Recovery of the Koopman modes of a Leading-Edge separated aerofoil flow via a proper orthogonal decomposition rank reduction

Abstract

Koopman modes are presented for a leading edge separated aerofoil flow with turbulent recirculation. The specific flow configuration is a NACA 0015 aerofoil at an angle of attack of 18◦ and a chord based Reynolds number of 3 × 104. This decomposition approximates the evolution of a nonlinear system by a linear operator, the eigenvectors of which represent the spatial form of the fluctuations, and the eigenvalues represent the associated temporal frequencies and growth rates. Proper orthogonal decomposition (POD) modes are used to create a reduced rank linear operator from which the Koopman modes are determined. The sensitivity to the number of PODmodes used in the rank reduction is assessed. The dominant frequencies identified by the Koopman eigenvalues coincide with the dominant frequencies determined from a Fourier analysis of probe histories.