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FIGURE 12.14 Comparison with experimental data from van Breugel et al., 1969 (dp = 40 [xm, ps = 2300 kg m-3, D = 0.30 m, Ug = 6.30 ms-1, Gs = 390 kg m-2s-1). (From Ranade, 1999).

computational model, however, exhibits extreme sensitivity with respect to particle-particle restitution coefficient and therefore cannot be used to simulate practical riser flows.

Kuipers and van Swaaij (1999) also observed that it was not possible to simulate the downflow near the riser wall without modifying the underlying interphase momentum exchange model. The pronounced lateral segregation and solids downflow near the wall with velocities much higher than terminal-settling velocities may occur due to the formation of clusters. Typical size of these clusters and how these clusters affect the dynamics of gas-solid flows in vertical risers is not properly understood. Several ad hoc modifications based on fitting a limited set of experimental data have been attempted. Matsen (1982) proposed a correlation to estimate slip velocity of clusters as a function of single-particle terminal settling velocity and volume fraction of solids. The ratio of slip velocity to terminal settling velocity at 10% solids volume fraction is about 5. Kuipers and van Swaaij (1999) used a correlation proposed by Nieuwland et al. (1994) to correct the interphase drag coefficient to account for cluster formation in the riser flows. This correlation predicts the ratio of slip velocity to terminal settling velocity as about 30. Thus, these two correlations to account for the influence of clusters on the interphase drag force term differ significantly from each other. It appears that cluster formation, their size and slip velocity may be functions of more parameters than just the solids volume fraction and terminal settling velocity. In order to further understand various issues in the simulations of gas-solid flows in a riser, it will be instructive to examine the results of numerical experiments. Here we describe the results of some such numerical experiments to illustrate the influence of relevant variables such as riser diameter, particle diameter and solids flux on predicted results.

For these numerical experiments, a base case of gas-solid flow with the following parameters was considered: particle diameter 100 xm, particle density 2000 kg m-3, gas density 5 kg m-3, riser diameter 0.30 m, gas superficial velocity 10 m s-1 and solids flux of 400 kg m-2 s-1. The model of Ranade (1999) was used along with the turbulence model to simulate the base case and various other cases with systematic variation of the main governing parameters of gas-solid flows in risers. The data used for these numerical experiments are listed in Table 12.2. Additional simulations were also carried out to examine the interaction between parameters by simultaneously varying more than one parameter. Unless otherwise mentioned, for all simulations, the particle-particle restitution coefficient was set to one, the particle-wall restitution coefficient was set to 0.9 and the speculiarity coefficient was set to 0.5. The influence of several parameters on the predicted values of solids velocity, slip velocity, solids volume fraction, solids granular temperature and gas phase turbulent kinetic energy was studied. Analysis of the results obtained by these numerical experiments will be useful to guide the development of a computational model to simulate industrial fluidized beds.

The influence of riser diameter on the predicted results is shown in Fig. 12.15. It can be seen that there are significant qualitative differences in the predicted radial

TABLE 12.2 Data Used for Numerical Experiments and Predicted Pressure Drop

No.

D,

dp,

Ps,

Pg,

Ug

Gs,

Ap/L

0 0

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