Kinematic and Acoustic Similarities of Separated Turbulent Boundary Layers

Abstract

A similarity model for separated turbulent boundary layer is proposed as a function of the velocity associated with the maximum local mean shear $U_m = \tau_m /\rho$. A linear relation between mean velocity and reduced wall-normal coordinate is observed for approximately 40–50% of the boundary layer height. A corresponding similarity model of the far-field sound pressure levels was also derived. The proposed scaling law shows less variability than the classical trailing-edge noise scaling within a range of the freestream velocity and airfoil’s angle of attack. In comparison to classical trailing-edge noise, the sound pressure level scaling of separated flow is tuned by a factor of $U_m^2$, a non-dimensional velocity variable associated with the maximum mean shear stress in the separated boundary layer.