Fluid flows in porous media are characterized by three main regimes: Darcy, Forchheimer, turbulent flows, respectively. In the present study we are interested in an idealized foam of Kelvin-type for which direct numerical simulations are performed at the pore scale. The geometry is discretized with a conforming finite element mesh on which the Navier-Stokes Equations (NSE) are computed either with a steady-state solver or an unsteady one. We intend to compute the bifurcation diagram of a periodic Kelvin cell made up of triangular struts. For that purpose, the continuation diagram is first obtained with the Asymptotic Numerical Method [1] that computes all steady-state solutions. Then a linear stability analysis is then performed to discriminate between stable and unstable solutions. Hopf bifurcation points (where steady-state and time-periodic solutions co-exist) are also computed. Finally, above these critical points unsteady computations are performed to integrate in time the flow solution. The pressure drop curve versus Reynolds number has been computed for two porosities (80 and 97\%). The three regimes are determined along with the associated critical Reynolds numbers. Furthermore, the critical Reynolds number at which the Hopf bifurcation takes place is also accurately computed along with the corresponding critical pulsation of the time periodic solution. The latter has also been confirmed by the time integration approach. Beyond this Hopf bifurcation point we have also computed a secondary instability corresponding to a wake instability. This corresponds to the configuration where the wake induced by one strut impacts on a strut along the flow's path. The main idea of the developed tools is to find information on the dynamic behavior of the flow by using steady solutions, which are obviously less computationally costly than unsteady ones. We were able to find some bifuraction points in a complex 3D foam structures.