Abstract
A numerical simulation of the laminar flow field and convection–diffusion mass transfer in a regular system of parallel fully absorbing fibers for the range of Reynolds numbers up to Re = 300 is performed. An isolated row of equidistant circular fibers arranged normally to the external flow is considered as the simplest model for a hollow-fiber membrane contactor. The drag forces acting on the fibers with dependence on Re and on the ratio of the fiber diameter to the distance between the fiber axes, as well as the fiber Sherwood number versus Re and the Schmidt number, Sc, are calculated. A nonlinear regression formula is proposed for calculating the fiber drag force versus Re in a wide range of the interfiber distances. It is shown that the Natanson formula for the fiber Sherwood number as a function of the fiber drag force, Re, and Sc, which was originally derived in the limit of high Peclet numbers, is applicable for small and intermediate Reynolds numbers; intermediate and large Peclet numbers, where Pe = Re × Sc; and for sparse and moderately dense rows of fibers.
Highlights
Studies of convection–diffusion transfer in fibrous media are essential for the development of various technological processes
At low flow velocities, corresponding to low Reynolds numbers Re < 1, the flow field depends on the single parameter α—the fiber packing density, whereas at higher velocities, at Re ≥ 1, it is governed by the two parameters of α and Re
For the range 100 ≤ Re ≤ 300 and for of the Navier–Stokes and convection–diffusion equations: Schmidt numbers are marked non-dense rows, we suggest a simple formula, which is obtained using the corresponding regression on the curves
Summary
Studies of convection–diffusion transfer in fibrous media are essential for the development of various technological processes. Fibers 2018, 6, 90 density, whereas at higher velocities, at Re 1, it is governed by the two parameters of and Re. In studying transport processes in real porous media, the models with known flow fields are used in order eliminate the the influence structural. The so-called cell models arranged normally to the laminar flow with square or hexagonal packing or a single row of parallel with axially symmetric flow past a fiber in a cell are commonly used at low Reynolds numbers. In this paper,the wediffusion considermass the diffusion transfer inofa Reynolds wider range of Reynolds numbers up to on the obtained flow field, the fiber drag force and the fiber retention efficiency are obtained versus.
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