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The effect of spanwise wavelength of surface heterogeneity on turbulent secondary flows

Published online by Cambridge University Press:  29 April 2020

Dea D. Wangsawijaya Open the ORCID record for Dea D. Wangsawijaya [Opens in a new window] ,
Rio Baidya Open the ORCID record for Rio Baidya [Opens in a new window] ,
Daniel Chung Open the ORCID record for Daniel Chung [Opens in a new window] ,
Ivan Marusic  and
Nicholas Hutchins
Dea D. Wangsawijaya*
Affiliation:
Department of Mechanical Engineering, The University of Melbourne, Victoria3010, Australia
Rio Baidya
Affiliation:
Department of Mechanical Engineering, The University of Melbourne, Victoria3010, Australia Institute of Fluid Mechanics and Aerodynamics, Universität der Bundeswehr München, 85577Neubiberg, Germany
Daniel Chung
Affiliation:
Department of Mechanical Engineering, The University of Melbourne, Victoria3010, Australia
Ivan Marusic
Affiliation:
Department of Mechanical Engineering, The University of Melbourne, Victoria3010, Australia
Nicholas Hutchins
Affiliation:
Department of Mechanical Engineering, The University of Melbourne, Victoria3010, Australia
*
†Email address for correspondence: d.wangsawijaya@student.unimelb.edu.au
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Abstract

We examine the behaviour of turbulent boundary layers over surfaces composed of spanwise-alternating smooth and rough strips, where the width of the strips $S$ varies such that $0.32\leqslant S/\overline{\unicode[STIX]{x1D6FF}}\leqslant 6.81$, where $\overline{\unicode[STIX]{x1D6FF}}$ is the boundary-layer thickness averaged over one spanwise wavelength of the heterogeneity. The experiments are configured to examine the influences of spanwise variation in wall shear stress over a large $S/\overline{\unicode[STIX]{x1D6FF}}$ range. Hot-wire anemometry and particle image velocimetry (PIV) reveal that the half-wavelength $S/\overline{\unicode[STIX]{x1D6FF}}$ governs the diameter and strength of the resulting mean secondary flows and hence the observed isovels of the mean streamwise velocity. Three possible cases are observed: limiting cases (either $S/\overline{\unicode[STIX]{x1D6FF}}\ll 1$ or $S/\overline{\unicode[STIX]{x1D6FF}}\gg 1$), where the secondary flows are confined near the wall or near the roughness change, and intermediate cases ($S/\overline{\unicode[STIX]{x1D6FF}}\approx 1$), where the secondary flows are space filling and at their strongest. These secondary flows, however, exhibit a time-dependent behaviour which might be masked by time averaging. Further analysis of the energy spectrogram and fluctuating flow fields obtained from PIV show that the secondary flows meander in a similar manner to that of large-scale structures occurring naturally in turbulence over smooth walls. The meandering of the secondary flows is a function of $S/\overline{\unicode[STIX]{x1D6FF}}$ and is most prominent when $S/\overline{\unicode[STIX]{x1D6FF}}\approx 1$.

JFM classification

Turbulent Flows: Turbulent boundary layers

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Type
JFM Papers
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Journal of Fluid Mechanics , Volume 894 , 10 July 2020 , A7
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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
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, 044602.CrossRefGoogle Scholar
Bai, H. L., Hutchins, K. N. & Monty, J. P. 2018 Turbulence modifications in a turbulent boundary layer over a rough wall with spanwise-alternating roughness strips. Phys. Fluids 30, 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
Chan, L., Chung, D., MacDonald, M., 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. A., Monkewitz, P. A. & Nagib, H. M. 2009 Criteria for assessing experiments in zero pressure gradient boundary layers. Fluid Dyn. Res. 41, 021404.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
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
Colombini, M. 1993 Turbulence-driven secondary flow and formation of sand ridges. J. Fluid Mech. 254, 701–719.CrossRefGoogle Scholar
Colombini, M. & Parker, G. 1995 Longitudinal streaks. J. Fluid Mech. 304, 161–183.CrossRefGoogle Scholar
Dennis, D. J. C. & Nickels, T. B. 2008 On the limitations of Taylor’s hypothesis in constructing long structures in a turbulent boundary layer. J. Fluid Mech. 614, 197–206.CrossRefGoogle Scholar
Finnigan, J. 2000 Turbulence in plant canopies. Annu. Rev. Fluid Mech. 32, 519–571.CrossRefGoogle Scholar
Flores, O. & Jiménez, J. 2010 Hierarchy of minimal flow units in the logarithmic layer. Phys. Fluids 22 (7), 071704.CrossRefGoogle 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
de Giovanetti, M., Sung, H. J. & Hwang, Y. 2017 Streak instability in turbulent channel flow: the seeding mechanism of large-scale motions. J. Fluid Mech. 832, 483–513.CrossRefGoogle Scholar
Goldstein, D. B. & Tuan, T. C. 1998 Secondary flow induced by riblets. J. Fluid Mech. 363, 115–151.CrossRefGoogle Scholar
Grayson, K., de Silva, C. M., Hutchins, N. & Marusic, I. 2018 Impact of mismatched and misaligned laser light sheet profiles on PIV performance. Exp. Fluids 59, 2.CrossRefGoogle Scholar
Hama, F. R. 1954 Boundary-layer characteristics for rough and smooth surfaces. Trans. Soc. Nav. Archit. Mar. Engrs 62, 333–351.Google Scholar
Harun, Z., Monty, J. P., Mathis, R. & Marusic, I. 2013 Pressure gradient effects on the large-scale structure of turbulent boundary layers. J. Fluid Mech. 715, 477–498.CrossRefGoogle Scholar
Hinze, J. O. 1967 Secondary currents in wall turbulence. Phys. Fluids 10, S122–S125.CrossRefGoogle Scholar
Hinze, J. O. 1973 Experimental investigation on secondary currents in the turbulent flow through a straight conduit. Appl. Sci. Res. 28, 453–465.CrossRefGoogle Scholar
Hutchins, N. & Marusic, I. 2007a Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J. Fluid Mech. 579, 1–28.CrossRefGoogle Scholar
Hutchins, N. & Marusic, I. 2007b Large-scale influences in near-wall turbulence. Phil. Trans. R. Soc. Lond. A 365, 647–664.CrossRefGoogle Scholar
Hutchins, N., Nickels, T. B., Marusic, I. & Chong, M. S. 2009 Hot-wire spatial resolution issues in wall-bounded turbulence. J. Fluid Mech. 635, 103–136.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
Jelly, T. O., Jung, S. Y. & Zaki, T. A. 2014 Turbulence and skin friction modification in channel flow with streamwise-aligned superhydrophobic surface texture. Phys. Fluids 26, 095102.CrossRefGoogle Scholar
Jeong, J., Hussain, F., Schoppa, W. & Kim, J. 1997 Coherent structures near the wall in a turbulent channel flow. J. Fluid Mech. 332, 185–214.CrossRefGoogle Scholar
Kevin, Monty, J. & Hutchins, N. 2019a The meandering behaviour of large-scale structures in turbulent boundary layers. J. Fluid Mech. 865, R1.CrossRefGoogle Scholar
Kevin, Monty, J. & Hutchins, N. 2019b Turbulent structures in a statistically three-dimensional boundary layer. J. Fluid Mech. 859, 543–565.CrossRefGoogle Scholar
Kevin, 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
Kim, K. C. & Adrian, R. J. 1999 Very large-scale motion in the outer layer. Phys. Fluids 11 (2), 417–422.CrossRefGoogle Scholar
Kline, S. J., Reynolds, W. C., Schraub, F. A. & Runstadlers, P. W. 1967 The structure of turbulent boundary layers. J. Fluid Mech. 30 (4), 741–773.CrossRefGoogle Scholar
Lee, J., Jelly, T. O. & Zaki, T. A. 2015 Effect of Reynolds number on turbulent drag reduction by superhydrophobic surface texture. Flow Turbul. Combust. 95 (2–3), 277–300.CrossRefGoogle Scholar
Lee, J. H., Kevin, Monty, J. P. & Hutchins, N. 2016 Validating underresolved turbulence intensities for PIV experiments in canonical wallbounded turbulence. Exp. Fluids 57, 129.CrossRefGoogle Scholar
Lee, J. H., Sung, H. J. & Adrian, R. J. 2019 Space–time formation of very-large-scale motions in turbulent pipe flow. J. Fluid Mech. 881, 1010–1047.CrossRefGoogle Scholar
Ligrani, P. M. & Bradshaw, P. 1987 Subminiature hot-wire sensors: development and use. J. Phys. E: Sci. Instrum. 20, 323–332.CrossRefGoogle Scholar
Marusic, I., Chauhan, K. A., Kulandaivelu, V. & Hutchins, N. 2015 Evolution of zero-pressure-gradient boundary layers from different tripping conditions. J. Fluid Mech. 783, 379–411.CrossRefGoogle Scholar
Mathis, R., Hutchins, N. & Marusic, I. 2009 Large-scale amplitude modulation of the small-scale structures in turbulent boundary layers. J. Fluid Mech. 628, 311–337.CrossRefGoogle Scholar
McLean, S. R. 1981 The role of non-uniform roughness in the formation of sand ribbons. Mar. Geol. 42, 49–74.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. ASCE 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 heterogeneity. J. Fluid Mech. 838, 516–543.CrossRefGoogle Scholar
Medjnoun, T., Vanderwel, C. & Ganapathisubramani, B. 2020 Effects of heterogeneous surface geometry on secondary fows in turbulent boundary layers. J. Fluid Mech. 886, A31.CrossRefGoogle Scholar
Moody, L. F. 1944 Friction factors for pipe flow. ASME Trans. 66, 671–684.Google Scholar
Nakagawa, H., Nezu, I. & Tominaga, A. 1981 Turbulent structure with and without cellular secondary currents over various bed configurations. Annu. DPRI 24B (2), 315–338.Google Scholar
Nezu, I. & Nakagawa, H. 1984 Cellular secondary currents in straight conduit. ASCE J. Hydraul. Engng 110 (2), 173–193.CrossRefGoogle Scholar
Nikuradse, J.1933 Strömungsgesetze in rauhen rohren. VDI Forschungsheft 361, English translation: 1950 Laws of flow in rough pipes. NACA Tech. Mem. 1292.Google 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
Prandtl, L. 1952 Essentials of Fluid Dynamics. Hafner Publishing Company.Google Scholar
Raupach, M. R. & Shaw, R. H. 1982 Averaging procedure for flow within vegetation canopies. Boundary-Layer Meteorol. 22, 79–90.CrossRefGoogle Scholar
Sillero, J. A., Jiménez, J. & Moser, R. D. 2014 Two-point statistics for turbulent boundary layers and channels at Reynolds numbers up to 𝛿+ ≈ 2000. Phys. Fluids 26, 105109.CrossRefGoogle Scholar
de Silva, C. M., Gnanamanickam, E. P., Atkinson, C., Buchmann, N. A., Hutchins, N., Soria, J. & Marusic, I. 2014 High spatial range velocity measurements in a high Reynolds number turbulent boundary layer. Phys. Fluids 26, 025117.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
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
Stroh, A., Schäfer, K., Frohnapfel, B. & Forooghi, P. 2020 Rearrangement of secondary flow over spanwise heterogeneous roughness. J. Fluid Mech. 885, R5.CrossRefGoogle Scholar
Talluru, K. M., Kulandaivelu, V., Hutchins, N. & Marusic, I. 2014 A calibration technique to correct sensor drift issues in hot-wire anemometry. Meas. Sci. Technol. 25, 105304.CrossRefGoogle Scholar
Taylor, G. I. 1938 The spectrum of turbulence. Proc. R. Soc. Lond. A 164, 476–490.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, 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., Stroh, A., Kriegseis, J., Frohnapfel, B. & Ganapathisubramani, B. 2019 The instantaneous structure of secondary flows in turbulent boundary layers. J. Fluid Mech. 865, 845–870.CrossRefGoogle Scholar
Vermaas, D. A., Uijttewaal, W. S. J. & Hoitink, A. J. F. 2011 Lateral transfer of streamwise momentum caused by a roughness transition across a shallow channel. Water Resour. Res. 47, W02530.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, 1634–1649.CrossRefGoogle Scholar
Wangsawijaya, D. D., de Silva, C. M., Baidya, R., Chung, D., Marusic, I. & Hutchins, N. 2019 The instantaneous structure of turbulent boundary layer over surfaces with spanwise heterogeneity. In Proceedings of the 11st International Symposium on Turbulence and Shear Flow Phenomena, International Symposium on Turbulence and Shear Flow Phenomena.Google Scholar
Wieneke, B. 2005 Stereo-PIV using self-calibration on particle images. Exp. Fluids 39, 267–280.CrossRefGoogle Scholar
Willert, C. 1997 Stereoscopic digital particle image velocimetry for application in wind tunnel flows. Meas. Sci. Technol. 8, 1465–1479.CrossRefGoogle Scholar
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, 025111.CrossRefGoogle Scholar
Xu, F., Zhong, S. & Zhang, S. 2018 Vortical structures and development of laminar flow over convergent-divergent riblets. Phys. Fluids 30, 051901.CrossRefGoogle Scholar
Yang, J. & Anderson, W. 2018 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
Zampiron, A., Cameron, S. & Nikora, V. 2020 Secondary currents and very-large-scale motions in open-channel flow over streamwise ridges. J. Fluid Mech. 887, A17.CrossRefGoogle Scholar