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.

Theoretical Calculation of Stability for NASA Stage 57 Stator

“…As a result, a theoretical stability coefficient that locates the theoretical stability line in the compressor map was established. As it was shown by [2], errors lied in the 1-7 percent range for the cases studied (a set of 46 points), in addition [3] shown that the stability margin coefficient could be used to classify different experimental arrangements attending to its stability and [4] used an improved version of the stability theorem to calculate the performance also over the instable region. However these experimental validations were conducted mainly for rotors.…”

“…In [3], this model was used to establish the theoretical stability of the NASA stage 35 rotor. Although this model was only derived for rotors, [4] has shown that its applicability could be extended to stators. As a result, a theoretical stability coefficient that locates the theoretical stability line in the compressor map was established.…”

“…The theory used in this paper is described in [4] where it was proved that there exists a dimensionless number which can be used to establish the stability of any configuration. This number is the stability coefficient, c , given by Equation (1):…”

“…Reference [4] proved that those points with a value of c less than one have the potential for being unstable; they are in fact unstable when a high performance rotor that works with a theoretical flow pattern is adequately perturbed. This result is supported by the stability theorem given in [4] which can be written as:…”

“…However these experimental validations were conducted mainly for rotors. Therefore, the main aim of this paper is to investigate if the theorem can be used to predict possible instabilities due to the stator, just as it has been suggested by [4]. For this purpose, the same set of 595 test points presented by Brought to you by | Purdue University Libraries Authenticated Download Date | 6/15/15 2:34 PM…”