Compressibility-Induced Intermittency in Airfoil Flows

The present study focuses on the cycle-to-cycle variation in aerodynamic loads induced by compressibility effects at low-to-moderate Reynolds numbers (Re). To this end, we perform two-dimensional direct numerical simulations (DNS) of flow over a NACA0012 airfoil at an angle of attack of 5º and Re = 50,000 under both incompressible and compressible (Mach 0.4) conditions. Both test cases exhibit qualitatively similar flow features characterized by a closed laminar separation bubble (LSB) with an unstable shear layer that leads to vortex shedding. However, the unsteady behavior of lift (CL) and drag (CD) coefficients differs significantly between the two cases. While the variation in CL and CD for the incompressible case is sinusoidal with a constant amplitude, the compressible case shows a more broadband behavior with intermittent excursions in load coefficients. An ensemble analysis of extreme drag events using Conditional Proper Orthogonal Decomposition (CPOD) reveals that these intermittent spikes are associated with the amplification of closely packed perturbations generated in the LSB, which ultimately trigger vortex merging near the trailing edge on the suction side of the airfoil. A similar vortex merging phenomenon is also observed at a higher Re of 500,000 at Mach 0.4. However, not all merging events at this higher Re result in extreme drag excursions, suggesting the presence of a circulation threshold beyond which the merged vortex can induce such events.