Effect of spanwise domain size on direct numerical simulations of airfoil noise during flow separation and stall

It is well established that a large spanwise domain size is required for accurate numerical simulations of flow past an airfoil in stall. A number of numerical experiments support this conclusion with regard to aerodynamic and turbulence statistics. However, very little has been reported concerning the effect of the span length on aeroacoustic results. In this paper, a detailed investigation is carried out into the influence of spanwise domain length on the prediction of airfoil stall noise when spanwise periodic boundary conditions are applied. This study is based on direct numerical simulations of an NACA0012 airfoil at Re∞ = 50 000 and M∞ = 0.4 at near- and full-stall conditions. There are three main findings in this paper. First, the far-field acoustics are found to be highly sensitive to the choice of spanwise domain length. In the full-stall case, a span length equal to 20% of the airfoil chord over-predicts the radiated noise by more than 10 dB at low-to-medium frequencies relative to a case with one chord length in span. Discrepancies are found to occur for acoustic wavelengths shorter than the spanwise domain size. Under near-stall conditions, the changes caused by the small spanwise domain are noticeably milder. Second, the lower noise predictions from the large span simulation at low frequencies are attributed to the spanwise breakup of large scale flow structures and reduced spanwise coherence near the trailing edge. Third, a more destructive source phase relationship is observed with a large span for medium frequencies, which was inhibited by the periodic forcing in the small span case.