On the radiated noise due to boundary-layer transition

Abstract

A theory is presented for the noise radiated by the incompressible boundary-layer transition that occurs on an infinite, rigid flat plate. It is hypothesized that it is the intermittency of the boundary-layer flow within the transition zone that is dominant in noise production. Using Lighthill’s analogy, it is shown that dipole, quadrupole, and octupole sources are generated. The dipole sources are attributable to the shear stress fluctuations that occur in transitional flow while the others are due to fluctuating Reynolds stresses and their images. Under the assumption that dipole sources are more efficient than quadrupoles or octupoles when the Mach number is very small, the power spectrum of the radiated noise due to the dipole contribution is derived. The spectral level rises at 6 dB/octave, peaks at a frequency corresponding to the time it takes for a turbulence burst to convect through the transition region, and then drops off again at 6 dB/octave. The radiation efficiency is analyzed and found to be quite low; it is only 20% of that for a fully developed turbulent boundary-layer flow.

Turbulent boundary-layer noise: direct radiation at Mach number 0.5

“…In a similar manner, the noise generated by specific features of the TBL has been investigated. In particular, Lauchle (1980) considered sound wave production during the boundary-layer transition. In an attempt to shed a new light on sound sources of TBL, Hardin (1991) analysed the noise generated by various vortical phenomena such as the formation of horseshoe vortices and the emergence of viscous sublayer bursts.…”

Transition noise—The role of fluctuating displacement thickness

“…In essence, the analytical methods parallel those of an earlier analysis in which the role of a fluctuating shear stress was addressed [1]. Based on numerical calculations of the power spectral density and on the relative magnitudes of the radiation efficiency, the mechanism treated in the present paper is foind to be much more productive as a noise source than is the shear stress mechanism.…”

“…7 is a prediction for the shear stress contribution to the transition zone noise [1]. Clearly, the fluctuating displacement thickness mechanism appears to dominate.…”

“…shear stress on the radiated noise due to incompressible boundary-layer transition [1]. In the development of that solution, several types of sources were identified under the assumption of the boundary layer flow being confined to one side of an infinite rigid planar surface.…”

“…The power spectrum and radiation efficiency are predicted using analytical techniques similar to those of Ref. [1]. To help in the verification of this theory, three examples will be presented in which experimental data exist.…”