Trailing-edge noise from the scattering of spanwise-coherent structures

A large-eddy simulation of turbulent, compressible flow around a NACA 0012 airfoil at zero angle of attack and Mach number 0.115 is used to study mechanisms of trailing-edge noise. The boundary layers at both sides of the airfoil have a forced transition near the airfoil leading edge, and are turbulent near the trailing-edge. Flow-acoustic correlations and spectral (frequency-domain) proper orthogonal decomposition (SPOD) are used to evaluate turbulent structures that are relevant for the radiated sound. Homogeneity in the spanwise direction allows application of a Fourier decomposition in span prior to both correlations and SPOD. It is known that acoustic theory, based on an analysis of the tailored Green's function modeling trailing-edge scattering, shows that only spanwise wave numbers k(z) satisfying k(z) < k, where k is the acoustic wave number, lead to radiated sound; two-dimensional disturbances (k(z) = 0) always satisfy this criterion, and thus spanwise-coherent structures are expected to be important for trailing-edge noise. Analysis of turbulence statistics of the boundary layer close to the trailing edge shows that the well-known, dominant streaky structures have k(z) > k and thus should not contribute to the radiated sound. To investigate this further using simulation data, flow-acoustic correlations are obtained using either the standard two-point analysis or considering two-dimensional disturbances in velocity and pressure fields, and results show significant correlation coefficients (of about 0.5) once two-dimensional disturbances near the trailing edge are isolated. A further increase of correlation peaks (up to 0.7) is obtained once the antisymmetric parts of the fields is considered, reflecting the classical antisymmetric nature of trailing-edge scattering. SPOD is then used for frequencies around the peak radiated sound to examine the structure of two-dimensional disturbances in the trailingedge region and their contribution to radiated sound. Leading SPOD modes show coherent hydrodynamic waves propagating from the region of boundary-layer tripping toward the trailing edge, characterizing a noncompact source akin to wave packets seen in turbulent jets. These leading SPOD modes have significant contribution to the radiated sound, as two modes lead to 50% of the acoustic intensity for the lower studied frequencies. The present results point to the scattering of spanwise-coherent boundary-layer structures as the dominant mechanism of trailing-edge noise in this flow.