Collisions between particles in multiphase flows: Focus on contact mechanics and heat conduction

Abstract The topic of heat transfer between colliding particles or between particles impinging on solid surfaces is, in spite of its practical significance, still not widely studied in literature: efforts have, till now, led to only a handful of models. At the same time this problem is crucial not only for many types of multiphase flows but also for other systems involving colliding bodies. Therefore the first objective of the research was to study heat conduction between colliding particles for the case when the local deformation in the contact region can be treated as consisting of two regions: one deformating elastically and the other plastically. This requires investigation of collision dynamics and therefore this paper also contains a short review of the existing models for modelling particle–particle and particle–wall collisions. The second important result of the work presented here is a new relation for the coefficient of restitution that was developed by fitting a dimensionless relation involving the salient physical parameters to numerical experiments based on collision models.

[1]  Hertz On the Contact of Elastic Solids , 1882 .

[2]  Thorsten Pöschel,et al.  Collision dynamics of granular particles with adhesion. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  C. Thornton,et al.  Rebound behaviour of spheres for plastic impacts , 2003 .

[4]  R. Brach Rigid Body Collisions , 1989 .

[5]  A. C. Hoffmann,et al.  An extension of the hard-sphere particle–particle collision model to study agglomeration , 2010 .

[6]  Paul Zulli,et al.  Particle scale study of heat transfer in packed and bubbling fluidized beds , 2009 .

[7]  G. Weir,et al.  The coefficient of restitution for the idealized impact of a spherical, nano-scale particle on a rigid plane , 2008, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[8]  V. Popov Contact Mechanics and Friction , 2010 .

[9]  M. M. Chen,et al.  A theoretical analysis of heat transfer due to particle impact , 1988 .

[10]  Arun S. Mujumdar,et al.  A Numerical Study of Heat Transfer Mechanisms in Gas–Solids Flows Through Pipes Using a Coupled CFD and DEM Model , 2003 .

[11]  Colin Thornton,et al.  A semi-analytical model for oblique impacts of elastoplastic spheres , 2009, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[12]  Pawel Kosinski,et al.  Extended hard-sphere model and collisions of cohesive particles. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  Goodarz Ahmadi,et al.  Inter-particle heat transfer in a riser of gas–solid turbulent flows , 2005 .

[14]  Jintang Li,et al.  APPLICATION OF THE DISCRETE ELEMENT MODELLING IN AIR DRYING OF PARTICULATE SOLIDS , 2002 .

[15]  P. Kosinski,et al.  Heat conduction during collisions of cohesive and viscoelastic particles , 2013 .

[16]  Edmund Taylor Whittaker,et al.  A Treatise on the Analytical Dynamics of Particles and Rigid Bodies: THE GENERAL THEORY OF ORBITS , 1988 .

[17]  Alex C. Hoffmann,et al.  Modelling of dust lifting using the Lagrangian approach , 2005 .

[18]  P. Cundall,et al.  A discrete numerical model for granular assemblies , 1979 .

[19]  Shlomo Djerassi Collision with friction; Part B: Poisson’s and Stornge’s hypotheses , 2008 .

[20]  Ahmet S. Yigit,et al.  On the impact of a spherical indenter and an elastic-plastic transversely isotropic half-space , 1994 .

[21]  D. Tabor A simple theory of static and dynamic hardness , 1948, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[22]  C. Thornton,et al.  Energy dissipation during normal impact of elastic and elastic-plastic spheres , 2005 .

[23]  J. Keller Impact With Friction , 1986 .

[24]  Grant M. Campbell,et al.  Discrete Modeling and Suggested Measurement of Heat Transfer in Gas–Solids Flows , 2003 .

[25]  Heat Transfer Between Colliding Surfaces and Particles , 2012 .

[26]  M. Kaviany,et al.  Heat transfer during impact , 1992 .

[27]  Yutaka Tsuji,et al.  Lagrangian numerical simulation of plug flow of cohesionless particles in a horizontal pipe , 1992 .

[28]  A. Yu,et al.  A new computational method for studying heat transfer in fluid bed reactors , 2010 .

[29]  Gilles Flamant,et al.  DEM-LES simulation of coal combustion in a bubbling fluidized bed Part II: coal combustion at the particle level , 2004 .

[30]  Kai Zhang,et al.  A particle-to-particle heat transfer model for dense gas–solid fluidized bed of binary mixture , 2011 .

[31]  L. Vu-Quoc,et al.  Modeling the dependence of the coefficient of restitution on the impact velocity in elasto-plastic collisions , 2002 .

[32]  S. Djerassi Collision with friction; Part A: Newton’s hypothesis , 2009 .

[33]  C. Thornton Coefficient of Restitution for Collinear Collisions of Elastic-Perfectly Plastic Spheres , 1997 .

[34]  Measurement of Surface Heat Transfer Due to Particle Impact , 1995 .

[35]  H. Deresiewicz A note on Hertz's theory of impact , 1968 .

[36]  Spahn,et al.  Model for collisions in granular gases. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[37]  G. Kuwabara,et al.  Restitution Coefficient in a Collision between Two Spheres , 1987 .

[38]  Eldin Wee Chuan Lim Master Curve for the Discrete-Element Method , 2008 .

[39]  Christine M. Hrenya,et al.  Comparison of soft-sphere models to measurements of collision properties during normal impacts , 2005 .

[40]  Colin Thornton,et al.  Coefficients of restitution for elastoplastic oblique impacts , 2003 .

[41]  Alex C. Hoffmann,et al.  Simulation of solid particles behaviour in a driven cavity flow , 2009 .

[42]  Aibing Yu,et al.  Finite element modeling of the transient heat conduction between colliding particles , 2008 .

[43]  A. C. Hoffmann,et al.  An Eulerian–Lagrangian model for dense particle clouds , 2007 .

[44]  Raymond M. Brach,et al.  Friction, Restitution, and Energy Loss in Planar Collisions , 1984 .

[45]  B. Oesterlé,et al.  Simulation of particle-to-particle interactions in gas solid flows , 1993 .

[46]  William James Stronge,et al.  Smooth dynamics of oblique impact with friction , 2013 .