Improved One-Shot Approach for Modeling Viscous Transonic Limit Cycle Oscillations

In this paper, the harmonic-balance-based One-shot method is presented for modeling limit cycle oscillations (LCO) of two-degree-of-freedom (2-DOF) pitch/plunge airfoils in viscous, transonic flow regimes. It is shown that using the original version of the One-shot approach for which the reduced velocity is prescribed as an input, only the stable LCO branch can be captured. A modification to the technique is proposed to extend its capability to capture the unstable LCO branch below the linear flutter point. In this new approach, the amplitude of pitching is prescribed instead of the reduced velocity. This necessitates simultaneously updating the reduced frequency and the reduced velocity at each aeroelastic iteration. The update procedure is based on optimization of a simple figure-of-merit. The original and improved versions of the One-shot approach are implemented in a single solver with minor modifications to attain maximum flexibility in determining LCO conditions. Numerical results demonstrate a good agreement with those reported in the literature as well as those obtained using the HB/LCO method and a traditional time-accurate approach. Finally, the computational efficiency of the One-shot method is discussed.