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Heat transfer in laminar Couette flow laden with rigid spherical particles

Published online by Cambridge University Press:  17 November 2017

M. Niazi Ardekani Open the ORCID record for M. Niazi Ardekani [Opens in a new window] ,
O. Abouali Open the ORCID record for O. Abouali [Opens in a new window] ,
F. Picano  and
L. Brandt
M. Niazi Ardekani
Affiliation:
Linné Flow Centre and SeRC (Swedish e-Science Research Centre), KTH Mechanics, S-100 44 Stockholm, Sweden
O. Abouali*
Affiliation:
Linné Flow Centre and SeRC (Swedish e-Science Research Centre), KTH Mechanics, S-100 44 Stockholm, Sweden School of Mechanical Engineering, Shiraz University, Mollasadra Street, Shiraz 71348-51154, Iran
F. Picano
Affiliation:
Department of Industrial Engineering, University of Padova, Via Venezia 1, 35131 Padua, Italy
L. Brandt
Affiliation:
Linné Flow Centre and SeRC (Swedish e-Science Research Centre), KTH Mechanics, S-100 44 Stockholm, Sweden
*
†Email address for correspondence: [email protected]
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Abstract

We study heat transfer in plane Couette flow laden with rigid spherical particles by means of direct numerical simulations. In the simulations we use a direct-forcing immersed boundary method to account for the dispersed phase together with a volume-of-fluid approach to solve the temperature field inside and outside the particles. We focus on the variation of the heat transfer with the particle Reynolds number, total volume fraction (number of particles) and the ratio between the particle and fluid thermal diffusivity, quantified in terms of an effective suspension diffusivity. We show that, when inertia at the particle scale is negligible, the heat transfer increases with respect to the unladen case following an empirical correlation recently proposed in the literature. In addition, an average composite diffusivity can be used to approximate the effective diffusivity of the suspension in the inertialess regime when varying the molecular diffusion in the two phases. At finite particle inertia, however, the heat transfer increase is significantly larger, smoothly saturating at higher volume fractions. By phase-ensemble-averaging we identify the different mechanisms contributing to the total heat transfer and show that the increase of the effective conductivity observed at finite inertia is due to the increase of the transport associated with fluid and particle velocity. We also show that the contribution of the heat conduction in the solid phase to the total wall-normal heat flux reduces when increasing the particle Reynolds number, so that particles of low thermal diffusivity weakly alter the total heat flux in the suspension at finite particle Reynolds numbers. On the other hand, a higher particle thermal diffusivity significantly increases the total heat transfer.

JFM classification

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 834 , 10 January 2018 , pp. 308 - 334
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Copyright
© 2017 Cambridge University Press 

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References

Ahuja, A. S. 1975 Augmentation of heat transport in laminar flow of polystyrene suspensions. I. Experiments and results. J. Appl. Phys. 46 (8), 3408–3416.CrossRefGoogle Scholar
Ardekani, M. N., Costa, P., Breugem, W. P. & Brandt, L. 2016 Numerical study of the sedimentation of spheroidal particles. Intl J. Multiphase Flow 87, 16–34.Google Scholar
Breedveld, V., Van Den Ende, D., Bosscher, M., Jongschaap, R. J. J. & Mellema, J. 2002 Measurement of the full shear-induced self-diffusion tensor of noncolloidal suspensions. J. Chem. Phys. 116 (23), 10529–10535.CrossRefGoogle Scholar
Brenner, H. 1961 The slow motion of a sphere through a viscous fluid towards a plane surface. Chem. Engng Sci. 16 (3–4), 242–251.CrossRefGoogle Scholar
Breugem, W.-P. 2012 A second-order accurate immersed boundary method for fully resolved simulations of particle-laden flows. J. Comput. Phys. 231 (13), 4469–4498.Google Scholar
Chung, Y. C. & Leal, L. G. 1982 An experimental study of the effective thermal conductivity of a sheared suspension of rigid spheres. Intl J. Multiphase Flow 8 (6), 605–625.CrossRefGoogle Scholar
Costa, P., Boersma, B. J., Westerweel, J. & Breugem, W. P. 2015 Collision model for fully resolved simulations of flows laden with finite-size particles. Phys. Rev. E 92 (5), 053012.Google ScholarPubMed
Dan, C. & Wachs, A. 2010 Direct numerical simulation of particulate flow with heat transfer. Intl J. Heat Fluid Flow 31 (6), 1050–1057.CrossRefGoogle Scholar
Feng, Z. G. & Michaelides, E. E. 2008 Inclusion of heat transfer computations for particle laden flows. Phys. Fluids 20 (4), 040604.CrossRefGoogle Scholar
Feng, Z. G. & Michaelides, E. E. 2009 Heat transfer in particulate flows with direct numerical simulation (DNS). Intl J. Heat Mass Transfer 52 (3), 777–786.CrossRefGoogle Scholar
Fornari, W., Formenti, A., Picano, F. & Brandt, L. 2016a The effect of particle density in turbulent channel flow laden with finite size particles in semi-dilute conditions. Phys. Fluids 28, 033301.Google Scholar
Fornari, W., Picano, F. & Brandt, L. 2016b Sedimentation of finite-size spheres in quiescent and turbulent environments. J. Fluid Mech. 788, 640–669.CrossRefGoogle Scholar
Hashemi, Z., Abouali, O. & Kamali, R. 2014 Three dimensional thermal lattice Boltzmann simulation of heating/cooling spheres falling in a Newtonian liquid. Intl J. Therm. Sci. 82, 23–33.CrossRefGoogle Scholar
Hirt, C. W. & Nichols, B. D. 1981 Volume of fluid (VoF) method for the dynamics of free boundaries. J. Comput. Phys. 39 (1), 201–225.CrossRefGoogle Scholar
Incropera, F. P., Lavine, A. S., Bergman, T. L. & Dewitt, D. P. 2007 Fundamentals of Heat and Mass Transfer. Wiley.Google Scholar
Kempe, T. & Fröhlich, J. 2012 An improved immersed boundary method with direct forcing for the simulation of particle laden flows. J. Comput. Phys. 231 (9), 3663–3684.CrossRefGoogle Scholar
Ladd, A. J. C. 1994a Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 1. Theoretical foundation. J. Fluid Mech. 271, 285–309.Google Scholar
Ladd, A. J. C. 1994b Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 2. Numerical results. J. Fluid Mech. 271, 311–339.CrossRefGoogle Scholar
Lambert, R. A., Picano, F., Breugem, W.-P. & Brandt, L. 2013 Active suspensions in thin films: nutrient uptake and swimmer motion. J. Fluid Mech. 733, 528–557.Google Scholar
Lashgari, I., Picano, F., Breugem, W. P. & Brandt, L. 2014 Laminar, turbulent, and inertial shear-thickening regimes in channel flow of neutrally buoyant particle suspensions. Phys. Rev. Lett. 113 (25), 254502.CrossRefGoogle ScholarPubMed
Lashgari, I., Picano, F., Breugem, W. P. & Brandt, L. 2016 Channel flow of rigid sphere suspensions: particle dynamics in the inertial regime. Intl J. Multiphase Flow 78, 12–24.Google Scholar
Leal, L. G. 1973 On the effective conductivity of a dilute suspension of spherical drops in the limit of low particle Péclet number. Chem. Engng Commun. 1 (1), 21–31.Google Scholar
Madanshetty, S. I, Nadim, A. & Stone, H. A. 1996 Experimental measurement of shear-induced diffusion in suspensions using long time data. Phys. Fluids 8 (8), 2011–2018.Google Scholar
Marchioro, M., Tanksley, M. & Prosperetti, A. 1999 Mixture pressure and stress in disperse two-phase flow. Intl J. Multiphase Flow 25 (6), 1395–1429.CrossRefGoogle Scholar
Maxwell, J. C. 1904 A Treatise on Electricity and Magnetism, 3rd edn, vol. 1. Clarendon.Google Scholar
Metzger, B., Rahli, O. & Yin, X. 2013 Heat transfer across sheared suspensions: role of the shear-induced diffusion. J. Fluid Mech. 724, 527–552.Google Scholar
Nielsen, L. E. 1974 The thermal and electrical conductivity of two-phase systems. Ind. Engng Chem. Fundam. 13 (1), 17–20.CrossRefGoogle Scholar
Picano, F., Breugem, W. P. & Brandt, L. 2015 Turbulent channel flow of dense suspensions of neutrally buoyant spheres. J. Fluid Mech. 764, 463–487.CrossRefGoogle Scholar
Picano, F., Breugem, W. P., Mitra, D. & Brandt, L. 2013 Shear thickening in non-Brownian suspensions: an excluded volume effect. Phys. Rev. Lett. 111 (9), 098302.CrossRefGoogle ScholarPubMed
Pietrak, K. & Wisniewski, T. S. 2015 A review of models for effective thermal conductivity of composite materials. J. Power Technol. 95 (1), 14–24.Google Scholar
Roma, A. M., Peskin, C. S. & Berger, M. J. 1999 An adaptive version of the immersed boundary method. J. Comput. Phys. 153 (2), 509–534.Google Scholar
Shin, S. & Lee, S. H. 2000 Thermal conductivity of suspensions in shear flow fields. Intl J. Heat Mass Transfer 43 (23), 4275–4284.CrossRefGoogle Scholar
Sohn, C. W. & Chen, M. M. 1981 Microconvective thermal conductivity in disperse two-phase mixtures as observed in a low velocity Couette flow experiment. Trans. ASME J. Heat Transfer 103 (1), 47–51.CrossRefGoogle Scholar
Souzy, M., Yin, X., Villermaux, E., Abid, C. & Metzger, B. 2015 Super-diffusion in sheared suspensions. Phys. Fluids 27 (4), 041705.Google Scholar
Stickel, J. J. & Powell, R. L. 2005 Fluid mechanics and rheology of dense suspensions. Annu. Rev. Fluid Mech. 37, 129–149.CrossRefGoogle Scholar
Ström, H. & Sasic, S. 2013 A multiphase DNS approach for handling solid particles motion with heat transfer. Intl J. Multiphase Flow 53, 75–87.Google Scholar
Sun, B., Tenneti, S., Subramaniam, S. & Koch, D. L. 2016 Pseudo-turbulent heat flux and average gas-phase conduction during gas–solid heat transfer: flow past random fixed particle assemblies. J. Fluid Mech. 798, 299–349.CrossRefGoogle Scholar
Tavassoli, H, Kriebitzsch, S. H. L., van der Hoef, M. A., Peters, E. A. J. F. & Kuipers, J. A. M. 2013 Direct numerical simulation of particulate flow with heat transfer. Intl J. Multiphase Flow 57, 29–37.CrossRefGoogle Scholar
Uhlmann, M. 2005 An immersed boundary method with direct forcing for simulation of particulate flow. J. Comput. Phys. 209 (2), 448–476.Google Scholar
Wang, L., Koch, D. L., Yin, X. & Cohen, C. 2009 Hydrodynamic diffusion and mass transfer across a sheared suspension of neutrally buoyant spheres. Phys. Fluids 21 (3), 033303.CrossRefGoogle Scholar
Zhang, Q. & Prosperetti, A. 2010 Physics-based analysis of the hydrodynamic stress in a fluid–particle system. Phys. Fluids 22 (3), 033306.Google Scholar
Zydney, A. L & Colton, C. K 1988 Augmented solute transport in the shear flow of a concentrated suspension. Physico-Chem. Hydrodyn. 10 (1), 77–96.Google Scholar