On the effect of streamwise disturbance on the airfoil-turbulence interaction noise

Usually the prediction of airfoil-gust interaction noise is mainly based on the flat plate solution, and only the transverse velocity disturbance that is perpendicular to the flat plate surface is considered. However, the solution might underestimate the sound generation in non-uniform mean flows for finite thickness airfoils, in which the velocity disturbance in the streamwise direction could probably produce sound as well. The effect is studied in this work by using both numerical simulations and theoretical analysis. To highlight the effect of streamwise disturbance, the anisotropic turbulences with constant transverse velocity components while varying streamwise components are employed, which can be realised by adjusting the integral length scales in the Gaussian energy spectra. The simulation results explicitly show that more sound is produced by the streamwise components for airfoils at higher Mach numbers when the flow non-uniformities are more significant. An analytical model based on acoustic analogy to account for the sound generation by the coupling between the gust and non-uniform mean flows is proposed, which explains the observations in the numerical simulation well. Also, a correction to Amiet's flat plate solution using the proposed model yields better agreement with the numerical results, especially for anisotropic turbulences with larger integral length scale in the streamwise direction.