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Influences of wall disturbances on coherent structures in supersonic turbulent boundary layers

壁面扰动对超声速湍流边界层拟序结构的影响研究

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Abstract

In the present study, the influences of wall disturbances on coherent structures and the corresponding turbulent transport in supersonic turbulent boundary layers are investigated. The free-stream Mach number is set as 2.0. The database is scrutinized to present the instantaneous distributions and spectral properties of momentum and heat transfer related flow quantities. In their important roles in enhancing the momentum and heat transfer, the wall disturbances lead to the energetic turbulent fluctuations with the length scales of the wall disturbance wavelength and its harmonics in the near-wall region. The large-scale motions are also excited with the spanwise length scales of the turbulent boundary layer thicknesses, which, by reasoning, is caused by nonlinear interactions between wall disturbances and turbulent motions at some certain scales. They also produce intense density and pressure fluctuations that penetrate the boundary layer by deforming the sonic surfaces and radiate towards the free stream, where the fluctuations remain isentropic processes in nature. During this process, the steady wall disturbances are distorted by the turbulence, therefore endued with the features of multi-scale and multi-frequency instead of remaining energetic at a single wavelength or frequency.

摘要

本文研究了壁面扰动对来流马赫数为2.0的超声速湍流边界层中相干结构和湍流输运的影响. 通过对直接数值模拟数据的分 析, 本文讨论了与动量和热传输相关的物理量的瞬时分布和谱特性. 研究发现, 壁面扰动在增**动量和热传输方面发挥重要作用, 其在 **壁区域引起了与壁面扰动波长及其谐波长度尺度的能量湍流脉动. 同时, 壁面扰动也激发了大尺度运动, 其长度尺度为湍流边界层 厚度, 这是由壁面扰动和某些尺度的湍流运动之间的非线性相互作用所致. 壁面扰动还引起了较**的密度和压力脉动, 通过改变声速 面而穿透边界层, 保持等熵的特性向自由流辐射. 在此过程中, 稳态壁面扰动被湍流扭曲, 从而具有了多尺度和多频率的特征.

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References

  1. M. R. Raupach, R. A. Antonia, and S. Rajagopalan, Rough-wall turbulent boundary layers, Appl. Mech. Rev. 44, 1 (1991).

    Article  ADS  Google Scholar 

  2. J. Jiménez, Turbulent flows over rough walls, Annu. Rev. Fluid Mech. 36, 173 (2004).

    Article  ADS  MathSciNet  Google Scholar 

  3. H. Schlichting, and K. Gersten, Boundary-Layer Theory (Springer Science & Business Media, New York, 2003).

    Google Scholar 

  4. R. J. A. M. Stevens, and C. Meneveau, Flow structure and turbulence in wind farms, Annu. Rev. Fluid Mech. 49, 311 (2017).

    Article  ADS  MathSciNet  Google Scholar 

  5. D. Howell, and B. Behrends, A review of surface roughness in antifouling coatings illustrating the importance of cutoff length, Biofouling 22, 401 (2006).

    Article  CAS  PubMed  Google Scholar 

  6. U. Piomelli, Recent advances in the numerical simulation of rough-wall boundary layers, Phys. Chem. Earth Parts ABC 113, 63 (2019).

    Article  ADS  Google Scholar 

  7. D. Chung, N. Hutchins, M. P. Schultz, and K. A. Flack, Predicting the drag of rough surfaces, Annu. Rev. Fluid Mech. 53, 439 (2021).

    Article  ADS  Google Scholar 

  8. M. Kadivar, D. Tormey, and G. McGranaghan, A review on turbulent flow over rough surfaces: Fundamentals and theories, Int. J. Thermofluids 10, 100077 (2021).

    Article  Google Scholar 

  9. D. Chung, L. Chan, M. MacDonald, N. Hutchins, and A. Ooi, A fast direct numerical simulation method for characterising hydraulic roughness, J. Fluid Mech. 773, 418 (2015), ar**v: 1502.07043.

    Article  ADS  CAS  Google Scholar 

  10. G. Z. Ma, C. X. Xu, H. J. Sung, and W. X. Huang, Scaling of rough-wall turbulence by the roughness height and steepness, J. Fluid Mech. 900, R7 (2020).

    Article  MathSciNet  CAS  Google Scholar 

  11. G. Z. Ma, C. X. Xu, H. J. Sung, and W. X. Huang, Scaling of rough-wall turbulence in a transitionally rough regime, Phys. Fluids 34, 031701 (2022).

    Article  ADS  CAS  Google Scholar 

  12. A. A. Townsend, Turbulent Shear Flow (Cambridge University Press, New York, 1976).

    Google Scholar 

  13. K. A. Flack, M. P. Schultz, and T. A. Shapiro, Experimental support for Townsend’s Reynolds number similarity hypothesis on rough walls, Phys. Fluids 17, 035102 (2005).

    Article  ADS  Google Scholar 

  14. K. A. Flack, and M. P. Schultz, Review of hydraulic roughness scales in the fully rough regime, J. Fluids Eng. 132, (2010).

  15. K. A. Flack, and M. P. Schultz, Roughness effects on wall-bounded turbulent flows, Phys. Fluids 26, 101305 (2014).

    Article  ADS  Google Scholar 

  16. A. Inagaki, M. C. L. Castillo, Y. Yamashita, M. Kanda, and H. Takimoto, Large-eddy simulation of coherent flow structures within a cubical canopy, Bound.-Layer Meteorol. 142, 207 (2012).

    Article  ADS  Google Scholar 

  17. D. Chung, J. P. Monty, and N. Hutchins, Similarity and structure of wall turbulence with lateral wall shear stress variations, J. Fluid Mech. 847, 591 (2018).

    Article  ADS  MathSciNet  Google Scholar 

  18. T. Medjnoun, C. Vanderwel, and B. Ganapathisubramani, Effects of heterogeneous surface geometry on secondary flows in turbulent boundary layers, J. Fluid Mech. 886, A31 (2020).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  19. A. Stroh, K. Schäfer, P. Forooghi, and B. Frohnapfel, Secondary flow and heat transfer in turbulent flow over streamwise ridges, Int. J. Heat Fluid Flow 81, 108518 (2020).

    Article  Google Scholar 

  20. A. Stroh, K. Schäfer, B. Frohnapfel, and P. Forooghi, Rearrangement of secondary flow over spanwise heterogeneous roughness, J. Fluid Mech. 885, R5 (2020), ar**v: 1910.07205.

    Article  ADS  MathSciNet  CAS  Google Scholar 

  21. S. Leonardi, P. Orlandi, and R. A. Antonia, Properties of d- and k-type roughness in a turbulent channel flow, Phys. Fluids 19, 125101 (2007).

    Article  ADS  Google Scholar 

  22. P. Orlandi, and S. Leonardi, DNS of turbulent channel flows with two-and three-dimensional roughness, J. Turbulence 7, N73 (2006).

    Article  ADS  Google Scholar 

  23. P. Orlandi, S. Leonardi, R. Tuzi, and R. A. Antonia, Direct numerical simulation of turbulent channel flow with wall velocity disturbances, Phys. Fluids 15, 3587 (2003).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  24. P. Orlandi, S. Leonardi, and R. A. Antonia, Turbulent channel flow with either transverse or longitudinal roughness elements on one wall, J. Fluid Mech. 561, 279 (2006).

    Article  ADS  Google Scholar 

  25. D. C. Chu, and G. E. Karniadakis, A direct numerical simulation of laminar and turbulent flow over riblet-mounted surfaces, J. Fluid Mech. 250, 1 (1993).

    Article  ADS  CAS  Google Scholar 

  26. R. García-Mayoral, G. Gómez-de-Segura, and C. T. Fairhall, The control of near-wall turbulence through surface texturing, Fluid Dyn. Res. 51, 011410 (2019).

    Article  ADS  Google Scholar 

  27. D. Modesti, S. Endrikat, N. Hutchins, and D. Chung, Dispersive stresses in turbulent flow over riblets, J. Fluid Mech. 917, A55 (2021).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  28. O. Flores, and J. Jiménez, Effect of wall-boundary disturbances on turbulent channel flows, J. Fluid Mech. 566, 357 (2006).

    Article  ADS  Google Scholar 

  29. L. Chan, M. MacDonald, D. Chung, N. Hutchins, and A. Ooi, Secondary motion in turbulent pipe flow with three-dimensional roughness, J. Fluid Mech. 854, 5 (2018).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  30. M. Aghaei Jouybari, G. J. Brereton, and J. Yuan, Turbulence structures over realistic and synthetic wall roughness in open channel flow at Reτ = 1000, J. Turbulence 20, 723 (2019).

    Article  ADS  MathSciNet  Google Scholar 

  31. J. H. Lee, H. J. Sung, and P. Å. Krogstad, Direct numerical simulation of the turbulent boundary layer over a cube-roughened wall, J. Fluid Mech. 669, 397 (2011).

    Article  ADS  CAS  Google Scholar 

  32. F. E. Goddard Jr, Effect of uniformly distributed roughness on trubulent skin-friction drag at supersonic speeds, J. Aerosp. Sci. 26, 1 (1959).

    Article  Google Scholar 

  33. K. R. Czarnecki, The Problem of Roughness Drag at Supersonic Speeds, Technical Report, 1966.

  34. H. W. Liepman, and F. E. Goddard, Note on the mach number effect upon the skin friction of rough surfaces, 1957.

  35. D. E. Berg, Surface roughness effects on a Mach 6 turbulent boundary layer, AIAA J. 17, 929 (1979).

    Article  ADS  Google Scholar 

  36. R. Bowersox, in Survey of high-speed rough wall boundary layers: Invited presentation: Proceedings of the 37th AIAA Fluid Dynamics Conference and Exhibit, Miami, 2007, p. 3998.

  37. D. Modesti, S. Sathyanarayana, F. Salvadore, and M. Bernardini, Direct numerical simulation of supersonic turbulent flows over rough surfaces, J. Fluid Mech. 942, A44 (2022).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  38. C. J. Tyson, and N. D. Sandham, Numerical simulation of fully-developed compressible flows over wavy surfaces, Int. J. Heat Fluid Flow 41, 2 (2013).

    Article  Google Scholar 

  39. Z. Sun, Y. Zhu, Y. Hu, and S. Zhang, Direct numerical simulation of a fully developed compressible wall turbulence over a wavy wall, J. Turbulence 19, 72 (2018).

    Article  ADS  MathSciNet  Google Scholar 

  40. O. J. H. Williams, D. Sahoo, M. Papageorge, and A. J. Smits, Effects of roughness on a turbulent boundary layer in hypersonic flow, Exp. Fluids 62, 195 (2021).

    Article  Google Scholar 

  41. R. M. Latin, and R. D. W. Bowersox, Flow properties of a supersonic turbulent boundary layer with wall roughness, AIAA J. 38, 1804 (2000).

    Article  ADS  Google Scholar 

  42. I. W. Ekoto, R. D. W. Bowersox, T. Beutner, and L. Goss, Supersonic boundary layers with periodic surface roughness, AIAA J. 46, 486 (2008).

    Article  ADS  Google Scholar 

  43. S.J. Peltier, Behavior of turbulent structures within a Mach 5 mechanically distorted boundary layer, Dissertation for Doctoral Degree (Texas A&M University, 2013).

  44. S. J. Peltier, R. A. Humble, and R. D. W. Bowersox, Crosshatch roughness distortions on a hypersonic turbulent boundary layer, Phys. Fluids 28, 045105 (2016).

    Article  ADS  Google Scholar 

  45. M. A. Jouybari, J. Yuan, G. J. Brereton, and F. A. Jaberi, Supersonic turbulent channel flows over two and three dimensional sinusoidal rough walls, ar**v: 2012.02852.

  46. X. X. Yuan, Y. L. Fu, J. Q. Chen, M. Yu, and P. X. Liu, Supersonic turbulent channel flows over spanwise-oriented grooves, Phys. Fluids 34, 016109 (2022).

    Article  ADS  CAS  Google Scholar 

  47. L. Duan, M. M. Choudhari, and M. Wu, Numerical study of acoustic radiation due to a supersonic turbulent boundary layer, J. Fluid Mech. 746, 165 (2014).

    Article  ADS  CAS  Google Scholar 

  48. L. Duan, M. M. Choudhari, and C. Zhang, Pressure fluctuations induced by a hypersonic turbulent boundary layer, J. Fluid Mech. 804, 578 (2016).

    Article  ADS  MathSciNet  PubMed  PubMed Central  Google Scholar 

  49. W. K. Blake, Mechanics of Flow-Induced Sound and Vibration, Volume 2: Complex Flow-Structure Interactions (Academic Press, 2017).

  50. T. Meyers, J. B. Forest, and W. J. Devenport, The wall-pressure spectrum of high-Reynolds-number turbulent boundary-layer flows over rough surfaces, J. Fluid Mech. 768, 261 (2015).

    Article  ADS  CAS  Google Scholar 

  51. L. A. Joseph, N. J. Molinaro, W. J. Devenport, and T. W. Meyers, Characteristics of the pressure fluctuations generated in turbulent boundary layers over rough surfaces, J. Fluid Mech. 883, A3 (2020).

    Article  ADS  MathSciNet  Google Scholar 

  52. M. Yu, P. X. Liu, Z. G. Tang, X. X. Yuan, and C. X. Xu, Effects of wall disturbances on the statistics of supersonic turbulent boundary layers, Phys. Fluids 35, 025126 (2023).

    Article  ADS  CAS  Google Scholar 

  53. A. J. Musker, Explicit expression for the smooth wall velocity distribution in a turbulent boundary layer, AIAA J. 17, 655 (1979).

    Article  ADS  Google Scholar 

  54. M. Klein, A. Sadiki, and J. Janicka, A digital filter based generation of inflow data for spatially develo** direct numerical or large eddy simulations, J. Comput. Phys. 186, 652 (2003).

    Article  ADS  Google Scholar 

  55. A. M. Kempf, S. Wysocki, and M. Pettit, An efficient, parallel low-storage implementation of Klein’s turbulence generator for LES and DNS, Comput. Fluids 60, 58 (2012).

    Article  MathSciNet  Google Scholar 

  56. Y. S. Zhang, W. T. Bi, F. Hussain, and Z. S. She, A generalized Reynolds analogy for compressible wall-bounded turbulent flows, J. Fluid Mech. 739, 392 (2014).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  57. M. C. Wilder, and D. K. Prabhu, in Rough-wall turbulent heat transfer experiments in hypersonic free flight: Proceedings of AIAA Aviation 2019 Forum, 2019, p. 3009.

  58. Y. Kuwata, and K. Suga, Direct numerical simulation of turbulence over anisotropic porous media, J. Fluid Mech. 831, 41 (2017).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  59. M. E. Rosti, L. Brandt, and A. Pinelli, Turbulent channel flow over an anisotropic porous wall—drag increase and reduction, J. Fluid Mech. 842, 381 (2018).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  60. M. Bernardini, D. Modesti, F. Salvadore, and S. Pirozzoli, STREAmS: A high-fidelity accelerated solver for direct numerical simulation of compressible turbulent flows, Comput. Phys. Commun. 263, 107906 (2021).

    Article  MathSciNet  CAS  Google Scholar 

  61. S. Pirozzoli, Generalized conservative approximations of split convective derivative operators, J. Comput. Phys. 229, 7180 (2010).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  62. S. Pirozzoli, and M. Bernardini, Turbulence in supersonic boundary layers at moderate Reynolds number, J. Fluid Mech. 688, 120 (2011).

    Article  ADS  MathSciNet  Google Scholar 

  63. F. R. Hama, Boundary-layer characteristics for smooth and rough surfaces, Trans. Soc. Nav. Archit. Mar. Eng. 62, 333 (1954).

    Google Scholar 

  64. C. KW Tam, Supersonic jet noise, Annu. Rev. Fluid Mech. 27, 17 (1995).

    Article  ADS  Google Scholar 

  65. J. Laufer, Some statistical properties of the pressure field radiated by a turbulent boundary layer, Phys. Fluids, 7, 1191 (1964).

    Article  ADS  Google Scholar 

  66. H. Oertel, Kinematics of Mach waves inside and outside supersonic jets, in: Recent Developments in Theoretical and Experimental Fluid Mechanics (Springer, 1979), pp. 121–136.

  67. D. A. Buchta, and J. B. Freund, The near-field pressure radiated by planar high-speed free-shear-flow turbulence, J. Fluid Mech. 832, 383 (2017).

    Article  ADS  MathSciNet  Google Scholar 

  68. D. A. Buchta, and J. B. Freund, Intense sound radiation by high-speed flow: Turbulence structure, gas properties, and near-field gas dynamics, Phys. Rev. Fluids 4, 044605 (2019).

    Article  ADS  Google Scholar 

  69. J. Westerweel, C. Fukushima, J. M. Pedersen, and J. C. R. Hunt, Mechanics of the Turbulent-Nonturbulent Interface of a Jet, Phys. Rev. Lett. 95, 174501 (2005).

    Article  ADS  CAS  PubMed  Google Scholar 

  70. M. Khashehchi, A. Ooi, J. Soria, and I. Marusic, Evolution of the turbulent/non-turbulent interface of an axisymmetric turbulent jet, Exp. Fluids 54, 1449 (2013).

    Article  Google Scholar 

  71. R. K. Anand, B. J. Boersma, and A. Agrawal, Detection of turbulent/non-turbulent interface for an axisymmetric turbulent jet: Evaluation of known criteria and proposal of a new criterion, Exp. Fluids 47, 995 (2009).

    Article  Google Scholar 

  72. K. Chauhan, J. Philip, C. M. de Silva, N. Hutchins, and I. Marusic, The turbulent/non-turbulent interface and entrainment in a boundary layer, J. Fluid Mech. 742, 119 (2014).

    Article  Google Scholar 

  73. J. Philip, C. Meneveau, C. M. de Silva, and I. Marusic, Multiscale analysis of fluxes at the turbulent/non-turbulent interface in high Reynolds number boundary layers, Phys. Fluids 26, 015105 (2014).

    Article  ADS  Google Scholar 

  74. R. Jahanbakhshi, and C. K. Madnia, Entrainment in a compressible turbulent shear layer, J. Fluid Mech. 797, 564 (2016).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  75. N. Hutchins, and I. Marusic, Evidence of very long meandering features in the logarithmic region of turbulent boundary layers, J. Fluid Mech. 579, 1 (2007).

    Article  ADS  Google Scholar 

  76. G. Z. Ma, C. X. Xu, H. J. Sung, and W. X. Huang, Outer-layer similarity and energy transfer in a rough-wall turbulent channel flow, J. Fluid Mech. 2023.

  77. D. D. Wangsawijaya, R. Baidya, D. Chung, I. Marusic, and N. Hutchins, The effect of spanwise wavelength of surface heterogeneity on turbulent secondary flows, J. Fluid Mech. 894, A7 (2020).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  78. M. Bernardini, and S. Pirozzoli, Wall pressure fluctuations beneath supersonic turbulent boundary layers, Phys. Fluids 23, 085102 (2011).

    Article  ADS  Google Scholar 

  79. M. Yu, P. X. Liu, Y. L. Fu, Z. G. Tang, and X. X. Yuan, Wall shear stress, pressure, and heat flux fluctuations in compressible wall-bounded turbulence, part I: One-point statistics, Phys. Fluids 34, 065139 (2022).

    Article  ADS  CAS  Google Scholar 

  80. M. Yu, P. X. Liu, Y. L. Fu, Z. G. Tang, and X. X. Yuan, Wall shear stress, pressure and heat flux fluctuations in compressible wall-bounded turbulence, II. Spectra, correlation and nonlinear interactions, Phys. Fluids 34, 065140 (2022).

    Article  ADS  CAS  Google Scholar 

  81. M. Yu, C. X. Xu, and S. Pirozzoli, Compressibility effects on pressure fluctuation in compressible turbulent channel flows, Phys. Rev. Fluids 5, 113401 (2020).

    Article  ADS  Google Scholar 

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Acknowledgements

This work was supported by the National Key R&D Program of China (Grant No. 2019YFA0405201), Bei**g Fluid Dynamics Scientific Research Center, China Postdoctoral Science Foundation, and National Natural Science Foundation of China (Grant Nos. 92052301, 12202469, and 12272396).

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  1. State Key Laboratory of Aerodynamics, Mianyang, 621000, China

    Ming Yu  (余明), Qingqing Zhou  (周清清), Hongmin Su  (粟虹敏), Qilong Guo  (郭启龙) & **anxu Yuan  (袁先旭)

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Contributions

Ming Yu designed the research and wrote and reviewed the manuscript. Qingqing Zhou performed formal analysis for Sects. 3 and 4.1 and revised the manuscript. Hongmin Su performed formal analysis for Sects. 4.2 and 4.3. Qilong Guo helped with the management and coordination responsibility for the research activity planning and execution. **anxu Yuan helped organize the manuscript and acquired the research funding.

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Correspondence to **anxu Yuan  (袁先旭).

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Yu, M., Zhou, Q., Su, H. et al. Influences of wall disturbances on coherent structures in supersonic turbulent boundary layers. Acta Mech. Sin. 39, 323075 (2023). https://doi.org/10.1007/s10409-023-23075-x

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