Wall voidage

The effect of local enthalpy at CHF is due primarily to the wall voidage, which impairs the critical flux, and secondarily to the bulk voidage, which affects the flow pattern. The coupled effects of local subcooling and flow velocity in a subcooled bubbly flow were first reported by Griff el and Bonilla (1965), neglecting the pressure effect ... 

Louge, M., Lischer, J., and Chang, H., Measurements of Voidage Near the wall of a Circulating Fluidized bed Riser, Powder Tech., 62 269-276 (1990)... 

The first term, (1 - ty) /(I - z), corrects for the voidage difference between that in thejet and that in the emulsion phase. The second term, ( - z) /(I - z), takes into account the fact that only a fraction of the particles having the entrainment velocity Ve will be entrained, the remainder rebounding back to thejet wall due to collisions with the particles already in thejet. Substituting Eq. (63) into Eq. (62), we have... 

All the preceding sections were concerned with one-dimensional voidage distribution in the vertical direction. However, maldistribution of solids in the radial direction, generally dilute in the center and dense next to the wall, often causes unfavorable residence time distributions for both the solids and the fluidizing gas, thus resulting in undesirable product distribution. Although it has long been known that in vertical flow of G/S systems solids are preferentially scattered toward the wall, accurate measurement has not been easy. 

The form of the above equations suggests that the only properties of the bed on which the pressure gradient depends are its specific surface S (or particle size d) and its voidage e. However, the structure of the bed depends additionally on the particle size distribution, the particle shape and the way in which the bed has been formed in addition both the walls of the container and the nature of the bed support can considerably affect the way the particles pack. It would be expected, therefore, that experimentally determined values of pressure gradient would show a considerable scatter relative to the values predicted by the equations. The importance of some of these factors is discussed in the next section. 

The preceding model successfully explains the role played by the particles in the heat transfer processes occurring in the dense-phase fluidized bed at voidage a < 0.7. But it predicts very large values when the contact time of particles with the heating surface decreases because the nonuniformity of the solids concentration near the wall is not taken into account in this model. 

Now, the actual linear velocity with respect to the retaining vessel of a fluid flowing through a fluidized bed of voidage e is m0/e, where u0 is the superficial fluid velocity, that is, the volumetric fluid flow rate divided by the horizontal cross-sectional area of the otherwise empty retaining vessel, being positive for the upward direction. Similarly, the actual linear velocity of the particles with respect to the retaining wall is ud/(l - e), where ud is the solid mass flow rate... 

Voidage profiles represent one of the most important aspects of the flow structure of fast fluidization, which play an important role in gas and solids mixing, mass and heat transfer, and conversion in a chemical reactor. Considerable efforts have been given to studying the axial and radial variation of solids concentration axially, dilute at the top and dense at the bottom, and radially, dilute in the center and dense in the vicinity of the wall. As already mentioned in Section II, these variations depend mainly on gas velocity and solids circulation rate and are also influenced by the configuration of the apparatus. 

Boundaries in fast fluidization refer mainly to the column wall as well as the inlet and outlet. Effect of the wall on pressure drop due to friction between the fluidized solids and the wall surface is minimal (Li et al, 1978), although it is the very cause of radial distribution of parameters. The configuration of the inlet and the outlet often strongly affect gas-solids flow, especially with regard to axial voidage profile. 

Radial voidage profile displays the structure of dilute at the center and dense near the wall. 

Diameter, mm Length, mm Channel diameter, mm Wall thickness, mm Cells per sq. inch Voidage... 

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