Fuel & Advanced Combustion. Lecture Chemical Reaction
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1 Fuel & Advaced Cmbust Lecture Cemcal eact
2 Ideal Gas Mdel e deal gas equat f state s: V m m M were s te Uversal Gas Cstat (8.34 kj/kml K, M s te mlecular wegt ad s te umber f mles. Secfc teral eergy (uts: kj/kg Secfc etaly (uts: kj/kg u( cv ( d ( c ( d Secfc etry (uts: kj/kg K s, s ( l( ( ( = bar, s etry at
3 Ideal Gas Mdel fr Mxtures e mass m f a mxture s equal t te sum f te mass f cmets m m e mass fract, x, f ay gve seces s defed as: x m ad m x e mxture teral eergy U ad etaly H (uts: kj s: were u ad U mu m u H m m are mass secfc values (uts: kj/kg e mxture secfc teral eergy u ad etaly s: u U m m u xu m H m m x m 3
4 4 e mxture teral eergy U ad etaly H (uts: kj s: H u U were are mlar secfc values (uts: kj/kml u ad e ttal umber f mles te mxture s: Ideal Gas Mdel fr Mxtures e mle fract, y, f ay gve seces s defed as: y y ad y y u u e mxture mlar secfc teral eergy ad etaly (uts kj/ kml s:
5 5 Ideal Gas Mdel fr Mxtures e artal ressure f a cmet,, te mxture (uts: ka s: y V V y r Mass secfc etry (kj/kg K mlar secfc mxture etry (kj/ml K : s x s l / l( y s y s l l e mxture mlecular wegt, M, s gve by: M y M m m M
6 Cmst f Stadard Dry Ar Ar s a mxture f gases cludg xyge (O, trge(n, arg (Ar, carb dxde (CO, water vaur (H 0. Fr cmbust dry ar s take t be cmsed f % O ad 79% N by vlume (y O =0., y N =0.79. N O tt N tt O y y N O 3.76 Fr every mle f O tere are 3.76 mles f N. Mlecular wegt f ar s M ar y M y O M O y N M N 0.(3 0.79( kg/kml e amut f water mst ar at temerature s secfed by te secfc umdty (w r te relatve umdty (F defed as fllws: w mh O H O F 0 F m ( ar sat 6
7 Cmbust Stcmetry If suffcet xyge s avalable, a ydrcarb fuel ca be cmletely xdzed, te carb s cverted t carb dxde (CO ad te ydrge s cverted t water (H O. e verall cemcal equat fr te cmlete cmbust f e mle f rae (C 3 H 8 wt xyge s: C3H8 ao bco cho Elemets cat be created r destryed, s C balace: 3 = b b= 3 H balace: 8 = c c= 4 O balace: a = b + c a= 5 # f mles seces us te stcmetrc react s: C3H8 5O 3CO 4HO 7
8 Cmbust Stcmetry Ar ctas mlecular trge N, f rducts are at a lw temerature te trge s t sgfcatly affected by te react, t s csdered ert. e cmlete react f a geeral ydrcarb C H wt ar s: C H a( O bco ch O dn 3.76N C balace: = b b = H balace: = c c = / O balace: a = b + c a = b + c/ a = + /4 N balace: (3.76a = d d = 3.76a/ d = 3.76( + /4 C H ( O N CO H O 3.76 N 4 Examle: e stcmetrc react f ctae (C 8 H 8 = 8 ad = 8 C.5( O 3.76N 8CO 9HO N 8H8 47 8
9 Cmbust Stcmetry e stcmetrc mass based ar/fuel rat fr C H fuel s: A/ F s m m ar fuel O M ar 4 M M C M H fuel M 3.76 M 4 N Substtutg te resectve mlecular wegts ad dvdg t ad bttm by e gets te fllwg exress tat ly deeds te rat f te umber f ydrge atms t ydrge atms (/ te fuel. A/ F s ( F / A s ( Nte abve equat ly ales t stcmetrc mxture Examle: Fr ctae (C 8 H 8, / =.5 (A/F s = 5. (gasle (A/F s 4.6 9
10 Fuel Lea Mxture Fuel-ar mxtures wt mre ta stcmetrc ar (excess ar ca bur Wt excess ar yu ave fuel lea cmbust At lw cmbust temeratures, te extra ar aears te rducts as O ad N : C H g ( ( O 3.76N CO HO dn eo 4 a fuel lea mxture as excess ar, s g > Abve react equat as tw ukws (d, e ad we ave tw atm balace equats (O, N s ca slve fr te ukws 0
11 Fuel-ar mxtures wt less ta stcmetrc ar (excess fuel ca bur. Wt less ta stcmetrc ar yu ave fuel rc cmbust, tere s suffcet xyge t xdze all te C ad H te fuel t CO ad H O. C H Fuel c Mxture Get cmlete cmbust were carb mxde (CO ad mlecular ydrge (H als aear te rducts. g ( ( O 3.76N CO HO dn eco fh 4 a fuel rc mxture as suffcet ar g < Abve react equat as tree ukws (d, e, f ad we ly ave tw atm balace equats (O, N s cat slve fr te ukws uless addtal frmat abut te rducts s gve.
12 Off-Stcmetrc Mxtures e equvalece rat, f, s cmmly used t dcate f a mxture s stcmetrc, fuel lea, r fuel rc. f A/ F A/ F s mxture F / A F / A mxture s Stcmetrc mxture: C H stcmetrc f = fuel lea f < fuel rc f > Off-stcmetrc mxture: ( O 3.76N rducts 4 C H f ( O 3.76N 4 rducts g f
13 Off-stcmetrc Cdts Oter termlgy used t descrbe w muc ar s used cmbust: 0% stcmetrc ar = 0% teretcal ar = 0% excess ar C3H8 g ( ( O 3.76N g. 4 Examle: Csder a react f ctae wt 0% excess ar, wat s f? Stcmetrc : C8H8.5( O 3.76N 8CO 9HO 47N 0% excess ar s: C8H8.(.5( O 3.76N 8CO 9HO ao bn O balace:.(.5( = a a =.5, N balace:.(.5(3.76( = b b = 5.7 mxture s fuel lea A/ F s.5(4.76 / f 0.9. A/ F.(.5(4.76 / f.9 mxture 3
14 Frst Law Aalyss fr eactg System Csder a cstat ressure rcess wc f mles f fuel react wt a mles f ar t rduce mles f rduct: f F a A eactats rducts W eactats Q rducts State State eact Alyg Frst Law wt state beg te reactats at, ad state beg rducts at, : 4
15 5 Q H H H H V U V U ( ( ( ( Frst Law Aalyss fr eactg System ( ( V V U U Q W U Q
16 Etaly f eact Csder te case were te fal temerature f te rducts s te same as te tal temerature f te reactats (e.g., calrmeter s used t measure Q. W eact Q = = = = e eat released uder ts stuat s referred t as te etaly f react, H, Q H ( ( ( ( uts : kj er kg r kml f fuel 6
17 Heat f Cmbust e maxmum amut f eergy s released frm a fuel we reacted wt a stcmetrc amut f ar ad all te ydrge ad carb ctaed te fuel s cverted t CO ad H O C H ( O N CO H O 3.76 N 4 s maxmum eergy s cmmly referred t as te eat f cmbust, r te eatg value, gve er ut mass f fuel r ar H = H H < 0 (extermc H = H H > 0 (edtermc 7
18 Heat f Cmbust ere are tw ssble values fr te eat f cmbust deedg weter te water te rducts s take t be saturated lqud r vaur. f g Frm steam tables: fg = g f > 0 S e term ger eat f cmbust ad eatg value (HHV s used we te water te rducts s take t be te lqud state ( H0 = f e term lwer eat f cmbust ad eatg value (LHV s used we te water te rducts s take t be te vaur state ( H0 = g 8
19 Heat f Cmbust, gracal (kj/kg fuel eactats 0 rducts wt HO (g lw rducts wt HO (l g fg,ho er kg fuel 98K 9
20 Surce: ulkrabek 0
21 Fuel A/F Eergy desty (MJ/L fuel Secfc eergy (MJ/kg ar Gasle* Butal Etal Metal Hydrge 34.3 ** 4. * Desel abut 0% mre eergy er vlume ta gasle ** lquefed ydrge as rugly ¼ te eergy desty f gasle
22 Heat f Frmat Csder te fllwg reacts takg lace at atmserc ressure ad wt = = 98K / O C( s O ( g H ( g H ( g CO ( g O( l Q 86,000 kj / kml H Q 394,000 kj / kml CO O I tese reacts H O ad CO are frmed frm ter elemets ter atural state at stadard temerature ad ressure (S atm ad 98K. eacts f ts tye are called frmat reacts ad te crresdg measured eat release Q s referred t as te stadard eat f frmat ( s: f f, H O f, CO Q Q 86,000 kj / kml 394,000 kj / kml Values fr stadard eat f frmat fr dfferet seces are tabulated
23 Heat f Frmat fr Dfferet Fuels 3
24 Etaly Scale fr a eactg System By teratal cvet, te etaly f every elemet ts atural state (e.g., O (g, N (g, H (g, C(s at S as bee set t zer.e, ( atm,98k f 0 Csder te fllwg detty: (, (atm,98k [ (, (atm,98k] erefre, te etaly f te t cmet a mxture s: (,, [ (, (atm,98k] f cemcal etaly 98K sesble etaly K c d 98, 4
25 -5000 Etaly (kj/kg CO H O f, emerature K e data s als fud te JANNAF tables rvded at curse web ste 5
26 6
27 Adabatc Flame emerature Csder te fllwg adabatc cstat ressure rcess: eactats ( Fuel Ar rducts ( a Fr a cstat ressure rcess, te fal rducts temerature, a, s kw as te adabatc flame temerature (AF. Q ( ( a ( ( 0 Fr a gve react were te s are kw fr bt te reactats ad te rducts, a ca be calculated exlctly. 7
28 8 Adabatc Flame emerature a ( ( f f d c d c a,, 98, 98, O f a f K K (98 ( (98 (,, H Sesble eat f reactats (equal t 0 f = 98K Sesble eat f rducts f f a K K,, (98 ( (98 (
29 Adabatc Flame emerature, examle C 8H8 l.5( O 3.76N 8CO 9HO 47 ( N Csder cstat ressure cmlete cmbust f stcmetrc lqud butae-ar tally at 98K ad atm { ( a (98K} ( (98K f, f, 8 Nte: f, O f, N 0 CO ( a CO (98K 9 H O ( a H O (98K 47 N ( a N (98K 8 f, CO 9 f, H O Lk u etaly f frmat values ad terate a 40K f, C H 8 8 9
30 Adabatc Flame emerature wt rducts at equlbrum a, 30
31 Adabatc Flame emerature, examle Nw csder ctae ar wt 0% excess ar C 8H8.(.5( O 3.76N 8CO 9HO.5O 5. 7 N 8 CO ( a CO (98K 9 H O ( a H O (98K.5 O ( a O (98K 5.7 ( (98K 8 Lk u values ad terat gves a = 6K N a N f, CO 9 f, H O f, C H same as fr f = Excess ar adds 6 mles f datmc mlecules (O ad N t te rducts tat des t ctrbute t eat release just saks t u. 8 H 8 3
32 Adabatc Flame emerature wt rducts at equlbrum trmetae ydrge ctae etal 3
33 Cstat Vlume AF Csder te case were te st s fxed ad te cylder s erfectly sulated s te rcess s adabatc (Q = 0 W eact Q Q u u ( ( u a u ( ( 0 Nte = u + v = u +, s ( ( ( ( a 33
34 34 a f f a K K,, (98 ( (98 ( Extra term cmared t cstat ressure AF ( term > 0 Cstat Vlume AF f a f K K (98 ( (98 (,, e AF fr a cstat vlume rcess s larger ta fr a cstat ressure rcess. e AF s lwer fr cstat ressure rcess sce tere s dv wrk de
35 35 a CV V V Cstat Vlume Cmbust ressure Assumg deal gas beavur: Fr large ydrcarbs lke ctae te mle rat term s clse t e ( ( N O H CO N O l H C (
36 Stcmetrc ctae-ar (H = 47.9 MJ/kg-fuel: C 8H8 N CV.5( O 3.76N 8CO 9HO 47 a Ege Fuel Cmars Stcmetrc ydrge-ar (H = 4.6 MJ/kg-fuel: H CV 0.5( O 3.76N H O.88 N a Stcmetrc etal-ar (H = 9.7 MJ/kg-fuel: 6.8 C H6O.5( O 3.76N CO 3HO 3. CV 3 N a
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