Most smaller satellites and other larger but simpler space craft with a less demanding mass fraction tend to use cold gas thruster, importantly with a common or as few as possible pressure vessels, however such thrusters have a tragically low performance, and as such, most lager space craft will use either monopropellant or even bipropellant thrusters. This of course comes at the cost of complexity and a larger mass fraction however. my question is, could a compromise be made between the two mechanisms, where several reaction thrusters could be pressurised from the same combustion chamber, not too dissimilar to rocket engines with multiple nozzles. What would be the practical limitations of such a system- how could the cooling of the pressurisation lines be managed?
You want to use a hot gas thruster with one combustion chamber and several selectable nozzles?
But how should the active nozzle selected? You need something like a valve with one input and as many outputs as the nozzles. But this valve would be damaged by the hot corrosive gas. Problematic for a satellite operating over several years.
Valves for the cold propellants exist for many decades and are known to be reliable. No satellite operator would trust a hot gas valve without successful history.
Fluidic thrust vectoring would be a reasonable design approach for vectoring a hot gas attitude control thruster.
An attitude control thruster with a single combustion chamber but steerable exhaust would be a type of thrust vectoring nozzle. Gimbaled nozzles can vector thrust, but at the expense of mechanical complexity and mass. An alternative is fluidic thrust vectoring, which has no moving parts.
Fluidic thrust vectoring in aircraft is accomplished using air from the turbine compressor. http://nal-ir.nal.res.in/12145/1/cp191.pdf These vectoring nozzles on aircraft are usually limited to trust deflections of 15*. The 15* deflection used in aviation would not be adequate for spacecraft attitude thrusters. For spacecraft attitude control, the deflection would need to be closer to 90*. This could be attained by design of the outlets from the suction collar. In effect, the collar and outlets become a valve for the hot gas.
If this design were applied to attitude control rockets, the vectoring flow would need to be supplied from another source, likely a cold gas supply. The system would have the cold gas supply and control valves similar to a cold gas thruster system, but the output cold gas would be “amplified” by using it to vector hot gas after it combusts.
Fluidics valves have non-linear response, similar to transistors. They can be assembled into logic elements and used for control circuits such as Hydro-mechanical gas turbine Fuel Controls. They have been used for military applications and civil aviation gas turbines due to their robustness to acceleration, vibration, temperature and electromagnetic pulses.
Fluidics logic and control systems have a 50+ year history of application in aerospace, so it should be acceptable technology for satellites.
At first glance something like that might seem like a good trade-off, but as it is stated, once you start to dig deeper, a design like that would lead you down a thermo-fluidic nightmarish rabbit hole you really don't want to go through.
When you design a rocket engine, the geometry, dimensions, combustion temperature and other parameters are carefully designed at each point in the design in order to obtained a specific performance out of it. Roughly speaking, the combustion will be fed on one side of the chamber and the combustion will push reaction mass (most of it still burning) towards the nozzle, as it approaches the throat the material speeds up but you also deposits a lot of energy in the throat of the nozzle increasing the temperature, and then the nozzle itself is designed to obtained an optimal expansion ratio. Your whole cooling has to be designed accordingly, and you want to have a very stable plasma flow throughout the whole design, and design it in a way that supports the expected load from the high pressure. The minimum defect can seriously mess up performance or destroy the engine.
Now, for something like the proposed approach you could:
Have a single combustion chamber with multiple exits. You will likely have issues trying to direct the exhaust towards the desired output. The sudden change in the direction of the flow when changing the active nozzles will also cause destabilizing effects in the plasma flow, messing up things like your fuel to oxidizer ratio and combustion temperature which could simply kill the combustion process or destroy the chamber. In addition, when changing the number of active outputs you would also need to change the pressure inside the combustion chamber in order to keep the exhaust velocity of all nozzles within an expected operational range.
You can have a single combustion chamber with a single exit, but some system to redirect the exhaust through the ship. At this point you would need the combustion to keep the necessary pressure in the whole system, so you need sturdier and better insulated structures, and add all that additional mass. Then, as the exhaust cools down it also looses energy making the whole system way less efficient. The whole thing of rocket engines and motors is convert the highest combustion temperature possible into the highest kinetic energy possible without melting the whole thing in the process. Once it starts to cool down (and therefore slowdown) without reaching the exhaust there is little to no sense in having combustion in the first place.
It's just easier to just take the propellant from a pressurized tank to small monopropellant thrusthers which is how is done for monopropellant spacecraft propulsion.
Hope this helps!