Problems
(Those with an asterisk require a numerical solution.)
1. A mixture of hydrogen, oxygen, and nitrogen, having partial pressures in the ratio 2:1:5 in the order listed, is observed to detonate and produce a detonation wave that travels at 1890 m/s when the initial temperature is 292 K and the initial pressure is 1 atm. Assuming fully relaxed conditions, calculate the peak pressure in the detonation wave and the pressure and temperature just after the passage of the wave. Prove that u2 corresponds to the C−J condition. Reasonable assumptions should be made for this problem. That is, assume that no dissociation occurs, that the pressure after the wave passes is much greater than the initial pressure, that existing gas dynamic tables designed for air can be used to analyze processes inside the wave, and that the specific heats are independent of pressure.
2. Calculate the detonation velocity in a gaseous mixture of 75% ozone (O3) and 25% oxygen (O2) initially at 298 K and 1 atm pressure. The only products after detonation are oxygen molecules and atoms. Take the 
and all other thermochemical data from the JANAF tables in the appendices.
and all other thermochemical data from the JANAF tables in the appendices.Report the temperature and pressure of the C−J point as well.
For the mixture described in the previous problem, calculate the adiabatic (deflagration) temperature when the initial cold temperature is 298 K and the pressure is the same as that calculated for the C−J point.
Compare and discuss the results for these deflagration and detonation temperatures.
3. Two mixtures (A and B) will propagate both a laminar flame and a detonation wave under the appropriate conditions:
Which mixture will have the higher flame speed? Which will have the higher detonation velocity? Very brief explanations should support your answers. The stoichiometric coefficient i is the same for both mixtures.
4. What would be the most effective diluent to a detonable mixture to lower, or prevent, detonation possibility: carbon dioxide, helium, nitrogen, or argon? Order the expected effectiveness.
5. ∗Calculate the detonation velocity of an ethylene air mixture at an equivalence ratio of 1 and initial conditions of 1 atm and 298 K. Repeat the calculations substituting the nitrogen in the air with equal amounts of He, Ar, and CO2. Explain the results. A chemical equilibrium analysis code, such as CEA from NASA, may be used for the analysis.
6. ∗Compare the effects of pressure on the detonation velocity of a stoichiometric propane air mixture with the effect of pressure on the deflagration velocity by calculating the detonation velocity at pressures of 0.1, 1, 10, and 100 atm. Explain the similarities or differences in the trends. A chemical equilibrium analysis code, such as CEA from NASA, may be used for the analysis.
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