Circulation dynamics of small-amplitude pitching airfoil undergoing laminar-to-turbulent transition

This study is motivated by the non-linear behavior of the lift response of a pitching airfoil with a small amplitude and frequency where a linear behavior is expected. The validated gamma -Re-theta transition model coupled with k-omega SST (shear stress transport) turbulence model was utilized to solve the unsteady Reynolds-averaged Navier-Stokes (URANS) equations for a harmonically pitching NACA 0012 at Reynolds numbers 75 x 10(3), 200 x 10(3) and reduced frequencies 0.05 - 0.3. First, the numerical setup was validated against experimental results for a pitching airfoil undergoing laminar-to-turbulent transition. Then, the circulation dynamics were investigated following an exact derivation of the Kutta condition. Unlike the classical Kutta condition which assumes a vanishing pressure loading at the sharp trailing-edge, it is shown that the transition induces non-linearity in the lift dynamics by creating a significant pressure variation across the boundary layer in the vicinity of the trailing-edge, affecting the development of the bound circulation around the airfoil. Moreover, the effects of reduced frequency, pitching amplitude and Reynolds number on the circulation dynamics were studied in both frequency and time domains. The results shed light on the further enhancement of potential flow-based solutions to capture non-linearity in the lift dynamics due to transition. (C) 2020 Elsevier Ltd. All rights reserved.

Automated summary

This study uses the unsteady Reynolds-averaged Navier-Stokes equations to simulate the lift response of a pitching airfoil, and reveals that the pressure variation induced by the transition leads to non-linearity in the lift dynamics, affecting the development of the bound circulation around the airfoil.