A Numerical Study of Porous-fluid Coupled Flow Systems with Mass Transfer

Abstract

This thesis concerns the study of coupled flow systems which compose of a porous medium layer and a homogenous fluid layer. The study consists of three parts: channel partially filled with a porous medium, fluid-porous domains coupled by interfacial stress jump, microchannel reactors with porous walls. The low Reynolds number flow is studied in present work. The flow through a channel partially filled with fibrous porous medium was analyzed to investigate the interfacial boundary conditions. The fibrous medium was modeled as a periodic array of circular cylinders, in a hexagonal arrangement, using the boundary element method. The area and volume average methods were applied to relate the pore scale to the representative elementary volume scale. The permeability of the modeled fibrous medium was calculated from the Darcy?s law with the volume-averaged Darcy velocity. The slip coefficient, interfacial velocity, effective viscosity and shear jump coefficients at the interface were obtained with the averaged velocities at various permeability or Darcy numbers. Next, a numerical method was developed for flows involving an interface between a homogenous fluid and a porous medium. The numerical method is based on the lattice Boltzmann method for incompressible flow. A generalized model, which includes Brinkman term, Forcheimmer term and nonlinear convective term, was used to govern the flow in the porous medium region. At the interface, a shear stress jump that includes the inertial effect was imposed for the lattice Boltzmann equation, together with a continuity of normal stress. The present method was implemented on three cases each of which has a porous medium partially occupying the flow region: channel flow, plug flow and lid-driven cavity flow. The present results agree well with the analytical and/or the finite-volume solutions. Finally, a two-dimensional flow model was developed to simulate mass transfer in a microchannel reactor with a porous wall. A two-domain approach, based on the lattice Boltzmann method, was implemented. For the fluid part, the governing equation used was the Navier?Stokes equation; for the porous medium region, the generalized Darcy?Brinkman?Forchheimer extended model was used. For the porous-fluid interface, a stress jump condition was enforced with a continuity of normal stress, and the mass interfacial conditions were continuities of mass and mass flux. The simplified analytical solutions are deduced for zeroth order, Michaelis-Menten and first order type reaction, respectively. Based on the simplified analytical solutions, generalized results with good correlation of numerical data were found based on combined parameter of effective channel distance. The effects of Damkohler number, Peclet number, release ratio and Mechaelis-Menten constant were studied. Effectiveness factor, reactor efficiency and utilization efficiency were defined. The generalized results could find applications for the design of cell bioreactors and enzyme reactors with porous walls.