Open-cell foams are employed in various applications such as the filtration of liquids, as carriers for catalysts, for heat insulation as well as noise absorption. An optimization of the foam structures with respect to these applications, e.g. by adjusting porosity, strut shape or pore density, is often constrained by the maximum pressure drop that can be tolerated. The pressure gradient is usually predicted using the Darcy-Forchheimer law, which requires knowledge of the corresponding coefficients of viscous and inertial permeability, also known as Darcy and Forchheimer coefficients, respectively. In order to study the influence of different morphological parameters on these effective properties, pore-scale simulations of the fluid flow inside artificial foam structures were performed, whose strut shape and porosity could be manipulated within a certain range. While the foams were computer-generated from Laguerre tesselations of random packings of spheres that were subsequently annealed and relaxed, the solutions of the mass and momentum conservation equations were obtained using the lattice-Boltzmann method. For comparison purposes, three conventional ceramic foam filters of 20 and 30 PPI pore count were also included, for which the detailed geometry was acquired through 3D CT-scanning. The obtained variations of viscous and inertial permeability were compared against existing correlations, which were found unable to accurately capture the strong influence of porosity. Aiming at the development of an improved correlation, a simplified approach on the basis of Happels cell model was developed, which yields predictions that agree reasonably well with the results of the detailed simulations. Within the considered range, the variation of the strut shape was found to be less influential.