Solids mass flux

Fig. 15-4, except that transport is possible in the dense phase in which the pressure gradient, though quite large, is still usually not as large as for hydraulic transport. The entire curve shifts up and to the right as the solids mass flux increases. A comparison of typical operating conditions for dilute and dense phase pneumatic transport is shown in Table 15-1. 

Figure 14. Radial profiles of solid mass flux in fast fluidized bed. (From Herb, Dou, Tuzla and Chen, 1992.)...

The interaction of parametric effects of solid mass flux and axial location is illustrated by the data of Dou et al. (1991), shown in Fig. 19. These authors measured the heat transfer coefficient on the surface of a vertical tube suspended within the fast fluidized bed at different elevations. The data of Fig. 19 show that for a given size particle, at a given superficial gas velocity, the heat transfer coefficient consistently decreases with elevation along the bed for any given solid mass flux Gs. At a given elevation position, the heat transfer coefficient consistently increases with increasing solid mass flux at the highest elevation of 6.5 m, where hydrodynamic conditions are most likely to be fully developed, it is seen that the heat transfer coefficient increases by approximately 50% as Gv increased from 30 to 50 kg/rrfs. 

The data of Fig. 20 also point out an interesting phenomenon—while the heat transfer coefficients at bed wall and bed centerline both correlate with suspension density, their correlations are quantitatively different. This strongly suggests that the cross-sectional solid concentration is an important, but not primary parameter. Dou et al. speculated that the difference may be attributed to variations in the local solid concentration across the diameter of the fast fluidized bed. They show that when the cross-sectional averaged density is modified by an empirical radial distribution to obtain local suspension densities, the heat transfer coefficient indeed than correlates as a single function with local suspension density. This is shown in Fig. 21 where the two sets of data for different radial positions now correlate as a single function with local mixture density. The conclusion is That the convective heat transfer coefficient for surfaces in a fast fluidized bed is determined primarily by the local two-phase mixture density (solid concentration) at the location of that surface, for any given type of particle. The early observed parametric effects of elevation, gas velocity, solid mass flux, and radial position are all secondary to this primary functional dependence. 

Herb, B. E., Dou, S., Tuzla, K., and Chen, J. C., Solid Mass Fluxes in Circulating Fluidized Beds, Powder Technol., 197-205 (1992)... 

However, the present results already allow a conclusion to be drawn with respect to the solids mass flux mc loss which is lost from the cyclone as a result of attrition inside the cyclone. From Eq. (23) it follows withw = -0.5 and with the definition of Ra c... 

Cyclones. According to the model presented above, Eq. (24), a minimum loss rate due to cyclone attrition requires to avoid both high inlet velocities Ue and high solids mass fluxes mc m at the cyclone inlet. The latter requirement can be fulfilled by locating the cyclone inlet above the transport disengaging height (TDH) (Kunii and Levenspiel, 1991). In addition, an enlargement of the freeboard section will reduce the amount of particles that are entrained and thus the mass flux, mc in. 

Stationary, traveling wave solutions are expected to exist in a reference frame attached to the combustion front. In such a frame, the time derivatives in the set of equations disappear. Instead, convective terms appear for transport of the solid fuel, containing the unknown front velocity, us. The solutions of the transformed set of equations exist as spatial profiles for the temperature, porosity and mass fraction of oxygen for a given gas velocity. In addition, the front velocity (which can be regarded as an eigenvalue of the set of equations) is a result from the calculation. The front velocity and the gas velocity can be used to calculate the solid mass flux and gas mass flux into the reaction zone, i.e., msu = ps(l — e)us and... 

Results of the model for two parameters, i.e., the spatial temperature profile and the mass flux into the reaction zone as a function of gas mass flux are presented in Fig. 8.7. The temperature profile of the solid fuel flame (Fig. 8.7, left) is similar to that of a premixed laminar flame it consists of a preheat zone and a reaction zone. (The spatial profile of the reaction source term, which is not depicted here, further supports this conclusion.) The temperature in the burnt region (i.e., for large x) increases with the gas mass flux. The solid mass flux (Fig. 8.7, right) initially increases with an increase of the air flow, until a maximum is reached. For higher air flows, it decreases again until the flame is extinguished. 

Fig. 8.7 Results of the fixed bed model. Spatial profiles of the temperature, T(x), for mgu = 4.9-14.6 x 10-3 g cm-2 s-1 in steps of 2.4 x 10-3 g cm-2 s-1 (left), and the solid mass flux, msu = ps(l - e)us, into the reaction zone as a function of gas mass flux (right).

The raw data of the thermocouples consist of the temperature as a function of time (Fig. 8.9, left). In the raw data, the passing of the conversion front can be observed by a rapid increase in temperature. Because the distance between the thermocouples is known, the velocity of the conversion front can be determined. The front velocity can be used to transform the time domain in Fig. 8.9 (left) to the spatial domain. The resulting spatial flame profiles can be compared with the spatial profiles resulting from the model. The solid mass flux can also be plotted as a function of gas mass flow rate. The trend of this curve is similar to the model results (Fig. 8.9, right). 

Fig. 8.9 Typical measurement result. Example of raw data of the thermocouples (left) and the solid mass flux as a function of gas mass flux (right).

Phase Diagram (Zenz and Othmer) As shown in Fig. 17-2, Zenz and Othmer, (Fluidization and Fluid Particle Systems, Reinhold, New York, 1960) developed a gas-solid phase diagram for systems in which gas flows upward, as a function of pressure drop per unit length versus gas velocity with solids mass flux as a parameter. Line OAB in Fig. 17-2 is the pressure drop versus gas velocity curve for a packed bed, and line BD is the curve for a fluidized bed with no net solids flow through it. Zenz indicated that there was an instability between points D and H because with no solids flow, all the particles will be... 

High solid mass flux down the dipleg... 

Equations 9.3-22 and 9.3-26 are the basic equations of the melting model. We note that the solid-bed profile in both cases is a function of one dimensionless group ijj, which in physical terms expresses the ratio of the local rate of melting per unit solid-melt interface JX /X to the local solid mass flux into the interface Vszps, where ps is the local mean solid bed density. The solid-bed velocity at the beginning of melting is obtained from the mass-flow rate... 

In practice, so-called overspray occurs this characterizes the non-deposited liquid drops. In the model, a factor kos considers the overspray, as a ratio of the mass flux of the overspray and the injected solid mass flux. The efficiency of the separator (filter, cyclone) is considered by a factor ksep, which describes the ratio of the re-fed mass flux to the granulator to the fed mass flux into the separator. The factor kgrowth describes the ratio of the mass flux which comes from the separator and is used for the layering and growth (continuous phase) and the mass flux which comes from the separator (dust) and is used as new internal seeds (disperse phase). 

If the solids mass flux s is measured as shown earlier, then the particle velocity can be calculated ... 

Figure 2 Solid mass flux G, as a function of the superficial velocity uo in the riser...

When the dimensionless solid mass flux was plotted against the total mass toad in the bed the relationship was found to be linear (Figure 4) and from this and on the basis of the data plotted in Figures 2 and 3 a novel scaling parameter, the dimensionless mass turnover, M, was defined as follows ... 

Figure 4 Solids mass flux in the riser as a function of the total mass load in the system...

Karri, S.B.R. Knowlton, T.M. A comparison of annulus solids flow direction and radial solids mass flux profiles at low and high mass fluxes in a riser. In Circulating Fluidized Bed Technology VI Werther, J., Ed. Dechema Frankfurt, Germany, 1999 71-76. 

However, it is not always easy to distinguish between the flow behavior encountered in the fast fluidization and the transport bed reactors [56]. The transport reactors are sometimes called dilute riser (transport) reactors because they are operated at very low solids mass fluxes. The dense riser transport reactors are operated in the fast fluidization regime with higher solids mass fluxes. The transition between these two flow regimes appears to be gradual rather than abrupt. However, fast fluidization generally applies to a higher overall suspension density (typically 2 to 15% by volume solids) and to a situation wherein the flow continues to develop over virtually the entire... 

Based on the method for deriving the general time-averaged conservation laws, another independent formulation to evaluate the solids density can be obtained from the solids mass flux. The mean mass flux mt in the ith direction is expressed (Sun, 1989) as... 

FIGURE 22.1 Typical results for dynamic holdup in gas-flowing sohds-fixed bed contactors. Dynamic holdup as a function of superficial gas velocity for different values of flowing solids flow rates. Dynamic holdup increases with S, different symbols correspond to different flowing solids mass fluxes in the range 1.32-6.13 kg/m sec. (From Roes, A.W.M. and van Swaaij, W.P.M., Chem. Eng. 17, 81, 1979. With permission.)... 

Void Fraction of Packing Phase Type and Size (p-m) Solid Mass Flux (kg/m sec) Superficial Gas Velocity (m/sec)... 

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