Abstract
A five-mode truncation of the Navier—Stokes equation for incompressible flow through a cubic array of spheres is analyzed for its stationary and time-dependent solutions. Under the imposed symmetry requirements, the stationary solutions accurately depict the appearance of a vortex pair, and the volume-averaged velocity is in excellent agreement with the Ergun equation up to Re = 250. At the point the deviation from empirical data begins, the unique stationary solution destabilizes via a Hopf bifurcation point. A numerical analysis of the resulting periodic solution shows that for a certain range of imposed pressure gradient the system exhibits chaotic behavior, approached through a period-doubling subharmonic bifurcation sequence.
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