Active layer velocity

In Equation (4.42) u = U/ i(.x,y) = f(y) is the active layer velocity function which includes the actual active layer depth. At mid-chord, the global material balance for the entire cross section is satisfied and since the subtended angle there (i.e., 0) goes to zero, Equation 4.42 reduces to... 

Figure 4.15 Active layer velocity as function of kiln speed, (a) 41 cm diameter pilot kiln, (b) 1 m diameter rotary drum, and (c) 2.5 m diameter industrial kiln (Boateng, 1998).

Because the active layer velocity is about three or four times greater than that in the plug flow region, mixing effects are confined to this region. However, if fine or denser particles are used as tracers, then the velocity distribution will help to determine the extent to which the tracers will travel before percolating down. These scenarios will be the subject of the next chapter. 

These devices showed EL enhancements to ammonia, methylamine, di-methylamine, trimethylamine, and sulfur dioxide that increased in magnitude with concentration until saturation was reached [14]. The LEDs with larger active layers produced the greatest change in EL intensity with exposure to sulfur dioxide and the amines. Intensity changes were attributed principally to surface recombination velocity effects, as the significant forward biases employed should eliminate the depletion width. 

The results of one such calculation are shown as solid curves in Fig. 5.15 [5.110]. Additional generalized curves and closed-form solutions appear in the references [5.14, 15, 89, 92, 93, 95, 96, 101, 104, 110]. The various solutions all agree on the importance of low recombination velocity at the substrate/active layer growth interface and thus on the importance of low lattice mismatch. They also indicate that near threshold the quantum efficiency can be higher in transmission than in the reflection mode owing to one added optical reflection at the vacuum surface [5.95]. From the various separate models have come several versions of an optimum structure, but all are similar in general dimensions and structure as outlined above. 

The active layer depth and bed flow properties depend on the coefficient of restitution of the material. The flow properties of interest include granular temperature, which is a measure of kinetic energy in random motion of particles, and dilation. Granular temperature was found to be high at regions of low concentration with high mean velocity. These experiments also characterize the shape of the active layer to... 

Figure 4.2 Measured exposed surface velocity profile in the active layer (15 percent fill and 5rpm).

The motion is essentially two-dimensional in the transverse plane since the transverse velocity is several orders of magnitude greater than the axial velocity. Also particle flux into the active layer at the right quadrant is assumed to equal the particle flux into the plug flow... 

We can now invoke the simplifications derived from the thin flow assumption to solve for the velocity distribution in the active layer. This requires some normalization using A and H (Figure 4.8). 

Equations (4.34) and (4.39) represent the integro-differential equations for the bulk material flow in the bed active layer. However, in order to proceed further a suitable form for the velocity profile is required. 

In choosing this suitable velocity function, it is necessary to account for the boundary conditions (i) at the free surface, and (ii) at the interface between the active and the plug flow region of the bed and also to satisfy the requirement of continuity at the point where the solution in the active layer is joined to the plug flow solution. However, it is necessary to first consider the material balance for the bed section being considered. The material balance at an arbitrary x-position in the free surface plane establishes = rhpp (Figure 4.11) or stated mathematically. 

Recognizing that the bulk density is simply the particle density times the solid fraction (p = ppv), and that, within the plug flow region u = wr, this equation simplifies to (dropping the subscript AL for velocity in the active layer)... 

In solving for the active layer depth and velocity using Equation (4.43) there are two possible constraints that may be used to terminate the iteration, that is, either by ensuring that the mass flow in the active layer is balanced at each. -position from the apex, using Equation (4.42), or by ensuring that global mass in the active layer is balanced at mid-chord using Equation (4.43). 

This is the quadratic equation required for the prediction of the active layer depth, which in turn is substituted into the velocity profile to obtain the velocity distribution in the two-dimensional domain. 

Figure 4.12 Calculation scheme for active layer depth and velocity distribution.

The prediction of the velocity distribution for a 41 cm diameter pilot kiln is shown in Figure 4.13. Validation of the model is carried out using experimental results of the 1 m rotary drum (Figure 4.14). Here predicted and measured active layer depths are compared for the materials studied. As seen, the model underpredicts at low degree of fill... 

The bulk velocity distribution in the active layer does not change with addition of fines and the bed behavior (e.g., rolling, slumping, etc.) remains unchanged with fines (Henein, 1980). 

The governing equations for mixing and segregation are derived by considering an equilibrium balance of material for the control volume (Figure 5.3). First, particles drift into the control volume by convection as a result of the bulk velocity in the active layer. The rate of jetsam dispersion into and out of the control volume may be represented, respectively, as and where A is the area normal to... 

The diffusion flux in the active layer occurs as a result of particle collision in the continuously shearing active layer. The diffusion coefficient and the bulk velocity are determined by the flow model detailed in Chapter 4. by is the kinetic diffusivity which had been computed from the granular temperature as (Savage, 1983 Hsiau and Hunt, 1993)... 

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