BIFURCATION-ANALYSIS OF SURGE AND ROTATING STALL IN AXIAL-FLOW COMPRESSORS

The surge and rotating stall post-instability behaviors of axial flow compressors are investigated from a bifurcation-theoretic perspective, using a model and system data presented by Greitzer (1976a). For this model, a sequence of local and global bifurcations of the nonliner sy stem dynamics is uncovered. This includes a global bifurcation of a pa ir of large-amplitude periodic solutions. Resulting from this bifurcat ion are a stable oscillation (''surge'') and an unstable oscillation ( ''anti-surge''). The latter oscillation is found to have a deciding si gnificance regarding the particular post-instability behavior experien ced by the compressor. These results are used to reconstruct Greitzer' s (1976b) findings regarding the manner in which post-instability beha vior depends on system parameters. Although the model does not directl y reflect nonaxisymmetric dynamics, use of a steady-state compressor c haracteristic approximating the measured characteristic of Greitzer (1 976a) is found to result in conclusions that compare well with observa tion. Thus, the paper gives a convenient and simple explanation of the boundary between surge and rotating stall behaviors, without the use of more intricate models and analyses including nonaxisymmetric flow d ynamics.