THERMODYNAMICS of COMBUSTION

Transcription

1 Internal Cobuston Engnes MAK 493E THERMODYNAMICS of COMBUSTION Prof.Dr. Ce Soruşbay Istanbul Techncal Unversty Internal Cobuston Engnes MAK 493E Therodynacs of Cobuston Introducton Proertes of xtures Cobuston stochoetry Cobuston n IC-engnes Checal energy Heat of reacton Heat of foraton Checal equlbru Adabatc flae teerature Dssocaton reactons

2 Introducton Therodynacs deals wth equlbru states and how checal cooston can be calculated for a syste of known atoc/olecular cooston f two ndeendent therodynac roertes are known. Systes undergong checal reactons are not n general, n checal equlbru - reactons are rate-controlled Checal cooston at a gven nstant n te s controlled by the therodynac roertes, checal reacton rates and flud dynacs of the syste. Introducton Frst Law of Therodynacs for a therodynac syste, the te rate of change of energy of the syste s equal to the rate at whch work s done on the syste + the rate at whch heat s transferred to the syste. Neglectng PE and KE wthn syste, energy conssts of nternal energy due to, - theral energy due to translaton, rotaton and vbraton of olecules - so called sensble energy, - checal energy due to checal bonds between atos n the olecules, For syste of ass, work done W and heat transfer rate to the syste q, frst law can be wrtten as, d( u) W q dt

3 Introducton echancal work - ower s, W dx A dt dv dt frst law becoes, d ( u ) dv dt dt q therodynac roertes can be evaluated by assung that the whole syste s unfor or by dvdng the syste nto subsystes that are assued unfor, j nuber of cells wth volues V j u J j V j j u j Introducton For a closed syste energy balance can be obtaned ntegratng frst law equaton wth-resect-to te, ( u u W Q ) where W t dv dt t dt Q t t q dt d ( u V ) for constant ressure, q dt d ( h) q dt ntegratng, ( h Q h ) 3

4 Introducton If the checal cooston s constant, checal energy does not change - for deal gases, u u h h T T T T c v dt c dt c c R v Proertes of Mxtures For xtures of gases, syste ass s obtaned fro the su of asses of searate seces, densty of syste s the su of seces denstes, ass fracton s ass of seces, dvded by total ass, and by defnton y y 4

5 Proertes of Mxtures Slarly ole fracton s ole of seces, dvded by total nuber of oles, or rato of olar concentraton of seces to total olar concentraton, N n x N n and x Molecular weght s, M N x M relaton between ole fracton and ass fracton, N / M M y x N / M M Proertes of Mxtures xture nternal energy and enthaly er unt ass, u y u h y h nternal energy and enthaly er ole of xture, uˆ x uˆ h ˆ ressure of xture for an deal gas, s equal to su of artal of coonent gases f each exsted alone n the xture volue at xture teerature, x h ˆ x 5

6 Proertes of Mxtures volue of xture for an deal gas, s equal to su of artal volues whch the coonent gases would occuy f each exsted alone at the ressure and teerature of the xture, V x V V Cobuston Stochoetry When olecules undergo checal reacton, the reactant atos are rearranged to for new cobnatons. For exale, hydrogen and oxygen react to for water : H O H O two atos of hydrogen and one ato of oxygen for one olecule of water - nuber of atos of H and O ust be the sae on both sdes Such reacton equaton reresents ntal and fnal states and does not ndcate actual ath of reacton, whch ay nvolve any nteredate stes and nteredate seces. 6

7 Cobuston Stochoetry Relatve asses of olecules are obtaned by ultlyng nuber of oles of each seces by the olecular weghts (kg/kg-ol) For hydrogen-oxygen reacton, ol H kg kg - ol H ol H O kg ol H O H O H O ol O 8 kg ass of reactants equals ass of roducts, although ols of reactants do not equal oles of roducts - fxed and T, deal gas, 3 kg kg ol O volue H / volue O volue H O Cobuston Stochoetry Stochoetrc calculatons are done by erforng ato balance for each of the eleents n xture. The theoretcal aount of ar requred to burn a fuel coletely to roducts wth no dssocaton s defned as stochoetrc ar. In ost cobuston calculatons dry ar s assued as a xture of 79% (vol) N and % (vol) O or oles of N er ole O Molecular weght of ure ar s 8.96, as t also contans sall aounts of argon, carbon doxde, hydrogen etc. 7

8 Dry Ar % (vol) % (ass) N O Ar CO Ne, neon He, helu Kr, krton Xe, xenon H, hydrogen IC Engne Cobuston In IC engnes, colete cobuston of the fuel wth ar, under deal condtons - stochoetrc xture wth no dssocaton, gves, C n H n O 4 n CO 3.76N H O 3.76 n N 4 Under real engne condtons, CO, CO, H, O, H, O, NO are also roduced as a result of the dssocaton reactons (arçalana reaksyonları). Sulhur n the fuel roduces SO etc. 8

9 Fuel / Ar Rato Mols of stochoetrc ar er ol of fuel, nar stoch 4.76 n n 4 fuel Stochoetrc Fuel / Ar rato by weght, f stoch fuel ar M fuel n M n ar fuel ar stoch M 9.0 n / The ercent excess ar s, ( ar actual ar used, ar-stoch stochoetrc ar) 00 % excessar 00 ar fuel n n 00 no no stoch ar n ar stoch ar stoch ar stoch ar stoch n O stoch Equvalence Rato The fuel/ar equvalence rato s defned as the actual fuel / ar ass rato, dvded by stochoetrc fuel / ar ass rato, f f stoch % excess ar s defned as, 00 ( ) % excessar ar excess rato s defned as, (hava fazlalık katsayısı) 9

10 Equvalence Rato Stochoetrc xture,.0 Lean xture, (fakr karışı) Rch xture, (zengn karışı) Stochoetrc Cobuston Fuel cooston, for kg of fuel, c h o n s w a kg of carbon kg of hydrogen kg of oxygen kg of ntrogen kg of sulhur kg of water kg of ash, etc c + h + o + n + s + w + a = kg 0

11 Stochoetrc Cobuston For colete cobuston of the fuel the followng reactons take lace carbon : C O CO ol C + ol O ol CO kg C + 3 kg O 44 kg CO kg C + (3/) kg O (44/) kg CO hydrogen : H O HO kg H + 6 kg O 8 kg H O kg H + 8 kg O 9 kg H O Stochoetrc Cobuston sulhur : S O SO 3 kg C + 3 kg O 64 kg CO kg C + kg O kg CO oxygen requred wll be, for c kg carbon for h kg hydrogen for s kg sulhur 8c/3 kg 8h kg s kg nu aount of O needed for colete cobuston of kg of fuel 8c 3 O n 8 h s o [kg-o / kg-fuel]

12 Stochoetrc Cobuston where O n 8c [kg-o / kg-fuel] 3 3 8h s o 8 c The aount of oxygen n ar s 3.3 % by ass, n n o ar ar n 44c [kg-ar / kg-fuel] [kg-ar / kg-fuel] Stochoetrc Cobuston For IC engne fuels ar n 4 5 [kg-ar / kg-fuel] the rato of ar ncluded n the cobuston rocess, to the theoretcally u ar requred gves the ar excess rato, ar ar n equvalence rato

13 Checal Energy To descrbe the checal energy released when fuel reacts wth ar to for roducts, checal seces n the reactants and roducts and ther states are secfed. Heat of vaorzaton of lqud fuels and heat of yrolyss of sold fuels s sall coared wth the checal energy relased by cobuston. But effect of water condensaton can be ortant. For lean HC-ar xtures wth low T, roducts ay be assued to be colete (usually CO, H O, O and N ). But wth hgh roduct T and rch xtures t s generally necessaary to nclude other seces and assue checal equlbru to deterne seces ole fractons. If roducts are not n checal equlbru, then checal knetc analyss (or easureents) s requred to deterne end state. Heat of Reacton Consder F and A xture of ass, constant-volue cobuston wth heat transfer, Q v, fro state to state u u u u Qv sensble checal for n seces, u at state can be obtaned by, ( u ) sensble ( u( T )) n T y ( c T To sensble v ) r dt n y ( u ( T )) To ( c v ) r dt sensble T o s ref teerature, (c v ) r s secfc heat of reactant xture 3

14 Heat of Reacton Slarly, ( u ) sensble T To ( c v ) dt If heat heat transfer s just large enough to brng roducts teerature back to the reactants teerature, and f ths T s taken as the ref T, T o for sensble energy, then ( u u ) 0 sensble and Q v s the checal energy released by the reacton (sabt hacdek reaksyon ısısı) The quantty [(+f)/f](-q v /) s the lower heatng value (LHV) of the fuel for constant-volue cobuston. If the water n the roducts s condensed, that quantty becoes the hgher heatng value (HHV) of the fuel for constant-v cobuston Heat of Reacton If reacton takes lace at constant ressure, h h h h Q sensble checal agan f T = T = T o, then Q s the checal energy released. For constant-ressure case, f oles of gaseous roducts N are larger than oles of gaseous reactants Nr, then soe of the checal s exended to ush asde the abent ressure. Thus, Q Q v ( V ) ( N N ) RT ˆ NRˆ T r o o Here overbar shows quantty er ole 4

15 Heat of Reacton For the reacton, C n H n O N n CO H O 3.76 n N 4 assue fuel s n gas hase and gaseous water, N 4 f > 4, N>0, snce both Q v and Q are negatve, Q v > Q for ost cases of nterest, the dfference s neglgable. Heat of Reacton Heat of reacton can be obtaned for reactons at T other than T o Q To T ( c ) dt Q r ( T ) o T To ( c ) dt Q Q ( To ) ( hs hs ) h s s the sensble enthaly Q (T o ) s negatve for an exotherc reacton 5

16 Heat of Reacton Enthalhy of reactants and roducts Heat of Foraton Heat of reacton of fuels cobustng n ar or oxygen wth startng and endng onts at 5 O C and at gves fuel heatng value. These values are tabulated for coon fuels. Ths cannot be aled to all reactons - needs enorous aounts of tabulated data. Instead selected reactons and ther heat of reactons can be added to obtan any gven reacton and ts heat of reacton. Heat of foraton of a artcular seces s defned as the heat of reacton er ole of roduct fored sotherally fro eleents n ther standard states. Standard state s chosen as the ost stable for of the eleent at at and 5 O C Heat of Foraton of eleents, h o n ther standard state s assgned a value of zero. These are gven n JANAF tables. 6

17 Heat of Foraton Absolute enthaly of a substance can be calculated fro, sensble enthaly relatve to reference T lus the heat of foraton at ref T, hˆ T To cˆ dt hˆ o where o ĥ s the heat of foraton Here overbar, ^ shows quantty er ole Adabatc Flae Teerature at constant-ressure cobuston ( H ) ( H ) H R R TR P T P ( T ) H ( T ) H 0 R P P o at constant-volue cobuston U ( T ) U ( T ) U 0 R R P P o 7

18 Adabatc Flae Teerature Products Checal Equlbru Checal equlbru s acheved for constant T and systes when rate change of concentratons goes to zero for all seces - very fast reacton rates or very sall change n concentratons. For a syste of J seces n checal equlbru, and T do not change, whch ay be secfed by statng that Gbbs free energy of the syste (G = H TS) does not change : ( dg), 0 T J G j N g ˆ j j gˆ hˆ Tsˆ j j j 8

19 Checal Equlbru Consderng the followng reacton, aabb cc dd for checal equlbru, the equlbru constants, K c C a A d D b B x x c C a A x x d D b B cd ab Dssocaton Reactons For exale, CO H O H CO k f A ex ( E f f / RT ) k A ex ( E b b b / RT) here k f and k b are the forward and backward reacton rate constants, A s the re-exonental factor, E s the actvaton energy. 9

20 Dssocaton Reactons Cobuston wth dssocaton, C n H n 4 CO H O H CO CO O O 3. 76N β CO β CO β CO 3 H O β K 4 H K β O 5 4 β β β5 3 N R R β 6 N Dssocaton Reactons Carbon balance, Hydrogen balance, Oxygen balance, n / 3 4 ( n / 4) 3 5 Equaton of state, V NRT an reacton equaton + 6 equatons to fnd the values of 6 unknowns =,, 6 0

21 Dssocaton Effects on Flae Teerature Flae teerature reduces as a result of dssocaton reactons. H R Wth dssocaton P Tb T Teerature