Granular flow velocity fluctuations

To model the particle velocity fluctuation covariances caused by particle-particle collisions and particle interactions with the interstitial gas phase, the concept of kinetic theory of granular flows is adapted (see chap 4). This theory is based on an analogy between the particles and the molecules of dense gases. The particulate phase is thus represented as a population of identical, smooth and inelastic spheres. In order to predict the form of the transport equations for a granular material the classical framework from the kinetic theory of... 

In the analysis of flow of granular material, two types of flow can be distinguished. The first is slow frictional flow where the particles remain in continuous contact with each other the internal forces result from Coulomb friction between contacting particles. The second type of flow is much more rapid the particles are not in constant contact with their neighbors. The energy associated with the velocity fluctuations is comparable to that of the mean motion. In this type of flow, the internal forces arise because of the transfer of momentum during collisions between particles. The constitutive relations for this rapid flow are rate-dependent. This type of flow, therefore, is referred to as viscous flow (sometimes just rapid flow). Steady,... 

H. Ahn, C. E. Brennen, and R. H. Sabersky. "Measurements of velocity, velocity fluctuation, density, and stresses in chute flows of granular materials," J. Applied Mech., 58, 792-803,1991. 

S. S. Hsiau and M. L. Hunt. "Shear-induced particle diffusion and longitudinal velocity fluctuations in a granular-flow mixing layer," /. Fluid Mech., 251, 299-313, 1993. 

Specifically, at least three typical features are related with nonequilibrium granular flow systems (i) feasibility of one granular temperature (ii) non-Gaussian behavior of velocity distribution, and (iii) strong correlated density fluctuations in forms of bubbling or clustering. In the following section, we detail the above three points. 

In experiments, microscopic, noninvasive observation of the velocity distribution, correlated density fluctuation, or clustering will be helpful to quantify the collective behavior of granular flows under different heating or energy driving conditions. 

In the literature numerous two-fluid models of different complexity have been proposed to predict the fluidized bed reactor cold flow and reactive flow behaviors. Four decades ago emphasis was placed on the modeling of the velocity fluctuation co-variance terms in the dispersed particle fluid phase momentum equations. The early one-dimensional models were normally closed by an elasticity modulus parameterization for the particle phase collisional pressure and a constant viscosity parameter for the corresponding shear stresses. Later, with the improved computer memory and speed capacities, multi-dimensional flow models and more advanced model closures were developed based on the kinetic theory of granular flow (KTGF). Moreover, the... 

---