# Calculating (transient) rate of cycles of practical thermodynamic engines (turbojet, multi-cylinder car engines etc..)

I tried to make a plan for a turbojet engine with my physics knowledge and I'm stumped in the first step. For any sustained real engine, I need to somehow take a fraction of the energy output and use that to drive the engine into the next cycle. Take carnot cycle for example. For an engine based on that cycle, I need to take part of the total energy output in one cycle and use that to supply the work done in the cold isotherm in next cycle. Or we could use two out of phase carnot cycles and somehow couple them together and depending on how we actually build the engines, there will be some physics that will determine the equilibrium frequency of the engine(cycles per second). I can't seem to find out what the actual physics is in the case of gas turbine engines. All I found after doing google search are the phrases "compressor-turbine matching" and "compressor turbine operating line" with no solid physics whatsoever. However, it is clear that you increase the cycle rate by increasing fuel injection rate so it must be a function of that. But how do I calculate the rate of cycles(here turbine rpm will do) in this case?

• The engine does have a fly wheel, right? Jul 22 '20 at 22:43
• @ChetMiller No. It's just two fans(one works as compressor, and the other as turbine) connected by a shaft and a combustion chamber in the middle. Of course the whole thing is encased in an aluminum chassis. Jul 22 '20 at 22:48
• Since the Joule cycle (Brayton cycle for you in the US) is a continuous process, you need to calculate mass flows, not RPM. The compressor absorbs energy by compressing air, which in turn is heated and expanded in the combustion chamber and thus able to release more energy when flowing through the turbine. Jul 23 '20 at 19:58
• @PeterKämpf yes I’m starting to realise that as I picked up a book on propulsion. And i am starting to think it was a stupid question because as someone recently told me, not all things are calculated from first principles here, specially the compressor operating line(given it’s dimensions). They are just measured experimentally. However, if I find out a way of quantifying the leading order physics that gives the mass flow etc. vs the volume expansion at the combustion chamber, I’ll post that as a wiki. Until then, answers are welcome. Jul 24 '20 at 5:41
• Those cycles apply to a small parcel of working fluid going through a series of volume and pressure states. It has nothing with "next cycles". Jul 30 '20 at 13:19