Direct numerical simulations of tonal noise generated by laminar flow past airfoils

A numerical investigation is presented of noise generated by flow past symmetric NACA airfoils with different thickness and at various angles of attack at M=0.4 and a Reynolds number based on chord of Re=50,000. Direct numerical simulations (DNS) are employed to directly compute both the near-field hydrodynamics and the far-field sound. The DNS data are then used to investigate whether the approach of determining tonal noise radiation based on the surface pressure difference, as done in the classical trailing-edge theory of Amiet, yields satisfactory results for finite thickness airfoils subject to mean loading effects. In addition, the accuracy of Amiet's surface pressure jump function is evaluated. Overall, increasing airfoil thickness to 12% chord, which corresponds to a trailing-edge angle of 16.8°, an unexpected phase change between the incident and scattered pressure is found at the frequency of the forced instability waves. This phase change is attributed to the flow oscillating around the trailing edge at a separate wake frequency. For the largest incidence investigated, Amiet's response function does not predict the total surface pressure difference as accurately as for zero of small incidence at the vortex shedding frequency, resulting in a poor prediction of the directivity and amplitude of the acoustic pressure. Moreover, predicting the airfoil self-noise based on the surface pressure difference appears not to be generally applicable at higher angles of attack because the radiated sound is only partly due to classical trailing-edge noise mechanisms. In these cases, it appears as if volume in the flow cannot be neglected