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Reciprocating compressor capacity

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Section summary
1. Reciprocating compressor capacity calculation formula
2. Usual values
3. Other relations (mass flowrate, power)
4. Multistage compression

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1. Reciprocating compressor capacity calculation formula

In a reciprocating compressor, the capacity depends on the volume displaced by the piston during its movement. The swept volume of one piston can be calculated the following way

Not all the cylinder volume can be used for the compression as there is always the clearance at the end of the cylinder that remains with some air inside. This phenomena can be quantified by defining the volumetric efficiency of the compressor


Ev should be calculated rigourously thanks to the actual volume and swept volume, but for quick estimations, the volumetric efficiency can be estimated thanks to the following expression


The volumetric capacity of a single piston can then be calculated thanks to


This value needs to be multiplied by the number of cylinders to find out the capacity of the reciprocating compressor.

With

V_d=Swept volume (m3)
V_s=Actual volume capacity (m3)
V_c=Clearance volume (m3)
c=clearance=V_c/V_d=Swept volume (m3)
E_v=volumetric efficiency (-)

τ=compression ration = p_discharge / p_suction(-)

St=Piston Stroke (m)
k=isentropic coeffient (-)
D=Cylinder internal diameter (m)

2. Usual values

For air k=1.4
L=0.04 for lubricated compressors (only for estimation)
c must be defined according to the compressor type but should range from 0.04 to 0.16

3. Other relations (mass flowrate, power)

The mass capacity of the compressor can be calculated, per cylinder with

The power necessary to perform the compression can be calculated the following way by using the mass capacity, the pressures and temperatures reach and taking into account the efficiency of the compressor :

The overall efficiency of the reciprocating compressor can be determined thanks to the following graph :

A reciprocating compressor has a cooling system built-in. This particularity, which cannot be implemented for centrifugal compressors, allows to have a discharge temperature close (but not equal) to the isentropic discharge temperature.

4. Multistage compression

Reciprocating compressors are often used in multistage compression with intercoolers in order to maintain the temperatures in a range manageable for the machine. If the compression ratio is > 3, multistage compression is then advised.

Figure 1 : Principle of operation of a reciprocating compressor, 2 stages, 2 cylinders double effect