Another name for the Bell-Coleman cycle is the Ideal reverse Brayton cycle.
The air refrigeration system works on the Joule cycle or Reverse Brayton cycle or Bell-Coleman Cycle.
The Bell-Coleman air refrigeration cycle is the modification of the reversed Carnot cycle with air as a working medium.
It can be operated as an open cycle in which the cold air available at the outlet of the expander is used for refrigeration and is let out in the atmosphere.
In the closed cycle, the same air is circulated repeatedly. The cold air available at the outlet of the expander is employed to cool the other fluid in the heat exchanger. The other fluid acts as the secondary refrigerant in this cycle.