Model Forum / General / Rockets / February 2007

consider that the N20 is expanding into a HOT,pressurized combustion
chamber.(and has to be over ~500degF to release its O2)

Why is the N20 temp relevant?

On Feb 21, 6:50 pm, runswithkni...@gmail.com wrote:

Using the ideal gas relationships and conservation of energy,

p1V1/T1 = p2V2/T2, where p is absolute pressure, V is volume, and T is
the absolute temperature.

On Feb 21, 5:50 pm, runswithkni...@gmail.com wrote:

Essentially, you have a cold gas thruster situation.  As the gas goes
out of the tank, the gas temperature in the tank will drop.  There is
a good discussion along with equations in the book, "Space Propulsion
Analysis and Design", Humble, Henry and Larson.  My edition is from
1995 and on page 145 it gives you the information.   In your case, the
internal energy of the gas in the tank is dropping since it is used to
propel gas out the valve.

Equations in a nut shell:

Gas internal energy drop = U-dot = -(mdot)(cp)(Tgas)

mdot = mass flowrate of gas out tank
cp = specific heat of gas
Tgas = temperature of gas in tank

Internal energy of gas in tank = U = (mgas)(cp)(Tgas)

mgas = mass of gas in tank

Solve for initial U knowing mgas, cp and Tgas.  You could use the
perfect gas law to get mgas at initial conditions.

Then solve for U-dot over a time increment say delta-t.  Calculate
mdot from:

mdot = (Ahole)(Ptank)/(C*)

Ahole = tank outlet hole area
Ptank = tank pressure
C* = in terms of gamma, Tgas, gas constant (too long to write here and
I'm too lazy)

I would set Ptank to the value for the last time increment.  For the
first time step that would be the initial pressure.

U at the new time increment is Unew = Uold - (Udot)(delta-t)
mgas at the new time increment is Mnew = Mold - (mdot)(delta-t)

Now, use U equation to solve to the gas temperature at the new time
increment:

Tgas = U/[(mgas)(cp)]

Determine the gas density in the tank: gasdensity = mgas/(tank volume)

New tank pressure is: Ptank = (gasdensity)(gas constant R)(Tgas)
Note: Watch your units

Just keep doing this in a loop to get gas temperature and other
parameters as a function of time.  Check out the book for a better
discussion.

John Wickman