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Turbophoresis of small inertial particles: theoretical considerations and application to wall-modelled large-eddy simulations

Published online by Cambridge University Press:  26 November 2019

Perry L. Johnson Open the ORCID record for Perry L. Johnson [Opens in a new window] ,
Maxime Bassenne Open the ORCID record for Maxime Bassenne [Opens in a new window]  and
Parviz Moin
Perry L. Johnson*
Affiliation:
Center for Turbulence Research, Stanford University, Stanford, CA94305, USA
Maxime Bassenne
Affiliation:
Center for Turbulence Research, Stanford University, Stanford, CA94305, USA
Parviz Moin
Affiliation:
Center for Turbulence Research, Stanford University, Stanford, CA94305, USA
*
†Email address for correspondence: [email protected]
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Abstract

In wall-bounded turbulent flows, the wall-normal gradient in turbulence intensity causes inertial particles to move preferentially toward the wall, leading to elevated concentration levels in the viscous sublayer. At first glance, wall-modelled large-eddy simulations may seem ill suited for accurately simulating this behaviour, given that the sharp gradients and coherent structures in the viscous sublayer and buffer region are unresolved in this approach. In this paper, a detailed inspection of conservation equations describing the influence of turbophoresis and near-wall structures on particle concentration profiles reveals a more nuanced view depending on the friction Stokes number. The dynamics of low and moderate Stokes number particles indeed depends strongly on the complex spatio-temporal details of streaks, ejections, and sweeps in the near-wall region. This significantly impacts the near-wall particle concentration through a biased sampling effect which provides a net force away from the wall on the particle ensemble caused by the tendency of inertial particles to accumulate in low-speed ejection regions. At higher Stokes numbers, however, this biased sampling is of minimal importance, and the particle concentration becomes inversely proportional to the wall-normal particle velocity variance at a given distance from the wall. As a result, wall-modelled large-eddy simulations can predict concentration profiles with more accuracy in the high Stokes number regime than low Stokes numbers simply by modifying the interpolation scheme for particles between the first grid point and the boundary. However, accurate representation of low and moderate Stokes number particles depends critically on information not present in standard wall-modelled large-eddy simulations.

JFM classification

Multiphase and Particle-laden Flows: Particle/fluid flow Turbulent Flows: Turbulence simulation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 883 , 25 January 2020 , A27
Copyright
© 2019 Cambridge University Press

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References

Arcen, B. & Tanière, A. 2009 Simulation of a particle-laden turbulent channel flow using an improved stochastic Lagrangian model. Phys. Fluids 21, 043303.CrossRefGoogle Scholar
Armenio, V., Piomelli, U. & Fiorotto, V. 1999 Effect of the subgrid scales on particle motion. Phys. Fluids 11 (10), 3030–3042.CrossRefGoogle Scholar
Bae, H. J., Lozano-Durán, A., Bose, S. T. & Moin, P. 2018 Turbulence intensities in large-eddy simulation of wall-bounded flows. Phys. Rev. Fluids 3 (1), 014610.CrossRefGoogle ScholarPubMed
Balachandar, S. & Eaton, J. K. 2010 Turbulent dispersed multiphase flow. Annu. Rev. Fluid Mech. 42 (1), 111–133.CrossRefGoogle Scholar
Bassenne, M., Esmaily, M., Livescu, D., Moin, P. & Urzay, J. 2019 A dynamic spectrally enriched subgrid-scale model for preferential concentration in particle-laden turbulence. Intl J. Multiphase Flow 116, 270–280.CrossRefGoogle Scholar
Bassenne, M., Johnson, P. L., Urzay, J. & Moin, P. 2018 On wall modeling for LES of particle-laden turbulent channel flows. In Center for Turbulence Research Annual Research Briefs, pp. 93–109. Stanford University.Google Scholar
Benson, M., Tanaka, T. & Eaton, J. K. 2005 Effects of wall roughness on particle velocities in a turbulent channel flow. Trans. ASME J. Fluids Engng 127, 250–256.CrossRefGoogle Scholar
Bernardini, M. 2014 Reynolds number scaling of inertial particle statistics in turbulent channel flows. J. Fluid Mech. 758, R1.CrossRefGoogle Scholar
Bianco, F., Chibbaro, S., Marchioli, C., Salvetti, M. V. & Soldati, A. 2012 Intrinsic filtering errors of Lagrangian particle tracking in LES flow fields. Phys. Fluids 24 (4), 045103.CrossRefGoogle Scholar
Bijlard, M. J., Oliemans, R. V. A., Portela, L. M. & Ooms, G. 2010 Direct numerical simulation analysis of local flow topology in a particle-laden turbulent channel flow. J. Fluid Mech. 653, 35–56.CrossRefGoogle Scholar
Bose, S. T. & Park, G. I. 2018 Wall-modeled large-eddy simulation for complex turbulent flows. Annu. Rev. Fluid Mech. 50, 535–561.CrossRefGoogle ScholarPubMed
Bragg, A. D. & Collins, L. R. 2014 New insights from comparing statistical theories for inertial particles in turbulence: I. Spatial distribution of particles. New J. Phys. 16, 055013.Google Scholar
Breuer, M. & Hoppe, F. 2017 Influence of a cost efficient Langevin subgrid-scale model on the dispersed phase of large eddy simulations of turbulent bubble laden and particle laden flows. Intl J. Multiphase Flow 89, 23–44.CrossRefGoogle Scholar
Cabot, W. & Moin, P. 2000 Approximate wall boundary conditions in the large-eddy simulation of high Reynolds number flow. Flow Turbul. Combust. 63 (1), 269–291.CrossRefGoogle Scholar
Capecelatro, J., Desjardins, O. & Fox, R. O. 2016 Strongly coupled fluid-particle flows in vertical channels. I. Reynolds-averaged two-phase turbulence statistics. Phys. Fluids 28 (3), 033306.Google Scholar
Caporaloni, M., Tampieri, F., Trombetti, F. & Vittori, O. 1975 Transfer of particles in nonisotropic air turbulence. J. Atmos. Sci. 32, 565–568.2.0.CO;2>CrossRefGoogle Scholar
Caraman, N., Borée, J. & Simonin, O. 2003 Effect of collisions on the dispersed phase fluctuation in a dilute tube flow: experimental and theoretical analysis. Phys. Fluids 15 (12), 3602–3612.CrossRefGoogle Scholar
Chapman, D. R. 1979 Computational aerodynamics development and outlook. AIAA J. 17, 1293–1313.CrossRefGoogle Scholar
Chibbaro, S. & Minier, J.-P. 2008 Langevin PDF simulation of particle deposition in a turbulent pipe flow. J. Aero. Sci. 39, 555–571.CrossRefGoogle Scholar
Choi, H. & Moin, P. 2012 Grid-point requirements for large eddy simulation: Chapman’s estimates revisited. Phys. Fluids 24 (1), 30–35.CrossRefGoogle Scholar
Dreeben, T. D. & Pope, S. B. 1998 Probability density function/Monte Carlo simulation of near-wall turbulent flows. J. Fluid Mech. 357, 141–166.CrossRefGoogle Scholar
Durbin, P. A. 1991 Near-wall turbulence closure modeling without damping functions. Theor. Comput. Fluid Dyn. 3, 1–13.Google Scholar
Durbin, P. A. 1993 A Reynolds stress model for near-wall turbulence. J. Fluid Mech. 249, 465–498.CrossRefGoogle Scholar
Eaton, J. K. & Fessler, J. R. 1994 Preferential concentration of particles by turbulence. Intl J. Multiphase Flow 20, 169–209.CrossRefGoogle Scholar
Elghobashi, S. 1994 On predicting particle-laden turbulent flows. Appl. Sci. Res. 52 (4), 309–329.CrossRefGoogle Scholar
Esmaily, M. & Horwitz, J. A. K. 2018 A correction scheme for two-way coupled point-particle simulations on anisotropic grids. J. Comput. Phys. 375, 960–982.CrossRefGoogle Scholar
Fede, P., Simonin, O., Villedieu, P. & Squires, K. 2006 Stochastic modling of the turbulent subgrid flud velocity along inertial particle trajectories. In Proceedings of the Summer Program Center for Turbulence Research, pp. 247–258. Stanford University.Google Scholar
Germano, M., Piomelli, U., Moin, P. & Cabot, W. H. 1991 A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A 3 (7), 1760–1765.CrossRefGoogle Scholar
Guha, A. 1997 A unified Eulerian theory of turbulent deposition to smooth and rough surfaces. J. Aero. Sci. 28 (8), 1517–1537.CrossRefGoogle Scholar
Guha, A. 2008 Transport and deposition of particles in turbulent and laminar flow. Annu. Rev. Fluid Mech. 40, 311–341.CrossRefGoogle Scholar
Guingo, M. & Minier, J. P. 2008 A stochastic model of coherent structures for particle deposition in turbulent flows. Phys. Fluids 20 (5), 053303.CrossRefGoogle Scholar
Henry, C., Minier, J.-P., Mohaupt, M., Profeta, C., Pozorski, J. & Tanière, A. 2014 A stochastic approach for the simulation of collisions between colloidal particles at large time steps. Intl J. Multiphase Flow 61, 94–107.CrossRefGoogle Scholar
Horwitz, J. A. K. & Mani, A. 2016 Accurate calculation of Stokes drag for point-particle tracking in two-way coupled flows. J. Comput. Phys. 318, 85–109.CrossRefGoogle Scholar
Horwitz, J. A. K. & Mani, A. 2018 Correction scheme for point-particle models applied to a nonlinear drag law in simulations of particle-fluid interaction. Intl J. Multiphase Flow 101, 74–84.CrossRefGoogle Scholar
Innocenti, A., Marchioli, C. & Chibbaro, S. 2016 Lagrangian filtered density function for LES-based stochastic modelling of turbulent dispersed flows. Phys. Fluids 28, 115106.CrossRefGoogle Scholar
Ireland, P. J., Bragg, A. D. & Collins, L. R. 2016a The effect of Reynolds number on inertial particle dynamics in isotropic turbulence. Part 1. Simulations without gravitational effects. J. Fluid Mech. 796, 617–658.CrossRefGoogle Scholar
Ireland, P. J., Bragg, A. D. & Collins, L. R. 2016b The effect of Reynolds number on inertial particle dynamics in isotropic turbulence. Part 2. Simulations with gravitational effects. J. Fluid Mech. 796, 659–711.CrossRefGoogle Scholar
Jin, C., Potts, I. & Reeks, M. W. 2015 A simple stochastic quadrant model for the transport and deposition of particles in turbulent boundary layers. Phys. Fluids 27, 053305.CrossRefGoogle Scholar
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166.CrossRefGoogle Scholar
Konan, N. A., Simonin, O. & Squires, K. D. 2011 Detached eddy simulations and particle Lagrangian tracking of horizontal rough wall turbulent channel flow. J. Turbul. 12, N22.CrossRefGoogle Scholar
Kuerten, J. G. 2016 Point-particle DNS and LES of particle-laden turbulent flow – a state-of-the-art review. Flow Turbul. Combust. 97 (3), 689–713.CrossRefGoogle Scholar
Kuerten, J. G. M. 2006 Subgrid modeling in particle-laden channel flow. Phys. Fluids 18 (2), 025108.CrossRefGoogle Scholar
Kuerten, J. G. M. & Vreman, A. W. 2015 Effect of droplet interaction on droplet-laden turbulent channel flow. Phys. Fluids 27 (5), 053304.CrossRefGoogle Scholar
Kuerten, J. G. M. & Vreman, A. W. 2016 Collision frequency and radial distribution function in particle-laden turbulent channel flow. Intl J. Multiphase Flow 87, 66–79.CrossRefGoogle Scholar
Kussin, J. & Sommerfeld, M. 2002 Experimental studies on particle behaviour and turbulence modification in horizontal channel flow with different wall roughness. Exp. Fluids 33 (1), 143–159.CrossRefGoogle Scholar
Lavezzo, V., Soldati, A., Gerashchenko, S., Warhaft, Z. & Collins, L. R. 2010 On the role of gravity and shear on inertial particle accelerations in near-wall turbulence. J. Fluid Mech. 658, 229246.CrossRefGoogle Scholar
Li, Y., McLaughlin, J. B., Kontomaris, K. & Portela, L. 2001 Numerical simulation of particle-laden turbulent channel flow. Phys. Fluids 13 (10), 2957–2967.CrossRefGoogle Scholar
Liakopoulos, A. 1984 Explicit representations of the complete velocity profile in a turbulent boundary layer. AIAA J. 22 (6), 844.CrossRefGoogle Scholar
Lilly, D. K. 1992 A proposed modification of the Germano subgrid-scale closure method. Phys. Fluids A 4 (3), 633–635.CrossRefGoogle Scholar
Marchioli, C. 2017 Large-eddy simulation of turbulent dispersed flows: a review of modelling approaches. Acta Mechanica 228 (3), 741–771.Google Scholar
Marchioli, C., Picciotto, M. & Soldati, A. 2007 Influence of gravity and lift on particle velocity statistics and transfer rates in turbulent vertical channel flow. Intl J. Multiphase Flow 33 (3), 227–251.CrossRefGoogle Scholar
Marchioli, C., Salvetti, M. V. & Soldati, A. 2008a Appraisal of energy recovering sub-grid scale models for large-eddy simulation of turbulent dispersed flows. Acta Mechanica 201, 277–296.Google Scholar
Marchioli, C., Salvetti, M. V. & Soldati, A. 2008b Some issues concerning large-eddy simulation of inertial particle dispersion in turbulent bounded flows. Phys. Fluids 20 (4), 040603.CrossRefGoogle Scholar
Marchioli, C. & Soldati, A. 2002 Mechanisms for particle transfer and segregation in a turbulent boundary layer. J. Fluid Mech. 468, 283–315.CrossRefGoogle Scholar
Marchioli, C., Soldati, A., Kuerten, J. G. M., Arcen, B., Tanière, A., Goldensoph, G., Squires, K. D., Cargnelutti, M. F. & Portela, L. M. 2008c Statistics of particle dispersion in direct numerical simulations of wall-bounded turbulence: results of an international collaborative benchmark test. Intl J. Multiphase Flow 34, 879–893.CrossRefGoogle Scholar
Maxey, M. R. 1987 The gravitational settling of aerosol particles in homogeneous turbulence and random flow fields. J. Fluid Mech. 174, 441.CrossRefGoogle Scholar
Michałek, W. R., Kuerten, J. G. M., Zeegers, J. C. H., Liew, R., Pozorski, J. & Geurts, B. J. 2013 A hybrid stochastic-deconvolution model for large-eddy simulation of particle-laden flow. Phys. Fluids 25, 123302.CrossRefGoogle Scholar
Milici, B., De Marchis, M., Sardina, G. & Napoli, E. 2014 Effects of roughness on particle dynamics in turbulent channel flows: a DNS analysis. J. Fluid Mech. 739, 465–478.CrossRefGoogle Scholar
Minier, J.-P. 2015 On Lagrangian stochastic methods for turbulent polydisperse two-phase reactive flows. Prog. Energy Combust. Sci. 50, 1–62.CrossRefGoogle Scholar
Minier, J.-P. 2016 Statistical descriptions of polydisperse turbulent two-phase flows. Phys. Rep. 665, 1–122.Google Scholar
Minier, J.-P., Chibbaro, S. & Pope, S. B. 2014 Guidelines for the formulation of Lagrangian stochastic models for particle simulations of single-phase and dispersed two-phase turbulent flows. Phys. Fluids 26 (11), 113303.CrossRefGoogle Scholar
Moin, P. & Mahesh, K. 1998 Direct numerical simulation: a tool in turbulence research. Annu. Rev. Fluid Mech. 30, 539–578.CrossRefGoogle Scholar
Park, G. I., Bassenne, M., Urzay, J. & Moin, P. 2017 A simple dynamic subgrid-scale model for LES of particle-laden turbulence. Phys. Rev. Fluids 1, 044301.Google Scholar
Park, G. I. & Moin, P. 2016 Space-time characteristics of wall-pressure fluctuations in wall-modeled large eddy simulation. Phys. Rev. Fluids 2, 024404.Google Scholar
Pascarelli, A., Piomelli, U. & Candler, G. V. 2000 Multi-Block large-eddy simulations of turbulent boundary layers. J. Comput. Phys. 157 (1), 256–279.CrossRefGoogle Scholar
Pope, S. B. 1994 Lagrangian PDF methods for turbulent flows. Annu. Rev. Fluid Mech. 26, 23–63.CrossRefGoogle Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Pouransari, H. & Mani, A. 2017 Effects of preferential concentration on heat transfer in particle-based solar receivers. J. Solar Energy Engng 139, 021008.Google Scholar
Pozorski, J. & Apte, S. V. 2009 Filtered particle tracking in isotropic turbulence and stochastic modmodel of subgrid-scale dispersion. Intl J. Multiphase Flow 35, 118–128.CrossRefGoogle Scholar
Rashidi, M., Hetstroni, G. & Banerjee, S. 1990 Particle-turbulence interaction in a boundary layer. Intl J. Multiphase Flow 16, 935–949.CrossRefGoogle Scholar
Ray, B. & Collins, L. R. 2014 A subgrid model for clustering of high-inertia particles in large-eddy simulations of turbulence. J. Turbul. 15 (6), 366–385.CrossRefGoogle Scholar
Reade, W. C. & Collins, L. R. 2000 Effect of preferential concentration on turbulent collision rates. Phys. Fluids 12, 2530–2540.CrossRefGoogle Scholar
Reeks, M. W. 1983 The transport of discrete particles in inhomogeneous turbulence. J. Aero. Sci. 14 (6), 729–739.CrossRefGoogle Scholar
Sagaut, P. 2006 Large Eddy Simulation for Incompressible Flows. Springer.Google Scholar
Salazar, J. P. L. C. & Collins, L. R. 2012 Inertial particle relative velocity statistics in homogeneous isotropic turbulence. J. Fluid Mech. 696, 45–66.CrossRefGoogle Scholar
Sandham, N. D., Johnstone, R. & Jacobs, C. T. 2017 Surface-sampled simulations of turbulent flow at high Reynolds number. Intl J. Numer. Meth. Fluids 85 (9), 525–537.CrossRefGoogle Scholar
Schiller, L. & Naumann, A. Z. 1933 Uber die grundlegenden berechnungen bei der schwekraaftaubereitung. Z. Verein. Deutsch. Ing. 77, 318–320.Google Scholar
Scotti, A. & Meneveau, C. 1999 A fractal model for large eddy simulation of turbulent flow. Physica D 127, 198–232.Google Scholar
Sikovsky, D. P. 2014 Singularity of inertial particle concentration in the viscous sublayer of wall-bounded turbulent flows. Flow Turbul. Combust. 92, 41–64.CrossRefGoogle Scholar
Sommerfeld, M. 1992 Modelling of particle-wall collisions in confined gas-particle flows. Intl J. Multiphase Flow 18 (6), 905–926.CrossRefGoogle Scholar
Spalart, P. R. 2009 Detached-eddy simulation. Annu. Rev. Fluid Mech. 41, 181–202.CrossRefGoogle Scholar
Tang, Y. & Akhavan, R. 2016 Computations of equilibrium and non-equilibrium turbulent channel flows using a nested-LES approach. J. Fluid Mech. 793, 709–748.CrossRefGoogle Scholar
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. MIT Press.Google Scholar
Vreman, A. W. 2007 Turbulence characteristics of particle-laden pipe flow. J. Fluid Mech. 584, 235–279.CrossRefGoogle Scholar
Wang, Q., Squires, K. D., Chen, M. & McLaughlin, J. B. 1997 On the role of the lift force in turbulence simulations of particle deposition. Intl J. Multiphase Flow 23 (4), 749–763.CrossRefGoogle Scholar
Yamamoto, Y., Potthoff, M., Tanaka, T., Kajishima, T. & Tsuji, Y. 2001 Large-eddy simulation of turbulent gas-particle flow in a vertical channel: effect of considering inter-particle collisions. J. Fluid Mech. 442, 303–334.CrossRefGoogle Scholar
Yang, F. L. & Hunt, M. L. 2006 Dynamics of particle-particle collisions in a viscous liquid. Phys. Fluids 18 (12), 121506.CrossRefGoogle Scholar
Yeung, P. K. & Pope, S. B. 1988 An algorithm for tracking fluid particles in numerical simulations of homogeneous turbulence. J. Comput. Phys. 79 (2), 373–416.CrossRefGoogle Scholar