Fluidization void fraction calculation

Calculations of the overall collection efficiency for the fluidized bed filter begin with specification of the values of the superficial gas velocity, Uq, minimum fluidization velocity, bed height at minimum fluidization, void fraction at minimum... 

Peng ZB, Doroodchi E, Luo C, Moghtaderi B Influence of void fraction calculation on fidelity of CFD-DEM simulation of gas-solid bubbling fluidized beds, AIChE J 60 2000-2018, 2014. http //dx.doi.org/10.1002/aic.14421. 

Owing to the high computational load, it is tempting to assume rotational symmetry to reduce to 2D simulations. However, the symmetrical axis is a wall in the simulations that allows slip but no transport across it. The flow in bubble columns or bubbling fluidized beds is never steady, but instead oscillates everywhere, including across the center of the reactor. Consequently, a 2D rotational symmetry representation is never accurate for these reactors. A second problem with axis symmetry is that the bubbles formed in a bubbling fluidized bed are simulated as toroids and the mass balance for the bubble will be problematic when the bubble moves in a radial direction. It is also problematic to calculate the void fraction with these models. 

In equations 9.34 and 9.35 m/is the value of the void fraction at minimum fluidization. It should be noted that emf is not equal to the void fraction in the packed bed and in order to use equation 9.35 to calculate umf it is necessary to know the value of emf. 

If it is possible to measure the height of the bed at incipient fluidization, Lmf, then emf can be calculated from equation 9.34 or simply from the ratio of Lmf to the height of the packed bed if the void fraction in the latter is known. 

It can be observed that it is possible to calculate the height corresponding to the minimum fluidizing condition. From the knowledge of the values of solid density, gas density, and void fraction, one can easily determine the pressure drop. 

Resin manufacturers often express the fluidization properties of their resins in terms of the percentage expansion of the bed related to Its packed depth. This expansion cannot be calculated directly from the above equation since a range of bead sizes is present. Typical data ate shown in Fig. 13.3-1, taken from a Rohm and Haas pamphlet. These curves can be correlated by an equation giving the expansion as a function of the 1.5 power of the flow rate. An equation of almost identical form can be derived from the Richardson-Zaki equation by expressing the expansion in terms of the void fraction and using appropriate values for n. 

Anthracite coal of 1500 kg/m density is to be fluidized with air at 140 kPa in a vessel 3 m in diameter. 48 tons of coal, ground to an average diameter of 70-mesh (US Standards) are placed in the vessel, which is filled to a height of 2 m. Calculate the static void fraction and the minimum void fraction at height for fluidization. 

In the absence of experimental data, it is possible to predict the minimum fluidization velocity by equating the pressure drop given by (13.3-1) and that calculated from a pressure drop equation for flow through a packed bed just before incipient fluidization. The resulting equation contains a shape factor and the void fraction at minimum fluidization, which may not be available. This may be correlated with respect to the particle diameter. Finally, according to Leva [1960], this leads to... 

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