An Investigation into the Four-Dimensional Acoustic Analogy Model for Homogeneous Media and the Prediction of Flow-Induced Noise in Spatio-Temporal Fields

Abstract

In practical engineering, the prevalence of uniform flow-induced noise poses significant challenges. Traditional models, notably Lighthill's acoustic analogy, have primarily focused on the acoustic pressure distribution, neglecting the integral role of acoustic velocity. This study introduces a novel four-dimensional (4D) acoustic wave equation model derived from the Navier-Stokes equations for fluid mechanics. This model uniquely incorporates acoustic pressure alongside three directional acoustic velocities as fundamental acoustic variables, offering a comprehensive framework for noise prediction. By integrating these variables, a 4D Ffowcs Williams-Hawkings (FW-H) equation is formulated, encapsulating the complexities of an arbitrary smooth permeable surface surrounding the noise-generating structure. Furthermore, this research innovates by establishing a time-domain integral formula for the 4D FW-H equation, incorporating a time-domain Green's function that accounts for the influence of uniform flow. Through numerical simulations involving stationary and rotating point sources within a uniformly moving medium, the efficacy of the proposed method is demonstrated. The method exhibits exceptional accuracy in capturing far-field 4D acoustic signals, aligned with analytical solutions, and reveals the characteristic Doppler effect in the acoustic fields of rotating monopole and dipole sources. A detailed investigation into the noise distribution within spatio-temporal fields under varying incident velocities, wave numbers, and propagation distances is conducted. Findings indicate a pronounced convective effect on the acoustic vector signal within a moving medium, with near-field 4D acoustic variables exhibiting nonlinear relationships with incoming flow velocity, wave number, and propagation distance, whereas far-field variables adhere to linear propagation patterns. This study diverges from conventional methodologies by considering the uniform flow's impact and devising an acoustic model capable of swiftly and accurately determining sound pressure and acoustic velocity. The developed acoustic calculation model offers valuable reference data for noise reduction and engineering structure optimization.