Flow of Single-Phase Fluids through Fibrous Beds

Abstract

radius of tube in calculations for reaction along cylindrical channel. cm dimensionless reaction rate, jR&(plate) ; {% (cylinder) average reaction rate over total reactive surface Reynolds number, dvp/g seconds average velocity, centimeter/second dimensionless velocity profile, for laminar flow, distance in axial direction, cm distance in transverse direction, cm3h20 plate) 1 = dimensionless position along y coordinate, y/h p = density, grams/cm3 literature Cited Acrivos, A,, ChambrB, P. L., I n d . Eng. Chem.49,1025 (1957). Pn = apparent reaction order for weak acids = coefficients in series approximation t o boundary layer Droblem y r ( n ) = gamma function of variable n, tabulated function = dimensionless radial position, r/R A pore model for the flow of a single-phase fluid through a bed of random fibers is proposed. An effective pore number, Ne, accounts for the influence of dead space on flow; deflection number, N6, characterizes the effect of fiber deflection on pressure drop. Experimental data were obtained with glass, nylon, and Dacron fibers of 8to 28-micron diameter and with fluids of viscosity ranging from 1 to 22 cp. A generalized friction factor-Reynolds number equation i s presented. The effects of dead space in a fibrous bed on flow and of fiber deflection on pressure drop have no parallels in a granular bed.

Pedotransfer functions for permeability: A computational study at pore scales

“…[17] The Kozeny and Kozeny-Carman equations have been found, however, to yield poor estimates of permeability at the extremes of porous medium types: either when total fluid discharge through a porous medium is negligible or at the other extreme where the effect of the medium on the overall flow is local and small [Kyan et al, 1970;Xu and Yu, 2008]. These results are consistent with the pore-scale computational experiments of Lemaitre and Adler [1990] mentioned above and the experiments reported here.…”

“…When applied over a wide range of porous media, computational experiments reveal a nonlinear relationship between permeability and its predictors, contrary to Kozeny's result. This nonlinearity is manifested by the wide range of values of the Kozeny coefficient observed at the extreme ends of porosity [Sullivan, 1942;Kyan et al, 1970;Davies and Dollimore, 1980;Adler et al, 1990;Xu and Yu, 2008]. On one hand, Kozeny's linear (in the predictor nR 2 ) approximation appears satisfactory within a restricted range of porosities, 0:2 < n < 0:7.…”

“…Heijs and Lowe [1995] found that the Kozeny-Carman equation predicted the permeability of a particular random array of spheres well (porosity n ¼ 0:6), but failed to do so in a soil sample that had porosity near one. Sullivan [1942], Kyan et al [1970], Davies and Dollimore [1980], and Xu and Yu [2008] all note that the Kozeny coefficient varies nonlinearly with porosity and most significantly at its extreme values.…”

Pore-level engineering of macroporous media for increased performance of solar-driven thermochemical fuel processing

“…3 and 4, respectively, for samples with porosity of 0.45, 0.59, 0.73 and 0.85. In comparison to the semi-empirical models by Conduit flow theory [5], Carman-Kozeny correlation [7], Ergun et al [10], Happel and Brenner [8], and Kyan et al [9] -introduced in Table 1 -the Carman-Kozeny model fits the computed permeabilities best with a relative RMS of 29.7%. The model is based on the semi-heuristic Carman-Kozeny equation [7] with a shape factor k K = 5 defined for packed beds of spheres.…”

“…To predict the permeability of a porous medium, approximations based on the semi-heuristic packed-bed model of Carman and Kozeny [7] are used with a modified shape factor for e.g. assemblies of parallel cylinders [8] and fibrous beds [9]. Another drag flow approach was analytically derived by Ergun [10] for packed columns.…”