<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(St \approx 0.2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>S</mi> <mi>t</mi> <mo>≈</mo> <mn>0.2</mn> </mrow> </math></EquationSource> </InlineEquation> and 0.4–Strouhal numbers based on rod diameter and free-stream velocity. At <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(St \approx 0.2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>S</mi> <mi>t</mi> <mo>≈</mo> <mn>0.2</mn> </mrow> </math></EquationSource> </InlineEquation>, the dominant feature is von Kármán vortex shedding from the rod. At <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(St \approx 0.4\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>S</mi> <mi>t</mi> <mo>≈</mo> <mn>0.4</mn> </mrow> </math></EquationSource> </InlineEquation>, 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 <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(u_2\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>u</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation> component (upwash/downwash relative to the aerofoil). This structure also appears at <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(St \approx 0.2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>S</mi> <mi>t</mi> <mo>≈</mo> <mn>0.2</mn> </mrow> </math></EquationSource> </InlineEquation>, but as the rank-2 SPOD-p mode. A mode-switching occurs around <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(St \approx 0.3\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>S</mi> <mi>t</mi> <mo>≈</mo> <mn>0.3</mn> </mrow> </math></EquationSource> </InlineEquation>: 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.</p>

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

  • Filipe R. do Amaral,
  • Marios I. Spiropoulos,
  • Florent Margnat,
  • David Marx,
  • Vincent Valeau,
  • Peter Jordan

摘要

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