Voidage velocity

The nonideal nature of G/S fluidization, shown as the bulging curve for zero solids flow in the voidage-velocity plot of Fig. 60, is considered to be caused by gas aggregation at low velocities and solids aggregation at high velocities. Alternately, the G/S system may be visualized to be equivalent to a binary mixture of the aggregated gas bubbles with a volume fraction of (e — 0) on the one hand, and of the aggregated solid particles in the form of clusters with a volume fraction of (1 — e) on the other. At low gas velocities,... 

Mullin, J.W. and Giarside, J. (1970) Voidage-velocity relationships in the design of suspended-bed crystallizers. British Chemical Engineering, 15, 773-775. 

In the case of a packed column, the terms on the right-hand side should each be divided by the voidage, ie, the volume fraction not occupied by the soHd packing (71). In unpacked columns at low values of the sHp velocity approximates the terminal velocity of an isolated drop, but the sHp velocity decreases with holdup and may also be affected by column internals such as agitators, baffle plates, etc. The sHp velocity can generally be represented by (73) ... 

Fig. 3. Zenz plot. Correlation of bed voidage, S, the volume fraction of the fluidized bed that is occupied by gas, for values of S from 1.0 to 0.5, and dimensionless velocity and particle properties, where p — p )/(3 PgU ). The horizontal lines represent the different values of e = 0.5...

The relation between superficial velocity (U) and bed voidage (e) in a fluidised bed can be described by the classical correlation first postulated by Richardson and Zaki 49... 

A sensitivity analysis showed that the calculated value of pressure gradient was very sensitive to the value of the coefficient of friction pF. but was relatively insensitive to the slip velocity uB and to the bed 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 ... 

Ishii and Murakami (1991) evaluated the CFB scaling relationships of Horio et al. (1989) using two cold CFB models. Solids flux, pressure drop, and optical probe measurements were used to measure a large number of hydrodynamic parameters to serve as the basis for the comparison. Fair to good similarity was obtained between the beds. Dependent hydrodynamic parameters such as the pressure drop and pressure fluctuation characteristics, cluster length and voidage, and the core diameter were compared between the two beds. The gas-to-solid density ratio was not varied between the beds. As seen in Table 7, the dimensionless solids flux decreased as the superficial velocity was increased because the solids flux was held constant. 

The Hydrodynamic Theory of fluidized bed stability was proposed by Foscolo and Gibilaro who adapted the stability principle of Wallis. They postulated that a fluidized bed is composed of two interpenetrating fluids. One fluid is the gas phase, and the solids phase is also considered as a continuous fluid phase. In this theory, voidage disturbances in the bed propagate as dynamic and kinetic waves. The stability of the fluidized bed depends upon the relative velocities of these two waves. The velocities of the kinetic wave (ue) and the dynamic wave (nj are ... 

The bubble voidage in the draft tube, ebr, was calculated on the basis of the velocity of a rising gas slug relative to its surrounding solids. The total gas superficial velocity in the draft tube, lJjn can be derived to be... 

Use trial and error between Eqs. (12)—(14) to evaluate U (the equilibrium particle velocity in the draft tube after acceleration), er (the equilibrium voidage in the draft tube after acceleration), and f (the solid friction factor). 

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... 

Equation (64) predicts correctly the increase in solid entrainment into thejet with increases in jet velocity and the decrease with increases in solid loading in a two-phase jet. Since neither the voidage nor the particle velocity inside thejet were measured, direct verification of Eq. (64) was not performed. 

We next consider the volume fractions of the various regions in the fluidized bed. The volume fraction of bubbles, fb, m3 bubbles (m3 bed)-1, can be assessed from the point of view of either voidage or velocity. In terms of voidage, if we assume the void fraction... 

A first-order reaction, A -> products, is conducted in a fluidized-bed reactor. Before fluidization, the bed is 1.8 m deep (Lpa), with a voidage (epa) of 0.42. The feed gas (P/ = 0.45 kgm-3 p,y = 4.2 x 10-5 Pa s) flows through the bed at a velocity three times the minimum fluidization velocity. The following data are also available ... 

A binary suspension consists of equal masses of spherical particles of the same shape and density whose free falling velocities in the liquid are 1 mm/s and 2 mm/s, respectively. The system is initially well mixed and the total volumetric concentration of solids is 0.2. As sedimentation proceeds, a sharp interface forms between the clear liquid and suspension consisting only of small particles, and a second interface separates the suspension of fines from the mixed suspension. Using a suitable model for the behaviour of the system, estimate the falling rates of the two interfaces. It may be assumed that the sedimentation velocity uc in a concentrated suspension of voidage e is related to the free falling velocity u0 of the particles by ... 

If, in the upper zone, the settling velocity of the fine particles and the voidage are ux and ex respectively,... 

The relation between bed voidage e and fluid velocity uc for particulate fluidisation of uniform particles which are small compared with the diameter of the containing vessel is given by ... 

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