Quasi Steady Prediction of Coupled Bending Torsion Flutter Under Classic Surge

Abstract

In this paper, a quasisteady method is developed for predicting the coupled bendingtorsion flutter in a compressor cascade during classic surge. The classic surge is one of the major compressor flow field instabilities involving pulsation of the main flow through the compressor. The primary reason for the occurrence of the classic surge is the stalling of the blade rows and if the conditions are favorable this can trigger flutter, which is a selfexcited aero elastic instability. The classic surge flow is modeled by using the wellestablished model of Moore and Greitzer and the obtained flow condition is used to determine the aerodynamic loads of the cascade using the linearized Whitehead's theory. The cascade stability is then examined by solving the two dimensional structural model by treating it as a complex eigenvalue problem. The structural stability is analyzed for a range of values of the frequency ratio and primary emphasis is given for the frequency ratio value of 0.9 as many interesting features could be revealed. The cascade shows a bifurcation from bending flutter to the torsional one signifying that only one of the flutter modes are favored at any instant in time. The torsional flutter is found to be the dominant flutter mode for a range of frequency ratios during classic surge whereas the bending flutter is found to occur only for some values of frequency ratio very close to unity as the torsional loads acting on the blades are found to be orders of magnitude higher than the bending loads. A rapid initiation of torsional flutter is seen to occur during classic surge for frequency ratio values very close to unity and it is perceived that during blade design, frequency ratios should be kept below 0.9 to prevent the flutter possibilities. An estimate of structural energy variation with time indicates that even if the total structural energy is negative one of the modes can go unstable during classic surge.