# How can flow in a centrifugal compressor at fixed conditions vary?

Consider a centrifugal compressor. The compressor map usually plots the adiabatic head vs volumetric inlet flow for rated conditions of pressure, molecular weight and temperature at a given speed. But when pressure, temperature, molecular weight and speed are fixed, how can the inlet flow be made to vary ? Is it accomplished through the use of inlet vanes ?

• What do you mean by speed? RPMs of the turbine? Sep 15 '15 at 16:20
• Yes, rotation speed. Sep 15 '15 at 17:25

In general every compressor (axial and radial) will deliver a certain flow rate depending on the back-pressure down stream of the compressor. So by changing the pressure difference over the compressor: for example closing a throttle upstream or downstream of the compressor the flow rate will change accordingly. This can also be achieved by changing the geometry of the compressor. One possibility are the mentioned variable inlet guide vanes.

Below is a compressor map taken from Wikipedia. As you can see (away from the surge line) every mass flow rate is connected to a pressure ratio. At constant rotor speed, the flow rate changes according to the pressure ratio which is needed.

The generic equation for mass flow through a cross-section of area $A$, traveling at velocity $V$ is

$$\dot m = \rho \, V \, A$$

where $\rho$ is the density of the fluid and $\dot m$ is the mass flow rate. If the molecular weight, temperature, and pressure of the fluid are fixed, then density is fixed too. That leaves $V$ and $A$ to play with. Since $V$ will be largely determined by the compressor rotation speed, all you have left is to change the cross-sectional area of the inlet.

Calculating the area for a particular flow rate is a bit more difficult in practice however, since the fluid velocity will want to increase as the area is increased. Also, if the compressor is going to pump liquid, then there isn't much that can be done to alter the flow rate without incurring cavitation in the pump.

There is another alternative; you can feed back some of the outlet from the compressor to the inlet, so that the net outlet of the pump is reduced. You could control the fraction of feed back (a.k.a. reflux) with a valve.

• So if I follow you, the only way to increase the flowrate under the conditions described is through modification of the geometry of the inlet ? Sep 15 '15 at 18:00
• Yeah, or if you can, modify the pump internals in some way to make it move less fluid on each rotation. If it's a piston pump, shorten the stroke, if it's a turbine, change the blade size and/or angle. Sep 15 '15 at 18:02