Experimental measurements of the frequency spectra and frequency cross‐spectra of the wall pressure fluctuations beneath a turbulent boundary layer were made in a low‐noise flow facility. The data, taken over a range of flow speeds, clearly display a dimensionless frequency (ωδ/uτ=50) at which the spectra achieve a maximum and a low‐frequency range with an approximately ω2 rolloff. The scaling laws for the low‐, mid‐, and high‐frequency regions of the spectrum are established. The cross‐spectral data, obtained over a range of streamwise separations (0.21≤ξ/δ≤16.4), allow for the computations of the decay Γ(ξ,ω) and convection velocity Uc(ξ,ω) of the wall pressure field. These data show the existence of two distinct wave number groups: a high wave number group that scales on the similarity variable k1ξ=ωξ/Uc(ξ,ω) associated with turbulent sources in the log region of the boundary layer, in which eddies decay in proportion to their size, and a low wave number group that defines the cutoff for the large‐scal...

Spectral features of wall pressure fluctuations beneath turbulent boundary layers

Aerodynamic noise of a serrated trailing edge

Wall pressure and shear stress spectra from direct numerical simulations of turbulent plane channel flow are presented in this paper. Simulations have been carried out at a series of Reynolds numbers up to Re? = 1440, which corresponds to Re = 6:92 x 10(4) based on channel width and centerline velocity. Single-point and two-point statistics for velocity, pressure, and their derivatives have been collected, including velocity moments up to fourth order.§ The results have been used to study the Reynolds number dependence of wall pressure and shear stress spectra. It is found that the point spectrum of wall pressure collapses for Re? ? 360 under a mixed scaling for frequencies lower than the peak frequency of the frequency-weighted spectrum, and under viscous scaling for frequencies higher than the peak. Point spectra of wall shear stress components are found to collapse for Re? ? 360 under viscous scaling. The normalized mean square wall pressure increases linearly with the logarithm of Reynolds number. The rms wall shear stresses also increase with Reynolds number over the present range, but suggest some leveling off at high Reynolds number.

Wall Pressure and Shear Stress Spectra from Direct Simulations of Channel Flow

A new analytical model is developed for the prediction of noise from serrated trailing edges. The model generalizes Amiet’s trailing-edge noise theory to sawtooth trailing edges, resulting in a complicated partial differential equation. The equation is then solved by means of a Fourier expansion technique combined with an iterative procedure. The solution is validated through comparison with the finite element method for a variety of serrations at different Mach numbers. The results obtained using the new model predict noise reduction of up to 10 dB at 90 above the trailing edge, which is more realistic than predictions based on Howe’s model and also more consistent with experimental observations. A thorough analytical and numerical analysis of the physical mechanism is carried out and suggests that the noise reduction due to serration originates primarily from interference effects near the trailing edge. A closer inspection of the proposed mathematical model has led to the development of two criteria for the effectiveness of the trailing-edge serrations, consistent but more general than those proposed by Howe. While experimental investigations often focus on noise reduction at 90 above the trailing edge, the new analytical model shows that the destructive interference scattering effects due to the serrations cause significant noise reduction at large polar angles, near the leading edge. It has also been observed that serrations can significantly change the directivity characteristics of the aerofoil at high frequencies and even lead to noise increase at high Mach numbers.

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D.M. Chase

Papers

The character of the turbulent wall pressure spectrum at subconvective wavenumbers and a suggested comprehensive model