To begin the explanation of why the screw compressor possesses its unique capacity, power, and efficiency characteristics, a basic machine will be analyzed. This compressor is assumed to be operating at constant speed and without the capacity control capabilities that will be introduced in Section 5.8. A fundamental characteristic of the basic screw compressor is its built-in volume ratio, vi, which is defined as follows:

In contrast to the reciprocating compressor, the screw compressor has no suction and discharge valves but accepts a certain volume of suction gas in a cavity and reduces this volume a specific amount before discharge. Some typical values of vi used by manufacturers are 2.6, 3.6, 4.2, and 5.0. For a given rotor diameter each different vi is associated with a different rotor length. Each vi corresponds to a certain pressure ratio that varies from one refrigerant to another. Table 5.1 presents estimates of pressure ratios using the following equation that is applicable to an isentropic compression of a perfect gas:

If the pressure ratio against which the compressor pumps is precisely equal to that developed within the compressor, then the discharge port is uncovered at the instant that the pressure of the refrigerant in the cavity has been raised to that of the discharge line, and the compressed gas is expelled into the discharge line by the continued rotation of the screws. This situation is represented by Figure 5.5a, which shows the pressure changes in one cavity between the screws as rotation progresses. It is rare, however, that the developed pressure within the compressor precisely matches that prevailing in the discharge line. Figures 5.5b and 5.5c demonstrate what happens when the developed pressure is lower or higher, respectively, than the discharge-line pressure.

In Figure 5.5b the compressed refrigerant has not yet reached the dischargeline pressure when the discharge port is uncovered, so there is a sudden rush of gas from the discharge line into the compressor that almost instantaneously increases the pressure. Thereafter, the continued rotation of the screws expels this gas as well as the refrigerant ready to be discharged.

The third situation, as shown in Figure 5.5c, occurs when the discharge-line pressure is lower than that achieved within the compressor. At the instant the discharge port is uncovered there is a sudden rush of gas out of the compressor into the discharge line.

Another picture of the drawbacks of the mismatch of the internally developed pressure and that in the discharge line is shown in the pressure-volume diagrams of Figure 5.6 which concentrate only on the compression and discharge processes. Since the area under a compression or expansion curve on the pressure-volume diagram indicates work done in the process, the horn in Figure 5.6a indicates nonproductive work in the process. Losses are caused by unrestrained expansions that are the result of gas under pressure venting freely from a high pressure to a low pressure. Unrestrained expansions occur in both over compression and under compression, but the most penalizing of the two is in over compression where a limited volume of gas in the compressor vents to the extensive volume of the discharge line. The losses are less in under- compression where the gas expands unrestrained from the extensive volume of the discharge line to fill the compressor cavity.