Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-24T02:24:16.013Z Has data issue: false hasContentIssue false
  • English
  • Français

Turbulent thermal convection driven by heated inertial particles

Published online by Cambridge University Press:  10 November 2016

R. Zamansky ,
F. Coletti ,
M. Massot  and
A. Mani
R. Zamansky*
Affiliation:
Institut de Mécanique des Fluides de Toulouse (IMFT) – Université de Toulouse, CNRS-INPT-UPS, Toulouse, France Center for Turbulence Research, Stanford University, CA 94305, USA
F. Coletti
Affiliation:
University of Minnesota, Aerospace Engineering and Mechanics, 110 Union St, SE Minneapolis, MN 55455, USA
M. Massot
Affiliation:
Ecole Centrale Paris, Laboratoire EM2C – UPR CNRS 288 et Fédération de Mathématiques – FR CNRS 3487, Grande Voie des Vignes, 92295 Chatenay-Malabry CEDEX, France
A. Mani
Affiliation:
Center for Turbulence Research, Stanford University, CA 94305, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The heating of particles in a dilute suspension, for instance by radiation, chemical reactions or radioactivity, leads to local temperature fluctuations in the fluid due to the non-uniformity of the disperse phase. In the presence of a gravity field, the fluid is set in motion by the resulting buoyancy forces. When the particle density is different than that of the fluid, the fluid motion alters the spatial distribution of the particles and possibly strengthens their concentration inhomogeneities. This in turn causes more intense local heating. Direct numerical simulations in the Boussinesq limit show this feedback loop. Various regimes are identified depending on the particle inertia. For very small particle inertia, the macroscopic behaviour of the system is the result of many thermal plumes that are generated independently of each other. For significant particle inertia, clusters of particles are observed and their dynamics controls the flow. The emergence of very intermittent turbulent fluctuations shows that the flow is influenced by the larger structures (turbulent convection) as well as by the small-scale dynamics that affect particle segregation and thus the flow forcing. Assuming thermal equilibrium between the particles and the fluid (i.e. infinitely fast thermal relaxation of the particle), we investigate the evolution of statistical observables with the change of the main control parameters (namely the particle number density, the particle inertia and the domain size), and propose a scaling argument for these trends. Concerning the energy density in the spectral space, it is observed that the turbulent energy and temperature spectra follow a power law, the exponent of which varies continuously with the Stokes number. Furthermore, the study of the spectra of the temperature and momentum forcing (and thus of the concentration/temperature and velocity/temperature correlations) gives strong support to the proposed feedback loop mechanism. We then discuss the intermittency of the flow, and analyse the effect of relaxing some of the simplifying assumptions, thus assessing the relevance of the original studied configuration.

JFM classification

Turbulent Flows: Turbulent convection
Type
Papers
Information
Journal of Fluid Mechanics , Volume 809 , 25 December 2016 , pp. 390 - 437
Check for updates
Copyright
© 2016 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

Acrivos, A., Hinch, E. & Jeffrey, D. 1980 Heat transfer to a slowly moving fluid from a dilute fixed bead of heated spheres. J. Fluid Mech. 101, 403–421.Google Scholar
Ahmed, A. M. & Elghobashi, S. 2000 On the mechanisms of modifying the structure of turbulent homogeneous shear flows by dispersed particles. Phys. Fluids 12 (11), 2906–2930.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
Alméras, E., Risso, F., Roig, V., Cazin, S. & Plais, C. 2015 Mixing by bubble-induced turbulence. J. Fluid Mech. 776, 458–474.Google Scholar
Balachandar, S. & Eaton, J. K. 2010 Turbulent dispersed multiphase flow. Annu. Rev. Fluid Mech. 42, 111–133.CrossRefGoogle Scholar
Batchelor, G. K. 1972 Sedimentation in a dilute dispersion of spheres. J. Fluid Mech. 52, 245–268.Google Scholar
Bec, J., Homann, H. & Krstulovic, G. 2014a Clustering, fronts, and heat transfer in turbulent suspensions of heavy particles. Phys. Rev. Lett. 112, 234503.Google Scholar
Bec, J., Homann, H. & Ray, S. S. 2014b Gravity-driven enhancement of heavy particle clustering in turbulent flow. Phys. Rev. Lett. 112, 184501.CrossRefGoogle ScholarPubMed
Biferale, L., Calzavarini, E., Toschi, F. & Tripiccione, R. 2003 Universality of anisotropic fluctuations from numerical simulations of turbulent flows. Europhys. Lett. 64 (4), 461–467.CrossRefGoogle 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.CrossRefGoogle Scholar
Bolgiano, R. J. 1959 Turbulent spectra in a stably stratified atmosphere. J. Geophys. Res. 64 (12), 2226–2229.CrossRefGoogle Scholar
Borue, V. & Orszag, S. A. 1997 Turbulent convection driven by a constant temperature gradient. J. Sci. Comput. 12 (3), 305–351.Google Scholar
Bouche, E., Cazin, S., Roig, V. & Risso, F. 2013 Mixing in a swarm of bubbles rising in a confined cell measured by mean of plif with two different dyes. Exp. Fluids 54 (6), 1552.Google Scholar
Brenner, M. P. 1999 Screening mechanisms in sedimentation. Phys. Fluids 11 (4), 754–772.Google Scholar
Bruneau, D., Feuillebois, F., Anthore, R. & Hinch, E. 1996 Intrinsic convection in a settling suspension. Phys. Fluids 8, 2236–2238.CrossRefGoogle Scholar
Caflisch, R. E. & Luke, J. H. 1985 Variance in the sedimentation speed of a suspension. Phys. Fluids 28 (3), 759–760.Google Scholar
Canuto, C., Hussaini, M., Quarteroni, A. & Zang, T. 1988 Spectral Methods in Fluid Dynamics. Springer.Google Scholar
Capecelatro, J., Desjardins, O. & Fox, R. O. 2014 Numerical study of collisional particle dynamics in cluster-induced turbulence. J. Fluid Mech. 747, R2.CrossRefGoogle 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.CrossRefGoogle Scholar
Celani, A., Lanotte, A., Mazzino, A. & Vergassola, M. 2000 Universality and saturation of intermittency in passive scalar turbulence. Phys. Rev. Lett. 84, 2385–2388.Google Scholar
Chillá, F., Ciliberto, S., Innocenti, C. & Pampaloni, E. 1993 Boundary layer and scaling properties in turbulent thermal convection. Il Nuovo Cimento D 15 (9), 1229–1249.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.Google Scholar
Corrsin, S. 1951 On the spectrum of isotropic temperature fluctuations in an isotropic turbulence. J. Appl. Phys. 22 (4), 469–473.CrossRefGoogle Scholar
Davis, R. H. & Acrivos, A. 1985 Sedimentation of noncolloidal particles at low Reynolds numbers. Annu. Rev. Fluid Mech. 17, 91–118.Google Scholar
Dejoan, A. & Monchaux, R. 2013 Preferential concentration and settling of heavy particles in homogeneous turbulence. Phys. Fluids 25 (1), 013301.Google Scholar
Druzhinin, O. A. & Elghobashi, S. 1998 Direct numerical simulations of bubble-laden turbulent flows using the two-fluid formulation. Phys. Fluids 10 (3), 685–697.Google Scholar
Druzhinin, O. A. & Elghobashi, S. 1999 On the decay rate of isotropic turbulence laden with microparticles. Phys. Fluids 11 (3), 602–610.Google Scholar
Druzhinin, O. A. & Elghobashi, S. E. 2001 Direct numerical simulation of a three-dimensional spatially developing bubble-laden mixing layer with two-way coupling. J. Fluid Mech. 429, 23–61.CrossRefGoogle Scholar
Dumont, T., Genieys, S., Massot, M. & Volpert, V. 2002 Interaction of thermal explosion and natural convection: critical conditions and new oscillating regimes. SIAM J. Appl. Maths 63 (1), 351–372.Google Scholar
Eaton, J. K. 2009 Two-way coupled turbulence simulations of gas-particle flows using point-particle tracking. Intl J. Multiphase Flow 35 (9), 792–800; special issue: Point-Particle Model for Disperse Turbulent Flows.CrossRefGoogle Scholar
Eaton, J. K. & Fessler, J. R. 1994 Preferential concentration of particles by turbulence. Intl J. Multiphase Flow 20, 169–209.Google Scholar
Elghobashi, S. & Truesdell, G. C. 1993 On the two way interaction between homogeneous turbulence and dispersed solid particles. I: turbulence modification. Phys. Fluids A 5 (7), 1790–1801.Google Scholar
Even, S. 2012 Graph Algorithms, 2nd edn. Cambridge University Press.Google Scholar
Feng, Z.-G. & Michaelides, E. E. 2008 Inclusion of heat transfer computations for particle laden flows. Phys. Fluids 20 (4), 040604.Google Scholar
Ferenc, J.-S. & Néda, Z. 2007 On the size distribution of poisson Voronoi cells. Physica A 385, 518–526.Google Scholar
Ferrante, A. & Elghobashi, S. 2003 On the physical mechanisms of two-way coupling in particle-laden isotropic turbulence. Phys. Fluids 15 (2), 315–329.Google Scholar
Fessler, J. R., Kulick, J. D. & Eaton, J. K. 1994 Preferential concentration of heavy particles in a turbulent channel flow. Phys. Fluids 6 (11), 3742–3749.Google Scholar
Frankel, A., Pouransari, H., Coletti, F. & Mani, A. 2016 Settling of heated particles in homogeneous turbulence. J. Fluid Mech. 792, 869–893.Google Scholar
Gan, H., Chang, J., Feng, J. J. & Hu, H. H. 2003 Direct numerical simulation of the sedimentation of solid particles with thermal convection. J. Fluid Mech. 481, 385–411.CrossRefGoogle Scholar
Garcia-Villalba, M., Kidanemariam, A. G. & Uhlmann, M. 2012 DNS of vertical plane channel flow with finite-size particles: Voronoi analysis, acceleration statistics and particle-conditioned averaging. Intl J. Multiphase Flow 46, 54–74.Google Scholar
Garg, R., Narayanan, C., Lakehal, D. & Subramaniam, S. 2007 Accurate numerical estimation of interphase momentum transfer in Lagrangian–Eulerian simulations of dispersed two-phase flows. Intl J. Multiphase Flow 33, 1337–1364.Google Scholar
Génieys, S. & Massot, M.2001 From Navier–Stokes equations to the Oberbeck–Boussinesq approximation: a unified approach. Tech. Rep. Hal-00762993, version 1, pp. 133. MAPLY Laboratory, Lyon. Available at: https://hal.archives-ouvertes.fr/hal-00762993.Google Scholar
Goto, S. & Vassilicos, J. C. 2008 Sweep-stick mechanism of heavy particle clustering in fluid turbulence. Phys. Rev. Lett. 100, 054503.Google Scholar
Gotoh, K., Yamada, S. & Nishimura, T. 2004 Influence of thermal convection on particle behavior in solid-liquid suspensions. Adv. Powder Technol. 15 (5), 499–514.Google Scholar
Guazzelli, E. & Hinch, J. 2011 Fluctuations and Instability in Sedimentation. Annu. Rev. Fluid Mech. 43, 97–116.Google Scholar
Hinch, E. 1988 Sedimentation of small particles. In Disorder and Mixing (ed. Guyon, E., Nadal, J.-P. & Pomeau, Y.), ATO ASI Series, vol. 152, pp. 153–162. Springer.CrossRefGoogle Scholar
Hinch, E. J. 1977 An averaged-equation approach to particle interactions in a fluid suspension. J. Fluid Mech. 83, 695–720.Google Scholar
Holzer, M. & Siggia, E. D. 1994 Turbulent mixing of a passive scalar. Phys. Fluids 6 (5), 1820–1837.Google Scholar
Kotouc, M., Bouchet, G. & Dusek, J. 2009 Drag and flow reversal in mixed convection past a heated sphere. Phys. Fluids 21, 054104.Google Scholar
Ladd, A. J. C. 1997 Sedimentation of homogeneous suspensions of non-brownian spheres. Phys. Fluids 9 (3), 491–499.Google Scholar
Lakkaraju, R., Schmidt, L. E., Oresta, P., Toschi, F., Verzicco, R., Lohse, D. & Prosperetti, A. 2011 Effect of vapor bubbles on velocity fluctuations and dissipation rates in bubbly Rayleigh–Bénard convection. Phys. Rev. E 84, 036312.Google Scholar
Lakkaraju, R., Stevens, R., Oresta, P., Verzicco, R., Lohse, D. & Prosperetti, A. 2013 Heat transport in bubbling turbulent convection. Proc. Natl Acad. Sci. USA 110 (23), 237–242.Google Scholar
Lakkaraju, R., Toschi, F. & Lohse, D. 2014 Bubbling reduces intermittency in turbulent thermal convection. J. Fluid Mech. 745, 1–24.Google Scholar
Lance, M. & Bataille, J. 1991 Turbulence in the liquid phase of a uniform bubbly air–water flow. J. Fluid Mech. 222, 95–118.Google Scholar
Lohse, D. & Xia, K.-Q. 2009 Small-scale properties of turbulent Rayleigh–Bénard convection. Annu. Rev. Fluid Mech. 42, 335–364.Google Scholar
Martínez Mercado, J., Chehata Gómez, D., Van Gils, D., Sun, C. & Lohse, D. 2010 On bubble clustering and energy spectra in pseudo-turbulence. J. Fluid Mech. 650, 287–306.Google Scholar
Maxey, M., Patel, B., Chang, E. & Wang, L. 1997 Simulations of dispersed turbulent multiphase flow. Fluid Dyn. Res. 20, 143–156.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
Mercier, M. J., Ardekani, A. M., Allshouse, M. R., Doyle, B. & Peacock, T. 2014 Self-propulsion of immersed objects via natural convection. Phys. Rev. Lett. 112, 204501.Google Scholar
Mizukami, M., Parthasarathy, R. & Faeth, G. 1992 Particle-generated turbulence in homogeneous dilute dispersed flows. Intl J. Multiphase Flow 18 (3), 397–412.Google Scholar
Monchaux, R., Bourgoin, M. & Cartellier, A. 2010 Preferential concentration of heavy particles: a Voronoï analysis. Phys. Fluids 22, 103304.Google 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
Mudde, R. F. 2005 Gravity-driven bubbly flows. Annu. Rev. Fluid Mech. 37 (1), 393–423.Google Scholar
Nicolai, C., Jacob, B. & Piva, R. 2013 On the spatial distribution of small heavy particles in homogeneous shear turbulence. Phys. Fluids 25 (8), 083301.Google Scholar
Nilsen, C., Andersson, H. I. & Zhao, L. 2013 A Voronoï analysis of preferential concentration in a vertical channel flow. Phys. Fluids 25 (11), 115108.Google Scholar
Obukhov, A. 1959 Description of turbulence in terms of Lagrangian variables. Adv. Geophys. 6, 113–116.Google Scholar
Obukhov, A. M. 1949 The structure of the temperature field in a turbulent flow. Izv. Akad. Nauk. SSSR 13, 58.Google Scholar
Oresta, P. & Prosperetti, A. 2013 Effects of particle settling on Rayleigh–Bénard convection. Phys. Rev. E 87, 063014.Google Scholar
Oresta, P., Verzicco, R., Lohse, D. & Prosperetti, A. 2009 Heat transfer mechanisms in bubbly Rayleigh–Bénard convection. Phys. Rev. E 80, 026304.Google Scholar
Ouellette, N. T., Xu, H., Bourgoin, M. & Bodenschatz, E. 2006 Small-scale anisotropy in lagrangian turbulence. New J. Phys. 8 (6), 102.CrossRefGoogle Scholar
Overholt, M. R. & Pope, S. B. 1996 Direct numerical simulation of a passive scalar with imposed mean gradient in isotropic turbulence. Phys. Fluids 8 (11), 3128–3148.Google Scholar
Pekurovsky, D. 2012 P3dfft: a framework for parallel computations of fourier transforms in three dimensions. SIAM J. Sci. Comput. 34 (4), C192–C209.Google Scholar
Riboux, G., Risso, F. & Legendre, D. 2010 Experimental characterization of the agitation generated by bubbles rising at high reynolds number. J. Fluid Mech. 643, 509–539.CrossRefGoogle Scholar
Shirgaonkar, A. A. & Lele, S. K. 2006 On the extension of the Boussinesq approximation for inertia dominated flows. Phys. Fluids 18 (6), 066601.Google Scholar
Spiegel, E. A. & Veronis, G. 1960 On the Boussinesq approximation for a compressible fluid. Astrophys. J. 131, 442–447.CrossRefGoogle Scholar
Squires, K. D. & Eaton, J. K. 1991 Preferential concentration of particles by turbulence. Phys. Fluids A 3 (5), 1169–1178.Google 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.Google Scholar
Tagawa, Y., Mercado, J. M., Prakash, V. N., Calzavarini, E., Sun, C. & Lohse, D. 2012 Three-dimensional Lagrangian Voronoï analysis for clustering of particles and bubbles in turbulence. J. Fluid Mech. 693, 201–215.Google Scholar
Tagawa, Y., Roghair, I., Prakash, V. N., van Sint Annaland, M., Kuipers, H., Sun, C. & Lohse, D. 2013 The clustering morphology of freely rising deformable bubbles. J. Fluid Mech. 721, R2.Google Scholar
Takagi, S., Ogasawara, T. & Matsumoto, Y. 2008 The effects of surfactant on the multiscale structure of bubbly flows. Phil. Trans. R. Soc. Lond. A 366 (1873), 2117–2129.Google Scholar
Tanaka, T. & Eaton, J. K. 2008 Classification of turbulence modification by dispersed spheres using a novel dimensionless number. Phys. Rev. Lett. 101, 114502.Google Scholar
Uhlmann, M. & Doychev, T. 2014 Sedimentation of a dilute suspension of rigid spheres at intermediate galileo numbers: the effect of clustering upon the particle motion. J. Fluid Mech. 752, 310–348.Google Scholar
Vié, A., Pouransari, H., Zamansky, R. & Mani, A. 2016 Particle-laden flows forced by the disperse phase: comparison between Lagrangian and Eulerian simulations. Intl J. Multiphase Flow 79, 144–158.CrossRefGoogle 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
Weiland, R. H., Fessas, Y. P. & Ramarao, B. V. 1984 On instabilities arising during sedimentation of two-component mixtures of solids. J. Fluid Mech. 142, 383–389.Google Scholar
Wood, A., Hwang, W. & Eaton, J. 2005 Preferential concentration of particles in homogeneous and isotropic turbulence. Intl J. Multiphase Flow 31 (10–11), 1220–1230.Google Scholar
Yeung, P. K. & Pope, S. 1988 An algorithm for tracking fluid particles in numerical simulations of homogeneous turbulent. J. Comput. Phys. 79, 373–416.Google Scholar
Yoshimoto, H. & Goto, S. 2007 Self-similar clustering of inertial particles in homogeneous turbulence. J. Fluid Mech. 577, 275–286.Google Scholar
Zamansky, R., Coletti, F., Massot, M. & Mani, A. 2014 Radiation induces turbulence in particle-laden fluids. Phys. Fluids 26 (7), 071701.Google Scholar
Zonta, F., Marchioli, C. & Soldati, A. 2008 Direct numerical simulation of turbulent heat transfer modulation in micro-dispersed channel flow. Acta Mechanica 195 (1–4), 305–326.Google Scholar