Topology optimisation of a porous unit cell in a fluid flow considering Forchheimer drag

When the Reynolds number exceeds approximately 10, drag from porous media becomes nonlinear and cannot be handled by Darcy's theory. The Darcy–Forchheimer law, which considers drag through porous media as a quadratic function, covers this region up to the Reynolds number of the order 102. In this research, we study the optimal shape of a porous unit cell based on this law and topology optimisation. Darcy's permeability and Forchheimer's quadratic drag term are calculated based on the averaging theorem and finite element method. The topology optimisation method is based on classical flow channel optimisation. The pressure drop is considered as the objective function of topology optimisation. By changing the input flow velocity in cell model analysis, the optimal shape becomes accustomed to the specified flow speed. We derive 2D and 3D optimal cell shapes for both low and high velocity regions.