Numerical Study of the Three-Dimensional Laminar Flow around a Cubic Metal Foam Cell

The present study examines numerically a three-dimensional (3D) laminar and stationary flow around an idealized metal foam cell shaped as an empty cube with cylindrical edges. The physical configuration adopted consists of an isolated cell placed inside a plane channel crossed by air as a working fluid. The numerical investigation is carried out using the dimensionless Navier-Stokes equations resolved by finite volume method. The flow configurations given for several Reynolds numbers are described entirely using 2D and 3D maps. The plane maps give streamlines at the side and top fiber planes: the vertical side of the cell is normal to the flow. In addition, the critical locations and zones characterizing the flow are also localized: the saddle points, separation nodes, attachment points, foci of the recirculation zones, and the attachment lines. For the Reynolds number in the range 75 <= Re <= 500, the results show that the topography of the streamlines at the vertical plane in the middle of the lateral fibers of the cell (z = 5.3D(p)) is developed into arc-shaped vortex rollers in the gap. In the wake, two saddle points reveal the zones of influence of these spiral structures, formed by two vortices (Bt and Nw) and zones of upwash and downwash. At a high value of Re (Re = 500), the upwash weakens but does not disappear. Two recirculation bubbles are associated with the two saddles, in the gap and the wake of the upper fibers, parallel to the flow. At Re = 500, the distribution flow loses its symmetry and displays matter transfer between the two recirculation. The displacement of the saddle point in the wake is 9.65 times that in the gap. No vortex shedding is observed in the wake of cell due to the nullity of the frequency shedding (f = 0) .The results indicate also that decreasing the pore diameter favors recirculation inside the cell gap. These recirculation lengths ( L-rz , L-ry ) located respectively in the wake of planes z = 5.3D(p) and y = D-p reduce the drag coefficient in equal proportion (51%) in the range 75 <= Re <= 500. It appears that the wake of the lateral fibers of the z=5.3D(p) ane contributes better to the drag coefficient. We consider that the predominance of downwash associated with the instability of saddle point S.2 in the wake when Re increases leads to a decrease in the drag coefficient in the wake.