The present work deals with the numerical simulations of 3D incompressible flow through periodic porous structures, consisting of cubic cells with different strut geometry and structure tilting with respect to the flow direction. Simulation results are obtained for different porosities, while covering a range of Reynolds numbers from laminar-steady flow (Darcy regime) up to the transition to laminar-unsteady flow (moderate Forchheimer regime). These results are post-processed in order to characterize the influence of the periodic porous structures on the flow statistics related to the Darcy-Forchheimer law. Based on this analysis, along with 3D simulation results previously obtained for different random foams, correlations for the Darcy and Forchheimmer permeability coefficients are developed from a theoretical background, being expressed only as functions of the cell geometrical parameters and tortuosity estimation. However, the influences of flow tortuosity and cell orientation on the Darcy coefficient are found to cancel each other. The proposed correlation for the Darcy coefficient performs very well for both periodic and random porous structures, when compared with recent correlations available in the literature. The performance of the correlation proposed for the Forchheimmer coefficient is found to be satisfactory, however, different correlation constants were found for periodic and random structures. The proposed correlation for the Forchheimer permeability coefficient depends on the flow tortuosity inside the porous structure, which must be estimated either through 3D fluid flow simulations or using tortuosity correlations. In this respect, a correlation is proposed for predicting the flow tortuosity inside porous structures, as an alternative for avoiding 3D simulations. (C) 2019 Elsevier Ltd. All rights reserved.