Abstracts - KTH Mechanics

178
Mass transfer and dispersion from a cylinder surface immersed in
a granular bed in alignment with the fluid flow
J. M. P. Q. Delgado a
There are several situations of practical interest, both in nature and in man made
processes, in which there is fluid flow through a bed of inert particles, packed against
a mass of solid (or immiscible fluid) that dissolves in (or reacts with) the moving fluid.
Examples may be found in diverse fields, such as dilute catalyst fixed bed reactors,
fluidised bed combustion, ore leaching and water contamination by buried waste or
NAPLs (non aqueous phase liquids).
The present work describes the mass transfer process between a moving fluid and
a slightly soluble cylinder (with length L and diameter d1) buried in a packed bed, in
alignment with the direction of flow. The bed of inert particles (with diameter d) is
taken to have uniform voidage.
The partial differential equation (PDE) was solved numerically using a finitedifference
method. A second-order central differencing scheme was adopted for the
discretisation of the diffusive terms and the convective term was discretised using the
CUBISTA high-resolution scheme proposed by Alves et al. 1, which preserves
boundedness, even for highly advective flows.
Numerical solution of the PDE describing mass conservation of the solute gave the
concentration field near the soluble surface and the mass transfer flux was integrated
to give values of the Sherwood number as a function of the relevant parameters. A
mathematical expression is proposed that describes accurately the dependence found
numerically between the value of the Sherwood number and the values of Peclet
number, Schmidt number, d/d1 and aspect ratio, L/d1, of the cylinder. For large
enough diameter of the cylinder, the problem degenerates into mass transfer from a
plane surface and the same equation applies, with L/d1=0.
The equation was tested through the measurement of diffusivity for different
solutes released by slightly soluble solids, and the experimental values obtained were
in excellent agreement with the values found in literature.
An important feature of the work is the detailed discussion of the finite differences
method adopted, with emphasis on the high-resolution schemes used in the
discretization of the convection term of the PDE.
a Dep. Engenharia Química, Faculdade de Engenharia-Universidade Porto, 4200-465 Porto, Portugal.
1 Alves et al., Int. J. Numer. Meth. Fluids 41, 47 (2003).