2D modeling of moving particles with phase-change effect

Abstract The main aim of this work is to study the behavior of particulate flows taking into account the interfacial heat transfer on the particle surface including the phase change phenomena. Two flow configurations of increasing complexity are studied with the aim of unraveling fundamental properties of heat transfer in two-phase flows. The first configuration corresponds to the fluid flow past a single cylindrical ice particle melted in the water. The focus is on the influence of the Reynolds number on the melting time of a single particle and comparison of numerical data against Nu-based models. The second configuration refers to ice particles moving up in the water due to the gravity force in a two-dimensional channel. Here, the focus is on the study of particle dynamics in the presence of neighboring particles, including the influence of the viscous torque on the particle trajectories and finally on the melting time compared to the case of a single particle. An implicit fictitious boundary method (FBM) over a fixed Cartesian grid is extended to model the heat transfer and the phase change in particulate flows in two dimensions. The hydrodynamic forces acting on the particles are calculated directly through the surface integrals without the use of any semi-empirical correlations. The particle collisions are modeled directly using the hard sphere approach, taking into account the inelastic collisions. The interface velocity of the melting (solid–liquid) was calculated by means of the Stefan condition for each particle. To illustrate the impact of particle rotation caused by the viscous torques on the particle trajectory, a set of simulations was performed with and without viscous torque effect. A comparative analysis of the results showed that when the viscous moment is taken into account, the particle melting time is reduced significantly. Additionally, based on an analysis of the time history of the volume-averaged velocity in the entire domain, three regimes were found. In particular, the first regime is characterized by the acceleration of particles due to the gravity force, the second is the transitional regime and the last is the passive regime, where the melted particles follow the flow induced by particles in the past. During the last regime the particles do not have any influence on the fluid flow. The influence of the initial configuration of particles on the flow pattern and regimes is discussed.

[1]  Gretar Tryggvason,et al.  Mass transfer and chemical reactions in bubble swarms with dynamic interfaces , 2005 .

[2]  Runyu Yang,et al.  Discrete particle simulation of particulate systems: A review of major applications and findings , 2008 .

[3]  Stefan Turek,et al.  The Fictitious Boundary Method for the Implicit Treatment of Dirichlet Boundary Conditions with Applications to Incompressible Flow Simulations , 2003 .

[4]  Joseph J. McCarthy,et al.  Heat transfer in rotary kilns with interstitial gases , 2008 .

[5]  E. Meiburg,et al.  Numerical simulation of finite Reynolds number suspension drops settling under gravity , 2005 .

[6]  Zhaosheng Yu,et al.  A fictitious domain method for particulate flows with heat transfer , 2006, J. Comput. Phys..

[7]  J. Kuipers,et al.  Numerical study of segregation using a new drag force correlation for polydisperse systems derived from lattice-Boltzmann simulations , 2007 .

[8]  R. Glowinski,et al.  Fluidization of 1204 spheres: simulation and experiment , 2002, Journal of Fluid Mechanics.

[9]  Efstathios E. Michaelides,et al.  Inclusion of heat transfer computations for particle laden flows , 2008 .

[10]  William H. Press,et al.  Numerical recipes in Fortran 77 and Fortran 90 : the art of scientific and parallel computing , 1996 .

[11]  Suresh V. Garimella,et al.  FIXED-GRID FRONT-TRACKING ALGORITHM FOR SOLIDIFICATION PROBLEMS, PART I: METHOD AND VALIDATION , 2003 .

[12]  H. L. Stone.  ITERATIVE SOLUTION OF IMPLICIT APPROXIMATIONS OF MULTIDIMENSIONAL PARTIAL DIFFERENTIAL EQUATIONS , 1968 .

[13]  Z. Feng,et al.  Heat transfer in particulate flows with Direct Numerical Simulation (DNS) , 2009 .

[14]  James J. Feng,et al.  Direct simulation of initial value problems for the motion of solid bodies in a Newtonian fluid Part 1. Sedimentation , 1994, Journal of Fluid Mechanics.

[15]  H. S. Carslow,et al.  Conduction of Heat in Solids, Second Edition , 1986 .

[16]  E. Michaelides,et al.  The effect of particle interactions on the sedimentation process of non-cohesive particles , 2003 .

[17]  Richard J Goldstein,et al.  Forced convection heat transfer from a circular cylinder in crossflow to air and liquids , 2004 .

[18]  Richard J Goldstein,et al.  An Experimental Study of Natural Convection Heat Transfer in Concentric and Eccentric Horizontal Cylindrical Annuli , 1978 .

[19]  Fernando J. Muzzio,et al.  Experimentally Validated Numerical Modeling of Heat Transfer in Granular Flow in Rotating Vessels , 2011 .

[20]  Stefan Turek,et al.  Fictitious boundary and moving mesh methods for the numerical simulation of rigid particulate flows , 2007, J. Comput. Phys..

[21]  Brahma Deo,et al.  Cold Model Investigations of Melting of Ice in a Gas-Stirred Vessel , 2011 .

[22]  P. Saffman.  The lift on a small sphere in a slow shear flow , 1965, Journal of Fluid Mechanics.

[23]  A. Wachs,et al.  Direct Numerical Simulation of particulate flow with heat transfer , 2010 .

[24]  G. Segré,et al.  Radial Particle Displacements in Poiseuille Flow of Suspensions , 1961, Nature.

[25]  P. Moin,et al.  DIRECT NUMERICAL SIMULATION: A Tool in Turbulence Research , 1998 .

[26]  C. Williamson.  Vortex Dynamics in the Cylinder Wake , 1996 .

[27]  W. Shyy,et al.  Elafint: a Mixed Eulerian-Lagrangian Method for Fluid Flows with Complex and Moving Boundaries , 1996 .

[28]  Ng Niels Deen,et al.  Review of discrete particle modeling of fluidized beds , 2007 .

[29]  James J. Feng,et al.  Simulation of the sedimentation of melting solid particles , 2003 .

[30]  O. Zienkiewicz.  The Finite Element Method In Engineering Science , 1971 .

[31]  Richard J Goldstein,et al.  An experimental and theoretical study of natural convection in the annulus between horizontal concentric cylinders , 1976, Journal of Fluid Mechanics.

[32]  Ng Niels Deen,et al.  Numerical Simulation of Dense Gas-Solid Fluidized Beds: A Multiscale Modeling Strategy , 2008 .

[33]  J. C. Jaeger,et al.  Conduction of Heat in Solids , 1952 .

[34]  Christoph Beckermann,et al.  Equiaxed dendritic solidification with convection: Part III. Comparisons with NH4Cl-H2O experiments , 1996 .

[35]  Keizo Yabumoto,et al.  Spontaneous structures in three-dimensional bubbling gas-fluidized bed by parallel DEM–CFD coupling simulation , 2008 .

[36]  C. Rhie,et al.  Numerical Study of the Turbulent Flow Past an Airfoil with Trailing Edge Separation , 1983 .

[37]  Joel H. Ferziger,et al.  Computational methods for fluid dynamics , 1996 .

[38]  P. Nikrityuk,et al.  Numerical simulation of the transient temperature distribution inside moving particles , 2012 .