Hostname: page-component-745bb68f8f-cphqk Total loading time: 0 Render date: 2025-02-06T08:12:08.907Z Has data issue: false hasContentIssue false
  • English
  • Français

Effects of heterogeneous surface geometry on secondary flows in turbulent boundary layers

Published online by Cambridge University Press:  17 January 2020

T. Medjnoun Open the ORCID record for T. Medjnoun [Opens in a new window] ,
C. Vanderwel Open the ORCID record for C. Vanderwel [Opens in a new window]  and
B. Ganapathisubramani Open the ORCID record for B. Ganapathisubramani [Opens in a new window]
T. Medjnoun*
Affiliation:
Aerodynamics and Flight Mechanics Research Group, University of Southampton,SouthamptonSO17 1BJ, UK
C. Vanderwel
Affiliation:
Aerodynamics and Flight Mechanics Research Group, University of Southampton,SouthamptonSO17 1BJ, UK
B. Ganapathisubramani
Affiliation:
Aerodynamics and Flight Mechanics Research Group, University of Southampton,SouthamptonSO17 1BJ, UK
*
†Email address for correspondence: t.medjnoun@soton.ac.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

The effect of spanwise heterogeneous surface geometry on turbulent boundary layer secondary flows and on skin friction is investigated experimentally. The surfaces consist of smooth streamwise-aligned ridges of different shapes and widths with spanwise wavelengths comparable to the boundary layer thickness ($S/\unicode[STIX]{x1D6FF}\approx O(1)$). Cross-stream stereoscopic particle image velocimetry combined with oil-film interferometry is used to investigate the flow field and assess the drag. Results show that the spanwise distribution of the skin friction varies as a consequence of the mean flow heterogeneity and is highly dependent on surface geometry. The swirling strength maps revealed remarkable changes in the secondary flow structures for different ridge shapes. For wide ridges, topological changes occur showing the appearance of tertiary vortices coexisting with the large-scale secondary structures. An imbalance in favour of these tertiary structures occurs over a certain width which take over the secondary structures, causing a swap in the locations of the low- and high-momentum pathways. Furthermore, the results indicate that the spanwise spacing alone is insufficient to characterise the surface heterogeneity. A new parameter ($\unicode[STIX]{x1D709}$), which is based on the ratio of the perimeter over and below the mean surface height, is shown to adequately capture the changes in skin friction and streamwise circulation of the secondary motions. Triple decomposition allowed the quantification of the dispersive stresses for all these cases, which can contribute up to $55\,\%$ of the total shear stress when strong secondary motions occur.

JFM classification

Turbulent Flows: Turbulent boundary layers
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 886 , 10 March 2020 , A31
Copyright
© The Author(s), 2020. Published by 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

Akomah, A., Hangan, H. & Naughton, J. 2011 Very high Reynolds number boundary layers over 3d sparse roughness and obstacles: the mean flow. Exp. Fluids 51 (3), 743.CrossRefGoogle Scholar
Alfredsson, P. H., Segalini, A. & Örlü, R. 2011 A new scaling for the streamwise turbulence intensity in wall-bounded turbulent flows and what it tells us about the outer peak. Phys. Fluids 23 (4), 041702.CrossRefGoogle Scholar
Anderson, W., Barros, J. M., Christensen, K. T. & Awasthi, A. 2015 Numerical and experimental study of mechanisms responsible for turbulent secondary flows in boundary layer flows over spanwise heterogeneous roughness. J. Fluid Mech. 768, 316–347.CrossRefGoogle Scholar
Anderson, W., Yang, J., Shrestha, K. & Awasthi, A. 2018 Turbulent secondary flows in wall turbulence: vortex forcing, scaling arguments, and similarity solution. Environ. Fluid Mech. 18 (6), 1351–1378.CrossRefGoogle Scholar
Awasthi, A. & Anderson, W. 2018 Numerical study of turbulent channel flow perturbed by spanwise topographic heterogeneity: amplitude and frequency modulation within low- and high-momentum pathways. Phys. Rev. Fluids 3 (4), 044602.CrossRefGoogle Scholar
Bai, H. L., Kevin, K., Hutchins, N. & Monty, J. P. 2018 Turbulence modifications in a turbulent boundary layer over a rough wall with spanwise-alternating roughness strips. Phys. Fluids 30 (5), 055105.CrossRefGoogle Scholar
Barros, J. M. & Christensen, K. T. 2014 Observations of turbulent secondary flows in a rough-wall boundary layer. J. Fluid Mech. 748, R1.CrossRefGoogle Scholar
Benschop, H. & Breugem, W. 2017 Drag reduction by herringbone riblet texture in direct numerical simulations of turbulent channel flow. J. Turbul. 18 (8), 717–759.CrossRefGoogle Scholar
Bisset, D. K., Hunt, J. C. R. & Rogers, M. M. 2002 The turbulent/non-turbulent interface bounding a far wake. J. Fluid Mech. 451, 383–410.CrossRefGoogle Scholar
Blay Esteban, L., Dogan, E., Rodríguez-Lopéz, E. & Ganapathisubramani, B. 2017 Skin-friction measurements in a turbulent boundary layer under the influence of free-stream turbulence. Exp. Fluids 58 (9), 115.CrossRefGoogle Scholar
Castro, I. P. 2007 Rough-wall boundary layers: mean flow universality. J. Fluid Mech. 585, 469–485.CrossRefGoogle Scholar
Castro, I. P., Segalini, A. & Alfredsson, P. H. 2013 Outer-layer turbulence intensities in smooth-and rough-wall boundary layers. J. Fluid Mech. 727, 119–131.CrossRefGoogle Scholar
Chan, L., MacDonald, M., Chung, D., Hutchins, N. & Ooi, A. 2018 Secondary motion in turbulent pipe flow with three-dimensional roughness. J. Fluid Mech. 854, 5–33.CrossRefGoogle Scholar
Chauhan, K., Philip, J., de Silva, C. M., Hutchins, N. & Marusic, I. 2014 The turbulent/non-turbulent interface and entrainment in a boundary layer. J. Fluid Mech. 742, 119–151.CrossRefGoogle Scholar
Chung, D., Monty, J. P. & Hutchins, N. 2018 Similarity and structure of wall turbulence with lateral wall shear stress variations. J. Fluid Mech. 847, 591–613.CrossRefGoogle Scholar
Colombini, M. 1993 Turbulence-driven secondary flows and formation of sand ridges. J. Fluid Mech. 254, 701–719.CrossRefGoogle Scholar
Corrsin, T. & Kistler, A. L.1955 Free-stream boundaries of turbulent flows. NACA Tech. Rep. 1244. Washington, DC.Google Scholar
Djenidi, L., Talluru, K. M. & Antonia, R. A. 2018 Can a turbulent boundary layer become independent of the Reynolds number? J. Fluid Mech. 851, 1–22.CrossRefGoogle Scholar
Flack, K. A. & Schultz, M. P. 2010 Review of hydraulic roughness scales in the fully rough regime. J. Fluids Engng 132 (4), 041203.CrossRefGoogle Scholar
Flack, K. A. & Schultz, M. P. 2014 Roughness effects on wall-bounded turbulent flows. Phys. Fluids 26 (10), 101305.CrossRefGoogle Scholar
Goldstein, D. B. & Tuan, T.-C. 1998 Secondary flow induced by riblets. J. Fluid Mech. 363, 115–151.CrossRefGoogle Scholar
Gyr, A. & Kinzelbach, W. 2004 Bed forms in turbulent channel flow. Appl. Mech. Rev. 57 (1), 77–93.Google Scholar
Hinze, J. O. 1967 Secondary currents in wall turbulence. Phys. Fluids 10 (9), 122–S12.CrossRefGoogle Scholar
Hinze, J. O. 1973 Experimental investigation on secondary currents in the turbulent flow through a straight conduit. Appl. Sci. Res. 28 (1), 453–465.CrossRefGoogle Scholar
Hwang, H. G. & Lee, J. H. 2018 Secondary flows in turbulent boundary layers over longitudinal surface roughness. Phys. Rev. Fluids 3, 014608.CrossRefGoogle Scholar
Jiménez, J. 2004 Turbulent flows over rough walls. Annu. Rev. Fluid Mech. 36, 173–196.CrossRefGoogle Scholar
Kevin, K., Monty, J. & Hutchins, N. 2019 Turbulent structures in a statistically three-dimensional boundary layer. J. Fluid Mech. 859, 543–565.CrossRefGoogle Scholar
Kevin, K., Monty, J. P., Bai, H. L., Pathikonda, G., Nugroho, B., Barros, J. M., Christensen, K. T. & Hutchins, N. 2017 Cross-stream stereoscopic particle image velocimetry of a modified turbulent boundary layer over directional surface pattern. J. Fluid Mech. 813, 412–435.CrossRefGoogle Scholar
Krug, D., Philip, J. & Marusic, I. 2017 Revisiting the law of the wake in wall turbulence. J. Fluid Mech. 811, 421–435.CrossRefGoogle Scholar
Laskari, A., de Kat, R., Hearst, R. J. & Ganapathisubramani, B. 2018 Time evolution of uniform momentum zones in a turbulent boundary layer. J. Fluid Mech. 842, 554–590.CrossRefGoogle Scholar
McLelland, S. J., Ashworth, P. J., Best, J. L. & Livesey, J. R. 1999 Turbulence and secondary flow over sediment stripes in weakly bimodal bed material. J. Hydraul. Engng 125 (5), 463–473.CrossRefGoogle Scholar
Medjnoun, T., Vanderwel, C. & Ganapathisubramani, B. 2018 Characteristics of turbulent boundary layers over smooth surfaces with spanwise heterogeneities. J. Fluid Mech. 838, 516–543.CrossRefGoogle Scholar
Mejia-Alvarez, R. & Christensen, K. T. 2013 Wall-parallel stereo particle-image velocimetry measurements in the roughness sublayer of turbulent flow overlying highly irregular roughness. Phys. Fluids 25 (11), 115109.Google Scholar
Meyers, J., Ganapathisubramani, B. & Cal, R. B. 2019 On the decay of dispersive motions in the outer region of rough-wall boundary layers. J. Fluid Mech. 862, R5.CrossRefGoogle Scholar
Moinuddin, K. A. M., Joubert, P. N. & Chong, M. S. 2004 Experimental investigation of turbulence-driven secondary motion over a streamwise external corner. J. Fluid Mech. 511, 1–23.CrossRefGoogle Scholar
Nagib, H. M., Chauhan, K. A. & Monkewitz, P. A. 2007 Approach to an asymptotic state for zero pressure gradient turbulent boundary layers. Phil. Trans. R. Soc. Lond. A 365 (1852), 755–770.CrossRefGoogle 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
Naughton, J. W. & Sheplak, M. 2002 Modern developments in shear-stress measurement. Prog. Aerosp. Sci. 38 (6–7), 515–570.CrossRefGoogle Scholar
Nezu, I. & Nakagawa, H. 1984 Cellular secondary currents in straight conduit. J. Fluids Engng 110 (2), 173–193.Google Scholar
Nezu, I., Tominaga, A. & Nakagawa, H. 1993 Field measurements of secondary currents in straight rivers. J. Fluids Engng 119 (5), 598–614.Google Scholar
Nikora, V., McEwan, I., McLean, S., Coleman, S., Pokrajac, D. & Walters, R. 2007 Double-averaging concept for rough-bed open-channel and overland flows: theoretical background. J. Hydraul. Engng 133 (8), 873–883.CrossRefGoogle Scholar
Nikuradse, J. 1930 Untersuchungen über turbulente strömungen in nicht kreisförmigen rohren. Ing.-Arch. 1 (3), 306–332.CrossRefGoogle Scholar
Nugroho, B., Hutchins, N. & Monty, J. P. 2013 Large-scale spanwise periodicity in a turbulent boundary layer induced by highly ordered and directional surface roughness. Intl J. Heat Fluid Flow 41, 90–102.CrossRefGoogle Scholar
Pailhas, G., Barricau, P., Touvet, Y. & Perret, L. 2009 Friction measurement in zero and adverse pressure gradient boundary layer using oil droplet interferometric method. Exp. Fluids 47 (2), 195–207.CrossRefGoogle Scholar
Pathikonda, G. & Christensen, K. T. 2017 Inner–outer interactions in a turbulent boundary layer overlying complex roughness. Phys. Rev. Fluids 2, 044603.CrossRefGoogle Scholar
Placidi, M. & Ganapathisubramani, B. 2015 Effects of frontal and plan solidities on aerodynamic parameters and the roughness sublayer in turbulent boundary layers. J. Fluid Mech. 782, 541–566.CrossRefGoogle Scholar
Prandtl, L. 1952 Essentials of Fluid Dynamics. Blackie.Google Scholar
Raupach, M. R. & Shaw, R. H. 1982 Averaging procedures for flow within vegetation canopies. Boundary-Layer Meteorol. 22 (1), 79–90.CrossRefGoogle Scholar
Reynolds, R. T., Hayden, P., Castro, I. P. & Robins, A. G. 2007 Spanwise variations in nominally two-dimensional rough-wall boundary layers. Exp. Fluids 42 (2), 311–320.CrossRefGoogle Scholar
Reynolds, W. C. & Hussain, A. K. M. F. 1972 The mechanics of an organized wave in turbulent shear flow. Part 3. Theoretical models and comparisons with experiments. J. Fluid Mech. 54 (2), 263–288.CrossRefGoogle Scholar
Schlichting, H. 1979 Boundary-layer Theory, 7th edn. McGraw-Hill.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
Squire, D. T., Morrill-Winter, C., Hutchins, N., Schultz, M. P., Klewicki, J. C. & Marusic, I. 2016 Comparison of turbulent boundary layers over smooth and rough surfaces up to high Reynolds numbers. J. Fluid Mech. 795, 210–240.CrossRefGoogle Scholar
Squire, L. C. 1961 The motion of a thin oil sheet under the steady boundary layer on a body. J. Fluid Mech. 11, 161–179.CrossRefGoogle Scholar
Stroh, A., Hasegawa, Y., Kriegseis, J. & Frohnapfel, B. 2016 Secondary vortices over surfaces with spanwise varying drag. J. Turbul. 17 (12), 1142–1158.CrossRefGoogle Scholar
Tanner, L. H. & Blows, L. G. 1976 A study of the motion of oil films on surfaces in air flow, with application to the measurement of skin friction. J. Phys. E 9 (3), 194.CrossRefGoogle Scholar
Thakkar, M., Busse, A. & Sandham, N. 2017 Surface correlations of hydrodynamic drag for transitionally rough engineering surfaces. J. Turbul. 18 (2), 138–169.CrossRefGoogle Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow, 2nd edn. Cambridge University Press.Google Scholar
Türk, S., Daschiel, G., Stroh, A., Hasegawa, Y. & Frohnapfel, B. 2014 Turbulent flow over superhydrophobic surfaces with streamwise grooves. J. Fluid Mech. 747, 186–217.CrossRefGoogle Scholar
Vanderwel, C. & Ganapathisubramani, B. 2015 Effects of spanwise spacing on large-scale secondary flows in rough-wall turbulent boundary layers. J. Fluid Mech. 774, R2.CrossRefGoogle Scholar
Vanderwel, C., Placidi, M. & Ganapathisubramani, B. 2017 Wind resource assessment in heterogeneous terrain. Phil. Trans. R. Soc. Lond. A 375 (2091), 20160109.CrossRefGoogle ScholarPubMed
Vanderwel, C., Stroh, A., Kriegseis, J., Frohnapfel, B. & Ganapathisubramani, B. 2019 The instantaneous structure of secondary flows in turbulent boundary layers. J. Fluid Mech. 862, 845–870.CrossRefGoogle Scholar
Wang, Z. Q. & Cheng, N. S. 2005 Secondary flows over artificial bed strips. Adv. Water Resour. 28 (5), 441–450.CrossRefGoogle Scholar
Wang, Z. Q. & Cheng, N. S. 2006 Time-mean structure of secondary flows in open channel with longitudinal bedforms. Adv. Water Resour. 29 (11), 1634–1649.CrossRefGoogle Scholar
Westerweel, J., Fukushima, C., Pedersen, J. M. & Hunt, J. C. R. 2005 Mechanics of the turbulent-nonturbulent interface of a jet. Phys. Rev. Lett. 95, 174501.Google ScholarPubMed
Willingham, D., Anderson, W., Christensen, K. T. & Barros, J. M. 2014 Turbulent boundary layer flow over transverse aerodynamic roughness transitions: induced mixing and flow characterization. Phys. Fluids 26 (2), 025111.CrossRefGoogle Scholar
Wu, Y. & Christensen, K. T. 2007 Outer-layer similarity in the presence of a practical rough-wall topography. Phys. Fluids 19 (8), 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
Yang, J. & Anderson, W. 2017 Numerical study of turbulent channel flow over surfaces with variable spanwise heterogeneities: topographically-driven secondary flows affect outer-layer similarity of turbulent length scales. Flow Turbul. Combust. 100 (1), 1–17.CrossRefGoogle Scholar
Yuan, J. & Piomelli, U. 2014 Roughness effects on the Reynolds stress budgets in near-wall turbulence. J. Fluid Mech. 760, R1.CrossRefGoogle Scholar