A Semi-Empirical Surface Pressure Spectrum Model for Airfoil Trailing-Edge Noise Prediction

Abstract

A semi-empirical model to determine the wall pressure frequency spectrum beneath a twodimensional, pressure gradient turbulent boundary-layer is presented. The model is derived based on the experimental wall pressure data of various research groups. The experimental database includes both the equilibrium flat plate and non-equilibrium airfoil boundary-layer flow cases and covers a large range of Reynolds numbers, 1.0 × 10 3 < Re δ 2 < 3.0 × 10 4. The enhanced model is a combination of the modified Chase-Howe, Goody and Rozenberg models, and is a simple function of the ratio of pressure and timescales of the outer to inner part of the boundary-layer. The key advantage of the present model is that it incorporates the Reynolds number, the boundary-layer loading as well as pressure gradient effects through an amplitude scaling function and timescale ratio, and compares well to the experimental data. Spectral features of the detailed measurement data and various scaling behavior of the wall pressure spectrum are elaborately investigated. A summary of the results on the applicability and limitation of the model for various test cases is discussed. The enhanced model is further applied to develop an airfoil turbulent boundary-layer trailing-edge interaction (TBL-TE) far-field noise prediction scheme. Prediction results are compared with the well established experimental database and encouraging results are found. The enhanced Wall Pressure Fluctuation (WPF) as well as trailing-edge noise spectra models accuracy for the maximum noise level is in ±2dB range for the test cases examined. The model can be applied further for acoustic airfoil design and optimization and in various aeroacoustic applications. NOMENCLATURE Latin & Greek Symbols c [m] Chord length C f [−] Skin friction coefficient, C f = τ w /0.5ρ ∞ U ∞ 2 c 0 [m/s] Speed of sound

Effect of Surface Roughness Geometry on Boundary-Layer Transition and Far-Field Noise

“…To further validate the comparison between the present experiment and the measurements by Brooks et al [6], the model for the wallpressure spectrum as proposed by Kamruzzaman et al [53] is used to estimate the far-field noise through the trailing-edge noise formulation by Roger and Moreau [54], which is available in the OptydB library (see also Ref. [55]).…”

Numerical study of 3-D finlets using Reynolds-averaged Navier–Stokes computational fluid dynamics for trailing edge noise reduction

“…Because the RANS simulation is unable to predict the spanwise length scale, Λ3 is computed from the Corcos’ empirical model 19 as equation (7) where the constant b = 1.0 is suggested by Kamruzzaman et al. 21 Note that one of the important effects of 3-D finlets is to reduce Λ3 by decreasing the spacing between adjacent finlets; hence, equation (7) may not be valid for finlets with small spacing. Therefore, a new spanwise length scale model is needed for these cases, which will be introduced in the following section.…”

Effect of Sensor Mounting and Flow History on Measured Wall Pressure Spectra

“…Rozenberg argued that the effect of the pressure gradient on the wall pressure spectra could be evaluated correctly by Clauser's parameter. Later, Kamruzzaman et al [10] and Catlett et al [11] proposed the APG pressure models using a similar concept to Rozenberg's model. In contrast to those models, Hu [12] used the boundary layer shape factor to predict the spectral change due to the pressure gradient.…”