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A new equivalent sand grain roughness relation for two-dimensional rough wall turbulent boundary layers

Published online by Cambridge University Press:  08 April 2022

Misarah Abdelaziz Open the ORCID record for Misarah Abdelaziz [Opens in a new window] ,
L. Djenidi Open the ORCID record for L. Djenidi [Opens in a new window] ,
Mergen H. Ghayesh  and
Rey Chin Open the ORCID record for Rey Chin [Opens in a new window]
Misarah Abdelaziz*
Affiliation:
School of Mechanical Engineering, University of Adelaide, Adelaide, South Australia 5005, Australia
L. Djenidi
Affiliation:
Mechanical Engineering Discipline, The University of Newcastle, Callaghan, NSW 2308, Australia
Mergen H. Ghayesh
Affiliation:
School of Mechanical Engineering, University of Adelaide, Adelaide, South Australia 5005, Australia
Rey Chin
Affiliation:
School of Mechanical Engineering, University of Adelaide, Adelaide, South Australia 5005, Australia
*
†Email address for correspondence: [email protected]
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Abstract

The effects of different geometries of two-dimensional (2-D) roughness elements in a zero pressure gradient (ZPG) turbulent boundary layer (TBL) on turbulence statistics and drag coefficient are assessed using single hot-wire anemometry. Three kinds of 2-D roughness are used: (i) circular rods with two different heights, $k= 1.6$ and 2.4 mm, and five different streamwise spacing of $s_{x}= 6k$ to $24k$, (ii) three-dimensional (3-D) printed triangular ribs with heights of $k= 1.6$ mm and spacing of $s_{x}= 8k$ and (iii) computerized numerical control (CNC) machined sinewave surfaces with two different heights, $k= 1.6$ and 2.4 mm, and spacing of $s_{x}= 8k$. These roughnesses cover a wide range of ratios of the boundary layer thickness to the roughness height ($23 < \delta /k < 41$), where $\delta$ is the boundary layer thickness. All roughnesses cause a downward shift on the wall-unit normalised streamwise mean velocity profile when compared with the smooth wall profiles agreeing with the literature, with a maximum downward shift observed for $s_{x}= 8k$. In the fully rough regime, the drag coefficient becomes independent of the Reynolds number. Changing the roughness height while maintaining the same spacing ratio $s_{x}/k$ exhibits little influence on the drag coefficient in the fully rough regime. On the other hand, the effective slope $(ES)$ and the height skewness $(k_{sk})$ appear to be major surface roughness parameters that affect the drag coefficient. These parameters are used in a new expression for $k_{s}$, the equivalent sand grain roughness, developed for 2-D uniformly distributed roughness in the fully rough regime.

JFM classification

Turbulent Flows: Turbulent boundary layers
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 940 , 10 June 2022 , A25
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

REFERENCES

ASME 2009 Surface texture (surface roughness, waviness, and lay). Revision of ANSI/ASME B46.1-1995. Standard. ASME.Google Scholar
Barros, J.M., Schultz, M.P. & Flack, K.A. 2018 Measurements of skin-friction of systematically generated surface roughness. Intl J. Heat Fluid Flow 72, 1–7.CrossRefGoogle Scholar
Bons, J.P. 2002 $S_{t}$ and $C_{f}$ augmentation for real turbine roughness with elevated freestream turbulence. J. Turbomach. 124 (4), 632–644.CrossRefGoogle Scholar
Busse, A., Thakkar, M. & Sandham, N.D. 2017 Reynolds-number dependence of the near-wall flow over irregular rough surfaces. J. Fluid Mech. 810, 196–224.CrossRefGoogle Scholar
Chin, C.C., Hutchins, N., Ooi, A.S.H. & Marusic, I. 2009 Use of direct numerical simulation (DNS) data to investigate spatial resolution issues in measurements of wall-bounded turbulence. Meas. Sci. Technol. 20, 115401.CrossRefGoogle Scholar
Clauser, F.H. 1956 The turbulent boundary layer. Adv. Appl. Mech. 4, 1–51.CrossRefGoogle 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
Djenidi, L., Talluru, K.M. & Antonia, R.A. 2019 A velocity defect chart method for estimating the friction velocity in turbulent boundary layers. Fluid Dyn. Res. 51, 045502.CrossRefGoogle Scholar
Flack, K.A., Schultz, M.P. & Barros, J.M. 2020 Skin friction measurements of systematically-varied roughness: probing the role of roughness amplitude and skewness. Flow Turbul. Combust. 104 (2), 317–329.CrossRefGoogle Scholar
Flack, K.A., Schultz, M.P., Barros, J.M. & Kim, Y.C. 2016 Skin-friction behavior in the transitionally-rough regime. Intl J. Heat Fluid Flow 61, 21–30.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
Furuya, Y., Miyata, M. & Fujita, H. 1976 Turbulent boundary layer and flow resistance on plates roughened by wires. J. Fluids Engng 98 (4), 635–643.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
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
Jiménez, J. 2004 Turbulent flows over rough walls. Annu. Rev. Fluid Mech. 36, 173–196.CrossRefGoogle Scholar
Kamruzzaman, M.D., Djenidi, L., Antonia, R.A. & Talluru, K.M. 2015 Drag of a turbulent boundary layer with transverse 2D circular rods on the wall. Exp. Fluids 56 (6), 121.CrossRefGoogle Scholar
Krogstad, P.-Å. & Antonia, R.A. 1999 Surface roughness effects in turbulent boundary layers. Exp. Fluids 27 (5), 450–460.CrossRefGoogle Scholar
Krogstad, P.-Å. & Efros, V. 2012 About turbulence statistics in the outer part of a boundary layer developing over two-dimensional surface roughness. Phys. Fluids 24, 075112.CrossRefGoogle Scholar
Leonardi, S., Orlandi, P., Djenidi, L. & Antonia, R.A. 2015 Heat transfer in a turbulent channel flow with square bars or circular rods on one wall. J. Fluid Mech. 776, 512–530.CrossRefGoogle Scholar
Leonardi, S., Orlandi, P., Smalley, R.J., Djenidi, L. & Antonia, R.A. 2003 Direct numerical simulations of turbulent channel flow with transverse square bars on one wall. J. Fluid Mech. 491, 229–238.CrossRefGoogle Scholar
Ligrani, P.M. & Bradshaw, P. 1987 Spatial resolution and measurement of turbulence in the viscous sublayer using subminiature hot-wire probes. Exp. Fluids 5 (6), 407–417.CrossRefGoogle Scholar
MacDonald, M., Chan, L., Chung, D., Hutchins, N. & Ooi, A. 2016 Turbulent flow over transitionally rough surfaces with varying roughness densities. J. Fluid Mech. 804, 130–161.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
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
Musker, A.J. 1980 Universal roughness functions for naturally-occurring surfaces. Trans. Can. Soc. Mech. Engng 6 (1), 1–6.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
Nickels, T.B., Marusic, I., Hafez, S. & Chong, M.S. 2005 Evidence of the $k_{1}^{-1}$ law in a high-Reynolds-number turbulent boundary layer. Phys. Rev. Lett. 95, 074501.CrossRefGoogle Scholar
Nikuradse, J. 1933 Laws of flow in rough pipes. Translation from German published 1950 as NACA Tech. Memo 1292.Google Scholar
Perry, A.E. & Joubert, P.N. 1963 Rough-wall boundary layers in adverse pressure gradients. J. Fluid Mech. 17 (02), 193–211.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
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
Schlatter, P. & Örlü, R. 2010 Assessment of direct numerical simulation data of turbulent boundary layers. J. Fluid Mech. 659, 116–126.CrossRefGoogle Scholar
Schlichting, H. & Kestin, J. 1961 Boundary Layer Theory, vol. 121. Springer.Google 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
Sillero, J.A., Jiménez, J. & Moser, R.D. 2014 Two-point statistics for turbulent boundary layers and channels at Reynolds numbers up to $\delta ^{+} = 2000$. Phys. Fluids 26, 105109.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
Sun, B. 2019 Thirty years of turbulence study in China. Appl. Math. Mech. 40 (2), 193–214.CrossRefGoogle Scholar
Waigh, D.R. & Kind, R.J. 1998 Improved aerodynamic characterization of regular three-dimensional roughness. AIAA J. 36 (6), 1117–1119.CrossRefGoogle Scholar