Rocket Propulsion. Reacting Flow Issues

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1 Rocket Propulsion Reacting Flow Issues Rocket Thermochemistry- Combustor Calculations c* (T o /) /2 Must include effect of product dissociation for rocket chamber calculations will decrease T o and reduce Peform adiabatic flame temperature calculation with full equilibrium products pressure = chamber pressure total enthalpy unchanged Rocket Thermochemistry-2

2 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) = f actual /f stoichiometric φ = ; stoichiometric H 2 Example just enough oxidizer to completely consume fuel φ < ; fuel lean (excess ox.) φ > ; fuel rich (excess fuel) Rocket Thermochemistry-3 Stoichiometric Mixture: Hydrocarbon-O 2 Example Determine major products C x H y + ao2 (stable, low energy) xco2 + y 2 H 2O Required (stoich.) amount of oxidizer atom balances a = x+y/4 (mass conservation) In terms of φ? C x H y + ao2 factual? a φ = = f a? = φ stoich Rocket Thermochemistry-4 2

3 Adiabatic Combustion Temperature Equilibrium temperature that would be achieved if reactants were converted to equilibrium products Reactants Products without heat addition or loss () energy conservation ( st (2) Law) provides one equation E + Qin = E2 + W out need 2 nd condition to fix state 2 Adiabatic Flame Temperature (T ad ) control volume m & h Reactants Products = m& h 2 OR p constant h = h 2 W out = pdv = p( V 2 V ) E + pv = E2 + pv H = H 2 Constant Volume E = Rocket Thermochemistry-5 E 2 Example Method Gaseq m O m = 2 H 2 = 4 (.2 32) (.8 2) T ad γ products products Rocket Thermochemistry-6 3

4 Equilibrium Combustor Chemistry T ad peaks near stoichiometric mixture Peak in c* (and I sp ) for rich mixture (low ) c * (T o /) /2 To (K), c* (m/s) Rocket Thermochemistry φ c* atm T o I sp const γ nozzle To c* Isp 5 stoich O/F Mass Ratio 4 3 2, Isp/ (s) Raise p, higher T ad (less dissociation) Also increases Slightly higher c* I sp higher for same p e To (K), c* (m/s) Rocket Thermochemistry-8 Pressure Effects φ c* atm T o I sp const γ nozzle To c* Isp 5 stoich O/F Mass Ratio 4 3 2, Isp/ (s) 4

5 Nozzle Chemistry What happens to chemical composition in nozzle? As velocity increases temperature and pressure decrease will lead to change in composition Rocket Thermochemistry-9 Isentropic Expansion Constant γ is a very poor assumption for high temperature rocket product gases can t use p/p o =(T/T o ) γ/γ- even worse assumption p 2 p * p e if gas is reacting Can still calculate isentropic nozzle expansion for two cases p 2 flow stays in equilibrium through nozzle (shifting equil.) p h * flow is frozen - composition can not change find h (and thus u) that matches given p and s s Rocket Thermochemistry- p e 5

6 Example Method Gaseq Want to examine expansion of products Rocket Thermochemistry- Example Frozen Chemistry T e γ e Set p e for nozzle expansion e Rocket Thermochemistry-2 h o h e 6

7 Example Shifting Equilibrium T e γ e Exit composition e Rocket Thermochemistry-3 h o h e Frozen and Shifting Equilibrium 5 Both cases have same 4 entropy T drops 3 faster for 2 frozen flow u e (Isp) lower for frozen flow T(K),u(m/s) Rocket Thermochemistry-4 Frozen T u h Equilibrium O/F= p (atm) Downstream u T h h (kj/kg) 7

8 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 (c p effectively higher) Shifting Equilibrium Chemistry x(h2o), X(H2) H2O H2 H OH O2 O Frozen Chemistry.3 H 2.. p (atm) O/F=5.33 H H 2 O OH x(oh), X(H), X(O) Rocket Thermochemistry-5 Area Ratio Frozen flow requires larger expansion ratio to achieve same p e A/A* Equilibrium Frozen T A/A* O/F=5.33 A/A* u u (m/s) Rocket Thermochemistry-6.. p (atm) 8

9 Nonequilibrium Nozzle Flow For adiabatic nozzles, I sp will 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 τ chem vs. τ flow tends to get more frozen later in the nozzle colder & lower p low collision rate τ chem long velocity high τ flow short) Can solve nonequilibrium by including RATES in conservation/transport equations switching from equil. to frozen flow when estimated rates drop below some threshold Rocket Thermochemistry-7 9