Longitudinal laminar flow past arrays of cylinders

The problem of determining permeability of a longitudinal laminar flow parallel to the axes of cylinders is examined in detail for square and hexagonal arrays of cylinders. A multipole expansion method is employed to determine fluid velocity. The numerical results for the permeability are compared with those obtained by a cell theory and an asymptotic analysis. The cell theory agrees well with the numerical results for hexagonal arrays. The asymptotic analysis also shows good agreement with the numerical results for square and hexagonal arrays. Finally, we present formulas for determining the permeability for the periodic arrays of cylinders.