Journal of Fluid Mechanics


Convective effects and the role of quadrupole sources for aerofoil aeroacoustics

William R. Wolfa1a2 c1, João Luiz F. Azevedoa2 and Sanjiva K. Lelea1a3

a1 Department of Aeronautics & Astronautics, Stanford University, Stanford, CA 94305, USA

a2 Institute of Aeronautics and Space, São José dos Campos, SP 12201-970, Brazil

a3 Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA


The present investigation of aerofoil self-noise generation and propagation concerns the effects of mean flow and quadrupole sources on the broadband noise that arises from the interaction of turbulent boundary layers with the aerofoil trailing edge and the tonal noise that arises from vortex shedding generated by laminar boundary layers and trailing-edge bluntness. Compressible large-eddy simulations (LES) are conducted for a NACA0012 aerofoil with rounded trailing edge for four flow configurations with different angles of incidence, boundary layer tripping configurations and free-stream Mach numbers. The Reynolds number based on the aerofoil chord is fixed at ${\mathit{Re}}_{c} = 408\hspace{0.167em} 000$. The acoustic predictions are performed by the Ffowcs Williams & Hawkings (FWH) acoustic analogy formulation and incorporate convective effects. Surface and volume integrations of dipole and quadrupole source terms appearing in the FWH equation are performed using a three-dimensional wideband multi-level adaptive fast multipole method (FMM) in order to accelerate the calculations of aeroacoustic integrals. In order to validate the numerical solutions, flow simulation and acoustic prediction results are compared to experimental data available in the literature and good agreement is observed in terms of both aerodynamic and aeroacoustic results. For low-Mach-number flows, quadrupole sources can be neglected in the FWH equation and mean flow effects appear only for high frequencies. However, for higher speeds, convection effects are relevant for all frequencies and quadrupole sources have a more pronounced effect for medium and high frequencies. The convective effects are most readily observed in the upstream direction.

(Received October 27 2011)

(Reviewed April 10 2012)

(Accepted June 25 2012)

(Online publication August 10 2012)

Key Words:

  • aeroacoustics;
  • turbulent boundary layers;
  • vortex shedding


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