Assessing the effect of surface permeability on drag using an angular momentum integral equation

In previous work, an angular momentum integral (AMI) equation has been shown to cleanly distinguish the effects of turbulence and freestream pressure gradients for boundary layers over smooth, impermeable walls. Surface permeability and roughness generally tends to increase drag on a flat plate, but carefully engineered surfaces such as riblets or substrates with anisotropic permeability have shown some potential to reduce drag. This presentation introduces and demonstrates an extension of the AMI equation for flows over porous substrates to facilitate a quantitative assessment of how permeability and turbulent fluctuations throughout the flow (above and below the interface) impact drag relative to a baseline laminar impermeable case.