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Q: Explain the working principle of the Bell Coleman air refrigeration system. Also, find the coefficient of performance.

Working principle of the Bell Coleman air refrigeration system :

 The Bell Coleman air refrigeration system is based on a reverse Joule cycle.

• The components of the Bell Coleman air refrigeration system are shown in figure (a). In this system, the air is taken into the compressor from the atmosphere and compressed.
• The hot compressed air is cooled in a heat exchanger up to the atmospheric temperature (in ideal conditions). The cooled air is then expanded in an expander.
• The temperature of the air coming out from the expander is below the atmospheric temperature due to isentropic expansion.
• The low-temperature air coming out from the expander enters into the evaporator and absorbs the heat. The cycle is repeated again.
• The working of the air refrigeration cycle is represented in figure (b).

Process (1‐2): It represents the suction of air into the compressor.

 Process (2‐3): It represents the isentropic compression of air by the compressor.

 Process (3‐5): It represents the discharge of high-pressure air from the compressor into the heat exchanger. The reduction in the volume of air from V₃ to V₅ is due to the cooling of air in the heat exchanger.

 Process (5‐6): It represents the isentropic expansion of air in the expander.

 Process (6‐2): It represents the absorption of heat from the evaporator at constant pressure.

 Assumptions :

1. The compression and expansion processes are reversible adiabatic processes.
2. There is a perfect inter‐cooling in the heat exchanger.
3. There are no pressure losses in the system.

COP of Bell Coleman cycle :

_{COP =} Net refrigeration effect/ Net work supplied

Work done per kg of air for the isentropic compression process 2‐3 is given by,

 W_c = C _p (T₃ – T₂ )

 Work developed per kg of air for the isentropic expansion process 5‐6 is given by,

 W_e = C _p (T₅ –T₆ )

 Net work required :

 W_net  = (W_c – W_e ) = C _p (T₃ – T₂ ) – C _p (T₅ – T₆ )

The net refrigerating effect per kg of air is given by,

^Qadd = C _p (T₂ – T₆ )