Wave Number Frequency Spectra of a Lifting Wake for Broadband Noise Prediction

Abstract

Measurements of wave number frequency spectra of velocity fluctuations have been made using two three-component hot-wire probes in the wake of a rectangular NACA 0012 half-wing at a 5-deg angle of attack. Spectra were measured along spanwise lines in the near two-dimensional part of the wake, in the stretched region where the wake begins to wind around the vortex, directly above the vortex core, and radially from the core center. Dominated by the large-scale organized motions present in the wake, the spectra show little similarity with the von Karman isotropic turbulence spectrum. Outside the core, upwash spectra contain a single maximum at the passage frequency of these large structures. Motions associated with this peak are highly anisotropic, both in terms of velocity components and length scales. Similar anisotropy is also seen at higher wave numbers, suggesting either that the smaller scale turbulent motions are organized by the large eddies or that the nonsinusoidal components of those eddies contribute significantly to the spectrum at higher wave numbers. The implications of these results for broadband noise prediction have been assessed by considering the sound radiation from this turbulent flow over a semi-infinite flat plate. The major conclusion is that the correlation length scales of the flow are small compared to the acoustic wavelength and so are well represented by their values at zero spanwise wave number. However, the blade response function has a variation with spanwise wave number that cannot be ignored and significantly influences the spanwise directionality.