Some features of surface pressure fluctuations in turbulent boundary layers with zero and favorable pressure gradients

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Virginia Polytechnic Institute and State University

Various researchers are interested in the structure of the surface pressure fluctuations for the development and use of noise prediction techniques for helicopter and turbomachinery rotors. This study, conducted in the Virginia Tech low speed boundary layer wind tunnel, covered the effects of zero and favorable streamwise pressure gradient flows on the surface pressure fluctuation spectra, coherence and convective wave speeds in turbulent boundary layers for momentum Reynolds numbers from 3000 to 18,800. The acceleration parameter, pressure gradient flow. K is near 2x10⁻⁷ for the favorable Small pinhole condenser microphones were used to obtain the surface pressure fluctuation data for all test cases. The longitudinal and lateral coherence functions and the convective wave speeds were obtained for both streamwise pressure gradient flows.

The results presented are for the surface pressure fluctuation spectra nondimensionalized by different groupings of the outer and inner boundary layer variables. The grouping using the outer variables, Ue, πw and δ₁ collapse the spectra for the low to middle range of frequencies for most test cases. The grouping using the inner variables, Uπ and ν, collapse the spectra for the middle to high range of frequencies for all test cases. The value of p¹/rw was near 3.8 and 2.8 for the smallest values of d⁺ in the zero and favorable pressure gradient flows, respectively.

The spectral data was corrected using the correction developed by G.M. Corcos, but the pinhole correction developed by Bull and Thomas was not used in the data reduction process. However, some discussion is included on the effects of the pinhole correction for the results of this study.

The coherence exhibits a decay that is not exponential in some cases, but the Corcos similarity parameters ωΔx/Uc and ωΔz/Uc collapse the data for all test cases. C The ratio of Uc/Ue shows an increase with increasing ωδ₁/Ue up to a certain value of ωδ₁/Ue where Uc/Ue becomes constant. This was observed in the present results for both streamwise pressure gradient flows.

The experimental results presented show good agreement with previous research.