Strong transient effects of the flow around a harmonically plunging NACA0012 airfoil at low Reynolds numbers

The flow pattern around a NACA0012 airfoil undergoing harmonic plunging motion corresponding to the deflected wake phenomenon reported by Jones and Platzer (Exp Fluids 46:799–810, 2009) is investigated in detail using direct numerical simulations. An arbitrary Lagrangian–Eulerian formulation based on an unstructured side-centered finite volume method is utilized in order to solve the incompressible unsteady Navier–Stokes equations. The Reynolds number is chosen to be 252, and the reduced frequency of plunging motion (k = 2π fc/U_∞) and the plunge amplitude non-dimensionalized with respect to chord are set to be 12.3 and 0.12, respectively, as in the experimental study of Jones and Platzer (2009). The present numerical simulations reveal a highly persistent transient effect, and it takes two orders of magnitude larger duration than the heave period to reach the time-periodic state. In addition, the three-dimensional simulation reveals that the flow field is three-dimensional for the parameters used herein. The calculation reproduces the deflected wake and shows a good agreement with the experimental wake pattern. The instantaneous vorticity contours, finite-time Lyapunov exponent fields and particle traces are presented along with the aerodynamic parameters including the lift and thrust coefficients.