High-order accurate simulations of unsteady flow past plunging and pitching airfoils

Abstract

This paper presents simulations of unsteady flow past plunging and pitching airfoils using a high-order spectral difference (SD) method. Both third-order and fourth-order SD methods are employed on unstructured quadrilateral grids for the plunging airfoil at a low Reynolds number. The vortex shedding pattern of an airfoil in an oscillating plunge motion becomes asymmetric at a sufficiently high frequency. The SD method is able to capture this effect and reveal a fine structure that closely replicates the experimental photograph. Interestingly, our simulations also predict that the degree of this asymmetry increases with Reynolds number. Unsteady flow at a higher Reynolds number past a pitching airfoil is studied using the fifth-order SD method. Our predictions show very good agreements with the available experimental data. The developed high-order accurate SD algorithms could enable high-order accurate simulations of unsteady flow past flapping Micro-Air-Vehicles (MAVs).