Hostname: page-component-7dd5485656-tbj44 Total loading time: 0 Render date: 2025-10-31T09:39:57.417Z Has data issue: false hasContentIssue false
  • English
  • Français

Characteristics of turbulence in a face-centred cubic porous unit cell

Published online by Cambridge University Press:  25 June 2019

Xiaoliang He ,
Sourabh V. Apte Open the ORCID record for Sourabh V. Apte [Opens in a new window] ,
Justin R. Finn  and
Brian D. Wood Open the ORCID record for Brian D. Wood [Opens in a new window]
Xiaoliang He
Affiliation:
School of Mechanical, Industrial and Manufacturing Engineering, Oregon State University, Corvallis, OR 97330, USA
Sourabh V. Apte*
Affiliation:
School of Mechanical, Industrial and Manufacturing Engineering, Oregon State University, Corvallis, OR 97330, USA
Justin R. Finn
Affiliation:
Department of Civil Engineering and Industrial Design, School of Engineering, University of Liverpool, Liverpool L69 3BX, UK
Brian D. Wood
Affiliation:
School of Chemical, Biological, and Environmental Engineering, Oregon State University, Corvallis, OR 97330, USA
*
†Email address for correspondence: Sourabh.Apte@oregonstate.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

Direct numerical simulations (DNS) are performed in a triply periodic unit cell of a face-centred cubic (FCC) lattice covering the unsteady inertial, to fully turbulent, flow regimes. The DNS data are used to quantify the flow topology, integral scales, turbulent kinetic energy (TKE) transport and anisotropy distribution in the tortuous geometry. Several unique flow features are observed within this low porosity configuration, where the mean flow undergoes strong acceleration and deceleration regions with presence of three-dimensional helical motions, weak wake-like structures behind spheres, stagnation and jet-impingement-like flows together with merging and spreading jets in the main pore space. The jet-impingement and weak wake-like flow structures give rise to regions with negative total TKE production. Unlike flows in complex shaped ducts, the turbulence intensity levels in the cross-stream directions are found to be larger than those in the streamwise direction. Furthermore, due to the compact nature and confined geometry of the FCC packing, the turbulent integral length scales are estimated to be less than 10 % of the bead diameter even for the lowest Reynolds number studied, indicating the absence of macroscale turbulence structures for this configuration. This finding suggests that even for the highly anisotropic flow within the pore, the upscaled flow statistics are captured well by the representative volumes defined by the unit cell.

JFM classification

Low-Reynolds-number flows: Porous media Turbulent Flows: Turbulence simulation

Information

Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 873 , 25 August 2019 , pp. 608 - 645
Check for updates
Copyright
© 2019 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.)

Article purchase

Temporarily unavailable

References

Agnaou, M., Lasseux, D. & Ahmadi, A. 2016 From steady to unsteady laminar flow in model porous structures: an investigation of the first Hopf bifurcation. Comput. Fluids 136, 67–82.Google Scholar
Antohe, B. V. & Lage, J. L. 1997 A general two-equation macroscopic turbulence model for incompressible flow in porous media. Intl J. Heat Mass Transfer 40 (13), 3013–3024.Google Scholar
Apte, S. V., Martin, M. & Patankar, N. A. 2009 A numerical method for fully resolved simulation (FRS) of rigid particle–flow interactions in complex flows. J. Comput. Phys. 228 (8), 2712–2738.Google Scholar
Aris, R. 1969 Elementary Chemical Reactor Analysis. Prentice-Hall.Google Scholar
Banerjee, S., Krahl, R., Durst, F. & Zenger, C. 2007 Presentation of anisotropy properties of turbulence, invariants versus eigenvalue approaches. J. Turbul. 8 (32), 1–27.Google Scholar
Cantwell, B. J. 1992 Exact solution of a restricted Euler equation for the velocity-gradient tensor. Phys. Fluids A 4 (4), 782–793.Google Scholar
Cantwell, B. J. 1993 On the behavior of velocity-gradient tensor invariants in direct numerical simulations of turbulence. Phys. Fluids A 5 (8), 2008–2013.Google Scholar
Choi, K. S. & Lumley, J. L. 2001 The return to isotropy of homogeneous turbulence. J. Fluid Mech. 436, 59–84.Google Scholar
Chong, M. S., Perry, A. E. & Cantwell, B. J. 1990 A general classification of three-dimensional flow fields. Phys. Fluids A 2 (5), 765–777.Google Scholar
Chu, X., Weigand, B. & Vaikuntanathan, V. 2018 Flow turbulence topology in regular porous media: from macroscopic to microscopic scale with direct numerical simulation. Phys. Fluids 30 (6), 065102.Google Scholar
Corrsin, S. 1963 Estimate of the relations between Eulerian and Lagrangian scales in large Reynolds number turbulence. J. Atmos. Sci. 20, 115–119.Google Scholar
Datta, S. S., Chiang, H., Ramakrishnan, T. S. & Weitz, D. A. 2013 Spatial fluctuations of fluid velocities in flow through a three-dimensional porous medium. Phys. Rev. Lett. 111, 064501.Google Scholar
Dixon, A. G. & Cresswell, D. L. 1986 Effective heat transfer parameters for transient packed-bed models. AIChE J. 32 (5), 809–819.Google Scholar
Dixon, A. G. & Nijemeisland, M. 2001 CFD as a design tool for fixed-bed reactors. Ind. Engng Chem. Res. 40 (23), 5246–5254.Google Scholar
Dybbs, A. & Edwards, R. V. 1984 A new look at porous media mechanics – Darcy to turbulent. In Fundamentals of Transport Phenomena in Porous Media (ed. Bear, J. C. & Corapcioglu, Y.), pp. 199–254. Martinus Nijhoff Publishers.Google Scholar
Elsinga, G. E. & Marusic, I. 2010 Evolution and lifetimes of flow topology in a turbulent boundary layer. Phys. Fluids 22 (1), 015102.Google Scholar
Emory, M. & Iaccarino, G. 2014 Visualizing turbulence anisotropy in the spatial domain with componentality contours. In Proceedings of the Summer Program 2014, Center for Turbulence Research, Stanford University, pp. 123–138.Google Scholar
Ergun, S. 1952 Fluid flow through packed columns. Chem. Engng Prog. 48 (2), 89–94.Google Scholar
Evseev, A. R. 2017 Visual study of turbulent filtration in porous media. J. Porous Media 20 (6), 549–557.Google Scholar
Finn, J.2013 A numerical study of inertial flow features in moderate Reynolds number flow through packed beds of spheres. PhD dissertation, Oregon State University, Corvallis, OR.Google Scholar
Finn, J. & Apte, S. V. 2013 Relative performance of body fitted and fictitious domain simulations of flow through fixed packed beds of spheres. Intl J. Multiphase Flow 56, 54–71.Google Scholar
Gultitski, G., Kholmyansky, M., Kinzelbach, W., Luthi, B., Tsinober, A. & Yorish, S. 2007 Velocity and temperature derivatives in high-Reynolds-number turbulent flows in the atmospheric surface layer. Part 2. Accelerations and related matters. J. Fluid Mech. 589, 83–102.Google Scholar
Gunjal, P. R., Ranade, V. V. & Chaudhari, R. V. 2005 Computational study of a single-phase flow in packed beds of spheres. AICHE J. 51 (2), 365–378.Google Scholar
Gunn, D. J. 1987 Axial and radial dispersion in fixed beds. Chem. Engng Sci. 42 (2), 363–373.Google Scholar
Hamilton, N. & Cal, R. B. 2015 Anisotropy of the Reynolds stress tensor in the wakes of wind turbine arrays in cartesian arrangements with counter-rotating rotors. Phys. Fluids 27 (1), 015102.Google Scholar
He, X., Apte, S., Schneider, K. & Kadoch, B. 2018 Angular multiscale statistics of turbulence in a porous bed. Phys. Rev. Fluids 3, 084501.Google Scholar
Herr, M. & Dobrzynski, W. 2005 Experimental investigations in low-noise trailing edge design. AIAA J. 43 (6), 1167–1175.Google Scholar
Hester, E. T., Cardenas, M. B., Haggerty, R. & Apte, S. V. 2017 The importance and challenge of hyporheic mixing. Water Resour. Res. 53 (5), 3565–3575.Google Scholar
Hill, R. J. & Koch, D. L. 2002 The transition from steady to weakly turbulent flow in a close-packed ordered array of spheres. J. Fluid Mech. 465, 59–97.Google Scholar
Hill, R. J., Koch, D. L. & Ladd, A. J. C. 2001 The first effects of fluid inertia on flows in ordered and random arrays of spheres. J. Fluid Mech. 448, 213–241.Google Scholar
Hlushkou, D. & Tallarek, U. 2006 Transition from creeping via viscous-inertial to turbulent flow in fixed beds. J. Chromatogr. A 1126 (1–2), 70–85.Google Scholar
Jin, Y., Uth, M. F., Kuznetsov, A. V. & Herwig, H. 2015 Numerical investigation of the possibility of macroscopic turbulence in porous media: a direct numerical simulation study. J. Fluid Mech. 766, 76–103.Google Scholar
Koch, D. L. & Ladd, A. J. C. 1997 Moderate Reynolds number flows through periodic and random arrays of aligned cylinders. J. Fluid Mech. 349 (1), 31–66.Google Scholar
Latifi, M. A., Midoux, N., Storck, A. & Gence, J. N. 1989 The use of micro-electrodes in the study of the flow regimes in a packed bed reactor with single phase liquid flow. Chem. Engng Sci. 44 (11), 2501–2508.Google Scholar
de Lemos, M. J. S. & Pedras, M. H. J. 2001 Recent mathematical models for turbulent flow in saturated rigid porous media. Trans. ASME J. Fluids Engng 123 (4), 935–940.Google Scholar
Lumley, J. L. & Newman, G. R. 1977 The return to isotropy of homogeneous turbulence. J. Fluid Mech. 82 (1), 161–178.Google Scholar
Lüthi, B., Tsinober, A. & Kinzelbach, W. 2005 Lagrangian measurement of vorticity dynamics in turbulent flow. J. Fluid Mech. 528, 87–118.Google Scholar
Martin, J., Ooi, A., Chong, M. S. & Soria, J. 1998 Dynamics of the velocity gradient tensor invariants in isotropic turbulence. Phys. Fluids 10 (9), 2336–2346.Google Scholar
Masuoka, T. & Takatsu, Y. 1996 Turbulence model for flow through porous media. Intl J. Heat Mass Transfer 39 (13), 2803–2809.Google Scholar
Meneveau, C. 2011 Lagrangian dynamics and models of the velocity gradient tensor in turbulent flows. Annu. Rev. Fluid Mech. 43, 219–245.Google Scholar
Mickley, H. S., Smith, K. A. & Korchak, E. I. 1965 Fluid flow in packed beds. Chem. Engng Sci. 20 (3), 237–246.Google Scholar
Nakayama, A. & Kuwahara, F. 1999 A macroscopic turbulence model for flow in a porous medium. Trans. ASME J. Fluids Engng 121 (2), 427–433.Google Scholar
Natarajan, R. & Acrivos, A. 1993 The instability of the steady flow past spheres and disks. J. Fluid Mech. 254 (1), 323–344.Google Scholar
Nishino, K., Samada, M., Kasuya, K. & Torii, K. 1996 Turbulence statistics in the stagnation region of an axisymmetric impinging jet flow. Intl J. Heat Fluid Flow 17 (3), 193–201.Google Scholar
Nomura, K. K. & Post, G. K. 1998 The structure and dynamics of vorticity and rate of strain in incompressible homogeneous turbulence. J. Fluid Mech. 377, 65–97.Google Scholar
Ooi, A., Martin, J., Soria, J. & Chong, M. S. 1999 A study of the evolution and characteristics of the invariants of the velocity-gradient tensor in isotropic turbulence. J. Fluid Mech. 381, 141–174.Google Scholar
Orlandi, P., Modesti, D. & Pirozzoli, S. 2018 DNS of turbulent flows in ducts with complex shape. Flow Turbul. Combust. 100 (4), 1063–1079.Google Scholar
Patil, V. A. & Liburdy, J. A. 2013 Flow structures and their contribution to turbulent dispersion in a randomly packed porous bed based on particle image velocimetry measurements. Phys. Fluids 25 (11), 24.Google Scholar
Patil, V. A. & Liburdy, J. A. 2015 Scale estimation for turbulent flows in porous media. Chem. Engng Sci. 123, 231–235.Google Scholar
Pearson, J. R. A. & Tardy, P. M. J. 2002 Models for flow of non-Newtonian and complex fluids through porous media. J. Non-Newtonian Fluid Mech. 102 (2), 447–473.Google Scholar
Pedras, M. H. J. & De Lemos, M. J. S. 2001 Macroscopic turbulence modeling for incompressible flow through undeformable porous media. Intl J. Heat Mass Transfer 44 (6), 1081–1093.Google Scholar
Pope, S. 2000 Turbulent Flows. Cambridge University Press.Google Scholar
Roache, P. J. 2003 Conservatism of the grid convergence index in finite volume computations on steady-state fluid flow and heat transfer. Trans. ASME J. Fluids Engng 125 (4), 731–732.Google Scholar
Roberts, A. J. 2004 Shear dispersion along circular pipes is affected by bends, but the torsion of the pipe is negligible. SIAM J. Appl. Dyn. Syst. 3, 433–462.Google Scholar
Rode, S., Midoux, N., Latifi, M. A. & Storck, A. 1994 Hydrodynamics and liquid–solid mass transfer mechanisms in packed beds operating in cocurrent gas–liquid downflow: an experimental study using electrochemical shear rate sensors. Chem. Engng Sci. 49 (9), 1383–1401.Google Scholar
Seguin, D., Montillet, A. & Comiti, J. 1998a Experimental characterisation of flow regimes in various porous media – I: limit of laminar flow regime. Chem. Engng Sci. 53 (21), 3751–3761.Google Scholar
Seguin, D., Montillet, A., Comiti, J. & Huet, F. 1998b Experimental characterization of flow regimes in various porous media – II: transition to turbulent regime. Chem. Engng Sci. 53 (22), 3897–3909.Google Scholar
Shams, A., Roelofs, F., Komen, E. M. J. & Baglietto, E. 2013 Quasi-direct numerical simulation of a pebble bed configuration. Part I: Flow (velocity) field analysis. Nucl. Engng Des. 263, 473–489.Google Scholar
Suekane, T., Yokouchi, Y. & Hirai, S. 2003 Inertial flow structures in a simple-packed bed of spheres. AIChE J. 49 (1), 10–17.Google Scholar
Suga, K. 2016 Understanding and modelling turbulence over and inside porous media. Flow Turbul. Combust. 96 (3), 717–756.Google Scholar
Taylor, G. I. 1929 The criterion for turbulence in curved pipes. Proc. R. Soc. Lond. A 124 (794), 243–249.Google Scholar
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. MIT.Google Scholar
Uth, M. F., Jin, Y., Kuznetsov, A. V. & Herwig, H. 2016 A direct numerical simulation study on the possibility of macroscopic turbulence in porous media: effects of different solid matrix geometries, solid boundaries, and two porosity scales. Phys. Fluids 28 (6), 065101.Google Scholar
Van der Merwe, D. F. & Gauvin, W. H. 1971 Velocity and turbulence measurements of air flow through a packed bed. AIChE J. 17 (3), 519–528.Google Scholar
Wegner, T. H., Karabelas, A. J. & Hanratty, T. J. 1971 Visual studies of flow in a regular array of spheres. Chem. Engng Sci. 26 (1), 59–63.Google Scholar
Wen, C. Y. & Fan, L. 1975 Models for Flow Systems and Chemical Reactors, vol. 3. Dekker.Google Scholar
Whitaker, S. 1999 The Method of Volume Averaging, Theory and Applications of Transport in Porous Media, vol. 13. Springer.Google Scholar
Wood, B. D. 2007 Inertial effects in dispersion in porous media. Water Resour. Res. 43 (12), 16.Google Scholar
Wood, B. D., Apte, S. V., Liburdy, J. A., Ziazi, R. M., He, X., Finn, J. R. & Patil, V. A. 2015 A comparison of measured and modeled velocity fields for a laminar flow in a porous medium. Adv. Water Resour. 85, 45–63.Google Scholar
Zhou, J., Adrian, R. J., Balachandar, S. & Kendall, T. M. 1999 Mechanisms for generating coherent packets of hairpin vortices in channel flow. J. Fluid Mech. 387, 353–396.Google Scholar