Schl f Aerspace Chemcal D: Mtvatn Prevus D Analyss cnsdered systems where cmpstn f flud was frzen fxed chemcal cmpstn Chemcally eactng Flw but there are numerus stuatns n prpulsn systems where chemcal reactns can ccur burnng (jet engne cmbustrs, augmentrs, rcket cmbustn chambers, pstn engnes) supersnc cmpressn (supersnc nlets) supersnc expansn (rcket nzzles) ther ( cells, mnprpellant decmpstn) Equl Chem D -1 Usually Gven: Equl Chem D - Schl f Aerspace Basc Prblem reactant state (cmpstn, temp., pressure) cnstrants (heat transfer, resdence tme, ) reac tan ts Want t Fnd: prduct state (,, p ) Apprach: (Equlbrum) D analyss,.e., cnservatn eqns., state equatns Issues: hw t deal wth m 1, p 1, 1 1. chemcal energy. specfyng equlbrum cmpstn Q, p, m prducts 1
Schl f Aerspace Apprach utlne 1. Apply mass cnservatn atm balances r balancng stchmetrc reactns. Apply energy cnservatn defnng chemcal energy r enthalpy f frmatn. Apply entrpy cnservatn ( nd Law) maxmze entrpy t fnd equlbrum Equl Chem D - Atm Balances/Stchmetrc Schl f Aerspace eactns If cmpstn can change, we wll see the amunt f sme speces decrease and thers ncrease Are there any cnstrants n ths prcess? YES can t change the dentfy f the nucle (n absence f nuclear reactns) stchmetrc fr example, N can nt becme ceffcents w ways t express ths balancng stchmetrc reactn atm balances Equl Chem D -4 1 LS n n S n n
Schl f Aerspace Chemcal Energy In nnreactng D we cmbned all dfferent types f energy nt stagnatn enthalpy, h h u but f curse, the value f h depends n ur chce f reference state; des h(0k)=0 r h(98k)=0? ur gal fr chemcally reactng system want t fnd way t add chemcal energy h h u e chem but t d s, we need t defne a reference state where chemcal energy s zer Equl Chem D -5 Chemcal Schl f Aerspace Energy Example Cnsder the energes f and E chem Echem, Echem, Is energy f mre r less than fr? Whch has zer chemcal energy? Equl Chem D -6 Dfference n energy between speces s functn f temp.
Chemcal Schl f Aerspace Energy Example What happens f we have multple types f nucle? ways t defne zer chemcal energy state Example: and cntanng speces at fxed temperature 0 E chem Equl Chem D -7 E chem 0 E chem Equl Chem D -8 Schl f eat Aerspace f eactn What s the energy dfference between the prducts and reactants f p, dn t change, e.g., 1 eat f Q r Echem, Echem, 1 Echem, p r eactn result can t depend n what we call zer energy (reference state) < 0, exthermc > 0, endthermc E chem eat f reactn s hw much heat we wuld have t add t keep cnstant (at fxed p) fr specfed cmpstn change (reactn) 4
Schl f Aerspace eat f Frmatn eat f reactn f frm NE mle f speces frm the ZE energy speces (the elements) at fxed temperature and standard pressure ( ) r n a per mass bass w cmmn chces fr elements h, f h, f the (neutral) atms NASA ables the mst cmmn frm f a sngle JANNAF type f nucle at standard and p,, N, Ar, C (s) graphte Equl Chem D -9 eat Schl f Aerspace f Frmatn Example Cnsder agan and 1 h h h f1000 K, What s enthalpy f frmatn f (JANNAF)? h f 0 K, h f98 K, 0 98 1 h What s enthalpy f frmatn f? h h 1 h 1000 (K) f, h Equl Chem D -10 5
Equl Chem D -11 eat Schl f Aerspace f Frmatn Example Cnsder agan and h h f 0 K, h h f98 K, h f1000 K, 1 h 1 What s the enthalpy change gng frm ½ mle f @98K t @ 1000K? 0 98 1000 (K) h 1000K h 98K h f 98K, h h 1000K h 1000K h f 1 h 1000K h 98K 1000K, h K h 0K h f h 0K h 98K 1 1000 0K, 1000K 1 h K 1 h 98 enthalpy enthalpy General Schl f Aerspace Expressn fr Enthalpy S frm the prevus path example, we can wrte n general h c p, d h f ref, r n a per mass bass h sensble term c ref ref p, d chemcal term h f ref, Equl Chem D -1 6
Example Schl f Aerspace Enthalpes f Frmatn gh frmatn enthalpy speces gh energy, hard t make (unstable atms) Lw frmatn enthalpy Lw energy (<<0) very stable at lw C, Equl Chem D -1 Speces h f,98.15 K kj/ml C -110.5 C -9.5 C 4-74.87 18.00-41.8 49.17 8.99 Frm NIS-JANNAF database 4 th edtn (1998) (e.g., knetcs.nst.gv/janaf) can fnd newer updates t data Cmpstn Schl f Aerspace Influence n emperature S f the prducts have mre,,, vs. prd wll be lwer than f we culd shft them tward water m m m prd, prd Y Y Y Y Y h f Equl Chem D -14 7
Example: Schl f Aerspace Methane/xygen Cmbustr Gven: Gaseus methane and xygen m C m 4 98K, 1 bar enterng nn-adabatc cmbustr at 98 K, 1 bar Mass flwrate rat f xygen s 5 that fr methane eat lss results n 1000 K prduct temperature Fnd: eat lss rate per unt mass flw rate Assume: Q lss Q lss m 1000K, 5 bar m prd Y Equl Chem D -15 Example: Schl f Aerspace Methane/xygen Cmbustr Slutn let s start wth energy cns. (PIC) m C m 4 98K, 1 bar Q lss m? 1000K, 5 bar m prd Y Equl Chem D -16 8
Example: Schl f Aerspace Methane/xygen Cmbustr Slutn m C 4 prducts? m 98K, 1 bar Q lss m? 1000K, 5 bar m prd Y Equl Chem D -17 Q m Example: Schl f Aerspace Methane/xygen Cmbustr lss Slutn 1 MW 1 MW Equl Chem D -18 eactants P Prducts Q lss MJ 7. 56 m kg h h ref ref h h MW r kg s h h f, ref, f, ref, m C m 4 98K, 1 bar Q lss 1 4 18 7 7 44 7 7. C p (J/mlK) eact. m? 1000K, 5 bar m prd 5 MW MW 16 7 7. 4 P Y h f,98k (kj/ml) C 4 /7-74.87 5/7 --- Prd. MW 4 7 avg ver kg kml mx 4/7 7.4-41.8 C /7 45.7-9.5 1/7.1 --- kg kml mx 9
Smplfed Schl f Aerspace Eqn fr Arcraft Cmbustr Want smplfed expressn we can use fr engne cycle mdelng ar Cnsder an adabatc m a cmbustr mass cnservatn m energy cnserv. m arh m h grup chem. vs. sensble terms m h a m prd fa m h h 4 prd ref f m m h a prd a ref ar h m m prd m h prd 4 f prd ref m h ref m h h m h ref h? m prd 4 f ref, Fuel eatng Value energy release per mass at ref ~45MJ/kg fr jet Equl Chem D -19 Smplfed Schl f Aerspace Eqn fr Arcraft Cmbustr S m h m prd h 4 prd ref m h a a ref m h ar m a ref m? m prd 4 If we assume h sens, ( ref )=0, ~ ref m h m a m h 4 m ah Fuel-Ar at chem. term (fh fh 1 f h 4 h ) lks f m m a lke heat addtn (Q ) assume cpg, prducts and ar have same c p, ref 0 fh c p 1 f 4 4 fh 1 f c p and f h 4 c p 4 Equl Chem D -0 10