Comparison of the Isothermal, Isentropic and Polytropic Processes

The two actual methods used to calculate thermodynamic relationships are isentropic (adiabatic) and polytropic. These calculations are the basis for determining capacity, driver size, and mechanical design. The following explains the differences and when they are used.

Figure 100-7 shows the compression paths of three theoretical processes:
isothermal, isentropic, and polytropic. The theoretical work needed for isothermal
compression is described by the area ABEF. It can be seen that the isothermal work
is appreciably less than that of the isentropic area ABDF. Similarly, the isentropic
area is smaller than the polytropic area ABCF.

These differences can be attributed to differences in heat transfer (cooling). The isothermal process would require continuous cooling during compression to negate all of the temperature rise. In an actual compressor the theoretical isentropic discharge temperature can sometimes be achieved by a moderate amount of cooling during compression. Even so, the resultant process will not be purely isentropic due to other losses in an actual machine. The polytropic path BC best represents an actual process where there is no cooling during compression.

In practice, the isentropic and polytropic methods of analysis are both usable for designing and predicting the performance of compressors.

It turns out that the isentropic (adiabatic) method is commonly applied to positive displacement compressors, because these machines are often equipped with a cooling system that cools the casing or cylinder during compression, making the actual temperature rise approach that of the theoretical adiabatic process.

The polytropic process is typically applied to dynamic compressors in which there is no cooling during the compression that takes place in any individual stage. (There may be cooling between each stage or series of stages, but not within a given stage.)

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