Handbook of air conditioning and refrigeration / Shan K

11.30 CHAPTER ELEVEN
Refrigeration Capacity. In reciprocating compressors, the piston only performs compression
work during the upward stroke in a complete rotation of the crankshaft. Piston displacement ,
cfm [m3 V˙
p
/(60 s)], can be calculated as
V˙ p �
where Dcy � diameter of the cylinder, ft (m)
Lst � stroke of cylinder, ft (m)
N � number of cylinders
n � rotating speed of compressor, rpm
�Dcy 2 LstNn 4
(11.5)
From Eq. (9.72), the mass flow rate of the refrigerant m˙ r � V˙ p�v�suc, so from Eq. (9.25), the refrigeration
capacity Qrc, Btu/h (W), of a reciprocating compressor can be calculated as
where � suc � density of suction vapor, lb/ft 3 (kg/m 3 )
h 1� � enthalpy of superheated vapor leaving evaporator, Btu/lb (J/kg)
h 4 � enthalpy of subcooled liquid entering evaporator, Btu/lb (J/kg)
(11.6)
In the eight-cylinder reciprocating compressor using HCFC-22 as refrigerant described above, volumetric
efficiency � v depends mainly on compression ratio p dis/p suc. The smaller the p dis/p suc and the
lower the reexpansion of clearance volume, cylinder heating, and leakages through valves and pistons,
the greater the � v. Figure 11.18a shows the � v versus p dis/p suc curve for this compressor. For a
suction temperature of 40°F (4.4°C), the absolute saturated pressure is 68.5 � 14.7 � 83.2 psia
(574 kPa abs.). For a condensing temperature of 115°F (46.1°C), the absolute condensing pressure
is 243 � 14.7 � 257.7 psia (1777 kPa abs.). The compression ratio is therefore p dis/p suc � (257.7
� 3)/83.2 � 3.13. From Fig. 11.18a, � v � 0.81.
The upper part of Fig. 11.18a shows the refrigeration capacity versus suction temperature Q rc-
T suc curves. If T con remains constant and T suc increases, the refrigeration capacity rises accordingly
for the following reasons:
● For a specific compressor rotating at a specific speed, the piston displacement is constant.
● Volumetric efficiency increases as T suc rises.
Q rc � 60V˙ p� v� suc(h 1� � h 4)
● Density of the suction vapor refrigerant � suc increases as T suc increases because of higher saturated
pressure.
● For a constant T con and a fixed amount of subcooling, enthalpy h 4 is also constant. Enthalpy of
superheated refrigerant leaving evaporator at a fixed degree of superheat h 1� increases nearly
linearly between 40 and 80°F (4.4 and 26.7°C) as T suc rises. This also causes an increase of
refrigeration effect Q rf � h 1� � h 4. These factors result in a very slight upward bend in the
Q rc - T suc curve.
If the suction temperature T suc is at a constant value, an increase in condensing temperature T con results
in a decrease in � v and a decrease in Q rf because of a smaller h 4. Consequently, Q rc decreases
as T con rises, and Q rc increases as T con falls, as shown in Fig. 11.18.
Power Input. The refrigeration compressor consumes most of the energy input to a refrigeration
system. In a single-stage reciprocating refrigeration system, power input P in, kW, to the compressor
can be calculated from Eqs. (9.71) and (9.72):
P in � V˙ p� v� suc(h 2 � h 1�)
56.85� com
V˙ p
(11.7)