The volumetric efficiency is a key term in explaining trends in the refrigerating capacity and power requirement of reciprocating compressors. The volumetric efficiency of a compressor, ην in percent, is defined by the equation:
The displacement rate is the volume rate swept through by the pistons during their suction strokes. The volumetric efficiency is less than 100% because of such factors as leakage past the piston rings, pressure drop through the suction and discharge valves, heating of the suction gas when it enters the cylinder by the warm cylinder walls, and the reexpansion of gas remaining in the cylinder following discharge. The volumetric efficiency can be calculated from catalog data of the compressor, as in Example 4.1.
The variable that most directly controls the volumetric efficiency is the pressure ratio—the ratio of the absolute discharge pressure to the absolute suction pressure. Figure 4.2 shows nv calculated in the manner of Example 4.1, using catalog data for an 8-cylinder ammonia compressor operating at 1170 rpm.
Of the factors that influence the volumetric efficiency, a significant one is the reexpansion of refrigerant that remains in the cylinder when the piston completes its discharge stroke. The gas remaining at the end of the discharge stroke is called clearance gas and is the amount retained in the clearance volume. The effect of the clearance gas and clearance volume is shown in Figure 4.3 on a piston/cylinder laid on its side. The volumes in the pressure-volume graph correspond to those shown in the cylinder below. The clearance volume is designated as Vc, and as the piston starts its suction stroke the gas trapped in the clearance volume must first expand down to the suction pressure before refrigerant can be drawn on the cylinder.
If at a particular time the suction pressure is ps1, the piston moves until the pressure in the cylinder is ps1 at which point the volume in the cylinder is V1. It is at this position that refrigerant can be drawn into the cylinder, so the intake volume would be (V3–V1). Define a new type of volumetric efficiency and call it the clearance volumetric efficiency, ηνc. Keeping with the philosophy of volumetric efficiency as expressed in Eq. 4.1, the clearance volumetric efficiency is:
The magnitude of Vc is a function of the design and construction of the compressor, and most manufacturers try to keep this volume to a minimum. Vc is often expressed as a percentage of the swept volume in a term called the percent clearance, m
Finally, the volume V1 can be related to Vc by assuming that the expansion of the clearance gas to the suction pressure is an isentropic expansion—the reverse of an isentropic compression. The relationship of pressures and specific volumes in an isentropic process between point a and point b can be approximated by the relationship:
At a pressure ratio of 5.0, Figure 4.2 showed the actual volumetric efficiency ηv of that compressor to be 80%. The ideal volumetric efficiency would be 100%, and this ideal value is diminished by the various real processes (reexpansion of clearance gas, fluid friction, cylinder heating, etc.). The clearance volumetric efficiency of 92.5% in Example 4.2 explains approximately one-third of the drop of volumetric efficiency from 100% to the actual value of 80%.