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Currently studying about aircraft air cycle machines for my midterm, and this question still kinda stuck in me.

So in air cycle machine, in my understanding, the air pressure is raised twice. But I still don't understand, why is that?

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You have a system that takes hot high pressure air that was compressed in the engine, removes the heat while it is still at high pressure, then lets the pressure drop, reducing its temperature to below its starting temperature.

But the potential temperature drop is not sufficient if all you do is remove the heat from the initial bleed supply using nothing but heat exchangers, then let it expand to get your chilling effect.

But what you CAN do is exploit the kinetic energy in the flow, to repeat the compression heating/heat-removal-while-compressed cycle a second time and get a much larger final temperature drop. This is what the Air Cycle Machine does.

You use the velocity in the air flow to drive a turbine that drives a secondary compressor. Kinetic energy in the flow is extracted and converted into heat by raising the pressure a second time, then extracting the extra heat created by the secondary compression, through secondary heat exchangers.

So air coming from the engine was hot at high pressure, some of the heat was removed in the precooler, without reducing pressure and velocity, then the velocity energy is extracted to raise the pressure and temperature of the partly cooled air more, its excess heat is removed with secondary heat exchangers, then when the air gets to the other side of the turbine, it's allowed to expand to a much higher volume having both its heat and kinetic energy extracted, and the temperature drop is more extreme.

The double cycle - compression/heat removal/compression again/heat removal again/expansion to ambient - can take air leaving the compressor at, say 300 deg F, and chill it down to -40F. You can't allow that to happen because ice will form on the turbine, so you have to limit the discharge to just above freezing with the control system, but that's how efficient a "bootstrap" compressor ACM is.

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Inside the air cycle machine, air pressure is not raised twice. However, the machine is partly powered by high-pressure "bleed" air, so in a larger context the pressure has been raised before it enters the air cycle machine.

The air cycle machine (pack) cools the bleed air, compresses it, cools it again, then runs it through a turbine, a hot/cold mixing valve, and usually many other sensors and components that make the system very complex. By the time this "twice compressed" air reaches the cabin at sea level pressure, it can be extremely cold.

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