Abstract
Particle-resolved direct numerical simulations of non-isothermal gas–solid flows have been performed and analyzed from microscopic to macroscopic scales. The numerical configuration consists in an assembly of random motionless spherical particles exchanging heat with the surrounding moving fluid throughout the solid surface. Numerical simulations have been carried out using a Lagrangian VOF approach based on fictitious domain framework and penalty methods. The entire numerical approach (numerical solution and post-processing) has first been validated on a single particle through academic test cases of heat transfer by pure diffusion and by forced convection for which analytical solution or empirical correlations are available from the literature. Then, it has been used for simulating gas–solid heat exchanges in dense regimes, fully resolving fluid velocity and temperature evolving within random arrays of fixed particles. Three Reynolds numbers and four solid volume fractions, for unity Prandtl number, have been investigated. Two Nusselt numbers based, respectively, on the fluid temperature and on the bulk (cup-mixing) temperature have been computed and analyzed. Numerical results revealed differences between the two Nusselt numbers for a selected operating point. This outcome shows the inadequacy of the Nusselt number based on the bulk temperature to accurately reproduce the heat transfer rate when an Eulerian–Eulerian approach is used. Finally, a connection between the ratio of the two Nusselt numbers and the fluctuating fluid velocity–temperature correlation in the mean flow direction is pointed out. Based on such a Nusselt number ratio, a model is proposed for it.
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Wakao, N., Kaguei, S., Funazkri, T.: Effect of fluid dispersion coefficients on particle-to-fluid heat transfer coefficients in packed beds: correlation of Nusselt numbers. Chem. Eng. Sci. 34(3), 325 (1979)
Gunn, D.J.: Transfer of heat or mass to particles in fixed and fluidised beds. Int. J. Heat Mass Transf. 21(4), 467 (1978)
Feng, Z.G., Michaelides, E.E.: Heat transfer in particulate flows with Direct Numerical Simulation (DNS). Int. J. Heat Mass Transf. 52(3), 777 (2009)
Deen, N.G., Kriebitzsch, S.H.L., van der Hoef, M.A., Kuipers, J.A.M.: Direct numerical simulation of flow and heat transfer in dense fluid-particle systems. Chem. Eng. Sci. 81, 329 (2012)
Feng, Z.G., Musong, S.G.: Direct numerical simulation of heat and mass transfer of spheres in a fluidized bed. Powder Technol. 262, 62 (2014)
Tavassoli, H., Kriebitzsch, S.H.L., van der Hoef, M.A., Peters, E.A.J.F., Kuipers, J.A.M.: Direct numerical simulation of particulate flow with heat transfer. Int. J. Multiph. Flow 57, 29 (2013)
Uhlmann, M.: An immersed boundary method with direct forcing for the simulation of particulate flows. J. Comput. Phys. 209(2), 448 (2005)
Deen, N.G., Peters, E.A.J.F., Padding, J.T., Kuipers, J.A.M.: Review of direct numerical simulation of fluid-particle mass, momentum and heat transfer in dense gas-solid flows. Chem. Eng. Sci. 116, 710 (2014)
Tenneti, S., Sun, B., Garg, R., Subramaniam, S.: Role of fluid heating in dense gas-solid flow as revealed by particle-resolved direct numerical simulation. Int. J. Heat Mass Transf. 58(1), 471 (2013)
Sun, B., Tenneti, S., Subramaniam, S.: Modeling average gas-solid heat transfer using particle-resolved direct numerical simulation. Int. J. Heat Mass Transf. 86, 898 (2015)
Kruggel-Emden, H., Kravets, B., Suryanarayana, M.K., Jasevicius, R.: Direct numerical simulation of coupled fluid flow and heat transfer for single particles and particle packings by a LBM-approach. Powder Technol. 294, 236 (2016)
Tavassoli, H., Peters, E.A.J.F., Kuipers, J.A.M.: Direct numerical simulation of fluid-particle heat transfer in fixed random arrays of non-spherical particles. Chem. Eng. Sci. 129, 42 (2015)
Municchi, F., Radl, S.: Consistent closures for Euler–Lagrange models of bi-disperse gas-particle suspensions derived from particle-resolved direct numerical simulations. Int. J. Heat Mass Transf. 111, 171 (2017)
Wang, Y., Sierakowski, A.J., Prosperetti, A.: Fully-resolved simulation of particulate flows with particles-fluid heat transfer. J. Comput. Phys. 350, 638 (2017)
Vincent, S., Brändle de Motta, J.C., Sarthou, A., Estivalezes, J.L., Simonin, O., Climent, E.: A Lagrangian VOF tensorial penalty method for the DNS of resolved particle-laden flows. J. Comput. Phys. 256, 582 (2014)
Ritz, J.B., Caltagirone, J.P.: A numerical continuous model for the hydrodynamics of fluid particle systems. Int. J. Numer. Methods Fluids 30(8), 1067 (1999)
Kataoka, I.: Local instant formulation of two-phase flow. Int. J. Multiph. Flow 12(5), 745 (1986)
Caltagirone, J.P., Vincent, S.: Sur une méthode de pénalisation tensorielle pour la résolution des équations de Navier-Stokes. Comptes Rendus de l’Académie des Sciences - Series IIB - Mechanics 329(8), 607 (2001)
Fortin, M., Glowinski, R.: Méthodes de lagrangien augmenté: applications à la résolution numérique de problèmes aux limites. Méthodes mathématiques de l’informatique (Dunod, 1982)
Vincent, S., Caltagirone, J.P., Lubin, P., Randrianarivelo, T.N.: An adaptative augmented Lagrangian method for three-dimensional multimaterial flows. Comput. Fluids 33(10), 1273 (2004)
Vincent, S., Sarthou, A., Caltagirone, J.P., Sonilhac, F., Février, P., Mignot, C., Pianet, G.: Augmented Lagrangian and penalty methods for the simulation of two-phase flows interacting with moving solids. Application to hydroplaning flows interacting with real tire tread patterns. J. Comput. Phys. 230(4), 956 (2011)
Brändle de Motta, J.C., Breugem, W.P., Gazanion, B., Estivalezes, J.L., Vincent, S., Climent, E.: Numerical modelling of finite-size particle collisions in a viscous fluid. Phys. Fluids 25(8), 083302 (2013)
Khadra, K., Angot, P., Parneix, S., Caltagirone, J.P.: Fictitious domain approach for numerical modelling of Navier–Stokes equations. Int. J. Numer. Methods Fluids 34(8), 651 (2000)
Sarthou, A., Vincent, S., Caltagirone, J.P.: A second-order curvilinear to Cartesian transformation of immersed interfaces and boundaries. Application to fictitious domains and multiphase flows. Comput. Fluids 46(1), 422 (2011)
Kramers, H.: Heat transfer from spheres to flowing media. Physica 12(2), 61 (1946)
Ranz, W.E., Marshall, W.R.: Evaporation from drops: part II. Chem. Eng. Progress 48(4), 173 (1952)
Whitaker, S.: 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 (1972)
Feng, Z.G., Michaelides, E.E.: A numerical study on the transient heat transfer from a sphere at high Reynolds and Peclet numbers. Int. J. Heat Mass Transf. 43(2), 219 (2000)
Whitaker, S.: Diffusion and dispersion in porous media. AIChE J. 13(3), 420 (1967)
Quintard, M., Whitaker, S.: Transport in ordered and disordered porous media: volume-averaged equations, closure problems, and comparison with experiment. Chem. Eng. Sci. 48(14), 2537 (1993)
Vermorel, O., Bédat, B., Simonin, O., Poinsot, T.: Numerical study and modelling of turbulence modulation in a particle laden slab flow. J. Turbul. 4, N25 (2003)
Levec, J., Carbonell, R.G.: Longitudinal and lateral thermal dispersion in packed beds. Part I: theory. AIChE J. 31(4), 581 (1985)
Quintard, M., Kaviany, M., Whitaker, S.: Two-medium treatment of heat transfer in porous media: numerical results for effective properties. Adv. Water Resour. 20(2), 77 (1997)
Sun, B., Tenneti, S., Subramaniam, S., Koch, D.L.: 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 (2016)
Buist, K.A., Backx, B.J.G.H., Deen, N.G., Kuipers, J.A.M.: A combined experimental and simulation study of fluid-particle heat transfer in dense arrays of stationary particles. Chem. Eng. Sci. 169, 310 (2017)
Hamidouche, Z., Masi, E., Fede, P., Ansart, R., Neau, H., Hemati, M., Simonin, O.: In: Parente, A., De Wilde, J. (ed.,) Bridging Scales in Modelling and Simulation of Non-Reacting and Reacting Flows. Part I, Advances in Chemical Engineering, vol. 52, Academic Press, pp. 51–124 (2018)
Acknowledgements
This work was granted access to the HPC resources of CALMIP supercomputing center under the allocation P1529 and of CINES supercomputing center under the allocation A0022B10120. CALMIP and CINES are gratefully acknowledged. The authors wish to thank Ing. Pierre Elyakime for his support with the numerical code.
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Thiam, E.I., Masi, E., Climent, E. et al. Particle-resolved numerical simulations of the gas–solid heat transfer in arrays of random motionless particles. Acta Mech 230, 541–567 (2019). https://doi.org/10.1007/s00707-018-2346-5
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DOI: https://doi.org/10.1007/s00707-018-2346-5