Skip to main content
×
Home
    • Aa
    • Aa

Direct numerical simulation of turbulent channel flow up to $\mathit{Re}_{{\it\tau}}\approx 5200$

  • Myoungkyu Lee (a1) and Robert D. Moser (a1) (a2)
Abstract

A direct numerical simulation of incompressible channel flow at a friction Reynolds number ( $\mathit{Re}_{{\it\tau}}$ ) of 5186 has been performed, and the flow exhibits a number of the characteristics of high-Reynolds-number wall-bounded turbulent flows. For example, a region where the mean velocity has a logarithmic variation is observed, with von Kármán constant ${\it\kappa}=0.384\pm 0.004$ . There is also a logarithmic dependence of the variance of the spanwise velocity component, though not the streamwise component. A distinct separation of scales exists between the large outer-layer structures and small inner-layer structures. At intermediate distances from the wall, the one-dimensional spectrum of the streamwise velocity fluctuation in both the streamwise and spanwise directions exhibits $k^{-1}$ dependence over a short range in wavenumber $(k)$ . Further, consistent with previous experimental observations, when these spectra are multiplied by $k$ (premultiplied spectra), they have a bimodal structure with local peaks located at wavenumbers on either side of the $k^{-1}$ range.

Copyright
Corresponding author
Email address for correspondence: rmoser@ices.utexas.edu
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

N. Afzal 1976 Millikan’s argument at moderately large Reynolds number. Phys. Fluids 19 (4), 600602.

N. Afzal 1982 Fully developed turbulent flow in a pipe: an intermediate layer. Ing.-Arch. 52, 355377.

N. Afzal  & K. Yajnik 1973 Analysis of turbulent pipe and channel flows at moderately large Reynolds number. J. Fluid Mech. 61, 2331.

S. C. C. Bailey , M. Vallikivi , M. Hultmark  & A. J. Smits 2014 Estimating the value of von Kármán’s constant in turbulent pipe flow. J. Fluid Mech. 749, 7998.

M. Bernardini , S. Pirozzoli  & P. Orlandi 2014 Velocity statistics in turbulent channel flow up to $Re_{{\it\tau}}$ = 4000. J. Fluid Mech. 742, 171191.

G. Borrell , J. A. Sillero  & J. Jiménez 2013 A code for direct numerical simulation of turbulent boundary layers at high Reynolds numbers in BG/P supercomputers. Comput. Fluids 80, 3743.

O. Botella  & K. Shariff 2003 B-spline methods in fluid dynamics. Intl J. Comput. Fluid Dyn. 17 (2), 133149.

M. H. Buschmann  & M. Gad-el-Hak 2003 Generalized logarithmic law and its consequences. AIAA J. 41 (1), 4048.

K. T. Christensen  & R. J. Adrian 2001 Statistical evidence of hairpin vortex packets in wall turbulence. J. Fluid Mech. 431, 433443.

R. B. Dean  & P. Bradshaw 1976 Measurements of interacting turbulent shear layers in a duct. J. Fluid Mech. 78, 641676.

D. B. DeGraaff  & J. K. Eaton 2000 Reynolds-number scaling of the flat-plate turbulent boundary layer. J. Fluid Mech. 422, 319346.

J. C. Del Álamo  & J. Jiménez 2009 Estimation of turbulent convection velocities and corrections to Taylor’s approximation. J. Fluid Mech. 640, 526.

J. C. Del Álamo , J. Jiménez , P. Zandonade  & R. D. Moser 2004 Scaling of the energy spectra of turbulent channels. J. Fluid Mech. 500, 135144.

S. A. Dixit  & O. N. Ramesh 2013 On the $k_{1}^{-1}$ scaling in sink-flow turbulent boundary layers. J. Fluid Mech. 737, 329348.

P. A. Durbin  & B. A. Pettersson Reif 2010 Statistical Theory and Modeling for Turbulent Flows. Wiley.

G. K. El Khoury , P. Schlatter , A. Noorani , P. F. Fischer , G. Brethouwer  & A. V. Johansson 2013 Direct numerical simulation of turbulent pipe flow at moderately high Reynolds numbers. Flow Turbul. Combust. 91 (3), 475495.

H. H. Fernholz  & P. J. Finley 1996 The incompressible zero-pressure-gradient turbulent boundary layer: an assessment of the data. Prog. Aerosp. Sci. 32 (8), 245311.

M. Guala , S. E. Hommema  & R. J. Adrian 2006 Large-scale and very-large-scale motions in turbulent pipe flow. J. Fluid Mech. 554, 521542.

S. Hoyas  & J. Jiménez 2006 Scaling of the velocity fluctuations in turbulent channels up to $Re_{{\it\tau}}=2003$. Phys. Fluids 18 (1), 011702.

S. Hoyas  & J. Jiménez 2008 Reynolds number effects on the Reynolds-stress budgets in turbulent channels. Phys. Fluids 20 (10), 101511.

M. Hultmark , S. C. C. Bailey  & A. J. Smits 2010 Scaling of near-wall turbulence in pipe flow. J. Fluid Mech. 649, 103113.

M. Hultmark , M. Vallikivi , S. C. C. Bailey  & A. J. Smits 2012 Turbulent pipe flow at extreme Reynolds numbers. Phys. Rev. Lett. 108, 094501.

M. Hultmark , M. Vallikivi , S. C. C. Bailey  & A. J. Smits 2013 Logarithmic scaling of turbulence in smooth- and rough-wall pipe flow. J. Fluid Mech. 728, 376395.

N. Hutchins , K. Chauhan , I. Marusic , J. Monty  & J. Klewicki 2012 Towards reconciling the large-scale structure of turbulent boundary layers in the atmosphere and laboratory. Boundary-Layer Meteorol. 145 (2), 273306.

N. Hutchins  & I. Marusic 2007 Large-scale influences in near-wall turbulence. Phil. Trans. R. Soc. Lond. A 365 (1852), 647664.

N. Hutchins , T. B. Nickels , I. Marusic  & M. S. Chong 2009 Hot-wire spatial resolution issues in wall-bounded turbulence. J. Fluid Mech. 635, 103136.

J. Jiménez  & R. D. Moser 2007 What are we learning from simulating wall turbulence? Phil. Trans. R. Soc. Lond. A 365 (1852), 715732.

A. V. Johansson  & P. H. Alfredsson 1982 On the structure of turbulent channel flow. J. Fluid Mech. 122, 295314.

R. W. Johnson 2005 Higher order B-spline collocation at the Greville abscissae. Appl. Numer. Maths 52 (1), 6375.

J. Kim , P. Moin  & R. Moser 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133166.

K. C. Kim  & R. J. Adrian 1999 Very large-scale motion in the outer layer. Phys. Fluids 11 (2), 417.

G. J. Kunkel  & I. Marusic 2006 Study of the near-wall-turbulent region of the high-Reynolds-number boundary layer using an atmospheric flow. J. Fluid Mech. 548, 375402.

W. Y. Kwok , R. D. Moser  & J. Jiménez 2001 A critical evaluation of the resolution properties of B-spline and compact finite difference methods. J. Comput. Phys. 174 (2), 510551.

M. Lee , R. Ulerich , N. Malaya  & R. D. Moser 2014 Experiences from leadership computing in simulations of turbulent fluid flows. Comput. Sci. Engng 16 (5), 2431.

A. Lozano-Durán  & J. Jiménez 2014 Effect of the computational domain on direct simulations of turbulent channels up to $Re_{{\it\tau}}$ = 4200. Phys. Fluids 26 (1), 011702.

I. Marusic , R. Mathis  & N. Hutchins 2010a High Reynolds number effects in wall turbulence. Intl J. Heat Fluid Flow 31 (3), 418428.

I. Marusic , B. J. McKeon , P. A. Monkewitz , H. M. Nagib , A. J. Smits  & K. R. Sreenivasan 2010b Wall-bounded turbulent flows at high Reynolds numbers: recent advances and key issues. Phys. Fluids 22 (6), 065103.

I. Marusic , J. P. Monty , M. Hultmark  & A. J. Smits 2013 On the logarithmic region in wall turbulence. J. Fluid Mech. 716, R3.

Y. Mizuno  & J. Jiménez 2011 Mean velocity and length-scales in the overlap region of wall-bounded turbulent flows. Phys. Fluids 23 (8), 085112.

P. Moin 2009 Revisiting Taylor’s hypothesis. J. Fluid Mech. 640, 14.

J. P. Monty  & M. S. Chong 2009 Turbulent channel flow: comparison of streamwise velocity data from experiments and direct numerical simulation. J. Fluid Mech. 633, 461474.

J. P. Monty , N. Hutchins , H. C. H. Ng , I. Marusic  & M. S. Chong 2009 A comparison of turbulent pipe, channel and boundary layer flows. J. Fluid Mech. 632, 431442.

J. F. Morrison , B. J. McKeon , W. Jiang  & A. J. Smits 2004 Scaling of the streamwise velocity component in turbulent pipe flow. J. Fluid Mech. 508, 99131.

R. D. Moser , J. Kim  & N. N. Mansour 1999 Direct numerical simulation of turbulent channel flow up to $Re_{{\it\tau}}=590$. Phys. Fluids 11 (4), 943945.

H. M. Nagib  & K. A. Chauhan 2008 Variations of von Kármán coefficient in canonical flows. Phys. Fluids 20 (10), 101518.

T. Nickels , I. Marusic , S. Hafez  & M. S. Chong 2005 Evidence of the $k_{1}^{-1}$ law in a high-Reynolds-number turbulent boundary layer. Phys. Rev. Lett. 95 (7), 074501.

T. B. Nickels , I. Marusic , S. Hafez , N. Hutchins  & M. S. Chong 2007 Some predictions of the attached eddy model for a high Reynolds number boundary layer. Phil. Trans. R. Soc. Lond. A 365 (1852), 807822.

T. A. Oliver , N. Malaya , R. Ulerich  & R. D. Moser 2014 Estimating uncertainties in statistics computed from direct numerical simulation. Phys. Fluids 26 (3), 035101.

J. M. Österlund , A. V. Johansson , H. M. Nagib  & M. H. Hites 2000 A note on the overlap region in turbulent boundary layers. Phys. Fluids 12 (1), 14.

R. L. Panton 2007 Composite asymptotic expansions and scaling wall turbulence. Phil. Trans. R. Soc. Lond. A 365 (1852), 733754.

A. E. Perry , S. Henbest  & M. S. Chong 1986 A theoretical and experimental study of wall turbulence. J. Fluid Mech. 165, 163199.

B. J. Rosenberg , M. Hultmark , M. Vallikivi , S. C. C. Bailey  & A. J. Smits 2013 Turbulence spectra in smooth- and rough-wall pipe flow at extreme Reynolds numbers. J. Fluid Mech. 731, 4663.

M. P. Schultz  & K. A. Flack 2013 Reynolds-number scaling of turbulent channel flow. Phys. Fluids 25 (2), 025104.

J. A. Sillero , J. Jiménez  & R. D. Moser 2013 One-point statistics for turbulent wall-bounded flows at Reynolds numbers up to ${\it\delta}^{+}\approx 2000$. Phys. Fluids 25, 105102.

A. J. Smits  & I. Marusic 2013 Wall-bounded turbulence. Phys. Today 66 (9), 2530.

A. J. Smits , B. J. McKeon  & I. Marusic 2011 High-Reynolds number wall turbulence. Annu. Rev. Fluid Mech. 43 (1), 353375.

P. R. Spalart , R. D. Moser  & M. M. Rogers 1991 Spectral methods for the Navier–Stokes equations with one infinite and two periodic directions. J. Comput. Phys. 96 (2), 297324.

A. W. Vreman  & J. G. M. Kuerten 2014 Comparison of direct numerical simulation databases of turbulent channel flow at $Re_{{\it\tau}}=180$. Phys. Fluids 26 (1), 015102.

T. Wei  & W. W. Willmarth 1989 Reynolds-number effects on the structure of a turbulent channel flow. J. Fluid Mech. 204, 5795.

J. Westerweel , G. E. Elsinga  & R. J. Adrian 2013 Particle image velocimetry for complex and turbulent flows. Annu. Rev. Fluid Mech. 45 (1), 409436.

E. S. Winkel , J. M. Cutbirth , S. L. Ceccio , M. Perlin  & D. R. Dowling 2012 Turbulence profiles from a smooth flat-plate turbulent boundary layer at high Reynolds number. Exp. Therm. Fluid Sci. 40, 140149.

M. Wosnik , L. Castillo  & W. K. George 2000 A theory for turbulent pipe and channel flows. J. Fluid Mech. 421, 115145.

X. Wu , J. R. Baltzer  & R. J. Adrian 2012 Direct numerical simulation of a 30R long turbulent pipe flow at $R^{+}=685$ : large- and very large-scale motions. J. Fluid Mech. 698, 235281.

E.-S. Zanoun , F. Durst  & H. Nagib 2003 Evaluating the law of the wall in two-dimensional fully developed turbulent channel flows. Phys. Fluids 15 (10), 3079.

E.-S. Zanoun , H. Nagib  & F. Durst 2009 Refined $c_{f}$ relation for turbulent channels and consequences for high-$Re$ experiments. Fluid Dyn. Res. 41 (2), 021405.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Keywords:

Metrics

Full text views

Total number of HTML views: 33
Total number of PDF views: 1249 *
Loading metrics...

Abstract views

Total abstract views: 1291 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 23rd September 2017. This data will be updated every 24 hours.