• asymptotics
• baseflow
• homogenization
• micro-structure
• multiscale
• permeable
• porous
• sphere
• stability

The flow past a permeable sphere is studied. A two domain approach is employed. The flow is described by the Navier-Stokes equations in the free-fluid region and by the Darcy's law within the porous medium. At the interface a slip condition is provided for the solution of the external flow and a pressure-jump condition is provided for the solution of the porous problem. The homogenization is carried out via multi-scale asymptotics. The model is validated against DNS simulations found in literature. The baseflow is characterized. The effect of the parameters on the flow morphology is investigated. The global stability analysis is performed. The marginal stability curves are plotted. The effect of the parameters on the stability properties is investigated. A tool for the calculation of the micro-structure properties is developed. This tool is validated against results found in literature. The full structure of a sphere of constant permeability is designed. Full scale simulations of the flow past the designed sphere are performed. The results are compared with those of the homogenized model. The model is extended to the variable permeability case. Several permeability distributions are employed. The effect of the permeability distributions is investigated. A full-scale design of a sphere with variable permeability is performed. The flow field past and through the variable permeability sphere is studied.