Coherent hydrodynamic waves and trailing-edge noise

Abstract

© 2017, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.The turbulent flow over a NACA 0012 airfoil at zero angle of attack was analysed numerically using a compressible-flow large-eddy simulation for Mach number M∞ = 0:115. Snapshots of the flow field were analysed using Proper Orthogonal Decomposition (POD) in frequency domain, in order to extract the dominant coherent structures of the flow. Homogeneity in the spanwise direction allows application of a Fourier decomposition in span prior to POD, and focus is given to two-dimensional disturbances since these are expected to dominate acoustic scattering. The POD results show, in general, coherent hydrodynamics waves propagating from the region of boundary-layer tripping towards the trailing-edge, characterising a non-compact source akin to wavepackets seen in turbulent jets. The results also show the high contribution of the first POD mode in the acoustic field for each analysed frequency. To understand how coherent structures in the turbulent field can be modelled, the optimal harmonic forcing and the associated linear response of the flow using the singular value decomposition of the linear resolvent operator was performed in a locally parallel analysis. Such resolvent analysis shows that the leading POD modes can be associated to optimal, linearised flow responses.