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Non-$k$-type behaviour of roughness when in-plane wavelength approaches the boundary layer thickness

Published online by Cambridge University Press:  22 January 2021

B. Nugroho Open the ORCID record for B. Nugroho [Opens in a new window] ,
J. P. Monty Open the ORCID record for J. P. Monty [Opens in a new window] ,
I. K. A. P. Utama Open the ORCID record for I. K. A. P. Utama [Opens in a new window] ,
B. Ganapathisubramani Open the ORCID record for B. Ganapathisubramani [Opens in a new window]  and
N. Hutchins Open the ORCID record for N. Hutchins [Opens in a new window]
B. Nugroho
Affiliation:
Department of Mechanical Engineering, The University of Melbourne, Victoria3010, Australia
J. P. Monty
Affiliation:
Department of Mechanical Engineering, The University of Melbourne, Victoria3010, Australia
I. K. A. P. Utama
Affiliation:
Department of Naval Architecture, Institut Teknologi Sepuluh Nopember, Surabaya60111, Indonesia
B. Ganapathisubramani
Affiliation:
Aerodynamics and Flight Mechanics Research Group, University of Southampton, SouthamptonSO171BJ, UK
N. Hutchins*
Affiliation:
Department of Mechanical Engineering, The University of Melbourne, Victoria3010, Australia
*
†Email address for correspondence: nhu@unimelb.edu.au
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Abstract

A surface roughness from a recently cleaned and painted ship's hull was scanned, scaled and replicated for laboratory testing to systematically investigate the influence of the ratio of in-plane roughness wavelength, $\lambda$, with respect to the boundary layer thickness $\delta$. The experiments were performed by geometrically scaling the surface which maintains a constant effective slope $ES_x$ and solidity $\varLambda$, while the ratio of $\lambda /\delta$ is varied. Here we scale the scanned roughness topography by a factor of 2.5 and 15, and measure the mean velocity profiles in the turbulent boundary layers developing over these surfaces at a range of free stream velocities and streamwise measurement locations. The results show that the $2.5\times$ scaled roughness, which has $\lambda /\delta \ll 1$, behaves in the expected $k$-type manner, with a roughness function ${\rm \Delta} U^+$ that is proportional to the viscous-scaled roughness height. The $15\times$ surface, however, which has $\lambda /\delta \approx 1$, exhibits very different non-$k$-type behaviour. This larger surface does not approach the fully rough asymptote and also exhibits a drag penalty that is comparable to the $2.5\times$ case despite the sixfold increase in the roughness height. Measurements on a spanwise–wall-normal plane reveal that the $15\times$ surface has introduced a large-scale spanwise variation in mean streamwise velocity (dispersive stresses) that extend far beyond the logarithmic region. Together this evidence suggests that a demarcation between $k$-type and non-$k$-type behaviour can occur in situations where the in-plane roughness wavelength approaches the boundary layer thickness. This finding has important implications to how we scale small-scale roughness from high Reynolds number (Re) large-scale applications for testing in low Re small-scale laboratory facilities or simulations.

JFM classification

Turbulent Flows: Turbulent boundary layers

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JFM Papers
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Journal of Fluid Mechanics , Volume 911 , 25 March 2021 , A1
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© The Author(s), 2021. Published by Cambridge University Press

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References

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
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, 1351–1378.CrossRefGoogle Scholar
Angelis, V. D., Lombardi, P. & Banerjee, S. 1997 Direct numerical simulation of turbulent flow over a wavy wall. Phys. Fluids 9, 2429.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
Bhaganagar, K., Kim, J. & Coleman, G. 2004 Effect of roughness on wall-bounded turbulence. Flow Turbul. Combust. 72, 463–492.CrossRefGoogle Scholar
Bradshaw, P. 1987 Turbulent secondary flows. Annu. Rev. Fluid Mech. 19, 53–74.CrossRefGoogle Scholar
Chan, L., MacDonald, M., Chung, D., Hutchins, N. & Ooi, A. 2015 A systematic investigation of roughness height and wavelength in turbulent pipe flow in the transitionally rough regime. J. Fluid Mech. 771, 743–777.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, 5–53.CrossRefGoogle Scholar
Chung, D., Monty, J. & Hutchins, N. 2018 Similarity and structure of wall turbulence with lateral wall shear stress variations. J. Fluid Mech. 847, 591–613.CrossRefGoogle Scholar
Clauser, F. H. 1954 Turbulent boundary layers in adverse pressure gradients. J. Aeronaut. Sci. 21, 91–108.CrossRefGoogle Scholar
Flack, K. A., Schultz, M. P. & Barros, J. M. 2020 Skin friction measurements of a systematically-varied roughness: probing the role of roughness amplitude and skewness. Flow Turbul. Combust. 104, 317–329.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
Flack, K. A., Schultz, M. P. & Shapiro, T. A. 2005 Experimental support for townsend's reynolds number similarity hypothesis on rough wall. Phys. Fluids 17, 035102.CrossRefGoogle Scholar
Forooghi, P., Stroh, A., Magagnato, F., Jakirlić, S. & Frohnapfel, B. 2017 Toward a universal roughness correlation. J. Fluids Engng 139 (12), 121201.CrossRefGoogle Scholar
Forooghi, P., Weidenlener, A., Magagnato, F., Böhm, B., Kubach, H., Koch, T. & Frohnapfel, B. 2018 DNS of momentum and heat transfer over rough surfaces based on realistic combustion chamber deposit geometries. Intl J. Heat Fluid Flow 69, 83–94.CrossRefGoogle Scholar
Hama, F. R. 1954 Boundary-layer characteristics for smooth and rough surfaces. Trans. Soc. Nav. Archit. Mar. Engrs 62, 333–358.Google Scholar
Hamed, A. M., Kamdar, A., Castillo, L. & Chamorro, L. P. 2015 Turbulent boundary layer over 2D and 3D large-scale wavy walls. Phys. Fluids 27, 106601.CrossRefGoogle Scholar
Hinze, J. O. 1967 Secondary currents in wall turbulence. Phys. Fluids 10, S122–S125.CrossRefGoogle Scholar
Hudson, J. D., Dykhno, L. & Hanratty, T. J. 1996 Turbulence production in flow over a wavy wall. Exp. Fluids 20, 257–265.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
Hutchins, N., Monty, J. P., Nugroho, B., Ganapathisubramani, B. & Utama, I. K. A. P 2016 Turbulent boundary layers developing over rough surfaces: from the laboratory to full-scale systems. In Proceedings of 20th Australasian Fluid Mechanics Conference, Perth, Australia.Google Scholar
Jelly, T. O. & Busse, A. 2019 Reynolds number dependence of Reynolds and dispersive stresses in turbulent channel flow past irregular near-gaussian roughness. Intl J. Heat Fluid Flow 80, 108485.CrossRefGoogle Scholar
Jiménez, J. 2004 Turbulent flows over rough walls. Annu. Rev. Fluid Mech. 36, 173–196.CrossRefGoogle Scholar
Kline, S. J., Reynolds, W. C., Schraub, F. A. & Rundstadler, P. W. 1967 The structure of turbulent boundary layers. J. Fluid Mech. 30, 741–773.CrossRefGoogle Scholar
Kruse, N, Gunther, A & von Rohr, P. R. 2003 Dynamics of large-scale structures in turbulent flow over a wavy wall. J. Fluid Mech. 485, 87–96.CrossRefGoogle Scholar
Kruse, N., Kuhn, S. & von Rohr, P. R. 2006 Wavy wall effects on turbulence production and large-scale modes. J. Turbul. 7 (31), 1–23.CrossRefGoogle Scholar
Ligrani, P. M. & Bradshaw, P. 1987 Spatial resolution and measurement of turbulence in the viscous sublayer using subminiature hot-wires probes. Exp. Fluids 5, 407–417.CrossRefGoogle Scholar
Marusic, I., Monty, J. P., Hultmark, M. & Smits, A. J. 2013 On the logarithmic region in wall turbulence. J. Fluid Mech. 716, R3.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
Monty, J. P., Allen, J. J., Lien, K. & Chong, M. S. 2011 Modification of the large-scale features of high Reynolds number wall turbulence by passive surface obtrusions. Exp. Fluids 51, 1755–1763.CrossRefGoogle Scholar
Monty, J. P., Dogan, E., Hanson, R., Scardino, A. J., Ganapathisubramani, G. & Hutchins, N. 2016 An assessment of the ship drag penalty arising from light calcareous tubeworm fouling. Biofouling 32 (4), 451–464.CrossRefGoogle ScholarPubMed
Morgan, J. & McKeon, B. J. 2018 Relation between a singly-periodic roughness geometry and spatio-temporal turbulence characteristics. Intl J. Heat Fluid Flow 71, 322–333.CrossRefGoogle Scholar
Nakagawa, S., Na, Y. & Hanratty, T. J. 2003 Influence of a wavy boundary on turbulence. I. Highly rough surface. Exp. Fluids 35, 422–436.CrossRefGoogle Scholar
Nakato, M., Onogi, H., Himeno, Y., Tanaka, I. & Suzuki, T. 1985 Resistance due to surface roughness. In Proceedings of the 15th Symposium on Naval Hydrodynamics, pp. 553–568.Google Scholar
Napoli, E., Armenio, V. & De Marchis, M. 2008 The effect of the slope of irregularly distributed roughness elements on turbulkent wall-bounded flows. J. Fluid Mech. 613, 385–394.CrossRefGoogle Scholar
Nikuradse, J. 1933 Strömungsgesetze in Rauhen Rohren, vol. 361. VDI-Forsch.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
Perry, A. E. 1982 Hot-wire Anemometry. Oxford University Press.Google 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
Perry, A. E., Schofield, W. H. & Joubert, P. N. 1969 Rough wall turbulent boundary layers. J. Fluid Mech. 37, 383–413.CrossRefGoogle Scholar
Reda, C. J., Ketter, J. & Fan, C. 1974 Compressible turbulent skin friction on rough and rough/wavy walls in adiabatic flow. In 7th Fluid and Plasma Dynamics Conference.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, 263–288.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. & Flack, K. A. 2009 Turbulent boundary layers on a systematically varied rough wall. Phys. Fluids 21, 015104.CrossRefGoogle Scholar
Sun, Z., Zhu, Y., Hu, Y. & Zhang, S. 2018 Direct numerical simulation of a fully developed compressible wall turbulence over a wavy wall. J. Turbul. 19 (1), 72–105.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
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow, 2nd edn. Cambridge University Press.Google Scholar
Wangsawijaya, D. D., Baidya, R., Chung, D., Marusic, I. & Hutchins, N. 2020 The effect of spanwise wavelength of surface heterogeneity on turbulent secondary flows. J. Fluid Mech. 894,A7.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
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
Zenklusen, A., Kuhn, S. & von Rohr, P. R. 2012 Structural dissimilarity of large-scale structures in turbulent flows over wavy walls. Exp. Fluids 24, 055112.CrossRefGoogle Scholar
Zilker, D. P., Cook, G. W. & Hanratty, T. J. 1977 Influence of the amplitude of a solid wavy wall on a turbulent flow. Part 1. Non-separated flows. J. Fluid Mech. 82 (1), 29–51.CrossRefGoogle Scholar