Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-10-31T11:41:15.398Z Has data issue: false hasContentIssue false

Direct numerical simulation-based characterization of pseudo-random roughness in minimal channels

Published online by Cambridge University Press:  04 May 2022

Jiasheng Yang
Affiliation:
Institute of Fluid Mechanics, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany
Alexander Stroh
Affiliation:
Institute of Fluid Mechanics, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany
Daniel Chung
Affiliation:
Department of Mechanical Engineering, University of Melbourne, Victoria 3010, Australia
Pourya Forooghi*
Affiliation:
Department of Mechanical and Production Engineering, Aarhus University, 8000 Aarhus, Denmark
*
Email address for correspondence: forooghi@mpe.au.dk

Abstract

Direct numerical simulations (DNS) are used to systematically investigate the applicability of the minimal-channel approach (Chung et al., J. Fluid Mech., vol. 773, 2015, pp. 418–431) for the characterization of roughness-induced drag on irregular rough surfaces. Roughness is generated mathematically using a random algorithm, in which the power spectrum (PS) and probability density function (p.d.f.) of the surface height can be prescribed. Twelve different combinations of PS and p.d.f. are examined, and both transitionally and fully rough regimes are investigated (roughness height varies in the range $k^+ = 25$–100). It is demonstrated that both the roughness function (${\rm \Delta} U^+$) and the zero-plane displacement can be predicted with ${\pm }5\,\%$ accuracy using DNS in properly sized minimal channels. Notably, when reducing the domain size, the predictions remain accurate as long as 90 % of the roughness height variance is retained. Additionally, examining the results obtained from different random realizations of roughness shows that a fixed combination of p.d.f. and PS leads to a nearly unique ${\rm \Delta} U^+$ for deterministically different surface topographies. In addition to the global flow properties, the distribution of time-averaged surface force exerted by the roughness onto the fluid is calculated. It is shown that patterns of surface force distribution over irregular roughness can be well captured when the sheltering effect is taken into account. This is made possible by applying the sheltering model of Yang et al. (J. Fluid Mech., vol. 789, 2016, pp. 127–165) to each specific roughness topography. Furthermore, an analysis of the coherence function between the roughness height and the surface force distributions reveals that the coherence drops at larger streamwise wavelengths, which can be an indication that very large horizontal scales contribute less to the skin-friction drag.

Type
JFM Papers
Copyright
© The Author(s), 2022. 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

REFERENCES

Alves Portela, F. & Sandham, N.D. 2020 A DNS/URANS approach for simulating rough-wall turbulent flows. Intl J. Heat Fluid Flow 85, 108627.CrossRefGoogle Scholar
Anderson, W. & Meneveau, C. 2011 Dynamic roughness model for large-eddy simulation of turbulent flow over multiscale, fractal-like rough surfaces. J. Fluid Mech. 679, 288314.CrossRefGoogle 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, 17.CrossRefGoogle Scholar
Bhaganagar, K. 2008 Direct numerical simulation of unsteady flow in channel with rough walls. Phys. Fluids 20 (10), 101508.CrossRefGoogle Scholar
Bons, J. 2005 A critical assessment of Reynolds analogy for turbine flows. J. Heat Transfer 127 (5), 472485.CrossRefGoogle Scholar
Bons, J.P., Taylor, R.P., McClain, S.T. & Rivir, R.B. 2001 The many faces of turbine surface roughness. J. Turbomech. 123, 739748.CrossRefGoogle Scholar
Brereton, G.J., Jouybari, M.A. & Yuan, J. 2021 Toward modeling of turbulent flow over surfaces of arbitrary roughness. Phys. Fluids 33 (6), 065121.CrossRefGoogle Scholar
Brereton, G.J. & Yuan, J. 2018 Wall-roughness eddy viscosity for Reynolds-averaged closures. Intl J. Heat Fluid Flow 73, 7481.CrossRefGoogle Scholar
Busse, A., Lützner, M. & Sandham, N.D. 2015 Direct numerical simulation of turbulent flow over a rough surface based on a surface scan. Comput. Fluids 116, 129147.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, 196224.CrossRefGoogle Scholar
Cardillo, J., Chen, Y., Araya, G., Newman, J., Jansen, K. & Castillo, L. 2013 DNS of a turbulent boundary layer with surface roughness. J. Fluid Mech. 729, 603637.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, 743777.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, 533.CrossRefGoogle Scholar
Chan-Braun, C., García-Villalba, M. & Uhlmann, M. 2011 Force and torque acting on particles in a transitionally rough open-channel flow. J. Fluid Mech. 684, 441474.CrossRefGoogle Scholar
Chau, L. & Bhaganagar, K. 2012 Understanding turbulent flow over ripple-shaped random roughness in a channel. Phys. Fluids 24 (11), 115102.CrossRefGoogle Scholar
Chevalier, M, Schlatter, P., Lundbladh, A & Henningson, D. 2007 SIMSON–A pseudo-spectral solver for incompressible boundary layer flow. Tech. Rep. TRITA-MEK 2007:07, pp. 1–100. Royal Institute of Technology.Google Scholar
Chung, D., Chan, L., MacDonald, M., Hutchins, N. & Ooi, A. 2015 A fast direct numerical simulation method for characterising hydraulic roughness. J. Fluid Mech. 773, 418431.CrossRefGoogle Scholar
Chung, D., Hutchins, N., Schultz, M.P. & Flack, K.A. 2021 Predicting the drag of rough surfaces. Annu. Rev. Fluid Mech. 53, 439471.CrossRefGoogle Scholar
Clauser, F.H. 1956 The turbulent boundary layer. Adv. Appl. Mech. 4, 151.CrossRefGoogle Scholar
Coceal, O. & Belcher, S.E. 2004 A canopy model of mean winds through urban areas. Q. J. R. Meteorol. Soc. 130 (599), 13491372.CrossRefGoogle Scholar
De Marchis, M., Saccone, D. & Milici, B. 2020 Large eddy simulations of rough turbulent channel flows bounded by irregular roughness: advances toward a universal roughness correlation. Flow Turbul. Combust. 105, 627648.CrossRefGoogle Scholar
Finnigan, J.J. & Shaw, R.H. 2008 Double-averaging methodology and its application to turbulent flow in and above vegetation canopies. Acta Geophys. 56 (1), 534561.CrossRefGoogle Scholar
Flack, K.A. 2018 Moving beyond Moody. J. Fluid Mech. 842, 14.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. & Barros, J.M. 2020 Skin friction measurements of systematically-varied roughness: probing the role of roughness amplitude and skewness. Flow Turbul. Combust. 104 (2–3), 317329.CrossRefGoogle Scholar
Flores, O. & Jiménez, J. 2010 Hierarchy of minimal flow units in the logarithmic layer. Phys. Fluids 22 (7), 071704.CrossRefGoogle Scholar
Forooghi, P., Stripf, M. & Frohnapfel, B. 2018 a A systematic study of turbulent heat transfer over rough walls. Intl J. Heat Mass Transfer 127, 11571168.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., Stroh, A., Schlatter, P. & Frohnapfel, B. 2018 b Direct numerical simulation of flow over dissimilar, randomly distributed roughness elements: a systematic study on the effect of surface morphology on turbulence. Phys. Rev. Fluids 3, 044605.CrossRefGoogle Scholar
Forooghi, P., Weidenlener, A., Magagnato, F., Böhm, B., Kubach, H., Koch, T. & Frohnapfel, B. 2018 c DNS of momentum and heat transfer over rough surfaces based on realistic combustion chamber deposit geometries. Intl J. Heat Fluid Flow 69, 8394.CrossRefGoogle Scholar
Goldstein, D., Handler, R. & Sirovich, L. 1993 Modeling a no-slip flow boundary with an external force field. J. Comput. Phys. 105 (2), 354366.CrossRefGoogle Scholar
Hama, F.R. 1954 Boundary-Layer Characteristics for Smooth and Rough Surfaces. Society of Naval Architects and Marine Engineers.Google 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 20th Australasian Fluid Mechanics Conference, vol. 1235.Google Scholar
Jackson, P.S. 1981 On the displacement height in the logarithmic velocity profile. J. Fluid Mech. 111, 1525.CrossRefGoogle 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, 173196.CrossRefGoogle Scholar
Jiménez, J. & Moin, P. 1991 The minimal flow unit in near-wall turbulence. J. Fluid Mech. 225, 213240.CrossRefGoogle Scholar
Jouybari, M.A., Brereton, G.J. & Yuan, J. 2019 Turbulence structures over realistic and synthetic wall roughness in open channel flow at $Re_{\tau } = 1000$. J. Turbul. 20 (11–12), 723749.CrossRefGoogle Scholar
Jouybari, M.A., Yuan, J., Brereton, G.J. & Murillo, M.S. 2021 Data-driven prediction of the equivalent sand-grain height in rough-wall turbulent flows. J. Fluid Mech. 912, A8.CrossRefGoogle Scholar
Kameda, T., Mochizuki, S. & Osaka, H. 2018 On the virtual origin determined from momentum equation analysis using experimental data within the roughness sublayer. Exp. Fluids 59 (10), 146.CrossRefGoogle Scholar
Kuwata, Y. & Kawaguchi, Y. 2019 Direct numerical simulation of turbulence over systematically varied irregular rough surfaces. J. Fluid Mech. 862, 781815.CrossRefGoogle Scholar
Leonardi, S. & Castro, I.P. 2010 Channel flow over large cube roughness: a direct numerical simulation study. J. Fluid Mech. 651, 519539.CrossRefGoogle Scholar
MacDonald, M., Chung, D., Hutchins, N., Chan, L., Ooi, A. & Garcıa-Mayoral, A. 2016 The minimal channel: a fast and direct method for characterising roughness. J. Phys.: Conf. Ser. 708, 012010.Google Scholar
MacDonald, M., Chung, D., Hutchins, N., Chan, L., Ooi, A. & Garcia-Mayoral, R. 2017 The minimal-span channel for rough-wall turbulent flows. J. Fluid Mech. 816, 542.CrossRefGoogle Scholar
MacDonald, M., Hutchins, N. & Chung, D. 2019 Roughness effects in turbulent forced convection. J. Fluid Mech. 861, 138162.CrossRefGoogle Scholar
MacDonald, M., Ooi, A., García-Mayoral, R., Hutchins, N. & Chung, D. 2018 Direct numerical simulation of high aspect ratio spanwise-aligned bars. J. Fluid Mech. 843, 126155.CrossRefGoogle Scholar
Macdonald, R.W. 2000 Modelling the mean velocity profile in the urban canopy layer. Boundary-Layer Meteorol. 97 (1), 2545.CrossRefGoogle Scholar
Mangavelli, S.C., Yuan, J. & Brereton, G.J. 2021 Effects of surface roughness topography in transient channel flows. J. Turbul. 22 (7), 434460.CrossRefGoogle Scholar
Mazzuoli, M. & Uhlmann, M. 2017 Direct numerical simulation of open-channel flow over a fully rough wall at moderate relative submergence. J. Fluid Mech. 824, 722765.CrossRefGoogle Scholar
Moody, L.F. 1944 Friction factors for pipe flow. Trans. ASME 66 (8), 671677.Google 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, 385394.CrossRefGoogle Scholar
Nikora, V.I., et al. 2019 Friction factor decomposition for rough-wall flows: theoretical background and application to open-channel flows. J. Fluid Mech. 872, 626664.CrossRefGoogle Scholar
Nikuradse, J. 1933 Stroemungsgesetze in Rauhen Rohren. VDI-Verl.Google Scholar
Orlandi, P. & Leonardi, S. 2006 DNS of turbulent channel flows with two- and three-dimensional roughness. J. Turbul. 7, N73.CrossRefGoogle Scholar
Pargal, S., Yuan, J. & Brereton, G.J. 2021 Impulse response of turbulent flow in smooth and riblet-walled channels to a sudden velocity increase. J. Turbul. 22 (6), 353379.CrossRefGoogle Scholar
Pérez-Ràfols, F. & Almqvist, A. 2019 Generating randomly rough surfaces with given height probability distribution and power spectrum. Tribol. Intl 131, 591604.CrossRefGoogle Scholar
Perry, A.E. & Joubert, P.N. 1963 Rough-wall boundary layers in adverse pressure gradients. J. Fluid Mech. 17 (2), 193211.CrossRefGoogle Scholar
Perry, A.E., Schofield, W.H. & Joubert, P.N. 1969 Rough wall turbulent boundary layers. J. Fluid Mech. 37 (2), 383413.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, 541566.CrossRefGoogle Scholar
Quadrio, M. & Luchini, P. 2003 Integral space–time scales in turbulent wall flows. Phys. Fluids 15 (8), 22192227.CrossRefGoogle Scholar
van Rij, J.A., Belnap, B.J. & Ligrani, P.M. 2002 Analysis and experiments on three-dimensional, irregular surface roughness . J. Fluids Engng 124 (3), 671677.CrossRefGoogle Scholar
Schlichting, H. 1936 Experimentelle untersuchungen zum rauhigkeitsproblem. Ing.-Arch. 7, 134.CrossRefGoogle Scholar
Schultz, M.P. & Flack, K.A. 2009 Turbulent boundary layers on a systematically varied rough wall. Phys. Fluids 21 (1), 015104.CrossRefGoogle Scholar
Scotti, A. 2006 Direct numerical simulation of turbulent channel flows with boundary roughened with virtual sandpaper. Phys. Fluids 18 (3), 031701.CrossRefGoogle Scholar
Sigal, A. & Danberg, J.E. 1990 New correlation of roughness density effect on the turbulent boundary layer. AIAA J. 28 (3), 554556.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
Suga, K., Craft, T.J. & Iacovides, H. 2006 An analytical wall-function for turbulent flows and heat transfer over rough walls. Intl J. Heat Fluid Flow 27 (5), 852866.CrossRefGoogle Scholar
Thakkar, M., Busse, A. & Sandham, N. 2017 Surface correlations of hydrodynamic drag for transitionally rough engineering surfaces. J. Turbul. 18 (2), 138169.CrossRefGoogle Scholar
Townsend, A.A. 1976 The Structure of Turbulent Shear Flow, 2nd edn. Cambridge University Press.Google 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. 862, 845870.CrossRefGoogle Scholar
Velandia, J. & Bansmer, S. 2019 Topographic study of the ice accretion roughness on a generic aero-engine intake. AIAA Paper 2019-1451.CrossRefGoogle Scholar
Waigh, D.R. & Kind, R.J. 1998 Improved aerodynamic characterization of regular three-dimensional roughness. AIAA J. 36 (6), 11171119.CrossRefGoogle Scholar
Yang, X.I.A., Sadique, J., Mittal, R. & Meneveau, C. 2016 Exponential roughness layer and analytical model for turbulent boundary layer flow over rectangular-prism roughness elements. J. Fluid Mech. 789, 127165.CrossRefGoogle Scholar
Yuan, J. & Jouybari, M.A. 2018 Topographical effects of roughness on turbulence statistics in roughness sublayer. Phys. Rev. Fluids 3, 114603.CrossRefGoogle Scholar
Yuan, J. & Piomelli, U. 2014 Estimation and prediction of the roughness function on realistic surfaces. J. Turbul. 15 (6), 350365.CrossRefGoogle Scholar