1AE6450 Rocket PropulsionRocket Thermochemistry-1Copyright © 2004,2006 by Jerry M. Seitzman. All rights reserved.Rocket PropulsionReacting Flow IssuesAE6450 Rocket PropulsionRocket Thermochemistry-2Copyright © 2004,2006 by Jerry M. Seitzman. All rights reserved.•c*∝ (To/MW)1/2• Must include effect of product dissociation for rocket chamber calculations– will decrease Toand reduce MW• Peform adiabatic flame temperaturecalculation with full equilibrium products– pressure = chamber pressure– total enthalpy unchangedCombustor Calculations2AE6450 Rocket PropulsionRocket Thermochemistry-3Copyright © 2004,2006 by Jerry M. Seitzman. All rights reserved.Equivalence Ratio• Common to present initial conditions in terms of fuel-oxidizer ratio, f– sometimes mass fuel/mass oxidizer–or moles fuel/moles oxidizer• Equivalence ratio φ (or Φ) = factual/fstoichiometric– φ = 1; stoichiometric• just enough oxidizer tocompletely consume fuel– φ < 1; fuel lean (excess ox.)– φ > 1; fuel rich (excess fuel)H2ExampleAE6450 Rocket PropulsionRocket Thermochemistry-4Copyright © 2004,2006 by Jerry M. Seitzman. All rights reserved.Stoichiometric Mixture:Hydrocarbon-O2Example• Determine major products(stable, low energy)→+2aOHCyxφφ=⇒== ?1?aaffstoichactual• Required (stoich.) amount of oxidizer– atom balances(mass conservation)• In terms of φ→+2? aOHCyxa =OHyxCO222+x+y/43AE6450 Rocket PropulsionRocket Thermochemistry-5Copyright © 2004,2006 by Jerry M. Seitzman. All rights reserved.Adiabatic Combustion Temperature• Equilibrium temperature that would be achieved if reactants were converted to equilibrium products without heat addition or loss– energy conservation (1stLaw)provides one equation– need 2ndcondition to fix state 2• Adiabatic Flame Temperature (Tad)– control volume– OR p constant• Constant Volume ReactantsProductsReactants(1)Products(2)outinWEQE +=+2121hmhm&&=021EE =()12VVppdVWout−==∫1211pVEpVE +=+21hh =21HH =AE6450 Rocket PropulsionRocket Thermochemistry-6Copyright © 2004,2006 by Jerry M. Seitzman. All rights reserved.Example Method – GaseqTad()()428.0322.022=××=HOmmMWproductsγγγγproducts4AE6450 Rocket PropulsionRocket Thermochemistry-7Copyright © 2004,2006 by Jerry M. Seitzman. All rights reserved.•Tadpeaks near stoich-iometricmixture• Peak in c* (and Isp) for rich mixture (low MW)H2-O2 10 atm10001500200025003000350040000510O/F Mass RatioTo (K), c* (m/s)01020304050MW, Isp/10 (s)Toc*MWIspc*MWToIspconst γ nozzlestoichEquilibrium Combustor Chemistry10.8240.67φφφφc*∝ (To/MW)1/2AE6450 Rocket PropulsionRocket Thermochemistry-8Copyright © 2004,2006 by Jerry M. Seitzman. All rights reserved.Pressure Effects• Raise p, higher Tad (less dis-sociation)•Also increases MW• Slightly higher c*•Isphigher for same peH2-O2 100 atm10001500200025003000350040000510O/F Mass RatioTo (K), c* (m/s)01020304050MW, Isp/10 (s)Toc*MWIspToc*MWstoichIspconst γ nozzle10.8240.67φφφφ5AE6450 Rocket PropulsionRocket Thermochemistry-9Copyright © 2004,2006 by Jerry M. Seitzman. All rights reserved.• What happens to chemical composition in nozzle?• As velocity increases– temperature and pressure decrease– will lead to change in compositionNozzle ChemistryAE6450 Rocket PropulsionRocket Thermochemistry-10Copyright © 2004,2006 by Jerry M. Seitzman. All rights reserved.• Constant γ is a very poor assumption for high temperature rocket product gases– can’t use p/po=(T/To)γ/γ-1– even worse assumptionif gas is reacting• Can still calculate isentropicnozzle expansion for two cases– flow stays in equilibriumthrough nozzle (shifting equil.)– flow is frozen - compositioncan not change– find h (and thusu) that matches given p and sIsentropic Expansionhspep2p*pep2p*6AE6450 Rocket PropulsionRocket Thermochemistry-11Copyright © 2004,2006 by Jerry M. Seitzman. All rights reserved.Example Method – GaseqWant to examine expansion of productsAE6450 Rocket PropulsionRocket Thermochemistry-12Copyright © 2004,2006 by Jerry M. Seitzman. All rights reserved.Example – Frozen Chemistry•Set pefor nozzle expansionTeMWeγγγγeheho7AE6450 Rocket PropulsionRocket Thermochemistry-13Copyright © 2004,2006 by Jerry M. Seitzman. All rights reserved.Example – Shifting EquilibriumMWeγγγγeTe•Exit compositionhehoAE6450 Rocket PropulsionRocket Thermochemistry-14Copyright © 2004,2006 by Jerry M. Seitzman. All rights reserved.Frozen and Shifting Equilibrium• Both cases have same entropy• T drops faster for frozen flow•ue(Isp) lower for frozen flow0100020003000400050000.01 0.1 1 10 100p (atm)T(K) ,u(m/s)20004000600080001000012000h (kJ/kg)TuhH2-O2 O/F=5.33EquilibriumFrozenThuDownstream8AE6450 Rocket PropulsionRocket Thermochemistry-15Copyright © 2004,2006 by Jerry M. Seitzman. All rights reserved.0.30.40.50.60.70.01 0.1 1 10 100p (atm)x(H2O), X(H2)00.010.020.030.040.05x(OH), X(H), X(O)H2OH2HOHO2OShifting Equilibrium Chemistry• As T drops, minor species recombine (H,OH)• Chemical energy converted to thermal energy• T does not have to drop as much to reach same p(cpeffectively higher)H2-O2 H2OHOHO/F=5.33FrozenChemistryH2AE6450 Rocket PropulsionRocket Thermochemistry-16Copyright © 2004,2006 by Jerry M. Seitzman. All rights reserved.Area Ratio• Frozen flow requires larger expansion ratio to achieve same pe0204060801000.01 0.1 1 10 100p (atm)A/A*010002000300040005000u (m/s)A/A*uEquilibriumFrozenH2-O2 O/F=5.33A/A*T9AE6450 Rocket PropulsionRocket Thermochemistry-17Copyright © 2004,2006 by Jerry M. Seitzman. All rights reserved.Nonequilibrium Nozzle Flow• For adiabatic nozzles, Ispwill fall between these frozen and equilibrium limits (will not be isentropic) –nonequlibrium flow– chemistry is not so fast compared to time that flow spends in nozzle that composition stays in equilibrium, but not so slow to be frozen • τchemvs. τflow– tends to get more frozen later in the nozzlecolder & lower p⇒low collision rate⇒τchemlongvelocity high ⇒τflow short)• Can solve nonequilibrium by– including RATES in conservation/transport equations– “switching” from equil. to frozen flow when estimated rates drop below some