Question

Consider Figure 1, R134a is used as refrigerant for a vapor-compression refrigeration system. The required evaporator pressure is 1.8bar. The refrigerant vapor leaves the evaporator having 5C of superheat. The compressor delivery pressure is 7.4bar and the condenser liquid is 5C undercooled before throttling. The plant has a brine circulating system and the temperature rise of the brine is limited to 5K. Sea water is used as coolant for the condenser. Assuming the compression is isentropic, answer the following questions: i. Represent the refrigeration cycle relative to saturated lines on a P-h diagram (2 marks) ii. Calculate the power required of the compressor if the mass flow rate of R134a is 0.35kg/s (3 marks) iii. Estimate the Coefficient of Performance (COP) of this vapor-compression cycle (3 marks) iv. Calculate the rate at which the brine must be circulated in litres/sec Page 3 of 7 For brine: specific heat is 2.93 kJ/kgK; density is 1190 kg/m3 (2 marks) v. If the sea water temperature entering the condenser is 20C, mass flow rate of sea water is 7 litres/sec, what is the temperature of sea water leaving the condenser? For sea water: specific heat is 4.18 kJ/kgK; density is 1000 kg/m3 (3 marks) vi. Calculate the surface area of the condenser (heat exchanger) for an overall hear transfer coefficient of 2920 W/m2K (3 marks) vii. Using a P-h diagram, explain the effect of suction superheating and liquid sub-cooling on the performance of this VCR cycle. In particular, how they influence the changes of compressor power input, the cooling capacity and the cycle COP.

Answer 1

The task involves explaining the refrigeration cycle on a P-h diagram, calculating the compressor power based on mass flow rate and enthalpy difference, estimating COP, determining brine circulation rate, finding the sea water exit temperature from the condenser, and analyzing the effects of superheating and sub-cooling on a vapor-compression refrigeration cycle.

This question pertains to the application of thermodynamics, specifically the principles of a vapor-compression refrigeration cycle. It requires analyzing and understanding the performance of the refrigeration cycle, the power requirement of a compressor, and the coefficient of performance (COP), among other concepts.

Performance of the Refrigeration Cycle

The refrigeration cycle for R134a can be represented on a pressure-enthalpy (P-h) diagram by identifying four key states: 1. The state where refrigerant leaves the evaporator after gaining superheat. 2. The state where the refrigerant leaves the compressor after isentropic compression. 3. The state where the refrigerant is sub-cooled after condensation. 4. The state post-expansion valve, just before entering the evaporator again.

Power Requirement of the Compressor

Using the mass flow rate and the enthalpy difference between points 1 and 2 mentioned above, the power required for the compressor can be calculated.

Coefficient of Performance

The COP can be estimated by taking the ratio of the cooling effect (heat extracted in the evaporator) to the work done by the compressor.

Moreover, the brine circulation rate can be determined using its specific heat capacity, the permissible temperature rise, and its density. As for the sea water, its exit temperature from the condenser can be calculated using the conservation of energy, knowing the heat rejected by the condenser, the mass flow rate of sea water, and the specific heat capacity of sea water.

To understand the effect of superheating and sub-cooling on the VCR cycle, a student would analyze changes to the heat absorbed in the evaporator, the work done by the compressor, and the overall COP.