Skip to main content Accessibility help
×
Home

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

  • L. Chan (a1), M. MacDonald (a1), D. Chung (a1), N. Hutchins (a1) and A. Ooi (a1)...

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.

Copyright

Corresponding author

Email address for correspondence: lzhchan@unimelb.edu.au

References

Hide All
Acharya, M., Bornstein, J. & Escudier, M. P. 1986 Turbulent boundary-layers on rough surfaces. Exp. Fluids 4, 3347.
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, 579605.
ASME2009 Surface texture (surface roughness, waviness, and lay): an American standard. ASME B46.1-2009 (revision of ANSI/ASME B46.1-1995).
Bhaganagar, K., Coleman, G. & Kim, J. 2007 Effect of roughness on pressure fluctuations in a turbulent channel flow. Phys. Fluids 19, 028103.
Bhaganagar, K., Kim, J. & Coleman, G. 2004 Effect of roughness on wall-bounded turbulence. Flow Turbul. Combust. 72, 463492.
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.
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.
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, 491519.
Cunningham, K. S. & Gotlieb, A. I. 2004 The role of shear stress in the pathogenesis of atherosclerosis. Lab. Invest. 85, 923.
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, 717.
Efros, V. & Krogstad, P. A. 2011 Development of a turbulent boundary layer after a step from smooth to rough surface. Exp. Fluids 51, 15631575.
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, 175209.
Flack, K. A. & Schultz, M. P. 2010 Review of hydraulic roughness scales in the fully rough regime. Trans. ASME: J. Fluids Engng 132, 041203.
Flack, K. A., Schultz, M. P. & Connelly, J. S. 2007 Examination of a critical roughness height for outer layer similarity. Phys. Fluids 19, 095104.
Fukagata, K. & Kasagi, N. 2002 Highly energy-conservative finite difference method for the cylindrical coordinate system. J. Comput. Phys. 181, 478498.
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.
Granville, P. S. 1958 The frictional resistance and turbulent boundary layer of rough surfaces. J. Ship Res. 2, 5274.
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.
Hama, F. R. 1954 Boundary-layer characteristics for smooth and rough surfaces. Trans. Soc. Nav. Archit. Mar. Engrs 62, 333358.
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, 137.
Iaccarino, G. & Verzicco, R. 2003 Immersed boundary technique for turbulent flow simulations. Appl. Mech. Rev. 56, 331347.
Jimenez, J. 2004 Turbulent flows over rough walls. Annu. Rev. Fluid Mech. 36, 173196.
Kim, J. & Moin, P. 1985 Application of a fractional-step method to incompressible Navier–Stokes equations. J. Comput. Phys. 59, 308323.
Krogstad, P. A. & Antonia, R. A. 1999 Surface roughness effects in turbulent boundary layers. Exp. Fluids 27, 450460.
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, 228254.
Leonardi, S. & Castro, I. P. 2010 Channel flow over large cube roughness a direct numerical simulation study. J. Fluid Mech. 651, 519539.
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.
Mahesh, K., Constantinescu, G. & Moin, P. 2004 A numerical method for large-eddy simulation in complex geometries. J. Comput. Phys. 197, 215240.
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.
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, 431442.
Moody, L. F. 1944 Friction factors for pipe flow. Trans. ASME 66, 671684.
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, 385394.
Nickels, T. B. 2004 Inner scaling for wall-bounded flows subject to large pressure gradients. J. Fluid Mech. 521, 217239.
Orlandi, P. 2013 The importance of wall-normal Reynolds stress in turbulent rough channel flows. Phys. Fluids 25, 110813.
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, 405438.
Prandtl, L. & Schlichting, H.1955 The resistance law for rough plates. Tech. Rep. 258. Navy Department, translated by P. Granville.
Raupach, M. R., Antonia, R. A. & Rajagopalan, S. 1991 Rough-wall turbulent boundary layers. Appl. Mech. Rev. 44, 125.
Raupach, M. R. & Shaw, R. H. 1982 Averaging procedures for flow within vegetation canopies. Boundary-Layer Meteorol. 22, 7990.
Sabot, J. & Comte-Bellot, G. 1976 Intermittency of coherent structures in the core region of fully developed turbulent pipe flow. J. Fluid Mech. 74, 767796.
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, 10831097.
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. 514523. Springer.
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, 385391.
Schlichting, H. 1936 Experimentelle untersuchungen zum Rauhigkeitsproblem. Ing.-Arch. 7, 134.
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), 8798.
Schultz, M. P. & Flack, K. A. 2009 Turbulent boundary layers on a systematically varied rough wall. Phys. Fluids 21, 015104.
Scotti, A. 2006 Direct numerical simulation of turbulent channel flows with boundary roughened with virtual sandpaper. Phys. Fluids 18, 031701.
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), 251257.
Thom, A. S. 1971 Momentum absorption by vegetation. Q. J. R. Meteorol. Soc. 97, 414428.
Townsend, A. A. 1980 The Structure of Turbulent Shear Flow. Cambridge University Press.
Wagner, C., Hüttl, T. J. & Friedrich, R. 2001 Low Reynolds number effects derived from direct numerical simulations of turbulent pipe flow. Comput. Fluids 30, 581590.
Wu, Y. & Christensen, K. T. 2007 Outer-layer similarity in the presence of a practical rough-wall topography. Phys. Fluids 19, 085108.
Wu, X. & Moin, P. 2008 A direct numerical simulation study on the mean velocity characteristics in turbulent pipe flow. J. Fluid Mech. 608, 81112.
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, 6299.
Yuan, J. & Piomelli, U. 2014 Estimation and prediction of the roughness function on realistic surfaces. J. Turbul. 15, 350365.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

Related content

Powered by UNSILO

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

  • L. Chan (a1), M. MacDonald (a1), D. Chung (a1), N. Hutchins (a1) and A. Ooi (a1)...

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.