  Flutter stability is a dominant design constraint of modern gas and steam
turbines. To further increase the feasible design space, flutter-tolerant
designs are currently explored, which may undergo Limit Cycle Oscillations
(LCOs) of acceptable, yet not vanishing, level. Bounded self-excited
oscillations are a priori a nonlinear phenomenon, and can thus only be
explained by nonlinear interactions such as dry stick-slip friction in
mechanical joints. The currently available simulation methods for blade flutter
account for nonlinear interactions, at most, in only one domain, the structure
or the fluid, and assume the behavior in the other domain as linear. In this
work, we develop a fully-coupled nonlinear frequency domain method which is
capable of resolving nonlinear flow and structural effects. We demonstrate the
computational performance of this method for a state-of-the-art aeroelastic
model of a shrouded turbine blade row. Besides simulating limit cycles, we
predict, for the first time, the phenomenon of nonlinear instability, i.e., a
situation where the equilibrium point is locally stable, but for sufficiently
strong perturbation (caused e.g. by an impact), the dry frictional dissipation
cannot bound the flutter vibrations. This implies that linearized theory does
not necessary lead to a conservative design of turbine blades. We show that
this phenomenon is due to the nonlinear contact interactions at the tip
shrouds, which cause a change of the vibrational deflection shape and
frequency, which in turn leads to a loss of aeroelastic stability. Finally, we
extend the well-known energy method to capture these effects, and conclude that
it provides a good approximation and is useful for initializing the
fully-coupled solver.
