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

\[ \frac{T_2}{T_1} = \left(\frac{p_2}{p_1}\right)^{(\gamma-1)/\gamma} \] \[ \gamma = \frac{C_p}{C_v} \] 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 τ_{one 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)

Interactive Compressor Temperature Calculator

⚠️ ENGINEERING NOTICE & EDUCATIONAL DISCLAIMER: This interactive calculator is provided exclusively for preliminary estimation and educational purposes. It is not intended for detailed design or equipment procurement without certified vendor rating. No warranty, expressed or implied, is provided, and no liability is assumed.

Unit System:

Inlet Temperature (\(T_1\)) [°C]:

Inlet Pressure (\(p_1\)) [bar abs]:

Outlet Pressure (\(p_2\)) [bar abs]:

Ratio of Specific Heats (\(\gamma = C_p/C_v\)):

Polytropic Coefficient (\(n\), optional):

Number of Stages (\(n_{stages}\)):

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 = T₁.τⁿ

With

🏭 Practical Plant Engineering Rules of Thumb & Safety Limits

Maximum Discharge Temperature Limits: For hydrocarbon and lubricated air compressors, discharge temperature should be limited to 135°C to 150°C (275°F to 300°F) to prevent lubricating oil degradation, carbon deposition, and valve coking.
Stage Compression Ratio Limit: To avoid excessive discharge temperatures and mechanical stress, single-stage pressure ratio (\(\tau\)) should generally not exceed 3.5 to 4.0 for air and light hydrocarbon gases.
Intercooling Design: When overall pressure ratio exceeds limits, multi-stage compression with intercoolers returning gas to ambient inlet temperature is mandatory to save compression power and maintain safe metallurgy.
Polytropic vs Isentropic: Real centrifugal compressors operate polytropically. Polytropic efficiency (\(\eta_p\)) typically ranges from 75% to 85% depending on machine size and Reynolds number.

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