Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-27T18:44:05.334Z Has data issue: false hasContentIssue false
  • English
  • Français

Numerical and experimental study of mechanisms responsible for turbulent secondary flows in boundary layer flows over spanwise heterogeneous roughness

Published online by Cambridge University Press:  06 March 2015

William Anderson ,
Julio M. Barros ,
Kenneth T. Christensen  and
Ankit Awasthi
William Anderson*
Affiliation:
Mechanical Engineering Department, University of Texas at Dallas, Richardson, TX 75080, USA
Julio M. Barros
Affiliation:
Department of Mechanical Engineering, United States Naval Academy, Annapolis, MD 21402, USA
Kenneth T. Christensen
Affiliation:
Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN 46556, USA Department of Civil and Environmental Engineering and Earth Sciences, University of Notre Dame, Notre Dame, IN 46556, USA International Institute for Carbon-Neutral Energy Research (WPI-I2CNER), Kyushu University, Nishi-ku, Fukuoka 819-0395, Japan
Ankit Awasthi
Affiliation:
Mechanical Engineering Department, University of Texas at Dallas, Richardson, TX 75080, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We study the dynamics of turbulent boundary layer flow over a heterogeneous topography composed of roughness patches exhibiting relatively high and low correlation in the streamwise and spanwise directions, respectively (i.e. the roughness appears as streamwise-aligned ‘strips’). It has been reported that such roughness induces a spanwise-wall normal mean secondary flow in the form of mean streamwise vorticity associated with counter-rotating boundary-layer-scale circulations. Here, we demonstrate that this mean secondary flow is Prandtl’s secondary flow of the second kind, both driven and sustained by spatial gradients in the Reynolds-stress components, which cause a subsequent imbalance between production and dissipation of turbulent kinetic energy that necessitates secondary advective velocities. In reaching this conclusion, we study (i) secondary circulations due to spatial gradients of turbulent kinetic energy, and (ii) the production budgets of mean streamwise vorticity by gradients of the Reynolds stresses. We attribute the secondary flow phenomena to extreme peaks of surface stress on the relatively high-roughness regions and associated elevated turbulence production in the fluid immediately above. An optimized state is attained by entrainment of fluid exhibiting the lowest turbulent stresses – from above – and subsequent lateral ejection in order to preserve conservation of mass.

JFM classification

Turbulent Flows: Turbulent boundary layers Turbulent Flows: Turbulent Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 768 , 10 April 2015 , pp. 316 - 347
Check for updates
Copyright
© 2015 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

Adrian, R. 2007 Hairpin vortex organization in wall turbulence. Phys. Fluids 19, 041301.CrossRefGoogle Scholar
Adrian, R., Christensen, K. & Liu, Z.-C. 2000a Analysis and interpretation of instantaneous turbulent velocity fields. Exp. Fluids 29, 275–290.CrossRefGoogle Scholar
Adrian, R., Meinhart, C. & Tomkins, C. 2000b Vortex organization in the outer region of the turbulent boundary layer. J. Fluid Mech. 422, 1–54.CrossRefGoogle Scholar
Adrian, R. & Westerweel, J. 2011 Particle Image Velocimetry. Cambridge University Press.Google Scholar
Anderson, W. 2013 Passive scalar roughness lengths for atmospheric boundary layer flow over complex, fractal topographies. Environ. Fluid Mech. 13, 479–501.CrossRefGoogle Scholar
Anderson, W. & Chamecki, M. 2014 Numerical study of turbulent flow over complex aeolian dune fields: the White Sands National Monument. Phys. Rev. E 89, 013005.CrossRefGoogle ScholarPubMed
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. & Meneveau, C. 2011 Dynamic large-eddy simulation model for boundary layer flow over multiscale, fractal-like surfaces. J. Fluid Mech. 679, 288–314.CrossRefGoogle Scholar
Anderson, W., Passalacqua, P., Porté-Agel, F. & Meneveau, C. 2012 Large-eddy simulation of atmospheric boundary layer flow over fluvial-like landscapes using a dynamic roughness model. Boundary-Layer Meteorol. 144, 263–286.CrossRefGoogle Scholar
Barros, J.2014 Cross-plane stereo PIV measurements of a turbulent boundary layer over highly irregular roughness. PhD thesis, University of Illinois at Urbana-Champaign.Google 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
Belcher, S., Harman, I. & Finnigan, J. 2012 The wind in the willows: flows in forest canopies in complex terrain. Annu. Rev. Fluid Mech. 44, 479–504.CrossRefGoogle Scholar
Best, J. 2005 The fluid dynamics of river dunes: a review and some future research directions. J. Geophys. Res. 110, F04S02.CrossRefGoogle Scholar
Bons, J., Taylor, R., McClain, S. & Rivir, R. 2001 The many faces of turbine surface roughness. Trans. ASME: J. Turbomach. 123, 739–748.Google Scholar
Bou-Zeid, E., Meneveau, C. & Parlange, M. 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, 025105.CrossRefGoogle Scholar
Bou-Zeid, E., Parlange, M. & Meneveau, C. 2007 On the parameterization of surface roughness at regional scales. J. Atmos. Sci. 64, 216–227.CrossRefGoogle Scholar
Bradshaw, P. 1987 Turbulent secondary flows. Annu. Rev. Fluid Mech. 19, 53–74.CrossRefGoogle Scholar
Brundrett, E. & Baines, W. D. 1964 The production and diffusion of vorticity in duct flow. J. Fluid Mech. 19, 375–394.CrossRefGoogle Scholar
Brutsaert, W. 1982 Evaporation into the Atmosphere. Springer.CrossRefGoogle Scholar
Calaf, M., Meneveau, C. & Meyers, J. 2010 Large eddy simulation study of fully developed wind-turbine array boundary layers. Phys. Fluids 22, 015110.CrossRefGoogle Scholar
Calaf, M., Parlange, M. & Meneveau, C. 2011 Large eddy simulation study of scalar transport in fully developed wind-turbine array boundary layers. Phys. Fluids 23, 126603.CrossRefGoogle Scholar
Castro, I. 2007 Rough-wall boundary layers: mean flow universality. J. Fluid Mech. 585, 469–485.CrossRefGoogle Scholar
Chester, S., Meneveau, C. & Parlange, M. 2007 Modelling of turbulent flow over fractal trees with renormalized numerical simulation. J. Comput. Phys. 225, 427–448.CrossRefGoogle Scholar
Christensen, K. & Adrian, R. 2001 Statistical evidence of hairpin vortex packets in wall turbulence. J. Fluid Mech. 431, 433–443.CrossRefGoogle Scholar
Coceal, O., Dobre, A., Thomas, T. G. & Belcher, S. 2007 Structure of turbulent flow over regular arrays of cubical roughness. J. Fluid Mech. 589, 375–409.CrossRefGoogle Scholar
Colebrook, C. & White, C. 1937 Experiments with fluid friction in roughened pipes. Proc. R. Soc. Lond. A 161, 367–381.Google Scholar
Dennis, D. & Nickels, T. 2011a Experimental measurement of large-scale three-dimensional structures in a turbulent boundary layer. Part 1. Vortex packets. J. Fluid Mech. 673, 180–217.CrossRefGoogle Scholar
Dennis, D. & Nickels, T. 2011b Experimental measurement of large-scale three-dimensional structures in a turbulent boundary layer. Part 2. Long structures. J. Fluid Mech. 673, 218–244.CrossRefGoogle Scholar
Elsinga, G., Adrian, R., Oudheusden, B. V. & Scarano, F. 2010 Three-dimensional vortex organization in a high-Reynolds number supersonic turbulent boundary layer. J. Fluid Mech. 644, 35–60.CrossRefGoogle Scholar
Fishpool, G., Lardeau, S. & Leschziner, M. 2009 Persistent non-homogeneous features in periodic channel-flow simulations. Flow Turbul. Combust. 83, 323–342.CrossRefGoogle Scholar
Flack, K. & Schultz, M. 2010 Review of hydraulic roughness scales in the fully rough regime. Trans. ASME: J. Fluids Engng 132, 041203.Google 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
Gessner, F. 1973 The origin of secondary flow in turbulent flow along a corner. J. Fluid Mech. 58, 1–25.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
Higgins, C., Parlange, M. & Meneveau, C. 2004 Energy dissipation in large-eddy simulation: dependence on flow structure and effects of eigenvector alignments. In Atmospheric Turbulence and Mesoscale Meteorology, chap. 3, pp. 51–70. Cambridge University Press.CrossRefGoogle Scholar
Hinze, J. 1967 Secondary currents in wall turbulence. Phys. Fluids (Suppl.) 10, S122–S125.CrossRefGoogle Scholar
Hinze, J. 1973 Experimental investigation on secondary currents in the turbulent flow through a straight conduit. Appl. Sci. Res. 28, 453–465.CrossRefGoogle Scholar
Hoagland, L.1960 Fully developed turbulent flow in straight rectangular ducts – secondary flow, its cause and effect on the primary flow. PhD thesis, Massachusetts Institute of Technology.Google 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
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
Jimenez, J. 2004 Turbulent flow over rough walls. Annu. Rev. Fluid Mech. 36, 173–196.CrossRefGoogle Scholar
Laufer, J.1954 The structure of turbulence in fully developed pipe flow. NACA Tech. Mem. 1174.Google Scholar
Livingstone, I., Wiggs, G. & Weaver, C. 2006 Geomorphology of desert sand dunes: a review of recent progress. Earth-Sci. Rev. 80, 239–257.CrossRefGoogle Scholar
Madabhushi, R. & Vanka, S. 1991 Large eddy simulation of turbulence-driven secondary flow in a square duct. Phys. Fluids A 3, 2734–2745.CrossRefGoogle Scholar
Mejia-Alvarez, R., Barros, J. & Christensen, K. 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
Mejia-Alvarez, R. & Christensen, K. 2010 Low-order representations of irregular surface roughness and their impact on a turbulent boundary layer. Phys. Fluids 22, 015106.CrossRefGoogle Scholar
Mejia-Alvarez, R. & Christensen, K. 2013 Wall-parallel stereo PIV measurements in the roughness sublayer of turbulent flow overlying highly-irregular roughness. Phys. Fluids 25, 115109.Google Scholar
Monin, A. & Obukhov, A. 1954 Basic laws of turbulent mixing in the ground layer of the atmosphere. Tr. Geofiz. Inst., Akad. Nauk SSSR 151, 163–187.Google Scholar
Monin, A. & Yaglom, A. 1971 Statistical Fluid Mechanics: Mechanics of Turbulence. The MIT Press.Google Scholar
Nikuradse, J. 1930 Turbulente Strömung in nicht kreisförmigen Rohren. Ing.-Arch. 1, 306–332.CrossRefGoogle Scholar
Nikuradse, J.1933 Laws of flow in rough pipes. NACA Tech. Mem. 1292.Google Scholar
Nugroho, B., Hutchins, N. & Monty, J. 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
Nugroho, B., Monty, J., Hutchins, N. & Gnanamanickam, E. 2014 Roll-modes generated in turbulent boundary layers with passive surface modifications. In Proceedings of American Institute of Aeronautics and Astronautics, 52nd Aerospace Sciences Meeting, National Harbor.Google Scholar
Orszag, S. 1970 Transform method for calculation of vector coupled sums: application to the spectral form of the vorticity equation. J. Atmos. Sci. 27, 890–895.2.0.CO;2>CrossRefGoogle Scholar
Palmer, J. A., Mejia-Alvarez, R., Best, J. L. & Christensen, K. T. 2012 Particle-image velocimetry measurements of flow over interacting barchan dunes. Exp. Fluids 52, 809–829.CrossRefGoogle Scholar
Perkins, H. 1970 The formation of streamwise vorticity in turbulent flow. J. Fluid Mech. 44, 721–740.CrossRefGoogle Scholar
Piomelli, U. & Balaras, E. 2002 Wall-layer models for large-eddy simulation. Annu. Rev. Fluid Mech. 34, 349–374.CrossRefGoogle Scholar
Pope, S. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Porté-Agel, F., Meneveau, C. & Parlange, M. 2000 A scale-dependent dynamic model for large-eddy simulation: application to a neutral atmospheric boundary layer. J. Fluid Mech. 415, 261–284.CrossRefGoogle Scholar
Prandtl, L. 1952 Essentials of Fluid Dynamics. Blackie.Google Scholar
Raupach, M., Antonia, R. & 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
Schlichting, H.1937 Experimental investigation of the problem of surface roughness. NACA Tech. Mem. 823.Google Scholar
Schultz, M. 2007 Effects of coating roughness and biofouling on ship resistance and powering. Biofouling 23, 331–341.CrossRefGoogle ScholarPubMed
Schultz, M. & Flack, K. 2009 Turbulent boundary layers on a systematically varied rough wall. Phys. Fluids 21, 015104.CrossRefGoogle Scholar
Sheng, J., Malkiel, E. & Katz, J. 2009 Buffer layer structures associated with extreme wall stress events in a smooth wall turbulent boundary layer. J. Fluid Mech. 633, 17–60.CrossRefGoogle Scholar
Smagorinsky, J. 1963 General circulation experiments with the primitive equations. Mon. Weath. Rev. 91, 99–164.2.3.CO;2>CrossRefGoogle Scholar
Tokgoz, S., Elsinga, G., Delfos, R. & Westerweel, J. 2012 Spatial resolution and dissipation rate estimation in Taylor–Couette flow for tomographic PIV. Exp. Fluids 53, 561–583.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. 1976 The Structure of Turbulent Shear Flow. Cambridge University Press.Google Scholar
Vermaas, D., Uijttewall, W. & Hoitink, A. 2011 Lateral transfer of streamwise momentum caused by a roughness transition across a shallow channel. Water Resour. Res. 47, W02530.CrossRefGoogle Scholar
Volino, R., Schultz, M. & Flack, K. 2007 Turbulence structure in rough- and smooth-wall boundary layers. J. Fluid Mech. 592, 263–293.CrossRefGoogle Scholar
Wang, Z.-Q. & Cheng, N.-S. 2005 Secondary flows over artificial bed strips. Adv. Water Resour. 28, 441–450.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.Google Scholar
Wu, Y. & Christensen, K. T. 2006 Population trends of spanwise vortices in wall turbulence. J. Fluid Mech. 568, 55–76.CrossRefGoogle 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
Zhou, J., Adrian, R. & Balachandar, S. 1996 Autogeneration of near-wall vortical structures in channel flow. Phys. Fluids 8, 288–290.CrossRefGoogle Scholar
Zhou, J., Adrian, R., Balachandar, S. & Kendall, T. 1999 Mechanisms for generating coherent packets of hairpin vortices in channel flow. J. Fluid Mech. 387, 353–359.CrossRefGoogle Scholar