Slip velocity between phases

Relation for the slip velocity between phases in the core region... 

Gas sparging can be modeled using the Eulerian multiphase model or the algebraic slip mixture model. For the Eulerian multiphase model, two sets of momentum equations are used, and the same comments regarding the slip velocity between phases apply, although the issue is not as critical. That is, the velocity data used for the gas phase could be corrected slightly from the liquid-phase velocities but need not be because the gas phase has so little inertia compared to the liquid phase. When the algebraic slip mixture model is used, separate boundary conditions are not required for the individual phases, so a correction of the velocity data is not required. 

The slip velocity between gas and liquid is v, = Vc Vi. For two-phase gas/liqiiid flow, Ri + Rc = 1. A very common mistake in practice is to assume that in situ phase volume fractious are equal to input volume fraclions. 

The results of an example calculation for a recirculating fluidized bed coal devolatilizer of 0.51 m in diameter handling coal of average size 1200 pm at 870°C and 1550 kPa are presented in Fig. 11. The calculation is based on operating the fluidized bed above the draft tube at 4 times the minimum fluidization velocity. It is also based on the selection of a distributor plate to maintain the downcomer at the minimum fluidization condition. If the two-phase theory applies, this means that the slip velocity between the gas and the particles in the downcomer must equal to the interstitial minimum fluidizing velocity as shown below. 

The solids particle velocity in the gas-solid two-phase jet can be calculated as shown in Eq. (27), assuming that the slip velocity between the gas and the solid particles equals the terminal velocity of a single particle. It should be noted that calculation of jet momentum flux by Eq. (26) for concentric jets and for gas-solid two-phase jets is only an approximation. It involves an implicit assumption that the momentum transfer between the concentric jets is very fast, essentially complete at the jet nozzle. This assumption seems to work out fine. No further refinement is necessary at this time. For a high velocity ratio between the concentric jets, some modification may be necessary. 

It is readily apparent that finer and finer structures get resolved as the number of spatial grids is increased. Statistical quantities, such as average slip velocity between the gas and particle phases, obtained by averaging over the whole domain, were found to depend on the grid resolution employed in the simulations and they became nearly grid-size independent only when grid sizes of the order of a few ( 10) particle diameters were used. Thus, if one sets out to solve microscopic TFM equations, grid sizes of the order of few particle... 

A final piece of the proof-of-concept calculations is to compare the predictions obtained by solving the filtered TFM equations with highly resolved simulations of the microscopic TFM equations. For this purpose, Andrews and Sundaresan (2005) performed simulations of the microscopic TFM equations in a 16 x 32 cm periodic domain at various resolutions (e.g., see Fig. 29). From these simulations, they extracted domain-average quantities in the statistical steady state (see Agrawal et al., 2001 for a discussion of how these data are gathered). Fig. 33 shows the domain-average slip velocity between the gas and particle phases at various grid resolutions (shown by the squares connected by... 

Here, fcL is in m s , /0l is in m s-1, gc is in kgm m kgf 1 s 2, pL is in kg in-3, and u9 is in m 1. The above relation is graphically illustrated and compared with a similar relation for the downflow conditions in Fig. 7-18. Better values of kL are obtained for slower liquid velocities in upflow compared to downflow, presumably due to an increase in circulation inside the liquid drops, caused, among other things, by the greater slip velocity between the liquid and the gas phase. It should be noted.that the estimation of aL and kL from the above relations requires a prior knowledge of (AP/AZ)LG. 

Imafuku et al.46 measured the gas holdup in a batch (i.e., no liquid flow) three-phase fluidized-bed column. They found that the presence of solids caused significant coalescence of bubbles. They correlated the gas holdup with the slip velocity between the gas and liquid. They found that the gas holdup does not depend upon the type of gas distributor or the shape of the bottom of the column when solid particles are completely suspended. Kato et al.53 found that the gas holdup in an air-water-glass sphere system was somewhat less than that of the air-water system and that the larger solid particles showed a somewhat smaller... 

Up — Uc represents the resultant slip velocity between the particulate and continuous phase. Some other commonly used drag coefficient correlations are listed in Appendix 4.2. For fluid particles such as gas bubbles or liquid drops, the drag coefficient may be different than that predicted by the standard drag curve, due to internal circulation and deformation. For example, Johansen and Boysen (1988) proposed the following equation to calculate Cd, which is valid for ellipsoidal bubbles in the range 500 < Re < 5000 ... 

Slip, or relative velocity between phases, occurs for vertical flow as well as for horizontal. No completely satisfactory, flow regime-independent correlation for volume fraction or holdup exists for vertical flow. Two frequently used flow regime-independent methods are those by Hughmark and Pressburg AIChE J., 7, 677 [1961]) and Hughmark Chem. Eng. Prog., 58[4], 62 [April 1962]). Pressure drop in upflow may be calculated by the procedure described in Hu mark Ind. Eng. Chem. Fundam., 2, 315-321 [1963]). The mechanistic, flow regime-based methods are advisable for critical applications. 

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. 

Us = slip velocity between drop and continuous phase. 

Slip velocity between fluid and particle phase defined by... 

Effect of Drum Speed on Solids and Fluid Mean Residence Times. Due to the difference in the axial velocity of the two phases (slip velocity) the mean residence time of the solid particles in the drum is in general higher than that of the fluid. The ratio of the mean residence time (t/Xj) is a measure of the slip velocity between... 

If the two-phase theory applies, the slip velocity between the gas and the particles in the downcomer must equal the interstitial minimum fluidizing velocity as... 

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