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A sharp interface implicit immersed boundary method is developed and used for direct numerical simulations of the flow through open-cell solid foams with a cellular structure. The complex solid structure of the foam is resolved on a non-boundary fitted Cartesian computational-grid. A single representative unit cell of the foam is considered in a periodic domain, and its geometry is approximated based on the structural packing of a tetrakaidecahedron. Simulations are performed for a wide range of porosities (0.638-0.962) and Reynolds numbers (0-500). Flow is enforced by applying a constant body force (momentum source) for three different flow directions along the {100}, {110}, and {111} lattice-vectors. The drag force on the foam is calculated and a non-dimensional drag/pressure drop correlation is proposed that fits the entire data set with an average deviation of 5.6%. Moreover, the accurate numerical simulations have helped to elucidate the detailed fluid-solid interaction in complex porous media. © 2016 The Authors AIChE Journal published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers AIChE J, 63: 1152-1173, 2017 [ABSTRACT FROM AUTHOR]