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Clustering in Euler–Euler and Euler–Lagrange simulations of unbounded homogeneous particle-laden shear

Published online by Cambridge University Press:  16 November 2018

M. Houssem Kasbaoui Open the ORCID record for M. Houssem Kasbaoui [Opens in a new window] ,
Donald L. Koch Open the ORCID record for Donald L. Koch [Opens in a new window]  and
Olivier Desjardins
M. Houssem Kasbaoui*
Affiliation:
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA
Donald L. Koch
Affiliation:
Smith School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, NY 14853, USA
Olivier Desjardins
Affiliation:
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA
*
†Email address for correspondence: [email protected]
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Abstract

Particle-laden flows of sedimenting solid particles or droplets in a carrier gas have strong inter-phase coupling. Even at low particle volume fractions, the two-way coupling can be significant due to the large particle to gas density ratio. In this semi-dilute regime, the slip velocity between phases leads to sustained clustering that strongly modulates the overall flow. The analysis of perturbations in homogeneous shear reveals the process by which clusters form: (i) the preferential concentration of inertial particles in the stretching regions of the flow leads to the formation of highly concentrated particle sheets, (ii) the thickness of the latter is controlled by particle-trajectory crossing, which causes a local dispersion of particles, (iii) a transverse Rayleigh–Taylor instability, aided by the shear-induced rotation of the particle sheets towards the gravity normal direction, breaks the planar structure into smaller clusters. Simulations in the Euler–Lagrange formalism are compared to Euler–Euler simulations with the two-fluid and anisotropic-Gaussian methods. It is found that the two-fluid method is unable to capture the particle dispersion due to particle-trajectory crossing and leads instead to the formation of discontinuities. These are removed with the anisotropic-Gaussian method which derives from a kinetic approach with particle-trajectory crossing in mind.

JFM classification

Instability: Instability Multiphase and Particle-laden Flows: Multiphase and Particle-laden Flows Multiphase and Particle-laden Flows: Multiphase flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 859 , 25 January 2019 , pp. 174 - 203
Copyright
© 2018 Cambridge University Press 

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References

Al Taweel, A. M. & Landau, J. 1977 Turbulence modulation in two-phase jets. Intl J. Multiphase Flow 3 (4), 341–351.Google Scholar
Aliseda, A., Cartellier, A., Hainaux, F. & Lasheras, J. C. 2002 Effect of preferential concentration on the settling velocity of heavy particles in homogeneous isotropic turbulence. J. Fluid Mech. 468, 77–105.Google Scholar
Anderson, K., Sundaresan, S. & Jackson, R. 1995 Instabilities and the formation of bubbles in fluidized beds. J. Fluid Mech. 303, 327–366.Google Scholar
Baron, F.1982 Macro-simulation tridimensionnelle d’ecoulements turbulents cisailles. PhD thesis, google-Books-ID: 78yrtgAACAAJ.Google Scholar
Batchelor, G. K. & Nitsche, J. M. 1991 Instability of stationary unbounded stratified fluid. J. Fluid Mech. 227, 357–391.Google Scholar
Boivin, M., Simonin, O. & Squires, K. D. 1998 Direct numerical simulation of turbulence modulation by particles in isotropic turbulence. J. Fluid Mech. 375, 235–263.Google Scholar
Capecelatro, J. & Desjardins, O. 2013a Eulerian–Lagrangian modeling of turbulent liquid–solid slurries in horizontal pipes. Intl J. Multiphase Flow 55, 64–79.Google Scholar
Capecelatro, J. & Desjardins, O. 2013b An Euler–Lagrange strategy for simulating particle-laden flows. J. Comput. Phys. 238, 1–31.Google Scholar
Capecelatro, J., Desjardins, O. & Fox, R. O. 2015 On fluid–particle dynamics in fully developed cluster-induced turbulence. J. Fluid Mech. 780, 578–635.Google Scholar
Capecelatro, J., Pepiot, P. & Desjardins, O. 2014 Numerical characterization and modeling of particle clustering in wall-bounded vertical risers. Chem. Engng J. 245, 295–310.Google Scholar
Desjardins, O., Fox, R. O. & Villedieu, P. 2008 A quadrature-based moment method for dilute fluid-particle flows. J. Comput. Phys. 227 (4), 2514–2539.Google Scholar
Druzhinin, O. A. 1994 Concentration waves and flow modification in a particleladen circular vortex. Phys. Fluids 6 (10), 3276–3284.Google Scholar
Druzhinin, O. A. 1995 On the two-way interaction in two-dimensional particle-laden flows: the accumulation of particles and flow modification. J. Fluid Mech. 297, 49–76.Google Scholar
Druzhinin, O. A. 2001 The influence of particle inertia on the two-way coupling and modification of isotropic turbulence by microparticles. Phys. Fluids 13 (12), 3738–3755.Google Scholar
Elghobashi, S. & Truesdell, G. C. 1993 On the twoway interaction between homogeneous turbulence and dispersed solid particles. I: turbulence modification. Phys. Fluids A 5 (7), 1790–1801.Google Scholar
Elghobashi, S. E. & AbouArab, T. W. 1983 A twoequation turbulence model for twophase flows. Phys. Fluids 26 (4), 931–938.Google Scholar
Estivalezes, J. L. & Villedieu, P. 1996 High-order positivity-preserving kinetic schemes for the compressible Euler equations. SIAM J. Numer. Anal. 33 (5), 2050–2067.Google Scholar
Falkovich, G., Fouxon, A. & Stepanov, M. G. 2002 Acceleration of rain initiation by cloud turbulence. Nature 419 (6903), 151–154.Google Scholar
Ferrante, A. & Elghobashi, S. 2007 On the accuracy of the two-fluid formulation in direct numerical simulation of bubble-laden turbulent boundary layers. Phys. Fluids 19 (4), 045105.Google Scholar
Ferry, J. & Balachandar, S. 2001 A fast Eulerian method for disperse two-phase flow. Intl J. Multiphase Flow 27 (7), 1199–1226.Google Scholar
Fevrier, P., Simonin, O. & Squires, K. D. 2005 Partitioning of particle velocities in gassolid turbulent flows into a continuous field and a spatially uncorrelated random distribution: theoretical formalism and numerical study. J. Fluid Mech. 533, 1–46.Google Scholar
Fox, R. O. 2008 A quadrature-based third-order moment method for dilute gas–particle flows. J. Comput. Phys. 227 (12), 6313–6350.Google Scholar
Gerz, T., Schumann, U. & Elghobashi, S. E. 1989 Direct numerical simulation of stratified homogeneous turbulent shear flows. J. Fluid Mech. 200, 563–594.Google Scholar
Gillandt, I., Fritsching, U. & Bauckhage, K. 2001 Measurement of phase interaction in dispersed gas/particle two-phase flow. Intl J. Multiphase Flow 27 (8), 1313–1332.Google Scholar
Good, G. H., Ireland, P. J., Bewley, G. P., Bodenschatz, E., Collins, L. R. & Warhaft, Z. 2014 Settling regimes of inertial particles in isotropic turbulence. J. Fluid Mech. 759, R3.Google Scholar
Gustavsson, K., Meneguz, E., Reeks, M. & Mehlig, B. 2012 Inertial-particle dynamics in turbulent flows: caustics, concentration fluctuations and random uncorrelated motion. New J. Phys. 14 (11), 115017.Google Scholar
Hardalupas, Y., Taylor, A. M. K. P. & Whitelaw, J. H. 1989 Velocity and particle–flux characteristics of trubulent particle-laden jets. Proc. R. Soc. Lond. A 426 (1870), 31–78.Google Scholar
Ireland, P. J., Bragg, A. D. & Collins, L. R. 2016 The effect of Reynolds number on inertial particle dynamics in isotropic turbulence. Part 2. Simulations with gravitational effects. J. Fluid Mech. 796, 659–711.Google Scholar
Ireland, P. J. & Desjardins, O. 2017 Improving particle drag predictions in Euler–Lagrange simulations with two-way coupling. J. Comput. Phys. 338, 405–430.Google Scholar
Jenny, P., Roekaerts, D. & Beishuizen, N. 2012 Modeling of turbulent dilute spray combustion. Prog. Energy Combust. Sci. 38 (6), 846–887.Google Scholar
Kasbaoui, M. H., Koch, D. L., Subramanian, G. & Desjardins, O. 2015 Preferential concentration driven instability of sheared gassolid suspensions. J. Fluid Mech. 770, 85–123.Google Scholar
Kasbaoui, M. H., Patel, R. G., Koch, D. L. & Desjardins, O. 2017 An algorithm for solving the Navier–Stokes equations with shear-periodic boundary conditions and its application to homogeneously sheared turbulence. J. Fluid Mech. 833, 687–716.Google Scholar
Kaufmann, A., Moreau, M., Simonin, O. & Helie, J. 2008 Comparison between Lagrangian and mesoscopic Eulerian modelling approaches for inertial particles suspended in decaying isotropic turbulence. J. Comput. Phys. 227 (13), 6448–6472.Google Scholar
Koch, D. L. 1990 Kinetic theory for a monodisperse gassolid suspension. Phys. Fluids A 2 (10), 1711–1723.Google Scholar
Kong, B., Fox, R. O., Feng, H., Capecelatro, J., Patel, R., Desjardins, O. & Fox, R. O. 2017 Eulereuler anisotropic gaussian mesoscale simulation of homogeneous cluster-induced gasparticle turbulence. AIChE J. 63 (7), 2630–2643.Google Scholar
Lau, T. C. W. & Nathan, G. J. 2014 Influence of Stokes number on the velocity and concentration distributions in particle-laden jets. J. Fluid Mech. 757, 432–457.Google Scholar
Lees, A. W. & Edwards, S. F. 1972 The computer study of transport processes under extreme conditions. J. Phys. C 5 (15), 1921–1928.Google Scholar
Levermore, C. D. & Morokoff, W. J. 1998 The Gaussian moment closure for gas dynamics. SIAM J. Appl. Maths 59 (1), 72–96.Google Scholar
Masi, E. & Simonin, O. 2014 Algebraic-closure-based moment method for unsteady Eulerian simulations of non-isothermal particle-laden turbulent flows at moderate Stokes numbers in dilute regime. Flow Turbul. Combust. 92 (1–2), 121–145.Google Scholar
Maxey, M. R. 1987 The gravitational settling of aerosol particles in homogeneous turbulence and random flow fields. J. Fluid Mech. 174, 441–465.Google Scholar
Maxey, M. R. & Riley, J. J. 1983 Equation of motion for a small rigid sphere in a nonuniform flow. Phys. Fluids 26 (4), 883–889.Google Scholar
McGraw, R. 1997 Description of aerosol dynamics by the quadrature method of moments. Aerosol Sci. Technol. 27 (2), 255–265.Google Scholar
Meyer, D. W. 2012 Modelling of turbulence modulation in particle- or droplet-laden flows. J. Fluid Mech. 706, 251–273.Google Scholar
Modarress, D., Elghobashi, S. & Tan, H. 1984 Two-component LDA measurement in a two-phase turbulent jet. AIAA J. 22 (5), 624–630.Google Scholar
Mostafa, A. A., Mongia, H. C., Mcdonel, V. G. & Samuelsen, G. S. 1989 Evolution of particle-laden jet flows – a theoretical and experimental study. AIAA J. 27 (2), 167–183.Google Scholar
Pai, M. G. & Subramaniam, S. 2012 Two-way coupled stochastic model for dispersion of inertial particles in turbulence. J. Fluid Mech. 700, 29–62.Google Scholar
Poelma, C., Westerweel, J. & Ooms, G. 2007 Particle–fluid interactions in grid-generated turbulence. J. Fluid Mech. 589, 315–351.Google Scholar
Prevost, F., Boree, J., Nuglisch, H. J. & Charnay, G. 1996 Measurements of fluid/particle correlated motion in the far field of an axisymmetric jet. Intl J. Multiphase Flow 22 (4), 685–701.Google Scholar
Ravichandran, S. & Govindarajan, R. 2015 Caustics and clustering in the vicinity of a vortex. Phys. Fluids 27 (3), 033305.Google Scholar
Rogallo, R. S.1981 Numerical experiments in homogeneous turbulence. NASA STI/Recon Tech. Rep. N 81, 31508.Google Scholar
Sabat, M., Vié, A., Larat, A. & Massot, M.2016 Fully Eulerian simulation of 3D turbulent particle laden flow based on the anisotropic Gaussian closure. Firenze, Italy.Google Scholar
Schmid, P. J. 2007 Nonmodal stability theory. Annu. Rev. Fluid Mech. 39 (1), 129–162.Google Scholar
Shuen, J. S., Solomon, A. S. P., Faeth, G. M. & Zhang, Q. F. 1985 Structure of particle-laden jets – measurements and predictions. AIAA J. 23 (3), 396–404.Google Scholar
Simonin, O., Fevrier, P. & Laviville, J. 2002 On the spatial distribution of heavy-particle velocities in turbulent flow: from continuous field to particulate chaos. J. Turbul. 3, N40.Google Scholar
Squires, K. D. & Eaton, J. K. 1991 Preferential concentration of particles by turbulence. Phys. Fluids A 3 (5), 1169–1178.Google Scholar
Thomson, W. 1887 XXXIV. Stability of motion (continued from the May, June, and August Numbers). Broad river flowing down an inclined plane bed. Phil. Mag. Ser. 5 24 (148), 272–278.Google Scholar
Vikas, V., Wang, Z. J., Passalacqua, A. & Fox, R. O. 2011 Realizable high-order finite-volume schemes for quadrature-based moment methods. J. Comput. Phys. 230 (13), 5328–5352.Google Scholar
Vi, A., Doisneau, F. & Massot, M. 2015 On the anisotropic Gaussian velocity closure for inertial-particle laden flows. Commun. Comput. Phys. 17 (1), 1–46.Google Scholar
Wang, L.-P. & Maxey, M. R. 1993 Settling velocity and concentration distribution of heavy particles in homogeneous isotropic turbulence. J. Fluid Mech. 256, 27–68.Google Scholar
Wilkinson, M., Mehlig, B. & Bezuglyy, V. 2006 Caustic activation of rain showers. Phys. Rev. Lett. 97 (4), 048501.Google Scholar
Williams, F. A. 1958 Spray combustion and atomization. Phys. Fluids 1 (6), 541–545.Google Scholar
Yang, C. Y. & Lei, U. 1998 The role of the turbulent scales in the settling velocity of heavy particles in homogeneous isotropic turbulence. J. Fluid Mech. 371, 179–205.Google Scholar
Yang, T. S. & Shy, S. S. 2005 Two-way interaction between solid particles and homogeneous air turbulence: particle settling rate and turbulence modification measurements. J. Fluid Mech. 526, 171–216.Google Scholar