 # Compressor temperature elevation

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

## 1. Formula - isentropic compression

For 1 compressor stage 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. 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