Often turbo-compressors exhibit the maximum efficiency
condition very close to the stall limit, so that it would be highly
interesting to have a deep comprehension of this phenomenon.
Despite the large diffusion of the multi-stage centrifugal compressors
in different fields of the technology, such as natural gas
pipe-lines or chemical factories, at the best authors’ knowledge,
to date no theoretical model exists for rotating stall in these machines.
This paper deals with a model for simulating multi-stage
centrifugal compressor flow pattern during rotating stall. The
model is not able to capture the stall inception, so the velocity
and pressure fields are calculated throughout the machine once
rotating stall has developed.
The model consists of an implementation of that proposed by
Moore for single-stage centrifugal compressors, so the simplifying
hypotheses are: irrotational upstream fluid flow, inviscid
and incompressible flow, stationary flow in the frame rotating at
the same frequency of the stall cell; infinite blades are supposed
both in rotors and return channel. Even if these fluid-dynamic
hypotheses are really strong, it is worth of note that the reference
models for rotating stall simulation in turbo-compressors
(namely the Moore’s models) are based, at the present time, on
them.
In a previous step of this research, the authors utilized a semiempirical
approach, with phases changes between first and second
diffuser based on experimental data. Now this hypothesis
is removed and the model is fully analytical. The mathematical
model is solved by numerical way, leaving the original semianalytical
scheme of Moore, so allowing the stall cell propagation
frequency to be calculated. The computer code is written in
C language for Linux operating system. It was tested in singlestage
configuration with results according to Moore’s theory; for
two-stage setup, obtained results appear consistent and qualitatively
according with experimental tests and, unlike the single
stage analysis, only fast rotation waves were found.
