Solid flow mass flux

The results presented so far in this section correspond to the regime of fully developed riser flow. Kuipers and van Swaaij (1996) applied the KTGF-based model developed by Nieuwland et al. (1996b,c) to study the effect of riser inlet configuration on the (developing) flow in CFB riser tubes and found that the differences in computed radial profiles of hydrodynamic key variables (i.e., gas and solids phase mass fluxes) rapidly disappear with increasing elevation in the riser tube. 

Ultrasound can thus be used to enhance kinetics, flow, and mass and heat transfer. The overall results are that organic synthetic reactions show increased rate (sometimes even from hours to minutes, up to 25 times faster), and/or increased yield (tens of percentages, sometimes even starting from 0% yield in nonsonicated conditions). In multiphase systems, gas-liquid and solid-liquid mass transfer has been observed to increase by 5- and 20-fold, respectively [35]. Membrane fluxes have been enhanced by up to a factor of 8 [56]. Despite these results, use of acoustics, and ultrasound in particular, in chemical industry is mainly limited to the fields of cleaning and decontamination [55]. One of the main barriers to industrial application of sonochemical processes is control and scale-up of ultrasound concepts into operable processes. Therefore, a better understanding is required of the relation between a cavitation coUapse and chemical reactivity, as weU as a better understanding and reproducibility of the influence of various design and operational parameters on the cavitation process. Also, rehable mathematical models and scale-up procedures need to be developed [35, 54, 55]. 

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. 

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). 

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... 

In Fig. 5.5, the flow configuration and velocity and temperature distributions at the time instant of 12.5 s are depicted. Even though the flow is subsonic, due to the high Reynolds number, the flow structure in the region upstream of the solid propellant is minimally affected by the time-dependent boundary shape due to phase change. However, the thermal characteristics near the propellant interface show clear signs of time dependency, indicating that the mass flux of... 

Compared to rivers and lakes, transport in porous media is generally slow, three-dimensional, and spatially variable due to heterogeneities in the medium. The velocity of transport differs by orders of magnitude among the phases of air, water, colloids, and solids. Due to the small size of the pores, transport is seldom turbulent. Molecular diffusion and dispersion along the flow are the main producers of randomness in the mass flux of chemical compounds. 

Charge transfer occurs when particles collide with each other or with a solid wall. For monodispersed dilute suspensions of gas-solid flows, Cheng and Soo (1970) presented a simple model for the charge transfer in a single scattering collision between two elastic particles. They developed an electrostatic theory based on this mechanism, to illustrate the interrelationship between the charging current on a ball probe and the particle mass flux in a dilute gas-solid suspension. This electrostatic ball probe theory was modified to account for the multiple scattering effect in a dense particle suspension [Zhu and Soo, 1992]. 

Evaluating the performance of a gas-solid transport system usually requires a means of macroscopic field description of the distribution of basic flow properties such as pressure, mass fluxes, concentrations, velocities, and temperatures of phases in the system. To conduct such an evaluation, the Eulerian continuum or multifluid approach is usually the best choice among the available approaches. 

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... 

Figure 13. The pattern map for an upward vapor-liquid flow of R21 refrigerant through the assemblage with plain fins (8FPI). Here 1, 2, 3, 4 are the areas of annular flow, cell flow, froth flow, plug and bubble flows respectively. Solid lines indicate transition between flow modes and dashed lines indicate constant mass flux condition.

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... 

Similar results may be obtained for convective mass transfer. If a fluid of species concentration Ci, flows over a surface at which the species concentration is maintained at some value Clilv C, transfer of the species by convection will occur. Species 1 is typically a vapor that is transferred into a gas stream by evaporation or sublimation at a liquid or solid surface, and we are interested in determining the rate at which this transfer occurs. As for the case of heat transfer, such a calculation may be based on the use of a convection coefficient [3, 5]. In particular we may relate the mass flux of species 1 to the product of a transfer coefficient and a concentration difference... 

In the applications of gas-solid flows, measurements of particle mass fluxes, particle concentrations, gas and particle velocities, and particle aerodynamic size distributions are of utmost interest. The local particle mass flux is typically determined using the isokinetic sampling method as the first principle. With the particle velocity determined, the isokinetic sampling can also be used to directly measure the concentrations of airborne particles. For flows with extremely tiny particles such as aerosols, the particle velocity can be approximated as the same as the flow velocity. Otherwise, the particle velocity needs to be measured independently due to the slip effect between phases. In most applications of gas-solid flows, particles are polydispersed. Determination of particle size distribution hence becomes important. One typical instrument for the measurement of particle aerodynamic size distribution of particles is cascade impactor or cascade sampler. In this chapter, basic principles, applications, design and operation considerations of isokinetic sampling and cascade impaction are introduced. 

However, for a fully developed gas-solid pipe flow, the particle diffusive mass flux is usually negligibly small compared with the particle mass flux (Zhu et al., 1991a). Hence, the isokinetic sampling of a gas-solid suspension flow in principle is able to yield the particle mass concentration provided that the particle velocity can be determined. This principle has served as the most primary method for the calibration of measuring systems on particle mass concentration. 

The applications of isokinetic sampling cover but are not limited to the sampling of aerosols such as flu gas in chimney, soots (unbumed carbons) from diesel engine exhaust, dusts suspended in the atmosphere, and fumes from various sprayers measurements of particulate mass fluxes in pneumatic transport pipelines and other particulate pipe flows solid fuel (also some liquid fuels) distributions in furnaces, engines, and other types of combustors and calibrations of instruments for the measurements of particle mass concentrations. Isokinetic sampling can also be applied to flows with liquid droplets. In this case, the droplet sample is usually collected by an immiscible liquid (Koo et al., 1992 Zhang and Ishii, 1995). 

Isokinetic sampling is for the direct measurements of particulate mass fluxes or concentrations of aerosols (assuming no slip between aerosols and the gas flow) in gas-solid suspension flows. This is accomplished by inserting a thin-wall tube into the particulate suspension flow to draw samples at the isokinetic condition and by passing the collected particles into a sampling train. Typical... 

Both the transmission-type probe and the reflection-type probe, need be calibrated for their measuring range in local solids concentration. The calibration of optic fiber probes is known to be a difficult problem. Calibration methods fall into two categories the first is to calibrate a probe against agitated or fluidized liquid—solid systems the second is to use particle free-fall in gas—solid systems or the traditional pressure drop method for fluidized solids the third is in a flow system with particle density deduced from mass flux of particles and measurement where phase velocities were nearly equal. 

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