Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-26T16:38:53.536Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  12 January 2011

JAE HWA LEE ,
HYUNG JIN SUNG  and
PER-ÅGE KROGSTAD
JAE HWA LEE
Affiliation:
Department of Mechanical Engineering, KAIST, 373-1 Guseong-dong, Yuseong-gu, Daejeon 305-701, Republic of Korea
HYUNG JIN SUNG*
Affiliation:
Department of Mechanical Engineering, KAIST, 373-1 Guseong-dong, Yuseong-gu, Daejeon 305-701, Republic of Korea
PER-ÅGE KROGSTAD
Affiliation:
Department of Energy and Process Engineering, Norwegian University of Science and Technology, Trondheim N-7491, Norway
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

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.

JFM classification

Boundary Layers: Boundary layer structure Turbulent Flows: Turbulent boundary layers Turbulent Flows: Turbulence simulation
Type
Papers
Information
Journal of Fluid Mechanics , Volume 669 , 25 February 2011 , pp. 397 - 431
Copyright
Copyright © Cambridge University Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Adrian, R. J. 1996 Stochastic estimation of the structure of turbulent fields. In Eddy Structure Identification (ed. Bonnet, J. P.), pp. 145–196. Springer.CrossRefGoogle Scholar
Adrian, R. J., Meinhart, C. D. & Tomkins, C. D. 2000 Vortex organization in the outer region of the turbulent boundary layer. J. Fluid Mech. 422, 1–54.CrossRefGoogle Scholar
Ashrafian, A., Andersson, H. I. & Manhart, M. 2004 DNS of turbulent flow in a rod-roughened channel. Intl J. Heat Fluid Flow 25, 373–383.CrossRefGoogle Scholar
Bakken, O. M. & Krogstad, P.-Å. 2005 Reynolds number effects in the outer layer of the turbulent flow in a channel with rough walls. Phys. Fluids 17, 065101.CrossRefGoogle Scholar
Bhaganagar, K., Kim, J. & Coleman, G. 2004 Effect of roughness on wall-bounded turbulence. Flow Turbul. Combust. 72, 463–492.CrossRefGoogle Scholar
Bogard, D. G. & Tiederman, W. G. 1986 Burst detection with single-point velocity measurements. J. Fluid Mech. 76, 89–112.Google Scholar
Castro, I. P. 2007 Rough-wall boundary layers: mean flow universality. J. Fluid Mech. 585, 469–485.CrossRefGoogle Scholar
Cheng, H. & Castro, I. P. 2002 Near wall flow over urban like-roughness. Boundary-Layer Meteorol. 104, 229–259.Google Scholar
Coceal, O., Thomas, T. G., Castro, I. P. & Belcher, S. E. 2006 Mean flow and turbulent statistics over groups of urban-like cubical obstacles. Boundary-Layer Meteorol. 121, 491–519.CrossRefGoogle Scholar
Christensen, K. T. & Adrian, R. J. 2001 Statistical evidence of hairpin vortex packets in wall turbulence. J. Fluid Mech. 431, 433–443.CrossRefGoogle Scholar
Degraaff, D. B. & Eaton, J. K. 2000 Reynolds-number scaling of the flat-plate turbulent boundary layer. J. Fluid Mech. 422, 319–346.CrossRefGoogle Scholar
Djenidi, L., Antonia, R. A., Ameilh, M. & Anselmet, F. 2008 A turbulent boundary layer over a two-dimensional rough wall. Exp. Fluids 44, 37–47.CrossRefGoogle Scholar
Flack, K. A., Schultz, M. P. & Connelly, J. S. 2007 Examination of a critical roughness height for outer layer similarity. Phys. Fluids 19, 095104.CrossRefGoogle Scholar
Ganapathisubramani, B., Hutchins, W. T., Hambleton, E. K., Longmire, E. K. & Marusic, I. 2005 Investigation of large-scale coherence in a turbulent boundary layer using two-point correlations. J. Fluid Mech. 524, 57–80.Google Scholar
Ganapathisubramani, B., Longmire, E. K. & Marusic, I. 2003 Characteristics of vortex packets in turbulent boundary layers. J. Fluid Mech. 478, 35–46.CrossRefGoogle Scholar
Jackson, P. S. 1981 On the displacement height in the logarithmic profiles. J. Fluid Mech. 111, 15–25.CrossRefGoogle Scholar
Jimenez, J. 2004 Turbulent flows over rough walls. Annu. Rev. Fluid Mech. 36, 173–196.CrossRefGoogle Scholar
Keirsbulck, L., Labraga, L., Mazouz, A. & Tournier, C. 2002 Surface roughness effects on turbulent boundary layer structures. Trans. ASME: J. Fluids Engng 124, 127–135.Google Scholar
Kim, K., Baek, S.-J. & Sung, H. J. 2002 An implicit velocity decoupling procedure for the incompressible Navier–Stokes equations. Intl J. Numer. Methods Fluids 38, 125–138.CrossRefGoogle Scholar
Kim, J., Kim, D. & Choi, H. 2001 An immersed boundary finite-volume method for simulations of flow in complex geometries. J. Comput. Phys. 171, 132–150.CrossRefGoogle Scholar
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166.CrossRefGoogle Scholar
Kline, S. J., Reynolds, W. C., Schraub, F. A. & Runstadler, P. W. 1967 The structure of turbulent boundary layers. J. Fluid Mech. 30, 741–773.CrossRefGoogle Scholar
Kline, S. J. & Robinson, S. K. 1989 Quasi-coherent structures in the turbulent boundary layer. Part 1. Status report on a community-wide summary of the data. In Near-Wall Turbulence (ed. Kline, S. J. & Afgan, N. H.), pp. 218–247. Hemisphere.Google Scholar
Krogstad, P.-Å., Andersson, H. I., Bakken, O. M. & Ashrafian, A. 2005 An experimental and numerical study of channel flow with rough walls. J. Fluid Mech. 530, 327–352.CrossRefGoogle Scholar
Krogstad, P.-Å. & Antonia, R. A. 1994 Structure of turbulent boundary layers on smooth and rough walls. J. Fluid Mech. 277, 1–21.CrossRefGoogle Scholar
Krogstad, P.-Å. & Antonia, R. A. 1999 Surface roughness effects in turbulent boundary layers. Exp. Fluids 27, 450–460.Google Scholar
Krogstad, P.-Å., Antonia, R. A. & Browne, L. W. B. 1992 Comparison between rough- and smooth-wall turbulent boundary layers. J. Fluid Mech. 245, 599–617.CrossRefGoogle Scholar
Krogstad, P.-Å. & Nickels, T. 2006 Turbulent boundary layer with a step change in surface roughness. In Conference on Modelling Fluid Flow (ed. Lajos, T.), pp. 568–573. Cambridge University Press.Google Scholar
Lee, J. H., Lee, S. H., Kim, K. & Sung, H. J. 2009 Structure of the turbulent boundary layer over a rod-roughened wall. Intl J. Heat Fluid Flow 25, 1087–1098.CrossRefGoogle Scholar
Lee, S. H. & Sung, H. J. 2007 Direct numerical simulation of the turbulent boundary layer over a rod-roughened wall. J. Fluid Mech. 584, 125–146.CrossRefGoogle Scholar
Leonardi, S. & Castro, I. P. 2010 Channel flow over large cube roughness: a direct numerical simulation study. J. Fluid Mech. 651, 519–539.CrossRefGoogle Scholar
Leonardi, S., Orlandi, P., Djenidi, L. & Antonia, R. A. 2004 Structure of turbulent channel flow with square bars on one wall. Intl J. Heat Fluid Flow 25, 384–392.CrossRefGoogle Scholar
Leonardi, S., Orlandi, P., Smalley, R. J., Djenidi, L. & Antonia, R. A. 2003 Direct numerical simulations of turbulent channel flow with transverse square bars on one wall. J. Fluid Mech. 491, 229–238.CrossRefGoogle Scholar
Lund, T. S., Wu, X. & Squires, K. D. 1998 Generation of turbulent inflow data for spatially-developing boundary layer simulation. J. Comput. Phys. 140, 233–258.CrossRefGoogle Scholar
Marusic, I. & Kunkel, G. J. 2003 Streamwise turbulence intensity formulation for flat-plate boundary layers. Phys. Fluids 15, 2461–2464.CrossRefGoogle Scholar
Orlandi, P. & Leonardi, S. 2006 DNS of turbulent channel flows with two- and three-dimensional roughness. J. Turbul. 7, 1–12CrossRefGoogle Scholar
Perry, A. E., Schofield, W. H. & Joubert, P. N. 1969 Rough wall turbulent boundary layers. J. Fluid Mech. 37, 383–413.CrossRefGoogle Scholar
Raupach, M. R., Antonia, R. A. & Rajagopalan, S. 1991 Rough-wall turbulent boundary layers. Appl. Mech. Rev. 44, 1–25.CrossRefGoogle Scholar
Robinson, S. K. 1991 Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23, 601–639.CrossRefGoogle Scholar
Schultz, M. P. & Flack, K. A. 2005 Outer layer similarity in fully rough turbulent boundary layers. Exp. Fluids 38, 328–340.CrossRefGoogle Scholar
Schultz, M. P. & Flack, K. A. 2007 The rough-wall turbulent boundary layer from the hydraulically smooth to the fully rough regime. J. Fluid Mech. 580, 381–405.CrossRefGoogle Scholar
Schultz, M. P., Volino, R. J. & Flack, K. A. 2009 Turbulent boundary layer over a small, 2-D, k-type roughness. Bull. Am. Phys. Soc. 54, 177.Google Scholar
Shockling, M. A., Allen, J. J. & Smits, A. J. 2006 Roughness effects in turbulent pipe flow. J. Fluid Mech. 564, 267–285.CrossRefGoogle Scholar
Smalley, R. J., Antonia, R. A. & Djenidi, L. 2001 Self-preservation of rough-wall turbulent boundary layers. Eur. J. Mech. B – Fluids 20, 591–602.CrossRefGoogle Scholar
Snyder, W. H. & Castro, I. P. 2002 The critical Reynolds number for rough-wall boundary layers. J. Wind Engng Indust. Aerodyn. 90, 41–54.CrossRefGoogle Scholar
Spalart, P. R. 1988 Direct simulation of a turbulent boundary layer up to Re θ = 1410. J. Fluid Mech. 187, 61–98.CrossRefGoogle Scholar
Tomkins, C. D. & Adrian, R. J. 2003 Spanwise structure and scale growth in turbulent boundary layers. J. Fluid Mech. 490, 37–74.CrossRefGoogle Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow, p. 429. Cambridge University Press.Google Scholar
Volino, R. J., Schultz, M. P. & Flack, K. A. 2007 Turbulence structure in rough- and smooth-wall boundary layers. J. Fluid Mech. 592, 263–293.CrossRefGoogle Scholar
Volino, R. J., Schultz, M. P. & Flack, K. A. 2009 Turbulence structure in a boundary layer with two-dimensional roughness. J. Fluid Mech. 635, 75–101.CrossRefGoogle Scholar
Wu, Y. & Christensen, K. T. 2007 Outer-layer similarity in the presence of a practical rough-wall topography. Phys. Fluids 19, 085108.CrossRefGoogle Scholar
Wu, Y. & Christensen, K. T. 2010 Spatial structure of a turbulent boundary layer with irregular surface roughness. J. Fluid Mech. 655, 380–418.CrossRefGoogle Scholar
Zhou, J., Adrian, R. J., Balachandar, S. & Kendall, T. M. 1999 Mechanisms for generating coherent packets of hairpin vortices. J. Fluid Mech. 387, 353–396.CrossRefGoogle Scholar