Page 430 - Compression Machinery for Oil and Gas

Downstream Chapter 10 409

Since these forces are produced at or near the rotor mid-span, which coincides
with the point of maximum rotor deflection, their effect on rotor stability is
maximized (unless a damper seal design is used). For the conventional straight
through compressor arrangement, the balance piston is located closer to a bear-
ing centerline and is often considered to have less of an influence on rotor sta-
bility compared to a mid-span located back-to-back center seal. If this center
seal causes the rotordynamics to be unstable or exhibit a low or negative log
decrement, then other types of center seal designs to reduce aerodynamic exci-
tation such as the use of shunt holes or swirl breaks can be investigated. If these
designs are insufficient to suppress an instability then other type seals such as a
honeycomb or hole pattern seals may be required. The compressor manufac-
turer experience with all of these designs should be carefully reviewed.

Centrifugal Compressor Design and Performance
The behavior of a compressor stage can be characterized in terms of parameters
which specify its operating conditions as well as its performance. The dimen-
sionless representation makes it possible to disregard the actual dimensions of
the machine and its real operating conditions (flow rate and speed of rotation)
and is thus more general as compared to the use of dimensional quantities.
Parameters commonly used to describe the performance of centrifugal com-
pressors are as follows:
Machine Mach number. The Mach number, M U , is defined as the ratio
between the machine tip speed and the velocity of sound at the reference
conditions.
U 2
Mu ¼ (10.1)
a 0
where U 2 ¼impeller peripheral speed; A 0 ¼speed of sound at inlet conditions.
Flow coefficient. The inlet flow coefficient for a centrifugal compressor is
defined as follows:

4Q
φ ¼ 2 (10.2)
1
π D U 2
where
Q¼volume flow
D¼impeller tip diameter
U¼impeller tip speed
Reynolds number. The Reynolds number, Re, is defined as the ratio between
inertial forces and viscous forces, evaluated in relation to assigned reference
conditions. For centrifugal machines the following formulation is frequently
used:
U 2 b 2 ρ 00
Re ¼ (10.3)
μ 0