The twostage cascade refrigeration system shown below is use

The two-stage cascade refrigeration system shown below is used to maintain a room at a temperature of-160 degree F. Freon 503 is used in the low temperature cycle (denoted as cycle II), and Freon 22 is used in the high temperature cycle (denoted as cycle I). The working temperatures of the evaporator and condenser are -180 degree F, and 100 degree F, respectively. The temperature at the entrance of the expansion valve in cycle II is -30 degree F, and the temperature at the exit of the expansion valve in cycle I is -50 degree F. Assuming the processes in the compressors to be reversible and adiabatic, if the lift is 28,000 BTU/hr, compute: The compressor HP for cycle I The compressor HP for cycle II Ratio of flow rates in cycle I/cycle II

Solution

Equations :

Power consumption by Compressor for Cycle I = m1 (h7 - h6)

= 416.9(118.97-99.5)

= 8117.04 Btu/hr

= 3.19 hp [ 1 Btu/hr = 0.0000393 hp]

Power consumption by Compressor for Cycle II = m2 (h3 - h2)

= 554.83(61.84 - 53.32)

= 4727.15 Btu/hr

= 1.86 hp

Ratio of mass flow rates = m1/m2

= 416.9/554.83 = 0.7514

In the above equations m1 and m2 are found from following equations :

Given : Lift = 28000 Btu/hr = m2 (h2 - h1) = m2 (53.32 - 2.855)

So, m2 = 554.83 lb/hr

Energy Balance for intermediate heat exchanger (between cycle I and II) :

m1(h6 - h5) = m2(h3-h4)

Or, m1 (99.5 - 21) = 554.83(61.84 - 2.855)

Or, m1 = 416.9 lb/hr

N.B. Here h1 , h2, h3 and h4 are the enthalpy properties for R 503 where data are approximated to close value available in the absence of property table till -180 degF and as well as superheated data.

h5, h6, h7 and h8 are the enthalpy properties for R22 and the data are exact.