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Direct numerical simulation of the turbulent boundary layer over a cube-roughened wall


Direct numerical simulation (DNS) of a spatially developing turbulent boundary layer (TBL) over a wall roughened with regularly arrayed cubes was performed to investigate the effects of three-dimensional (3-D) surface elements on the properties of the TBL. The cubes were staggered in the downstream direction and periodically arranged in the streamwise and spanwise directions with pitches of px/k = 8 and pz/k = 2, where px and pz are the streamwise and spanwise spacings of the cubes and k is the roughness height. The Reynolds number based on the momentum thickness was varied in the range Reθ = 300−1300, and the roughness height was k = 1.5θin, where θin is the momentum thickness at the inlet, which corresponds to k/δ = 0.052–0.174 from the inlet to the outlet; δ is the boundary layer thickness. The characteristics of the TBL over the 3-D cube-roughened wall were compared with the results from a DNS of the TBL over a two-dimensional (2-D) rod-roughened wall. The introduction of cube roughness affected the turbulent Reynolds stresses not only in the roughness sublayer but also in the outer layer. The present instantaneous flow field and linear stochastic estimations of the conditional averaging showed that the streaky structures in the near-wall region and the low-momentum regions and hairpin packets in the outer layer are dominant features in the TBLs over the 2-D and 3-D rough walls and that these features are significantly affected by the surface roughness throughout the entire boundary layer. In the outer layer, however, it was shown that the large-scale structures over the 2-D and 3-D roughened walls have similar characteristics, which indicates that the dimensional difference between the surfaces with 2-D and 3-D roughness has a negligible effect on the turbulence statistics and coherent structures of the TBLs.

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R. J. Adrian 1996 Stochastic estimation of the structure of turbulent fields. In Eddy Structure Identification (ed. J. P. Bonnet ), pp. 145196. Springer.

R. J. Adrian , C. D. Meinhart & C. D. Tomkins 2000 Vortex organization in the outer region of the turbulent boundary layer. J. Fluid Mech. 422, 154.

A. Ashrafian , H. I. Andersson & M. Manhart 2004 DNS of turbulent flow in a rod-roughened channel. Intl J. Heat Fluid Flow 25, 373383.

O. M. Bakken & P.-Å Krogstad . 2005 Reynolds number effects in the outer layer of the turbulent flow in a channel with rough walls. Phys. Fluids 17, 065101.

K. Bhaganagar , J. Kim & G. Coleman 2004 Effect of roughness on wall-bounded turbulence. Flow Turbul. Combust. 72, 463492.

I. P. Castro 2007 Rough-wall boundary layers: mean flow universality. J. Fluid Mech. 585, 469485.

H. Cheng & I. P. Castro 2002 Near wall flow over urban like-roughness. Boundary-Layer Meteorol. 104, 229259.

O. Coceal , T. G. Thomas , I. P. Castro & S. E. Belcher 2006 Mean flow and turbulent statistics over groups of urban-like cubical obstacles. Boundary-Layer Meteorol. 121, 491519.

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

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

L. Djenidi , R. A. Antonia , M. Ameilh & F. Anselmet 2008 A turbulent boundary layer over a two-dimensional rough wall. Exp. Fluids 44, 3747.

K. A. Flack , M. P. Schultz & J. S. Connelly 2007 Examination of a critical roughness height for outer layer similarity. Phys. Fluids 19, 095104.

B. Ganapathisubramani , W. T. Hutchins , E. K. Hambleton , E. K. Longmire & I. Marusic 2005 Investigation of large-scale coherence in a turbulent boundary layer using two-point correlations. J. Fluid Mech. 524, 5780.

B. Ganapathisubramani , E. K. Longmire & I. Marusic 2003 Characteristics of vortex packets in turbulent boundary layers. J. Fluid Mech. 478, 3546.

P. S. Jackson 1981 On the displacement height in the logarithmic profiles. J. Fluid Mech. 111, 1525.

J. Jimenez 2004 Turbulent flows over rough walls. Annu. Rev. Fluid Mech. 36, 173196.

K. Kim , S.-J. Baek & H. J. Sung 2002 An implicit velocity decoupling procedure for the incompressible Navier–Stokes equations. Intl J. Numer. Methods Fluids 38, 125138.

J. Kim , D. Kim & H. Choi 2001 An immersed boundary finite-volume method for simulations of flow in complex geometries. J. Comput. Phys. 171, 132150.

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

S. J. Kline , W. C. Reynolds , F. A. Schraub & P. W. Runstadler 1967 The structure of turbulent boundary layers. J. Fluid Mech. 30, 741773.

P.-Å. Krogstad , H. I. Andersson , O. M. Bakken & A. Ashrafian 2005 An experimental and numerical study of channel flow with rough walls. J. Fluid Mech. 530, 327352.

P.-Å. Krogstad & R. A. Antonia 1994 Structure of turbulent boundary layers on smooth and rough walls. J. Fluid Mech. 277, 121.

P.-Å. Krogstad & R. A. Antonia 1999 Surface roughness effects in turbulent boundary layers. Exp. Fluids 27, 450460.

P.-Å. Krogstad , R. A. Antonia & L. W. B. Browne 1992 Comparison between rough- and smooth-wall turbulent boundary layers. J. Fluid Mech. 245, 599617.

S. H. Lee & H. J. Sung 2007 Direct numerical simulation of the turbulent boundary layer over a rod-roughened wall. J. Fluid Mech. 584, 125146.

S. Leonardi & I. P. Castro 2010 Channel flow over large cube roughness: a direct numerical simulation study. J. Fluid Mech. 651, 519539.

S. Leonardi , P. Orlandi , L. Djenidi & R. A. Antonia 2004 Structure of turbulent channel flow with square bars on one wall. Intl J. Heat Fluid Flow 25, 384392.

S. Leonardi , P. Orlandi , R. J. Smalley , L. Djenidi & R. A. Antonia 2003 Direct numerical simulations of turbulent channel flow with transverse square bars on one wall. J. Fluid Mech. 491, 229238.

T. S. Lund , X. Wu & K. D. Squires 1998 Generation of turbulent inflow data for spatially-developing boundary layer simulation. J. Comput. Phys. 140, 233258.

I. Marusic & G. J. Kunkel 2003 Streamwise turbulence intensity formulation for flat-plate boundary layers. Phys. Fluids 15, 24612464.

P. Orlandi & S. Leonardi 2006 DNS of turbulent channel flows with two- and three-dimensional roughness. J. Turbul. 7, 112

A. E. Perry , W. H. Schofield & P. N. Joubert 1969 Rough wall turbulent boundary layers. J. Fluid Mech. 37, 383413.

M. R. Raupach , R. A. Antonia & S. Rajagopalan 1991 Rough-wall turbulent boundary layers. Appl. Mech. Rev. 44, 125.

S. K. Robinson 1991 Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23, 601639.

M. P. Schultz & K. A. Flack 2005 Outer layer similarity in fully rough turbulent boundary layers. Exp. Fluids 38, 328340.

M. P. Schultz & K. A. Flack 2007 The rough-wall turbulent boundary layer from the hydraulically smooth to the fully rough regime. J. Fluid Mech. 580, 381405.

M. A. Shockling , J. J. Allen & A. J. Smits 2006 Roughness effects in turbulent pipe flow. J. Fluid Mech. 564, 267285.

R. J. Smalley , R. A. Antonia & L. Djenidi 2001 Self-preservation of rough-wall turbulent boundary layers. Eur. J. Mech. B – Fluids 20, 591602.

W. H. Snyder & I. P. Castro 2002 The critical Reynolds number for rough-wall boundary layers. J. Wind Engng Indust. Aerodyn. 90, 4154.

P. R. Spalart 1988 Direct simulation of a turbulent boundary layer up to Reθ = 1410. J. Fluid Mech. 187, 6198.

C. D. Tomkins & R. J. Adrian 2003 Spanwise structure and scale growth in turbulent boundary layers. J. Fluid Mech. 490, 3774.

R. J. Volino , M. P. Schultz & K. A. Flack 2007 Turbulence structure in rough- and smooth-wall boundary layers. J. Fluid Mech. 592, 263293.

R. J. Volino , M. P. Schultz & K. A. Flack 2009 Turbulence structure in a boundary layer with two-dimensional roughness. J. Fluid Mech. 635, 75101.

Y. Wu & K. T. Christensen 2007 Outer-layer similarity in the presence of a practical rough-wall topography. Phys. Fluids 19, 085108.

Y. Wu & K. T. Christensen 2010 Spatial structure of a turbulent boundary layer with irregular surface roughness. J. Fluid Mech. 655, 380418.

J. Zhou , R. J. Adrian , S. Balachandar & T. M. Kendall 1999 Mechanisms for generating coherent packets of hairpin vortices. J. Fluid Mech. 387, 353396.

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Journal of Fluid Mechanics
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