• computational fluid dynamics
• drag reduction
• fluid dynamics
• permeable substrates

In the present thesis, a methodology is proposed to characterise anisotropic permeable substrates, to identify the configurations that can offer the best drag reduction properties and understand if Brinkman's equation is a good model.

In the first part of the work, a sufficiently deep anisotropic permeable substrate is considered, in which the fibres are very small compared to the lengthscales of the flow in the outer region. The Stokes equations are assumed to be the governing equation of the motion within the substrate. The Darcy equation is considered for the macroscopic velocities. From the solutions of these equations with a constant pressure gradient, the permeabilities in the streamwise, spanwise and wall-normal direction are obtained. Different configurations are analysed in terms of drag reduction properties. As a result, fibres with a cross cross-section are proposed to be the best-suited to achieve a high anisotropy ratio.

In the second part of the work, a study is carried out to understand if Brinkman's equation is a good model, to find the best fit value for the effective macroscopic viscosity and to get a better understanding of the flow behaviour at the substrate-fluid interface. These analyses are limited to permeable substrates with a circular cross-section. The results indicate that the Brinkman's equation is valid only for porous mediums with a very high value of porosity. For the ones that satisfy this condition, the results show that the effective macroscopic viscosity is lower than unity, and it is different in the streamwise and spanwise directions. In addition, the continuity of the macroscale solution at the substrate-free flow interface is discussed.