On the Theoretical Calculation of the Stability Line of an Axial-flow Compressor Stage

Abstract

Recently, an analytical model to calculate the stability of an axial-flow compressor rotor has been presented in the scientific literature. The range of validity of that theoretical characterization was supported by several lemmas and theorems. One of the main results was the definition of a dimensionless coefficient for determining the location of the stability line in the rotor map. In this work the mathematical structure of that solution is studied. As a result of this detailed study, a new stability theorem and a new stability coefficient are obtained. This stability coefficient is an improvement of the previous one since it is physically and mathematically well defined in all the operational points of the compressor map. As a consequence, the new model is able to capture the stall inception for rotors and stators as well as the full characteristic curve (pressure rise versus mass flow rate) including rotating stall and possibly reverse flow. It is proved, as a consequence of the restriction imposed by the Stability Theorem, that each local component (rotor or stator) has its own instability point and its own post-stall characteristic curve. This theoretical criterion for predicting the averaged characteristic curve is in good accord with the experimental data. The stability coefficient is also verified for a compressor stage. Finally, the model is shown to provide an adequate quantitative and qualitative description of the averaged stall line giving a physical explanation of the mechanism involved in the instable region of the compressor map.