Modeling of Flow about Pitching and Plunging Airfoil Using High-Order Schemes

Abstract

Abstract : A high-order non-uniform compact finite-difference algorithm with numerical filtering and low storage Runga-Kutta scheme is developed to perform numerical simulations on orthogonal grids generated about plunging and pitching airfoils. The grids, which move with the pitching and plunging airfoil, are generated using Streamfunction as a coordinate approach (SFC). SFC is widely used in combination with lower-order schemes in Computational Fluid Dynamics. The straightforward implementation of SFC create rather coarse grid at the solution accuracy, non-uniform SFC grid with appropriate grid stretching and filtering of solution is implemented. The different kinds of SFC grid generation methods and the grid clustering in the vicinity of stagnation point are discussed. The applications of the developed grid generator and numerical solver to problems based on linearized Euler equations, for which analytical solutions are available, are shown first. Then, the methodology is applied to unsteady aerodynamics of pitching and plunging airfoils. The application of the developed grid generator and numerical solver to plunging airfoil problems are discussed and compared with available experimental data including lift force for plunging NACA0012 airfoil and visualization of vortical flowfield for plunging SD7003 airfoil. Finally, the use of flapping airfoil for control of gust-induced oscillations of airfoil lift force is discussed.