Thermodynamics question (propellant gas)

[jelanier]

I understand the ideal gas law equation and the use of the gamma and it's relationships.
But what happens when a burning propellant strand is contained in a pressure vessel?

The gas temperature is already heated as it pressurizes the closed chamber.
The gas temperature at 100psi pressure would be 3204K. At 1000psi it would be 3408K. I know this from running a chemical equilibrium program. Those temperatures are at combustion chamber pressures in a rocket motor.

I could simply use the ideal gas law and assume a temperature of 3400K and predict the maximum chamber pressure as based on the total mass of propellant converted into gas. I could calculate the amount of propellant to use so as to not exceed the pressure vessel rating. Or, is the temperature and pressure going to go much higher that those shown for the rocket chamber? (by integrating the totals and applying ideal gas law)

So my question is: How would you accurately predict time vs pressure and temperature for such an apparatus? (temperature is the variable I am struggling with)

Thanks,

Jim

 

[mfb]

How do you relate pressure and temperature? With adiabatic compression? This will not work for combustion, as you add additional energy and probably change the amount of gas (the number of molecules can change).
I think I would try to use energy conservation - look at the total energy before, add the energy released from combustion, solve for temperature and pressure with the gas composition afterwards.

 

[jelanier]

Yes, it is an interesting problem. Since P(V^k) is constant with n being constant, I would think that this problem (having variable n and fixed V) would have P((V/n)^k) constant. The difficulty comes from the added energy from combustion as you suggest. It is as if you are injecting hot gas into a fixed volume. I need to think about this some more. Perhaps an actual experiment will get my gears turning in the right direction.