Fluid Flows Through Two-Dimensional Irregular Composite Channels

The present analysis is concerned with the study of two-dimensional fluid flow problems through channels of irregular composite materials. The fluid is assumed to be steady, incompressible, with a negligible gravitational force, and is constrained to flow in an infinite long channel in which the height assumes a series of piecewise constant values. An analytical study in the fully developed section of the composite channel is presented when the channel is of constant height and composed of several layers of porous media, each of uniform porosity. Numerical solutions are utilised using CFD based on the control volume method to solve the Brinkman equation, which governs fluid flow through porous media. In the fully developed flow regime the analytical and numerical solutions are graphically indistinguishable. A geometrical configuration involving several discontinuities of channel height, and where the entry and exit sections are layered, is considered and the effect of different permeabilities is demonstrated. Several numerical investigations which form a first attempt to mathematically model some geological structures, e.g. a fault or a fracture, are performed. Further, flow through fractures composed of randomly generated permeability values are also discussed and the effect on the overall pressure gradient is considered.