Numerical Modal Analysis of the Correlation Between Spanwise Vortex Shedding and Far-field Aeolian Noise for Square and Circular Wall-mounted Cylinders

For square and circular finite wall-mounted cylinders (FWMCs) with an aspect ratio exceeding 10, the vortex shedding near the tip area leads to the generation of multiple tonal noises. The quantitative analysis of the spanwise distributions of the vortex modal energy with different frequencies was quite limited. This study employs dynamic mode decomposition to decompose the wake of FWMC into distinct frequencies to evaluate the modal energy distribution of pressure fluctuations at each frequency along the spanwise direction. Large eddy simulation combined with the Ffowcs Williams–Hawkings (FW–H) acoustics analogy is applied to a square and a circular FWMC with aspect ratio of 13.6 at a Reynolds number of 2.3 × 10⁴. Two indicators to describe the spanwise energy contribution are proposed. The results reveal that, for square FWMC, the primary modal energy corresponding to Strouhal number (St) equal to 0.14 is concentrated below 30% of the cylinder height L owing to the 3D effect. A transition mode of St ≈ 0.12 is identified in the midspan (0.3L–0.7L) without significant contribution to far-field noise spectrum. For circular FWMC, the modal energy is distributed over several frequencies, vortices cells corresponding to the main noise band (0.2 < St < 0.23) are distributed below 0.7L, and the vortices cells in the noise band of 0.15 < St < 0.19 distributed from the midspan to the upper part in a dispersed manner. The noise band with St ≈ 0.08 corresponds to tip-associated vortices gathering above 0.8L.