Hi Alex,
My understanding is different regarding a typical ACM.
The sequence I have been taught is the same i.e.
Primary heat exchanger, ACM compressor, Secondary heat exchanger, ACM turbine, water seperator.
I was taught that the ACM is very similar to a turbocharger, and has no external input of power. I was taught the airflow itself drives the ACM, and that the ACM (well a turbocompressor ACM) is a single shaft turbocompressor with a straight shaft (no gearing) linking the compressor to the turbine.
The compressor by definition is a compressor, and therefore is driven by the turbine, it merely compresses the air entering the compressor. I was taught the airflow over the turbine of the ACM drives the compressor of the ACM. The air does work in driving the ACM turbine and therefore looses energy..ie pressure, and therefore the temp drops. Therefore no external input of power.
I have had a look at the 737 manual and it looks to be a turbocompressor ACM. Other types of ACM obviously work differently such as the brake turbine or turbofan ACM.
All the best,
Tom.