Simulation of the Impurity Absorption from a Laminar Flow in a System of Hollow-Fiber Membranes

Abstract

The external stationary flow of a viscous incompressible fluid and the convective-diffusion mass transfer of a solute in an ordered system of parallel hollow fiber membranes arranged normally to the flow direction are calculated in the ranges of Reynolds numbers \(\operatorname{Re} \) = 0.01–100 and Schmidt numbers \({\text{Sc}}\) = 1–1000. The Navier–Stokes equations and the equation of convective diffusion were solved using the methods of computational fluid dynamics with a no-slip boundary condition and with a constant solute concentration condition on the outer surface of the streamlined fiber. The calculations were performed for a row of fibers and for a multi-fiber system consisting of four and sixteen rows of fibers. The outlet concentrations and the fiber solute retention efficiencies \(\eta \) were calculated depending on the packing density of the fibers and the \(\operatorname{Re} \) and \({\text{Sc}}\) numbers. It is shown that it is possible to use the fiber solute retention efficiency \(\eta \) defined for a single row of fibers to predict the retention efficiency of an extended multi-row fibrous bed.