Numerical and analytical investigations of the effect of the streamwise disturbance on the airfoil-anisotropic turbulence interaction noise

The distortion of transverse velocity component in a turbulent flow was viewed as the main cause of the airfoil leading edge noise, and the streamwise component was therefore seldom considered in the analytical prediction models. However, in real cases, the streamwise fluctuations can also interact with the non-uniform mean flow and produce sound. To study the effect of streamwise disturbance, numerical simulations for anisotropic turbulences with Gaussian energy spectra are conducted. By carefully adjusting the value of the turbulence integral length scales, the kinetic energy of the streamwise fluctuation component is changed while the sound contribution due to the transverse velocity is fixed. The results of thick airfoils at different Mach numbers show that turbulences with higher kinetic energy in the streamwise direction can generate more sound mainly in the upstream direction. Also, an analytical model is proposed to investigate the sound production by the turbulent components interacting with the non-uniform mean flow. The model is inspired by acoustic analogy and is solved employing Born approximation method. It is revealed that a dipole typed source is formed when the streamwise disturbance couples with the mean flow, producing extra sound and altering the acoustic far-field directivities. A correction to the flat plate solution using the proposed model yields better agreement with the numerical results, especially for anisotropic turbulences with higher turbulent kinetic energy in the streamwise direction.