For periodic arrays of spheres the permeability is obtained numerically as a function of the dimensionless wave number kD in the flow direction, where D is the sphere diameter, k = 2π/λ is the wave number, and λ is the distance between the spheres in the flow direction. Our numerical results for the solids fraction of 0.45 show that for kD <∼ 6.5 the permeability increases with increasing kD. But, it decreases for ∼6.5 < kD <∼ 8.5 and reaches a local minimum at kD ∼ 8.5, and then increases again with increasing kD. Since the Fourier spectrum of the area fraction is zero for kD = 8.98, this result suggests that the area fraction plays an important role in determining the dependence of permeability on the distance between the spheres in the flow direction. For smaller solids fractions, the positions of the local maximum and minimum of permeability shift to slightly smaller kD's.
All Science Journal Classification (ASJC) codes
- Civil and Structural Engineering
- General Materials Science
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering
- Finite Element Method