Hostname: page-component-848d4c4894-5nwft Total loading time: 0 Render date: 2024-05-04T04:00:02.661Z Has data issue: false hasContentIssue false
  • English
  • Français

Clustering of inertial particles in turbulent flow through a porous unit cell

Published online by Cambridge University Press:  22 February 2022

Sourabh V. Apte Open the ORCID record for Sourabh V. Apte [Opens in a new window] ,
Thibault Oujia Open the ORCID record for Thibault Oujia [Opens in a new window] ,
Keigo Matsuda Open the ORCID record for Keigo Matsuda [Opens in a new window] ,
Benjamin Kadoch Open the ORCID record for Benjamin Kadoch [Opens in a new window] ,
Xiaoliang He Open the ORCID record for Xiaoliang He [Opens in a new window]  and
Kai Schneider Open the ORCID record for Kai Schneider [Opens in a new window]
Sourabh V. Apte*
Affiliation:
School of Mechanical, Industrial and Manufacturing Engineering, Oregon State University, Corvallis, OR 97330, USA
Thibault Oujia
Affiliation:
Aix–Marseille Université, I2M–CNRS, Marseille, France
Keigo Matsuda
Affiliation:
Research Institute for Value-Added-Information Generation (VAiG), Japan Agency for Marine-Earth Science and Technology (JAMSTEC), Yokohama 236-0001, Japan
Benjamin Kadoch
Affiliation:
Aix–Marseille Université, IUSTI–CNRS, Marseille, France
Xiaoliang He
Affiliation:
Pacific Northwest National Laboratory, Richland, WA 99352, USA
Kai Schneider
Affiliation:
Aix–Marseille Université, I2M–CNRS, Marseille, France
*
†Email address for correspondence: Sourabh.Apte@oregonstate.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

Direct numerical simulation is used to investigate effects of turbulent flow in the confined geometry of a face-centred cubic porous unit cell on the transport, clustering and deposition of fine particles at different Stokes numbers ($St = 0.01, 0.1, 0.5, 1, 2$) and at a pore Reynolds number of 500. Particles are advanced using one-way coupling and the collision of particles with pore walls is modelled as perfectly elastic with specular reflection. Tools for studying inertial particle dynamics and clustering developed for homogeneous flows are adapted to take into account the embedded, curved geometry of the pore walls. The pattern and dynamics of clustering are investigated using the volume change of Voronoi tesselation in time to analyse the divergence and convergence of the particles. Similar to the case of homogeneous, isotropic turbulence, the cluster formation is present at large volumes, while cluster destruction is prominent at small volumes and these effects are amplified with the Stokes number. However, unlike homogeneous, isotropic turbulence, the formation of a large number of very small volumes was observed at all Stokes numbers and attributed to the collision of particles with the pore wall. Multiscale wavelet analysis of the particle number density indicates that the peak of the energy density spectrum, representative of enhanced particle clustering, shifts towards larger scales with an increase in the Stokes number. Scale-dependent skewness and flatness quantify the intermittent void and cluster distribution, with cluster formation observed at small scales for all Stokes numbers, and void regions at large scales for large Stokes numbers.

JFM classification

Multiphase and Particle-laden Flows: Particle/fluid flow Multiphase and Particle-laden Flows: Multiphase flow Turbulent Flows: Turbulence simulation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 937 , 25 April 2022 , A9
Check for updates
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

Agbangla, G.C., Climent, É. & Bacchin, P. 2012 Experimental investigation of pore clogging by microparticles: evidence for a critical flux density of particle yielding arches and deposits. Sep. Purif. Technol. 101, 42–48.CrossRefGoogle Scholar
Apte, S.V., Mahesh, K. & Lundgren, T. 2008 Accounting for finite-size effects in simulations of disperse particle-laden flows. Intl J. Multiphase Flow 34 (3), 260–271.CrossRefGoogle 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.CrossRefGoogle Scholar
Aris, R. 1999 Elementary Chemical Reactor Analysis. Courier Corporation.Google Scholar
Aurenhammer, F. 1991 Voronoi diagrams—a survey of a fundamental geometric data structure. ACM Comput. Surv. (CSUR) 23 (3), 345–405.CrossRefGoogle Scholar
Barber, C.B., Dobkin, D.P. & Huhdanpaa, H. 1996 The quickhull algorithm for convex hulls. ACM Trans. Math. Softw. (TOMS) 22 (4), 469–483.CrossRefGoogle Scholar
Bassenne, M., Urzay, J., Schneider, K. & Moin, P. 2017 Extraction of coherent clusters and grid adaptation in particle-laden turbulence using wavelet filters. Phys. Rev. Fluids 2 (5), 054301.CrossRefGoogle Scholar
Bec, J., Biferale, L., Cencini, M., Lanotte, A., Musacchio, S. & Toschi, F. 2007 Heavy particle concentration in turbulence at dissipative and inertial scales. Phys. Rev. Lett. 98 (8), 084502.CrossRefGoogle ScholarPubMed
Carlson, J., Gurley, D., King, G., Price-Smith, C. & Waters, F. 1992 Sand control: why and how? Oilfield Rev. 4 (4), 41–53.Google Scholar
Coleman, S.W. & Vassilicos, J.C. 2009 A unified sweep-stick mechanism to explain particle clustering in two-and three-dimensional homogeneous, isotropic turbulence. Phys. Fluids 21 (11), 113301.CrossRefGoogle Scholar
Cook, B.K., Lee, M.Y., DiGiovanni, A.A., Bronowski, D.R., Perkins, E.D. & Williams, J.R. 2004 Discrete element modeling applied to laboratory simulation of near-wellbore mechanics. Intl J. Geomech. 4 (1), 19–27.CrossRefGoogle Scholar
Dai, J. & Grace, J.R. 2010 Blockage of constrictions by particles in fluid–solid transport. Intl J. Multiphase Flow 36 (1), 78–87.CrossRefGoogle Scholar
Daubechies, I. 1993 Ten Lectures on Wavelets. Society of Industrial and Applied Mathematics.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.CrossRefGoogle Scholar
Eaton, J.K. & Fessler, J.R. 1994 Preferential concentration of particles by turbulence. Intl J. Multiphase Flow 20, 169–209.CrossRefGoogle Scholar
Esmaily-Moghadam, M. & Mani, A. 2016 Analysis of the clustering of inertial particles in turbulent flows. Phys. Rev. Fluids 1 (8), 084202.CrossRefGoogle Scholar
Farge, M. 1992 Wavelet transforms and their applications to turbulence. Annu. Rev. Fluid Mech. 24, 395–457.CrossRefGoogle Scholar
Farge, M. & Schneider, K. 2015 Wavelet transforms and their applications to MHD and plasma turbulence: a review. J. Plasma Phys. 81 (6), 435810602.CrossRefGoogle Scholar
Ferenc, J.-S. & Néda, Z. 2007 On the size distribution of Poisson Voronoi cells. Physica A 385 (2), 518–526.CrossRefGoogle 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.CrossRefGoogle Scholar
Finn, J.R., Li, M. & Apte, S.V. 2016 Particle based modelling and simulation of natural sand dynamics in the wave bottom boundary layer. J. Fluid Mech. 796, 340–385.CrossRefGoogle Scholar
Goto, S. & Vassilicos, J.C. 2006 Self-similar clustering of inertial particles and zero-acceleration points in fully developed two-dimensional turbulence. Phys. Fluids 18 (11), 115103.CrossRefGoogle Scholar
He, X., Apte, S.V., Finn, J.R. & Wood, B.D. 2019 Characteristics of turbulence in a face-centred cubic porous unit cell. J. Fluid Mech. 873, 608–645.CrossRefGoogle Scholar
He, X., Apte, S., Schneider, K. & Kadoch, B. 2018 Angular multiscale statistics of turbulence in a porous bed. Phys. Rev. Fluids 3 (8), 084501.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle Scholar
Mahmud, H.B., Van Hong, L. & Lestariono, Y. 2019 Sand production: a smart control framework for risk mitigation. Petroleum 6 (1), 1–13.CrossRefGoogle Scholar
Mallat, S. 2009 A Wavelet Tour of Signal Processing, 3rd edn. Academic Press.Google Scholar
Matsuda, K., Onishi, R., Hirahara, M., Kurose, R., Takahashi, K. & Komori, S. 2014 Influence of microscale turbulent droplet clustering on radar cloud observations. J. Atmos. Sci. 71 (10), 3569–3582.CrossRefGoogle Scholar
Matsuda, K., Schneider, K. & Yoshimatsu, K. 2021 Scale-dependent statistics of inertial particle distribution in high Reynolds number turbulence. Phys. Rev. Fluids 6, 064304.CrossRefGoogle Scholar
Maxey, M.R. 1987 The gravitational settling of aerosol particles in homogeneous turbulence and random flow fields. J. Fluid Mech. 174, 441–465.CrossRefGoogle Scholar
Meneveau, C. 1991 Analysis of turbulence in the orthonormal wavelet representation. J. Fluid Mech. 232, 469–520.CrossRefGoogle Scholar
Monchaux, R., Bourgoin, M. & Cartellier, A. 2010 Preferential concentration of heavy particles: a Voronoï analysis. Phys. Fluids 22 (10), 103304.CrossRefGoogle Scholar
Monchaux, R., Bourgoin, M. & Cartellier, A. 2012 Analyzing preferential concentration and clustering of inertial particles in turbulence. Intl J. Multiphase Flow 40, 1–18.CrossRefGoogle Scholar
Monin, A.S. & Yaglom, A.M. 1965 Statistical Fluid Mechanics: Mechanics of Turbulence. The MIT Press.Google Scholar
Orlandi, P., Davide, M. & Pirozzoli, S. 2018 DNS of turbulent flows in ducts with complex shape. Flow Turbul. Combust. 100 (4), 1063–1079.CrossRefGoogle Scholar
Oujia, T., Matsuda, K. & Schneider, K. 2020 Divergence and convergence of inertial particles in high Reynolds number turbulence. J. Fluid Mech. 905, A14.CrossRefGoogle Scholar
Pandya, V.B., Bhuniya, S. & Khilar, K.C. 1998 Existence of a critical particle concentration in plugging of a packed bed. Am. Inst. Chem. Engrs AIChE J. 44 (4), 978.CrossRefGoogle 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
Ramachandran, V. & Fogler, H.S. 1999 Plugging by hydrodynamic bridging during flow of stable colloidal particles within cylindrical pores. J. Fluid Mech. 385, 129–156.CrossRefGoogle Scholar
Saucier, R.J. 1974 Considerations in gravel pack design. J. Petrol. Technol. 26 (02), 205–212.CrossRefGoogle Scholar
Schneider, K., Farge, M. & Kevlahan, N. 2004 Spatial intermittency in two-dimensional turbulence: a wavelet approach. In Series on knots and everything. Woods Hole Mathematics (ed. N. Tongring & R.C. Penner), vol. 34. pp. 302–328. World Scientific.CrossRefGoogle Scholar
Schneider, K. & Vasilyev, O.V. 2010 Wavelet methods in computational fluid dynamics. Annu. Rev. Fluid Mech. 42, 473–503.CrossRefGoogle 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.CrossRefGoogle Scholar
Sumbekova, S., Cartellier, A., Aliseda, A. & Bourgoin, M. 2017 Preferential concentration of inertial sub-kolmogorov particles: the roles of mass loading of particles, stokes numbers, and Reynolds numbers. Phys. Rev. Fluids 2 (2), 024302.CrossRefGoogle Scholar
Sundaram, S. & Collins, L.R. 1997 Collision statistics in an isotropic particle-laden turbulent suspension. Part 1. Direct numerical simulations. J. Fluid Mech. 335, 75–109.CrossRefGoogle Scholar
Toschi, F. & Bodenschatz, E. 2009 Lagrangian properties of particles in turbulence. Annu. Rev. Fluid Mech. 41, 375–404.CrossRefGoogle Scholar
Valdes, J.R. & Santamarina, J.C. 2006 Particle clogging in radial flow: microscale mechanisms. SPE J. 11 (02), 193–198.CrossRefGoogle Scholar
Wang, L.-P., Wexler, A.S. & Zhou, Y. 2000 Statistical mechanical description and modelling of turbulent collision of inertial particles. J. Fluid Mech. 415, 117–153.CrossRefGoogle Scholar
Wood, B.D., He, X. & Apte, S.V. 2020 Modeling turbulent flows in porous media. Annu. Rev. Fluid Mech. 52 (1), 171–203.CrossRefGoogle Scholar
Yi, X., Valkó, P.P. & Russell, J.E. 2005 Effect of rock strength criterion on the predicted onset of sand production. Intl J. Geomech. 5 (1), 66–73.CrossRefGoogle Scholar