Hostname: page-component-8448b6f56d-wq2xx Total loading time: 0 Render date: 2024-04-24T20:54:55.380Z Has data issue: false hasContentIssue false
  • English
  • Français

Pseudo-turbulent heat flux and average gas–phase conduction during gas–solid heat transfer: flow past random fixed particle assemblies

Published online by Cambridge University Press:  01 June 2016

Bo Sun ,
Sudheer Tenneti ,
Shankar Subramaniam  and
Donald L. Koch
Bo Sun
Affiliation:
Department of Mechanical Engineering, CoMFRE: Multiphase Flow Research and Education, Iowa State University, Ames, IA 50011, USA
Sudheer Tenneti
Affiliation:
Department of Mechanical Engineering, CoMFRE: Multiphase Flow Research and Education, Iowa State University, Ames, IA 50011, USA
Shankar Subramaniam*
Affiliation:
Department of Mechanical Engineering, CoMFRE: Multiphase Flow Research and Education, Iowa State University, Ames, IA 50011, USA
Donald L. Koch
Affiliation:
Department of Chemical and Biomolecular Engineering, Cornell University, Ithaca, NY 14853, USA
*
†Email address for correspondence: shankar@iastate.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

Fluctuations in the gas-phase velocity can contribute significantly to the total gas-phase kinetic energy even in laminar gas–solid flows as shown by Mehrabadi et al. (J. Fluid Mech., vol. 770, 2015, pp. 210–246), and these pseudo-turbulent fluctuations can also enhance heat transfer in gas–solid flow. In this work, the pseudo-turbulent heat flux arising from temperature–velocity covariance, and average fluid-phase conduction during convective heat transfer in a gas–solid flow are quantified and modelled over a wide range of mean slip Reynolds number and solid volume fraction using particle-resolved direct numerical simulations (PR-DNS) of steady flow through a random assembly of fixed isothermal monodisperse spherical particles. A thermal self-similarity condition on the local excess temperature developed by Tenneti et al. (Intl J. Heat Mass Transfer, vol. 58, 2013, pp. 471–479) is used to guarantee thermally fully developed flow. The average gas–solid heat transfer rate for this flow has been reported elsewhere by Sun et al. (Intl J. Heat Mass Transfer, vol. 86, 2015, pp. 898–913). Although the mean velocity field is homogeneous, the mean temperature field in this thermally fully developed flow is inhomogeneous in the streamwise coordinate. An exponential decay model for the average bulk fluid temperature is proposed. The pseudo-turbulent heat flux that is usually neglected in two-fluid models of the average fluid temperature equation is computed using PR-DNS data. It is found that the transport term in the average fluid temperature equation corresponding to the pseudo-turbulent heat flux is significant when compared to the average gas–solid heat transfer over a significant range of solid volume fraction and mean slip Reynolds number that was simulated. For this flow set-up a gradient-diffusion model for the pseudo-turbulent heat flux is found to perform well. The Péclet number dependence of the effective thermal diffusivity implied by this model is explained using a scaling analysis. Axial conduction in the fluid phase, which is often neglected in existing one-dimensional models, is also quantified. As expected, it is found to be important only for low Péclet number flows. Using the exponential decay model for the average bulk fluid temperature, a model for average axial conduction is developed that verifies standard assumptions in the literature. These models can be used in two-fluid simulations of heat transfer in fixed beds. A budget analysis of the mean fluid temperature equation provides insight into the variation of the relative magnitude of the various terms over the parameter space.

JFM classification

Convection: Convection Multiphase and Particle-laden Flows: Fluidized beds Multiphase and Particle-laden Flows: Multiphase and Particle-laden Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 798 , 10 July 2016 , pp. 299 - 349
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.)

Footnotes

‡

Present address: CD-Adapco, Lebanon, NH 03766, USA

References

Abanades, J. C., Anthony, E. J., Lu, D. Y., Salvador, C. & Alvarez, D. 2004 Capture of CO2 from combustion gases in a fluidized bed of CaO. Environ. Energy Engng 50 (7), 1614–1622.Google Scholar
Acrivos, A., Hinch, E. J. & Jeffrey, D. J. 1980 Heat transfer to a slowly moving fluid from a dilute fixed bed of heated spheres. J. Fluid Mech. 101 (2), 403–421.Google Scholar
Adrian, R. J. 1991 Particle-imaging techniques for experimental fluid mechanics. Annu. Rev. Fluid Mech. 23 (1), 261–304.CrossRefGoogle Scholar
Adrian, R. J. 2005 Twenty years of particle image velocimetry. Exp. Fluids 39 (2), 159–169.Google Scholar
Anderson, T. B. & Jackson, R. 1967 A fluid mechanical description of fluidized beds. Ind. Engng Chem. Fundam. 6, 527–539.Google Scholar
Beetstra, R., van der Hoef, M. A. & Kuipers, J. A. M. 2007 Drag force of intermediate Reynolds number flows past mono- and bidisperse- arrays of spheres. AIChE J. 53, 489.Google Scholar
Bekri, S., Thovert, J. F. & Adler, P. M. 1995 Dissolution of porous media. Chem. Engng Sci. 50 (17), 2765–2791.Google Scholar
Benyahia, S., Syamlal, M. & O’Brien, T. J.2012 Summary of MFIX Equations 2012-1. Tech. Rep.Google Scholar
Bird, R. B., Stewart, W. E. & Lightfoot, E. N. 2002 Transport Phenomena, 2nd edn. Wiley.Google Scholar
Brenner, H. 1980 Dispersion resulting from flow through spatially periodic porous media. Phil. Trans. R. Soc. Lond. A 297 (1430), 81–133.Google Scholar
Brenner, H. & Gaydos, L. J. 1977 The constrained Brownian movement of spherical particles in cylindrical pores of comparable radius: models of the diffusive and convective transport of solute molecules in membranes and porous media. J. Colloid Interface Sci. 58 (2), 312–356.Google Scholar
Brown, R. C. 2011 Thermochemical Processing of Biomass: Conversion into Fuels, Chemicals and Power. Wiley.Google Scholar
Capuani, F., Frenkel, D. & Lowe, C. P. 2003 Velocity fluctuations and dispersion in a simple porous medium. Phys. Rev. E 67 (5), 056306.Google Scholar
Carbonell, R. G. & Whitaker, S. 1983 Dispersion in pulsed systems-II: theoretical developments for passive dispersion in porous media. Chem. Engng Sci. 38 (11), 1795–1802.Google Scholar
Crimaldi, J. P. 2008 Planar laser induced fluorescence in aqueous flows. Exp. Fluids 44 (6), 851–863.Google Scholar
Deen, N. G., Kreibitzsch, S. H. L., van der Hoef, M. A. & Kuipers, J. A. M. 2012 Direct numerical simulation of flow and heat transfer in dense fluid-particle system. Chem. Engng Sci. 81, 329–344.CrossRefGoogle Scholar
Deen, N. G., Peters, E. A. J. F., Padding, J. T. & Kuipers, J. A. M. 2014 Review of direct numerical simulation of fluid-particle mass, momentum and heat transfer in dense gas–solid flows. Chem. Engng Sci. 116, 710–724.Google Scholar
Delgado, J. M. P. Q. 2006 A critical review of dispersion in packed beds. Heat Mass Transfer 42 (4), 279–310.Google Scholar
Drew, D. A. & Passman, S. L. 1998 Theory of Multicomponent Fluids. Springer.Google Scholar
Edwards, D. A., Shapiro, M., Brenner, H. & Shapira, M. 1991 Dispersion of inert solutes in spatially periodic, two-dimensional model porous media. Trans. Porous Med. 6 (4), 337–358.Google Scholar
Eidsath, A., Carbonell, R. G., Whitaker, S. & Herrmann, L. R. 1983 Dispersion in pulsed systems-III: comparison between theory and experiments for packed beds. Chem. Engng Sci. 38 (11), 1803–1816.Google Scholar
Feng, Z. G. & Michaelides, E. E. 2009 Heat transfer in particulate flows with direct numerical simulation (DNS). Intl J. Heat Mass Transfer 52, 777–786.CrossRefGoogle Scholar
Fox, R. O. 2003 Computational Models for Turbulent Reacting Flows. Cambridge University Press.Google Scholar
Garg, R.2009 Modeling and simulation of two-phase flows. PhD thesis, Iowa State University.Google Scholar
Garg, R., Tenneti, S., Mohd-Yusof, J. & Subramaniam, S. 2010 Direct numerical simulation of gas–solid flow based on the immersed boundary method. In Computational Gas–solid Flows and Reacting Systems: Theory, Methods and Practice (ed. Pannala, S., Syamlal, M. & O’Brien, T. J.), IGI Global.Google Scholar
Gunn, D. J. & Desouza, J. F. C. 1974 Heat-transfer and axial dispersion in packed-beds. Chem. Engng Sci. 29, 1363–1371.Google Scholar
Haeri, S. & Shrimpton, J. S. 2013 A new implicit fictitious domain method for the simulation of flow in complex geometries with heat transfer. J. Comput. Phys. 237, 21–45.Google Scholar
Halvorsen, B., Guenther, C. & O’Brien, T. J. 2003 CFD calculations for scaling of a bubbling fluidized bed. In Proceedings of the AIChE Annual Meeting, pp. 16–21.Google Scholar
Handley, D. & Heggs, P. J. 1968 Momentum and heat transfer mechanisms in regular shaped packings. AIAA J. 46, 251–264.Google Scholar
Hill, R. J., Koch, D. L. & Ladd, A. J. C. 2001a The first effects of fluid inertia on flows in ordered and random arrays of spheres. J. Fluid Mech. 448, 213–241.Google Scholar
Hill, R. J., Koch, D. L. & Ladd, A. J. C. 2001b Moderate Reynolds number flows in ordered and random arrays of spheres. J. Fluid Mech. 448, 243–278.Google Scholar
van der Hoef, M. A., Beetstra, R. & Kuipers, J. A. M. 2005 Lattice-Boltzmann simulations of low-Reynolds-number flow past mono- and bidisperse arrays of sphere: results for the permeability and drag force. J. Fluid Mech. 528, 233–254.Google Scholar
Hrenya, C. & Morris, A.2014 Pachinko revisited: predicting granular flows and their heat transfer. In Proceedings of 2014 American Institute of Chemical Engineers Annual Meeting.Google Scholar
Incropera, F. P., Dewitt, D. P., Bergman, T. L. & Lavine, A. S. 2006 Fundamentals of Heat and Mass Transfer, 6th edn. Wiley.Google Scholar
Jeong, N. & Choi, D. H. 2011 Estimation of the thermal dispersion in a porous medium of complex structures using a lattice Boltzmann method. Intl J. Heat Mass Transfer 54 (19), 4389–4399.Google Scholar
Kashiwa, B. A. & Gaffney, E. S.2003 Design basis for CFDLib. Tech. Rep. LA-UR-03-1295. Los Alamos National Lab.Google Scholar
Kaviany, M. 2012 Principles of Heat Transfer in Porous Media. Springer.Google Scholar
Koch, D. L. 1993 Hydrodynamic diffusion in dilute sedimenting suspensions at moderate Reynolds numbers. Phys. Fluids A 5 (5), 1143–1155.Google Scholar
Koch, D. L. & Brady, J. F. 1985 Dispersion in fixed beds. J. Fluid Mech. 154, 399–427.Google Scholar
Koch, D. L. & Brady, J. F. 1987a A non-local description of advection–diffusion with application to dispersion in porous media. J. Fluid Mech. 180, 387–403.Google Scholar
Koch, D. L. & Brady, J. F. 1987b Nonlocal dispersion in porous media: nonmechanical effects. Chem. Engng Sci. 42 (6), 1377–1392.Google Scholar
Kunii, D. & Smith, J. M. 1961 Heat transfer characteristics of porous rocks. 2. Thermal conductivities of unconsolidated particles with flowing fluids. AIChE J. 7, 29–34.Google Scholar
Kuwahara, F., Nakayama, A. & Koyama, H. 1996 A numerical study of thermal dispersion in porous media. Trans. ASME J. Heat Transfer 118 (3), 756–761.Google Scholar
Littman, H., Barile, R. G. & Pulsifer, A. H. 1968 Gas-particle heat transfer coefficients in packed beds at low Reynolds numbers. Ind. Engng Chem. Fundam. 7, 554.Google Scholar
Lowe, C. P. & Frenkel, D. 1996 Do hydrodynamic dispersion coefficients exist? Phys. Rev. Lett. 77 (22), 4552–4555.Google Scholar
Maier, R. S., Kroll, D. M., Bernard, R. S., Howington, S. E., Peters, J. F. & Davis, H. T. 2000 Pore-scale simulation of dispersion. Phys. Fluids 12 (8), 2065–2079.Google Scholar
Maier, R. S., Kroll, D. M., Bernard, R. S., Howington, S. E., Peters, J. F. & Davis, H. T. 2003 Hydrodynamic dispersion in confined packed beds. Phys. Fluids 15 (12), 3795–3815.Google Scholar
Manz, B., Gladden, L. F. & Warren, P. B. 1999 Flow and dispersion in porous media: lattice-Boltzmann and NMR studies. AIChE J. 45 (9), 1845–1854.Google Scholar
Mehrabadi, M., Tenneti, S. & Subramaniam, S. 2015 Pseudo-turbulent gas-phase velocity fluctuations in homogeneous gas–solid flow: fixed particle assemblies and freely evolving suspensions. J. Fluid Mech. 770, 210–246.Google Scholar
Mostaghimi, P., Bijeljic, B. & Blunt, M. 2012 Simulation of flow and dispersion on pore-space images. SPE J. 17 (4), 1–131.Google Scholar
Özgümüş, T., Mobedi, M., Özkol, Ü. & Nakayama, A. 2013 Thermal dispersion in porous media-a review on the experimental studies for packed beds. Appl. Mech. Rev. 65 (3), 031001.Google Scholar
Pedras, M. H. J. & de Lemos, M. J. S. 2008 Thermal dispersion in porous media as a function of the solid–fluid conductivity ratio. Intl J. Heat Mass Transfer 51 (21), 5359–5367.Google Scholar
Pope, S. B. 1998 The vanishing effect of molecular diffusivity on turbulent dispersion: implications for turbulent mixing and the scalar flux. J. Fluid Mech. 359, 299–312.Google Scholar
Shen, J., Kaguei, S. & Wakao, N. 1981 Measurements of particle-to-gas heat-transfer coefficients from one-shot thermal responses in packed-beds. Chem. Engng Sci. 36, 1283–1286.Google Scholar
Shen, L., Zheng, M., Xiao, J. & Xiao, R. 2008 A mechanistic investigation of a calcium-based oxygen carrier for chemical looping combustion. Combust. Flame 154 (3), 489–506.Google Scholar
Sirivat, A. & Warhaft, Z. 1983 The effect of a passive cross-stream temperature gradient on the evolution of temperature variance and heat flux in grid turbulence. J. Fluid Mech. 128, 323–346.Google Scholar
Subramaniam, S. & Pope, S. B. 1998 A mixing model for turbulent reactive flows based on euclidean minimum spanning trees. Combust. Flame 115, 487–514.Google Scholar
Sun, B., Tenneti, S. & Subramaniam, S. 2015 Modeling average gas–solid heat transfer using particle-resolved direct numerical simulation. Intl J. Heat Mass Transfer 86, 898–913.Google Scholar
Sun, J., Battaglia, F. & Subramaniam, S. 2007 Hybrid two-fluid DEM simulation of gas–solid fluidized beds. Trans. ASME J. Fluids Engng 129 (11), 1394–1403.Google Scholar
Syamlal, M., Rogers, W. & O’Brien, T. J.1993 MFIX Documentation: theory guide. Tech. Rep. National Energy Technology Laboratory, Department of Energy.Google Scholar
Tavassoli, H., Kreibitzsch, S. H. L., van der Hopf, 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
Tenneti, S.2013 Momentum, energy and scalar transport in polydisperse gas–solid flows using particle-resolved direct numerical simulations. PhD thesis, Iowa State University.Google Scholar
Tenneti, S., Garg, R., Hrenya, C. M., Fox, R. O. & Subramaniam, S. 2010 Direct numerical simulation of gas–solid suspensions at moderate Reynolds number: quantifying the coupling between hydrodynamic force and particle velocity fluctuations. Powder Technol. 203, 57–69.Google Scholar
Tenneti, S., Garg, R. & Subramaniam, S. 2011 Drag law for monodisperse gas-golid systems using particle-resolved direct numerical simulation of flow past fixed assembiles of spheres. Intl J. Multiphase Flow 37 (9), 1072–1092.Google Scholar
Tenneti, S. & Subramaniam, S. 2014 Particle-resolved direct numerical simulation for gas–solid flow model development. Annu. Rev. Fluid Mech. 46, 199–230.Google Scholar
Tenneti, S., Sun, B., Garg, R. & Subramaniam, S. 2013 Role of fluid heating in dense gas–solid flow as revealed by particle-resolved direct numerical simulation. Intl J. Heat Mass Transfer 58, 471–479.Google Scholar
Tyagi, M. & Acharya, S. 2005 Large eddy simulations of flow and heat transfer in rotating ribbed duct flows. Trans. ASME J. Heat Transfer 127, 486–498.Google Scholar
Van Cruyningen, I., Lozano, A. & Hanson, R. K. 1990 Quantitative imaging of concentration by planar laser-induced fluorescence. Exp. Fluids 10 (1), 41–49.Google Scholar
Wakao, N. & Kaguei, S. 1982 Heat and Mass Transfer in Packed Beds, Topics in Chemical Engineering, vol. 1. Gordon and Breach Science.Google Scholar
Wakao, N., Kaguei, S. & Funazkri, T. 1979 Effect of fluid dispersion coefficients on particle-to-fluid heat transfer coefficients in packed beds. Chem. Engng Sci. 34, 325–336.Google Scholar
Wakao, N., Tanisho, S. & Shiozawa, B. 1977 Thermal response of packed beds at low Reynolds numbers. Heat Transfer Japan Res. 6 (4), 56–60.Google Scholar
Whitaker, S. 1999 The Method of Volume Averaging. Springer.Google Scholar
White, B. L. & Nepf, H. M. 2003 Scalar transport in random cylinder arrays at moderate Reynolds number. J. Fluid Mech. 487, 43–79.Google Scholar
Xu, Y. & Subramaniam, S. 2010 Effect of particle clusters on carrier flow turbulence: a direct numerical simulation study. Flow Turbul. Combust. 85, 735–761.Google Scholar
Yagi, S., Kunii, D. & Wakao, N. 1960 Studies on axial effective thermal conductivities in packed beds. AIChE J. 6 (4), 543–546.Google Scholar
Yi, C.-K., Jo, S.-H., Seo, Y., Lee, J.-B. & Ryu, C.-K. 2007 Continuous operation of the potassium-based dry sorbent CO2 capture process with two fluidized-bed reactors. Intl J. Greenh. Gas Control 1 (1), 31–36.Google Scholar
Yin, X. & Sundaresan, S. 2009 Drag law for bidisperse gas–solid suspensions containing equally sized spheres. Ind. Engng Chem. Res. 48, 227–241.Google Scholar
Yu, Z., Shao, X. & Wachs, A. 2006 A fictitious domain method for particulate flows with heat transfer. J. Comput. Phys. 217, 424–452.Google Scholar