Extinction Dynamics of a Co-flow Diffusion Flame by Very Small Water Droplets Injected into the Air Stream

Transcription

1 Naval Reseach Laboatoy Washngton, DC NRL/MR/ Extncton Dynamcs of a Co-flow Dffuson Flame by Vey Small Wate Doplets Injected nto the A Steam Ramagopal Ananth Rchad C. Mowey Navy Technology Cente fo Safety and Suvvablty Chemsty Dvson July 28, 2008 Appoved fo publc elease; dstbuton s unlmted.

2 Fom Appoved REPORT DOCUMENTATION PAGE OMB No Publc epotng buden fo ths collecton of nfomaton s estmated to aveage 1 hou pe esponse, ncludng the tme fo evewng nstuctons, seachng exstng data souces, gatheng and mantanng the data needed, and completng and evewng ths collecton of nfomaton. Send comments egadng ths buden estmate o any othe aspect of ths collecton of nfomaton, ncludng suggestons fo educng ths buden to Depatment of Defense, Washngton Headquates Sevces, Dectoate fo Infomaton Opeatons and Repots ( ), 1215 Jeffeson Davs Hghway, Sute 1204, Alngton, VA Respondents should be awae that notwthstandng any othe povson of law, no peson shall be subject to any penalty fo falng to comply wth a collecton of nfomaton f t does not dsplay a cuently vald OMB contol numbe. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. 1. REPORT DATE (DD-MM-YYYY) 2. REPORT TYPE 3. DATES COVERED (Fom - To) Memoandum Repot 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER Extncton Dynamcs of a Co-flow Dffuson Flame by Vey Small Wate Doplets Injected nto the A Steam 6. AUTHOR(S) Ramagopal Ananth and Rchad C. Mowey 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 5d. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Naval Reseach Laboatoy 4555 Ovelook Avenue, SW Washngton, DC PERFORMING ORGANIZATION REPORT NUMBER NRL/MR/ SPONSORING / MONITORING AGENCY NAME(S) AND ADDRESS(ES) Offce of Naval Reseach One Lbety Cente 875 Noth Randolph St. Alngton, VA SPONSOR / MONITOR S ACRONYM(S) 11. SPONSOR / MONITOR S REPORT NUMBER(S) 12. DISTRIBUTION / AVAILABILITY STATEMENT Appoved fo publc elease; dstbuton s unlmted. 13. SUPPLEMENTARY NOTES 14. ABSTRACT Computatons ae pefomed to examne the effectveness of mono-dspese wate doplets n extngushng a co-flow, popane dffuson flame by njectng the doplets nto the a steam. The calculatons show that the doplets entaned nto the eacton kenel at the flame base ae cucal fo extncton. The eacton kenel detaches fom the bune m and blows-off when the doplet concentaton s nceased to a ctcal value (extncton concentaton). At the ctcal value, the maxmum chan-banchng eacton (H2+O=OH+H) ate n the eacton kenel was found to be educed by a facto of 5 n ou computatons. A lage decease n the eacton ate ndcates that the maxmum heat geneatons ate and Damkhole numbe ae too low to sustan the flame, and cause the flame blow-off. Lage dops ae moe effectve than small dops, and the extncton concentaton of wate nceases fom 10.5% to 15% by mass as the sze s educed fom 32 to 4 mco m. As the doplet sze s nceased futhe (>32 mco m), the tend wll evese as the evapoaton ates get too small despte nceased penetaton of flame coe by the dops. 15. SUBJECT TERMS Wate mst Extncton Popane combuston Dffuson flame 16. SECURITY CLASSIFICATION OF: a. REPORT Cupbune b. ABSTRACT c. THIS PAGE Unclassfed Unclassfed Unclassfed 17. LIMITATION OF ABSTRACT 18. NUMBER OF PAGES UL 62 19a. NAME OF RESPONSIBLE PERSON Ramagopal Ananth 19b. TELEPHONE NUMBER (nclude aea code) (202) Standad Fom 298 (Rev. 8-98) Pescbed by ANSI Std. Z39.18

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4 CONTENTS 1.0 INTRODUCTION THEORETICAL NUMERICAL RESULTS AND DISCUSSION CONCLUSIONS ACKNOWLEDGMENTS REFERENCES...42 APPENDIX A- CONSERVATION EQUATIONS... A-1

5 NOMENCLATURE A C Dn Pe-exponental coeffcent n Ahenus ate fo fowad eacton, Dag coeffcent fo sphecal wate doplet C j, Mass concentaton of spece j n eacton, Kg/m 3 C H2O,s Satuaton concentaton of wate vapo at doplet suface, Kg/m 3 C H2O,n Concentaton of wate vapo n the gas mxtue suoundng the doplet, Kg/m 3 C p,d C p,h2o C p, C pm D j D m d Da Specfc heat of lqud wate, J/KgK Specfc heat of wate vapo, J/KgK Specfc heat of gas spece, J/KgK Specfc heat of gas mxtue, J/KgK Dffuson coeffcent of spece n a bnay mxtue of speces and j, m 2 /sec Dffusvty of spece n a gas mxtue, m 2 /sec Doplet damete, m Damkohle numbe E Total enegy densty of gas mxtue, J/m 3 E F d G Actvaton enegy of fowad eacton, J/Kgmole Gas-lqud couplng tem fo momentum Gashof numbe G Incdent adaton ntensty, W/m 2 g Gavty vecto h fg h h 0 h J K Latent heat of vapozaton of wate, J/Kg Specfc enthalpy of fomaton of spece, J/Kgmole Standad enthalpy of fomaton of spece, J/Kgmole Heat tansfe coeffcent fo sphecal wate doplet, W/m 2 K Dffuson mass tansfe flux fo spece, Kg/m 2 sec Chemcal equlbum constant fo eacton v

6 k f k b k M Fowad knetc constant fo evesble eacton Backwad knetc constant fo evesble eacton Wate vapo mass tansfe coeffcent fo the doplet, m/sec Molecula weght of spece, Kg/Kgmole m m Evapoaton ate of wate doplet, Kg/sec Mass of wate doplet, Kg N Total numbe of speces N R Numbe of chemcal eactons N Numbe of speces n eacton Np Numbe densty of doplets, #/m 3 N 0 p Numbe densty of doplets n nlet a, #/m 3 Nu Nusselt numbe fo wate doplet p Pessue, Newtons/m 2 P atm Atmosphec pessue, Newtons/m 2 P sat Vapo pessue of wate at tempeatue T, Newtons/m 2 P Pandtl numbe q c Convectve heat flux, W/m 2 q Radaton heat flux, W/m 2 R Unvesal gas constant R R Re Re S m S h S S 0 Sc Sh T Volumetc chemcal eacton ate fo spece appeang n th eacton, Kgmole/m 3 sec Net chemcal eacton ate fo spece, Kg/m 3 sec Reynolds numbe fo gas flow Doplet Reynolds numbe Radal coodnate, m Gas-lqud couplng tem fo mass Gas-lqud couplng tem fo enegy Gas-lqud couplng tem foe spece Standad entopy of fomaton of spece Schmdt numbe Shewood numbe fo doplet Tempeatue, K v

7 T T b T vap T ef t u u X w X 0 w x Y Doplet tempeatue, K Bolng pont tempeatue of wate Mnmum wate vapozaton tempeatue set at 287 K Refeence tempeatue, K Tme, sec Gas velocty vecto, m/sec Doplet velocty vecto, m/sec Mass facton of wate n a Mass facton of wate n nlet a Axal coodnate, m Mass facton of gas spece Geek Symbols β Tempeatue exponent n Ahenus ate expesson fo fowad eacton η j, Concentaton exponent n Ahenus ate expesson ε Doplet emssvty ξ Radaton paamete, m τ Stess tenso, Newtons/m 2 λ λ m μ μ m Themal conductvty of spece, J/m.sec.K Themal conductvty of gas mxtue, J/m.sec.K Dynamc vscosty of spece, Kg/m-sec Dynamc vscosty of gas mxtue, Kg/m-sec υ, Stochometc coeffcents fo spece n eacton γ, Thd body effcences fo spece n eacton ρ gas densty, Kg/m 3 ρ p lqud wate densty, Kg/m 3 φ j Ω μ,j Ω D,j σ p Dmensonless mxtue popety n the expesson fo mxtue vscosty, μ m Collson ntegal fo gas vscosty Collson ntegal fo spece dffuson Radaton scatteng facto fo doplet phase v

8 Extncton Dynamcs of a Co-flow Dffuson Flame by Vey Small Wate Doplets Injected nto the A Steam 1.0 INTRODUCTION Development of wate mst technology has been dven by the need to eplace halogenbased, Halon 1301, fe-fghtng agent. Halon 1301 affects the eath s ozone laye advesely, theefoe t s banned fom futhe poducton. Halon 1301 s a gaseous agent that can eadly dffuse and nteact chemcally wth combuston pocess by shuttng off chan-banchng eactons that ae ctcal to the popagaton of combuston. Wate nteacts wth the combuston pocess manly by physcal mechansms [1]. It s a mult-phase agent, whose tanspot, dstbuton, and evapoaton mpose challenges that necesstate consdeable eseach effots. In ths pape, we pesent tansent, ax-symmetc, computatons on the effects of monodspesed, extemely small damete (4 to 32 µm), wate doplets on a co-flow, dffuson flame fomed between two concentc cylndcal jets of popane gas (nne jet) and a (oute jet). Typcally, wate mst s geneated by focng wate though hgh-pessue spay nozzles and mst doplets have dametes between 50 and 200 µm. Spnkle systems on the othe hand poduce doplets n the ange of 1000 µm [2] whle wate hose systems poduce much lage doplets. Most pevous fe suppesson studes [2-4] wth wate doplets have consdeed doplets fom spnkles and hgh pessue spay nozzles [5-6]. Ndubzu et al. [7] conducted expemental studes of wate mst suppesson of co-flow, methane dffuson flames fomed n a slot bune (Wolfhad-Pake bune) and fo pool fes [8]. They used hgh-pessue nozzles to fom msts wth Saute mean damete (SMD) of 30 to 66 μm. They showed that the flame tempeatue s educed sgnfcantly at 7% mass facton of wate (SMD 66 μm) n the nlet a used fo co-flow. Pasad et al. [9] modeled the expements of Ndubzu et al. [7] by solvng full Nave-Stokes (NS) equatons, and usng Eulean-Eulean sectonal appoach. The model pedcted that the extncton concentaton nceases monotoncally fom 17.5 to moe than 50% by mass as the dop sze s nceased fom 50 to 150 μm. Recently, Lao et al. [10] developed a smple model (computatonally fast) fo wate mst suppesson of a co-flow dffuson flame by usng bounday laye appoxmatons to the NS equatons. The U.S. Navy has developed fxed, total floodng, wate mst technology fo extngushng fes n the machney space of a shp usng sngle-flud, hgh momentum, hgh pessue spay nozzles [5]. Wate mst and othe total floodng agents ae beng developed fo othe pats of the shp ncludng electonc spaces, flammable lqud stoage aeas, magazne potecton, and othe hghly obstucted spaces. Ulta fne mst (UFM) conssts of extemely small wate doplets, whch ae fomed at atmosphec pessue usng ultasound vbaton of pezoelectc dscs smla to that used n commecal humdfes. Recently, technology has been developed fo extactng lage thoughput of ulta fne mst geneated fom the pezoelectc dscs [11]. A sgnfcant numbe of studes ae avalable on the fe suppesson effectveness of hgh-pessue nozzle mst [12, Manuscpt appoved June 25,

9 13]. Relatvely lttle s undestood especally egadng the suppesson and extncton of fes usng UFM. UFM doplets can follow the flud flow steamlnes and each behnd obstuctons [14, 15] due to vey small neta. They do not wet sufaces sgnfcantly and may cause only a mnmal damage to electoncs [16] due to sgnfcant evapoaton n dy a even at ambent tempeatue. Futhemoe, UFM doplets have lage settlng tmes due to vey low gavty effects. Theefoe, a hgh concentaton of the doplets may be suspended n a compaed to the tadtonal wate mst fomed by the hgh pessue nozzles. Also, extemely small sze doplets 1 to 10 µm can scatte and absob the themal adaton fom a fe most effectvely accodng to Ravguuajan et al. [17] when the doplet adus equals the wavelength of the themal adaton. Vey few studes of dffuson-flame extncton wth UFM ae avalable n the lteatue. Ndubzu et al. [18-20] conducted expements on the effects of UFM on a foced convecton bounday laye flame fomed ove a bunng polymethyl-methacylate (PMMA) plate. They measued doplet dstbuton cuves (volume fequency % vs damete), whch show a peak at 6 µm, SMD n the age of 3 µm, and 90% (by volume) of the doplets have szes below 20 µm. The wate doplets ae njected nto the a flow ove the bunng plate. Ndubzu et al. [18-20] showed that, at a fxed nlet a velocty, the flame detaches fom the leadng edge of the plate and blows off as the UFM mass facton s nceased to a ctcal value (extncton concentaton). The extncton wate mass facton was shown to decease lnealy fom 7 to 1.5% as the nlet a velocty s nceased fom 60 to 120 cm/sec. Ananth et al. [21, 22] modeled the PMMA expements of Ndubzu et al. [18-20] and obtaned computatonal solutons of the tme dependent Nave-Stokes equatons fo the extncton of the PMMA bounday laye flame due to the njecton of monodspesed wate doplets. They used an Eulean-Eulean sectonal appoach to model the doplet dynamcs and showed that the degee of doplet evapoaton nea the leadng edge of the flame plays a key ole n extngushng the flame. The computatons show that the eacton kenel detaches fom the leadng edge of the plate and the flame blows-off at o above the extncton concentaton. They used sngle step chemsty and showed that the maxmum heat elease ate (o eacton ates) deceases sgnfcantly at extncton. It s geneally known [23] that flame blow-off occus when the maxmum Damkhole numbe (Da) o maxmum heat elease ate fall below a ctcal value. Ananth et al. [22] pedcted that the extncton mass facton of wate deceases fom 9.5 to 1.8% as the a velocty s nceased fom 60 to 170 cm/sec fo 6 μm dops. The calculatons of Ananth et al. [22] exhbt a mnmum n extncton concentaton as the dop damete s nceased fom 6 to 100 μm. At a fxed a velocty of 84 cm/sec, the wate extncton concentaton deceases fom 9.5 to 5.5 mass % as the dop sze s nceased fom 6 to 40 μm. A futhe ncease (40 to 100 μm) n the dop damete nceases the extncton concentaton fom 5.5 to 13.5 mass %. The computatons show clealy that lage dops ae moe effectve than small dops n the ange between 6 and 40 μm, and the convese s tue at dop szes above 40 μm. As the a velocty s nceased to 170 cm/sec, the computatons show that the extncton concentaton s less dependent on the dop sze. Lentat and Chellah [24, 25] modeled extncton of one-dmensonal, counte-flow, dffuson flames by wate doplets, and showed that the physcal effects domnate ove any chemcal effects. In the counte-flow geomety, lage jet veloctes of a and methane (ode of 2 m/sec) ae employed. 2

10 They showed that the extncton stan ate s loweed wth the addton of wate to the a steam, and the physcal effects domnate ove any chemcal effects. Usng a Lagaangan appoach, they calculated the doplet tajectoes and a non-monotonc elatonshp between extncton stan ate and dop sze (5-50 μm). The calculatons show a mnmum n the extncton stan ate wth nceased dop sze fom 5 to 50 μm. Zeges et al. [26] pefomed expements on the monodspesed wate doplets extncton of counte-flow, popane, dffuson flames. They showed that the extncton concentaton emaned constant between 14 and 30 μm and then nceased wth nceasng dop sze between 30 and 42 μm. Recently, Fshe et al. [27] pefomed expements on UFM (polydspesed, D 10 =6.2 µm) extncton of a co-flow, dffuson flame fomed between two concentc jets of a and popane, smla to the geomety consdeed n the cuent pape. They pefomed flow patcle magng velocmety and flame magng to show that the wate dops evapoate well outsde the flame, and the wate vapo s entaned at the base of the flame. As the wate concentaton s nceased, the flame base lfts up fom the bune and blows-off at extncton. Fshe et al. [27] epoted that the flame extngushed at 12.5% mass of wate dops (D 10 =6.2 μm) n nlet a, whch s satuated wth wate vapo (1.4 mass %). The co-flow geomety and the flow ates of a and popane consdeed n the expements of Fshe et al. [27] ae smla to those consdeed n the ecent computatonal wok of Ananth et al. [28]. Ananth et al. [28] showed that 4 µm monodspesed doplets evapoate at the C sothem, whch s well outsde the eacton zone of the flame. They also showed that the pedcted extncton concentaton fo 6 µm dops s n excellent ageement wth that measued n the expements of Fshe et al. [27]. Shllng et al. [29] conducted expements on the ulta fne wate mst (8.2 µm volume medan damete) extncton of heptane pool flame fomed n a cup-bune. They measued that about 14.5 mass % wate s needed to extngush the flame. Adga et al. [15] conducted computatonal and expemental studes of UFM extncton of a 120 KW heptane pool fe nsde a 28 m 3 compatment. The expements show about 9 mass% wate s needed to extngush the fe n 5 mnutes. The extngushment tme deceased wth nceased concentaton of wate n the compatment. In the cuent pape, we consde an ax-symmetc dffuson flame fomed between two concentc cylndcal jets of a and popane. Afte a stable flame s establshed, a suppesson agent (ntogen o mono-dspesed doplets) s njected nto the oute a jet at the bottom of the bune at a fxed mass facton. We obtan numecal solutons of the lamna, tansent, Nave- Stokes and enegy equatons fo the gas phase and the Lagangan fom of the doplet consevaton equatons usng fnte-volume technques wth the CFD softwae package Fluent n cylndcal geomety as descbed by Ananth et al. [28]. In the case of ntogen, the specfc heat and latent heat effects ae absent, and the flame extncton occus due to oxygen dluton as the ntogen concentaton n the co-flow a s nceased to a ctcal value. The pedcted extncton concentaton s n excellent ageement wth the ecent measuements epoted by Lntes et al. [30]. In the case of wate njecton wth the co-flow a, the doplets tajectoes ae calculated fom the njecton pont and nto the flame. The doplets tavel up aganst gavty, and entan nto the flame. As the doplets appoach the flame, they evapoate, absobng enegy equal to the latent heat of vapozaton, to fom wate vapo. Wate vapo absobs addtonal enegy as 3

11 the sensble heat due to ts hghe (two tmes) heat capacty than that of the a. These pocesses lead to coolng at the flame and subsequent educton n the combuston eacton ate due to the lowe tempeatue. The wate vapo also dlutes the oxygen n the a and dectly educes the combuston eacton ate and heat geneaton. Ultmately, flame extncton occus when the heat geneaton ate s not suffcent to heat the flow of fuel, a, and wate (by convecton and dffuson) to the flame tempeatue. Fo fxed a and fuel gas flow ates nto the bune, thee exsts a ctcal combuston ate o ctcal Damkhole numbe (Da) below whch the flame blows off fom the edge of the nne fuel tube and extngushes. Ths s smla to the blow-off phenomena descbed by Chen and Ten [23] nea the leadng edge of a bounday laye flame. We choose a chan-banchng eacton as an ndcato to follow the extncton pocess caused by the coolng and dluton effects of wate. The chan-banchng eacton ate s maxmum at the flame base and s shown to decease below a ctcal value, as the njected doplet mass facton was nceased above a ctcal value, untl flame extngushment occued. The doplet sze was vaed fom 4 to 32 µm to study ts effect on the extncton doplet concentaton. The pedcted extncton concentatons of wate fo 4 and 8 µm szes ae consstent wth the expemental measuements of Fshe et al. [27] fo 6.2 µm aveage sze (D 10 ) dops. The evapoaton ate nceases as the nvese of the squae of the damete (d 2 law) fo fxed mass concentaton of wate. Theefoe, an ode of magntude decease n dop sze nomnally should lead to two odes of magntude ncease n the evapoaton ate fo UFM compaed to that fo spay nozzle mst. Howeve, combuston occus wthn a naow band of equvalence ato wthn the coe egon of the flame, whee fesh fuel gas and a come n contact. Theefoe, the heat geneaton ates ae nhomogeneous. Ths means that the dynamcs of doplet evapoaton (the locaton and the ate of evapoaton) wll have a ctcal, but not yet completely undestood, ole n detemnng whethe extncton occus n dffuson flames. Fo example, extemely small wate doplets mght evapoate befoe eachng the flame egon contanng the maxmum heat geneaton ates. Extncton would not occu because of the gap between the egon of evapoaton and the egon of hgh heat geneaton. On the othe hand, elatvely lage doplets mght penetate the coe of the flame but may have evapoaton ates that ae too low fo flame extngushment. The mnmum value of the mass facton (extncton concentaton) of the doplets n a needed to extngush a flame s not known. The effect of doplet sze on the extncton concentaton s also not well undestood. Inceasng the doplet sze nceases neta and may nhbt entanment nto the coe of the flame as well as educng the evapoaton ate. All of these ssues can have ctcal mplcatons n hghly obstucted aeas such as the electonc and machney spaces of a shp. 2.0 THEORETICAL The bune conssts of two concentc tubes wth dametes 2.5 cm and 10 cm as shown n Fgue 1. Popane s njected nto the nne tube and dy a s njected nto the annula egon espectvely. As the popane emeges fom the nne tube, t mxes wth the a steam. Upon gnton, a dffuson flame s fomed just above the m of the nne tube. As the gases get hot, they acceleate and dag the suoundng a nto the flame. The flow of hot gases nfluences the flow of a below the m of the nne tube. Theefoe, we nclude an entance egon of 3 cm 4

12 length below the m of the nne tube n the model to account fo the effects of the flamegeneated flud dynamcs on the njected a steamlnes. Ths ncludes the effects of the bounday-laye fomaton on the sde walls of the entance egon, whee the doplets tavel slowe than n the bulk. Fgue 1 shows a sketch of 1900 and 373 K tempeatue sothems of the flame. The egon between the two sothems s the themal bounday laye (pe-heat zone). Fgue 1 also shows the flame base, the egon whee the flame attaches to the edge of the fuel tube. In the dffuson flame, heat s eleased along the ente length of the flame as mxng occus between oxygen n the a and the ntemedate speces geneated by combuston. Fesh oxygen meets fesh fuel at the base of the flame, whee the combuston ate s the hghest. Fgue 1 shows the eacton kenel, whch s defned as the egon suoundng the locaton of the maxmum eacton ate wthn the flame base. The eacton ate falls steeply (by an ode of magntude) outsde the eacton kenel. The themal bounday laye extends well beyond the eacton kenel and the doplets must penetate the themal bounday to each nto the eacton kenel. Ths pont wll be nvestgated n detal late n the pape dung the dscusson of extncton phenomena. In addton to dffuson, the buoyancy-dven flow due to hgh tempeatue gadents affects the degee of entanment of a nto the flame and the assocated mxng among speces. The Gashof numbe, G, s of the ode of 2x10 8 based on an aveage tempeatue of 1500 K and the damete of the oute tube. Ths s much bgge than the squae of the njected a Reynolds numbe of 4 x 10 5 (Re=650). Ths suggests that the bulk of the a s affected by the natual convecton and devates sgnfcantly fom the steamlnes of the njected a at the bottom of the bune. Theefoe, the flud flow set up by the natual convecton s ntnscally tansent as votces fom and se up the chmney as sketched n Fgue 1. The buoyancy effects on the flame base ae elatvely small. Nea extncton, the flame base becomes hghly tansent pmaly due to the ntoducton of wate doplets. Vey lttle theoetcal wok can be found n the lteatue fo co-flow, popane, dffuson flames fomed n an ax-symmetc geomety even n the absence of wate doplets. A full descpton of the chemsty fo popane combuston nvolves ove 400 eactons and 80 speces, and eques vey hgh computatonal powe. Computatonally effcent (educed), popane chemcal mechansms that ae valdated by expements ae not avalable n the lteatue fo the pesent geomety. In ths pape, we do not ntend to conduct a study of the chemcal mechansms. Instead, a educed mechansm consstng of 35 speces and 217 eactons s used to 5

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14 descbe the combuston chemsty. Ths s the same as GRI 3.0 (Gas Reseach Insttute, mechansm except the ntogen contanng speces (N 2 s ncluded) ae neglected. GRI 3.0 s used wdely n lteatue fo methane combuston contanng a small facton of popane. It does not nclude all of the popane pyolyss poducts. Specfcally, t does not contan C 3 H 6, C 3 H 5, C 3 H 4, and C 3 H 3 whch ae ncluded n the San Dego popane mechansm, whch was studed by Cheng et al. [31] fo pemxed, counte-flow geomety. Howeve, GRI 3.0 ncludes all of the oxdaton chemsty and the fomaton of the pyolyss poduct C 3 H 7. As dscussed late n the pesent pape, we also pefomed computatons fo ntogen as the extngushment agent nstead of the wate doplets. The computatons pedct the extncton concentaton of ntogen wthn 10 % of the expemental measuements epoted ecently by Lntes et al. [30] n a cup-bune. The cup-bune expements of Lntes et al. [30] also show that the ntogen extncton concentaton s 23 % lowe fo methane flame than fo popane flame. Theefoe, the use of GRI 3.0 n place of full popane chemsty n ou Nave- Stokes model may cause less than 10 to 23 % eo n the extncton concentatons fo a physcal agent such as ntogen. A system of two-dmensonal, tansent, Nave-Stokes and enegy equatons ae solved n cylndcal geomety (x,), whee x and ae axal and adal dstances as shown n Fgue 1. We assume axal symmety and the tanspot n ϕ decton ae neglected. The equatons fo lamna combuston n the gas phase ae gven n Appendx A by equatons (A1-A39). They nclude pessue-velocty couplng, gavty tem n the x-decton, Dufou effects, gas adaton effects wthout soot, and the GRI 3.0 combuston eacton chemsty. Gas densty depends on tempeatue accodng to the deal gas law. The dffusve fluxes ae wtten based on deal gas mxtue popetes, whch ae evaluated usng Chapman-Enskog equatons. The tanspot and themodynamc paametes povded n the GRI 3.0 database ae used fo ndvdual speces. Radatve tanspot does not play a cucal ole n the extncton because of the small sze (1.25 cm) of the flame. Howeve, a gay-body adaton loss fom the flame to the suoundngs s ncluded usng a smple P-1 adaton model fo the gas medum. A sepaate gay gas adaton equaton (P-1 model) s solved and adatve flux fom hot gases s computed to nclude n the enegy equaton as shown n the Appendx. Soot fomaton s neglected because t s expected to be small nea the base of the flame, whee the extncton phenomena occu. Soot concentaton s expected to ncease downsteam, and s not consdeed n the computatons of flame extncton. A set of odnay dffeental equatons descbe the speces consumpton and poducton ates, R, due to the chemcal eactons alone. Ahenus eacton ates ae evaluated usng the chemcal database of GRI 3.0. Even though wate mst extngushes the flame manly by physcal mechansms athe than chemcal, t s convenent to follow the extncton phenomena n tme by followng the pogess of a chan banchng eacton ate. The GRI3.0. mechansm contans the followng chan banchng eactons: O+H 2 =OH+H (1) O 2 +H=OH+O (2) 7

15 The computatons showed that both the eacton ates have vey smla contous. They both peak at the base of the flame fomng a eacton kenel, whch s the egon of hgh ate of eacton. We wll show that the maxmum ate of eacton (1) nsde the kenel deceases damatcally wth tme dung the extncton pocess fo dffeent values of doplet concentatons and szes, theefoe, eacton (1) s a easonable ndcato of the pogess towads extncton. Snce chan-banchng s an essental pocess of combuston, a decease n chanbanchng ate sgnfes a decease n the combuston ate and the assocated Damkhole numbe, Da. We wll show that eacton (1) povdes a smple, coheent, ntepetaton of the complex computatons of the extncton phenomena. It s lkely that othe choces of the eacton steps may also help explan the computatonal esults. Inlet velocty and composton ae fxed. At the outlet, the pessue s set to be atmosphec. Ths allows fo both nflow and outflow of gas at the top of the oute tube. No slp s pescbed on all the bune walls. The top edge of the nne tube gets hot due to the heat tansfe fom the flame, whch stablzes at the m of the nne tube. The heat loss to the nne tube s ncluded n the model by assumng that the tube wall s at 600 K fo a length of 1 mm below the top edge. The est of the nne tube wall and the ente oute tube wall ae set at ambent tempeatue. The fuel flow velocty, tempeatue, and composton at the edge of the nne tube ae also specfed. In the cup-bune expements [27, 30], the fuel gas passes though a bed of glass beads, whch ae exposed to the flame. Measuements of fuel tempeatue, composton, and velocty at the ext of the nne tube ae not yet avalable. Howeve, Ndubzu et al. [7] measued a fuel tempeatue of about 623 K at the ext of a slot bune flled wth sand. Ths s because of heat feed back upsteam by conducton and adaton fom the flame to the sand patcles at low fuel veloctes, whch ae typcally encounteed n co-flow bunes. Theefoe, we mposed 600 K bounday condton fo the fuel emegng fom the nne tube n the cuent computatons. We also mposed 2 cm/sec velocty fo the fuel flow fom the tube so that t s equvalent to 1 cm/sec velocty at STP condtons. Futhemoe, we neglect back dffuson of speces fom the flame nto the fuel tube despte the low fuel velocty, and assume that the fuel emegng fom the tube s 100% popane consstent wth eale woks [9, 30, 32]. The dynamcs of each doplet fom njecton at the nlet to complete dsappeaance by vapozaton o outflow s descbed by a set of odnay dffeental equatons, whch ae gven n Appendx A by equatons (A49-A60). They descbe dop tajectoes, mass, momentum, and enegy balances fo each doplet of wate. The doplet s assumed to be sphecal and the ntenal gadents of momentum and enegy ae neglected n vew of extemely small sze ange consdeed n the computatons. Ths assumpton s typcally used fo wate [9, 22, 24, 25, 28, 32]. Lqud wate has fve tmes hghe themal conductvty than a typcal hydocabon lqud such as heptane. We estmate that the conducton tme scale fo ntenal doplet heat tansfe (d p 2 /4α l ) s ten tmes smalle than the evapoaton tme scale fo a 4 μm doplet. Hee, d p and α l ae the doplet damete and themal dffusvty of lqud wate espectvely. Theefoe, the doplet s assumed to be at unfom tempeatue wth no ntenal cculaton. Fo extemely small doplets, themophoetc foce acts n the decton of deceasng tempeatue and can deceleate the doplet as t appoaches the flame. Howeve, at small dop sze, the doplet evapoates vey quckly befoe t s exposed to a sgnfcant tempeatue gadent. We estmate less than 2% devaton between doplet and gas veloctes due to the themophoetc effects fo 4 8

16 μm damete nea the 600 K sothem (2000K/cm gadent) at the base of the flame usng the elatonshp gven by Talbot et al. [33]. The Bownan and Saffman lft foces become sgnfcant only fo submcon dops, theefoe they ae also neglected compaed to the dag foce. We consde ntal doplet szes as small as 4 μm, whch can only pesst n satuated a at oom tempeatue. Theefoe, we assume that the njected a s 100% humd (o 1.8 % mass wate vapo) when the doplets ae pesent egadless of the sze. Afte a base-case flame s establshed, we swtch the a composton fom dy a to a mxtue of 100% humd a and doplets (nlet bounday condton). The mono-dspesed doplets have pe-specfed mass facton. As the mst tavels up t pushes out the dy a that exsts ntally n the bune. At the mst font, some mxng occus due to dffuson of wate vapo fom the mst egon to the dy a and the local humdty dops below 100%. Ths causes doplets to evapoate at oom tempeatue nea the mst font fo the case of vey small dops. Howeve, the evapoaton ates ae vey small (10-9 kg/sec) compaed to those nsde the flame. In the bulk of the mst, the a emans satuated and doplets eman at the ntal sze untl they each the flame and nteact wth the hot gases. All the walls ae set as eflectve boundaes. The doplets n contact wth the hot pat (1 mm length) of the bune tube ae set to evapoate completely. Doplet evapoaton ates play ctcal ole n the flame extncton and ae detemned by the heat tansfe ate to the dop suface. The conducton/convecton heat tanspot to the sphecal suface of the dop domnates ove the adaton tanspot at small dop dametes (4 to 32 µm). Tseng and Vskanta [34] computed evapoaton ates of a sem-tanspaent, sngle, doplet nsde a combuston envonment usng a (spectal) band model. The model ncludes the thee modes of heat tanspot as well as the mass tansfe effects. Fgue 12 of the pape shows that the adaton absopton fom a gas at 1500 K has no effect on the lfetme of 10 µm dops. Incluson of adatve heat tansfe deceases the lfetme by about 40% fo a 100 µm dop. Theefoe, the adaton effects on the wate doplets ae neglected. We wll show that only a small poton of the mst entans nto the flame base, and the entaned doplets evapoate completely nea the flame edges (600 K sothem). Most of the mst tavels vetcally up the chmney. The evapoaton ates of the bulk mst ae not affected sgnfcantly by adaton fom the flame because the mst s njected at 100% humdty, whch mnmzes the mass tansfe dvng foce needed fo evapoaton. Recently, Tseng and Vskanta [35] modeled adaton absopton and scatteng though a sheet of mst based on Me scatteng theoy fo sem-tanspaent, lnealy ansotopc wate dops. In the Fgue 12, Tseng and Vskanta [35] showed deceased total absoptance and nceased total tansmttance of adaton fom an extenal (black-body) enegy souce wth nceased suface doplet densty (poduct of numbe densty and sheet thckness). Fom the Fgues 12 and 13, we estmate the absoptance and tansmttance though 5 cm (oute tube adus) thck bulk mst to be 0.28 and 0.5 espectvely nea extncton wate concentaton (12 mass%) and 10 µm dop damete. Theefoe, the bulk mst contbuton to the adaton loss fom the flame base s neglected fo the small, non-sooty, flame wth low emssvty and steep gadents. Howeve, n eal applcatons fo lage-scale sooty fes, wate mst contbuton to adaton effects can be sgnfcant fo lage, poly-dspese doplets. 9

17 Soluton of the doplet equatons (A49-A60) gves doplet velocty components, tempeatue, and damete as functons of tme. Collson between dops ae neglected at low lqud volume facton (10-4 ). Doplet fagmentaton s neglected because of low values of Webe numbe (10-5 ). The gas phase affects the doplet phase though equatons (A49-A60), and the doplet phase affects the gas phase though the couplng tems, whch appea as pont souces/snks n the gas phase equatons (A1-A6). The couplng tems descbe the exchange of mass, momentum, and enegy between the gas and doplet phases, and ae gven by equatons (A40-A48). In equaton (A40), S m epesents total mass (wate vapo) exchange ate fom the doplet phase nto the gas phase due to evapoaton. It depends on doplet sze and concentaton. Ths tem affects the gas densty and composton n the contnuty (A1) and spece (wate vapo) balance (A4) equatons espectvely. The wate vapo s fomed at C and t s heated up to the local gas tempeatue. The wate vapo has hghe specfc heat than the a. In addton to the sensble heat absopton, wate vapo dlutes the speces concentatons gven by equaton (A4) and deceases the oxygen concentaton avalable fo the combuston eacton. The couplng tem, F d, epesents the total dag exeted by the doplet phase on the gas phase, and s gven by equaton (A43). The tem, S h, epesents the total coolng ate due to the wate doplets, and s gven by equaton (A46). The total coolng ate ncludes the sensble heat absopton due to doplet heatng and latent heat of evapoaton. The second and thd tems on the ght hand sde of enegy equaton (A3) epesent the coolng ate, S h, and the combuston heat elease ate espectvely, and have opposte sgns. The heat elease ate depends on the eacton ates, R, whch deceases due to the oxygen dluton by wate vapo accodng to equaton (A13). The convectve tem on the left hand sde of enegy equaton (A3) epesents the enegy needed to heat up the gas phase fom ambent to the flame tempeatue. In equaton (A3), the tansent tem wll be negatve, f the sum of convectve and conductve heat loss and the coolng ate, S h, s hghe than the heat elease ate. Theefoe, the gas tempeatue deceases wth tme. A small decease n gas tempeatue futhe educes the heat elease ate sgnfcantly due to the exponental natue of the Ahenus equaton gven by (A14). Theefoe, the flame wll appoach extncton. Indeed, Da epesents the ato of heat elease ate and the heat loss ate by convecton and conducton. As the flame appoaches extncton, Da deceases. In the case of flame extncton usng an net gas (such as ntogen addton), all the couplng tems (A40-A48) vansh unlke the mst case. The net gas dlutes oxygen and spece concentatons n equaton (A13), and educes the eacton ate, R. Theefoe, the net gas addton educes the heat elease ate, the second tem on the ght hand sde of enegy equaton (A3). Ths dves the competton between the sum of convectve and conductve heat loss, and the heat elease ate n equaton (A3) towads flame extncton by deceasng Da below ts ctcal value. 10

18 3.0 NUMERICAL The gas-phase dffeental equatons ae dscetzed usng the fnte-volume method ove a mesh consstng of 100 x 220 tetahedal cells. The smallest cells (0.2 mm x 0.3 mm) ae placed n the flame base egon nea the m of the fuel tube. The cell sze nceases wth nceasng values of x and fom the nne tube m. The fnte-volume equatons ae solved usng mplct numecal schemes avalable n Fluent ncludng a stff chemsty solve. The gasphase equatons ae solved usng a segegated solve wth second-ode upwnd method. A SIMPLE famly of schemes (PISO) s used fo the pessue-velocty couplng. Ignton s acheved by asng a egon above the fuel tube to a hgh tempeatue fo a vey shot tme elatve to the smulaton tme. The doplets ae njected at a pe-specfed (constant) flux at the a nlet so that the mass facton of wate n the nlet a s fxed. The nlet flow of wate s dvded nto a numbe of njecton tacks (1 njecton/cell) along the nlet. Fo extemely small dops (4 μm), t s too expensve to solve the Lagangan doplet equatons fo evey doplet snce thee ae a few mllons of dops. Theefoe, the equatons ae usually solved fo a epesentatve dop fo evey few hunded dops njected. At a gven tme, the solutons obtaned fo the epesentatve dop ae scaled by a facto of few hundeds n a gven njecton tack to calculate the couplng tems (A40-A48) fo the ente mass of wate. As the dop sze nceases, the numbe of dops deceases sgnfcantly so that the doplet equatons ae solved fo evey doplet. Lagangan doplet equatons ae solved usng mplct schemes avalable n Fluent. Full couplng between the gas phase and doplet phase s acheved by updatng the doplet souce tems evey tme the gas-phase equatons ae teated. The gas-phase equatons ae teated ten tmes pe teaton of the doplet phase. The tme steps ae μsec fo the gas phase and 1-5 msec fo the doplet tackng. The esduals ae educed to 0.1% fo convegence. The esdual fo the gas phase enegy equaton s educed to 10-4 %. In a typcal computaton, the esdual of the contnuty equaton deceases the slowest wth the numbe of teatons, and contols the convegence. The calculatons ae computatonally ntense and ae pefomed on SGI Altx 3700 paallel machne (13.1 peak TeaFLOPS) though DOD Hgh Pefomance Computatonal esouces. It conssts of 2048 Intel Itanum 2 (1.6 GHz each) pocessos. A typcal CPU tme s 18 hous fo 2000 tme steps usng 36 pocessos wth a un tme of 28 hous. A typcal un eques tme steps. 4.0 RESULTS AND DISCUSSION Fst, we modeled the flame wthout any suppessant to establsh the base case. The left half of Fgue 2 shows the steamlnes and the tempeatue contous at tme=5.39 sec. The steamlnes show clealy that the ente flow n the tube s affected by the pesence of the flame. They extend fa beyond the themal contous. The flame s attached to the edges of the fuel tube ext, whee fesh a mxes wth the fesh fuel and the eactons occu apdly eleasng heat. As the gas tempeatue nceases, the gases expand and acceleate towads the top of the bune at veloctes as lage as 3 m/sec. As they acceleate, they dag a nto the flame as ndcated by the 11

19 12

20 steamlnes that ae bent towads the flame. The flame tempeatue nceases wth x to about 2000 K and deceases slowly as t appoaches the chmney ext. The lage tempeatue gadents n the adal decton cause buoyancy-dven flow, whch nceases wth the dstance, x, fom the fuel bune tube. The left half of Fgue 2 shows the fomaton of two votces n the bulk a. These votces begn to fom at some vetcal dstance (about 2 tmes the damete of the nne tube) fom the m of the nne tube. The votces gow n sze as they slowly tavel upwad n x-decton. The ght half of Fgue 2 shows the steamlnes of the njected a at 0.1 sec late (tme=5.49 sec). The two votces meged nto one. As the votex tavels futhe and exts at the top of the chmney, t entans a/combuston poducts fom outsde nto the chmney. The ente pocess epeats tself wth tme. The votces cause flckeng, whch s especally evdent at lage values of x. The flckeng effects ae much moe ponounced n shot, puffng, dffuson-flame fomed ove a lqud pool suface, whch exhbts flow nstabltes caused by the heat feed back [32]. Fgue 3 shows the adal tempeatue pofle at 10 mm (x=4 cm) above the bune. The tempeatue nceases wth the adal dstance and eaches a maxmum (about 2000 K) at the eacton kenel and deceases to ambent tempeatue n the bulk a. Clealy, the gadent s much steepe on the a sde than on the fuel sde. The gas tempeatue eaches the bolng pont fo wate (373 K) at about 5 mm adal dstance fom the peak. Fgue 3 also shows the concentaton (mole facton) dstbutons fo OH, H, O, CH 3, and C 2 H 6. Clealy, the OH, H, O adcals ae fomed n the eacton kenel located aound =1.0 cm fom the axs of symmety. The themal bounday laye extend much fathe than the eacton coe as ndcated by the tempeatue pofle, whch eaches ambent tempeatue at =1.5 cm. Clealy, any doplet tavelng towads the flame must suvve the themal bae to each nto the eacton kenel. The tempeatue and spece pofles also change wth the axal dstance, x. As the axal dstance nceases, the coe of the fuel gets hot and the peak tempeatue poston moves towads the axs of symmety. Ou computatons showed that the flame length s about 15 cm as ndcated by the value of x (x=18 cm), whee the tempeatue peak occus at the axs of symmety. 13

21 14

22 We ae not awae of eale wok on co-flow, popane, dffuson flame smulatons. The pesent computatons povde the detaled themal and chemcal stuctue of the flame. Howeve, n the pesent pape, we focus on the extncton phenomena athe than a detaled pesentaton of the base case wthout the mst. Fgue 2 clealy shows that the stuctue of the flame s tme dependent due to the buoyancy effects, whch cause flckeng. Howeve, the flow nea the flame base egon (wthn one adus heght fom the nne tube ext) s elatvely smooth. The co-flow a stablzes the flame base by pushng the votex fomaton downsteam. A small degee of oscllatons at the flame base pesst and cause the maxmum flame tempeatue to fluctuate slghtly wth tme. When we ntoduce doplets, the doplets also can cause fluctuatons due to the dsceet natue at small doplet concentatons by volume. Moe mpotantly, the doplets cause damatc changes n the flame poston wth tme. Ou computatons ae tme dependent, and theefoe nclude both the pmay tempoal effects due to doplets and the seconday tempoal effects due to buoyancy flow on the extncton of the flame. In the ntepetaton and dscusson of the computatonal esults, howeve, we focus on the pmay mechansms of flame extncton dynamcs caused by the wate doplets, and leave the dscusson of the two-dmensonal oscllatoy effects fo a futue tme. In the pesent pape, we wll show that the degee of doplet entanment and evapoaton n the flame base egon plays a ctcal ole n flame extngushment. Fst, we ntoduced ntogen nto the co-flow a. Computatons wee pefomed at dffeent values of the ntogen mass concentatons at the a nlet. As the ntogen concentaton eaches a ctcal value (extncton concentaton), the flame base detaches fom the nne tube and tavels downsteam (blows-off). Ou computatons pedct the ntogen extncton concentaton to be 36 mass %. Recently, Lntes et al. [30] epoted the ntogen extncton concentaton fo popane cup-bune flame to be 33.3 mass %. In the cup-bune expements, the measuements of tempeatue, velocty, composton of the fuel gas at the nne tube ext wee not epoted. As dscussed n the theoy secton, the condtons at the nne tube ext ae not well defned because they ae coupled to the flame downsteam. Ths s due to the back dffuson (and adaton) of heat and mass fom the flame to the nne tube ext upsteam, and dealzatons ae made n theoetcal models to decouple the bounday [9, 32]. Theefoe, small dffeences may exst between the actual condtons and the dealzed bounday condtons employed n the pesent computatons at the nne tube ext. Ths dealzaton and the use of GRI 3.0 mechansm may be esponsble fo about 10 % devaton between ou pedctons and the measued values fo the ntogen extncton concentatons. Lntes et al. [30] also epoted ntogen extncton concentatons fo ethane and methane flames n the cup-bune to be 35.3 and 26.5 mass % espectvely. The expements show that the extncton concentaton s nsenstve to the a flow velocty. Shenson et al. [36] pefomed cup-bune expements on the extncton of dffuson flames fomed ove n-heptane lqud pool by dffeent dluents, ncludng ntogen, ntoduced nto the a co-flow of about 4 cm/sec. They epoted 29.4 mass % (wthn 3% accuacy) ntogen n the a feed s needed to extngush both n-heptane and 2- popanol lqud pool flames. The lqud pools may have sgnfcantly dffeent suface tempeatues than the tempeatue of a gaseous jet at the ext of the nne tube. Based on the cup-bune expemental esults fo gases and lqud pools, wth the possble excepton of methane, the ntogen extncton concentaton appeas to be nsenstve to the condtons (velocty, tempeatue) at the ext of the nne tube bounday, and the chemcal natue (chan 15

23 length) of the hydocabon fuel. It may not be supsng that the detals of chemcal mechansms do not play a ctcal ole n co-flow dffuson flames unlke n pemxed flames fo physcal suppesson agents. Ths s lkely because tanspot effects domnate n co-flow flames and chemcal effects become sgnfcant only vey close to the extncton pont. Even n counteflow dffuson flames, whee the flame s hghly stetched and the flame s close to extncton to begn wth, the chemcal effects ae found to be nsgnfcant [24, 25]. Flame extncton can be vewed as a blow-off (o blow-out) phenomenon that occus when the heat geneaton ate due to the combuston eactons s nsuffcent to heat the fuel and a supply to the eacton font, and Da educes below a ctcal value [37], as explaned at the end of the theoy secton. The a and fuel supply to the eacton font occus by convecton and molecula dffuson. The eacton font les n a egon, whee the oxygen and fuel ae wthn the flammablty lmts. In the absence of an extncton agent, the ntnsc eacton ates ae vey hgh, and the a/fuel supply ates contol the locaton of the eacton font. If the fuel flow ate s nceased sgnfcantly to ovewhelm the heat geneaton, the flame font moves downsteam, and eventually blows off as Da deceases below a ctcal value [23]. Smlaly, addton of an net gas (e.g., ntogen) to a educes the heat geneaton ate due to oxygen dluton. Ou smulatons show that the flame font moves away fom the bune m and blows off as the mass facton of ntogen s nceased to a ctcal concentaton of 36% wth the fuel flow ate fxed. If nstead of ntogen, a gas wth hghe specfc heat than a s added, a dffeent effect comes nto play. Wate vapo has twce the specfc heat of a. Theefoe, wate vapo absobs moe enegy as sensble heat fom the flame font and educes ts tempeatue, n addton to the dluton effect. Ths cannot be easly obseved n pactce due to condensaton of vapo above the satuaton lmt. To quantfy the specfc heat effect, compute smulatons ae pefomed wth hgh mass factons of vapo wthout lettng condensaton occu. The smulatons show flame extncton by blow-off at wate vapo mass factons of 17 to 20 %. The oxygen dluton and specfc heat effects ae coupled and nonlnea. Ths s because both lead to a decease n flame tempeatue, whch deceases the ate of ctcal tempeatue-dependent eactons and the heat geneaton ate. At that pont, changes n flame poston acceleate, the flame becomes unstable, and eventually s extngushed. The two effects ae sepaate and dstnct, and ae detemned by two ndependent paametes: mass facton and specfc heat of the extncton agent. Evapoaton of wate dops ncludes thee effects: oxygen dluton, latent heat absopton, and exta sensble heat absopton due to the hghe specfc heat of wate vapo than a [7, 9]. Theefoe, the evapoaton ate plays a key ole that s absent fo gaseous extncton agents. The evapoaton ate depends on doplet concentaton and sze. Ths ntoduces doplet sze at the njecton plane as the addtonal ndependent paamete. Futhemoe, the doplet supply ate (o entanment) to the flame font depends on neta, dag, and gavty. The doplet dynamcs ntoduces othe ndependent paametes: the doplet-velocty-vecto components at the njecton plane. In ou smulatons, afte the base flame s establshed, we nject a mxtue of monodspese doplets and wate vapo at the a nlet, at a velocty dentcal to that of a. The wate vapo s equvalent to 100 % humdty (1.8 % by mass) at ambent condtons. We vay the doplet concentaton to detemne the pont of flame extncton fo a fxed doplet sze. We also detemne the effects of doplet sze on the extncton mass facton of wate doplets. 16

24 Next, we dscuss the computatons fo 8 μm wate doplets. The doplets ae ntoduced at a fxed concentaton of 10.2 % (+1.8 % vapo, 100 % humdty) by mass. Fgue 4a shows the doplets at 0.34 sec (tme=5.34 sec) afte we begn to nject the wate. The left half of Fgue 4a shows the doplet tajectoes, whch ae colo coded by the njecton poston along the a nlet. The blue sold ccles epesent doplet tacks njected close to the wall of the fuel tube and the ed ccles ae doplet tacks njected fathe fom the wall. Fgue 4a shows the two dmensonal vew of the ax-symmetc wate njectons. Theefoe, each doplet tack epesents a concentc ccles aound the flame. Also shown n Fgue 4a ae the steamlnes (sold lnes) of a, whch ae also colo-coded lke the doplet njectons. The doplets appea to follow the steamlnes closely due to lage suface-aea-to-volume ato. The doplets and a adjacent to the wall tavel at a sgnfcantly slowe velocty than those away fom the wall due to the no-slp condton mposed at the wall. Theefoe, the doplets (blue) adjacent to the wall have not eached the flame base egon at the m of the bune (nne tube) yet as shown n Fgue 4a. Indeed, the doplets take 0.6 sec fom the tme of njecton to each the flame base egon. We show the chan-banch eacton (H 2 +O=OH+H) ate contous n colo n Fgue 4a. The colos coespond to the magntudes of the eacton ate, whch ae shown on the left sde of the vetcal ba. The ed colo egon at the flame base epesents the eacton kenel, egon of hgh eactvty. The peak eacton ate occus wthn ths kenel. The eacton ate deceases wth the axal dstance as the poducts ae fomed, and the eactants get dluted. Fgue 4a also shows the 373 K sothem, whch s shown as a sold geen lne that cuts though the a steamlnes. It shows that the themal gadents extend a mllmete o less nea the flame base nto the a sde and the doplets ae about to each the bolng-pont tempeatue sothem (fo efeence, the adus of the nne tube s 12.5 mm n Fgue 4a). The ght half of Fgue 4a also shows the same chan-banchng eacton ate contous (colos coespond to the magntudes shown on the left sde of the vetcal ba) and the 373 K sothem fo efeence. In addton, t shows the 600 K sothem and the doplet evapoaton ate contous. The sothems begn on the sde of the bune wall and extend nto the flame because the top 1mm of the bune wall s kept at 600 K (bounday condton). The ght half of Fgue 4a does not show any evapoaton contous because the doplets have not eached the flame base yet 0.34 sec afte we stated njectng the doplets. The left half of Fgue 4b shows the doplet tajectoes at 0.39 sec afte we began to nject the wate (t=5.39 sec). The mst font s close to the 373 K sothem. Ths ndcates that when the doplets each the 373 K sothem, they begn to evapoate. Howeve, they ae completely evapoated befoe eachng the chan-banchng eacton kenel, whch s also shown n the left half of Fgue 4b. The blue coloed patcles njected close to the bune walls ae tanspoted to the flame base and come closest to the eacton kenel. The wate vapo fomed by the doplet evapoaton tavels along the gas path lnes shown n left half of Fgue 4b. Theefoe, the wate vapo fomed n font of the flame tavels though the eacton kenel at the 17

25 18

26 19

27 flame base and dlutes the eactants. It s clea fom Fgue 4b that the doplet evapoaton deceased the peak eacton ate n the eacton kenel sgnfcantly fom 1.73 fo the base case to 0.75 kgmol/m 3 sec wth doplets. Just beyond the eacton kenel, the eacton ate deceases wth x due to the doplet coolng but t then nceases to about the same values seen n Fgue 4a n the egon whee doplets have not eached yet. Ths s shown by the ed colo egon at lage values of x. Despte ths, one can see that the flame base has begun to lft up slghtly fom the bune m n compason to ts poston shown n Fgue 4a. The ght half of Fgue 4b shows the total evapoaton ate contous n elaton to the eacton ate contous. The colos coespond to the magntudes of the evapoaton ate, whch ae dsplayed on the ght sde of the vetcal ba. The effect of coolng on the eacton ate s expected to be the maxmum when the evapoaton and eacton ate contous ovelap. The ght half of Fgue 4b shows that the doplet evapoaton occus between the 373 K and 600 K sothems, and appoach close to the eacton ate contous at the flame base. But, thee s vey lttle ovelap between the contous. As x nceases, the doplet evapoaton occus at an nceasng dstance fom the eacton kenel as ndcated by the dvegng eacton and evapoaton contous shown n the ght half of Fgue 4b. The attachment postons of the two sothems on the bune wall have not changed sgnfcantly fom those n Fgue 4a. The left half of Fgue 5a shows that the doplets have taveled about one bunedamete dstance upwad at 0.54 sec afte we began njectng the wate (tme=5.54 sec). They begn to be nfluenced by the buoyancy flow as ndcated by the bendng of the doplet and a path lnes away fom the eacton contous. The doplets stll do not suvve to each nto the eacton kenel at the flame base as n Fgue 4b. Howeve, the eacton ate contous have changed sgnfcantly fom Fgue 4b. The eacton kenel lfted away fom the bune suface sgnfcantly and the doplets have penetated nto the flame base egon between the eacton kenel and the bune m. Also, the eacton ate deceases sgnfcantly at lage values of x unlke n Fgue 4b whee the eacton ate s compaable to that of Fgue 4a, the base-case flame. Howeve, the eacton ate nea the flame base has not changed sgnfcantly fom that n Fgue 4b. The ght half of Fgue 5a shows that the evapoaton contous extend futhe up the axs as the doplets tavel up the bune. The doplets stll evapoate between the 373 K and 600 K sothems lke n Fgue 4b. Howeve, the 600 K sothem moved up and attached at the cone of the bune athe than on the sde wall as shown n the ght half of Fgue 4b. Theefoe, the doplet coolng s sgnfcant nea the bune m. The magntude of the evapoaton ate emans about the same as n Fgue 4b. 20

28 21

29 22

30 The left half of Fgue 5b shows doplet tajectoes 0.74 sec afte we began njectng wate (tme=5.74 sec). The doplets have taveled moe than 1.5 bune dametes dstance upwad. The doplet tajectoes devate fom the gas steam lnes at the top of the pctue sgnfcantly because a esponds to buoyancy flow qucke than the doplets. The gas steamlnes ae shown as sold lnes n colo. Howeve, nea the flame base egon, the doplet tajectoes closely follow the gas steam lnes. The peak eacton ate wthn the eacton kenel of the flame emans unchanged. Howeve, the kenel lfts fathe fom the bune m than n Fgue 5a and the doplets have penetated futhe nto the flame base than n Fgue 5a. The ght half of Fgue 5b shows sgnfcant evapoaton n the flame base and the attachment poston of the 600 K sothem has changed sgnfcantly on to the top of the bune. The doplets stll evapoate between the 373 and 600 K sothems and the magntude of the evapoaton ate emans unchanged. Despte ths, as tme nceases, thee s slow coolng of the egon between the bune m and the eacton kenel esultng n addtonal flame lft away fom the bune m. The left half of Fgue 6 shows the eacton contous and the patcle tajectoes 0.89 sec afte we began njectng wate (tme=5.89 sec). The doplets have eached unde the flame and have begun to engulf the base of the flame. Now, the changes occu apdly as shown by sgnfcant movement n the poston of the eacton kenel, whch moves up and towads the axs of symmety. The eacton ate falls sgnfcantly to a maxmum of 0.38 Kgmol/m 3 sec n the flame tp. The wate vapo fomed by evapoaton s entaned well nto the flame and the fuel jet as ndcated by the gas steamlnes. The poston (elatve to the flame and 373 K sothem) and the magntude of the doplet evapoaton ate eman unchanged as shown n the ght half of Fgue 6. Yet, sgnfcant coolng of the flame base egon occus. The 600 K sothem attaches to the bune m almost nea the axs of symmety. The fuel gas above a lage poton of the bune ext s elatvely cool. As tme pogesses, the flame contnues to move away fom the bune m and eventually blows off. Fgues 4-6 show clealy that extngushment occus due to coolng of the egon between the bune m and the eacton kenel by the wate doplets. The doplets njected close to the bune wall ae entaned nto the egon nea the flame base and ae esponsble fo the extngushment by blow-off. The 8 μm doplets essentally evapoate between the 373 and 600 K sothems and the ates of evapoaton do not change sgnfcantly wth tme. Theefoe, the doplets do not suvve to each the eacton kenel nsde the flame base. Afte the doplets have taveled up and eached the bune m, the chan-banchng eacton ate deceases slowly n the ntal 0.35 sec and then apdly dung the next 0.15 sec to a ctcal value of 0.38 Kgmol/m 3 sec. At ths pont, the doplets and oxygen ente the egon between the eacton kenel and the bune m as the flame lfts away. The doplets cool the fuel mxtue as well as dlute t by fomng wate vapo. The eacton ate s not lage enough to heat the elatvely cold fuel to the gnton tempeatue fo combuston to occu. A Damkhole numbe can be defned as Da= δ(eacton ate/fuel flow ate), whee δ s the dstance between the eacton kenel and the bune m fo the base case, m. At the extncton pont, Da =0.933 fo the ctcal eacton ate of 0.38 Kgmol/m 3 sec and fuel flow ate of 4.07x10-4 Kgmol/m 2 sec. As Da falls below a ctcal value, the fuel supply ate s geate than the eacton ate, and the flame moves away fom the bune 23

31 24

32 m. Theefoe, the change n the eacton ate can be used as a gude to defne the extncton pont. We expect the ctcal eacton ate to be accuate wthn a facto of 2, snce the flame dd not extngush at 0.8 Kgmol/m 3 sec as shown late. Fgue 7a llustates the changes n the chan-banchng eacton ate futhe by followng the eacton kenel as t moves away fom the bune m wth nceasng tme. The kenel poston s detemned by locatng the computatonal cell contanng the maxmum eacton ate. It occus at x=3.18, 3.22, 3.31, 3.28, 3.84 cm at tme=5.34, 5.54, 5.64, 5.74, and 5.89 sec espectvely. The x values ae appoxmate and ndcate a slght degee of oscllaton n the locaton of the peak eacton ate. Fgue 7a shows the eacton ate dstbutons n the adal decton acoss the eacton kenel shown n Fgues 4-6 at dffeent tmes. Changes n the eacton ate occu unevenly ove tme befoe eachng the extncton value of 0.38 Kgmol/m 3 sec at the peak. The unevenness s lkely due to the dsceet natue of the doplets and due to small oscllatons that occu at the flame base due to flckeng. The dscete dops and flame flckeng cause small fluctuatons n local tempeatue and spece concentatons. Howeve, the key s that once the eacton ate s educed to an nsuffcent level to ovecome the convectve and conductve heat loss, the flame contnues to move towads extncton. The eacton ate wll eventually decease despte small (15 %) fluctuatons along the way towads extncton. The extncton value fo the eacton ate s a consevatve estmate obtaned fom numeous computatons fo dffeent dop szes and concentatons. Smlaly, Fgue 7b shows the OH adcal concentaton dstbuton adally acoss the eacton kenel at dffeent tmes. The peak OH adcal concentaton deceases by 43% and t plays an mpotant ole n the popagaton of the combuston pocess. The tempeatue acoss the eacton kenel s shown n Fgue 7c at dffeent tmes dung the extncton pocess. The eacton kenel peak tempeatue s dffeent fom the maxmum flame tempeatue, whch occus downsteam of the eacton kenel. Ths s expected because t takes a shot tme fo the gases to get heated by the elease of heat wthn the eacton kenel and s smla to the stuctue epoted by Ananth et al. [22]. Fgue 7c shows that the eacton kenel peak tempeatue changes unevenly but eventually deceases by about 100 K wth tme. The tempeatue seems to ncease slghtly as the flame appoaches extncton. Despte ths slght ncease, the eacton ate deceases sgnfcantly at extncton as shown n Fgue 7a. Clealy, a decease n the spece (H 2, O, OH, H) concentatons must be esponsble fo the educed eacton ate. Ths could be due to the fomaton of wate vapo that causes the dluton effect. Even though tempeatue s mpotant, t s the eacton ate that affects Da dectly and plays a cucal ole n detemnng flame extncton. To undestand ths fully, one must consde the enegy equaton, whch s complex and contans many moe vaables than llustated n Fgues 7a-c. Fgue 8a shows the doplet concentaton dstbuton along the thee sothems, 373 K, 500 K, and 600 K, two of whch ae shown n the ght half of Fgue 5a at tme=5.54 sec. The cuve length s the dstance along a gven sothem, whch changes wth tme as shown n Fgues 4-6. The cuve length s measued fom the bune m, and t nceases wth nceasng values of x. Fgue 8b shows the degee of doplet entanment/evapoaton along each sothem. The doplet dstbutons ae not smooth due to the dscete natue of the doplets at vey dlute 25

33 26

34 27

35 concentatons by volume. As the doplets move towads the hot gases suoundng the eacton kenel, the concentaton deceases contnuously fom 373 K to 600 K. No doplets wee found along the 900 K sothem. Fgue 8b shows the evapoaton ate, whch s small along the 373 K sothem and nceases apdly as the doplets penetate towad the 500 and 600 K sothems. As the doplets tavel towads the 600 K sothem, they educe n sze. Theefoe, the evapoaton ate nceases despte the educed lqud concentaton shown n Fgue 8a. The evapoaton ate s the degee of latent heat absopton fom the hot gases. As the evapoaton ate nceases, the wate vapo concentaton nceases whch causes dluton of oxygen and othe speces and hndes combuston. Fgue 8c shows the wate vapo concentaton due to the combned effects of vapozaton and the fomaton of wate fom the combuston chemsty. In an attempt to sepaate the two phenomena, we also show wate vapo concentatons at a tme (5.24 sec) befoe the doplets begn to nteact wth the flame base. These coespond closely to the base case, whee wate vapo s fomed solely due to combuston of popane. Fgue 8c shows clealy that the wate vapo fomed by the combuston pocess (.e., w/o evap ) s sgnfcantly smalle than that fomed by the doplet evapoaton. Theefoe, evapoaton s a key facto n achevng extncton by oxygen dluton and sensble heat absopton by the wate vapo, whch has much hghe specfc heat than a. At a slghtly hghe doplet concentaton of 12.2 mass % (+ 1.8% vapo,.e., 14 mass % total wate) than the extncton concentaton (12 mass % total wate), whch s shown n Fgues 4-6, the extncton pocess occus athe apdly. The doplets wee njected at the a nlet exactly same as n Fgues 4-6. Fom ou computatons, we obseved that the eacton kenel at the flame base begns to detach fom the m, when the doplets njected adjacent to the nne tube wall each the bune m at tme=5.49 sec. At tme=5.59 sec, the peak eacton ate n the eacton kenel at the flame base falls fom 1.8 to 0.33 kgmol/m 3 sec, and the kenel moves up fom 1 mm to 3.3 mm above the m. Fgue 9a shows the smulaton esults fo flame poston fo 14 mass % total wate at tme= 5.69 sec. The eacton kenel moves up about 8.5 mm fom the m as shown n Fgue 9a. As the tme pogesses futhe, the flame contnues to move away fom the bune, and blow-off occus. The left half of Fgue 9a shows that the doplets follow the a steam lnes closely and ente the egon undeneath the eacton kenel nto the fuel coe. Howeve, the doplets stll do not ente nto the eacton kenel at the flame base. They penetate slghtly past the 373 K sothem smla to the esults dsplayed n Fgue 6. The local coolng by the doplets leads to the decease n the eacton ate nsde the kenel, whch s suounded by the wate doplets. Howeve, the eacton ate away fom the kenel nceases wth x and eaches about 0.67 Kgmol/m 3 sec as ndcated by the ed coloed egon at the top n the left half of Fgue 9a. In ths egon, the doplets have not eached the flame yet and local coolng does not occu. The ght half of Fgue 9a shows clealy that the local coolng by the doplets njected vey close to the bune wall plays a key ole n educng the local eacton ate nsde the kenel. The eacton ate nsde the kenel s the key paamete that contols the extncton by blow-off fom the bune m. 28

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38 The evapoaton ate contous dsplayed n the ght half of Fgue 9a ae vey smla to those n Fgue 6 and ae agan bounded between the 373 and 600 K sothems. Clealy, nceasng the doplet concentaton dd not enable the doplets to penetate any futhe nto the eacton coe. The 600 K sothem moved up and towads the axs of symmety sgnfcantly due to coolng of the egon above the bune m by the doplet evapoaton lke n Fgue 6. The ght hand sde of the vetcal ba dsplays the magntudes of the evapoaton ate, whch s smla to that n Fgue 6 because the doplet concentatons dffe only by 20%. The left half of Fgue 9b dsplays the doplet tajectoes and the chan-banchng eacton ate contous at doplet concentaton of 7.2 mass % (+ 1.8% vapo,.e., 9 mass % total wate) n the nlet a. The computatons showed that the flame does not extngush at 9 mass % total wate concentaton as shown n Fgue 9b. The doplets cool the flame and the eacton kenel detaches slghtly fom the m as n Fgue 5a. But, the flame emans stable, attached at the new locaton, and emans unchanged wth tme unlke the extncton pocess dsplayed n Fgue 6. The doplet coolng leads to a educton n the eacton ate to 0.83 kgmol/m 3 sec, whch s well above the appoxmate extncton lmt of 0.38 kgmol/m 3 sec. The peak eacton ate nsde the kenel deceases wth x as shown n Fgue 9b. The doplets (blue coloed) njected adjacent to the bune wall entan towads the flame base but do not penetate sgnfcantly the egon between the eacton kenel and the bune m. The ght half of Fgue 9b s smla to Fgue 5a and shows that the 600 K sothem moved up to the cone of the bune. But, the sothem n Fgue 9b emans unchanged wth tme. Despte lowe doplet concentaton, the doplets evapoate between the 373 and 600 K sothems and the evapoaton ates ae compaable to those dsplayed n the ght half of Fgue 5a. Clealy, the locaton fo complete evapoaton of the doplets s detemned by the doplet damete athe than the doplet concentaton. Fgues 4-6 and 9a show that the doplets educe the chan-banchng eacton ate nsde the eacton kenel below a ctcal value (0.38 kgmol/m 3 sec) at flame extncton. In Fgue 10, we show that the maxmum local eacton ate deceases wth tme fo thee dffeent doplet concentatons. The extncton tme s defned as the tme needed fo the eacton ate to fall to the ctcal value. Theefoe, Fgue 10 shows that the extncton tme s 0.55 sec, at 12 mass % total wate (dops+vapo). At the ctcal eacton ate, the extncton tme deceases by a facto of 3.6 as the total wate concentaton s nceased fom 12 mass % to 14 mass %. At 9 mass % total wate, the eacton ate does not each the ctcal value and the flame s not extngushed even afte 1 sec. In Fgue 10, the tme s measued fom the pont at whch the doplets adjacent to the bune wall ae about to each the bune m (e.g., Fgue 4a) and the doplets begn to evapoate and nteact wth the flame tp. Theefoe, the tme does not nclude the tme equed fo the doplets to tavel up to the flame base. 31

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40 In pactce, mst fomed by nozzles o ultasound nstuments contans a dstbuton of doplet szes. The evapoaton ate s dectly elated to doplet sze. Theefoe, the effects of doplet sze wll be examned next. We nject 32 μm, mono-dspesed, doplets at 8.7 mass % doplet concentaton (10.5% total wate) wth the a (100 % humdty o 1.8 mass % wate vapo) at the entance of the bune smla to the njectons n Fgue 4a. Afte the njecton, the doplets tavel up and each the bune m (at tme=5.59 sec) moe slowly than the 8 μm dops. The left half of Fgue 11a shows the doplet tajectoes, the eacton ate contous, and the 373 K sothem 0.89 sec afte we njected wate (tme=5.89 sec) at extncton. The doplet tajectoes devate moe fom the a steam lnes than the 8 μm dops shown n Fgue 6. Ths s evdent even nea the flame base egon, whee the doplets seem to bend downwad towads the bune suface slghtly. Ths s due to a lage gavty effect on the doplet momentum than fo the 8 μm dops. Moe mpotantly, the doplets penetate the flame sgnfcantly fathe, suvvng well past the 373 K sothem, and each nto the eacton kenel at the flame base unlke n Fgue 6. The eacton ate dops well below the ctcal value to 0.26 kgmol/m 3 sec nsde the eacton kenel, whch s located about 7 mm above the bune m. Clealy, the kenel s well suounded by the doplets as they ente unde t nto the coe of the fuel jet. Fgue 11a clealy shows that 32 µm dops ae moe effectve than 8 µm dops. Ths s supsng snce lage dops evapoate slowe than the small dops accodng to the d 2 -law. The eason fo the hghe effectveness of lage dops can be seen n the ght half of Fgue 11a. The ght half of Fgue 11a shows the evapoaton ate contous n elaton to the eacton ate contous. Thee s now a sgnfcant ovelap between the two contous nea the flame base unlke n Fgue 6, whch s fo the 8 μm dops. One mght expect that doplet szes slghtly lage than 32 μm mght be optmum, and esult n complete ovelap between the eacton ate and evapoaton ate contous. The doplet evapoaton ate contous ae also thcke fo 32 μm dops than fo 8 μm dops. A compason of Fgues 11a and 6 shows that the bgge dops evapoate patly nsde of the eacton kenel whle the smalle dops evapoate completely outsde of the kenel egon. Theefoe, fo 32 μm dops, the latent heat absopton occus patally nsde the eacton kenel dectly leadng to educton n the maxmum local eacton ate well below the ctcal value needed fo flame extncton. The ght half of Fgue 11a also shows the 373, 600, 900, and 1200 K sothems. Clealy, doplet evapoaton occus well past the 600 K sothem and up to the 1200 K sothem. The magntude of the evapoaton ates s sgnfcantly smalle n Fgue 11a than n Fgue 6. The smalle evapoaton ates ae due to educed suface-aea-to-volume ato as the doplet sze s nceased. Despte the educed evapoaton ate, the flame s extngushed at 8.7 mass % doplet concentaton (+1.8 % vapo) fo 32 μm compaed to 10.2 mass % (+1.8 % vapo) needed fo 8 μm dops. Fo the lage dops, the evapoaton of dops nsde the eacton kenel of the flame base plays a sgnfcant ole n the doplet effectveness n extngushng the flame. Computatons at doplet concentatons of 7.2 mass % (+1.8 % vapo) do not lead to flame extngushment. The left half of Fgue 11b shows the doplet tajectoes and the eacton ate contous fo 4 μm dops njected wth the a at a doplet concentaton of 14.2 mass % (+1.8 % vapo,.e., 16 mass % total wate). It shows that the doplets do not each nto the eacton kenel. But, the 33

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