The attenuation of sound by turbulence in internal flows.

The attenuation of sound waves due to interaction with low Mach number turbulent boundary layers in internal flows (channel or pipe flow) is examined. Dynamic equations for the turbulent Reynolds stress on the sound wave are derived, and the analytical solution to the equation provides a frequency dependent eddy viscosity model. This model is used to predict the attenuation of sound propagating in fully developed turbulent pipe flow. The predictions are shown to compare well with the experimental data. The proposed dynamic equation shows that the turbulence behaves like a viscoelastic fluid in the interaction process, and that the ratio of turbulent relaxation time near the wall and the sound wave period is the parameter that controls the characteristics of the attenuation induced by the turbulent flow.

Pressure-Gradient Turbulent Boundary Layers Developing Around a Wing Section.

A direct numerical simulation database of the flow around a NACA4412 wing section at Rec = 400,000 and 5∘ angle of attack (Hosseini et al. Int. J. Heat Fluid Flow 61, 117-128, 2016), obtained with the spectral-element code Nek5000, is analyzed. The Clauser pressure-gradient parameter ß ranges from ≃ 0 and 85 on the suction side, and from 0 to - 0.25 on the pressure side of the wing. The maximum Re𝜃 and Reτ values are around 2,800 and 373 on the suction side, respectively, whereas on the pressure side these values are 818 and 346. Comparisons between the suction side with zero-pressure-gradient turbulent boundary layer data show larger values of the shape factor and a lower skin friction, both connected with the fact that the adverse pressure gradient present on the suction side of the wing increases the wall-normal convection. The adverse-pressure-gradient boundary layer also exhibits a more prominent wake region, the development of an outer peak in the Reynolds-stress tensor components, and increased production and dissipation across the boundary layer. All these effects are connected with the fact that the large-scale motions of the flow become relatively more intense due to the adverse pressure gradient, as apparent from spanwise premultiplied power-spectral density maps. The emergence of an outer spectral peak is observed at ß values of around 4 for λz ≃ 0.65δ99, closer to the wall than the spectral outer peak observed in zero-pressure-gradient turbulent boundary layers at higher Re𝜃 . The effect of the slight favorable pressure gradient present on the pressure side of the wing is opposite the one of the adverse pressure gradient, leading to less energetic outer-layer structures.