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

A semi-empirical model to determine the wall pressure frequency spectrum beneath a two-dimensional, 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 times 10³ < Re_δ2 < 3.0 times 10⁴. 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.