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

TL;DR

Problem: quantify how a rod wake interacts with a perpendicular aerofoil to generate noise and how coherent flow structures couple to acoustics. Approach: synchronized TR-PIV and microphone-array measurements analyzed with SPOD under SPOD-u and SPOD-p norms, complemented by conventional beamforming and low-rank CSMs. Findings: dominant energy peaks at $St \approx 0.2$ (von Kármán shedding) and $St \approx 0.4$ (rod wake impingement on the aerofoil); a mode switch around $St \approx 0.3$ separates cylinder vs aerofoil branches; coherence up to $60\%$ between $u_2$ and acoustic pressure near the aerofoil. Significance: demonstrates a framework linking flow structures to sound in rod–aerofoil interactions, enabling reduced-order acoustic models and improved noise-control insights for practical turbomachinery and rotorcraft contexts.

Abstract

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 $\mathit{St} \approx 0.2$ and $0.4$--Strouhal numbers based on rod diameter and free-stream velocity. At $\mathit{St} \approx 0.2$, the dominant feature is von Kármán vortex shedding from the rod. At $\mathit{St} \approx 0.4$, 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 $u_2$ component (upwash/downwash relative to the aerofoil). This structure also appears at $\mathit{St} \approx 0.2$, but as the rank-2 SPOD-p mode. A mode-switching occurs around $\mathit{St} \approx 0.3$: 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.

Figures (21)

• Figure 1: Sketch representing the TR-PIV and acoustic experiment set-up, including the rod (black rectangle and circle), aerofoil (grey profile and rectangle), microphone array (black dots), TR-PIV field of view (green rectangle), coordinate system (in red), and key dimensions. The dotted black line in both frames indicates the position of the TR-PIV laser sheet, which is perpendicular to the shown view. The flow direction is from left to right.
• Figure 2: Picture of the experimental set-up for the $x_1$--$x_2$ (vertical) TR-PIV measurements.
• Figure 3: Raw image of a sample snapshot.
• Figure 4: Sketch of the beamforming scanning mesh (orange dots), the microphone array (blue closed circles), the perpendicular rod (black closed circle), and the aerofoil (continuous line rectangle) projections on the mesh.
• Figure 5: Acoustic spectra for selected microphones. Left frame: digital microphones array (small dots), cylinder (closed black circle), aerofoil (vertical black lines), and the selected microphones (coloured markers). Right frame: acoustic spectra.