Modeling of multitype particle flow using the kinetic theory approach

Abstract

in Wiley InterScience (www.interscience.wiley.com). The effects of particle size and/or density on particle interaction and overall behavior of granular flow were studied using the kinetic theory approach. The kinetic theory for granular flow was extended to mixtures of multitype particles assuming a non-Maxwellian velocity distribution and energy non-equipartition. Each type of particles was considered as a separate phase with different velocity and granular temperature. The resulting momentum equation for each particulate phase includes phase interaction arising from collisional pressure and particle-particle drag force. When applied to simple shear granular flow of a binary mixture, this model predicts well the energy non-equipartition and the stresses of particulate systems with different sizes and densities. © 2005 AmericanInstitute of Chemical Engineers AIChE J, 51: 1620 -1632, 2005 Keywords: kinetic theory, particle collision, granular mixture, granular shear flow, energy non-equipartition IntroductionGranular flows exhibit complex behavior arising from the coexistence of two different behaviors within the flow: solid-like and fluid-like behaviors. Collisions of particles of different mechanical properties and corresponding fluctuations that occur during flow make the system more complicated. In this work, we investigate the effect of particle mechanical properties (size, particle density) on granular flow behavior using the kinetic theory approach.Originally the kinetic theory was developed by Chapman and Cowling 1 for gases to predict the behavior of mass point molecules whose interaction energies are conserved. Nearly two decades ago, this theory was extended to particulate flow where the interactions between particles are not conserved. Savage and Jeffrey 2 were probably the first to apply the kinetic theory to rapidly deforming material in the form of smooth hard spherical particles (ideal mixture). In their derivation, to calculate the stress tensor arising from interparticle collisions, they assumed that the collisions between particles were purely elastic. Although in some granular flows the restitution coefficient is restrained to values close to unity, its deviation from unity results in a significant variation in the properties of granular flow. This was shown first by Jenkins and Savage. 3 They extended the kinetic theory of an idealized granular mixture to predict the rapid deformation of granular material by including energy dissipation during collision for nearly inelastic particles. Later on, based on the original work of Savage and Jeffrey 2 and Jenkins and Savage, 3 Lun et al. 4 developed a theory that predicts the simple shear flow behavior for a wide range of restitution coefficients. Many models for granular flow were then developed based on the kinetic theory approach. [5][6][7] All the above-cited works assumed mixtures of identical density and size. However, real systems are composed of particles of different properties, in which segregation by size or density may occur during t...

Choosing Hydrodynamic Fields

“…However, the additional details are on the short time scale of the mean free time where the dynamics is entangled with many other microscopic degrees of freedom, and for which the underlying normal solution is not expected to apply. Of course, it has the additional computational difficulty of requiring the determination of many more transport coefficients in the constitutive equations ( approximate calculations have been made based on the Enskog kinetic theory, but the results remain incomplete; see [15,16]), and solving for ten coupled fields in contrast to six fields in the simple hydrodynamic description.…”

Enskog theory for polydisperse granular mixtures. I. Navier-Stokes order transport

“…A more recent theory [37] involves the lifting of both of these assumptions, except in the evaluation of collision integrals involving two unlike particles, in which case a Maxwellian velocity distribution is assumed for each particle type. Two current theories exist that do not involve either of these assumptions [38,39], though both are based on the Boltzmann equation and thus are limited to dilute flows.…”

“…Another key difference between existing polydisperse theories is the base state used in the Chapman-Enskog (CE) expansion. Some theories [8,9,10,11,12,13,14,37,39] assume an expansion about a perfectly elastic (molecular equilibrium) base state, and thus are restricted to nearly-elastic systems. However, in the CE method the base state must not be chosen a priori, but rather it is determined as the solution to the kinetic equation to zeroth order in the gradient expansion.…”

The effect of frictional pressure, geometry and wall friction on the modelling of a pseudo-2D bubbling fluidised bed reactor

“…• An alternative radial distribution function from the work of Iddir and Arastoopour [25] (Equation 34).…”