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.

中文翻译：

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完全耦合谐波平衡方法和精细能量方法的发展，用于计算带有非线性摩擦接触的叶片盘颤振引起的极限循环振荡

颤振稳定性是现代燃气轮机和蒸汽轮机的主要设计约束。为了进一步增加可行的设计空间，目前正在研究耐振设计，该设计可能会经历可接受但不会消失的水平的极限循环振荡（LCO）。有界的自激振荡是先验的非线性现象，因此只能用非线性相互作用来解释，例如机械接头中的干粘滑摩擦。当前可用的叶片颤振模拟方法最多只能在一个域，结构或流体中考虑非线性相互作用，并在另一域中将行为假定为线性。在这项工作中，我们开发了一种能够解决非线性流动和结构影响的全耦合非线性频域方法。我们演示了这种方法的计算性能，用于带罩涡轮叶片排的最新气弹模型。除了模拟极限循环外，我们还首次预测了非线性不稳定性现象，即平衡点局部稳定但存在足够强的扰动（例如由冲击引起）的情况，干摩擦耗散无法约束颤振。这意味着线性化理论并不一定会导致涡轮叶片的保守设计。我们表明，这种现象是由于尖端护罩处的非线性接触相互作用引起的，从而导致振动偏转形状和频率发生变化，进而导致气动弹性稳定性的损失。最后，我们扩展了众所周知的能量方法来捕获这些效果，