Noise Transmission from the Turbulent Boundary Layer

Abstract

A theoretical study is made of noise spectra radiated by vibration of thin, stiff, flat plates under the action of turbulent boundary layer pressure fluctuations. The transmitted radiation investigated arises from the streamwise convection of quasi-static pressure fluctuations by the mean flow, and is critically influenced by the dispersive character of wave propagation in the plates. At moderate subsonic Mach numbers the total transmitted power for sufficiently thin boundary layers varies approximately as a power of Mach number between five and six, rising more steeply as transonic velocities are approached and more gradually at sufficiently low Mach numbers. The dominant transmitted frequencies shift up with Mach number, in some typical cases varying as Mach number squared. Plate parameters which importantly influence sound transmission include mass/unit area, size of independent plate sections, frequency of lowest vibrational mode of the independent sections, and damping factors for the various vibrational modes. For sufficiently thin boundary layers, the transmitted spectrum shape is essentially independent of boundary layer thickness, but the spectrum level varies as approximately the fourth power of thickness. For thicker boundary layers, the dependence is flatter, and the Mach number dependence is also flattened. The anticipated effectiveness of transmission reducing procedures including damping and stiffening of the plate sections, and boundary layer suction are discussed. [This work was supported by the Air Force, Wright Air Development Center.]