Computation of mistuning effects on cascade flutter

A computational method is described for predicting utter of turbomachinery cascades with mistuned blades. Themethod solves the unsteady Euler/Navier–Stokes equations for multiple-blade passages on a parallel computer using themessage passing interface. A second-order implicit scheme with dual time-stepping andmultigrid is used. 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 frequencymistuning signi cantly changes the aerodynamic damping. The important effect of frequencymistuning is to average out the aerodynamic damping of the tuned blade row over the whole range of interblade phase 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 = coef cient of aerodynamic force in h direction CW = aerodynamic work coef cient c = blade chord length E = total energy per unit mass h = translational blade displacement p = static pressure T = utter period t = time u, v = ow velocity components in x and y directions ub, vb = grid velocity components in x and y directions ū, v ̄ = relative velocity components (u ¡ ub, v ¡ vb) a = rotational blade displacement h = stream tube thickness ratio in x direction N = utter damping coef cient q = density r = interblade phase angle x = utter frequency I