Decomposing the aerodynamic forces of low-Reynolds flapping airfoils

We present direct numerical simulations of flow around flapping NACA0012 airfoils at relatively small Reynolds numbers, $Re = 1000$. The simulations are carried out with TUCAN, an in-house code that solves the Navier-Stokes equations for an incompressible flow with an immersed boundary method to model the presence of the airfoil. The motion of the airfoil is composed of a vertical translation, heaving, and a rotation about the quarter of the chord, pitching. Both motions are prescribed by sinusoidal laws, with a reduced frequency of $k=1.41$, a pitching amplitude of 30deg and a heaving amplitude of one chord. Both, the mean pitch angle and the phase shift between pitching and heaving motions are varied, to build a database with 18 configurations. Four of these cases are analysed in detail using the force decomposition algorithm of Chang (1992) and Mart\'{\i}n Alc\'antara et al.(2015). This method decomposes the total aerodynamic force into added-mass (translation and rotation of the airfoil), a volumetric contribution from the vorticity (circulatory effects) and a surface contribution proportional to viscosity. In particular we will focus on the second, analysing the contribution of the leading and trailing edge vortices that typically appear in these flows.