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Compressor in environment control system (aircraft)

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It appears to be a refrigeration cycle (air-conditioning) designed for high capacity and low weight. The compressor recovers energy from the turbines and provides a load to the turbines so that they do work, which lowers the temperature of the expanded air. This is necessary to reach sub-ambient temperatures.
 
So I want to see if I understand what are you said:
1) In the primary heat exchanger the bleed air loss heat and the temperatures drops.
2) aftar that the air goes to the compressor, the temperatures increase but the amount of heat stay like after the primary heat exchanger.
3) the air enter to the second heat exchnger and the heat and also the temperatures decrease.
4) the air enter to the turbine and the tempurature decrease again.

am I right?
and all this to supply sub-ambient temperatures.
 
You need to refer to a thermodynamics book. I'm not a thermodynamics expert but I've looked at many example processes, so I can recognize your process drawing. Simply expanding an ideal gas (air is close to ideal) does not cool it. Work has to be extracted to cool it. That is what the turbines are for. For efficiency, in this case, that work is used to further compress the incoming air, which heats it as well as adding to it potential energy (delta PV).

The hot compressed air is cooled toward ambient temperature and then expanded in the turbines where it becomes sub-ambient. Air liquifaction plants use a similar cycle.
 
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