Wavelet-based pressure decomposition for airfoil noise in low-Mach number flows

The paper applies a wavelet filtering method based on the recursive denoising algorithm to airfoil noise in low-Mach number flows. The pressure field around the airfoil is decomposed into coherent contributions corresponding to denoised pressure and incoherent pressure corresponding to background noise. The pressure data are obtained from Large-Eddy Simulations. Both the flow and acoustic solvers are validated against experimental data at a zero angle of attack, Reynolds numbers, $Re = 3.2 × 10 5$ and $4 × 10 5$⁠, and Mach numbers, $M = 0.093$ and 0.058, respectively. The convergence trend and statistical nature of the wavelet algorithm are analyzed. Additionally, the decomposed pressures are examined by comparing the wavelet-based decomposition with the traditional wavenumber–frequency decomposition, and spectral analyses are conducted on the decomposed pressures. The results show that the denoised pressure represents physical phenomena associated with hydrodynamic wavy structures moving along the wall and sound propagation generated near the tripping region and the trailing edge. On the other hand, the incoherent pressure or background noise exhibits a small and constant amplitude closely adhering to the Gaussian distribution. Dynamic mode decomposition modes reveal that this background noise is prominent around the tripping and trailing-edge regions where flow perturbations are significant, but it either barely propagates to the far field or dissipates quickly. The far-field acoustic spectrum is predominantly influenced by the physical or denoised component. However, a cautious interpretation is necessary in the high-frequency range, where background noise still contributes to the far-field noise. The paper explores the potential applications of the wavelet algorithm in identifying and removing background noise.