Utilization of a Radial Temperature Model for Heat Conduction within Spherical Particles to Model Granular Assemblies

Abstract

A heat transfer (DEM) model for application in the particle based discrete element simulation method is presented. It utilizes an analytical solution of the heat diffusion equation for a solid spherical particle to obtain temporal and radial solutions of the temperature distributions within the particles. This radial temperature model avoids the shortcomings of the usual assumption of spatially uniform temperature profiles in particles. The concept is designed to minimize computing power and memory requirement in order to allow the computation of granular assemblies consisting of a large number of particles. Results obtained for a particle subject to transient convective boundary conditions are compared with a Crank-Nicholson implicit scheme as numerical reference solution. A first implementation of the radial temperature model in a discrete element code reveals the additional computational cost as negligible compared to the demands of contact identification and force calculation. IntroductionHeat transfer in granular media occurs in a wide range of applications such as catalytic packed beds, combustion of solid biomass, in recuperators or in sintering processes. It is common practice to describe the motion and the thermal behavior of the granular media by continuum models. These are based on the Eulerian approach, with the granular medium described as continuous functions of time and space.This macroscopic view leads to averaged values in time and space for the transport of mass, momentum, energy and species as well as "effective" material properties [1,2]. While providing satisfactory results for stationary granular materials such as packed beds, these approaches need empirical corrections, more or less arbitrary modeling, or even fail when modeling granular media in motion and transient heat transfer [3,4]. Anisotropic effects like mixing and segregation as well as the evolution of stress chains and heat convection by particle motion cannot be properly accounted for [5].Approaches using the Lagrangian view like the discreteelement method (DEM) do not suffer from these restrictions.In the DEM, each single particle and its interaction with the surrounding is subject to an individual description [6,7]. The equations of motion are applied to each particle and solved numerically. For extending this method to heat transfer, mechanisms such as convection between particles and the interstitial fluid or contact heat transfer between particles as well as conduction within a particle must be modeled. The conduction within a single particle is a matter of high technical importance as it characterizes the transient behavior of the granular media. The local temperature within the particle governs, for example, drying processes or the release of volatile matter within solid fuel particles. AnalysisIn the following, the analysis concentrates on spherical particles, a very common particle geometry in DEM simulations.A single particle subject to transient boundary conditions will develop a transient temperature distribution th...

Heat Transfer at a Particle‐Tube Wall Contact Point: Impact of Catalyst Configuration on Hot Spots

“…They used heat and mass transfer analogy to validate the CFD simulations with measured experimental data. Furthermore, there are also other studies around the creation of hot spots in PBRs such as evaluating melted catalytic particles in a hydro‐desulfurization (HDS) trickle‐bed reactor 47, 48, assessing radial transfer phenomena in a cross section of a PBR 49–52, and investigating partial oxidation of isobutyl alcohol in a PBR 53, 54.…”