Avenumber-frequency Spectra of Rbulent-boundary-layer Pressure Asured by Microphone Arrays

Measurements of frequency spectra of pressure along a wind-tunnel wall have been made by single microphones and by a longitudinal array of four flush 0.8-inch circular microphones connected with alternating and with common phase. The alternating-phase array was designed to suppress by its wavenumber filtering the background acoustic duct noise at frequencies near 3 kHz. The measured levels set upper limits on low-wavenumber boundary-layer pressure. Analysis indicates that the high-wavenumber (convective) contribution in this frequency range was probably negligible, but it could not be definitely established whether background noise dominated the spectra or whether the upper bound set on low-wavenumber boundary-layer noise is a close one. On assumption of wavenumber independence in most of the pertinent low-wavenumber domain, an upper bound is given for the wavenumber spectral density of boundary-layer pressure, and its generalization by assumption of {„-independence is discussed. At lower frequencies, in identifiable domains where single-microDhone and array spectra are dominated by the convective wavenumber comoonent of boundary-layer pressure, satisfactory agreement is found with theoretical predictions based on current knowledge of the spectral density in the convective-wavenumber domain and on a measured facial sensitivity distribution for the microphone. In general, salient features of the array spectra correlate well with expectation, and the array technique is demonstrated to be a useful one for the subject purposes. W*j .■«■UIMI—IDMII IUIII»I1HIWIWW Will ■ I ^m | .—W|— liwwyi.1 u LiuwM*MUjwmi UP M'IW i in 'niiinflrtinMw n Report No. 1769 Bolt Beranek and Newman Inc.