Reduced-order analysis and data reconstruction of airfoil turbulent acoustic signals using proper orthogonal decomposition and higher-order dynamic mode decomposition

Abstract

This study employs Higher-Order Dynamic Mode Decomposition (HODMD) and Proper Orthogonal Decomposition (POD) to analyze turbulent flow noise characteristics of a Clark-Y airfoil at Rec = 10⁵. By decomposing sound pressure signals, different frequency, direction, and amplitude components of sound waves are extracted for in-depth acoustic analysis. CFD simulations using LES with the WALE model reveal that laminar separation bubbles form at x/c = 0.28 and reattach at x/c = 0.45, generating a turbulent boundary layer and strong pressure fluctuations, identified as the primary source of low-frequency discrete noise. Modal decomposition and reconstruction of experimental sound pressure data across various angles of attack compare HODMD and POD in handling flow-induced noise. Results indicate HODMD effectively extracts dominant frequencies and high-frequency modal structures, while POD, though efficient in energy decomposition, suffers from mode mixing and lacks interpretability in high-frequency noise scenarios. By integrating Sound Pressure Level (SPL) analysis with HODMD, key frequencies associated with boundary layer transition noise are identified, revealing their time-evolution characteristics. The study highlights HODMD’s superiority in capturing dynamic evolution and stable modes of airfoil noise, providing valuable insights for aeroacoustic noise prediction and control strategies.