End-constriction

Stoichiometric quantities of Nb metal powder and NbClg are weighed under anhydrous conditions, triturated and placed in a quartz tube which is closed at one end. Constrictions b and d (Fig. 305) are then made in the end of the tube and it is connected to a high-vacuum source. (It should be remembered in calculating... 

Drum Without Lifters and Without Discharge End Constriction, 202 Drum Without Lifters and With Discharge End Constriction, 204 Drum With Lifters, 204... 

FLOW OF HIGHLY SETTLING SLURRIES IN ROTARY DRUMS, 207 Drum With an Open-End Dishcarge and No Lifters, 207 Drums With an End-Constriction, 220 Drum Without Lifters, 220 Drum With Lifters, 231... 

Most previous studies concentrated on the solution of Equation 3 by providing an approximate functional form for the term in the square brackets. Normally, the assumption is made that at the discharge end hj 0 for a drum with no end constriction, otherwise is the depth of the constriction lip, i.e., hj = (R - R ), where R is the radius of the constriction opening. The assumption for the values of h is particularly correct for lightly loaded drums, and it becomes less accurate as the drum loading is increased. Various approximate solutions to Equation 3 are given below for different authors using a unified nomenclature. 

For given F, drum geometry and material properties. Equation 9 is used to evaluate P, which is then used to evaluate the fractional hold-up, H. Equation 9 is applicable to inclined drums with no end constriction and no lifters. 

Hogg et al. [7], Karra and Fuerstenau [8] and Abouzeid and Fuerstenau [11,29] carried out extensive experimental studies on solids flow in rotating drums with and without end constriction. Abouzeid and Fuerstenau gave empirical expressions for the drum fractional hold-up in terms of a dimensionless feed rate function. Their expression for the fractional hold-up was designed to cover a wide range of drum dimensionless rotational speed, 0 S n < 0.9. Unfortunately, their expressions of H in of their papers differ, and it was not possible to reconcile the two expressions [11,29], However, their experimental findings will be used to assess model predictions based on Equation 3. 

Drum Without Lifters and Without Discharge End Constriction... 

Figure 3. Variation of solids fractional hold-up with drum speed (no lifters and no end constriction). Solids feed rate, (kg/s) , 6.3 x K)- , 12.5 x 10- A. 21.3 X 10- 0> 30.3 x 10- .

Figure 4. A comparison of measured and predicted solids residence time (no lifters and no end constriction). , Vahl and Kingma [43] , Hehl et al. [9].

The variation of solids fractional hold-up with drum speed is shown in Figure 5 for the case of a drum without lifters and with discharge end constriction. The variation is similar to that reported by Abouzeid and Fuerstenau [11,29]. The solids hold-up is much higher with the end constriction than with a free drum opening as shown in Figure 3. 

Figure 7 displays the effect of the drum speed on the solids fractional hold-up for a drum fitted with lifters, but with no discharge end constriction. At the same solids feed rate and drum speed, the presence of the lifters increases the drum solids hold-up (Figures 3 and 7). 

The variation of the drum fractional hold-up with the drum speed is shown in Figure 8 for the case of a drum fitted with an end constriction. The presence of lifters has little effect on the solids hold-up as compared with the case of a drum... 

Figure 9. Comparison of measured solids residence time with exact solution of Kramers and Croockewit [45] (for all configurations) O, without lifters and no end constriction , with lifters and no end constriction O, without lifters and with end constriction A, with lifters and with end constriction , Abouzeid and Fuerstenau [11,29].

In the previous section, the flow of a sand-water slurry in a horizontal drum with an open-end discharge was reviewed. Slurry hold-up was found to be a function of particle size, drum speed, feed flow rate, and composition. The experimental results also showed relatively low slurry hold-up and poor radial (transverse) mixing inside the drum. To overcome these problems for the case of dry solids, an end-constriction and lifters are normally used. The effects of such additions on the slurry hold-up and mean residence times of solids and fluid phases will be discussed in the next section. 

Ejfect of Drum Speed on Slurry Hold-up. It is instructive to discuss the effect of the end-constriction on the minimum slurry hold-up, before examining the effect of various parameters on the drum hold-up. In the case of a rotary drum with an end-constriction, material cannot flow out of the drum until it is filled to the height of the lip (R - R ). This means that a minimum slurry volume must be present in the drum before any material begins to flow over the discharge lip. The minimum slurry hold-up (percentage of the drum volume) can be calculated as ... 

For the flow of highly settling slurries through horizontal rotary drums with an end-constriction (overflow discharge), the following conclusions were obtained ... 

C. Delivered solids concentration, volume fraction D Drum inside diameter, m D, Pipe diameter, m D Discharge end-constriction diameter, m... 

Qp Slurry feed flow rate, kg/s Solids mass flow rate, kg/s R Radius of rotating drum, m R Radius of discharge end-constriction, m... 

For beds with a low degree of fill and no end constriction dams, one can practically assume a uniform bed depth throughout the entire kiln length (y = H) and, i 0. The residence time expression can be reduced to... 

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