Nonlinear optimal perturbation analysis of quasi-periodic flow around an airfoil

The nonlinear optimal perturbation (NLOP) analysis is a stability analysis method to extract the most growing disturbance at given evaluation time around the base flow. While the previous studies focused on the growth of small initial perturbation in theflow field, we consider the case with large magnitude of initial perturbation in the compressible external flow. For this purpose, the NLOP analysis method for large initial disturbance norm was newly formulated. The method was applied to the problem of the trailing edge noise phenomenon around the NACA 0012 airfoil. This trailing edge noise is known to be a quasi-periodic phenomenon in the subsonic andmoderate Reynolds number regime. The obtained nonlinear optimal perturbation showed a series of disturbance vortices on the suction side of airfoil like the two-dimensional Tollmien-Schlichting wave. This disturbance showed a similarity to that of NLOP for the circularcylinder as well as the formation of laminar separation bubble. The dependence of the NLOP on the evaluation time and the magnitude of the initial disturbance was investigated in relation to the induced fluid instability. The transient disturbance growth was also analyzed.