MAE 5310: COMBUSTION FUNDAMENTALS

1. MAE 5310: COMBUSTION FUNDAMENTALS Adiabatic Combustion Equilibrium September 12, 2012 Mechanical and Aerospace Engineering Department Florida Institute of Technology D. R. Kirk

2. ADIABATIC COMBUSTION EQUILIBRIUM • Previously we have considered: • Known Stoichiometry + 1st Law (Energy Balance) → Adiabatic Flame Temperature • Problems 1-4 • Known P and T + 2nd Law (Equilibrium Relations) → Stoichiometry • Problems 5-9 • Now we can combine these: • 1st Law (Energy Balance) + 2nd Law (Equilibrium Relations) → Adiabatic Flame Temperature + Stoichiometry • Problems 10-14 • Solution Scheme • Guess a T=Tguess • Do equilibrium calculation to solve for species concentrations at Tguess • Plug into 1st Law • We want F(Tguess)=0 • If F(Tguess) > 0, then initial guess was too high • If F(Tguess) < 0, then initial guess was too low • Increment Tguess

3. EXAMPLE: MONOPROPELLANT ROCKET PROPULSION • Monopropellant rockets are simple propulsion systems that rely on chemicals which, when energized, decompose • Decomposition creates both the fuel and an oxidizer (which allows the fuel to burn), which then react with each other • Because they only use a single propellant, monopropellant rockets are quite simple and reliable, but not very efficient • Mainly used to make small adjustments such as attitude control • Typical Specific Impulse: 100-300 sec • Typical Thrust: 0.1-100 N Monopropellant hydrazine (N2H4, see Problem 12) thrusters that were used for trajectory correction maneuvers (TCMs) during interplanetary cruise, thrust vector control (TVC) during VOI, orbit trim maneuvers during the mapping mission, and attitude control when the action wheels are being desaturated. The rocket motors are clustered in modules located on the end of outrigger booms in order to increase their moment arm and thus decrease attitude control propellant requirements. Twelve 0.9-N (Newton) and four 22-N rocket motors are used for attitude control, with thrust being provided by eight 445-N rocket motors or by the 0.9-N motors for small TCMs.

4. EXAMPLE: MONOPROPELLANT ROCKET PROPULSION • Rocket propellant chemists have proposed a new, high-energy liquid oxidizer, penta-oxygen, O5, which is also a monopropellant. • Calculate the monopropellant decomposition temperature at a chamber pressure of 10 atm. If it is assumed the only products are O atoms and O2 molecules. • Supplemental Information: • Heat of formation of new oxidizer is estimated to be very high: 1,025 kJ/mole • O5 enters system at 298 K • Amount of O2 and O should be calculated for one mole of O5 decomposing • Solution Technique • Solution is iterative • In order to calculate the final temperature of the mixture, one needs to the composition of the mixture at equilibrium – but – the composition of the mixture can only be found if the final temperature is known. • Strategy: • Guess final temperature and calculate mixture composition using equilibrium concept • Once composition is known at guessed temperature, adiabatic flame temperature is calculated and checked against guessed value • Repeat process until guessed and calculated temperatures are same • Answer lies somewhere between 4,000 and 5,000 K