Direct Numerical Simulation of the Sedimentation of Solid Particles with Thermal Convection

Dispersed two-phase flows often involve interfacial activities such as chemical reaction and phase change, which couple the fluid dynamics with heat and mass transfer. As a step toward understanding such problems, we numerically simulate the sedimentation of solid bodies in a Newtonian fluid with convection heat transfer. The two-dimensional Navier–Stokes and energy equations are solved at moderate Reynolds numbers by a finite-element method, and the motion of solid particles is tracked using an arbitrary Lagrangian–Eulerian scheme. Results show that thermal convection may fundamentally change the way that particles move and interact. For a single particle settling in a channel, various Grashof-number regimes are identified, where the particle may settle straight down or migrate toward a wall or oscillate laterally. A pair of particles tend to separate if they are colder than the fluid and aggregate if they are hotter. These effects are analysed in terms of the competition between the thermal convection and the external flow relative to the particle. The mechanisms thus revealed have interesting implications for the formation of microstructures in interfacially active two-phase flows. Disciplines Engineering | Mechanical Engineering Comments Suggested Citation: Gan, Hui, Jianzhong Chang, James J. Feng and Howard H. Hu. (2003). Direct numerical simulation of the the sedimentation of solid particles with thermal convection. Journal of Fluid Mechanics. Vol. 481. p. 385-411. Copyright 2003 Cambridge University Press. http://dx.doi.org/10.1017/S0022112003003938 This journal article is available at ScholarlyCommons: http://repository.upenn.edu/meam_papers/209 J. Fluid Mech. (2003), vol. 481, pp. 385–411. c © 2003 Cambridge University Press DOI: 10.1017/S0022112003003938 Printed in the United Kingdom 385 Direct numerical simulation of the sedimentation of solid particles with thermal convection By HUI GAN, J IANZHONG CHANG, JAMES J. FENG AND HOWARD H. HU The Levich Institute for Physicochemical Hydrodynamics, City College of the City University of New York, New York, NY 10031, USA Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104, USA (Received 11 September 2002 and in revised form 6 December 2002) Dispersed two-phase flows often involve interfacial activities such as chemical reaction and phase change, which couple the fluid dynamics with heat and mass transfer. As a step toward understanding such problems, we numerically simulate the sedimentation of solid bodies in a Newtonian fluid with convection heat transfer. The twodimensional Navier–Stokes and energy equations are solved at moderate Reynolds numbers by a finite-element method, and the motion of solid particles is tracked using an arbitrary Lagrangian–Eulerian scheme. Results show that thermal convection may fundamentally change the way that particles move and interact. For a single particle settling in a channel, various Grashof-number regimes are identified, where the particle may settle straight down or migrate toward a wall or oscillate laterally. A pair of particles tend to separate if they are colder than the fluid and aggregate if they are hotter. These effects are analysed in terms of the competition between the thermal convection and the external flow relative to the particle. The mechanisms thus revealed have interesting implications for the formation of microstructures in interfacially active two-phase flows.