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Section summary |
---|

1. Performance of an
impeller |

2. Head coefficient
of pressure coefficient |

3. Flow coefficient |

4. Compression ratio
calculation |

It is possible to estimate the performance of a centrifugal compressor, in terms of compression ratio or flowrate if the manufacturer has given some information about the impeller, in addition to basic dimensional data : the head coefficient, the flow coefficient and the polytropic efficiency.

This page aims at answering to the following questions : what is the head coefficient ? What is the flow coefficient ? What is the relation between the head and flow coefficient ? How to calculate the compression ratio given by an impeller ?

The head coefficient is an adimensional number that is comparing
the polytropic work that one gets during compression to the impeller
tip speed

**Equation 1 : calculation of
compressor head coefficient**

With

μ = pressure coefficient

W_{p} = polytropic work in J/kg

u_{2} = tip speed of the impeller in m/s

Order of magnitude of the pressure coefficient :

- Centrifugal flow impeller : 0.5 to 0.6
- Mixed flow impeller : 0.35
- Axial flow impeller : 0.05 to 0.25
- Peripheral flow impeller : 1.8

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The flow coefficient is calculated the following way :

**Equation 2 : flow coefficient
calculation**

With

δ = flow coefficient

u_{2} = tip speed of the impeller in m/s

R_{2} = impeller outside radius in m

Qv = compressor flowrate in m3/s

Order of magnitude of the flow coefficient :

- Centrifugal flow impeller : 0.04 to 0.2 with until 0.6 for mixed flow
- Axial flow impeller : 0.8 to 1.2
- Peripheral flow impeller : 0.04

Note that there is relation in between μ and δ : the lower the flow coefficient, the higher will be the pressure coefficient. The manufacturer can deliver the curve μ=f(δ) to help size the compressor but one must be careful that the relation will change if the gas handled changed or if the speed of the compressor varies beyond a certain limit

Thanks to the head coefficient it is possible to calculate which compression ratio will be given by an impeller. This calculation is based on the definition of the pressure coefficient and the definition of the polytropic work.

**Equation 3 : compression ratio
calculation**

With

τ = compression ratio

k = isentropic coefficient

μ = pressure coefficient

u_{2} = tip speed of the impeller in m/s

M = molar mass of the gas

η_{p} = polytropic coefficient

R = ideal gas constant

T_{suction} = suction temperature in K

Note that the compression ratio is actually independent from the
suction pressure.