Equation 4.10 presented a specially-defined compressor power requirement using the ideal work of compression Δhideal. This ideal work of compression applies to a process which is both adiabatic (no transfer of heat) and frictionless. The actual power requirement for the compressor that has been the subject of study is shown in Figure 4.13, and the actual work of compression, Δhcomp, can be calculated from the equation:
where P is the power required by the actual compressor.
The ratio of the ideal to the actual work of compression is defined as the adiabatic compression efficiency, ηc:
Using the actual power requirements of Figure 4.13 to determine Δhcomp and the values of Δhideal, the adiabatic compression efficiency can best be correlated by the compression ratio, as demonstrated by Figure 4.14. Such factors as the friction due to the mechanical rubbing of metal parts and the friction of the flow of refrigerant are losses that reduce the compression efficiency. The value ofηc drops at higher compression ratios because of increased forces of the rubbing parts, such as shafts on bearing and piston rings on cylinders. There is also a dropoff of ηc at low compression ratios and this reduced efficiency is probably due to flow friction. In fact, at a compression ratio of 1.0 the value of Δhideal is zero, so any actual work, even though small, drives ηc to zero.
Knowledge of the adiabatic compression efficiency has several important uses. In the first place, the value of ηc is a tool in comparing the effectiveness of two different compressors. Another use is to quickly estimate the work of compression for an operating compressor by determining Δhideal and dividing by ηc, expressed as a fraction. The trend shown in Figure 4.14 that is applicable to a specific compressor is fairly typical of most good compressors, namely ηc is about 70% at high compression ratios and 80% at low compression ratios. Chapter 2 in Sections 2.27 and 2.28 proposed and analyzed a standard vapor compression cycle in which the compression is assumed to be ideal. The compressor power calculated in that analysis would also be ideal, but can be converted easily to the actual power requirement by dividing by an appropriate adiabatic compression efficiency.
The trend in ηc shown in Figure 4.14 reveals another useful fact. Chapter 3 analyzed two-stage refrigeration systems and showed in Figure 3.25 that a reduction in total power is possible through the application of flash-gas removal and desuperheating. The compressor power of a single-stage compressor used as the basis of comparison and the power of the low- and high-stage compressors were based on ideal compression. If the actual power were to be estimated, the ideal work of compression must be divided by ηc. If the system were operating single-stage with a compression ratio of 9, for example, the adiabatic compression efficiency would be less than 70%. By converting to two stage and operating each compressor with a compression ratio of 3, the adiabatic compression efficiency would be elevated to 80%. This comparison shows that with an actual plant, the reduction in total power achieved to shifting to two-stage operation is even greater than that shown in Figure 3.25.