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For a given performance requirement, combustion pressure, propellant mixture, etc.
How can one vary between the various engine power cycles such as gas generator, staged combustion, expander, and how does this affect the sizing of the components such as piping, turbopumps, precombustors. If there are ways to check for it, how would one go about it?
Closed cycled engines have turbine of the high volume flow and low pressure drop type, and gas generator engines have the low volume flow and high pressure drop type. Gas generator turbines are typically hotter than closed cycle ones. The rest are typically scaled with peak pressure after the turbopump. There is a pressure budget on rocket engine propellant circuit. The peak pressure that's needed to make sure a certain chamber pressure goal given total mass flow is met, and thus the total HP through the shaft is determined. High chamber pressure is the only way to boost Isp, given equal tradeoff concerns governing nozzle design. The rest are basically thermal concerns that are the same with each type of engines, which the exception of expander cycle engine often needing very long combustion chamber to absorb enough heat.
