Simulation of Tonal Noise Generated by Transition Flow Past Airfoil Using High-Order Schemes on Unstructured Grids

Abstract

The time-dependent, compressible Navier-Stokes (N-S) equations describe both acoustic generation and propagation phenomena. Recently Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES) of transient multi-scale, multi-physics flow phenomena have become promising models of analysis for aeroacoustics. However, to minimize sound propagation error, a large number of grid elements would be necessary to resolve all the scales accurately. This study applies high-order (up to 4 th order) spatial and temporal schemes for an unstructured, pressure-based N-S solver. Unlike the popular Discontinuous Galerkin method, the present approach doesn’t increase the degrees-of-freedom in each cell but instead adds higher-order correction terms through a successive differentiation. Unlike the k-exact least square method, which involves a large amount of extra storage, the current method adds only slight overhead and can be applied to an existing CFD solver with minimal modification. High-order spatial and temporal accuracies of the present schemes are verified by comparison with analytical solutions. Several benchmark problems including acoustic signal propagation and tonal noise generation from an NACA0012 airfoil are used for validation and demonstration of the high-order schemes. Fine detailed physics are revealed by the demonstration cases, and high-order accuracy with minimal overhead is successfully demonstrated.