Mode decomposition and reconstruction of dynamic stall flow field of an elliptic airfoil

In order to investigate the dynamic stall characteristics of elliptic airfoils and capture the main unsteady structures of the flow field, a numerical method was established based on unsteady Reynolds-averaged Navier-Stokes equations with SST k-ω and γ-Re_θt turbulence transition models. The method was applied to simulate deep dynamic stall of an elliptic airfoil with a relative thickness of 16%. The unsteady characteristics of the flow field and the variations of aerodynamic coefficient were thoroughly discussed in the time domain. Dynamic mode decomposition (DMD) was employed to extract the characteristics of velocity and pressure fields, followed by flow field reconstruction and error evaluation using a conjugate-mode truncation method based on the theory of modal energy proportion. The results showed that the separation bubbles generated by the elliptic airfoil at the leading edge during the upstroke process served as a precursor to dynamic stall vortex formation. The modes of each order effectively characterized the dynamics of dynamic stall, consistent with the main flow features in the time domain. While conjugate modes contributed to the unsteady components of the flow field, the first-order DMD mode reflected the uniform flow field with characteristics of deep stall of the airfoil. Excluding the first-order mode, the reconstructed flow field retaining 75%—95% energy of the conjugate modes captured variations of the aerodynamic coefficients in the time domain to a certain extent, but failed to describe fine unsteady details accurately. The reconstructed flow field using 99% energy of the conjugate modes demonstrated a decent accuracy in aerodynamic coefficient prediction and effectiveness in dimensionality reduction despite certain deciations during severe flow separation and limited accuracy in capturing fine flow details of near-wall separation bubbles, showing promising potential for engineering applications.