Compaction and dilation rate dependence of stresses in gas-fluidized beds

Abstract

A particle dynamics-based hybrid model, consisting of monodisperse spherical solid particles and volume-averaged gas hydrodynamics, is used to study traveling planar waves ͑one-dimensional traveling waves͒ of voids formed in gas-fluidized beds of narrow cross-sectional areas. Through ensemble-averaging in a co-traveling frame, we compute solid phase continuum variables ͑local volume fraction, average velocity, stress tensor, and granular temperature͒ across the waves, and examine the relations among them. We probe the consistency between such computationally obtained relations and constitutive models in the kinetic theory for granular materials which are widely used in the two-fluid modeling approach to fluidized beds. We demonstrate that solid phase continuum variables exhibit appreciable "path dependence," which is not captured by the commonly used kinetic theory-based models. We show that this path dependence is associated with the large rates of dilation and compaction that occur in the wave. We also examine the relations among solid phase continuum variables in beds of cohesive particles, which yield the same path dependence. Our results both for beds of cohesive and noncohesive particles suggest that path-dependent constitutive models need to be developed.

How to generate valid local quantities of particle–fluid flows for establishing constitutive relations

“…θ obtained in the fluidized and moving beds as a function of ε s is consistent with the literature (note that in these studies the fluctuating kinetic energy is called as granular temperature), 43,44 given in Figure 11…”

Simulations of confined suspension flow at multiple length scales

“…The excluded volume of the particle is distributed over nearest neighbouring lattice sites via a similar interpolation scheme, and hence the local values of the particle volume fraction f is obtained at every grid cell. 60 The semi-resolved method is primarily used for gas-fluidized beds applications, 35,59,60,94 for which it is quite well developed. Typically for gas-fluidized beds the ratio d 1 /Dx z 1 ⁄ 3 , which is assumed to be the maximal size of the ratio (otherwise nonphysical behaviour is obtained).…”

“…Consequently, with the semi-resolved method, closures for quantities dependent on particle-particle interactions, like the particle pressure or the viscosity of the dispersed phase h s , can be obtained efficiently via this method. 35 Of course, these closures can also be obtained with DNS simulations, but at a much higher costs.…”

“…In Table 1 we have taken its minimal value, which is a fraction of the smallest particle diameter h ¼ 0.01d 2 . It is generally assumed that the lubrication force is saturated if the gap falls below a certain threshold, 29,35 which is caused by the particle roughness, for example.…”

Coarse-grained computations of demixing in dense gas-fluidized beds

“…When U s is well above the minimum fluidization rate of both species (as in Fig. 1), the bed exhibits 1D traveling waves (TWs) [13], and demixing occurs superposed on the persistent oscillatory motion driven by 1D-TWs. A typical computation of an entire demixing process in the above "tiny" system (2 × 10 7 integration steps of 12 500 particles shown in Fig.…”