# Cold Gas Thruster

#### EggbertTheAstronaut

##### New Member
Hello! I am designing a cold gas thruster for a project that will use either N2 or air and I'm having trouble figuring out what my chamber temperature would be. I understand in this case it would be the temperature of the gas before entering the nozzle but I'm not sure if that would just be ambient temperature, same as exit temperature (ambient temperature) or something else. I'm trying to find my chamber temperature so I can calculate my exit velocity and thrust.

Thanks!

#### Zeus-cat

##### Well-Known Member
You should go study the effects of compressing gas and letting it expand (temperature is just one aspect). I'm not dodging your question, you NEED to understand this based on what you are doing.

#### EggbertTheAstronaut

##### New Member
You should go study the effects of compressing gas and letting it expand (temperature is just one aspect). I'm not dodging your question, you NEED to understand this based on what you are doing.
Do you think you could be a bit more specific as to what I should look for? I understand that an increase in pressure can increase the gas's temperature and vice versa (as long as volume stays constant) but I don't know if that relationship holds for moving gases. Take PV=nRT for example. The inlet pressure to the nozzle is going to be 350 PSI and I know my inlet volume, does the number of moles turn into moles per second?
Thanks!

#### MClark

##### Well-Known Member
Temperature likely should be in Kelvin.
The chamber temp will be higher than exhaust due to pressure drop.
ISP is bad unless starting at extremely high pressure.

See attachment

Hope that helps.

Troy

#### Attachments

• Nozzle Flow - cold gas.pdf
671.4 KB · Views: 49

#### EggbertTheAstronaut

##### New Member
See attachment

Hope that helps.

Troy
That provided a lot of clarity, thanks!

#### rocket_troy

##### Well-Known Member
What that doesn't provide is a clear equation for Mach Number (which is ridiculous really). Anyway equation 1.29 in this link will suffice: http://www.braeunig.us/space/propuls.htm

with k being the ratio of specific heats: for air in your case
Pc being the chamber pressure. In your case it would like be the "source" pressure
Pa being the ambient pressure for typical rocket application - because ideal expansion is assumed with this equation, the pressure at the destination will equal the ambient pressure
Mn is the mach number which is normally M in most isentropic equations.

As the text says once you have M, it's pretty straight forward to calculate T,P,V,p and even A at any location along the nozzle axis.

TP

##### Well-Known Member
TRF Supporter
If you know basic thermodynamics from college or self-study, the basic equations and derivations are straightforward. The simplest equations are for an adiabatic isentropic perfect gas. In principle for charging the chamber for a high pressure source the air (for air specific heat ratio k=1.4) in your chamber will go up due to adiabatic compression. This commonly happens in SCUBA tanks as they are pressurized prior to a dive. I would think that you could use a higer bulk average temperature for your chamber if you used the tank right away after compression. If the pressurized tank sits for awhile the internal gas temperature will come down to ambient due to heat soak. For discharging the chamber the average bulk temperature will come down considerably as predicted by the equations.

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