- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Fluids

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Scalar statistics in variable property turbulent channel flows

Ashish Patel*, Bendiks J. Boersma, and Rene Pecnik†

  • Process and Energy Department, Delft University of Technology, Leeghwaterstraat 39, 2628 CB Delft, The Netherlands

  • *a.patel@tudelft.nl
  • †r.pecnik@tudelft.nl
PDF

Phys. Rev. Fluids 2, 084604 – Published 21 August, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.084604

Abstract

Direct numerical simulation of fully developed, internally heated channel flows with isothermal walls is performed using the low-Mach-number approximation of Navier-Stokes equation to investigate the influence of temperature-dependent properties on turbulent scalar statistics. Different constitutive relations for density ρ, viscosity μ, and thermal conductivity λ as a function of temperature are prescribed in order to characterize the turbulent scalar statistics. It is shown that the dominant effect caused by property variations on scalar statistics can be parameterized by two nondimensional parameters, namely the semilocal Reynolds number Reτ★≡Reτ(ρ¯/ρw)/(μ¯/μw) (the bar and subscript w denote Reynolds averaging and wall value respectively, while Reτ is the friction Reynolds number based on wall values), and the local Prandtl number Pr★=Prwμ¯/μw/λ¯/λw (Prw is the molecular Prandtl number based on wall values). Near-wall gradients in Reτ★ modulate the turbulent heat flux generation mechanism because of structural changes in turbulence. However, the influence of these modulations on the inner scaling of turbulent heat conductivity normalized by local mean viscosity is shown to be weak. Using this observation, a temperature transformation is derived that is invariant of Reτ★ variations and only exhibits a Pr★-dependent shift.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (30)

  1. J. Kim and P. Moin, Transport of passive scalars in a turbulent channel flow, in Turbulent Shear Flows 6 (Springer, Berlin, 1989), pp. 85–96.
  2. H. Kawamura, K. Ohsaka, H. Abe, and K. Yamamoto, DNS of turbulent heat transfer in channel flow with low to medium-high Prandtl number fluid, Int. J. Heat Fluid Flow 19, 482 (1998).
  3. F. Schwertfirm and M. Manhart, DNS of passive scalar transport in turbulent channel flow at high Schmidt numbers, Int. J. Heat Fluid Flow 28, 1204 (2007).
  4. H. Kawamura, H. Abe, and Y. Matsuo, DNS of turbulent heat transfer in channel flow with respect to Reynolds and Prandtl number effects, Int. J. Heat Fluid Flow 20, 196 (1999).
  5. S. Pirozzoli, M. Bernardini, and P. Orlandi, Passive scalars in turbulent channel flow at high Reynolds number, J. Fluid Mech. 788, 614 (2016).
  6. J. Y. Yoo, The turbulent flows of supercritical fluids with heat transfer, Annu. Rev. Fluid Mech. 45, 495 (2013).
  7. H. Nemati, A. Patel, B. J. Boersma, and R. Pecnik, Mean statistics of a heated turbulent pipe flow at supercritical pressure, Int. J. Heat Mass Transfer 83, 741 (2015).
  8. J. W. R. Peeters, R. Pecnik, M. Rohde, T. H. J. J. van der Hagen, and B. J. Boersma, Turbulence attenuation in simultaneously heated and cooled annular flows at supercritical pressure, J. Fluid Mech. 799, 505 (2016).
  9. 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).
  10. R. Lechner, J. Sesterhenn, and R. Friedrich, Turbulent supersonic channel flow, J. Turbulence 2, N1 (2001).
  11. H. Foysi, S. Sarkar, and R. Friedrich, Compressibility effects and turbulence scalings in supersonic channel flow, J. Fluid Mech. 509, 207 (2004).
  12. D. Modesti and S. Pirozzoli, Reynolds and Mach number effects in compressible turbulent channel flow, Int. J. Heat Fluid Flow 59, 33 (2016).
  13. F. Zonta, C. Marchioli, and A. Soldati, Modulation of turbulence in forced convection by temperature-dependent viscosity, J. Fluid Mech. 697, 150 (2012).
  14. F. Nicoud and T. Poinsot, DNS of a channel flow with variable properties, in International Symposium on Turbulence and Shear Flow Phenomena (TSFP-1) (Begell House, Santa Barbara, California, 1999), p. 697.
  15. A. Patel, J. W. R. Peeters, B. J. Boersma, and R. Pecnik, Semi-local scaling and turbulence modulation in variable property turbulent channel flows, Phys. Fluids 27, 095101 (2015).
  16. 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).
  17. J. Lee, S. Y. Jung, H. J. Sung, and T. A. Zaki, Turbulent thermal boundary layers with temperature-dependent viscosity, Int. J. Heat Fluid Flow 49, 43 (2014).
  18. B. A. Kader, Temperature and concentration profiles in fully turbulent boundary layers, Int. J. Heat Mass Transfer 24, 1541 (1981).
  19. H. Nemati, A. Patel, B. J. Boersma, and R. Pecnik, The effect of thermal boundary conditions on forced convection heat transfer to fluids at supercritical pressure, J. Fluid Mech. 800, 531 (2016).
  20. W. M. Kays and M. E. Crawford, Convective Heat and Mass Transfer (McGraw-Hill, New York, 1993).
  21. H. Kong, H. Choi, and J. S. Lee, Direct numerical simulation of turbulent thermal boundary layers, Phys. Fluids 12, 2555 (2000).
  22. Q. Li, P. Schlatter, L. Brandt, and D. S. Henningson, DNS of a spatially developing turbulent boundary layer with passive scalar transport, Int. J. Heat Fluid Flow 30, 916 (2009).
  23. P. G. Huang, G. N. Coleman, and P. Bradshaw, Compressible turbulent channel flows: DNS results and modelling, J. Fluid Mech. 305, 185 (1995).
  24. A. Trettel and J. Larsson, Mean velocity scaling for compressible wall turbulence with heat transfer, Phys. Fluids 28, 026102 (2016).
  25. A. Majda and J. Sethian, The derivation and numerical solution of the equations for zero Mach number combustion, Combust. Sci. Technol. 42, 185 (1985).
  26. S. K. Lele, Compact finite difference schemes with spectral-like resolution, J. Comput. Phys. 103, 16 (1992).
  27. B. J. Boersma, A 6th-order staggered compact finite difference method for the incompressible Navier-Stokes and scalar transport equations, J. Comput. Phys. 230, 4940 (2011).
  28. P. A. McMurtry, W. H. Jou, J. Riley, and R. W. Metcalfe, Direct numerical simulations of a reacting mixing layer with chemical heat release, AIAA J. 24, 962 (1986).
  29. J. Lee, S. Y. Jung, H. J. Sung, and T. A. Zaki, Effect of wall heating on turbulent boundary layers with temperature-dependent viscosity, J. Fluid Mech. 726, 196 (2013).
  30. Y. Morinishi, S. Tamano, and K. Nakabayashi, Direct numerical simulation of compressible turbulent channel flow between adiabatic and isothermal walls, J. Fluid Mech. 502, 273 (2004).

Outline

Information

Phys. Rev. Fluids 2, 084604– Published 21 August, 2017
  • Received 21 April 2017

©2017 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation