Cross-spectrum method for acoustic source identification and visualization of airfoil noise

Abstract

The identification and visualization of airfoil noise sources are critical for comprehending the interplay between flow and acoustics, and for understanding the generation and propagation of sound. In this paper, we introduce an innovative method, specifically designed to identify and visualize flow-induced noise sources associated with airfoil noise. This approach employs cross power spectral density analysis to distinctly identify flow-induced noise sources. The data for our study comes from large-eddy simulations of a NACA 0012 airfoil, characterized by a Reynolds number of 4×105, a Mach number of 0.058, and an angle of attack of 6.25∘. Different cross-spectrum formulations are examined and evaluated. The analysis includes a comparison of the cross-spectrum method's strengths and limitations relative to established data-driven approaches like dynamic mode decomposition (DMD) and spectral proper orthogonal decomposition (SPOD). We find that the cross-spectrum method provides both spectral magnitudes and phase topologies, allowing it to effectively compare sound intensities among various sources at specific frequencies, while retaining high-resolution spatiotemporal coherent flow and acoustic dynamics. One of the notable advantages of the cross-spectrum method over DMD or SPOD modes is its lesser reliance on extensive data manipulation in the form of large-size data matrix, making it a more efficient and user-friendly approach for practitioners, particularly when dealing with complex systems or high-dimensional datasets. This characteristic enhances its practicality and accessibility in the field of flow and acoustic visualization. Finally, the newly developed method is applied to three distinct flow transition scenarios to evaluate its proficiency in distinguishing acoustic generation and propagation mechanisms, depending on the specific transition case.