Page 63 - Compression Machinery for Oil and Gas

54 SECTION II Types of Equipment

It should also be noted that this formulation is also valid for viscous flows,
because the friction forces become internal forces. All these concepts are
applied in a very similar way in pipeline flows.
For a rotating row of vanes in order to change the velocity of the gas, the
vanes have to exert a force on the gas. This is fundamentally the same force that
F Ry that acts in the previous example for the pipe. This force has to act in the
direction of the circumferential rotation of the vanes in order to do work on the
gas. According to the conservation of momentum, the force that the blades exert
is balanced by the change in circumferential velocity times the associated mass
of the gas. This relationship is often referred to as the Euler’s law:
P ¼ _ m Δh ¼ _ m u 2 c u2 u 1 c u1 Þ
ð
where u is the circumferential blade velocity at the inlet (1) and exit (2) of the
impeller, and c u is the circumferential component of the gas velocity, taken in an
absolute reference frame at the inlet (1) and exit (2) (Fig. 3.25). At this point,
one of the advantages of centrifugal compressors over axial compressors
becomes apparent. In the axial compressor, the entire energy transfer has to
come from the turning of the flow imposed by the blade (c u2 c u1 ), while
the centrifugal compressor has added support from the centrifugal forces on

FIG. 3.25 Velocity vectors in a centrifugal impeller [3].