Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-10T23:30:15.315Z Has data issue: false hasContentIssue false
  • English
  • Français

Flow-roughness heterogeneity: critical obliquity and salient parameters

Published online by Cambridge University Press:  23 February 2021

Y. Zheng  and
W. Anderson Open the ORCID record for W. Anderson [Opens in a new window]
Y. Zheng
Affiliation:
Department of Mechanical Engineering, University of Texas at Dallas, Richardson, TX 75080USA
W. Anderson*
Affiliation:
Department of Mechanical Engineering, University of Texas at Dallas, Richardson, TX 75080USA
*
†Email address for correspondence: wca140030@utdallas.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

A uniform distribution of roughness elements of height, $h$, enhances turbulent momentum exchanges in wall flows of thickness, $\delta$. For $\delta/h$ above a nominal threshold, this distribution of elements enhances drag, but does not induce structural response to outer-/inertial-layer turbulence. Large-scale spatial variability in element attributes, however, can induce $\delta$-scale response in the instantaneous and Reynolds-averaged flow. For the case of a large-scale heterogeneity aligned orthogonal and parallel to the primary transport direction, the Reynolds-averaged flow responds with formation of an internal boundary layer (IBL) and counter-rotating secondary cells, respectively. For oblique flow-heterogeneity alignments, Anderson (J. Fluid Mech., vol. 886, 2020, p. A15), showed that IBL formation persists for flow-heterogeneity aligned at a series of oblique angles, before abruptly collapsing and transitioning to counter-rotating secondary cells at a critical obliquity. We define flow-roughness obliquity angle with symbol, $\theta$, where $\theta = 0$ and ${\rm \pi}/2$ corresponds with streamwise and spanwise heterogeneity, respectively, while the critical obliquity angle is denoted by $\theta_c$. We have used large-eddy simulation to perform a comprehensive parametric assessment on the effect of obliquity, element height, and spacing between adjacent ‘rows’ of elements, all of which is intended to identify the aforementioned critical obliquity. We once again report the aforementioned IBL persistence. It is shown that this response is a product of successive element sheltering, which can be recorded via the element frontal area index: as obliquity angle increases, there is a critical obliquity at which downflow elements fall in the sheltering zone of upflow elements; we find that $\theta_c = 22 {\rm \pi}/ 56$.

JFM classification

Turbulent Flows: Turbulence modelling
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 913 , 25 April 2021 , A12
Check for updates
Copyright
© The Author(s), 2021. 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

Akins, R.E., Peterka, J.A. & Cermak, J.E. 1977 Mean force and moment coefficients for buildings in turbulent boundary layers. J. Wind Engng Ind. Aerodyn. 2, 195–209.CrossRefGoogle Scholar
Allen, J.J., Shockling, M.A., Kunkel, G.J. & Smits, A.J. 2007 Turbulent flow in smooth and rough pipes. Phil. Trans. R. Soc. Lond. A 365 (1852), 699–714.Google ScholarPubMed
Anderson, W. 2012 An immersed boundary method wall model for high-reynolds number channel flow over complex topography. Intl J. Numer. Meth. Fluids 71, 1588–1608.CrossRefGoogle Scholar
Anderson, W 2019 Non-periodic phase-space trajectories of roughness-driven secondary flows in high-$Re_\tau$ boundary layers and channels. J. Fluid Mech. 869, 27–84.CrossRefGoogle Scholar
Anderson, W. 2020 Turbulent channel flow over heterogeneous roughness at oblique angles. J. Fluid Mech. 886, A15.CrossRefGoogle Scholar
Anderson, W., Barros, J.M., Christensen, K.T. & Awasthi, A. 2015 a 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., Li, Q. & Bou-Zeid, E. 2015 b Numerical simulation of flow over urban-like topographies and evaluation of turbulence temporal attributes. J. Turbul. 16, 809–831.CrossRefGoogle Scholar
Anderson, W. & Meneveau, C. 2010 A large-eddy simulation model for boundary-layer flow over surfaces with horizontally resolved but vertically unresolved roughness elements. Boundary-Layer Meteorol. 137, 397–415.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
Andreopoulos, J. & Wood, D.H. 1982 The response of a turbulent boundary layer to a short length of surface roughness. J. Fluid. Mech. 118, 143–164.CrossRefGoogle Scholar
Antonia, R.A. & Luxton, R.E. 1971 The response of a turbulent boundary layer to a step change in surface roughness. Part 1: smooth to rough. J. Fluid Mech. 48, 721–761.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
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
Bou-Zeid, E., Anderson, W., Katul, G.G. & Mahrt, L. 2020 The persistent challenge of surface heterogeneity in boundary-layer meteorology: a review. Boundary-Layer Meteorol. 177 (2–3), 227–245.CrossRefGoogle Scholar
Bou-Zeid, E., Meneveau, C. & Parlange, M.B. 2004 Large-eddy simulation of neutral atmospheric boundary layer flow over heterogeneous surfaces: blending height and effective surface roughness. Water Resour. Res. 40, W02505.CrossRefGoogle Scholar
Bou-Zeid, E., Meneveau, C. & Parlange, M. 2005 A scale-dependent Lagrangian dynamic model for large eddy simulation of complex turbulent flows. Phys. Fluids 17 (2), 025105.CrossRefGoogle Scholar
Castro, I.P. 2007 Rough-wall boundary layers: mean flow universality. J. Fluid Mech. 585, 469–485.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
Curley, A. & Uddin, M. 2015 Direct numerical simulation of turbulent flow around a surface mounted cube. AIAA Paper 3431.CrossRefGoogle Scholar
Fishpool, G.M., Lardeau, S. & Leschziner, M.A. 2009 Persistent non-homogeneous features in periodic channel-flow simulations. Flow Turbul. Combust. 83, 823–342.CrossRefGoogle Scholar
Flack, K.A. & Schultz, M.P. 2010 Review of hydraulic roughness scales in the fully rough regime. J. Fluids Engng 132, 041203.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 (9), 095104.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
Garratt, J.R. 1990 The internal boundary layer – a review. Boundary-Layer Meterol. 40, 171–203.CrossRefGoogle Scholar
Ghisalberti, M. 2009 Obstructed shear flows: similarities across systems and scales. J. Fluid Mech. 641, 51–61.CrossRefGoogle Scholar
Graham, J. & Meneveau, C. 2012 Modeling turbulent flow over fractal trees using renormalized numerical simulation: alternate formulations and numerical experiments. Phys. Fluids 24, 125105.CrossRefGoogle Scholar
Grass, A.J. 1971 Structural features of turbulent flow over smooth and rough boundaries. J. Fluid Mech. 50, 233–255.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
Hong, J., Katz, J., Meneveau, C. & Schultz, M. 2012 Coherent structures and associated subgrid-scale energy transfer in a rough-wall channel flow. J. Fluid Mech. 712, 92–128.CrossRefGoogle Scholar
Hussain, M. & Lee, B.E. 1980 A wind tunnel study of the mean pressure forces acting on large groups of low-rise buildings. J. Wind Engng Ind. Aerodyn. 6 (3), 207–225.CrossRefGoogle Scholar
Hutchins, N. & Marusic, I. 2007 Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J. Fluid Mech. 579, 1–28.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
Jimenez, J. 2004 Turbulent flow over rough wall. Annu. Rev. Fluid Mech. 36, 173–196.CrossRefGoogle Scholar
Kevin, M.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
Kevin, M.J. & Hutchins, N. 2019 Turbulent structures in a statistically three-dimensional boundary layer. J. Fluid Mech. 859, 543–565.CrossRefGoogle Scholar
Macdonald, R., Griffiths, R. & Hall, D. 1998 An improved method for the estimation of surface roughness of obstacle arrays. Atmos. Environ. 32, 1857–1864.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., Barros, J.M. & Christensen, K.T. 2013 Structural attributes of turbulent flow over a complex topography. In Coherent Flow Structures at the Earth's Surface, chap. 3, pp. 25–42. Wiley-Blackwell.CrossRefGoogle Scholar
Nugroho, B., Hutchins, N. & Monty, J.P. 2013 Large-scale spanwise periodicity in a turbulent boundary layer induced by highly ordered and direction surface roughness. Intl J. Heat Fluid Flow 41, 90–102.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
Raupach, M. 1992 Drag and drag partition on rough surfaces. Boundary-Layer Meteorol. 60, 375–395.CrossRefGoogle Scholar
Raupach, M.R., Antonia, R.A. & Rajagopalan, S. 1991 Rough-wall turbulent boundary layers. Appl. Mech. Rev. 44, 1–25.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, 311–320.CrossRefGoogle Scholar
Stoll, R., Gibbs, J.E., Salesky, S. & Anderson, W. 2020 Review: large-eddy simulation of the atmospheric boundary layer. Boundary-Layer Meteorol. 177 (2–3), 541–581.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
Townsend, A.A. 1951 The structure of the turbulent boundary layer. Math. Proc. Camb. Phil. Soc. 47, 375–395.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. 862, 845–870.CrossRefGoogle Scholar
Volino, R.J., Schultz, M.P. & Flack, K.A. 2007 Turbulence structure in rough- and smooth-wall boundary layers. J. Fluid Mech. 592, 263–293.CrossRefGoogle Scholar
Wang, C. & Anderson, W. 2018 Large-eddy simulation of turbulent flow over spanwise-offset barchan dunes: interdune vortex stretching drives asymmetric erosion. Phys. Rev. E 98, 033112.CrossRefGoogle 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. 2013 Turbulent boundary layer flow over transverse aerodynamic roughness transitions: induced mixing and flow characterization. Phys. Fluids 26, 025111.CrossRefGoogle Scholar
Wood, D.H. 1981 The growth of the internal layer following a step change in surface roughness. Report T.N. – FM 57, Deparment of Mechanical Engineering, University of Newcastle, Australia.Google Scholar
Wu, Y. & Christensen, K.T. 2007 Outer-layer similarity in the presence of a practical rough-wall topology. Phys. Fluids 19, 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
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, 127–165.CrossRefGoogle Scholar
Zagarola, M.V. & Smits, A.J. 1998 Mean-flow scaling of turbulent pipe flow. J. Fluid Mech. 373, 33–79.CrossRefGoogle Scholar
Zhu, X. & Anderson, W. 2018 Turbulent flow over urban-like fractals: prognostic roughness model for unresolved generations. J. Turbul. 19, 995–1016.CrossRefGoogle Scholar
Zhu, X., Iungo, G.V., Leonardi, S. & Anderson, W. 2016 Parametric study of urban-like topographic statistical moments relevant to a priori modelling of bulk aerodynamic parameters. Boundary-Layer Meteorol. 162, 231–253.CrossRefGoogle Scholar