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Compressor temperature elevation

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Section summary
1. Formula - isentropic compression
2. Usual values
3. Polytropic compression

1. Formula - isentropic compression

For 1 compressor stage

Calculation Temperarure Elevation in Compressor

Note : in case of multi staged compressor, if the compression ratio of each stage is unknown, it can be assumed at 1st approximation that τone stage=τ1/n

T1=Temperature entry compressor (K)
p1=Initial pressure (bar abs)

T2=Temperature outlet compressor (K) - isentropic discharge temperature
p2=Final pressure (bar abs)

τ=p2/p1
n=number of compression stages

Cp=Specific Heat at Constant Pressure (kJ/kg.K)
Cv=Specific Heat at Constant Volume (kJ/kg.K)

2. Usual values

For air Cp/Cv=1.4

3. Polytropic compression

Polytropic compression calculation, used for centrifugal compressors, is giving a discharge temperature higher than the isentropic compression model.

However, to be able to calculate the polytropic compression discharge temperature, it is necessary to know the polytropic compression coefficient n of the compressor. The polytropic coefficient can be calculated by knowing the polytropic efficiency of the compressor, given by the manufacturer, and an abacus.

Principle of abacus for calculating polytropic coefficient

Figure 1 : principle of an abacus allowing to calculate the polytropic coefficient for a centrifugal compressor

The same formula used for isentropic discharge temperature calculation can be applied but by replacing the isentropic coefficient by the polytropic coefficient.

T2 = T1n

With

T1=Temperature entry compressor (K)
p1=Initial pressure (bar abs)

T2=Temperature outlet compressor (K) - isentropic discharge temperature
p2=Final pressure (bar abs)

τ=p2/p1
n=polytropic coefficient


Source

Pneumatic Conveying Design Guide, David Mills, Elsevier Butterworth-Heinemann, 2004