Theoretical Calculation of Stability for NASA Stage 57 Stator

Abstract

The stability of 595 operational points, belonging to 25 different experimental arrangements of the NASA stage 57, is studied by means of a theoretical calculation based on a theorem recently presented in the scientific literature. This large number of tests is used for checking the results of the theory for a wide variation of the operational and the design parameters. This study completes a previous one by adding the calculations for the stator. Both rotor and stator results are related with the stage stability. While only seven test points appear as potentially unstable due to the rotor, nine test points do due to the stator. IntroductionIn order to improve the performance and to reduce the weight, volume, and cost of fans and compressors, a tentative solution to the problem of predicting the minimum number of blades per stage that assures the stability at the design point was presented in [1]. This model was based on the comparison of two characteristic times. This preliminary attempt was improved by the theory presented in [2] where an analytical model to calculate the stability of axial-flow compressor rotors was described. This characterization of stability was related to the minimum value of the ratio of two well-defined times whose exact definitions were obtained in a rational way for high-performance rotors subjected to non-small disturbances. 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. 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. 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

Analytical Calculation of Stall-inception and Surge Points for an Axial-flow Compressor Rotor

“…The Stability Theorem enunciated in the Introduction is discussed in Refs [14][15][16][17][18]. Reference [18] gives the Operational Theorem, which is a different enunciate of the Stability Theorem useful for calculating the post stall evolution of the constant-speed line. This Operational Theorem is similar to the Stability-Line hypothesis employed by Ref.…”

“…Refs. [16][17][18] estimate the coefficient  x as the axial solidity of the rotor, whose definition is given by Eq. (2).…”