Analysis of a Linear Model for Non-Synchronous Vibrations Near Stall

Abstract

Non-synchronous vibrations arising near the stall boundary of compressors are a recurring and potentially safety-critical problem in modern aero-engines. Recent numerical and experimental investigations have shown that these vibrations are caused by the lock-in of circumferentially convected aerodynamic disturbances and structural vibration modes, and that it is possible to predict unstable vibration modes using coupled linear models. This paper aims to further investigate non-synchronous vibrations by casting a reduced model for NSV in the frequency domain and analysing stability for a range of parameters. It is shown how, and why, under certain conditions linear models are able to capture a phenomenon, which has traditionally been associated with aerodynamic non-linearities. The formulation clearly highlights the differences between convective non-synchronous vibrations and flutter and identifies the modifications necessary to make quantitative predictions.

Suppression of Nonsynchronous Vibration Through Intentional Aerodynamic and Structural Mistuning

“…To introduce aerodynamic mistuning, we assume that there are different types of blades with different flow fields but we keep the force coefficients constant. This is a reasonable assumption since they were found to vary little between operating points and have little influence on stability [1,19]. In the model described above this is represented by a modified attenuation coefficient r a,n , which depends on the blade as illustrated in Fig.…”

“…The aerodynamic disturbance can be quantified as a superposition of the force induced directly by the blade vibration F v (t) and that caused by a circumferentially propagating vortical disturbance F a (t), which will also be referred to as the aerodynamic disturbance in the following. In References [1] and [19] this is laid out in detail. The equation of motion for the system of N B blades is given by:…”

“…Following the same approach as in [19], we will now derive an expression for the forces acting on one blade. The force due to vibration F v is proportional to the blade deflection and can be expressed with the complex coefficient Cv :…”

“…The model was validated against numerical and experimental results in [1,19]. To study the effects of mistuning on a representative case, the force coefficients C * a , Cv as well as vibration frequency ω R v and number of blades N B are set to those of the transonic research compressor investigated in [1].…”

“…This has been extensively studied in the context of flutter and forced response, see for example References [16][17][18] The aim of this paper is to demonstrate and explain the effectiveness of different types of mistuning (structural and aero-dynamic) to prevent convective NSV. This will be achieved by incorporating mistuning in the model developed in Reference [1] and [19], which was previously validated against experimental measurements for the Darmstadt transonic compressor.…”