Energy 43 (2012) 19e29. Contents lists available at SciVerse ScienceDirect. Energy. journal homepage:

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1 Eergy 43 (2012) 19e29 tets lists available at civerse ciecedirect Eergy jural hmepage: Validati ad aalysis f detailed kietic mdels fr ethylee cmbusti haqi Xu a,b, Alexader A. Kv a, * a Divisi f mbusti Physics, Departmet f Physics, ud iversity, P.O Bx 118, E ud, wede b Natial Key abratry f mbusti, Flw ad Therm-tructure, Nrthwester Plytechical iversity, Xi a, Peple s Republic f hia article if abstract Article histry: Received 19 Jue 2011 Received i revised frm 29 eptember 2011 Accepted 4 Nvember 2011 Available lie 2 December 2011 Keywrds: Ethylee Igiti Flame prpagati Mdel validati Preset wrk aims at evaluati f ctemprary cmprehesive detailed kietic mechaisms fr ethylee cmbusti, icludig the Kv mechaism, N Butae mechaism, a Dieg (D) mechaism ad mechaism. These mdels have bee validated by extesive cmparis with available experimetal data ethylee igiti ad flame prpagati. The experimetal data frm the literature have bee carefully examied t accurately assess the mdels predictig perfrmace. Nticeable differeces i the predictis f ethylee igiti ad flame prpagati uder a variety f cditis have bee bserved. Mrever, sesitivity aalysis has bee cducted t idetify imprtat reactis fr the predicti f ethylee igiti ad flames. Fr ethylee igiti, it was fud that 2 H 4 csumpti reactis with radicals OH, O ad subsequet reactis f viyl with xyge have dmiat effect predicted igiti delays. The pathway aalysis has als bee perfrmed fr each mechaism t idetify differet reacti pathways i ethylee igiti prcess. Fr ethylee flames, sesitivity aalysis shws that HeO ad 1 chemistry reactis sigificatly ifluece the lamiar burig velcity i lea ethylee/air flames, while 2 chemistry reactis becme f icreasig imprtace i fuel-rich flames. Furthermre, t better uderstad the mdels predictig behavir, the differeces i the reacti rate cstats ad rutes f 2 H 4 ad viyl chemistry have bee aalyzed ad discussed. Ó 2011 Elsevier td. All rights reserved. 1. Itrducti Ethylee has received a wide research iterest i recet years, sice it is a key itermediate i the xidati f higher alkaes ad alkees, ad thereby plays a imprtat rle i the cmbusti chemistry f mst practical fuels. It is e f the mst imprtat petrchemicals prduced thrugh steam crackig [1]. Mrever, ethylee itself is a very reactive fuel as well as a typical crackig ad decmpsiti prduct f strable JP-type hydrcarb fuels fr high-speed airbreathig prpulsi applicatis, such as pulse detati egies ad cramjet [2]. Recet advaces i the develpmet f detailed chemical kietic mechaisms fr hydrcarb fuels csiderably help t ly i deep uderstadig f cmbusti phemea, but als i accurately predictig cmbusti prcesses, such as igiti, flame prpagati ad exticti characteristics which are the key parameters fr cmbusti applicatis. * rrespdig authr. Tel.: þ ; fax: þ address: Alexader.Kv@frbrf.lth.se (A.A. Kv). Igiti delay time ad lamiar flame burig velcity are crucial characteristics f fuel cmbusti frm bth fudametal ad practical csideratis ad fte used as key parameters fr chemical kietic mechaisms validati ad ptimizati. A csiderable amut f available experimetal data ethylee igiti ad flames has bee reprted ver the past several decades. everal detailed kietic mechaisms [3e6] fr ethylee cmbusti have bee prpsed ad develped t reprduce, iter alia, available experimetal data ethylee xidati. Hwever, due t remaiig ucertaities bth i the rates ad reacti pathways amg differet detailed kietic mechaisms, ticeable discrepacies i the predicti behavirs f ethylee igiti ad flames have bee bserved. The purpse f the preset study was validati ad aalysis f several ctemprary cmprehesive detailed kietic mechaisms fr ethylee cmbusti, icludig the Kv mechaism [3], N Butae mechaism [4], a Dieg mechaism [5] ad mechaism [6]. Oe shuld te that althugh the mdel frm N was validated fr -Butae [7] (hece the ame) it was als validated fr flames f methae, ethae, ethylee ad prpae [4]. I rder t precisely assess mdelig results, experimetal data fr ethylee igiti ad flames frm the literatures have bee /$ e see frt matter Ó 2011 Elsevier td. All rights reserved. di: /j.eergy

2 20. Xu, A.A. Kv / Eergy 43 (2012) 19e29 Table 1 ummary f available 2 H 4 /O 2 igiti delay experimets i shck tubes. Equivalece rati F % Diluet (Ar) P(atm) T(K) Igiti criteria/detecti methd Ref. 0.21e3.5 96e99 0.2e e2350 H* set/icidet shck [10] 0.5, , e e2300 O þ O 2 emissi 10% f max [11] 1, 1.5, 2 84, 85, 92e95 1.0e e1650 OH* max [12] 0.125e2 93e99 3, e1900 OH* max/idewall [13] 0.46e e e1400 OH* absrpti max rate f chage [14] 0.5, 1, e93 1.1e e2365 O þ O 2 emissi fr [O][O] [15] maximum/icidet shck 1, 1.5, 3 98, 97, 96 1e5 1400e2100 H* set/idewall [16] 0.5, 1, e e e2100 O 2 emissi set [17] 1 96, 75 1e3 1000e1800 H* set/edwall [18] 1, (N 2 ), 75(N 2 ) 1e4 800e1620 H* set/idewall [19] 0.5, 0.75, 1 95e97 3e8 1100e1500 OH* set/idewall [2] 1 84, 92, e4 1253e1572 H* max/idewall [20] 0.5, 1 96, e e1900 OH* set, OH* max/edwall [21] 0.5, 1, , 75, 70.5(N 2 ) 5.9e e1520 H* set, 2 set, OH set/edwall [22] 1, 3 93, 96, 98 2, 10, e1650 H* set, OH* set, Visible light/edwall [23] carefully examied ad the were used t cmpare with the mdelig. Als, sesitivity ad reacti pathways aalyses at differet cditis were emplyed fr aalysig the predictig behavir f the mdels. 2. Igiti delays 2.1. Available experimetal data May igiti experimets have bee cducted t build ad exted igiti delay time database ad als t cmpare with previus studies ad mdel predictis. Numerus researchers [8e23] ivestigated igiti f ethylee highly diluted by arg r itrge i shck tubes which ca prvide the ear-cstatvlume reacti cditis with well-defied temperatures ad pressures [24]. Available experimetal data fr ethylee igiti are summarized i Table 1. Mst ethylee shck tube studies prir t 1999 were summarized i the wrk f chultz ad hepherd [8].I the recet studies, Hrig [20] perfrmed ethylee igiti (Ø ¼ 1) experimets at pressures 1e4 atm, cverig a temperature rage f w1250e1700 K by mitrig H* emissi maximum. The effects f pressure ad diluet arg igiti delay time were studied, ad it was fud that the igiti delay times were lger at higher dilutis ad lwer pressures. axea et al. [23] cducted experimets with differet dilutis (Ar ¼ 93%, 96%, 98%) i reflected shck waves ver a temperature rage f 1000e1650 K at pressures f 2, 10 ad 18 atm, equivalece rati f 3 ad 1. I their study, the igiti delay times shwed little variati with pressure ad equivalece rati at the cditis f 93% arg diluti, while the lger igiti delay times were bserved at lwer pressures fr higher diluted mixtures (Ar ¼ 96%, 98%). The authrs als cmpared their experimetal results with the predictis f the ptimized versi f mechaism ad fud that the mdel shws a very gd agreemet at high pressures (P ¼ 10 ad 18 atm), but verpredicts the igiti delay times i lw temperature rage (less tha 1250 K) at lw pressures. Varatharaja ad Williams [9] summarized the previus experimetal ethylee igiti delay results, ad validated their detailed ethylee reacti mechaism by usig these experimetal data. They ccluded that their mdelig results idicated gd agreemet with the high-temperature data (abve 1500 K), e.g. [17], whereas at lwer temperatures, the igiti times were very sesitive t the chice f the igiti criteri. Numerus ethylee igiti data have bee btaied uder a variety f experimetal cditis, hwever, it is difficult t cmpare these data directly due t the differeces i the igiti detecti methd ad igiti defiiti i these studies. Whe perfrmig detailed kietic mdel validati, it is ecessary t carefully csider the discrepacies amg differet igiti delay time studies. Hrig [20] ted that the igiti times recrded at the shck tube sidewall may be sigificatly shrter tha thse measured at the edwall due t perturbatis caused by ptetial -ideal gas-dyamic effects resulted frm the eergy release f the reacti, especially fr highly eergetic mixtures at higher temperatures. Kalita et al. [21] preseted cmparis f igiti delay times btaied frm edwall ad sidewall emissi traces. The results shwed the sidewall igiti was accelerated slightly at the higher temperatures ad culd be as much as 30% faster tha the edwall results at abut 1700 K ad 1 atm fr stichimetric mixture with 98% arg diluti. Additial effects eed t be csidered iclude the actual defiiti f igiti delay time. sually igiti criteria is based maximum r set emissi f cmbusti itermediate species such as H* r OH*. Varatharaja ad Williams [9] have cfirmed that the igiti times predicted by differet criteria ca typically differ by a factr f abut tw at high temperature ad lw pressure. These experimetal details ca be quite imprtat, particularly whe cmparig measuremets with the results f mdelig r ther experimets that might be based differet diagstics methds ad defiitis f igiti. T facilitate direct cmparis f experimetal data uder differet cditis, crrelatis f igiti delay time with cmpsiti ad temperature were usually utilized. The mst ppular crrelati frm is as fllwig: s ¼ Z½ 2 H 4 Š a ½O 2 Š b ½ArŠ c e Ea = RT (1) where Z is scalig cstat, [i] is the ccetrati f reactat i, T is mixture temperature ad Ea is the verall activati eergy. Remarkably, a umber f largely differet crrelatis have bee prpsed. Mst studies idetified strg depedece f igiti delay xyge ccetrati (pwer expet b i Eq. (1) varies frm 1.2 t 0.83), ad weak depedece f igiti ethylee ccetrati (pwer expet a varies frm 0 t 0.3). lket ad padaccii [2] ad Kalita et al. [21] believed the arg ccetrati depedecy is egligible, while axea et al. [23] csidered the arg ccetrati depedecy reasably sigificat. I additi, activati eergy variatis frm 17.1 t 35 kcal/ml were fud i previus studies. This might be due t the differet rages f temperature, cmpsiti ad pressure. Hrig [20] has fud the igiti time f ethylee shwed icreasig verall activati eergy with icreasig pressure i the rage f 1e4 atm. ice ethylee igiti delay data were btaied ver a wide rage f experimet cditis ad with differet defiitis f

3 . Xu, A.A. Kv / Eergy 43 (2012) 19e29 21 t thse f Baker ad kier [13] ad Kalita et al. [21] at pressures abut 3 atm, which ca be due t the igiti delay time based H set ad H maximum are t be shrter tha the data based OH maximum, as shw i Fig. 3 ad discussed i the fllwig. Fr Ø ¼ 1, Ar ¼ 92% cditis, measuremets f Hrig [20] shw the effect f pressure igiti delay. As shw i Fig. 2, the agreemet betwee the igiti delay times btaied by Drummd [12] usig OH maximum criteria at pressures abut 1.4e1.6 atm ad Hrig [20] usig H maximum criteria at pressure abut 1 atm is reasable Mdelig details Fig. 1. mparis f ethylee igiti delay data at Ø ¼ 1, Ar ¼ 96% (P w 1e3 atm) ad crrelatis fr igiti delays at P ¼ 3 atm. igiti, the apparet discrepacies were fud. Therefre, i rder t fcus the aalysis f the igiti delay data ad mdel evaluati, ly the cmparis f the stichimetric ethylee igiti delays ad sme crrelatis [2,23,25] at similar cditis (lw pressure, Ar ¼ 96% ad 92%) are respectively preseted i Figs. 1 ad 2. Fr Ø ¼ 1, Ar ¼ 96% cditis, the cmparis shws bvius disagreemet betwee experimetal data f Baker ad kier [13] ad f Kalita et al. [21] based OH* maximum emissi criteria at pressures abut 3 atm. The igiti delay times f Baker ad kier [13] pssess strger temperature depedecy that leads t lger delay times at lw temperatures ad shrter delay times at higher temperatures as cmpared t the data f Kalita et al. [21] ad crrelatis btaied by axea et al. [23] ad lket ad padaccii [2]. Measuremets f Hidaka et al. [16] ad f Brw ad Thmas [18] are i gd csistecy with thse f Baker ad kier [13] at high temperatures, hwever their data were btaied based H* emissi set which shuld give shrter delays tha the results btaied based OH* emissi maximum as will be shw i the fllwig. May researchers have idicated that igiti delay time is sesitive t pressure at lw pressures ad is shrter fr higher pressures. The delay times btaied by axea et al. [23], ad by Hrig [20] at pressures abut 2 atm are similar hemki-pr clsed hmgeeus batch reactr mdel [26] with cstat-vlume adiabatic assumpti was used fr the simulatis f ethylee igiti prcess. Fig. 3(a) shws typical predicted temperature, H ad OH ccetrati prfiles as a fucti f time at Ø ¼ 1, Ar ¼ 96% P w 2 atm. As ca be see, OH ccetrati typically shws fast icreasig after a lw ccetrati ad slw preigiti prcess, ad the relatively slw declie ccurs durig a perid f time. That may lead t ucertaity ad difficulty t determie igiti delay time whe usig OH maximum as igiti criteria fr mdel validati. I ctrast, H experieces a rapid icrease ad drp ver very shrt time. H maximum ca be readily defied, ad it was fud that H Fig. 2. mparis f ethylee igiti delay data at Ø ¼ 1, Ar ¼ 92% (P w 1e4 atm). Fig. 3. Typical mdel predictis (the Kv mdel [3]): (a). OH, H ccetratis ad temperature prfile (b). predicted igiti delay times defied usig differet criteria.

4 22. Xu, A.A. Kv / Eergy 43 (2012) 19e29 cmbiig chemilumiescece sub-mechaisms f Hall et al. [28] ad f Haber ad Vadsburger [29] with the GRI-mech. ad with the Kv reacti mechaisms. They fud sigificat discrepacies betwee these tw mdels ad ccluded that further develpmet f the chemilumiescece sub-mechaisms is required. Ne f the mechaisms aalyzed i the preset wrk iclude excited species; hece, t avid additial ambiguity, they were t supplemeted by still ucertai chemilumiescece submechaisms. O the ther had, Hall et al. [28] ccluded that H* fllws H peak withi 5% ver mst f the cditis studied, while OH ad OH* igiti times were fud t be csistet ly fr T < 1600 K. Fr T > 1600 K, OH ad OH* igiti errr may be as great as 30%. This shuld be kept i mid whe cmparig experimets ad mdel predictis discussed belw mparis f the experimets ad mdels Fig. 4. mparis f experimetal igiti delay times (symbls) with predicti results (lies) usig differet mdels at Ø ¼ 1, Ar ¼ 96%, P w 3 atm. maximum igiti time was much clser t the maximum temperature chage. I additi, the species set igiti time is als difficult t be well defied due t istrumetal depedecy. Therefre, it is better ad cveiet t use H maximum as experimetal igiti defiiti fr mdel validati. As shw i Fig. 3(b), predicted igiti delay times usig differet igiti criteria culd differ sigificatly at high temperatures. Mst f experimetal igiti delays are based the ccetratis f electrically excited H* ad OH*. These excited species are t ecessarily i a straightfrward relatiship with grudstate radicals H ad OH. A fair cmparis f the experimets ad mdelig therefre shuld iclude predicti f these excited species. Wagher et al. [27] cmpared mdel predictis f OH* I the fllwig the calculatis based OH maximum ad H maximum were perfrmed fr mdel evaluati t respectively cmpare with the experimetal data f Baker ad kier [13] ad Kalita et al. [21] at Ø ¼ 1, Ar ¼ 96% cditis ad thse f Hrig [20] at Ø ¼ 1, Ar ¼ 92%. mpariss f the stichimetric ethylee igiti delay times at Ar ¼ 96%, P w 3 atm cditis are preseted i Fig. 4. The calculatis usig the Kv mechaism are i very gd agreemet with the experimetal data frm Baker ad kier [13] i lw temperature rage (1100 < T < 1400 K), ad verpredict the experimetal data as temperature is icreasig. Additially, the Kv mechaism verpredicts the experimetal data btaied by Kalita et al. [21] thrughut their experimetal temperature rage, typically by a factr f tw. While the mdelig usig D ad mechaisms gives very gd agreemet with Kalita et al. [21] results, they uderpredict the data f Baker ad kier [13] i lwer temperature rage. N Butae mdel cat reprduce Fig. 5. mparis f experimetal data at Ø ¼ 1, Ar ¼ 92% [20] (symbls) ad predicti results (lies) usig differet mdels.

5 . Xu, A.A. Kv / Eergy 43 (2012) 19e29 23 well these experimet data, the predicti results are i betwee the Kv ad mdels at lw temperature (T < 1400 K), ad verpredicti becmes mre severe with icreasig temperature. Fig. 5 presets cmparis f experimetal data btaied by Hrig [20] ad predicted igiti delays usig differet mechaisms fr 92% arg diluted stichimetric 2 H 4 /O 2 mixture at differet pressures. As ca be see, the mdelig results usig mechaism shw the best agreemet with the experimetal data ver etire temperature rage at differet pressures, especially fr high temperature regi. The Kv mdelig results verpredict the experimet data typically by abut a factr f 2 at these cditis, while the D mechaism uderpredicts the experimetal igiti delays withi a factr f 2. N Butae mechaism bviusly verpredicts the experimet data, especially at lw pressure cditis. Besides, i all cases, ly D mechaism predicts table verall activati eergy chage with the pressure which was experimetally bserved by Hrig [20] Mdelig aalysis Brute-frce sesitivity aalysis was perfrmed t idetify imprtat reactis i the ethylee igiti prcess. The sesitivities f igiti delay time based H maximum criteria fr stichimetric mixture (Ar ¼ 92%) at pressure 2.1 atm ad temperature 1350 K are preseted i Fig. 6. esitivity aalysis shws that 2 H 4 iitial csumpti reactis with radicals O ad Fig. 6. esitivities f igiti delay time based H maximum criteria usig differet mechaisms fr Ø ¼ 1, Ar ¼ 92%, P ¼ 2.1 atm ad T ¼ 1350 K. Fig. 7. Pathway aalysis i igiti prcess at the time f T ¼ 1360 K fr Ø ¼ 1, Ar ¼ 92%, P ¼ 2.1 atm ad iitial T ¼ 1350 K.

6 24. Xu, A.A. Kv / Eergy 43 (2012) 19e29 Table 2 Measuremets f lamiar burig velcities i 2 H 4 /O 2 /N 2 flames. Equivalece rati F % Diluet O 2 /(N 2 þ O 2 ) P(atm) T(K) Experimet methd Ref. 0.5e1.4 18% 0.5, 1,2 298 uter-flw flame/liear extraplati [36] 21% 1 0.5e1.4 21% 0.5, 1, 2, 3, Outwardly prpagatig spherical flames/with [35] -liear extraplati 0.5e1.4 21% uter-flw flame/-liear extraplati [33] 0.5e1.4 21% 1, 2, Outwardly prpagatig spherical flames/-liear [31] extraplati 0.6e1.4 14%e18% Heat flux methd [32] 0.5e1.4 21% 1 298, 360, 400, 470 cuter-flw flame/liear extraplati [34] OH ad subsequet reactis f viyl with xyge have imprtat effect ethylee igiti predicti, hwever sigificat variati f the relative imprtace f varius reactis was als bserved, which might be attributed t the differet reacti rutes ad rate cstats f these reactis i differet mechaisms. It is als see that HO decmpsiti reacti ad reacti f HO with O 2 are much mre sesitive i the ad N Butae mechaisms tha i the Kv ad D mechaisms. T better uderstad the variaces amg these mechaisms, reacti pathway aalysis at the same cditis as the sesitivity aalysis was carried ut, as shw i Fig. 7. T facilitate the cmparis, the time f 10 K iitial icrease f the temperature (T ¼ 1360 K) was selected fr the reacti pathway aalysis fr all mechaisms. The maximum umber f species displayed i reacti pathways was limited t 10 accrdig t rakig f the maximum rate f depleti f all species. It ca be see that radicals 2 H 3 ad H 2 HO are csumed i differet ways. I the Kv mechaism, csiderable parts f 2 H 3 recmbie with 2 H 4 t frm 4 H 6 ad H, which is imprtat i this mechaism as idicated als by the sesitivity aalysis. This reacti is t icluded i D mechaism ad its rate is tw rders f magitude faster tha i N Butae mechaism. Mrever, mst f H 2 HO is cverted it O via itermediate prducti f H 3 O i the Kv mechaism, rather tha directly decmpse t prduce O ad H 3 as i ther mechaisms. I mechaism, HO ca directly frm O by reacti with 2 H 4, which is t icluded i ther mechaisms. Besides, reacti H 3 þ 2 H 4 ¼ 2 H 3 þ H 4 is t take it accut i D mechaism. Whe perfrmig mdel validati usig igiti delays, e shuld te that the experimetal data shuld be carefully assessed, give the great discrepacies ca arise i experimetal igiti data due t differet igiti criteria ad experimetal methd. Mrever, it is see that mdelig igiti delay times usig differet criteria have great variatis at high temperatures ad simulated ccetrati prfiles suggest H maximum as the igiti criteria frm bth experimetal ad mdel validati csiderati. The predicti perfrmace f these mdels fr igiti has bee assessed by cmparig with experimetal data at stichimetric cditi. me imprtat reactis, such as 2 H 4 iitial csumpti reactis with radicals O ad OH ad subsequet reactis f viyl with xyge have bee idetified t exert a sigificat effect ethylee igiti predicti. The differece i the reacti rates f these reactis ad ucertaities i differet mechaisms will be discussed belw. stretch-crrected lamiar burig velcities have bee btaied usig either cuterflw flames r utwardly prpagatig spherical flames i cstat pressure chambers with extraplati t zer stretch. Experimetal data fr the lamiar burig velcity f 2 H 4 /air mixtures at temperature f 298 K ad pressure f 1 atm are shw i Fig. 8. Ntable discrepacies are fud amg existig data, especially fr ear stichimetric ad rich mixtures, which might be due t differet extraplati methds i dealig with stretch effects flame speeds. Ji et al. [30] have revealed larger discrepacies tward fuel-rich mixtures betwee determiati f lamiar burig velcity usig liear ad -liear extraplatis. Jmaas et al. [31] ivestigated ethylee/air flames at rm temperature uder bth atmspheric ad elevated pressures, ad pited ut that ticeable differeces were bserved i the cmparis f their experimetal data ad calculated results. Kv et al. [32] perfrmed measuremets f the adiabatic burig velcity f 2 H 4 /O 2 /N 2 mixtures t determie the effects f cmpsiti whe xyge ctet i sythetic air was varied frm 18% t 14% by usig the heat flux methd which prduced stretched flames. Hirasawa et al. [33] ivestigated lamiar flames i a cuterflw cfigurati ad the lamiar burig velcities were btaied thrugh accurate determiati f referece speed ad stretch by usig digital particle image velcimetry (DPIV). Kumar et al. [34] have studied atmspheric pressure lamiar flames f premixed 2 H 4 /O 2 /N 2 mixtures i a cuterflw cfigurati with the mixture temperatures varyig frm 298 t 470 K. Their experimetal results were reasably predicted by tw chemical kietic mechaism ( ad D) at rm temperature, while the discrepacy becmes larger with icreasig preheat temperature. 3. amiar burig velcity 3.1. Available experimetal data everal grups have ivestigated the lamiar burig velcity f premixed ethylee/o 2 /N 2 mixtures at varius cditis by usig differet experimetal methds, as summarized i Table 2. These Fig. 8. mparis f experimetal data (symbls) ad mdelig (lies) f the lamiar burig velcities fr ethylee/air mixture at temperature 298 K ad atmspheric pressure.

7 . Xu, A.A. Kv / Eergy 43 (2012) 19e mparis f the experimets ad mdels Fig. 9. mparis f experimetal data (symbls) ad mdelig (lies) fr the lamiar burig velcities f ethylee/air mixture at atmspheric pressure ad temperatures f 360 ad 470 K Mdelig details Premixed adiabatic lamiar flames have bee mdeled usig hemki-pr [26] uder varius experimetal cditis. Multi-cmpet diffusi ad thermal diffusi ptis were take it accut. Adaptive mesh parameters were GRAD ¼ 0.05e0.1, ad RV ¼ 0.5. Ttal umber f grid pits i these calculatis was typically abut 160e260, relative ad abslute errr criteria were RTO ¼ 1E-4 ad ATO ¼ 1E-9. The experimetal data fr 2 H 4 /air lamiar flames at temperature f 298 K ad pressure f 1atm are cmpared with mdelig predictis i Fig. 8. The cmputed lamiar burig velcities usig the D mechaism shw higher values tha ther mechaisms, especially fr ear stichimetric mixtures, althugh the mdelig well reprduces the experimetal data btaied by Kumar et al. [34] usig cuter-flw flame with liear extraplati which might be leadig t higher results as discussed earlier. The cmputed results usig the Kv ad mechaisms are very clse ad i gd agreemet with the experimetal data btaied by Hassa et al. [35] ad Jmaas et al. [31] deduced frm utwardly prpagatig spherical flames with -liear extraplati methd. The small variace i the predicti usig the Kv mechaism shws lwer lamiar burig velcity fr lea mixtures tha mechaism. The mdelig usig N Butae mechaism shws idistiguishable results with the mdelig usig mechaism fr the mixtures with equivalece ratis less tha 0.9, hwever sigificat uderpredicti by N Butae mdel has bee fud fr ear stichimetric ad rich mixtures. ice mst f practical applicatis are t at rm temperature ad atmspheric pressure, it is imprtat t assess mdelig predictis fr the lamiar burig velcity f 2 H 4 /air mixtures at these elevated cditis. mpariss betwee experimetal ad mdelig results at preheat ubured mixture temperature ad elevated pressures have bee cducted, as respectively shw i Figs. 9 ad 10. As shw i Fig. 9, the mdels behavirs fr 2 H 4 þ N 2 (79%) þ O 2 (21%) mixture at temperatures f 360 K ad 470 K are similar t that at 298 K, the discrepacies f mdelig predicti icrease with the preheat temperature icreasig. It was Fig. 10. mparis f experimetal data (symbls) ad mdelig (lies) fr the lamiar burig velcities f ethylee/air mixture at rm temperature ad pressures f 0.5, 2, ad 5 atm.

8 26. Xu, A.A. Kv / Eergy 43 (2012) 19e29 fud that the differece f the mdelig results betwee the Kv mechaism ad mechaism fr the preheat temperature f 470 K is abut 6 cm/s at equivalet rati f 0.5, ad the differece f the mdelig results at the preheat temperature f 470 K betwee N Butae mechaism ad mechaism is as much as abut 22 cm/s at equivalet rati f 1.4. Fig. 10 presets cmparis f experimetal data at differet pressures btaied by Hassa et al. [35] ad Jmaas et al. [31] ad mdelig results. The mdelig results usig mechaism idicates gd predicti at the pressure f 0.5 atm ad 2 atm, ad slight uderpredicti f the lamiar burig velcities fr rich mixtures at the pressure f 5 atm. The mdelig results usig D mechaism shw a satisfactry predicti at the pressures f 2 atm ad 5 atm, hwever, sigificat verpredicti have bee fud at the pressure f 0.5 atm fr mixtures with equivalet ratis less tha 1.4. As bserved earlier, the mdelig results f N Butae mechaism idicate a gd agreemet with available experimetal data fr lea mixtures, hwever, uderpredicti fr rich mixtures becmes severe as the pressure icreasig. The mdelig results f the Kv mechaism have shw the best agreemet with the experimetal data at all equivalece ratis ad pressures studied. Recetly Kv et al. [32] have ivestigated the effect f variati f the xidizer cmpsiti the burig velcity f ethylee/n 2 /O 2 mixture usig the heat flux methd. The mle fracti f xyge i the N 2 þ O 2 mixture was defied by diluti factr D (D ¼ O 2 /(O 2 þ N 2 )), ad varied frm 18% t 14%. Fig. 11 shws cmparis f these experimetal data ad mdelig results. The experimetal adiabatic burig velcities f D ¼ 0.18 mixture btaied by Kv et al. [32] shws gd csistecy with the experimetal data btaied by Eglfpuls et al. [36] i lea flames, while, as discussed earlier, Eglfpuls et al. btaied higher values i rich flames usig liear extraplati f stretch i cuterflw flames. It ca be see that mdels preseted i Fig. 11 shw geerally gd predictis f the lamiar burig velcity at these cditis, hwever, sme discrepacies still exist. The mdel shws satisfactry agreemet with the preseted experimetal data. The D mdel verpredicts the experimetal data at ear stichimetric regi fr D ¼ 0.18 cditi. The N Butae mdel shws tably lwer values tha the measuremet i rich regi fr all cditis. The Kv mdel seems uderpredict the experimetal results ver etire rage f equivalet ratis, especially fr D ¼ Mdelig aalysis T further uderstad the mdels behavir ad idetify imprtat reactis, sesitivity aalysis fr lamiar burig velcity f ethylee/air mixtures at fuel-lea (V ¼ 0.7), stichimetric ad fuel-rich (V ¼ 1.4) cditis has bee perfrmed, as shw i Fig. 12. The reactis maifested i the sesitivity aalysis are listed i Table 3. It is see that HeO ad 1 chemistry reactis sigificatly ifluece the lamiar burig velcity i lea ethylee/air flames, ad 2 chemistry reactis becme cmparably sesitive t 1 chemistry i fuel-rich flames. Reacti R1: H þ O 2 ¼ O þ OH, as the mai brachig prcess, has crucial effect the lamiar burig velcity fr all equivalece ratis studied, ad the rmalized sesitivity cefficiet f this reacti icreases whe the mixture varies frm lea t rich cditis. O xidati reacti R8: O þ OH ¼ O 2 þ H, as the mst imprtat heat release ad H-prducig step, is dmiat fr fuel-lea flames ad imprtat i the stichimetric flame. Reactis cvertig HO t O are csiderably sesitive fr the predicti f the lamiar burig velcities at bth lea ad rich flame cditis. Fr all mechaisms, H-prducig decmpsiti reacti R9: Fig. 11. mparis f experimetal data (symbls) ad mdelig (lies) fr the lamiar burig velcities fr ethylee/o 2 /N 2 mixture with xyge ctet varyig withi D ¼ 0.18e0.14 at 298 K, P ¼ 1 atm.

9 . Xu, A.A. Kv / Eergy 43 (2012) 19e29 27 shws a psitive sesitivity i fuel-rich flames fr all mechaisms, while reacti R24: 2 H 3 þ H ¼ 2 H 2 þ H 2 shws a ihibiti effect as a termiatig reacti i fuel-rich flames fr the, N-Butae ad D mechaisms. It is als fud that reactis (R17) ad (R24) shw much higher sesitivity i D mechaism tha i ther mechaisms, while reacti R21 i the Kv mechaism has mre imprtat effect cmparig with reactis (R17) ad (R24) at fuel rich cditis. Als table that reactis ivlvig higher hydrcarbs thrugh recmbiati reactis at fuel-rich cditis d t shw imprtat ifluece the lamiar burig velcity predicti. 4. Reacti aalysis Fig. 12. Nrmalized sesitivity cefficiets fr the lamiar burig velcity f ethylee/air mixture at T ¼ 298 K, P ¼ 1 atm (Tp: lea V ¼ 0.7; middle: stichimetric; bttm: rich V ¼ 1.4). HO þ M ¼ O þ H þ M cmpetes with reacti R12: HO þ O 2 ¼ O þ HO 2 i fuel-lea flames ad termiatig reacti R13: HO þ H ¼ O þ H 2 i fuel-rich flames. I the mechaism, reacti R13 exhibits higher sesitivity cefficiets fr all mixtures, ad reacti R9 is less sesitive fr stichimetric ad fuel-rich flames, which is differet frm ther mechaisms. Frm 2 chemistry, reactis f 2 H 4 with radicals O ad OH shw a table sesitivity fr lea flame cditis, while have little effect ly i ad D mechaisms fr fuel-rich flames. Reacti R17: 2 H 3 þ O 2 ¼ H 2 HO þ O, actig as a chai-brachig reacti, have a psitive sesitivity cefficiets fr all equivalece ratis studied. Decmpsiti reacti R21: 2 H 3 (þm) ¼ 2 H 2 þ H(þM) Accrdig t the sesitivity aalyses f igiti ad flame prpagati, reactis ivlvig 2 H 4 ad viyl chemistry shw csiderable imprtace i ethylee xidati prcess. The kietic data fr these reactis eeds t be carefully csidered fr further imprvig predictig perfrmace f ethylee cmbusti mdels, especially fr fuel rich cditis. The differeces i the reacti rate cstats ad rutes amg fur mechaisms are preseted ad discussed as fllwig. 2 H 4 þ OH: Fr reactis 2 H 4 þ OH, ly the Kv mechaism takes additial reacti prducts H 2 O þ H 3 it accut as a imprtat pathway fr lw ad mderate temperature chemistry, which cverts active radical OH it relatively iactive radical H 3. 2 H 4 þ O: Fr reactis 2 H 4 þ O, prducti chael H 2 HO þ H is t icluded i mechaism, hwever, as shw i Fig. 6, it is csiderably imprtat i D ad N Butae mechaisms. Oly ad the Kv mechaisms csider H abstracti rute t prduce 2 H 3 þ OH which is imprtat reacti chael ad ctributes mre tha e third i 2 H 4 csumpti by reacti with O i bth mechaisms. 2 H 3 þ O 2 : Reacti betwee viyl ad mlecular xyge very sigificatly iflueces bth igiti ad flame prpagati. Fr reactis 2 H 3 þ O 2, reacti chael H 2 HO þ O is csidered as mai reacti chael, ad as a chai brachig reacti, it ca be very imprtat ad sesitive fr ethylee igiti ad flames. It is fud that this reacti rate i mechaism is fur times higher tha i the Kv ad N Butae mechaism, ad twice higher tha i D mechaism. I additi, 2 H 2 þ HO 2 is much mre imprtat chael fr reactis 2 H 3 þ O 2 i the Kv ad N Butae mechaisms cmpared t ad D mechaisms. The reacti rates aalysis als revealed that 2 H 3 csumpti i mechaism is faster tha i ther mechaisms. 2 H 3 (þm) ¼ 2 H 2 þ H(þM): This reacti has bee idetified as a relatively imprtat i fuel-rich flames fr all fur mechaisms, while sigificat differeces i rate cstats have bee fud. The rate cstat i the Kv mechaism is abut twice ad five times higher tha i the ad D mechaisms respectivelyat 1800 K, while it becmes abut five ad twety times higher tha i the ad D mechaisms respectively at temperature f 1000 K. 2 H 3 þ H ¼ 2 H 2 þ H 2 : this reacti has als bee fud as a imprtat ihibiti step i fuel-rich flames i the, D ad N-Butae mechaism. The reacti rate cstat i mechaism is mre tha twice higher tha i the D ad NButae mechaism, ad mre tha seve times higher tha i the Kv mechaism. Oe shuld te that cmplicated picture f the sesitivity spectra shw i Fig. 12 is largely defied by the chice f rate cstats ad by iclusi/missi f sme chaels csidered t be mir as summarized i Table 3. Therefre, direct variati f the rate cstats f mst sesitive reactis culd be misleadig if the list f reactis is icmplete, r may lead t deterirati f predictive perfrmace f a give mdel fr ther fuels icluded.

10 28. Xu, A.A. Kv / Eergy 43 (2012) 19e29 Table 3 Reactis maifested i flame sesitivity aalysis. N. Reacti V ¼ 0.7 V ¼ 1.0 V ¼ 1.4 D N HeO R1 a H þ O 2 ¼ O þ OH * * * * * * * * * * * * R2 HO 2 þ H ¼ OH þ OH þ þ þ þ þ þ þ þ þ þ þ e R3 H þ O 2 (þm) ¼ HO 2 (þm) þ þ þ * þ þ e þ e e e e R4 b HO 2 þ H ¼ H 2 þ O 2 þ þ þ þ þ e þ þ e e þ þ R5 H þ OH þ M ¼ H 2 O þ M þ þ þ þ þ þ þ þ þ þ e e R6 OH þ HO 2 ¼ H 2 O þ O 2 þ þ e þ þ þ e þ e e e e R7 OH þ O þ M ¼ HO 2 þ M e þ e e e þ e e e e e e 1 R8 O þ OH ¼ O 2 þ H * * * * * * þ * e e e e R9 HO þ M ¼ O þ H þ M þ þ þ * þ þ þ þ þ þ * þ R10 H 3 þ OH ¼ H 2 (s) þ H 2 O þ þ e þ þ þ e þ e e e e R11 H 3 þ HO 2 ¼ H 3 O þ OH þ e e þ þ e e e þ e e e R12 HO þ O 2 ¼ O þ HO 2 þ þ þ þ e e þ þ e e þ þ R13 HO þ H ¼ O þ H 2 þ e þ e þ þ þ þ þ þ þ þ R14 H 3 þ H(þM) ¼ H 4 (þm) þ þ e e þ þ e e þ þ þ e R15 HO þ OH ¼ H 2 O þ O e e þ e e e þ þ e e e e R28 H 2 (s) þ O 2 ¼ H þ OH þ O e e e e e e e e þ e þ e R29 H 2 þ O 2 ¼ H þ OH þ O B e e e B e e e B þ e e R30 H 2 þ O 2 ¼ HO þ OH e B e e e B e e e B e e R31 H 2 þ O 2 ¼ H 2 O þ O B B e e B B e e B B e þ R32 H 2 (s) þ H 2 O ¼> H 3 OH e B B e e B B e e B B þ 2 e 3 R16 2 H 4 þ OH] 2 H 3 þ H 2 O þ þ þ þ þ þ þ e þ þ e e R17 2 H 3 þ O 2 ¼ H 2 HO þ O þ þ þ þ þ þ þ þ þ * þ þ R18 2 H 4 þ O ¼ H 2 HO þ H B þ þ þ B e þ e B e e e R19 2 H 4 þ O ¼ 2 H 3 þ OH þ B B e þ B B e e B B e R20 H 2 O þ O ¼ H 2 þ O 2 e þ e B e e e B e e e B R21 c 2 H 3 (þm) ¼ 2 H 2 þ H(þM) þ e e þ þ e þ þ þ þ þ þ R22 2 H 2 þ O ¼ HO þ H e e þ þ e þ þ þ e þ e þ R23 2 H 4 þ O ¼ H 3 þ HO e þ þ e e e e e e e e e R24 2 H 3 þ H ¼ 2 H 2 þ H 2 e þ e e þ þ þ e þ * þ e R25 H 2 O þ H ¼ H 3 þ O e þ e e e þ e e e þ e e R26 2 H 5 (þm) ¼ 2 H 4 þ H(þM) e þ e e e þ e e e e e e R27 d 2 H 3 þ H 3 (þm) ¼ 3 H 6 (þm) e e e þ e e e þ e e e e R33 HO þ O 2 ¼ HO þ O þ O B B e B B B e B B B þ B R34 HO þ H ¼ H 2 (s) þ O e e e B e e e B e e þ B R35 HO þ H ¼ H 2 þ O B B B e B B B e B B B þ R36 2 H 4 þ H ¼ 2 H 3 þ H 2 e e e e e e e e e þ e e R37 2 H 3 þ O 2 ¼ 2 H 2 þ HO 2 e e e e e e e e e e þ þ R38 H 3 þ H 3 ¼ 2 H 5 þ H e e e e e e e e þ e e þ *: jsesitivity cefficietj > 0.1; þ: sesitive; e: -sesitive; B: abset. a The reverse reacti is used i N-Butae mechaism. b The reverse reacti is used i mechaism. c The reverse reacti is used i N-Butae mechaism. d 3 H 6 ¼ 2 H 3 þ H 3 is used i Kv ad N-Butae mechaism. K v D N K v D N K v 5. clusis Develpmet f a sigle detailed kietic mechaism suitable fr the mdelig f cmbusti f differet fuels icludig alkaes, alkees, xygeated species, etc. is a challegig task. I the preset wrk, several ctemprary cmprehesive detailed kietic mechaisms fr ethylee cmbusti, icludig the Kv mechaism, N Butae mechaism, a Dieg mechaism ad mechaism have bee extesively validated by cmparig with available experimetal data fr ethylee igiti ad flame prpagati uder a variety f cditis. The discrepacies f these mdels behavir have bee bserved ad further sesitivity aalysis fr each mechaism has bee perfrmed t idetify imprtat reactis fr the predicti f ethylee igiti ad flames. Reactis ivlvig iitial csumpti reactis with radicals O ad OH ad subsequet reactis f viyl with xyge have sigificat effect ethylee igiti. I additi, the sesitivity aalysis f the flame prpagati idicate that HeO ad 1 chemistry reactis sigificatly ifluece the lamiar burig velcity i lea ethylee/air flames, while 2 chemistry reactis becme icreasigly sesitive i fuel-rich flames. Furthermre, reactiby-reacti aalysis has bee cducted t lk iside the mdels. Remarkable variati f the reacti rutes ad rate cstats f reactis ivlvig 2 H 4 ad viyl chemistry have bee fud i differet mechaisms, which has bee csidered t lead t the differet mdelig behavirs. Due t still remaiig ucertaities, reactis ivlvig 2 H 4 ad viyl chemistry eed t be accurately re-evaluated fr further develpmet f detailed chemical mechaisms fr ethylee cmbusti. Ackwledgmet hia chlarship ucil is gratefully ackwledged fr the grat t. Xu.

11 . Xu, A.A. Kv / Eergy 43 (2012) 19e29 29 Refereces [1] Re T, Patel MK, Blk K. team crackig ad methae t lefis: eergy use, O 2 emissis ad prducti csts. Eergy 2008;33:817e33. [2] lket MB, padaccii J. cramjet fuels autigiti study. J Prpuls Pwer 2001;17(2):315e23. [3] Kv AA. Implemetati f the NN pathway f prmpt-no frmati i the detailed reacti mechaism. mbust Flame 2009;156(11):2093e105. [4] N mechaism available at: techlgy-chemistry-cmbusti-ch4. [5] hemical Kietic Mechaism fr mbusti Applicati. eter fr Eergy research, iversity f alifria at a Dieg. [6] Wag Hai, Yu Xiaqig, Jshi Ameya V, Davis ctt G, aski Alexader, Eglfpuls Fki, et al. mech versi II. High-temperature cmbusti reacti mdel f H 2 /O/1e4 cmpuds, II.htm; May [7] Mariv NM, Pitz WJ, Westbrk K, Vicitre AM, astaldi MJ, eka M. Armatic ad plycyclic armatic hydrcarb frmati i a lamiar premixed -butae flame. mbust Flame 1998;114:192e213. [8] chultz E, hepherd J. Validati f detailed reacti mechaisms fr detati simulati. Pasadea, A: Explsi Dyamic ab GAIT, alifria Istitute f Techlgy; Rept FM99e5. [9] Varatharaja B, Williams FA. Ethylee igiti ad detati chemistry, part 1: detailed mdelig ad experimetal cmparis. J Prpulsi Pwer 2002; 18(2):344e51. [10] Gay ID, Glass GP, Ker RD, Kistiakwsky GB. Ethylee Oxyge reacti i shck waves. J hem Phys 1967;47(1):313e20. [11] Hmer JB, Kistiakwsky GB. Oxidati ad pyrlysis f ethylee i shck waves. J hem Phys 1967;47(12):5290e5. [12] Drummd J. hck-iitiated exthermic reactis.v. Oxidati f ethylee. Aust J hem 1968;21(11):2641e8. [13] Baker JA, kier GB. hck-tube studies the igiti f ethylee-xygearg mixtures. mbust Flame 1972;19(3):347e50. [14] uzuki M, Mriwaki T, Okazaki, Okuda T, Tazawa T. Oxidati f ethylee i shck-tube. Astrautica Acta 1973;18(5):359e65. [15] Jachimwski J. A experimetal ad aalytical study f acetylee ad ethylee xidati behid shck waves. mbust Flame 1977;29:55e66. [16] Hidaka Y, Kataka T, uga M. hck-tube ivestigati f igiti i ethyleexyge-arg mixtures. B hem c Jp 1974;47(9):2166e70. [17] Hidaka Y, Nishimri T, at K, Hemi Y, Okuda R, Iami K, et al. hck-tube ad mdelig study f ethylee pyrlysis ad xidati. mbust Flame 1999;117(4):755e76. [18] Brw J, Thmas GO. Experimetal studies f shck-iduced igiti ad trasiti t detati i ethylee ad prpae mixtures. mbust Flame 1999;117(4):861e70. [19] adma P, Bambrey RJ, Bx K, Thmas GO. Ethylee cmbusti studied ver a wide temperature rage i high-temperature shck waves. mbust ci Techl 2002;174(11e12):111e27. [20] Hrig D. A study f the high-temperature autigiti ad thermal decpsiti f hydrcarbs. Reprt N TD-135; [21] Kalita DM, Hall JM, Peterse E. Igiti ad xidati f ethylee-xygediluet mixtures with ad withut silae. J Prpulsi Pwer 2005;21(6): 1045e56. [22] Peyazkv OG, evruk K, Tagirala V, Jshi N. High-pressure ethylee xidati behid reflected shck waves. P mbust Ist 2009;32(2): 2421e8. [23] axea, Kahadawala MP, idhu. A shck tube study f igiti delay i the cmbusti f ethylee. mbust Flame 2011;158(6):1019e31. [24] Has RK. Applicatis f quatitative laser sesrs t kietics, prpulsi ad practical eergy systems. P mbust Ist 2011;33(1):1e40. [25] Hai Wag, Alexader aski. A mprehesive Kietic mdel f ethylee ad acetylee xidati at high temperatures,, available at: edu/mechaisms/2-4/c2.pdf. [26] hemki-pr. Reacti Desig Ic., [27] Wagher A, Quiard J, earby G. Experimetal ad umerical ivestigatis f the relati betwee OH* emissi, flame speed ad mass csumpti rate. I: Prc. f the 3rd Eurpea mbusti Meetig, haia, rete, Greece; [28] Hall JM, Rickard MJA, Peterse E. mparis f characteristic time diagstics fr igiti ad xidati f fuel/xidizer mixtures behid reflected shck waves. mbust ci Techl 2005;177:455e83. [29] Haber, Vadsburger. A glbal reacti mdel fr OH* chemilumiescece applied t a lamiar flat-flame burer. mbust ci Techl 2003;175:1859e91. [30] Ji, Dames E, Wag Y, Wag H, Eglfpuls FN. Prpagati ad exticti f premixed 5e12 -alkae flames. mbust Flame 2010;157(2):277e87. [31] Jmaas G, Zheg X, Zhu D, aw K. Experimetal determiati f cuterflw igiti temperatures ad lamiar flame speeds f 2e3 hydrcarbs at atmspheric ad elevated pressures. P mbust Ist 2005;30(1): 193e200. [32] Kv AA, Dyakv IV, De Ruyck J. The effects f cmpsiti the burig velcity ad NO frmati i premixed flames f 2 H 4 þ O 2 þ N 2. Exp Thermal Fluid ci 2008;32(7):1412e20. [33] Hirasawa T, ug J, Jshi A, Yag Z, Wag H, aw K. Determiati f lamiar flame speeds usig digital particle image velcimetry: biary fuel bleds f ethylee, -Butae, ad tluee. P mbust Ist 2002;29(2): 1427e34. [34] Kumar K, Mittal G, ug -J, aw K. A experimetal ivestigati f ethylee/o 2 /diluet mixtures: lamiar flame speeds with preheat ad igiti delays at high pressures. mbust Flame 2008;153(3):343e54. [35] Hassa MI, Aug KT, Kw O, Faeth GM. Prperties f lamiar premixed hydrcarb/air flames at varius pressures. J Prpulsi Pwer 1998;14(4): 479e88. [36] Eglfpuls FN, Zhu D, aw K. Experimetal ad umerical determiati f lamiar flame speeds: mixtures f 2-hydrcarbs with xyge ad itrge. ympsium (Iteratial) mbust 1991;23(1):471e8.