Nonlinear and nonperiodic optimal forcing analysis on the subsonic flow around an airfoil*

Optimal forcing analysis is a method for extracting the external forces to provide the largest disturbance growth on the base flow field. This provides valuable insights into the physical mechanisms and flow controls. In this study, we proposed an optimal forcing analysis for an unsteady base flow field with a non-periodic temporal distribution considering the nonlinear time-evolution of disturbance field. This extension of the optimal forcing analysis is critical for understanding shock-relating fluid phenomena because it enables the identification of triggers that induce shock waves in the nonlinear time-evolution. 

The proposed method was applied to the two-dimensional subsonic flow around the NACA0012 airfoil with a low angle of attack AoA=2deg and Reynolds number Re=10^4 at M=0.5, 0.75. In a comparison of the extracted optimal forcing, we investigated the effect of compressibility on the instability mechanisms for finite-amplitude and non-periodic disturbances. In this analysis, we found that the magnitude and concentration region of optimal forcing affected the types of instability. Among them, the optimal forcing focused on the separation point with a long temporal wavelength successfully extracted the nonlinear evolution of the finite-amplitude pressure waves and the formation of weak shock waves. In this presentation, we discuss the physical mechanisms of the time evolution of the finite-amplitude disturbance field and the effect of compressibility.