Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-20T15:20:05.823Z Has data issue: false hasContentIssue false
  • English
  • Français

Direct effects of boundary permeability on turbulent flows: observations from an experimental study using zero-mean-shear turbulence

Published online by Cambridge University Press:  31 March 2021

Mark W. McCorquodale Open the ORCID record for Mark W. McCorquodale [Opens in a new window]  and
R.J. Munro Open the ORCID record for R.J. Munro [Opens in a new window]
Mark W. McCorquodale*
Affiliation:
Faculty of Engineering, The University of Nottingham, NottinghamNG7 2RD, UK
R.J. Munro*
Affiliation:
Faculty of Engineering, The University of Nottingham, NottinghamNG7 2RD, UK
*
†Email addresses for correspondence: mark.mccorquodale2@nottingham.ac.uk, rick.munro@nottingham.ac.uk
†Email addresses for correspondence: mark.mccorquodale2@nottingham.ac.uk, rick.munro@nottingham.ac.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

The interaction of zero-mean-shear turbulence (generated using an oscillating grid) with solid and permeable boundaries is studied experimentally. The influence of wall permeability is characterised using the permeability Reynolds number, $Re_K$, which represents the ratio of the typical pore size in the permeable medium to a viscous length scale. Instantaneous velocity measurements, obtained using two-dimensional particle imaging velocimetry, are used to study the effect boundary permeability has on the root mean square of fluctuating velocity components, the vertical flux of turbulent kinetic energy (TKE) and conditional turbulent statistics associated with events in which intercomponent energy transfer is concentrated. When $Re_K \lesssim 0.2$ the boundary acts as if it were impermeable; results indicate the interaction is dominated by the kinematic blocking effect of the boundary on the boundary-normal TKE flux, with additional mechanisms acting through intercomponent energy transfer. The results show these mechanisms are inhibited as $Re_K$ increases, due to the transportation of turbulent energy into the porous medium as the macroscopic blocking condition is relaxed, thereby reducing TKE within the boundary-affected region and inhibiting the formation of high-pressure stagnation events that are responsible for intercomponent energy transfer. The results illustrate how the turbulence structure above a permeable boundary is sensitive to the blocking effect on the boundary-normal turbulent velocity. In light of these results, we propose that further analysis is required to establish the validity of a commonly used model of the boundary conditions enforced at the boundary of porous media, in which a no-penetration boundary condition on the boundary-normal velocity component is proposed.

JFM classification

Turbulent Flows: Turbulent boundary layers Turbulent Flows: Homogeneous turbulence Boundary Layers: Boundary layer structure
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 915 , 25 May 2021 , A134
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

Aronson, D., Johansson, A.V. & Löfdahl, L. 1997 Shear-free turbulence near a wall. J. Fluid Mech. 338, 363–395.CrossRefGoogle Scholar
Atkinson, J.F., Damiani, L. & Harleman, D.R.F. 1987 Comparison of velocity measurements using a laser anemometer and a hot-film probe, with application to grid-stirring entrainment experiments. Phys. Fluids 30, 3290–3292.CrossRefGoogle Scholar
Bear, J. 2013 Dynamics of Fluids in Porous Media. Dover Publications.Google Scholar
Beavers, G.S. & Joseph, D.D. 1967 Boundary conditions at a naturally permeable wall. J. Fluid Mech. 30 (1), 197–207.CrossRefGoogle Scholar
Bodart, J., Cazalbou, J.B. & Joly, L. 2010 Direct numerical simulation of unsheared turbulence diffusing towards a free-slip or no-slip surface. J. Turbul. 11 (48), 1–18.CrossRefGoogle Scholar
Bottaro, A. 2019 Flow over natural or engineered surfaces: an adjoint homogenization perspective. J. Fluid Mech. 877, P1.CrossRefGoogle Scholar
Breugem, W.P., Boersma, B.J. & Uittenbogaard, R.E. 2006 The influence of wall permeability on turbulent channel flow. J. Fluid Mech. 562, 35–72.CrossRefGoogle Scholar
Brinkman, H.C. 1947 A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles. Appl. Sci. Res. A 1, 27–34.CrossRefGoogle Scholar
British Standards Institution 2010 BS EN ISO 11058:2010: Geotextiles and Geotextile-Related Products – Determination of Water Permeability Characteristics Normal to the Plane, Without Load. BSI.Google Scholar
Brumley, B.H. & Jirka, G.H. 1987 Near-surface turbulence in a grid-stirred tank. J. Fluid Mech. 183, 235–263.CrossRefGoogle Scholar
Cant, R., Castro, I. & Walklate, P. 2002 Plane jets impinging on porous walls. Exp. Fluids 32, 16–26.CrossRefGoogle Scholar
Connolly, J.P., Armstrong, N.E. & Miksad, R.W. 1983 Adsorption of hydrophobic pollutants in estuaries. J. Environ. Engng 109, 17–35.CrossRefGoogle Scholar
De Silva, I.P.D. & Fernando, H.J.S. 1994 Oscillating grids as a source of nearly isotropic turbulence. Phys. Fluids 6, 2455–2464.CrossRefGoogle Scholar
Defonseka, C. 2019 Water-Blown Cellular Polymers: A Practical Guide, 2nd edn. De Gruyter.CrossRefGoogle Scholar
Efstathiou, C. & Luhar, M. 2018 Mean turbulence statistics in boundary layers over high-porosity foams. J. Fluid Mech. 841, 351–379.CrossRefGoogle Scholar
Fernando, H.J.S. & De Silva, I.P.D. 1993 Note on secondary flows in oscillating grid, mixing box experiments. Phys. Fluids 5, 1849–1851.CrossRefGoogle Scholar
Hanh, S., Je, J. & Choi, H. 2002 Direct numerical simulation of turbulent channel flow with permeable walls. J. Fluid Mech. 450, 259–285.Google Scholar
Hannoun, I.A., Fernando, H.J.S. & List, E.J. 1988 Turbulence structure near a sharp density interface. J. Fluid Mech. 189, 189–209.CrossRefGoogle Scholar
Hassanizadeh, S.M. & Grey, W.G. 1979 General conservation equations for multi-phase systems: 1. Averaging procedure. Adv. Water Resour. 2, 131–144.CrossRefGoogle Scholar
Hassanizadeh, S.M. & Grey, W.G. 1990 Mechanics and thermodynamics of multiphase flow in porous media including interphase boundaries. Adv. Water Resour. 13, 169–186.CrossRefGoogle Scholar
Hopfinger, B.J. & Linden, P.F. 1982 Formation of thermoclines in zero-mean-shear turbulence subjected to a stabilizing buoyancy flux. J. Fluid Mech. 11, 157–173.CrossRefGoogle Scholar
Hopfinger, B.J. & Toly, J.A. 1976 Spatially decaying turbulence and its relation to mixing across density interfaces. J. Fluid Mech. 78 (1), 155–175.CrossRefGoogle Scholar
Hunt, J.C.R. 1984 Turbulence structure in thermal convection and shear-free boundary layers. J. Fluid Mech. 138, 161–184.CrossRefGoogle Scholar
Hunt, J.C.R. & Graham, J.M.R. 1978 Free-stream turbulence near plane boundaries. J. Fluid Mech. 84 (2), 209–235.CrossRefGoogle Scholar
Hunt, J.C.R. & Morrison, J.F. 2000 Eddy structure in turbulent boundary layers. Eur. J. Mech. B/Fluids 19, 679–694.CrossRefGoogle Scholar
Johnson, B.A. & Cowen, E.A. 2018 Turbulent boundary layers absent mean shear. J. Fluid Mech. 835, 217–251.CrossRefGoogle Scholar
Katz, A.J. & Thompson, A.H. 1986 Quantitative prediction of permeability in porous rock. Phys. Rev. B 34 (11), 8179–8181.CrossRefGoogle ScholarPubMed
Keane, R.D. & Adrian, R.J. 1990 Optimization of particle velocimeters. Part I: double pulsed systems. Meas. Sci. Technol. 1, 1202–1215.CrossRefGoogle Scholar
Kim, T, Blois, G., Best, J.L. & Christensen, K.T. 2020 Experimental evidence of amplitude modulation in permeable-wall turbulence. J. Fluid Mech. 887, A3.CrossRefGoogle Scholar
Kit, E.L.G., Strang, E.J. & Fernando, H.J.S. 1997 Measurement of turbulence near shear-free density interfaces. J. Fluid Mech. 334, 293–314.CrossRefGoogle Scholar
Kuwata, Y. & Suga, K. 2016 Transport mechanism of interface turbulence over porous and rough walls. Flow Turbul. Combust. 97, 1071–1093.CrossRefGoogle Scholar
Kuwata, Y. & Suga, K. 2017 Direct numerical simulation of turbulence over anisotropic porous media. J. Fluid Mech. 831, 41–71.CrossRefGoogle Scholar
Lage, J.L. 1998 The fundamental theory of flow through permeable media from Darcy to turbulence. In Transport Phenomena in Porous Media (ed. D.B. Ingham & I. Pop), chap. 1, pp. 1–30. Elsevier.CrossRefGoogle Scholar
Li, Q., Pan, M., Zhou, Q. & Dong, Y. 2020 Turbulent drag modification in open channel flow over an anisotropic porous wall. Phys. Fluids 32, 015117.CrossRefGoogle Scholar
Magnaudet, J. 2003 High-Reynolds-number turbulence in a shear-free boundary layer: revisiting the Hunt–Graham theory. J. Fluid Mech. 484, 167–196.CrossRefGoogle Scholar
Manes, C., Poggi, D. & Ridolfi, L. 2011 Turbulent boundary layers over permeable walls: scaling and near-wall structure. J. Fluid Mech. 687, 141–170.CrossRefGoogle Scholar
Manes, C., Pokrajac, D., McEwan, I. & Nikora, V. 2009 Turbulence structure of open channel flows over permeable and impermeable beds: a comparative study. Phys. Fluids 21, 125109.CrossRefGoogle Scholar
Masaló, I., Guadayol, Ò., Peters, F. & Oca, J. 2008 Analysis of sedimentation and resuspension processes of aquaculture biosolids using an oscillating grid. Aquac. Engng 38, 135–144.CrossRefGoogle Scholar
McCorquodale, M.W. & Munro, R.J. 2017 Experimental study of oscillating-grid turbulence interacting with a solid boundary. J. Fluid Mech. 813, 768–798.CrossRefGoogle Scholar
McCorquodale, M.W. & Munro, R.J. 2018 a Analysis of intercomponent energy transfer in the interaction of oscillating-grid turbulence with an impermeable boundary. Phys. Fluids 30, 015105.CrossRefGoogle Scholar
McCorquodale, M.W. & Munro, R.J. 2018 b A method for reducing mean flow in oscillating-grid turbulence. Exp. Fluids 59, 182.CrossRefGoogle Scholar
McDougall, T.J. 1979 Measurements of turbulence in a zero-mean-shear mixed layer. J. Fluid Mech. 94 (3), 409–431.CrossRefGoogle Scholar
McKenna, S.P. & McGillis, W.R. 2004 Observations of flow repeatability and secondary circulation in an oscillating grid-stirred tank. Phys. Fluids 16 (9), 3499–3502.CrossRefGoogle Scholar
Mujal-Colilles, A., Dalziel, S.B. & Bateman, A. 2015 Vortex rings impinging on permeable boundaries. Phys. Fluids 27, 015106.CrossRefGoogle Scholar
Mullens, S., Luyten, J. & Zeschky, J. 2006 Characterization of Structure and Morphology, pp. 225–266. John Wiley and Sons.Google Scholar
Munro, R.J. 2012 The interaction of a vortex ring with a sloped sediment layer: critical criteria for incipient grain motion. Phys. Fluids 24, 026604.CrossRefGoogle Scholar
Munro, R.J., Bethke, N. & Dalziel, S.B. 2009 Sediment resuspension and erosion by vortex rings. Phys. Fluids 21, 046601.CrossRefGoogle Scholar
Musta, M.N. & Krueger, P.S. 2015 Interaction of steady jets with an array of permeable screens. Exp. Fluids 56, 61.CrossRefGoogle Scholar
Nield, D.A. & Bejan, A. 2013 Convection in Porous Media. Springer.CrossRefGoogle Scholar
Nokes, R.I. 1988 On the entrainment rate across a density interface. J. Fluid Mech. 188, 185–204.CrossRefGoogle Scholar
Orlandi, P. & Verzicco, R. 1993 Vortex rings impining on walls: axisymmetric and three-dimensional simulations. J. Fluid Mech. 256, 615–646.CrossRefGoogle Scholar
Orlins, J.J. & Gulliver, J.S. 2003 Turbulence quantification and sediment resuspension in an oscillating grid chamber. Exp. Fluids 34, 662–677.CrossRefGoogle Scholar
Perot, B. & Moin, P. 1995 Shear free turbulent boundary layers. Part 1. Physical insights into near-wall turbulence. J. Fluid Mech. 295, 199–227.CrossRefGoogle Scholar
Pokrajac, D. & Manes, C. 2009 Velocity measurements of a free-surface turbulent flow penetrating a porous medium composed of uniform-size spheres. Transp. Porous Med. 78, 367–383.CrossRefGoogle Scholar
Rosti, M.E., Brandt, L. & Pinelli, A. 2018 Turbulent channel flow over an anisotropic porous wall – drag increase and reduction. J. Fluid Mech. 842, 381–394.CrossRefGoogle Scholar
Rosti, M.E., Cortelezzi, L. & Quadrio, M. 2015 Direct numerical simulation of turbulent channel flow over porous walls. J. Fluid Mech. 784, 396–442.CrossRefGoogle Scholar
Sharma, A. & García-Mayoral, R. 2020 Turbulent flows over dense filament canopies. J. Fluid Mech. 888, A2.CrossRefGoogle Scholar
Suga, K., Matsumura, Y., Ashitaka, Y., Tominaga, S. & Kaneda, M. 2010 Effects of wall permeability on turbulence. Intl J. Heat Fluid Flow 31, 974–984.CrossRefGoogle Scholar
Suga, K., Mori, M. & Kaneda, M. 2011 Vortex structure of turbulence over permeable walls. Intl J. Heat Fluid Flow 32, 586–595.CrossRefGoogle Scholar
Suga, K., Nakagawa, Y. & Kaneda, M. 2017 Spanwise turbulence structure over permeable walls. J. Fluid Mech. 822, 186–201.CrossRefGoogle Scholar
Szycher, M. 2012 Szycher's Handbook of Polyurethanes, 2nd edn. CRC Press.CrossRefGoogle Scholar
Thomas, N.H. & Hancock, P.E. 1977 Grid turbulence near a moving wall. J. Fluid Mech. 82 (3), 481–496.CrossRefGoogle Scholar
Thompson, S.M. & Turner, J.S. 1975 Mixing across an interface due to turbulence generated by an oscillating grid. J. Fluid Mech. 67 (2), 349–368.CrossRefGoogle Scholar
Valsaraj, K.T., Ravikrishna, R., Orlins, J.J., Smith, J.S., Gulliver, J.S., Reible, D.D. & Thibodeaux, L.J. 1997 Sediment-to-air mass transfer of semi-volatile contaminants due to sediment resuspension in water. Adv. Environ. Res. 1, 145–156.Google Scholar
Voermans, J.J., Ghisalberti, M. & Ivey, G.N. 2017 The variation of flow and turbulence across the sediment-water interface. J. Fluid Mech. 824, 413–437.CrossRefGoogle Scholar
Wagner, C. & Friedrich, R. 1998 On the turbulence structure in solid and permeable pipes. Intl J. Heat Fluid Flow 19, 459–469.CrossRefGoogle Scholar
Wagner, C. & Friedrich, R. 2000 DNS of turbulent flow along passively permeable walls. Intl J. Heat Fluid Flow 21, 489–498.CrossRefGoogle Scholar
Walker, D.T., Leighton, R.I. & Garza-Rios, L.O. 1996 Shear-free turbulence near a flat free surface. J. Fluid Mech. 320, 19–51.CrossRefGoogle Scholar
Walker, J.D.A., Smith, C.R., Cerra, A.W. & Doligalski, T.L. 1987 The impact of a vortex ring on a wall. J. Fluid Mech. 181, 99–140.CrossRefGoogle Scholar
Webb, S. & Castro, I.P. 2006 Axisymmetric jets impinging on porous walls. Exp. Fluids 40, 951–961.CrossRefGoogle Scholar
Whitaker, S. 1999 The Method of Volume Averaging. Springer.CrossRefGoogle Scholar
Yokojima, S. 2011 Effect of wall permeability on wall-bounded turbulent flows. J. Phys. Soc. Japan 80, 033401.CrossRefGoogle Scholar
Zhu, W., van Hout, R. & Katz, J. 2007 PIV measurements in the atmospheric boundary layer within and above a mature corn canopy. Part II: quadrant-hole analysis. J. Atmos. Sci. 64, 2825–2838.CrossRefGoogle Scholar