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IMA Journal of Applied Mathematics 2003 68(2):205-228; doi:10.1093/imamat/68.2.205
© 2003 by Institute of Mathematics and its Applications
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Bifurcation analysis of surge and rotating stall in the Moore–Greitzer compression system

Csaba Hos1, Alan Champneys2 and László Kullmann3

1 Department of Hydraulic Machines, Budapest University of Technology and Economics (BME), 1521 Budapest, Pf. 91, Hungary 2 Department of Engineering Mathematics, University of Bristol, Queen's Building, University Walk, Bristol BS8 1TR, UK 3 Department of Hydraulic Machines, Budapest University of Technology and Economics (BME), 1521 Budapest, Pf. 91, Hungary

A simple compression system model, described by a set of three ordinary nonlinear differential equations (the Moore–Greitzer model) is studied using bifurcation analysis to give a qualitative understanding of the presence of surge and rotating stall. First, three parameter values are chosen and a reduced planar system is studied to detect the local bifurcations of pure surge modes. The global bifurcation diagrams are then completed with the help of the continuation software AUTO. A special feature of this 2D system is a set of parameter values where two Takens–Bogdanov points merge. As a next step, the interaction of surge and rotating stall modes is analysed using the same branch tracking technique. Several novel bifurcation scenarios are described. Two-parameter bifurcation maps are computed and a satisfactory agreement with experimental results is found. An explanation is given for the onset of deep surge, rotating stall, classic surge and the hysteresis effects experienced in measurements.

Keywords: Moore–Greitzer compression system; rotating stall; Shil'nikov-like homoclinic orbit; surge; Takens–Bogdanov bifurcation.

Received 21 June 2002.


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