Granular flow regimes

FIGURE 4.6 Schematic representation of different regimes of granular flow regimes. 

A regime map of Fo versus the solid volume fraction, ap, for various gas-solid flows was presented by Hunt (1989), as shown in Fig. 4.3. Hunt (1989) suggested that except when Fo > 1 and ap > 0.1, use of the pseudocontinuum model is inappropriate. Thus, from Fig. 4.3, it can be seen that the pseudocontinuum model is applicable to packed beds, incipient fluidized beds, and granular flows, whereas it is not applicable to pneumatic transport flows, dilute suspensions, bubbling beds, and slugging fluidized beds [Glicksman and Decker, 1982 Hunt, 1989]. 

It must be noted here that most industrial fluidized bed reactors operate in a turbulent flow regime. Trajectory simulations of individual particles in a turbulent field may become quite complicated and time consuming. Details of models used to account for the influence of turbulence on particle trajectories are discussed in Chapter 4. These complications and constraints on available computational resources may restrict the number of particles considered in DPM simulations. Eulerian-Eulerian approaches based on the kinetic theory of granular flows may be more suitable to model such cases. Application of this approach to simulations of fluidized beds is discussed below. 

This model is supposed to capture the two extreme limits of granular flow, which are designating the rapid shear and quasi-static flow regimes. In the rapid shear flow regime the kinetic stress component dominates, whereas in the quasi-static flow regime the friction stress component dominates [127]. 

For gas-particle flows, fhe mosf obvious manifestation of non-equilibrium behavior is particle trajectory crossing (PTC) at KUp = oo (i.e. no collisions). PTC occurs in the very-dilute-flow regime ( p c 1) and is most easily identified when fhe granular femper-afure is null (Map = c ). An example of PTC is shown in Figure 1.4. The panel on fhe... 

This approach was also found to correlate power law fluid flow through granular beds of column to particle diameter ratio 5.8 < D/ds < 20 in the creeping (Darcy) flow regime (99). 

Equation (4.2) includes translational and collisional effects but not static effects. However, most engineering applications (e.g., chute flows) and other natural flow situations (mudflows, snow avalanches, debris flow, etc.) appear to fit into a regime for which the total stress must be represented by a linear combination of a rate-independent static component plus the rate-dependent viscous component just described (Savage, 1989). The flow patterns observed for material flow in rotary kilns appear to fit these descriptions and the constitutive equations for granular flow may apply within the relevant boundary conditions. 

In a very recent study by Farzaneh Kaloorazi [42], it was presumed that the mechanical behavior of dense granular flows is not approximated sufficiently accurately by the soil mechanics theory representing the mechanical behavior of the system as a rate independent plastic regime characterized by a constant friction coefficient. It was claimed that somewhat improved model predictions were obtained for bubbling fluidized bed combustors with a somewhat more comprehensive theory proposed by Jop et al. [77]. This alternative frictional pressure tensor closure was derived based on visco-plastic fluid analysis. 

K. Lu, E.E. Brodsky, and H.P. Kavehpour. Shear-weakening of the transitional regime for granular flow. Journal of Fluid Mechanics, 587 347-372, 9 2007. 

The reader may be surprised not to And a Reynolds number defined speciflcally for the disperse phase. This is because the disperse-phase viscosity is well defined only for Knp 1 (i.e. the collision-dominated or hydrodynamic regime). In this limit, Vp oc oc Knp/Map so that the disperse-phase Reynolds number would be proportional to Map/Krip when Map < 1. However, in many gas-particle flows the disperse-phase Knudsen number will not be small, even for ap 0.1, because the granular temperature (and hence the collision frequency) will be strongly reduced by drag and inelastic collisions. In comparison, molecular gases at standard temperature and pressure have KUp 1 even though the volume fraction occupied by the molecules is on the order of 0.001. This fact can be... 

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