula ins abili ies and accele a ion o expanding sphe ical lames. In J Hyd ogen Ene gy 2017;42(21):14821e8. [52] Zhang M, Chang M, Wang J, Huang Z. Flame dynamics analysis o highly hyd ogen-en ichmen p emixed u bulen combus ion. In J Hyd ogen Ene gy 2020;45(1):1072e83. [53] Wu F, Jomaas G, Law CK. An expe imen al in es iga ion on sel -accele a ion o cellula sphe ical lames. P oc Combus Ins 2013;34(1):937e45. [54] Sun Z-Y, Li G-X, Li H-M, Zhai Y, Zhou Z-H. Buoyan uns able beha io o ini ially sphe ical lean hyd ogen-ai p emixed lames. Ene gies 2014;7(8):4938e56. [55] Fai wea he M, O msby M, Sheppa d C, Woolley R. Tu bulen bu ning a es o me hane and me haneehyd ogen mix u es. Combus Flame 2009;156(4):780e90. [56] Kwon O, Rozenchan G, Law C. Cellula ins abili ies and sel - accele a ion o ou wa dly p opaga ing sphe ical lames. P oc Combus Ins 2002;29(2):1775e83. [57] Oka o EC, Nagano Y, Ki agawa T. Expe imen al and heo e ical analysis o cellula ins abili y in lean H2-CH4-ai lames a ele a ed p essu es. In J Hyd ogen Ene gy 2016;41(15):6581e92. [58] Law CK, Kwon O. E ec s o hyd oca bon subs i u ion on a mosphe ic hyd ogeneai lame p opaga ion. In J Hyd ogen Ene gy 2004;29(8):867e79. [59] Smallbone A, Tsuneyoshi K, Ki agawa T. Tu bulen and s able/uns able lamina bu ning eloci y measu emen s om ou wa dly p opaga ing sphe ical hyd ogen-ai lames a ele a ed p essu es. J The m Sci Technol 2006;1(1):31e41. [60] Wang J, Zhang M, Huang Z, Kudo T, Kobayashi H. Measu emen o he ins an aneous de ailed lame on s uc u e o syngas u bulen p emixed lames a high p essu e. In: 9 h asia-paci ic con e ence on combus ion, ASPACC 2013; 2013. [61] Wang J, Zhang M, Huang Z, Kudo T, Kobayashi H. Measu emen o he ins an aneous lame on s uc u e o syngas u bulen p emixed lames a high p essu e. Combus Flame 2013;160(11):2434e41. [62] Zhao H, Wang J, Bian Z, Cai X, Li X, Huang Z. Onse o cellula ins abili y and sel -accele a ion p opaga ion o syngas sphe ically expanding lames a ele a ed p essu es. In J Hyd ogen Ene gy 2019;44(51):27995e8006. [63] Bech old JK, Ma alon M. The dependence o he Ma ks ein leng h on s oichiome y. Combus Flame 2001;127(1):1906e13. [64] Cla in P. Dynamic beha io o p emixed lame on s in lamina and u bulen lows. P og Ene gy Combus Sci 1985;11(1):1e59. [65] Hu E, Huang Z, He J, Jin C, Zheng J. Expe imen al and nume ical s udy on lamina bu ning cha ac e is ics o p emixed me haneehyd ogeneai lames. In J Hyd ogen Ene gy 2009;34(11):4876e88. [66] Huang S, Huang R, Zhang Y, Zhou P, Wang Z, Yin Z. Rela ionship be ween cellula mo phology and sel - accele a ion in lean hyd ogen-ai expanding lames. In J Hyd ogen Ene gy 2019;44(59):31531e43. [67] Huang S, Huang R, Zhou P, Zhang Y, Yin Z, Wang Z. Role o cellula wa eleng hs in sel -accele a ion o lean hyd ogen- ai expanding lames unde u bulen condi ions. In J Hyd ogen Ene gy 2021;46(17):10494e505. in e na ional jou nal o hyd ogen ene gy xxx (xxxx) xxx 17 Please ci e his a icle as: Reyes M e al., S udy and cha ac e iza ion o he ins abili ies gene a ed in expanding sphe ical lames o hyd ogen/me hane/ai mix u es, In e na ional Jou nal o Hyd ogen Ene gy, h ps://doi.o g/10.1016/j.ijhydene.2022.05.063