Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-04T19:37:03.819Z Has data issue: false hasContentIssue false
  • English
  • Français

A systematic investigation of roughness height and wavelength in turbulent pipe flow in the transitionally rough regime

Published online by Cambridge University Press:  27 April 2015

L. Chan ,
M. MacDonald ,
D. Chung ,
N. Hutchins  and
A. Ooi
L. Chan*
Affiliation:
Department of Mechanical Engineering, The University of Melbourne, Victoria 3010, Australia
M. MacDonald
Affiliation:
Department of Mechanical Engineering, The University of Melbourne, Victoria 3010, Australia
D. Chung
Affiliation:
Department of Mechanical Engineering, The University of Melbourne, Victoria 3010, Australia
N. Hutchins
Affiliation:
Department of Mechanical Engineering, The University of Melbourne, Victoria 3010, Australia
A. Ooi
Affiliation:
Department of Mechanical Engineering, The University of Melbourne, Victoria 3010, Australia
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Direct numerical simulations (DNS) are conducted for turbulent flow through pipes with three-dimensional sinusoidal roughnesses explicitly represented by body-conforming grids. The same viscous-scaled roughness geometry is first simulated at a range of different Reynolds numbers to investigate the effects of low Reynolds numbers and low $R_{0}/h$, where $R_{0}$ is the pipe radius and $h$ is the roughness height. Results for the present class of surfaces show that the Hama roughness function ${\rm\Delta}U^{+}$ is only marginally affected by low Reynolds numbers (or low $R_{0}/h$), and observations of outer-layer similarity (or lack thereof) show no signs of sensitivity to Reynolds number. Then, building on this, a systematic approach is taken to isolate the effects of roughness height $h^{+}$ and wavelength ${\it\lambda}^{+}$ in a turbulent wall-bounded flow in both transitionally rough and fully rough regimes. Current findings show that while the effective slope $\mathit{ES}$ (which for the present sinusoidal surfaces is proportional to $h^{+}/{\it\lambda}^{+}$) is an important roughness parameter, the roughness function ${\rm\Delta}U^{+}$ must also depend on some measure of the viscous roughness height. A simplistic linear–log fit clearly illustrates the strong correlation between ${\rm\Delta}U^{+}$ and both the roughness average height $k_{a}^{+}$ (which is related to $h^{+}$) and $\mathit{ES}$ for the surfaces simulated here, consistent with published literature. Various definitions of the virtual origin for rough-wall turbulent pipe flow are investigated and, for the surfaces simulated here, the hydraulic radius of the pipe appears to be the most suitable parameter, and indeed is the only virtual origin that can ever lead to collapse in the total stress. First- and second-order statistics are also analysed and collapses in the outer layer are observed for all cases, including those where the largest roughness height is a substantial proportion of the reference radius (low $R_{0}/h$). These results provide evidence that turbulent pipe flow over the present sinusoidal surfaces adheres to Townsend’s notion of outer-layer similarity, which pertains to statistics of relative motion.

JFM classification

Boundary Layers: Pipe flow boundary layer Turbulent Flows: Turbulent boundary layers
Type
Papers
Information
Journal of Fluid Mechanics , Volume 771 , 25 May 2015 , pp. 743 - 777
Check for updates
Copyright
© 2015 Cambridge University Press 

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

Acharya, M., Bornstein, J. & Escudier, M. P. 1986 Turbulent boundary-layers on rough surfaces. Exp. Fluids 4, 33–47.CrossRefGoogle Scholar
Antonia, R. A., Teitel, M., Kim, J. & Browne, L. W. B. 1992 Low-Reynolds-number effects in a fully developed turbulent channel flow. J. Fluid Mech. 236, 579–605.CrossRefGoogle Scholar
ASME2009 Surface texture (surface roughness, waviness, and lay): an American standard. ASME B46.1-2009 (revision of ANSI/ASME B46.1-1995).Google Scholar
Bhaganagar, K., Coleman, G. & Kim, J. 2007 Effect of roughness on pressure fluctuations in a turbulent channel flow. Phys. Fluids 19, 028103.CrossRefGoogle Scholar
Bhaganagar, K., Kim, J. & Coleman, G. 2004 Effect of roughness on wall-bounded turbulence. Flow Turbul. Combust. 72, 463–492.CrossRefGoogle Scholar
Blackburn, H. M., Ooi, A. S. H. & Chong, M. S.2007 The effect of corrugation height on flow in a wavy-walled pipe. In Proceedings of the 16th Australasian Fluid Mechanics Conference, Gold Coast, Queensland, Australia, pp. 559–564.Google Scholar
Chin, C., Ooi, A. S. H., Marusic, I. & Blackburn, H. M. 2010 The influence of pipe length on turbulence statistics computed from direct numerical simulation data. Phys. Fluids 22, 115107.CrossRefGoogle Scholar
Coceal, O., Thomas, T. G., Castro, I. P. & Belcher, S. E. 2006 Mean flow and turbulence statistics over groups of urban-like cubical obstacles. Boundary-Layer Meteorol. 121, 491–519.CrossRefGoogle Scholar
Cunningham, K. S. & Gotlieb, A. I. 2004 The role of shear stress in the pathogenesis of atherosclerosis. Lab. Invest. 85, 9–23.CrossRefGoogle Scholar
De Marchis, M. & Napoli, E. 2012 Effects of irregular two-dimensional and three-dimensional surface roughness in turbulent channel flows. Intl J. Heat Fluid Flow 36, 7–17.CrossRefGoogle Scholar
Efros, V. & Krogstad, P. A. 2011 Development of a turbulent boundary layer after a step from smooth to rough surface. Exp. Fluids 51, 1563–1575.CrossRefGoogle Scholar
Eggels, J. G. M., Unger, F., Weiss, M. H., Westerweel, J., Adrian, R. J., Friedrich, R. & Nieuwstadt, F. T. M. 1994 Fully developed turbulent pipe flow: a comparison between direct numerical simulation and experiment. J. Fluid Mech. 268, 175–209.CrossRefGoogle Scholar
Flack, K. A. & Schultz, M. P. 2010 Review of hydraulic roughness scales in the fully rough regime. Trans. ASME: J. Fluids Engng 132, 041203.Google 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
Fukagata, K. & Kasagi, N. 2002 Highly energy-conservative finite difference method for the cylindrical coordinate system. J. Comput. Phys. 181, 478–498.CrossRefGoogle Scholar
George, J. & Simpson, R. L.2000 Some effects of sparsely distributed three-dimensional roughness elements on two-dimensional turbulent boundary layers. AIAA Paper 2000-0915.CrossRefGoogle Scholar
Granville, P. S. 1958 The frictional resistance and turbulent boundary layer of rough surfaces. J. Ship Res. 2, 52–74.CrossRefGoogle Scholar
Ham, F. & Iaccarino, G. 2004 Energy conservation in collocated discretization schemes on unstructured meshes. In Annual Research Briefs 2004, Center for Turbulence Research Stanford University/NASA Ames.Google Scholar
Hama, F. R. 1954 Boundary-layer characteristics for smooth and rough surfaces. Trans. Soc. Nav. Archit. Mar. Engrs 62, 333–358.Google Scholar
Hong, J., Katz, J. & Schultz, M. P. 2011 Near-wall turbulence statistics and flow structures over three-dimensional roughness in a turbulent channel flow. J. Fluid Mech. 667, 1–37.CrossRefGoogle Scholar
Iaccarino, G. & Verzicco, R. 2003 Immersed boundary technique for turbulent flow simulations. Appl. Mech. Rev. 56, 331–347.CrossRefGoogle Scholar
Jimenez, J. 2004 Turbulent flows over rough walls. Annu. Rev. Fluid Mech. 36, 173–196.CrossRefGoogle Scholar
Kim, J. & Moin, P. 1985 Application of a fractional-step method to incompressible Navier–Stokes equations. J. Comput. Phys. 59, 308–323.CrossRefGoogle Scholar
Krogstad, P. A. & Antonia, R. A. 1999 Surface roughness effects in turbulent boundary layers. Exp. Fluids 27, 450–460.CrossRefGoogle Scholar
Kwon, Y. S., Philip, J., de Silva, C. M., Hutchins, N. & Monty, J. P. 2014 The quiescent core of turbulent channel flow. J. Fluid Mech. 751, 228–254.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
Loulou, P., Moser, R. D., Mansour, N. N. & Cantwell, B. J.1997 Direct numerical simulation of incompressible pipe flow using a B-spline spectral method. NASA Tech. Mem. 110436.Google Scholar
Mahesh, K., Constantinescu, G. & Moin, P. 2004 A numerical method for large-eddy simulation in complex geometries. J. Comput. Phys. 197, 215–240.CrossRefGoogle Scholar
Mejia-Alvarez, R. & Christensen, K. T. 2010 Low-order representations of irregular surface roughness and their impact on a turbulent boundary layer. Phys. Fluids 22, 015106.CrossRefGoogle Scholar
Monty, J. P., Hutchins, N., Ng, H. C. H., Marusic, I. & Chong, M. S. 2009 A comparison of turbulent pipe, channel and boundary layer flows. J. Fluid Mech. 632, 431–442.CrossRefGoogle Scholar
Moody, L. F. 1944 Friction factors for pipe flow. Trans. ASME 66, 671–684.Google Scholar
Napoli, E., Armenio, V. & De Marchis, M. 2008 The effect of the slope of irregularly distributed roughness elements on turbulent wall-bounded flows. J. Fluid Mech. 613, 385–394.CrossRefGoogle Scholar
Nickels, T. B. 2004 Inner scaling for wall-bounded flows subject to large pressure gradients. J. Fluid Mech. 521, 217–239.CrossRefGoogle Scholar
Orlandi, P. 2013 The importance of wall-normal Reynolds stress in turbulent rough channel flows. Phys. Fluids 25, 110813.CrossRefGoogle Scholar
Perry, A. E. & Li, J. D. 1990 Experimental support for the attached-eddy hypothesis in zero-pressure-gradient turbulent boundary layers. J. Fluid Mech. 218, 405–438.CrossRefGoogle Scholar
Prandtl, L. & Schlichting, H.1955 The resistance law for rough plates. Tech. Rep. 258. Navy Department, translated by P. Granville.Google Scholar
Raupach, M. R., Antonia, R. A. & Rajagopalan, S. 1991 Rough-wall turbulent boundary layers. Appl. Mech. Rev. 44, 1–25.CrossRefGoogle Scholar
Raupach, M. R. & Shaw, R. H. 1982 Averaging procedures for flow within vegetation canopies. Boundary-Layer Meteorol. 22, 79–90.CrossRefGoogle Scholar
Sabot, J. & Comte-Bellot, G. 1976 Intermittency of coherent structures in the core region of fully developed turbulent pipe flow. J. Fluid Mech. 74, 767–796.CrossRefGoogle Scholar
Saha, S., Chin, C., Blackburn, H. M. & Ooi, A. S. H. 2011 The influence of pipe length on thermal statistics computed from DNS of turbulent heat transfer. Intl J. Heat Fluid Flow 32, 1083–1097.CrossRefGoogle Scholar
Satake, S., Kunugi, T. & Himeno, R. 2000 High Reynolds Number Computation for Turbulent Heat Transfer in a Pipe Flow, Lecture Notes in Computer Science, vol. 1940, High Performance Computing, pp. 514–523. Springer.Google Scholar
Scaggs, W. F., Taylor, R. P. & Coleman, H. W. 1988 Measurement and prediction of rough wall effects on friction factor – uniform roughness results. Trans. ASME: J. Fluids Engng 110, 385–391.Google Scholar
Schlichting, H. 1936 Experimentelle untersuchungen zum Rauhigkeitsproblem. Ing.-Arch. 7, 1–34.CrossRefGoogle Scholar
Schultz, M. P., Bendick, J. A., Holm, E. R. & Hertel, W. M. 2011 Economic impact of biofouling on a naval surface ship. Biofouling 27 (1), 87–98.CrossRefGoogle ScholarPubMed
Schultz, M. P. & Flack, K. A. 2009 Turbulent boundary layers on a systematically varied rough wall. Phys. Fluids 21, 015104.CrossRefGoogle Scholar
Scotti, A. 2006 Direct numerical simulation of turbulent channel flows with boundary roughened with virtual sandpaper. Phys. Fluids 18, 031701.CrossRefGoogle Scholar
Taylor, R. P., Coleman, H. W. & Hodge, B. K. 1985 Prediction of turbulent rough-wall skin friction using a discrete element approach. Trans. ASME: J. Fluids Engng 107 (2), 251–257.Google Scholar
Thom, A. S. 1971 Momentum absorption by vegetation. Q. J. R. Meteorol. Soc. 97, 414–428.CrossRefGoogle Scholar
Townsend, A. A. 1980 The Structure of Turbulent Shear Flow. Cambridge University Press.Google Scholar
Wagner, C., Hüttl, T. J. & Friedrich, R. 2001 Low Reynolds number effects derived from direct numerical simulations of turbulent pipe flow. Comput. Fluids 30, 581–590.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, X. & Moin, P. 2008 A direct numerical simulation study on the mean velocity characteristics in turbulent pipe flow. J. Fluid Mech. 608, 81–112.CrossRefGoogle Scholar
Yang, D., Meneveau, C. & Shen, L. 2013 Dynamic modelling of sea-surface roughness for large-eddy simulation of wind over ocean wavefield. J. Fluid Mech. 726, 62–99.CrossRefGoogle Scholar
Yuan, J. & Piomelli, U. 2014 Estimation and prediction of the roughness function on realistic surfaces. J. Turbul. 15, 350–365.CrossRefGoogle Scholar