A transition prediction method for flow over airfoils based on high-order dynamic mode decomposition

This article presents a novel approach for predicting transition locations over airfoils, which are used to activate turbulence model in a Reynolds-averaged Navier-Stokes flow solver. This approach combines Dynamic Mode Decomposition (DMD) with e^N criterion. The core idea is to use a spatial DMD analysis to extract the modes of unstable perturbations from a steady flowfield and substitute the local Linear Stability Theory (LST) analysis to quantify the spatial growth of Tollmien–Schlichting (TS) waves. Transition is assumed to take place at the stream-wise location where the most amplified mode’s N-factor reaches a prescribed threshold and a turbulence model is activated thereafter. To improve robustness, the high-order version of DMD technique (known as HODMD) is employed. A theoretical derivation is conducted to interpret how a spatial high-order DMD analysis can extract the growth rate of the unsteady perturbations. The new method is validated by transition predictions of flows over a low-speed Natural-Laminar-Flow (NLF) airfoil NLF0416 at various angles of attack and a transonic NLF airfoil NPU-LSC-72613. The transition locations predicted by our HODMD/e^N method agree well with experimental data and compare favorably to those obtained by some existing methods (LST/e^N or $\gamma -\stackrel{￣}{R{e}_{\theta \text{t}}}$). It is shown that the proposed method is able to predict transition locations for flows over different types of airfoils and offers the potential for application to 3D wings as well as more complex configurations.