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## Shortcuts In Multistage System Design Calculations

This chapter has explained how to compute capacity requirements of the lowand high-stage compressors in two-stage systems. The precise method requires the application of mass and energy balances around the intermediate-pressure devices. Repeated two-stage calculations are tedious, although design and sales organizations that perform frequent analyses can readily computerize these calculations. Even for the manual process, the calculations can be simplified through the use of a graph such as Figure 3.20.

A chart such as Figure 3.20 can accurately represent the mass and energy balance equations, because it is only the evaporating and the intermediate temperatures that influence this calculation. The application of Figure 3.20 is simply to multiply the kW (tons of refrigeration) capacity of the low-temperature evaporator by the multiplying factor to find the required refrigeration capacity of the high-stage compressor. The values of the ratios from Figure 3.20 show higher quantities than obtained with the procedures explained in this chapter. The reason is that Figure 3.20 acknowledges the inefficiencies of the booster compressor, which causes a greater load on the desuperheater than would be true of an ideal compression. The calculation procedures of this chapter can be made more realistic by using the actual power of the low-stage compressor rather than the ideal isentropic power.

Figure 3.20 applies when the low-stage compressor is of the reciprocating type and to some configurations of screw compressor installations. The features of screw compressor systems will be explained in greater depth in Chapter 5, but at the moment only those equipment characteristics will be discussed that are necessary to understand the analysis of two-stage operation with a lowstage screw compressor. To seal the spaces between the rotors of a screw compressor, oil is injected which intermingles with the refrigerant being compressed. The oil absorbs some of the compression heat and must be cooled before reinjection. Two popular methods of oil cooling—direct injection of liquid refrigerant and cooling with a thermosiphon heat exchanger—are shown in Figures 3.21 and 3.22, respectively.

In Figure 3.21, liquid refrigerant is injected directly into the compressor, and its vaporization neutralizes the heat added by compression. The discharge vapor leaving the compressor is not completely desuperheated, and the remainder of the desuperheating process takes place in the flash tank/intercooler with the vaporization of more liquid refrigerant. From a thermodynamic standpoint, it makes no difference whether refrigerant vaporizes within the compressor or within the flash tank/intercooler to perform the superheat. Consequently, the factors shown in Figure 3.20 apply to systems where the oil in the low-stage compressor is cooled by direct admission of refrigerant.

A different, and usually more favorable, situation results with the arrangement in Figure 3.22 where the oil is first separated from the the refrigerant vapor that is discharged from the compressor, then cooled in a thermosiphon heat exchanger. The thermosiphon heat exchanger receives liquid refrigerant, boils a portion of it in cooling the oil, and thus maintains natural convection circulation. The vapor generated in the thermosiphon heat exchanger passes directly to the condenser with the result that some of the heat of compression in the low-stage compressor is rejected directly to atmosphere. The amount of liquid that would otherwise be allocated to desuperheating and which must be compressed by the high-stage compressor is reduced by 15 to 30%. More precise data of the percentage will be presented in Chapter 5, Screw Compressors, but it is sufficient here to call attention to the fact that the multiplying factor of Figure 3.20 is reduced for the compressor cooling arrangement in Figure 3.22.

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