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Heat and momentum transfer to a particle in a laminar boundary layer

Published online by Cambridge University Press:  24 February 2020

Aaron M. Lattanzi Open the ORCID record for Aaron M. Lattanzi [Opens in a new window] ,
Xiaolong Yin  and
Christine M. Hrenya
Aaron M. Lattanzi
Affiliation:
University of Colorado at Boulder, Department of Chemical and Biological Engineering, Boulder, CO, USA
Xiaolong Yin
Affiliation:
Colorado School of Mines, Petroleum Engineering, Golden, CO, USA
Christine M. Hrenya*
Affiliation:
University of Colorado at Boulder, Department of Chemical and Biological Engineering, Boulder, CO, USA
*
†Email address for correspondence: [email protected]
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Abstract

Bounding walls or immersed surfaces are utilized in many industrial systems as the primary thermal source to heat a gas–solids mixture. Previous efforts to resolve the solids’ heat transfer near a boundary involve the extension of unbounded convection correlations into the near-wall region in conjunction with particle-scale theories for indirect conduction. Moreover, unbounded drag correlations are utilized in the near-wall region (without modification) to resolve the force exerted on a solid particle by the fluid. We rigorously test unbounded correlations and indirect conduction theory against outputs from direct numerical simulation of laminar flow past a hot plate and a static, cold particle. Here, local variables are utilized for consistency with unresolved computational fluid dynamics discrete element methods and lead to new unbounded correlations that are self-similar to those obtained with free-stream variables. The new drag correlation with local fluid velocity captures the drag force in both the unbounded system as well as the near-wall region while the classic, unbounded drag correlation with free-stream fluid velocity dramatically over-predicts the drag force in the near-wall region. Similarly, classic, unbounded convection correlations are found to under-predict the heat transfer occurring in the near-wall region. Inclusion of indirect conduction, in addition to unbounded convection, performs markedly better. To account for boundary effects, a new Nusselt correlation is developed for the heat transfer in excess of local, unbounded convection. The excess wall Nusselt number depends solely on the dimensionless particle–wall separation distance and asymptotically decays to zero for large particle–wall separation distances, seaming together the unbounded and near-wall regions.

JFM classification

Multiphase and Particle-laden Flows: Multiphase flow Granular media: Granular media
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 889 , 25 April 2020 , A6
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

Acrivos, A. & Taylor, T. D. 1962 Heat and mass transfer from single spheres in Stokes flow. Phys. Fluids 5 (4), 387–394.CrossRefGoogle Scholar
Anderson, T. B. & Jackson, R. 1967 Fluid mechanical description of fluidized beds. Equations of motion. Ind. Engng Chem. Fundam. 6 (4), 527–539.CrossRefGoogle Scholar
Ansart, R., García-Triñanes, P., Boissière, B., Benoit, H., Seville, J. P. K. & Simonin, O. 2017 Dense gas-particle suspension upward flow used as heat transfer fluid in solar receiver: PEPT experiments and 3d numerical simulations. Powder Technol. 307, 25–36.CrossRefGoogle Scholar
Bagchi, P. & Balachandar, S. 2002 Shear versus vortex-induced lift force on a rigid sphere at moderate Re. J. Fluid Mech. 473, 379–388.CrossRefGoogle Scholar
Bagchi, P., Ha, M. Y. & Balachandar, S. 2000 Direct numerical simulation of flow and heat transfer from a sphere in a uniform cross-flow. Trans. ASME J. Fluids Engng 123 (2), 347–358.CrossRefGoogle Scholar
Balachandar, S., Liu, K. & Lakhote, M. 2019 Self-induced velocity correction for improved drag estimation in Euler–Lagrange point-particle simulations. J. Comput. Phys. 376, 160–185.CrossRefGoogle Scholar
Batchelor, G. K. & O’Brien, R. W. 1977 Thermal or electrical conduction through a granular material. Proc. R. Soc. Lond. A 355 (1682), 313–333.Google Scholar
Bongo Njeng, A. S., Vitu, S., Clausse, M., Dirion, J.-L. & Debacq, M. 2018 Wall-to-solid heat transfer coefficient in flighted rotary kilns: experimental determination and modeling. Exp. Therm. Fluid Sci. 91, 197–213.CrossRefGoogle Scholar
Capecelatro, J. & Desjardins, O. 2013 An Euler–Lagrange strategy for simulating particle-laden flows. J. Comput. Phys. 238, 1–31.CrossRefGoogle Scholar
Chaudhuri, B., Muzzio, F. J. & Tomassone, M. S. 2006 Modeling of heat transfer in granular flow in rotating vessels. Chem. Engng Sci. 61 (19), 6348–6360.CrossRefGoogle Scholar
Cheng, G. J., Yu, A. B. & Zulli, P. 1999 Evaluation of effective thermal conductivity from the structure of a packed bed. Chem. Engng Sci. 54 (19), 4199–4209.CrossRefGoogle Scholar
Chun, B. & Ladd, A. J. C. 2007 Interpolated boundary condition for lattice Boltzmann simulations of flows in narrow gaps. Phys. Rev. E 75 (6), 066705.Google ScholarPubMed
Cong, T. N., He, Y., Chen, H., Ding, Y. & Wen, D. 2007 Heat transfer of gas–solid two-phase mixtures flowing through a packed bed under constant wall heat flux conditions. Chem. Engng J. 130 (1), 1–10.CrossRefGoogle Scholar
Cooper, M. G., Mikic, B. B. & Yovanovich, M. M. 1969 Thermal contact conductance. Intl J. Heat Mass Transfer 12 (3), 279–300.CrossRefGoogle Scholar
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
Deen, N. G., Kriebitzsch, 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 systems. 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.CrossRefGoogle Scholar
Delvosalle, C. & Vanderschuren, J. 1985 Gas-to-particle and particle-to-particle heat transfer in fluidized beds of large particles. Chem. Engng Sci. 40 (5), 769–779.CrossRefGoogle Scholar
Di Maio, F. P., Di Renzo, A. & Trevisan, D. 2009 Comparison of heat transfer models in DEM-CFD simulations of fluidized beds with an immersed probe. Powder Technol. 193 (3), 257–265.CrossRefGoogle Scholar
Feng, Z.-G. & Michaelides, E. E. 2000 A numerical study on the transient heat transfer from a sphere at high Reynolds and Peclet numbers. Intl J. Heat Mass Transfer 43 (2), 219–229.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 (34), 777–786.CrossRefGoogle Scholar
Flamant, G. & Menigault, T. 1987 Combined wall-to-fluidized bed heat transfer. Bubbles and emulsion contributions at high temperature. Intl J. Heat Mass Transfer 30 (9), 1803–1812.CrossRefGoogle Scholar
Gardiner, C. W. 1986 Handbook of Stochastic Methods for Physics, Chemistry, and the Natural Sciences, 2nd edn. Springer.CrossRefGoogle Scholar
Garg, R., Galvin, J., Li, T. & Pannala, S.2012 Documentation of open-source MFIX–DEM software for gas-solids flows. Available at:https://mfix.netl.doe.gov/doc/mfix-archive/mfix_current_documentation/dem_doc_2012-1.pdf.CrossRefGoogle Scholar
Ginzbourg, I. & Adler, P. 1994 Boundary flow condition analysis for the three-dimensional lattice Boltzmann model. J. Phys. II 4 (2), 191–214.Google Scholar
Ginzburg, I. & dHumières, D. 2003 Multireflection boundary conditions for lattice Boltzmann models. Phys. Rev. E 68 (6), 066614.Google ScholarPubMed
Haider, A. & Levenspiel, O. 1989 Drag coefficient and terminal velocity of spherical and nonspherical particles. Powder Technol. 58 (1), 63–70.CrossRefGoogle Scholar
Happel, J. & Brenner, H. 1983 Low Reynolds Number Hydrodynamics: With Special Applications to Particulate Media. Springer Netherlands.Google 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
Ireland, P. J. & Desjardins, O. 2017 Improving particle drag predictions in Euler–Lagrange simulations with two-way coupling. J. Comput. Phys. 338, 405–430.CrossRefGoogle Scholar
Jackson, R. 1997 Locally averaged equations of motion for a mixture of identical spherical particles and a Newtonian fluid. Chem. Engng Sci. 52 (15), 2457–2469.CrossRefGoogle Scholar
Jansen, C. & Krafczyk, M. 2011 Free surface flow simulations on GPGPUs using the LBM. Comput. Maths Applics. 61 (12), 3549–3563.CrossRefGoogle Scholar
Jessee, R.2015 An analytic solution of the thermal boundary layer at the leading edge of a heated semi-infinite flat plate under forced uniform flow. LSU Master’s Theses.Google Scholar
Kravets, B. & Kruggel-Emden, H. 2017 Investigation of local heat transfer in random particle packings by a fully resolved LBM-approach. Powder Technol. 318, 293–305.CrossRefGoogle Scholar
Kruggel-Emden, H., Kravets, B., Suryanarayana, M. K. & Jasevicius, R. 2016 Direct numerical simulation of coupled fluid flow and heat transfer for single particles and particle packings by a LBM-approach. Powder Technol. 294, 236–251.CrossRefGoogle Scholar
Kuipers, J. A. M., Prins, W. & Van Swaaij, W. P. M. 1992 Numerical calculation of wall-to-bed heat-transfer coefficients in gas-fluidized beds. AIChE J. 38 (7), 1079–1091.CrossRefGoogle Scholar
Kurose, R. & Komori, S. 1999 Drag and lift forces on a rotating sphere in a linear shear flow. J. Fluid Mech. 384, 183–206.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.CrossRefGoogle 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
Ladd, A. J. C. & Verberg, R. 2001 Lattice-Boltzmann simulations of particle–fluid suspensions. J. Stat. Phys. 104 (5–6), 1191–1251.CrossRefGoogle Scholar
Lattanzi, A. M. & Hrenya, C. M. 2016 A coupled, multiphase heat flux boundary condition for the discrete element method. Chem. Engng J. 304, 766–773.CrossRefGoogle Scholar
Lattanzi, A. M. & Hrenya, C. M. 2017 Indirect conduction in gas–solids systems: Static versus dynamic effects. AIChE J. 63 (10), 4685–4693.CrossRefGoogle Scholar
Lattanzi, A. M., Yin, X. & Hrenya, C. M. 2019a A fully-developed boundary condition for the random walk particle tracking method. Intl J. Heat Mass Transfer 131, 604–610.CrossRefGoogle Scholar
Lattanzi, A. M., Yin, X. & Hrenya, C. M. 2019b A hybrid lattice Boltzmann – random walk method for heat transfer in gas–solids systems. J. Comput. Phys. 1, 100007.Google Scholar
Martinek, J. & Ma, Z.2014 Granular flow and heat transfer study in a near-blackbody enclosed particle receiver. p. V001T02A012.CrossRefGoogle Scholar
McLaughlin, J. B. 1993 The lift on a small sphere in wall-bounded linear shear flows. J. Fluid Mech. 246, 249–265.CrossRefGoogle Scholar
Mehrabadi, M., Horwitz, J. A. K., Subramaniam, S. & Mani, A. 2018 A direct comparison of particle-resolved and point-particle methods in decaying turbulence. J. Fluid Mech. 850, 336–369.CrossRefGoogle 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.CrossRefGoogle Scholar
Mishra, I., Lattanzi, A., LaMarche, C., Morris, A. & Hrenya, C. 2019 Experimental validation of indirect conduction theory and effect of particle roughness on wall-to-particle heat transfer. AIChE J. 65, e16703.CrossRefGoogle Scholar
Morris, A. B., Ma, Z., Pannala, S. & Hrenya, C. M. 2016 Simulations of heat transfer to solid particles flowing through an array of heated tubes. Solar Energy 130, 101–115.CrossRefGoogle Scholar
Morris, A. B., Pannala, S., Ma, Z. & Hrenya, C. M. 2015 A conductive heat transfer model for particle flows over immersed surfaces. Intl J. Heat Mass Transfer 89, 1277–1289.CrossRefGoogle Scholar
Municchi, F., Goniva, C. & Radl, S. 2016 Highly efficient spatial data filtering in parallel using the opensource library CPPPO. Comput. Phys. Commun. 207, 400–414.CrossRefGoogle Scholar
Municchi, F. & Radl, S. 2017 Consistent closures for Euler–Lagrange models of bi-disperse gas-particle suspensions derived from particle-resolved direct numerical simulations. Intl J. Heat Mass Transfer 111, 171–190.CrossRefGoogle Scholar
Nijemeisland, M. & Dixon, A. G. 2004 CFD study of fluid flow and wall heat transfer in a fixed bed of spheres. AIChE J. 50 (5), 906–921.CrossRefGoogle Scholar
Patil, D. J., Smit, J., van Sint Annaland, M. & Kuipers, J. A. M. 2006 Wall-to-bed heat transfer in gas–solid bubbling fluidized beds. AIChE J. 52 (1), 58–74.CrossRefGoogle Scholar
Radl, S., Municchi, F. & Goniva, C.2016 Near-wall effects for momentum, heat and mass transport in gas-particle suspensions at moderate Reynolds numbers, p. H28.002.Google Scholar
Ranz, W. E. & Marshall, W. R. 1952 Evaporation from drops. Chem. Engng Prog. 48, 141–146.Google Scholar
Richter, A. & Nikrityuk, P. A. 2012 Drag forces and heat transfer coefficients for spherical, cuboidal and ellipsoidal particles in cross flow at sub-critical Reynolds numbers. Intl J. Heat Mass Transfer 55 (4), 1343–1354.CrossRefGoogle Scholar
Rong, D. & Horio, M. 1999 DEM simulation of char combustion in a fluidized bed. In Second International Conference on CFD in the Minerals and Process Industries CSIRO, pp. 65–70. CSIRO.Google Scholar
Saffman, P. G. 1965 The lift on a small sphere in a slow shear flow. J. Fluid Mech. 22 (2), 385–400.CrossRefGoogle Scholar
Salamon, P., Fernandez-Garcia, D. & Gomez-Hernandez, J. J. 2006 A review and numerical assessment of the random walk particle tracking method. J. Contam. Hydrol. 87, 277–305.CrossRefGoogle ScholarPubMed
Schlichting, H. & Gersten, K. 2017 Boundary-Layer Theory, 9th edn. Springer.CrossRefGoogle Scholar
Segre, G. & Silberberg, A. 1962a Behaviour of macroscopic rigid spheres in Poiseuille flow Part 1. Determination of local concentration by statistical analysis of particle passages through crossed light beams. J. Fluid Mech. 14 (1), 115–135.CrossRefGoogle Scholar
Segre, G. & Silberberg, A. 1962b Behaviour of macroscopic rigid spheres in Poiseuille flow Part 2. Experimental results and interpretation. J. Fluid Mech. 14 (1), 136–157.CrossRefGoogle Scholar
Shi, D., Vargas, W. L. & McCarthy, J. J. 2008 Heat transfer in rotary kilns with interstitial gases. Chem. Engng Sci. 63 (18), 4506–4516.CrossRefGoogle Scholar
Syamlal, M. & Gidaspow, D. 1985 Hydrodynamics of fluidization – prediction of wall to bed heat-transfer coefficients. AIChE J. 31 (1), 127–135.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
Tavassoli, H., Peters, E. A. J. F. & Kuipers, J. A. M. 2015 Direct numerical simulation of fluid–particle heat transfer in fixed random arrays of non-spherical particles. Chem. Engng Sci. 129, 42–48.CrossRefGoogle Scholar
Vargas, W. L. & McCarthy, J. J. 2002 Conductivity of granular media with stagnant interstitial fluids via thermal particle dynamics simulation. Intl J. Heat Mass Transfer 45 (24), 4847–4856.CrossRefGoogle Scholar
Wang, L., Koch, D., 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
Wen, C. & Chang, T. 1967 Particle to particle heat transfer in air fluidized beds. In Proceedings of International Symposium on Fluidization, Eindhoven, pp. 491–506.Google Scholar
Whitaker, S. 1972 Forced convection heat transfer correlations for flow in pipes, past flat plates, single cylinders, single spheres, and for flow in packed beds and tube bundles. AIChE J. 18 (2), 361–371.CrossRefGoogle Scholar
White, F. M. 2005 Viscous Fluid Flow, 3rd edn. McGraw-Hill Education.Google Scholar
Yang, Z. 2013 Lattice Boltzmann outflow treatments: convective conditions and others. Comput. Maths Applics. 65 (2), 160–171.CrossRefGoogle Scholar
Yohannes, B., Emady, H., Anderson, K., Paredes, I., Javed, M., Borghard, W., Muzzio, F. J., Glasser, B. J. & Cuitiño, A. M. 2016 Scaling of heat transfer and temperature distribution in granular flows in rotating drums. Phys. Rev. E 94 (4), 042902.Google ScholarPubMed
Zhou, H., Flamant, G. & Gauthier, D. 2004 DEM-LES simulation of coal combustion in a bubbling fluidized bed. Part II: coal combustion at the particle level. Chem. Engng Sci. 59 (20), 4205–4215.CrossRefGoogle Scholar
Zhou, Z. Y., Yu, A. B. & Zulli, P. 2009 Particle scale study of heat transfer in packed and bubbling fluidized beds. AIChE J. 55 (4), 868–884.CrossRefGoogle Scholar