# University of Toronto Institute for Aerospace Studies Faculty of

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```					       University of Toronto Institute for Aerospace Studies
Faculty of Applied Science And Engineering

AER 1304 Fundamentals of Combustion – Fall 2006
Midterm Test : November 14, 2006

Room: UTIAS Staff Lounge                                               Professor Ö. L. Gülder
Starting Time: 10:00                                           Duration of the Exam: 150 min

NOTE: •This is an “open-book” exam. •You are permitted to use your notes,
textbooks, reference books, and non-communicating hand-held calculators
during the exam. •Percentage value of each question is shown in the left mar-
gin preceding the question number. •Attempt all questions. •Do not forget to
write your name and student number on the front cover of all answer booklets.

QUESTIONS
1. One of the proposed approaches to reduce the particulate emissions from military and civilian
aircrafts is to blend ethanol, C2 H5 OH, into the jet fuel. Assume that 31.5% by mass ethanol
is added to a certain jet fuel that can be approximated by n-heptane, C7 H16 .
5%        a. What is the stoichiometric air-fuel ratio of this jet fuel/ethanol mixture?
20%         b. If we want the aircraft to have the same range of flight capability with the jet fuel/ethanol
blend as with the jet fuel, what percentage of change required in the fuel storage volume
onboard the aircraft? Assume that the thermal efficiency of the aircraft engine is the
same with both fuels, i.e., the percentage of the enthalpy of combustion converted to
propulsive force is the same in both cases.
¯
Enthalpy of formation of ethanol at standard conditions is, ho 2 H5 OH = -235000
f,C
kJ/kmol. Liquid density of ethanol at standard conditions is, ρliq = 789 kg/m3 . Molec-
ular masses of n-heptane and ethanol are 100 and 46, respectively.

20% 2. Calculate the ratio of the quenching diameter of a methane-air mixture to that of a hydrogen-
air mixture. Assume stoichiometric fuel-air mixtures at a temperature of 450 K and at 10
atm pressure. The adiabatic flame temperatures of methane-air and hydrogen-air under
these conditions are 2350 K and 2550 K, respectively; and the laminar burning speeds of
methane-air and hydrogen-air under these conditions are 55 cm/s and 290 cm/s, respectively.

20% 3. In the combustion chamber of a liquid hydrogen-oxygen rocket engine, the combustion
products are in equilibrium at 3400 K and 50 bar pressure. The mole fractions of H2
and H2 O in the product gas mixture are 0.294 and 0.635, respectively. Calculate the mole
fractions of OH and O atom.

AER 1304 Fundamentals of Combustion, Fall 2006        page 1 of 2                                   ÖLG
15% 4. The rate coefficients for the following elementary reaction

kf
H + CH4   kr
H2 + CH3

are given as follows

kf = 8.49 × 1014 exp [−68, 220/(Ru T )] cm3 /(mol s)

kr = 5.08 × 1013 exp [−93, 700/(Ru T )] cm3 /(mol s)

where activation energies are in kJ/kmol. Suppose we have a mixture of the gases H2 , CH3 ,
CH4 , and H at 2000 K, with partial pressures pH2 = 0.9 bar, pCH3 = 0.1 bar, pCH4 = 2 bar,
and pH = 0.001 bar. Is the reaction described by the above equation at equilibrium under
these conditions? If not, in what direction will the reaction proceed to reach equilibrium?

20% 5. Calculate the lifetime of a n-octane droplet of 0.4 mm diameter with a uniform surface
temperature of 100 o C evaporating into dry hot stagnant air at 600 K and 1 atm pressure.

AER 1304 Fundamentals of Combustion, Fall 2006              page 2 of 2                      ÖLG

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