Computation of mistuning effects on cascade flutter

Abstract

A computational method is described for predicting eutter of turbomachinery cascades with mistuned blades. Themethodsolves theunsteadyEuler/Navier‐Stokesequationsformultiple-bladepassageson aparallel computer usingthemessagepassinginterface. Asecond-orderimplicit schemewithdualtime-steppingand multigrid isused. Each individual blade is capable of moving with its own independent frequency and phase angle, thus modeling a cascade with mistuned blades. Flutter predictions are performed through the energy method. Both phase-angle and frequency mistuning are studied. It is found that phase-angle mistuning has little effect on stability, whereas frequencymistuningsignie cantlychanges theaerodynamicdamping.Theimportant effectoffrequencymistuning is to average out the aerodynamic damping of the tuned blade row over the whole range of interbladephase angles (IBPA). If a tuned blade row is stable over most of the IBPA range, the blades can be stabilized for the complete IBPA range through appropriate frequency mistuning. Nomenclature Ch = coefecient of aerodynamic force in h direction CW = aerodynamic work coefe cient c = blade chord length E = total energy per unit mass h = translational blade displacement p = static pressure T = e utter period t = time u, v = e ow velocity components in x and y directions ub, vb = grid velocity components in x and y directions ¯ u, ¯ v = relative velocity components (u i ub, v i vb) a = rotational blade displacement h = stream tube thickness ratio in x direction N = e utter damping coefe cient q = density r = interblade phase angle x = e utter frequency