Instability and transition of the flow over a multi-element high-liftairfoil

A series of three-dimensional numerical investigations of the incompressible flow over a 30P30N high-lift airfoil with a span of 20% chord, c, are performed at low Reynolds number (Rec ~ O(10 4 )) at an angle of attack = 4. A well-resolved direct numerical simulation is implemented via a high-order spectral element method. The present study focuses on Rec = 0.832 10 4 and aims to understand the instability mechanisms that fundamentally govern the transition route to turbulence over the high-lift airfoil. No artificial disturbances are introduced, and therefore, the flow transition originates from the instability of the small disturbances introduced by the truncation error. Counter-rotating Grtler vortices, characteristic of centrifugal instability, are observed in the streamwise direction shortly downstream of the main-airfoil-element leading edge; this agrees with the recent experimental observations of Wang et al. (2018) at the same Rec. This phenomenon, however, is unexpected over a convex surface. The appearance of Grtler vortices is likely caused by a curved shear layer emanating from the slat cove, just above the leading edge of the main-airfoil-element, as posited by Wang et al. (2018). The present work looks into this phenomenon more closely. The presence and intensity of the centrifugal effect are identified via the inviscid Rayleigh criterion and the Grtler number. As the flow evolves further downstream and starts to separate, Kelvin-Helmholtz (K-H) instability takes over and leads to the formation of quasi two-dimensional (2D) vortices. While propagating downstream, these quasi-2D coherent structures get distorted and reoriented towards the streamwise direction prior to the occurrence of more complex structures in the separation region. Such flow development aft of the separation region, for the Rec considered, qualitatively resembles a prototype of the transition observed immediately downstream of a laminar separation bubble. One question this study attempts to answer is whether the Grtler vortices extend sufficiently far downstream such that they start to interact with the K-H instability. In the current work, both low-and highorder mean statistics (coefficient of skin friction, mean-velocity profiles, Reynolds stress components, and turbulent kinetic energy budget, etc.) are calculated to highlight the flow features. Instantaneous vortical structures are also presented to provide insights into the flow evolution.

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