Trailing-edge noise from the scattering of spanwise-coherent structures
Author
Alex Sano
Advisor
- Advisor André Valdetaro Gomes Cavalieri
Concentration Area
Aerodinâmica, Propulsão e Energia
Defense Date
17/06/2016
Thesis Number
71822
Abstract
We study mechanisms of noise generation by an airfoil at zero angle of attack using flow-acoustic correlations, and spatial stability analysis at di?erent x/c velocity profiles along the airfoil. Firstly we use a large-eddy simulation (LES) of the compressible tur- bulent flow around a NACA0012 airfoil at Mach number 0.115. With this simulation we analyse flow fluctuations around the airfoil, such as pressure and velocity, and relate them to the far-field sound using standard correlation techniques. Similar to the results of Cavalieri et al. (2013), who have obtained more significant flow-acoustic correlation for turbulent jets when the axisymmetric mode was isolated, we have noticed higher correlations in the present problem when the two-dimensional mode, i.e., spanwise-averaged fluctuations, was isolated from the turbulent flow and subsequently correlated to the acoustic pressure. This result is justified theoretically by an analysis of the tailored Green's function for a half plane, where we find that a necessary condition for trailing edge scattering is |kz | < k, where kz is the spanwise wavenumber of turbulent disturbances and k is the acoustic wavenumber. Two-dimensional perturbations, associated to kz = 0, are always radiating. Isolation of spanwise-coherent disturbances is thus a means of filtering non-radiating structures. In light of the relation between the disturbances around the airfoil with the far-field noise, using standard correlation techniques, we use the methods of spatial stability analysis as a reduced-order model of two-dimensional flow fluctuations as hydrodynamic instability waves. Turbulent mean profiles in the trailing-edge region are used as base-flows. The analysis shows a number of marginally stable modes, with slow decay in the streamwise direction. Stability eigenfunctions are compared to the two-dimensional part of the LES fields, analysed using proper orthogonal decomposition; comparisons of power spectral densities and phases show good agreement for all flow variables, taken at relevant frequencies for trailing-edge noise. We can thus see the sound-producing mechanism in this flow to be the scattering of spanwise-coherent, hydrodynamic waves in the boundary-layer reaching the trailing edge.
