Bleeding flow characteristics downstream of isotropic porous square cylinders

Abstract

This study experimentally investigates the bleeding flow characteristics downstream of isotropic porous square cylinders as a function of permeability and pore configuration across a broad range of Darcy numbers ( $2.4 \times 10<^>{-5} \lt \textit{Da} \lt 2.9 \times 10<^>{-3}$ ). The porous cylinders, constructed with a simple cubic lattice design, were fabricated using a high-resolution three-dimensional printing technique. This novel design method, based on a periodic and scalable lattice structure, allows fine control over the number of lattice pores along the cylinder width, $D$ , and the corresponding permeability, independently of porosity. Permeability was carefully determined by measuring the pressure drop and superficial velocity for each porous structure considered in this study. High-resolution particle image velocimetry measurements were conducted in an open-loop wind tunnel to characterize the downstream flow structures. The results reveal that bleeding flow characteristics near the cylinder trailing edge are strongly influenced by both permeability and pore configuration. These structural behaviours are further explored using an analogy to multiple plane turbulent jets. This approach identifies three distinct flow regions downstream of porous square cylinders, determined by the structural pattern of the bleeding flow. Additionally, an analytical framework is developed to model the longitudinal extent of the merging region by integrating the momentum equation, incorporating the Darcy-Brinkman-Forchheimer model, with a boundary layer assumption. The analytical model is validated against experimental data, demonstrating its capability to predict the key dynamics of bleeding flow evolution. Our results provide new insights into the fluid dynamics of porous bluff bodies, establishing pore configuration and permeability as dominant parameters governing downstream flow structures.