Page 81 - Compression Machinery for Oil and Gas

Centrifugal Compressors Chapter 3 71

physics-based approach to model the aerodynamic excitation. CFD-based
methods generally require a CFD analysis for a representative impeller wheel
type, which can then be applied to similar impeller designs.
Rotordynamic stability is assessed by calculating the logarithmic decrement
(log dec), and the sensitivity of the applied cross-coupling. It is noted that API
617 provides two levels of stability analysis: level I and level II. The level I
method is considered a screening criterion that is valid within a certain zone
of average gas density and critical speed ratios. Level II is required elsewhere.
In a level I analysis, the API Wachel equation is used as a global destabilizing
force value in the log dec calculation. Many, if not most, of today’s centrifugal
compressors require an API level II stability analysis, where all destabilizing
forces are to be included, including annular seals and impeller excitations.
The API requirement is a minimum log dec of 0.1 when all destabilizing forces
are considered.
An example log dec stability plot is shown in Fig. 3.36. The log dec is plotted
against the applied impeller cross-coupling for various levels of increased
cross-coupling to show sensitivity. For this compressor example, the
bearings-only rotor configuration was predicted to be unstable (negative log
dec) at the nominal cross-coupling value (API K xy ). When including the seal
effects, the log dec of this example increases substantially. Also, for the rotor
with seal effects, a good stability margin (relative slope of the log dec line) is
noted. This means that the rotor stability for this example is not very sensitive to
cross-coupling with properly operating seals. It is noted that the seals are sta-
bilizing for the example shown, and this is not always the case. Labyrinth seals,
without any de-swirl mechanisms, are generally destabilizing and commonly
used in centrifugal compressors. A proper rotordynamic analysis should
account for the seal configuration for that particular rotor.

FIG. 3.36 Rotor stability plot.