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Incorporating intrinsic compressibility effects in velocity transformations for wall-bounded turbulent flows

Asif Manzoor Hasan1,*, Johan Larsson2, Sergio Pirozzoli3, and Rene Pecnik1,†

  • 1Process and Energy Department, Delft University of Technology, Leeghwaterstraat 39, 2628 CB, Delft, The Netherlands
  • 2Department of Mechanical Engineering, University of Maryland, College Park, Maryland 20742, USA
  • 3Dipartimento di Ingegneria Meccanica e Aerospaziale, Sapienza Università di Roma, Via Eudossiana 18, 00184 Roma, Italy

  • *a.m.hasan@tudelft.nl
  • †r.pecnik@tudelft.nl
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Phys. Rev. Fluids 8, L112601 – Published 9 November, 2023

DOI: https://doi.org/10.1103/PhysRevFluids.8.L112601

Abstract

A transformation that relates a compressible wall-bounded turbulent flow with nonuniform fluid properties to an equivalent incompressible flow with uniform fluid properties is derived and validated. The transformation accounts for both variable-property and intrinsic compressibility effects, the latter being the key improvement over the current state of the art. The importance of intrinsic compressibility effects contradicts the renowned Morkovin's hypothesis.

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References (50)

  1. P. Bradshaw and G. P. Huang, The law of the wall in turbulent flow, Proc. R. Soc. Lond. A 451, 165 (1995).
  2. Y.-S. Zhang, W.-T. Bi, F. Hussain, X.-L. Li, and Z.-S. She, Mach-number-invariant mean-velocity profile of compressible turbulent boundary layers, Phys. Rev. Lett. 109, 054502 (2012).
  3. E. R. Van Driest, Turbulent boundary layer in compressible fluids, J. Aeronau. Sci. 18, 145 (1951).
  4. A. Trettel and J. Larsson, Mean velocity scaling for compressible wall turbulence with heat transfer, Phys. Fluids 28, 026102 (2016).
  5. P. G. Huang, G. N. Coleman, and P. Bradshaw, Compressible turbulent channel flows: DNS results and modelling, J. Fluid Mech. 305, 185 (1995).
  6. A. Patel, B. J. Boersma, and R. Pecnik, The influence of near-wall density and viscosity gradients on turbulence in channel flows, J. Fluid Mech. 809, 793 (2016).
  7. C. Zhang, L. Duan, and M. M. Choudhari, Direct numerical simulation database for supersonic and hypersonic turbulent boundary layers, AIAA J. 56, 4297 (2018).
  8. K. P. Griffin, L. Fu, and P. Moin, Velocity transformation for compressible wall-bounded turbulent flows with and without heat transfer, Proc. Natl. Acad. Sci. 118, e2111144118 (2021).
  9. R. Hirai, R. Pecnik, and S. Kawai, Effects of the semi-local Reynolds number in scaling turbulent statistics for wall heated/cooled supersonic turbulent boundary layers, Phys. Rev. Fluids 6, 124603 (2021).
  10. T. Bai, K. P. Griffin, and L. Fu, Compressible velocity transformations for various noncanonical wall-bounded turbulent flows, AIAA J. 60, 4325 (2022).
  11. P. S. Volpiani, P. S. Iyer, S. Pirozzoli, and J. Larsson, Data-driven compressibility transformation for turbulent wall layers, Phys. Rev. Fluids 5, 052602 (2020).
  12. P. Bradshaw, Compressible turbulent shear layers, Annu. Rev. Fluid Mech. 9, 33 (1977).
  13. S. K. Lele, Compressibility effects on turbulence, Annu. Rev. Fluid Mech. 26, 211 (1994).
  14. M. Yu, C.-X. Xu, and S. Pirozzoli, Genuine compressibility effects in wall-bounded turbulence, Phys. Rev. Fluids 4, 123402 (2019).
  15. M. Yu, C.-X. Xu, and S. Pirozzoli, Compressibility effects on pressure fluctuation in compressible turbulent channel flows, Phys. Rev. Fluids 5, 113401 (2020).
  16. M. Yu and C.-X. Xu, Compressibility effects on hypersonic turbulent channel flow with cold walls, Phys. Fluids 33, 075106 (2021).
  17. M. Yu, P. Liu, Y. Fu, Z. Tang, and 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).
  18. Z.-H. Wan, N.-S. Liu, D.-J. Sun, X.-Y. Lu et al., Wall-cooling effects on pressure fluctuations in compressible turbulent boundary layers from subsonic to hypersonic regimes, J. Fluid Mech. 946, A14 (2022).
  19. G. N. Coleman, J. Kim, and R. D. Moser, A numerical study of turbulent supersonic isothermal-wall channel flow, J. Fluid Mech. 305, 159 (1995).
  20. 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).
  21. A. M. Hasan, J. Larsson, S. Pirozzoli, and R. Pecnik, unpublished (2023).
  22. M. Bernardini and S. Pirozzoli, Wall pressure fluctuations beneath supersonic turbulent boundary layers, Phys. Fluids 23, 085102 (2011).
  23. M. Cogo, F. Salvadore, F. Picano, and M. Bernardini, Direct numerical simulation of supersonic and hypersonic turbulent boundary layers at moderate-high Reynolds numbers and isothermal wall condition, J. Fluid Mech. 945, A30 (2022).
  24. A. Ceci, A. Palumbo, J. Larsson, and S. Pirozzoli, Numerical tripping of high-speed turbulent boundary layers, Theor. Comput. Fluid Dyn. 36, 865 (2022).
  25. A. Ceci (private communication).
  26. R. D. Moser, J. Kim, and N. N. Mansour, Direct numerical simulation of turbulent channel flow up to Reτ=590, Phys. Fluids 11, 943 (1999).
  27. A. J. Smits and J.-P. Dussauge, Turbulent Shear Layers in Supersonic Flow (Springer Science & Business Media, 2006).
  28. L. Duan, I. Beekman, and M. Martin, Direct numerical simulation of hypersonic turbulent boundary layers. Part 3. Effect of Mach number, J. Fluid Mech. 672, 245 (2011).
  29. H. M. Nagib and K. A. Chauhan, Variations of von Kármán coefficient in canonical flows, Phys. Fluids 20, 101518 (2008).
  30. M. Cogo, U. Baù, M. Chinappi, M. Bernardini, and F. Picano, Assessment of heat transfer and Mach number effects on high-speed turbulent boundary layers, J. Fluid Mech. 974, A10 (2023).
  31. S. B. Pope, Turbulent Flows (Cambridge University Press, 2000).
  32. H. Foysi, S. Sarkar, and R. Friedrich, Compressibility effects and turbulence scalings in supersonic channel flow, J. Fluid Mech. 509, 207 (1999).
  33. P. S. Iyer, P. S. Volpiani, J. Larsson, S. Pirozzoli, and M. R. Malik, A near-wall eddy viscosity for compressible turbulent flows based on velocity transformation with application to wall models, in APS/DFD Annual Meeting, B11.007 (2019).
  34. X. I. Yang and Y. Lv, A semi-locally scaled eddy viscosity formulation for LES wall models and flows at high speeds, Theor. Comput. Fluid Dyn. 32, 617 (2018).
  35. D. A. Johnson and L. King, A mathematically simple turbulence closure model for attached and separated turbulent boundary layers, AIAA J. 23, 1684 (1985).
  36. E. R. Van Driest, On turbulent flow near a wall, J. Aeronau. Sci. 23, 1007 (1956).
  37. P. S. Iyer and M. R. Malik, Analysis of the equilibrium wall model for high-speed turbulent flows, Phys. Rev. Fluids 4, 074604 (2019).
  38. A. Patel, R. Pecnik, J. Peeters, S. Hickel, and M. Moghadam, Turbulence modulation by variable density and viscosity, in Proceedings of the 2016 Summer Program: Studying Turbulence Using Numerical Simulation Databases - XVI (Stanford University, USA, 2016), pp. 213–222.
  39. P. S. Volpiani, M. Bernardini, and J. Larsson, Effects of a nonadiabatic wall on supersonic shock/boundary-layer interactions, Phys. Rev. Fluids 3, 083401 (2018).
  40. P. S. Volpiani, M. Bernardini, and J. Larsson, Effects of a nonadiabatic wall on hypersonic shock/boundary-layer interactions, Phys. Rev. Fluids 5, 014602 (2020).
  41. T. Toki, S. Teramoto, and K. Okamoto, Velocity and temperature profiles in turbulent channel flow at supercritical pressure, J. Propul. Power 36, 3 (2020).
  42. M. Lee and R. D. Moser, Direct numerical simulation of turbulent channel flow up to Reτ≈5200, J. Fluid Mech. 774, 395 (2015).
  43. S. Kawai, Heated transcritical and unheated non-transcritical turbulent boundary layers at supercritical pressures, J. Fluid Mech. 865, 563 (2019).
  44. A. M. O. Smith and T. Cebeci, Numerical Solution of the Turbulent-Boundary-Layer Equations (Douglas Aircraft Company, Douglas Aircraft Division, 1967).
  45. B. Baldwin and H. Lomax, Thin-layer approximation and algebraic model for separated turbulent flows, in 16th Aerospace Sciences Meeting (AIAA, 1978), p. 257.
  46. D. C. Wilcox et al., Turbulence Modeling for CFD, Vol. 2 (DCW industries La Canada, CA, 1998).
  47. E. R. Van Driest, The Problem of Aerodynamic Heating (Institute of the Aeronautical Sciences, 1956).
  48. P. Huang, P. Bradshaw, and T. Coakley, Skin friction and velocity profile family for compressible turbulent boundary layers, AIAA J. 31, 1600 (1993).
  49. V. Kumar and J. Larsson, Modular method for estimation of velocity and temperature profiles in high-speed boundary layers, AIAA J. 60, 5165 (2022).
  50. A. M. Hasan, J. Larsson, S. Pirozzoli, and R. Pecnik, Estimating mean profiles and fluxes in high-speed turbulent boundary layers using inner/outer-layer scalings, arXiv:2307.02199 [AIAA J. (to be published, 2023)].

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Phys. Rev. Fluids 8, L112601– Published 9 November, 2023
  • Received 28 February 2023
  • Accepted 3 October 2023
Article part of CHORUS
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