The radial profile of solids that exists in fast-fluidized beds and risers is even more surprising. At some point beyond the entrance region of the fast-fluidized bed or riser, particles segregate toward the wall to form a core–annulus profile, as illus- trated in Fig. 16. Studies using kinetic sampling probes, aγ-ray densitometer, and fiber optic probes were able to resolve this core–annulus profile [1,45–48]. Their results showed that the core consists of a lean concentration of solids moving up the riser, whereas the annulus consists of a dense concentration of particles. At moderate solids fluxes, particles in the annulus region actually exhibit a downward velocity, as shown in Fig. 16 [46,48,49]. Karri and Knowlton were able to quantify this downflow as a function of radial profile by measuring the solid mass fluxes in a 20-cm-diameter by 14-m-high riser [49]. Figure 17 presents their results where downflow in the annulus regions was observed for solid mass fluxes of 49 and 93
FIG. 16 Representation of the core–annulus profile in a riser where downflow is observed near the walls. (Adapted from Ref. 48.)
kg/m2s. Miller and Gidaspow [50] showed that the largest magnitude of annular downflow flux at and near the wall was near the bottom of the riser. At less than 2 m from the inlet of Miller’s 7.5-cm-diameter riser, downward fluxes were several times the average feed flux [51].
The implications of this behavior can be substantial. For many catalytic reac- tions, backmixing near the feed region and, to a lesser extent, up throughout the riser can have a significant impact on productivity. Fortunately, many of these reactions require very high solids fluxes where downflow may be less of an issue. For example, Fig. 17 shows that operating Karri and Knowlton’s riser [49] at or above solid fluxes of 195 kg/m2s, results in a core–annulus profile where particles at the wall move in the same direction as those in the core region (positive solids mass flux of⬃1 kg/m2s). In this case, backmixing was limited. Similar findings
FIG. 17 The effects of solids mass flux on the radial net solids mass flux profile. (Adapted from Ref. 49.)
FIG. 18 Representation of the core–annulus profile in a riser where upflow is observed near the walls. (Adapted from Ref. 49.)
have also been reported by Issangya et al. [52]. A representation of this behavior is presented in Fig. 18.
Particle segregation appears also to be influenced by the core–annulus profile in a riser. Karri and Knowlton [49] observed that in the presence of downflow, the particle size distribution in the annulus region was larger than that found in the core. In contrast, this effect appears to only occur for downflow operations. Particle segregation was not observed for core–annulus upflow profiles for either very high or low solid mass fluxes [49]. Jones et al. [53] examined this phenomena using, the Laser Doppler Velocimetry (LDV) of particle-laden jets. Their results showed that eddies or recirculation zones were responsible for this particle segrega- tion. Hence, the high shear and resulting recirculation zones generated from the solids downflow near the wall may be responsible for the segregation effect ob- served by Karri and Knowlton [49]. With upflow at the wall, the low shear may not generate strong enough eddies to effect the particle size distribution across the riser diameter.
There are also design features that can reduce backmixing in risers. Baffles can induce wakes and turbulence, which limit the core–annulus profile. Of course, the added attrition caused by baffles needs to be factored into the design process. Another option is to use secondary feeds to produce a higher plug flow or uniform solids velocity profile at the entrance region. A core–annulus profile may still develop further up the riser, but backmixing is less severe in this region.
As with the axial profile, the design of the entrance and exit region can have a substantial effect on the solid radial concentration profile. Rhodes et al. [42] used a nonisokinetic sampling probe to examine the radial solids loading in a 0.09-m- inner diameter by 7.2-m-high riser. Their results showed that a side solids feed resulted in a nonuniform radial distribution of solids beyond 40 L/D’s, as depicted in Fig. 19. In addition, Rhodes et al. noted that the asymmetries in solids radial distribution were more noticeable in the interphase between the dense and dilute regions. Thus, depending on the design of the feed region, a nonuniform radial profile may exist throughout many industrial risers.
In a similar fashion, the exit configuration of a riser can have an impact on the solids profile for several L/D’s below the exit region. Brereton and Grace [54] observed this effect for smooth and abrupt riser exits. As shown in Fig. 20, using
FIG. 19 Illustration of the nonuniform solids radial profile in a riser due to solids feed on the side of the riser (not drawn to scale). (Adapted from Ref. 28.)
FIG. 20 Effect of exit configuration on solids volume fraction for a 0.15-m-diameter by 9.3-m-high riser with a superficial gas velocity of 7.1 m/s, initial solids flux of 73 kg/m2s, and 148-
FIG. 21 Solids flux ratio with respect to radial position for a riser with a smooth, rounded exit at a superficial gas velocity of 4.2 m/s, solids flux of 50 kg/m2s, and 80-µm sand particles.
(From Ref. 55.)
a smooth, wide-radius bend to terminate the riser resulted in little deviation in the axial solids concentration profile. However, an abrupt bend, such as a square bend or tee, resulted in backmixing, which affected the overall riser solids volume frac- tion profile up to 20 L/D’s below the exit region.
Similar effects for solids fluxes are reflected in the data of Kruse and Werther [55] who compared normalized solid fluxes to radial solids loadings for a 0.4-m- diameter by 15.1-m-high riser, as shown in Figs. 21 and 22. For smooth bends, substantially less downflow is observed compared to the abrupt exit configurations. In addition, the region of downflow for the abrupt exit configuration was over twice the size of that observed for the smooth configuration.
These results provide a good example of the importance of riser design for chemical production. For combustors, where backmixing is tolerable and some- times even desired, asymmetric feed designs and abrupt exits are less critical. How-
FIG. 22 Solids flux ratio with respect to radial position for a riser with an abrupt, squared exit at a superficial gas velocity of 4.2 m/s, solids flux of 71 kg/m2s, and 80-µm sand particles.
FIG. 23 Illustration of riser entrance region for a more uniform solids loading profile.
ever, in chemical production such as in oxidation and chlorination, asymmetric solids profiles and backmixing can seriously reduce selectivity and activity. Fortu- nately, both the entrance and exit can be designed such that minimal asymmetric solids profiles and backmixing ensues. For the entrance region, care needs to be taken such that entering solids are well mixed with the entraining gas. One such design is shown in Fig. 23. A fluidizing gas is used to distribute incoming solids, and one or more jets are used to entrain catalyst into the riser. Similarly, the exit region should have either a long radius bend or a disengagement section. Typically, industrial risers have a stripper section at the top of the riser to not only strip gas but also minimize exit effects on the riser, as shown in Fig. 24.
Meso-Scale Behavior: Clusters and Streamers
Riser sections in circulating fluidized beds exhibit a core–annulus profile with downward flow resulting in the formation of clusters and streamers of particles.
This phenomenon was proposed by Squires et al. [56] and Yerushalmi and Avidan [21,57]. Under the assumption that the pressure drop equals the weight of the solids in suspension, the resulting slip velocity, calculated as
vslip⫽ vg⫺
Gs
ρsεs
(34)
was found to be several times larger than the terminal velocity [51]. Because the slip velocity cannot exceed the terminal velocity, it was postulated that the particles must be forming clusters that effectively act as larger particles. Today, cluster and streams are frequently observed. High-speed movies [24], laser sheet [58], infrared imagining [59], and fiber-optic probes [60–62] all reveal the presence of wave packet of particles near the riser wall moving with the downward annulus flow in continuous but dynamic and unstable sheets. These sheets of particles (commonly called clusters, streamers, swarms, strings, or strands) are represented in Fig. 25. Laser sheet and fiber-optic studies of Horio [43] and Rudnick and Werther [61] have further demonstrated that these clusters are three dimensional in nature and can be found in the annulus and core regions. In general, it was observed that clusters move in a direction parallel to the flow of the suspension phase. In other words, in a core–annulus profile with downward flow at the walls, clusters in the annulus region flow downward and clusters in the core region flow upward.
Soong et al. [63] experimentally measured the cluster length and time-averaged local solid volume fraction in riser flow. Their results were in agreement with Yerushalmi and Avidan’s [57] earlier empirical correlation of
dc⫹ dp⫹ εs(0.027⫺ 10dp)⫹ 32ε6s (35)
However, Soong et al. replaced the average local solids volume fraction of parti- cles,εs, by the solids volume fraction of a cluster,εcl, as
dc⫹ dp ⫹ εcl(0.027⫺ 10dp)⫹ 32ε6cl (36)
Gu and Chen [64] further correlated Soong’s data such that the solids volume fraction of a cluster can be related to the local solids volume fraction of particles using the expression
εcl⫽ εs,max
冤
1⫺冢
εs
εs,max
冣
3.4
冥
(37)where the maximum local solids volume fraction,εs,max, is 0.57. Tsuo and Gidaspow
[65] observed that, for Group A powders, the clusters were 2–3 cm in length in the down-flowing annulus region. Furthermore, cluster density increased with increasing solids flux, decreasing gas velocity, or decreasing pipe diameter.
The mechanism for the formation and degeneration of clusters in a riser is still under some dispute. Tsuo and Gidaspow [65] proposed that clusters are the result of partially inelastic collision with the walls. Particles hit the wall, lose energy, and fall, to collide with another particle. This process continues until a cluster is formed.
Senior and Grace [66] proposed that inelastic wall collisions cannot account for all the energy loss needed to form clusters. For this to happen, wall collisions would need a coefficient of restitution of less than 0.1, which is unlikely. Perfectly elastic collisions have a coefficient of restitution of 1. Instead, Senior and Grace proposed that the balance between shear-induced lift and drag forces on a particle act to momentarily detain particles at the wall region of the riser. After a particle collides with the wall, it has insufficient momentum to counteract the lift force. As a result, the particle continues to hit the wall, each time losing more lateral velocity. When the particle-to-wall friction slows the particle below the local gas velocity, lift forces acting in the opposite direction move the particle away from the wall to the near-wall regions. Clusters form when many particles undergo this lateral-velocity-reduction process. The downward motion of a cluster is caused by the net lift forces on a cluster being less than the sum of the forces on each individ- ual particle.
Particle migration to the wall is not only dependent on axial and lateral veloci- ties but also on the particle diameter. Lee and Durst [67] found that 100- and 200- µm-diameter glass beads readily accumulated at the wall, whereas larger particles, with a 400–800-µm diameter, did not. The larger particles were traveling at sig- nificantly lower axial velocities and were less influenced by lift forces directed to the wall. Tsuji et al. [68] was also able to measure this crossover of particles to the wall for smaller particles. Senior and Grace [66] were able to model these trajectories and found similar conclusions. For particles larger than 500 µm in diameter, no range of lateral velocities was found that slowed the particle signifi- cantly enough for crossover to the wall. Yet, for 230-µm particles, a significant concentration of particles was predicted to accumulate near the wall for initial lateral velocities of 4.5–5.5 cm/s. For 40-µm particles, concentrations were found to be an order of magnitude larger at the wall than that found for 230-µm particles with lateral velocities ranging from 3 to 22 cm/s.
What is interesting here is that if particle collisions with the wall help create the formation of clusters, how do cluster form in the core region as observed by Horio [43] and Rudnick and Werther [61]. Furthermore, Karri and Knowlton [49]
observed that particles in the annulus region with a downward flow had a larger particle size distribution than that in the core. In a core–annulus profile where both regions have an upflow profile, no particle size distribution effects were observed. Both of these results contradict the above postulate of Senior and Grace in which a wall is needed for cluster formation and larger particles prefer the core region. Most likely, the magnitude of the solids flux or solids concentration may have a significant impact on the locality of cluster formation and particle-size-segregation effects. These macroscopic properties may also need to be considered.
Horio [43] proposed that another mechanism may be responsible for cluster formation. A particle in flight can have either attractive or repulsive forces with nearby particles. Two particles traveling perpendicular to the gas flow tend to re- peal each other, whereas two particles aligned parallel with the flow tend to attract each other due to the nearest-neighbor effect on lift and drag. Yet, in riser flow, particle alignment is not stable, as particles undergo collisions, bumping, tumbling, and other nonelastic processes. This may be the very mechanism to ensure cluster- ing. The combination of nonelastic processes and the parallel-aligned particle flow may provide the attractive force needed to promote clustering.
Furthermore, Horio noted that buoyancy forces dominate in lean-phase regions, whereas gravitational forces dominate in dense-phase regions. This results in a shear between clusters and the lean-phase region. The interaction of these forces controls the development of particle groups to form steady but turbulent structures of a certain characteristic length. Two-dimensional simulations of particles show this very event, where a homogeneous suspension evolved into clusters [69].