Perpendicular rod wake/aerofoil interaction: microphone array and TR-PIV insights via SPOD and beamforming analysis

Resumo

© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2025.This paper investigates the acoustic and velocity fields due to a circular rod and an aerofoil placed in the wake of, and perpendicular to, a rod. Simultaneous measurements were conducted using a microphone array and time-resolved particle image velocimetry (TR-PIV). The interaction was characterized through acoustic spectra and the coherence between microphone signals and the three velocity components. Coherent structures were identified with spectral proper orthogonal decomposition (SPOD) using a norm based either on turbulence kinetic energy (SPOD-u) or on pressure (SPOD-p). An advantage of SPOD-p is that it identifies velocity modes associated with a large acoustic energy. Peaks of energy were observed at St≈0.2 and 0.4–Strouhal numbers based on rod diameter and free-stream velocity. At St≈0.2, the dominant feature is von Kármán vortex shedding from the rod. At St≈0.4, a wave-train structure in the rod wake impinging on the aerofoil leading edge is captured by the rank-1 SPOD-p mode, with coherence levels reaching 60% for the u2 component (upwash/downwash relative to the aerofoil). This structure also appears at St≈0.2, but as the rank-2 SPOD-p mode. A mode-switching occurs around St≈0.3: below this value, the rank-1 mode corresponds to von Kármán shedding (cylinder branch), while above it, the rank-1 mode tracks the interaction of the aerofoil with the rod wake (aerofoil branch). Both branches were also identified via beamforming using low-rank cross-spectral matrices derived from SPOD-p modes.