Numerical Study of Darcy Flow Through Porous Media Formed by Cylinders of Various Cross-Section Shapes

It is believed that the unique shape of shark dermal scales, known as denticles, is what gives a shark a hydrodynamic advantage against their underwater prey. A feature of the shark denticle that has been previously deemed irrelevant to hydrodynamics is the neck – a slender stem located beneath the crown. A recent DNS of a separating turbulent flow over shark denticles (Savino and Wu, arXiv:2403.14095), investigates the impact of the complete denticle, including the neck, on flow separation and drag reduction. The results show that denticles create microchannels between their necks, and a reverse pore flow (RPF) is formed in such porous cavity regions when the flow above is subjected to an adverse pressure gradient yet remains attached. This upstream-traveling RPF generates thrust, presenting a novel drag-reduction strategy. Among other features that enable the RPF and thrust, the non-circular cross-section of the denticle neck appears to favor the thrust generation. It possesses wide side bulges that enhance the pore flow shear and impaction; and a blunt front that potentially mitigate separation. The current research employs a 2D Darcy flow solver to predict the force generation capability of the pore flow. Various neck cross-section shapes, porosity, and Reynolds numbers are tested to explore the possible hydrodynamic advantages of the denticle neck.