A refrigeration unit operating on R-134a is used to maintaina freezer at -15C. T

Question

A refrigeration unit operating on R-134a is used to maintaina freezer at -15C. The refrigeration unit operates at a suction pressure of 140kPa and a discharge pressure of 900kPa. The condenser of the refrigeration unit is cooled by a water cooled heat exchanger. Cooling water flows through the condenser heat exchanger at a rate of 50kg/min, entering at a temperature of 20C and leaving at a temperature of 29 C. It is known that the refrigeration unit can be modelled as an ideal vapour compression cycle for the heat rejection, throttling and heat absorption stages , however the compressor is known to be non-isentropic. The discharge temperature from the compressor is 60C.

i) Determine the mass flow rate of the refrigerant, assuming a constant specific heat for the cooling water of Cwater=4.184 kJ/(kg.K). (11 marks)

ii)What is the required power input to the compressor and the isentropic efficiency of the compressor.

Explanation / Answer

given that

suction pressure = 140KPa

exit pressure of condensor = 900KPa

since the cycle is ideal vapour compression refrigeration cycle the refrigeration is saturated.

From the Steam table

At 140KPa and -150C h1 = 239.16 KJ/Kg

from the superheated table at 900KPa and 600C h2=295.13 KJ/Kg

at the end of condensation it is saturated water h3 = 95.47 KJ/Kg

since 3-4 is throttling h3 = h4

therefore h4 = 95.47 KJ/Kg

we know that net refrigerating effect = Mr*(h1-h4)

N.R.E = m*Cp*T = (50/60)*4.184*9 = 31.38 KJ/s

therefore Mr = 31.38/(239.16-95.47)

= 0.218 Kg/s

power required by compressor = Mr*(h2-h1)

   = 0.218*(295.13-239.16)

= 12.20 Kw

isoentropic efficiency = (h2I-h1)/(h2-h1)

where h2I = 284.77 KJ/Kg

compressor efficiency = (284.77-239.16)/(295.13-239.16)

= 0.814

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