Fundamentals of Flame Stabilities. Fundamentals of Flame Stabilities Lecture Notes 3

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1 ecre Noes 3 Hong G. Im Assocae Professor Deparmen of Mecancal Engneerng Unvers of Mcgan Ann Arbor Mcgan UA gm@mc.ed Prepared for specal lecres a Unversà degl d d Roma a apena Facolà d Ingegnera Aerospaale Marc Olne Inrnsc Flame Insables ecre 5/6 (Marc 14/16 - affman-alor nsabl - Addonal Isses rblen brnng veloc Dffson flame nsabl Edge flame nsabl Dffson flames n mcro-combsors - Flame srec: maemacal defnon - Marksen nmber and relevance o rblen combson

2 affman-alor Insabl Addonal nsabl mode for flames propagang n a narrow cannel (Hele-aw cell Poenal Applcaon - Mcro-combsor (n premed combson mode - Combson n engne crevce affman-alor Insabl affman & alor (1958 Epermenal Observaons & Analcal d - wo mmscble flds n a Hele-aw cell. - Insabl wen e drvng fld s less vscos.

3 Joln & vasnsk Analss Joln & vasnsk (1994 near sabl analss sng - Psedo-D Eler-Darc eqaons (-drecon parameered o be sown laer Dffsve-ermal nsabl no consdered ( ( v 0 p v f ± g ( : pward : downward v v v p μ v fv f ~ : momenm loss d λ cp v ( ~ : ea loss d Joln & vasnsk Analss Dsperson Relaon b 1 For small ea release: γ 1 f f f ( ( av b. Momenm loss enances nsabl f f > 0 for gases ( γuk Uk fb f / γ g / U Uk ω ~ Uk / c k U f k U f Uk / c ( ( p av av p b 1. Hea loss redces D- nsabl 3. Grav amplfes (pward or aenaes (downward e effec

4 - Insabl Mecansm Flame one Convecve ream Frcon Force Increased frcon force Increased veloc Propagang Flame fron Increase n vscos frcon de o ncreased veloc and vscos Inerenl drodnamc Frcon force does no aenae w formaon of csp. - nsabl connes o grow afer D- reaces eqlbrm. Compaonal Confgraon wo-dmensonal calclaon One-sep Arrens reacon emperare-dependen vscos Reference Frame agnan Flame fron agnan Gallean ransformaon Reference Frame U c U c ( -U c Flame fron U c U c

5 Assme Poselle flow (parabolc n -drecon Effecs of ea loss { } { } c c c ( 6 ( 6 ( U U U { } { } U U c c ( 6 ( 1 μ μ { } c ( 1 U μ μ olve for -averaged varables ( Y v d 0 ( ( Darc Appromaon { } { } w w w ( 6 ( 6 ( ( 1 ( 0 0 H b w ( ( 0 v ( ( ( P v a Re 1 ( ( ( P v v v a Re 1 ( [ ] ( [ ] ( ( ( v P e P e e Re a 1 ( ( ( R R a a 1 1 Re Re Pr H v v v Q μ μ μ ω ( ( ( R Re a c 1 ω μ μ Y Y Y v Y Y mass -momenm -momenm energ speces were (1 1 (1 ep R R Λ θ σ θ β ω Y ( 0 f f a R E β f 0 f σ Conservaon Eqaons

6 Ke parameer: Dsperson Relaon Pe α ω Normaled grow rae ω ** Dffsve-ermal e 0.7 e 1.0 e Normaled wave me nmber ** k ** Normaled amplde of flame wrnkle F ** ω Normaled grow rae affman-alor No - effec Normaled wave nmber k ** Wave nmber selecon s smlar o D- Effec of Pecle Nmber Normaled grow rae (a mamm k Normaled Hele-aw cell ckness /δ For - effec o be mporan: ω saff /ω normal Pe < 50 or /δ < Pecle nmber /α

7 Prevos Epermens Abd arf and Ronne ( No clear dependence of / on Pe - Epermenall lmed o g Pe CH 4 -ar C 3 H 8 -ar CH 4 -O -CO CH 4 -ar (6.35 mm cell C 3 H 8 -ar (6.35 mm cell 5 4 Horonal Upward Downward Horonal (6.35 mm cell / 4 3 / 3 1 Horonal orenaon onl Pecle nmber w/α 1 CH -ar mres (e? Pecle nmber w/α Nmercal Resls D- & D- onl Hea oss onl Mom oss onl Hea & Mom oss

8 mmar Cell Formaon Beavor Oer effecs D- mode domnan e Hea loss Normal Momenm oss 0.7 3~4 cells cells 1 cell 1.0 cells 1 cell 1 cell D- - mode domnan λ ** 0 F/λ 10 - ( ** 7 H0.5 ome Advanced bjecs on Flame Insables

9 Addonal Isses - rblen Combson rblen Brnng Veloc : Esng eores and epermens don agree among one anoer. Bra (ero ea release (large ea release rblen Brnng Veloc ( / Pope & Anand (ero ea release (large ea release vasnsk Yako Epermen (Re 1000 Goldn (Re 1000 F e case of e bendng effecs remans an open sse. (Ronne rblence Inens ('/ Effecs of ermal Epanson Cambra & Joln (199 - / ncreases as γ ( b / ncreases. - ermal epanson-ndced wrnklng (D- nsabl s more prononced for low rblence nens. Possble eplanaon for bendng effecs

10 Addonal Isses - Nonpremed Flames Nonpremed Flame Insables - ome epermenal observaons - Cell srcres pcall observed n e drecon of no flow sranng - Asmpoc analss sowed smlar pes of dffson flame nsables (Km 1997 Celllar nsabl for e < 1 Plsang nsabl near encon condon for e > 1. cemac of dffson flame nsabl (Km 1997 Heagonal celllar nsabl n asmmerc meane/ar je flames (o Jacono e al Addonal Isses - Edge Flames Edge Flame Insables (acer & Dold e > 1 for < c - Edges conne o propagae even wen e ralng dffson flame no longer ess (n a emporall oscllang mode. c

11 Addonal Isses - Mcro-Combson Nonpremed Combson n a Mcrocannel (Mese e al Cell srcres observed n a narrow cannel sbjeced o ea loss - Nmber of cells depends on mre and flow condons. Flame rec: Effecs of Aerodnamcs on Flame Propagaon

12 Flame rec - Inrodcon In man flame nsabl sdes was essenal o consder a flame speed depends on flow condons. - Marksen Flame speed depends on crvare - Dffsve-ermal nsabl: Flame speed canges de o mbalance beween mass and ea ranspor (ews nmber Formal eorecal descrpon of e ne effecs of flow feld on flame speed s needed. Flame rec - Defnon Karlov (1953: κ du d Wllams (1975: 1 da δκ κ Ka Karlov Nmber Ad ( Knemac consderaon n: n normal vecor V f : srface veloc (lab frame v: flow veloc (lab frame e e : angen vecors on srface p q V f nv n G 0

13 Flame rec - Defnon A. Maalon (1983 v n n V n n { ( ( ( G f } κ 0 G 0 B. Cng & aw (1984 κ v V n n ( ( s f C. Candel & Ponso (1990 κ nn: v v v ( ( ee p p ee q q : v ( n a ( n angenal sran crvare ( were v V; V V V n n s f f Noe a n A & B crvare effecs ma be nclded n e frs erm. Flame rec Pscal Implcaon Cng & aw (1984 (1 Flow nonnform along e flame srface ( v n v n ( ( κ v V n n s f (1 ( (3 s 0 onl f flow s oblqe o e srface ( V : Flow veloc n e neral frame f Vf n 0 for saonar flames (3 n 0 onl for crved flames.

14 Flame rec Eamples Eamples ( ( κ v V n n s f (a percal epandng flame v 0 b n 0 V n 0 0 s f κ (b ead spercal flame V n 0 v 0 0 f s κ (c ead crved flame n nform flow V n 0 b v 0 0 f s κ Flame rec Frer Eamples ead agnaon Flow (Hemen 1 a : sran rae (s a v a 0 0 0:-D slab k 1 s k 1: asmmerc n j e ( ( κ v V n n s f Vf n 0 v 1 1 r r ( a a ( D ar κ a a ( asmmerc v

15 Flame rec Frer Eamples percal Flames n e dr f ( ( p κ Vf vs Vf n n e q d drf vs 0 Vf n R f d 0 0 n n ( ep n ( eq n ep eq n ep eq n p q p q p q R1 R R R 1 κ f R f dr d > 0 for oward prop. < 0 for nward prop. Bnsen Flame Flame rec Frer Eamples ( ( κ v V n n s f ( ( Vf n 0 v 0 0 w n cos α 0 snα snα κ ( rwcosα cosα ( wcosα r r If α consan (ecep a e p n v ( 00 w wsn α κ R f ( < 0

16 Effecs of Flame rec - Penomenolog Ke Parameers: λ α D ( defcen Dj ( ecess cp α e ews nmber ; D / Dj Preferenal dffson D ( ( Eample: Bnsen flame p e e 1: no effec > 1: sronger p (lean propane/ar e < 1: p openng (lean drogen/ar ea mass def. ecess D / D 1: no effec j D / D < 1: sronger p j (rc drogen/ar D / D > 1: p openng j (rc propane Effecs of Flame rec for Bnsen Flames Epermenal Observaon (aw & ng 000 rc C 3 H 8 /ar lean C 3 H 8 /ar rc CH 4 /ar lean CH 4 /ar

17 Effecs of Flame rec - Conerflow Eample: Conerflow flames (κ > 0 Hea: loss Mass: gan e e 1: no effec > 1: weaker flame (lean propane/ar e < 1: sronger flame (lean drogen/ar D / D 1: no effec j D / D < 1: weaker flame j (rc drogen/ar D / D > 1: sronger flame j (rc propane Effecs of Flame rec n Conerflow Nmercal Resls: Flame emperare vs. rec

18 Effecs of Flame rec on Flame peed Marksen (1950 κ 0 1 μ f (ersc crvare effec Asmpoc Analss for ow rec Flames κ 0 1 κ 1MaKa Marksen leng δκ Ma Marksen nmber; Ka Karlov nmber δ Clavn & Wllams (198 Clavn & Garca (1983 ( e 1 1 β 1 γ Ma J D γ γ b b λ d γ ; J λ ( b λ b d D ln b λ ( Effecs of Flame rec on Flame peed Emprcal Correcons for arger Ka Fae e al. Ponso e al. κ 0 κ 0 1 MaKa ( κ 0 1 / C v 1 C / R ( ( R : rads of crvare Frer ambges - Defnon of flame speed - Defnon of flame ckness

19 Flame peed Correlaon Eenson o rblen Flames (Cen & Im 000 crvare effecs - wo brances n correlaon crves - Effecs of nseadness a g rblence Flame peed Correlaon Unsead Effecs (Im & Cen Flame response o armonc oscllaon n sran rae M ( ω a a 1 Asn 0 ma mn Ka ma Ka mn ( F ω Marksen ransfer fncon

20 References (1 Abd M. arf J. and Ronne P. D. p://carambola.sc.ed/researc/heleaw/heleawcells.ml Cambra P. and Joln G. Proc. Combs. Ins. v. 4 pp (199. Candel. M. and Ponso. J. Comb. c. ec. v. 70 p.1 (1990. Cen J. H. and Im H. G. Proc. Comb. Ins. v. 8 p. 11 (000. Cng. H. and aw C. K. Combs. Flame v. 55 p. 13 (1984. Clavn P. and Garca P. J. Méc. erm. appl. v. p. 45 (1983. Clavn P. and Wllams F. A. J. Fld Mec. v. 116 p. 51 (198. Im H. G. and Cen J. H. Proc. Comb. Ins. v. 8 p (000. Joln G. and vasnsk G. I. Combs. c. ecnol. v.98 p.11 (1994. Kang. H. Im H. G. and Baek. W. Combs. eor Modellng v.7 p.343 (003. Kang. H. Baek. W. and Im H. G. Combs. eor Modellng v.10 p. 659 (006. References ( Km J.. Comb. eor Modellng v. 1 p. 13 (1997. aw C. K. Combson Pscs Cambrdge Unvers Press (006. aw C. K. and ng C. J. Prog. Energ Combs. c. v. 6 p. 459 (000. o Jacono D. Papas P. Monkew P. A. Comb. eor Modellng v. 7 p. 635 (003. Maalon M. Combson cence and ecnolog v. 31 p. 169 (1983. Mese C. Masel R. I. or M. and annon M. A. Comb. eor Modellng v. 9 p. 77 (005. Ronne P. D. ome open sses n premed rblen combson Proc. of e U-Japan emnar on Modelng n Combson cence pp. 3- (1994. affman P. G. and alor G. Proc. R. oc. ondon A v.45 p. 31 (1958. acer R. W. and Dold J. W. Comb. eor Modellng v. 4 p. 435 (001.