Particle convection

Liquid-solid transitions in suspensions are especially complicated to study since they are accompanied by additional phenomena such as order-disorder transition of particulates [98,106,107], anisotropy [108], particle-particle interactions [109], Brownian motion, and sedimentation-particle convection [109], Furthermore, the size, size distribution, and shape of the filler particles strongly influence the rheological properties [108,110]. More comprehensive reviews on the rheology of suspensions and rubber modified polymer melts were presented by Metzner [111] and Masuda et al. [112], respectively. 

The scale models must be carefully designed. Failure to match the important dimensionless parameters will lead to erroneous simulation results. Modeling can be extended to particle convective heat transfer. Wear or erosion of in-bed surfaces can be qualitatively studied, although quantitative assessment requires the identification and simulation of additional wear-related parameters. 

In general, gas-to-particle or particle-to-gas heat transfer is not limiting in fluidized beds (Botterill, 1986). Therefore, bed-to-surface heat transfer coefficients are generally limiting, and are of most interest. The overall heat transfer coefficient (h) can be viewed as the sum of the particle convective heat transfer coefficient (h ), the gas convective heat transfer coefficient (h ), and the radiant heat transfer coefficient (hr). 

Overall bed-to-surface heat transfer coefficient = Gas convective heat transfer coefficient = Particle convective heat transfer coefficient = Radiant heat transfer coefficient = Jet penetration length = Width of cyclone inlet = Number of spirals in cyclone = Elasticity modulus for a fluidized bed = Elasticity modulus at minimum bubbling = Richardson-Zaki exponent... 

The correlation was tested against nine experimental sets of data with a mean-square error of 22%. Visser and Valk (1993) subsequently modified the particle convection term of the model of Borodulya et al. for low gas velocities. Their results indicated improved agreement for low velocity ranges. 

Han, G. Y., Experimental Study of Radiative and Particle Convective Heat Transfer in Fast Fluidized Beds, Ph.D. Dissertation, Lehigh University (1992)... 

Cross-flow filtration systems utilize high liquid axial velocities to generate shear at the liquid-membrane interface. Shear is necessary to maintain acceptable permeate fluxes, especially with concentrated catalyst slurries. The degree of catalyst deposition on the filter membrane or membrane fouling is a function of the shear stress at the surface and particle convection with the permeate flow.16 Membrane surface fouling also depends on many application-specific variables, such as particle size in the retentate, viscosity of the permeate, axial velocity, and the transmembrane pressure. All of these variables can influence the degree of deposition of particles within the filter membrane, and thus decrease the effective pore size of the membrane. 

The PDF codes presented in this chapter can be (and have been) extended to include additional random variables. The most obvious extensions are to include the turbulence frequency, the scalar dissipation rate, or velocity acceleration. However, transported PDF methods can also be applied to treat multi-phase flows such as gas-solid turbulent transport. Regardless of the flow under consideration, the numerical issues involved in the accurate treatment of particle convection and coupling with the FV code are essentially identical to those outlined in this chapter. For non-orthogonal grids, the accurate implementation of the particle-convection algorithm is even more critical in determining the success of the PDF simulation. 

For each test case, a non-reacting scalar (e.g., mixture fraction) should be used to determine the spatial distribution of its mean and variance (i.e., (f) and (f/2 . These results can then be compared with those found by solving the RANS transport equations (i.e., (4.70), p. 120 and (4.90), p. 125) with identical values for (U) and Tt. Fike-wise, the particle-weight distribution should be compared with the theoretical value (i.e., (7.74)). While small fluctuations about the theoretical value are to be expected, a systematic deviation almost always is the result of inconsistencies in the particle-convection algorithm. 

Convective flow between particles Convective flow through pores... 

C c Specific heat of particles Interparticle clearance hp Particle convective heat transfer coefficient... 

The governing heat transfer modes in gas-solid flow systems include gas-particle heat transfer, particle-particle heat transfer, and suspension-surface heat transfer by conduction, convection, and/or radiation. The basic heat and mass transfer modes of a single particle in a gas medium are introduced in Chapter 4. This chapter deals with the modeling approaches in describing the heat and mass transfer processes in gas-solid flows. In multiparticle systems, as in the fluidization systems with spherical or nearly spherical particles, the conductive heat transfer due to particle collisions is usually negligible. Hence, this chapter is mainly concerned with the heat and mass transfer from suspension to the wall, from suspension to an immersed surface, and from gas to solids for multiparticle systems. The heat and mass transfer mechanisms due to particle convection and gas convection are illustrated. In addition, heat transfer due to radiation is discussed. 

Heat transfer between a fluidized bed and an immersed surface can occur by three modes, namely, particle convection, gas convection, and radiation. 

It is seen that particle convection is important for almost all the conditions, except at low bed temperatures in a bed of large particles, where the gas convection becomes important. 

Development of a mechanistic model is essential to quantification of the heat transfer phenomena in a fluidized system. Most models that are originally developed for dense-phase fluidized systems are also applicable to other fluidization systems. Figure 12.2 provides basic heat transfer characteristics in dense-phase fluidization systems that must be taken into account by a mechanistic model. The figure shows the variation of heat transfer coefficient with the gas velocity. It is seen that at a low gas velocity where the bed is in a fixed bed state, the heat transfer coefficient is low with increasing gas velocity, it increases sharply to a maximum value and then decreases. This increasing and decreasing behavior is a result of interplay between the particle convective and gas convective heat transfer which can be explained by mechanistic models given in 12.2.2, 12.2.3, and 12.2.4. 

The model based on the concept of pure limiting film resistance involves the steady-state concept of the heat transfer process and omits the essential unsteady nature of the heat transfer phenomena observed in many gas-solid suspension systems. To take into account the unsteady heat transfer behavior and particle convection in fluidized beds, a surface renewal model can be used. The model accounts for the film resistance adjacent to the heat transfer... 

Particle convection, caused by the particle motion within the bed, is concerned with the heat transfer from a surface when it is in contact with the particulate emulsion phase instead of the void/bubble phase. Thus, the heat transfer coefficient of particle convection can be... 

The particle convective component hpc may be calculated from Eq. (12.39). The heat transfer coefficients of film can be calculated from Eq. (12.48)... 

In circulating fluidized beds, the clusters move randomly. Some clusters are swept from the surface, while others stay on the surface. Thus, the heat transfer between the surface and clusters occurs via unsteady heat conduction with a variable contact time. This part of heat transfer due to cluster movement represents the main part of particle convective heat transfer. Heat transfer is also due to gas flow which covers the surface (or a part of surface). This part of heat transfer corresponds to the gas convective component. 

The particle convection is in general important in the overall bed-to-surface heat transfer. When particles or particle clusters contact the surface, relatively large local temperature gradients are developed. This rate of heat transfer can be enhanced with increased surface renewal rate or decreased cluster residence time in the convective flow of particles in contact with the surface. The particle-convective component hpc can be expressed by the following equation, which is an alternative form of Eq. (12.39) ... 

For a very short cluster contact time or very large fluidizing particle, hf dominates the particle convection and thus Eq. (12.59) yields... 

Derive the axial profile of the particle convective heat transfer coefficient in a circulating fluidized bed of fine particles using the information given in 10.4.1. It can be assumed in the derivation that particles in the bed are all in a cluster form. 

Illustration Aggregation of area-conserving clusters in two dimensional chaotic flows. Particles, convected passively in a two-dimensional chaotic flow, aggregate on contact to form clusters. The capture radius of the clusters increases with the size of the cluster. Since these simulations are in two dimensions, the area of the aggregating clusters is conserved. 

Qi, C. and Ihab, H. Farag Heal Transfer Mechanism Due to Particle Convection in Circulating Fluidized Bed, in Circulating Fluidized Bed Technology IV (Amos A. Avidan, ed.), pp. 396-401. Somerset, Pennsylvania (1993). 

Figure 4 plots, against suspension density, the heat transfer coefficients measured by Basu (1990) over a wide range of bed temperature for 296 pm sand, by Kobro and Brereton (1986) at a temperature of 850°C for 250 pm sand and by Grace and Lim (1989) at 880°C for 250-300 pm sand. The overall heat transfer coefficient is shown to increase with bed temperature. Before radiation becomes dominant in heat transfer, the observed rise in heat transfer coefficient with bed temperature may be explained as follows. The gas convective component is expected to decrease mainly because of the inverse dependence of gas density on temperature. On the other hand, the particles convective component will increase with temperature, thus leading to an increase in gas conductivity, because the latter is dominant for... 

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