Turbulent Flow Over a Low-Camber Pitching Arc Wing

Aerodynamics of pitching airfoils and wings are of great importance to the design of air vehicles. This investigation presents the effect of camber on flow field and force coefficient for a pitching circular-arc airfoil. The wing considered in this study is a cambered plate of zero thickness which executes a linear pitch ramp, hold and return of 45$\,^{\circ}$ amplitude. The momentum equation is solved on a mesh that is attached to the wing and executes a pitching motion with the wing about a pivot point located at 0.25-chord or 0.50-chord distance from the leading edge. Turbulence is modeled by the $k-\omega$ SST model. Using the open-source software OpenFOAM, the conservation equations are solved on a dynamic mesh and the flow is resolved all the way to the wall ($y^+\approx 1$). The computations are performed for Re = 40,000 with the reduced pitch rate equal to $K=c\dot{\theta}/{2U_{\infty}} = 0.2$. The results are presented for three wings, namely, a flat plate (zero camber) and wings of 4\% and 10\% camber. It is found that the flow has complex features such as leading-edge vortex, near-wake vortex pairs, clockwise and counter-clockwise vortices, and trailing-edge vortex. While vortices are formed over the flat plate, they are formed both over and under the cambered wing.