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Section summary |
---|

1. Formula -
isentropic compression |

2. Usual values |

3. Polytropic 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 τ_{one stage}=τ1/n

p

T

p

τ=p

n=number of compression stages

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

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

For air Cp/Cv=1.4

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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.

**T _{2} = T_{1}.τ^{n}**

With

T_{1}=Temperature entry compressor (K)

p_{1}=Initial pressure (bar abs)

T_{2}=Temperature outlet compressor (K) - isentropic
discharge temperature

p_{2}=Final pressure (bar abs)

τ=p_{2}/p_{1}

n=polytropic coefficient

**Source**

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