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Wall shear stress and wall heat flux in a supersonic turbulent boundary layer subjected to concave surface curvature

Fulin Tong (童福林)1, Junyi Duan (段俊亦)2,3, Xiangxin Ji (纪相鑫)2,3, Siwei Dong (董思卫)1, Xianxu Yuan (袁先旭)1,*, and Xinliang Li (李新亮)2,3

  • 1State Key Laboratory of Aerodynamics, Mianyang 621000, China
  • 2LHD, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China
  • 3School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, China

  • *Corresponding author: yuanxianxu@cardc.cn
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Phys. Rev. Fluids 8, 124602 – Published 5 December, 2023

DOI: https://doi.org/10.1103/PhysRevFluids.8.124602

Abstract

Direct numerical simulation is employed to investigate the characteristics of wall shear stress (WSS) and wall heat flux (WHF) beneath a spatially developing supersonic turbulent boundary layer with a cold-wall thermal condition subjected to a concavely curved compression ramp with a deflection angle of 24∘. The Mach number is 2.25 and the friction Reynolds number is 769. Numerical data are exploited to characterize the effect of the concave surface curvature on the statistical and structural properties of the fluctuating WSS and WHF, including the probability density function, space-time correlations, and frequency spectra. Across the curved region, the occurrence probability of extreme negative events is strongly affected by the curvature, as manifested by a noticeable dissimilarity in the large negative tails of the probability density functions. The correlation results show that the streamwise extent of the WSS fluctuations becomes smaller, in contrast to that of the WHF fluctuations, and a considerable decrease in the convection velocity is observed downstream from the curvature. It is found that the curvature qualitatively modifies the WHF frequency spectra, leading to a shift to lower frequencies, while the spectral alternation is less pronounced for the WSS. Importantly, the mean WHF and WSS are also decomposed into different physically informed components, with the finding that the mean WSS generation is fundamentally changed by the curvature but the generation mechanism of the mean WHF is constant throughout the concave surface. Finally, an analysis of velocity and temperature structures is performed with the aid of bidimensional empirical mode decomposition to quantitatively demonstrate the contributions of specific spanwise length scales. We highlight that the outer large-scale organized structures, which are significantly energized by the concave surface, make an increasingly important contribution to the mean WSS and WHF generation.

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References (58)

  1. P. Bradshaw, Effects of streamline curvature on turbulent flow, Tech. Rep. AGARDograph 169 (1973).
  2. A. J. Smits, The response of turbulent boundary layers to sudden perturbations, Annu. Rev. Fluid Mech. 17, 321 (1985).
  3. E. R. Spina, A. J. Smits, and S. K. Robinson, The physics of supersonic turbulent boundary layers, Annu. Rev. Fluid Mech. 26, 287 (1994).
  4. W. B. Sturek and J. E. Danberg, Supersonic turbulent boundary layer in adverse pressure gradient. Part I: The experiment, AIAA J. 10, 475 (1972).
  5. W. B. Sturek and J. E. Danberg, Supersonic turbulent boundary layer in adverse pressure gradient. Part II: Data analysis, AIAA J. 10, 630 (1972).
  6. A. J. Laderman, Adverse pressure gradient effects on supersonic boundary layer turbulence, AIAA J. 18, 1186 (1980).
  7. M. Jayaram, M. W. Taylor, and A. J. Smits, The response of a compressible turbulent boundary layer to short regions of concave surface curvature, J. Fluid Mech. 175, 343 (1987).
  8. P. H. Hoffmann, K. C. Muck, and P. Bradshaw, The effect of concave surface curvature on turbulent boundary layers, J. Fluid Mech. 161, 371 (1985).
  9. J. F. Donovan, E. F. Spina, and A. J. Smits, The structure of a supersonic turbulent boundary layer subjected to concave surface curvature, J. Fluid Mech. 259, 1 (1994).
  10. I. Neel, A. N. Leidy, R. D. W. Bowersox, and N. R. Tichenor, Hypersonic boundary layer with streamwise curvature-driven adverse pressure gradient, in Eigth AIAA Flow Control Conference (AIAA, Reston, VA, 2016), AIAA Paper No. 2016–4248.
  11. Q. C. Wang and Z. G. Wang, Structural characteristics of the supersonic turbulent boundary layer subjected to concave curvature, Appl. Phys. Lett. 108, 114102 (2016).
  12. Q. C. Wang, Z. G. Wang, and Y. X. Zhao, An experimental investigation of the supersonic turbulent boundary layer subjected to concave curvature, Phys. Fluids 28, 096104 (2016).
  13. H. Thomann, Effect of streamwise wall curvature on heat transfer in a turbulent boundary layer, J. Fluid Mech. 33, 283 (1968).
  14. E. M. Fernando and A. J. Smits, A supersonic turbulent boundary layer in an adverse pressure gradient, J. Fluid Mech. 211, 285 (1990).
  15. D. R. Smith and A. J. Smits, A study of the effects of curvature and compression on the behavior of a supersonic turbulent boundary layer, Exp. Fluids 18, 363 (1995).
  16. Q. C. Wang, Z. G. Wang, and Y. X. Zhao, On the impact of adverse pressure gradient on the supersonic turbulent boundary layer, Phys. Fluids 28, 116101 (2016).
  17. F. L. Tong, X. L. Li, Y. H. Duan, and C. P. Yu, Direct numerical simulation of supersonic turbulent boundary layer subjected to a curved compression ramp, Phys. Fluids 29, 125101 (2017).
  18. M. B. Sun, N. D. Sandham, and Z. W. Hu, Turbulence structures and statistics of a supersonic turbulent boundary layer subjected to concave surface curvature, J. Fluid Mech. 865, 60 (2019).
  19. Q. C. Wang, Z. G. Wang, M. B. Sun, R. Yang, Y. X. Zhao, and Z. W. Hu, The amplification of large-scale motion in a supersonic concave turbulent boundary layer and its impact on the mean and statistical properties, J. Fluid Mech. 863, 454 (2019).
  20. X. S. Wu, J. H. Liang, and Y. X. Zhao, Direct numerical simulation of a supersonic turbulent boundary layer subjected to a concave surface, Phys. Rev. Fluids 4, 044602 (2019).
  21. G. L. Nicholson, J. J. Huang, L. Duan, and M. M. Choudhari, Simulation and modeling of hypersonic turbulent boundary layers subjected to adverse pressure gradients due to concave streamline curvature, in AIAA Aviation Forum (AIAA, Reston, VA, 2021), AIAA Paper No. 2021–2891.
  22. W. P. Li, Y. T. Fan, D. Modesti, and C. Cheng, Decomposition of the mean skin-friction drag in compressible turbulent channel flows, J. Fluid Mech. 875, 101 (2019).
  23. D. Sun, Q. L. Guo, X. X. Yuan, H. Y. Zhang, and C. Li, A decomposition formula for the wall heat flux of a compressible boundary layer, Adv. Aerodyn. 3, 33 (2021).
  24. Y. T. Fan, W. P. Li, and S. Pirozzoli, Decomposition of the mean skin-friction drag in zero-pressure-gradient turbulent boundary layers, Phys. Fluids 31, 086105 (2019).
  25. F. L. Tong, S. W. Dong, J. Lai, X. X. Yuan, and X. L. Li, Wall shear stress and wall heat flux in a supersonic turbulent boundary layer, Phys. Fluids 34, 015127 (2022).
  26. F. L. Tong, S. W. Dong, J. Y. Duan, X. X. Yuan, and X. L. Li, Effect of expansion on the wall heat flux in a supersonic turbulent boundary layer, Phys. Fluids 34, 105109 (2022).
  27. F. L. Tong, X. X. Yuan, J. Lai, J. Y. Duan, D. Sun, and S. W. Dong, Wall heat flux in a supersonic shock wave/turbulent boundary layer interaction, Phys. Fluids 34, 065104 (2022).
  28. F. L. Tong, J. Y. Duan, and X. L. Li, Characteristics of reattached boundary layer in shock wave and turbulent boundary layer interaction, Chin. J. Aeronaut. 35, 172 (2022).
  29. F. L. Tong, J. Lai, J. Y. Duan, S. W. Dong, X. X. Yuan, and X. L. Li, Effect of interaction strength on recovery downstream of incident shock interactions, Phys. Fluids 34, 1251274 (2022).
  30. X. L. Li, D. X. Fu, and Y. W. Ma, Direct numerical simulation of hypersonic boundary layer transition over a blunt cone with a small angle of attack, Phys. Fluids 22, 025105 (2010).
  31. X. L. Li, D. X. Fu, and Y. W. Ma, Direct numerical simulation of hypersonic boundary-layer transition over a blunt cone, AIAA J. 46, 2899 (2008).
  32. F. L. Tong, D. Sun, and X. L. Li, Direct numerical simulation of impinging shock wave and turbulent boundary layer interaction over a wavy-wall, Chin. J. Aeronaut. 34, 350 (2021).
  33. X. K. Zhu, C. P. Yu, F. L. Tong, and X. L. Li, Numerical study on wall temperature effects on shock wave/turbulent boundary layer interaction, AIAA J. 55, 131 (2017).
  34. X. Chen, J. Q. Chen, and X. X. Yuan, Hypersonic boundary layer transition on a concave wall induced by low-frequency blowing and suction, Phys. Fluids 34, 114105 (2022).
  35. X. Chen, G. L. Huang, and C. Lee, Hypersonic boundary layer transition on a concave wall: Stationary Görtler vortices, J. Fluid Mech. 865, 1 (2019).
  36. M. P. Martin, E. M. Taylor, M. Wu, and V. G. Weirs, A bandwidth-optimized WENO scheme for the effective direct numerical simulation of compressible turbulence, J. Comput. Phys. 220, 270 (2006).
  37. S. Gottlieb and C. W. Shu, Total variation diminishing Runge-Kutta Schemes, Math. Comput. 67, 73 (1998).
  38. S. Pirozzoli and M. Bernardini, Turbulence in supersonic boundary layers at moderate Reynolds number, J. Fluid Mech. 688, 120 (2011).
  39. S. Priebe and M. P. Martin, Turbulence in a hypersonic compression ramp flow, Phys. Rev. Fluids 6, 034601 (2021).
  40. S. Pirozzoli, F. Grasso, and T. B. Gatski, Direct numerical simulation and analysis of a spatially evolving supersonic turbulent boundary layer at M=2.25, Phys. Fluids 16, 530 (2004).
  41. E. J. Hopkins, E. R. Keener, T. E. Polek, and H. A. Dwyer, Hypersonic turbulent skin-friction and boundary-layer profiles on nonadiabatic flat plates, AIAA J. 10, 40 (1972).
  42. J. J. Huang, L. Duan, and M. M. Choudhari, Direct numerical simulation of hypersonic turbulent boundary layers: Effect of spatial evolution and Reynolds number, J. Fluid Mech. 937, A3 (2022).
  43. J. Fang, A. A. Zheltovodov, Y. F. Yao, C. Moulinec, and D. R. Emerson, On the turbulence amplification in shock-wave/turbulent boundary layer interaction, J. Fluid Mech. 897, A32 (2020).
  44. M. Eléna and J. Lacharme, Experimental study of a supersonic turbulent boundary layer using a laser Doppler anemometer, J. Méc. Théor. Appl. 7, 175 (1988).
  45. J. Jeong and F. Hussain, On the identification of a vortex, J. Fluid Mech. 285, 69 (1995).
  46. M. Grilli, S. Hickel, and N. A. Adams, Large-eddy simulation of a supersonic turbulent boundary layer over a compression-expansion ramp, Int. J. Heat Fluid Flow 42, 79 (2013).
  47. M. S. Loginov, N. A. Adams, and A. A. Zheltovodov, Large-eddy simulation of shock-wave/turbulent-boundary-layer interaction, J. Fluid Mech. 565, 135 (2006).
  48. R. L. Simpson, Turbulent boundary-layer separation, Annu. Rev. Fluid Mech. 21, 205 (1989).
  49. R. Örlü and P. Schlatter, On the fluctuating wall-shear stress in zero pressure-gradient turbulent boundary layer flows, Phys. Fluids 23, 021704 (2011).
  50. 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).
  51. H. Abe, H. Kawamura, and Y. Matsuo, Surface heat-flux fluctuations in a turbulent channel flow up to Reτ=1020 with Pr=0.025 and 0.71, Int. J. Heat Fluid Flow 25, 404 (2004).
  52. 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: Spectra, correlation and nonlinear interactions, Phys. Fluids 34, 065140 (2022).
  53. L. Duan, M. M. Choudhari, and M. W. Wu, Numerical study of acoustic radiation due to a supersonic turbulent boundary layer, J. Fluid Mech. 746, 165 (2014).
  54. M. Bernardini and S. Pirozzoli, Wall pressure fluctuations beneath supersonic turbulent boundary layers, Phys. Fluids 23, 085102 (2011).
  55. C. D. Daniel, S. Laizet, and J. C. Vassilico, Wall shear stress fluctuations: Mixed scaling and their effects on velocity fluctuations in a turbulent boundary layer, Phys. Fluids 29, 055102 (2017).
  56. Z. W. Hu, C. L. Morfey, and N. D. Sandham, Wall pressure and shear stress spectra from direct numerical simulations of channel flow up to Reτ=1440, AIAA J. 44, 1541 (2006).
  57. Y. T. Fan, W. P. Li, M. Atzori, R. Pozuelo, P. Schlatter, and R. Vinuesa, Decomposition of the mean skin-friction drag in adverse-pressure-gradient turbulent boundary layers, Phys. Rev. Fluids 5, 114608 (2020).
  58. C. Cheng, W. P. Li, A. Lozano-Durán, and H. Liu, Identity of attached eddies in turbulent channel flows with bidimensional empirical mode decomposition, J. Fluid Mech. 870, 1037 (2019).

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Phys. Rev. Fluids 8, 124602– Published 5 December, 2023
  • Received 18 June 2023
  • Accepted 7 November 2023
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