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Silent inflow condition for turbulent boundary layers

X. Gloerfelt and J.-C. Robinet

  • DynFluid Laboratory, Arts et Métiers ParisTech, 151 Boulevard de l'Hopital, 75013 Paris, France

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Phys. Rev. Fluids 2, 124603 – Published 29 December, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.124603

Abstract

The generation of a turbulent inflow is a tricky problem. In the framework of aeroacoustics, another important constraint is that the numerical strategy used to reach a turbulent state induces a spurious noise which is lower than the acoustic field of interest. For the study of noise radiated directly by a turbulent boundary layer on a flat plate, this constraint is severe since wall turbulence is a very inefficient source. That is why a method based on a transition by modal interaction using a base flow with an inflection point is proposed to cope with that. The base flow must be a solution of the equations so we use a profile behind a backward-facing step representative of experimental trip bands. A triad of resonant waves is selected by a local stability analysis of the linearized compressible equations and is added with a weak amplitude in the inlet plane. The compressible stability calculation allows the specification of the thermodynamic quantities at the inlet, which turns out to be fundamental to ensure a quiet inflow. A smooth transition is achieved with the rapid formation of Λ-shape vortices in a staggered organization as in subharmonic transition. The dominance of oblique waves promotes a rapid breakdown by the liftup mechanism of low-speed streaks. The quality of the fully turbulent state is assessed and the direct noise radiation from a turbulent boundary layer at Mach 0.5 is obtained with a very low level of spurious noise.

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References (97)

  1. X. Gloerfelt and T. Le Garrec, Generation of inflow turbulence for aeroacoustic applications, in AIAA/CEAS Aeroacoustics Conference (29th AIAA Aeroacoustics Conference), 5–7 May, 2008, Vancouver, Canada (AIAA, Reston, VA, 2008), paper AIAA 2008-2926.
  2. G. Aubard, X. Gloerfelt, and J.-C. Robinet, Characterisation of synthetic turbulence methods for large-eddy simulation of supersonic boundary layers, in Progress in Turbulence and Wind Energy IV, edited by M. Oberlack, J. Peinke, A. Talamelli, L. Castillo, and M. Hölling, Springer Proceedings in Physics, Vol. 141 (Springer, Berlin, Heidelberg, 2012), pp. 81–84.
  3. J. Chicheportiche and X. Gloerfelt, Effect of a turbulent incoming boundary layer on noise radiation by the flow over cylindrical cavities, in 17th AIAA/CEAS Aeroacoustics Conference (32nd AIAA Aeroacoustics Conference), 5–8 June, 2011, Portland, Oregon (AIAA, Reston, VA, 2011), paper AIAA 2011-2862.
  4. X. Gloerfelt and J. Berland, Turbulent boundary-layer noise: Direct radiation at Mach number 0.5, J. Fluid Mech. 723, 318 (2013).
  5. A. Powell, Aerodynamic noise and the plane boundary, J. Acoust. Soc. Am. 32, 982 (1960).
  6. N. Curle, The influence of solid boundaries upon aerodynamic sound, Proc. R. Soc. London, Ser. A 231, 505 (1955).
  7. X. Gloerfelt and J. Berland, Direct computation of turbulent boundary layer noise, in 15th AIAA/CEAS Aeroacoustics Conference (30th AIAA Aeroacoustics Conference), 11–13 May, 2009, Miami, Florida (AIAA, Reston, VA, 2009), paper AIAA 2009-3401.
  8. X. Gloerfelt, The link between wall pressure spectra and radiated sound from turbulent boundary layers, in 16th AIAA/CEAS Aeroacoustics Conference, 7–9 June, 2010, Stockholm, Sweden (AIAA, Reston, VA, 2010), paper AIAA 2010-3904.
  9. M. S. Howe, Surface pressures and sound produced by turbulent flow over smooth and rough walls, J. Acoust. Soc. Am. 90, 1041 (1991).
  10. G. Aubard, X. Gloerfelt, and J.-C. Robinet, Large-eddy simulation of broadband unsteadiness in a shock/boundary-layer interaction, AIAA J. 51, 2395 (2013).
  11. X. Gloerfelt and T. Le Garrec, Trailing edge noise from an isolated airfoil at a high Reynolds number, in 15th AIAA/CEAS Aeroacoustics Conference (30th AIAA Aeroacoustics Conference), 11–13 May, 2009, Miami, Florida (AIAA, Reston, VA, 2009), paper AIAA 2009-3201.
  12. T. Colonius and S. K. Lele, Computational aeroacoustics: Progress on nonlinear problems of sound generation, Progr. Aerospace Sci. 40, 345 (2004).
  13. M. Wang, J. B. Freund, and S. K. Lele, Computational prediction of flow-generated sound, Annu. Rev. Fluid Mech. 38, 483 (2006).
  14. S. K. Lele and J. W. Nichols, A second golden age of aeroacoustics?, Philos. Trans. R. Soc. London, Ser. A 372, 20130321 (2014).
  15. C. Bogey and C. Bailly, A family of low dispersive and low dissipative explicit schemes for noise computation, J. Comput. Phys. 194, 194 (2004).
  16. K. W. Thompson, Time-dependent boundary conditions for hyperbolic systems, J. Comput. Phys. 68, 1 (1987).
  17. T. J. Poinsot and S. K. Lele, Boundary conditions for direct simulations of compressible viscous flows, J. Comput. Phys. 101, 104 (1992).
  18. C. K. W. Tam and Z. Dong, Radiation and outflow boundary conditions for direct computation of acoustic and flow disturbances in a nonuniform mean flow, J. Comput. Acous. 4, 175 (1996).
  19. C. K. W. Tam, Advances in numerical boundary conditions for computational aeroacoustics, J. Comput. Acous. 6, 377 (1998).
  20. A. Keating, U. Piomelli, E. Balaras, and H.-J. Kaltenbach, A priori and a posteriori tests of inflow conditions for large-eddy simulations, Phys. Fluids 16, 4696 (2004).
  21. G. R. Tabor and M. H. Baba-Ahmadi, Inlet conditions for large eddy simulation: A review, Comp. Fluids 39, 553 (2010).
  22. X. Wu, Inflow turbulence generation methods, Annu. Rev. Fluid Mech. 49, 23 (2017).
  23. N. Hutchins, Caution: Tripping hazards, J. Fluid Mech. 710, 1 (2012).
  24. P. Schlatter and R. Örlü, Turbulent boundary layers at moderate Reynolds numbers: Inflow length and tripping effects, J. Fluid Mech. 710, 5 (2012).
  25. X. Gloerfelt, C. Bogey, and C. Bailly, Numerical evidence of mode switching in the flow-induced oscillations by a cavity, Int. J. Aeroacoustics 2, 193 (2003).
  26. S. Lee, S. K. Lele, and P. Moin, Simulation of spatially evolving turbulence and the applicability of Taylor hypothesis in compressible flow, Phys. Fluids A 4, 1521 (1992).
  27. T. S. Lund, X. Wu, and K. D. Squires, Generation of turbulent inflow data for spatially developing boundary layer simulations, J. Comput. Phys. 140, 233 (1998).
  28. H. Le, P. Moin, and J. Kim, Direct numerical simulation of turbulent flow over a backward-facing step, J. Fluid Mech. 330, 349 (1997).
  29. Y. Na and P. Moin, Direct numerical simulation of a separated turbulent boundary layer, J. Fluid Mech. 374, 379 (1998).
  30. Y. M. Chung and H. J. Sung, Comparative study of inflow conditions for spatially evolving simulation, AIAA J. 35, 269 (1997).
  31. R. Kraichnan, Diffusion by a random velocity field, Phys. Fluids 13, 22 (1970).
  32. W. Béchara, C. Bailly, P. Lafon, and S. Candel, Stochastic approach to noise modeling for free turbulent flows, AIAA J. 32, 455 (1994).
  33. A. Smirnov, S. Shi, and I. Celik, Random flow generation technique for large eddy simulation and particle-dynamics modeling, Trans. ASME: J. Fluids Eng. 123, 359 (2001).
  34. M. Billson, L.-E. Eriksson, and L. Davidson, Modeling of synthetic anisotropic turbulence and its sound emission, in 10th AIAA/CEAS Aeroacoustics Conference, Aeroacoustics Conferences (AIAA, Reston, VA, 2004), paper AIAA 2004-2857.
  35. N. D. Sandham, Y. F. Yao, and A. A. Lawal, Large-eddy simulation of transonic turbulent flow over a bump, Int. J. Heat Fluid Flow 24, 584 (2003).
  36. R. D. Sandberg and N. D. Sandham, Direct numerical simulation of turbulent flow past a trailing edge and the associated noise generation, J. Fluid Mech. 596, 353 (2008).
  37. O. Marsden, C. Bogey, and C. Bailly, Investigation of flow features around shallow round cavities subject to subsonic grazing flow, Phys. Fluids 24, 125107 (2012).
  38. N. Jarrin, S. Benhamadouche, D. Laurence, and R. Prosser, A synthetic-eddy-method for generating inflow conditions for large-eddy simulation, Int. J. Heat Fluid Flow 27, 585 (2006).
  39. M. Pamiès, P. E. Weiss, E. Garnier, S. Deck, and P. Sagaut, Generation of synthetic turbulent inflow data for large eddy simulation of spatially evolving wall-bounded flows, Phys. Fluids 21, 045103 (2009).
  40. M. Klein, A. Sadiki, and J. Janicka, A digital filter based generation of inflow data for spatially developing direct numerical or large eddy simulations, J. Comput. Phys. 186, 652 (2003).
  41. L. di Mare, M. Klein, P. Jones, and J. Janicka, Synthetic turbulence inflow conditions for large-eddy simulation, Phys. Fluids 18, 025107 (2006).
  42. I. Veloudis, Z. Yang, J. J. McGuirk, G. J. Page, and A. Spencer, Novel implementation and assessment of a digital filter based approach for the generation of LES inlet conditions, Flow, Turbulence Combust. 79, 1 (2007).
  43. E. Touber and N. D. Sandham, Large-eddy simulation of low-frequency unsteadiness in a turbulent shock-induced separation bubble, Theor. Comput. Fluid Dyn. 23, 79 (2009).
  44. P. Subbareddy, D. Peterson, G. V. Candler, and I. Marusic, A synthetic inflow generation method using the attached eddy hypothesis, in 24th AIAA Applied Aerodynamics Conference, 5–8 June, 2006, San Francisco, California (AIAA, Reston, VA, 2006), paper AIAA 2006-3672.
  45. P. R. Spalart, Direct simulation of a turbulent boundary layer up to Reθ=1410, J. Fluid Mech. 187, 61 (1988).
  46. P. Flohr and E. Balaras, Large-eddy simulation of a turbulent boundary layer, Technical Note 187, von Kármán Institute for Fluid Dynamics, Rhode Saint Genese Belgium, 1995 (unpublished).
  47. K. Liu and R. H. Pletcher, Inflow conditions for the large eddy simulation of turbulent boundary layers: A dynamic recycling procedure, J. Comput. Phys. 219, 1 (2006).
  48. A. Ferrante and S. E. Elghobashi, A robust method for generating inflow conditions for direct simulations of spatially developing turbulent boundary layers, J. Comput. Phys. 198, 372 (2004).
  49. G. Araya, L. Castillo, C. Meneveau, and K. Jansen, A dynamic multi-scale approach for turbulent inflow boundary conditions in spatially developing flows, J. Fluid Mech. 670, 581 (2011).
  50. S. Stolz and N. A. Adams, Large-eddy simulation of high-Reynolds-number supersonic boundary layers using the approximate deconvolution model and rescaling and recycling technique, Phys. Fluids 15, 2398 (2003).
  51. S. Xu and M. Martin, Assessment of inflow boundary conditions for compressible turbulent boundary layers, Phys. Fluids 16, 2623 (2004).
  52. P. Sagaut, E. Garnier, E. Tromeur, L. Larchevêque, and E. Labourasse, Turbulent inflow conditions for large-eddy simulation of compressible wall-bounded flows, AIAA J. 42, 469 (2004).
  53. A. Spille-Kohoff and H.-J. Kaltenbach, Generation of turbulent inflow data with a prescribed shear-stress profile, in DNS/LES Progress and Challenges, Proceedings of the Third AFOSR International Conference on Direct Numerical Simulation and Large Eddy Simulation (TAICDL) (Greyden Press, Dayton, Ohio, 2001), pp. 1–4, http://www.dtic.mil/dtic/tr/fulltext/u2/p013648.pdf.
  54. R. Laraufie, S. Deck, and P. Sagaut, A dynamic forcing method for unsteady turbulent inflow conditions, J. Comput. Phys. 230, 8647 (2011).
  55. P. Druault, S. Lardeau, J.-P. Bonnet, F. Coiffet, J. Delville, E. Lamballais, J. Largeau, and L. Perret, Generation of three-dimensional turbulent inlet conditions for large-eddy simulation, AIAA J. 42, 447 (2004).
  56. L. Perret, J. Delville, R. Manceau, and J.-P. Bonnet, Generation of turbulent inflow conditions for large-eddy simulation from stereoscopic PIV measurements, Int. J. Heat Fluid Flow 27, 576 (2006).
  57. Z. Xiong, S. Nagarajan, and S. Lele, Simple method for generating inflow turbulence, AIAA J. 42, 2164 (2004).
  58. P. Johansson and H. Andersson, Generation of inflow data for inhomogeneous turbulence, Theor. Comput. Fluid Dyn. 18, 371 (2004).
  59. P. J. Schmid and D. S. Henningson, Stability and Transition in Shear Flows, Applied Mathematical Sciences Vol. 142 (Springer, Berlin, 2001).
  60. P. S. Klebanoff, K. D. Tidstrom, and L. M. Sargent, The three-dimensional nature of boundary layer instability, J. Fluid Mech. 12, 1 (1962).
  61. Y. S. Kachanov and V. Y. Levchenko, The resonant interaction of disturbances at laminar-turbulent transition in a boundary layer, J. Fluid Mech. 138, 209 (1984).
  62. T. Herbert, Secondary instabilities of boundary layers, Annu. Rev. Fluid Mech. 20, 487 (1988).
  63. U. Rist and H. F. Fasel, Direct numerical simulation of controlled transition in a flat-plate boundary layer, J. Fluid Mech. 298, 211 (1995).
  64. S. Berlin, M. Wiegel, and D. Henningson, Numerical and experimental investigations of oblique boundary layer transition, J. Fluid Mech. 393, 23 (1999).
  65. S. Nagarajan, S. K. Lele, and J. H. Ferziger, Leading-edge effects in bypass transition, J. Fluid Mech. 572, 471 (2007).
  66. V. Ovchinnikov, M. M. Choudhari, and U. Piomelli, Numerical simulations of boundary-layer bypass transition due to high-amplitude free-stream turbulence, J. Fluid Mech. 613, 135 (2008).
  67. R. G. Jacobs and P. A. Durbin, Simulations of bypass transition, J. Fluid Mech. 428, 185 (2001).
  68. D. S. Henningson, A. Lundbladh, and A. V. Johansson, A mechanism for bypass transition from localized disturbances in wall-bounded shear flows, J. Fluid Mech. 250, 169 (1993).
  69. P. Andersson, M. Berggren, and D. S. Henningson, Optimal disturbances and bypass transition in boundary layers, Phys. Fluids 11, 134 (1999).
  70. P. Corbett and A. Bottaro, Optimal perturbations for boundary layers subject to stream-wise pressure gradient, Phys. Fluids 12, 120 (2000).
  71. A. Tumin and E. Reshotko, Optimal disturbances in compressible boundary layers, AIAA J. 41, 2357 (1984).
  72. S. Cherubini, J.-C. Robinet, A. Bottaro, and P. De Palma, Optimal wave packets in a boundary layer and initial phases of a turbulent spot, J. Fluid Mech. 656, 231 (2010).
  73. D. R. Williams, H. Fasel, and F. R. Hama, Experimental determination of the three-dimensional vorticity field in the boundary-layer transition process, J. Fluid Mech. 149, 179 (1984).
  74. S. Bake, H. H. Fernholz, and Y. S. Kachanov, Resemblance of K- and N-regimes of boundary-layer transition at late stages, Eur. J. Mech. B/Fluids 19, 1 (2000).
  75. T. A. Zaki and P. A. Durbin, Mode interaction and the bypass route to transition, J. Fluid Mech. 531, 85 (2005).
  76. A. M. Yaglom, Hydrodynamic Instability and Transition to Turbulence, Fluid Mechanics and Its Applications (Springer, Berlin, 2012), pp. 465–600.
  77. P. A. Elofsson and P. H. Alfredsson, An experimental study of oblique transition in plane Poiseuille flow, J. Fluid Mech. 358, 177 (1998).
  78. A. D. D. Craik, Non-linear resonant instability in boundary layers, J. Fluid Mech. 50, 393 (1971).
  79. P. Ricco and X. Wu, Response of a compressible laminar boundary layer to free-stream vortical disturbances, J. Fluid Mech. 587, 97 (2007).
  80. U. Rist and U. Maucher, Direct numerical simulation of 2-D and 3-D instability waves in a laminar separation bubble, in Application of Direct and Large Eddy Simulation to Transition and Turbulence (AGARD, France, 1994), pp. 34-1–34-7, http://www.dtic.mil/dtic/tr/fulltext/u2/a292121.pdf.
  81. R. D. Joslin, C. L. Streett, and C.-L. Chang, Spatial direct numerical simulation of boundary-layer transition mechanisms: Validation of PSE theory, Theor. Comput. Fluid Dyn. 4, 271 (1993).
  82. B. F. Armaly, F. Durst, J. C. F. Pereira, and B. Schönung, Experimental and theoretical investigation of backward-facing step flow, J. Fluid Mech. 127, 473 (1983).
  83. G. Biswa, M. Breuer, and F. Durst, Backward-facing step flows for various expansion ratios at low and moderate Reynolds numbers, Trans. ASME: J. Fluids Eng. 126, 362 (2004).
  84. R. E. Kelly, On the resonant interaction of neutral disturbances in two inviscid shear flows, J. Fluid Mech. 31, 789 (1968).
  85. M. B. Zelman and I. I. Maslennikova, Tollmien-Schlichting-wave resonant mechanism for subharmonic-type transition, J. Fluid Mech. 252, 449 (1993).
  86. T. C. Corke and R. A. Mangano, Resonant growth of three-dimensional modes in transitioning Blasius boundary layers, J. Fluid Mech. 209, 93 (1989).
  87. V. I. Borodulin, Y. S. Kachanov, and D. B. Koptsev, Experimental study of resonant interactions of instability waves in a self-similar boudary layer with an adverse pressure gradient: I. Tuned resonances, J. Turbulence 3, N62 (2002).
  88. V. I. Borodulin, Y. S. Kachanov, and D. B. Koptsev, Experimental study of resonant interactions of instability waves in a self-similar boudary layer with an adverse pressure gradient: III. Broadband disturbances, J. Turbulence 3, N64 (2002).
  89. T. C. Corke, Three-dimensional mode growth in boundary layers with tuned and detuned subharmonic resonance, Philos. Trans. R. Soc. London, Ser. A 352, 453 (1995).
  90. X. Wu and P. Moin, Direct numerical simulation of turbulence in a nominally zero-pressure-gradient flat-plate boundary layer, J. Fluid Mech. 630, 5 (2009).
  91. X. Wu and P. Moin, Transitional and turbulent boundary layer with heat transfer, Phys. Fluids 22, 085105 (2010).
  92. T. Sayadi, C. W. Hamman, and P. Moin, Direct numerical simulation of H-type and K-type transition to turbulence, Center for Turbulence Research, Annual Research Briefs (CTR, Stanford University, Stanford, California, 2011), pp. 109–121, https://web.stanford.edu/group/ctr/ResBriefs/2011/10_sayadi-color.pdf.
  93. T. Sayadi, C. W. Hamman, and P. Moin, Direct numerical simulation of complete H-type and K-type transitions with implications for the dynamics of turbulent boundary layers, J. Fluid Mech. 724, 480 (2013).
  94. P. Schlatter and R. Örlü, Assessment of direct numerical simulation data of turbulent boundary layers, J. Fluid Mech. 659, 116 (2010).
  95. J. Jimenez, S. Hoyas, M. P. Simens, and Y. Mizuno, Turbulent boundary layers and channels at moderate Reynolds numbers, J. Fluid Mech. 657, 335 (2010).
  96. X. Gloerfelt and F. Margnat, Effect of Mach number on boundary layer noise, in 20th AIAA/CEAS Aeroacoustics Conference, 16–20 June, 2014, Atlanta, Georgia (AIAA, Reston, VA, 2014), paper AIAA 2014-3291.
  97. X. Gloerfelt and E. Cohen, Influence of pressure gradients and Reynolds number on wall-pressure wavenumber-frequency spectra, in 22nd AIAA/CEAS Aeroacoustics Conference, 30 May–1 June, 2016, Lyon, France (AIAA, Reston, VA, 2016), paper AIAA 2016-2910.

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Phys. Rev. Fluids 2, 124603– Published 29 December, 2017
  • Received 27 July 2017

©2017 American Physical Society

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