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Rapid distortion theory of turbulent flow around a porous cylinder

Published online by Cambridge University Press:  11 March 2021

R. Zamponi Open the ORCID record for R. Zamponi [Opens in a new window] ,
S. Moreau  and
C. Schram
R. Zamponi*
Affiliation:
von Karman Institute for Fluid Dynamics, Waterloosest. 72, 1640Sint-Genesius-Rode, Belgium
S. Moreau
Affiliation:
Université de Sherbrooke, Boul. de l'Université 2500, J1K 2R1Sherbrooke, QC, Canada
C. Schram
Affiliation:
von Karman Institute for Fluid Dynamics, Waterloosest. 72, 1640Sint-Genesius-Rode, Belgium
*
†Email address for correspondence: [email protected]
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Abstract

The distortion of homogeneous isotropic turbulence interacting with a porous cylinder is calculated by means of the rapid distortion theory (RDT). The porous treatment, characterised by a constant static permeability, is modelled as an impedance boundary condition accounting for the Darcy's flow within the body. The RDT algorithm is first validated through comparisons with published velocity measurements in the stagnation region of an impermeable cylinder placed downstream of a turbulence grid. Subsequently, the impact of porosity on the velocity field is investigated through the analysis of the one-dimensional spectra at different locations near the body and the velocity variance along the stagnation streamline. The porous surface affects the incoming turbulence distortion near the cylinder by reducing the blocking effect of the body and by altering the vorticity deformation caused by the mean flow. The former leads to an attenuation of the one-dimensional velocity spectrum in the low-frequency range, whereas the latter results in an amplification of the high-frequency components. This trend is found to be strongly dependent on the turbulence scale and influences the evolution of the velocity fluctuations in the stagnation region. The porous RDT is finally adapted to model the turbulence distortion in the vicinity of the leading edge of a NACA-0024 profile fitted with melamine foam. The good agreement between the calculations and the experimental results demonstrates that the present methodology can improve the understanding of the physical mechanisms involved in the aerofoil-turbulence interaction noise reduction through porosity and be instrumental in designing such passive noise-mitigation treatments.

JFM classification

Acoustics: Aeroacoustics Turbulent Flows: Turbulence theory
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 915 , 25 May 2021 , A27
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Amiet, R.K. 1975 Acoustic radiation from an airfoil in a turbulent stream. J. Sound Vib. 41 (4), 407–420.CrossRefGoogle Scholar
Avallone, F., Casalino, D. & Ragni, D. 2018 Impingement of a propeller-slipstream on a leading edge with a flow-permeable insert: a computational aeroacoustic study. Intl J. Aeroacoust. 17 (6–8), 687–711.CrossRefGoogle Scholar
Ayton, L.J., Colbrook, M.J., Geyer, T., Chaitanya, P. & Sarradj, E. 2021 Reducing aerofoil–turbulence interaction noise through chordwise-varying porosity. J. Fluid Mech. 906, A1.CrossRefGoogle Scholar
Ayton, L.J. & Paruchuri, C. 2019 An analytical and experimental investigation of aerofoil–turbulence interaction noise for plates with spanwise-varying leading edges. J. Fluid Mech. 865, 137–168.CrossRefGoogle Scholar
Ayton, L.J. & Peake, N. 2016 Interaction of turbulence with the leading-edge stagnation point of a thin aerofoil. J. Fluid Mech. 798, 436–456.CrossRefGoogle Scholar
Bampanis, G. & Roger, M. 2020 On the turbulence-impingement noise of a naca-12 airfoil with porous inclusions. In 26th AIAA/CEAS Aeroacoustics Conference. Virtual event: American Institute of Aeronautics and Astronautics.CrossRefGoogle Scholar
Batchelor, G.K. 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.Google Scholar
Batchelor, G.K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.Google Scholar
Batchelor, G.K. & Proudman, I. 1954 The effect of rapid distortion of a fluid in turbulent motion. Q. J. Mech. Appl. Maths 7, 83.CrossRefGoogle Scholar
Bear, J. 1972 Dynamics of Fluids in Porous Media. Dover Publications.Google Scholar
Bearman, P.W. 1972 Some measurements of the distortion of turbulence approaching a two-dimensional bluff body. J. Fluid Mech. 53, 451.CrossRefGoogle Scholar
Britter, R.E., Hunt, J.C.R. & Mumford, J.C. 1979 The distortion of turbulence by a circular cylinder. J. Fluid Mech. 92, 269.CrossRefGoogle Scholar
Christophe, J. 2011 Application of hybrid methods to high frequency aeroacoustics. PhD thesis, Université Libre de Bruxelles.Google Scholar
Darwin, C. 1953 Note on hydrodynamics. Proc. Camb. Phil. Soc. 49, 342.CrossRefGoogle Scholar
Durbin, P.A. & Hunt, J.C.R. 1980 On surface pressure fluctuations beneath turbulent flow round bluff bodies. J. Fluid Mech. 100, 161.CrossRefGoogle Scholar
Geyer, T., Lucius, A., Schrödter, M., Schneider, M. & Sarradj, E. 2019 Reduction of turbulence interaction noise through airfoils with perforated leading edges. Acta Acust. United Ac. 105 (1), 109–122.CrossRefGoogle Scholar
Geyer, T., Sarradj, E. & Giesler, J. 2012 Application of a beamforming technique to the measurement of airfoil leading edge noise. Adv. Acoust. Vib. 2012, 905461.Google Scholar
Geyer, T., Sarradj, E., Giesler, J. & Hobracht, M. 2011 Experimental assessment of the noise generated at the leading edge of porous airfoils using microphone array techniques. In 17th AIAA/CEAS Aeroacoustics Conference (32nd AIAA Aeroacoustics Conference). American Institute of Aeronautics and Astronautics.CrossRefGoogle Scholar
Goldstein, M.E. 1978 Unsteady vortical and entropic distortions of potential flows round arbitrary obstacles. J. Fluid Mech. 89, 433.CrossRefGoogle Scholar
Graham, J.M.R. 2017 Rapid distortion of turbulence into an open turbine rotor. J. Fluid Mech. 825, 764–794.CrossRefGoogle Scholar
Hunt, J.C.R. 1973 A theory of turbulent flow round two-dimensional bluff bodies. J. Fluid Mech. 61, 625.CrossRefGoogle Scholar
Hunt, J.C.R., Kawai, H., Ramsey, S.R., Pedrizetti, G. & Perkins, R.J. 1990 A review of velocity and pressure fluctuations in turbulent flows around bluff bodies. J. Wind Engng Ind. Aerodyn. 35, 49–85.CrossRefGoogle Scholar
Jackson, R., Graham, J.M.R. & Maull, D.J. 1973 The lift on a wing in a turbulent flow. Aeronaut. Q. 24 (3), 155–166.CrossRefGoogle Scholar
Kisil, A. & Ayton, L.J. 2018 Aerodynamic noise from rigid trailing edges with finite porous extensions. J. Fluid Mech. 836, 117.CrossRefGoogle Scholar
Klettner, C.A., Eames, I. & Hunt, J.C.R. 2019 The effect of an unsteady flow incident on an array of circular cylinders. J. Fluid Mech. 872, 560–593.CrossRefGoogle Scholar
Lighthill, M.J. 1956 Drift. J. Fluid Mech. 1, 31.CrossRefGoogle Scholar
Macaraeg, M. 1998 Fundamental investigations of airframe noise. In 4th AIAA/CEAS Aeroacoustics Conference. American Institute of Aeronautics and Astronautics.CrossRefGoogle Scholar
Majumdar, S.J. & Peake, N. 1998 Noise generation by the interaction between ingested turbulence and a rotating fan. J. Fluid Mech. 359, 181–216.CrossRefGoogle Scholar
Milne, I.A. & Graham, J.M.R. 2019 Turbulence velocity spectra and intensities in the inflow of a turbine rotor. J. Fluid Mech. 870, R3.CrossRefGoogle Scholar
Miotto, R.F., Wolf, W.R. & de Santana, L.D. 2018 Leading-edge noise prediction of general airfoil profiles with spanwise-varying inflow conditions. AIAA J. 56 (5), 1711–1716.CrossRefGoogle Scholar
Mish, P.F. & Devenport, W.J. 2006 An experimental investigation of unsteady surface pressure on an airfoil in turbulence—Part 2: sources and prediction of mean loading effects. J. Sound Vib. 296, 447.CrossRefGoogle Scholar
Moreau, S. 2019 Turbomachinery noise predictions: present and future. Acoustics 1, 92.CrossRefGoogle Scholar
Moreau, S. & Roger, M. 2005 Effect of angle of attack and airfoil shape on turbulence-interaction noise. In 11th AIAA/CEAS Aeroacoustics Conference. American Institute of Aeronautics and Astronautics.CrossRefGoogle Scholar
Paruchuri, C., Joseph, P., Chong, T.P., Priddin, M. & Ayton, L.J. 2020 On the noise reduction mechanisms of porous aerofoil leading edges. J. Sound Vib. 485, 115574.Google Scholar
Power, H., Miranda, G. & Villamizar, V. 1984 Integral-equation solution of potential flow past a porous body of arbitrary shape. J. Fluid Mech. 149, 59.CrossRefGoogle Scholar
Priddin, M.J., Paruchuri, C., Joseph, P. & Ayton, L.J. 2019 A semi-analytic and experimental study of porous leading edges. In 25th AIAA/CEAS Aeroacoustics Conference. American Institute of Aeronautics and Astronautics.CrossRefGoogle Scholar
Ribner, H. & Tucker, M. 1953 Spectrum of turbulence in a contracting stream. Tech. Note No. 19. NACA.Google Scholar
Robison, R.A.V. & Peake, N. 2014 Noise generation by turbulence–propeller interaction in asymmetric flow. J. Fluid Mech. 758, 121–149.CrossRefGoogle Scholar
Roger, M. & Moreau, S. 2016 Airfoil turbulence-impingement noise reduction by porosity or wavy leading-edge cut: experimental investigations. In 45th International Congress and Exposition on Noise Control Engineering, Hamburg, Germany, pp. 6366–6375. Institute of Noise Control Engineering.Google Scholar
Roger, M., Schram, C. & De Santana, L.D. 2013 Reduction of airfoil turbulence-impingement noise by means of leading-edge serrations and/or porous material. In 19th AIAA/CEAS Aeroacoustics Conference. American Institute of Aeronautics and Astronautics.CrossRefGoogle Scholar
de Santana, L.D. 2015 Semi-analytical methodologies for airfoil noise prediction. PhD thesis, KU Leuven.Google Scholar
de Santana, L.D., Christophe, J., Schram, C. & Desmet, W. 2016 A rapid distortion theory modified turbulence spectra for semi-analytical airfoil noise prediction. J. Sound Vib. 383, 349.CrossRefGoogle Scholar
Sarradj, E. & Geyer, T. 2014 Symbolic regression modeling of noise generation at porous airfoils. J. Sound Vib. 333 (14), 3189–3202.CrossRefGoogle Scholar
Satcunathan, S., Zamponi, R., Meinke, M., Van de Wyer, N., Schram, C. & Schröder, W. 2019 Validation of a model for acoustic absorption in porous media. In 48th International Congress and Exhibition on Noise Control Engineering, Madrid, Spain, pp. 4329–4344. Institute of Noise Control Engineering.Google Scholar
Simonich, J.C., Amiet, R.K., Schlinker, R.H. & Greitzer, E.M. 1990 Rotor noise due to atmospheric turbulence ingestion. I – fluid mechanics. J. Aircraft 27 (1), 7–14.CrossRefGoogle Scholar
Sinnige, T., Corte, B.D., De Vries, R., Avallone, F., Merino-Martínez, R., Ragni, D., Eitelberg, G. & Veldhuis, L. 2019 Alleviation of propeller-slipstream-induced unsteady pylon loading by a flow-permeable leading edge. J. Aircraft 56 (3), 1214–1230.CrossRefGoogle Scholar
Tennekes, H. & Lumley, J.L. 1972 A First Course in Turbulence. MIT Press.CrossRefGoogle Scholar
Zamponi, R., Ragni, D., Van de Wyer, N. & Schram, C. 2019 Experimental investigation of airfoil turbulence-impingement noise reduction using porous treatment. In 25th AIAA/CEAS Aeroacoustics Conference. American Institute of Aeronautics and Astronautics.CrossRefGoogle Scholar
Zamponi, R., Satcunanathan, S., Moreau, S., Ragni, D., Meinke, M., Schröder, W. & Schram, C. 2020 On the role of turbulence distortion on leading-edge noise reduction by means of porosity. J. Sound Vib. 485C, 115561.CrossRefGoogle Scholar