# How is chamber pressure and temperature determined for cold gas thrusters?

I'm trying to get some theoretical performance numbers for a cold gas thruster using quasi-one-dimensional flow, and I don't know where to start. For combustion engines you would just take a given chamber pressure and the temperature from the combustion, but with a cold gas thruster you have neither of those. Moreover, due to the quick expansion of the gas from the tank, the temperature will be dropping, so my questions are:

• What would be the pressure for the thrust chamber in a cold gas thruster? I reckon it's not the actual tank pressure, cause then you wouldn't bother having a converging nozzle at all, just diverging. So, given a tank pressure, how would you calculate the pressure inside the engine?

• I suppose you have to take into account the cooling of the gas when expanding into the thrust chamber, but for that you'd need the chamber pressure to calculate the temperature drop. Am I missing anything?

EDIT1: My wording might have been a bit unclear, so as a clarification, the main question is why would you create a thrust chamber and a converging section for a cold gas thruster when you could easily achieve choked flow from the tank outlet itself. Adding to that, in the probable case that I'm missing some important functionality, how would one calculate the chamber pressure if you were to use one?

EDIT2: To anyone that might find this question in the future, here I was assuming the flow from the tank was coming already at mach 1 due to choked flow from the outlet. However, the usage of a regulator removes most, if not all, of that velocity, so you need a nozzle to accelerate the static gas at the outlet pressure.

EDIT3: Looking at it again, why would the inlet pressure be the outlet pressure of the regulator? If you look at that paper, there's an expansion chamber before the actual nozzle where the gas would expand. Then, the pressure would reach an equilibrium dependent on how much gas is leaving the nozzle and how much is being fed, at a pressure lower than the regulator outlet. Am I wrong?

• space.stackexchange.com/questions/18904/… May 19, 2017 at 21:16
• That didn't answer the question at all. I know what nozzles are for, but in the case of a cold gas thruster I'm struggling to do calculations for engine performance. May 19, 2017 at 23:11
• It addresses why you need a converging/diverging nozzle. It is clear that you don't understand that. May 20, 2017 at 1:46
• A converging-diverging nozzle is needed when you want to accelerate a fluid from subsonic to supersonic regimes, as a way to overcome the limitation of converging nozzles when choked flow is reached. I am asking why you would need one when you could easily achieve choked flow from the pressure vessel the gas is coming from. As a side note, could you please quit passive-agressively saying my question is pointless and if so write a decent response where you adress the points I'm clearly not understanding? That would actually be helpful. May 20, 2017 at 10:59

"Am I missing anything?" Yes. You have a fundamentally wrong idea of how cold gas thruster systems are designed. They don't have thrust chambers and they use de Laval nozzles to achieve the maximum practical exhaust velocity.

Here is a conceptual design for a typical cold gas thruster system Notice that the gas is supplied to the thrusters through a pressure regulator. The outlet pressure of this regulator would be the inlet pressure to the nozzles (assuming that the flow does not exceed the capability of the regulator, and neglecting frictional losses in the plumbing).

Given this, I am not sure what you actually want/need to calculate for your theoretical system. The paper that I extracted this image from gives some calculations that may possibly be of use. I have not included them here since I do not know what your goal is.

• Actually, now that you point that out, my assumption was not due to any misunderstanding of how nozzles work, but rather thinking that the flow from the tank was already moving at some speed. Now I see that, as it's going through a regulator, pressure is constant and velocity is 0, so to use the potential energy of the gas you do need a converging part. May 20, 2017 at 17:32
• Looking at it again, why would the inlet pressure be the outlet pressure of the regulator? If you look at that paper, there's an expansion chamber before the actual nozzle where the gas would expand. Then, the pressure would reach an equilibrium dependent on how much gas is leaving the nozzle and how much is being fed, at a pressure lower than the regulator outlet. Am I wrong? May 20, 2017 at 17:46
• I just learned a few good bits here. Thanks for the solid info, @Organic_Marble!
– user39728
Mar 14, 2021 at 3:42