A study of inertial effects in granular bed filtration

Abstract

The filtration efficiency of a granular bed filter was investigated in the domain where inertial effects are dominant. A filtration model predicting single sphere and total bed efficiencies based on trajectory calculations of dust particles in the voids of the granular bed was developed. The model uses the flow field in a bed of spheres arranged in a body-centered cubic array for which the filtration efficiency was found to be a function of a modified Stokes number defined by Sf' = St X F where the function Fdepends only on the Reynolds number. The value of the function F can be found experimentally or predicted from the Ergun correlation to be F = 1 + 0.0157 Re, The filtration efficiency calculated using the model agrees well with experimental results obtained in beds of dense cubic packing of spheres especially at relatively low Reynolds numbers (Re < 2W) and relatively high Stokes numbers (St' > 0.01). The prediction of the theoretical model also agrees well with experimental data for randomly packed beds at low porosities and low Reynolds numbes. Most theoretical models of filtration in granular beds are based on evaluating the filtration efficiency of a single granule and then integrating the results over the entire bed by assuming that all granules in the bed experience similar filtration conditions and have the same filtration efficiency. The single sphere efficiency is usually determined by calculating the trajectories of aerosol particles flowing toward a single sphere and modifying the gas flow field to account for the porosity of the bed. The major difficulty in using this approach is that the particle trajectories and therefore the filtration efficiency depends strongly on the actual threedimensional flow profile of the gas flowing through the bed. A representative and accurate threedimensional velocity profile for flow in a granular bed is not yet availabe in the literature so that simplified flow models must be used for trajectory calculations with results that do not agree well with experimental data.In the present work an improved version of the Snyder and Stewart (1966) flow model for a dense cubic packing of spheres is used to evaluate the filtration efficiency in a granular bed. The threedimensional flow model enables trajectory calculations to be made for a single sphere as well as for the entire bed. The calculated single sphere and total bed efficiencies are compared to determine the validity of the single sphere efficiency concept. The results for the single sphere and total bed efficiencies are also compared with experimental data obtained in both dense cubic packing of spheres and in randomly packed beds. CONCLUSIONS AND SIGNIFICANCEA filtration model predicting both single sphere and total bed efficiency was developed for a dense cubic packing using the flow field developed by Snyder and Stewart (1966). The model is based on trajectory calculations of dust particles inside the granular bed and assumes no bouncing of dust particles from the surface of the granules. The filtration efficien...

Experimental Determination of the Initial Collection Efficiency of Granular Beds in the Inertial-Impaction-Dominated Region

“…The more recent experimental work of Gal et al (1985), however, shows that quite different single-collector efficiencies were obtained using air and helium as carrier gases at identical conditions. Since the viscosities of helium and air are similar but the density of helium is only one-seventh that of air, the observed differences in the single-collector efficiency can only be explained through the Reynolds number.…”

“…In recent years a number of investigators have reported results on collection efficiency in granular beds : Thambimuthu, 1980;D'Ottavio and Goren, 1983;Gal et al, 1985;Walata et al, 1986;Takahashi et al, 1986. Without exception, these investigators used commercially available particle counters to measure concentration.…”

“…The chief advantages are that the data on whch these newer correlations are based are more extensive and are likely to be more accurate because of recent advanced particle counting instrumentation. Thus, the experimental results obtained were only compared with the four more recent correlations, namely, those of Thambimuthu (1980), D'Ottavio andGoren (1983), Gal et al (1985), and Yoshida and Tien (1985). 3.…”

Preparation of Granular Ceramic Filter and Prediction of Its Collection Efficiency

“…The single collector efficiency of a granular filter is defined as the ratio of the number of captured particles to the number of particles introduced in a single collector (Gutfinger and Tardos 1979;Alvin et al 1991;Kuo et al 2010). The total collection efficiency, E, is an exponential function of the physical properties, namely: filter thickness (L), powder size (d c ), porosity (s), and total single collector efficiency (h T ), as expressed in Equation (3) (Allen and Raabe 1985;Gal et al 1985;Kuo et al 2010):…”

Simulation of Aerosol Deposition in Granular Media

“…Among the several models that have been used for aerosol filtration studies, only the dense cubic packing model has been found to give good results on deposition rates (Gal et al, 1985). The structure of this model and its flow field expressions are, however, too complex to be used in simulation.…”