Resolvent-based design and experimental testing of porous materials for passive turbulence control

An extended version of the resolvent formulation is used to \textit{design} anisotropic porous materials as passive flow control devices for turbulent channel flow. The effect of these porous substrates is introduced into the governing equations via a generalized version of Darcy's law. Model predictions show that materials with high streamwise permeability and low wall-normal permeability ($\phi_{xy} = k_{xx}/k_{yy}\gg1$) can suppress resolvent modes resembling the energetic near-wall cycle. Based on these predictions, two anisotropic porous substrates with $\phi_{xy}\approx 8$ and $\phi_{xy} \approx 1/8$ were designed and fabricated for experiments in a benchtop water channel experiment. Particle Image Velocimetry (PIV) measurements were used to compute mean turbulence statistics and to educe coherent structure via snapshot Proper Orthogonal Decomposition (POD). Friction velocity estimates based on the Reynolds shear stress profiles do not show evidence of discernible friction reduction (or increase) over the streamwise-preferential substrate with $\phi_{xy}\approx 8$ relative to a smooth wall flow at identical bulk Reynolds number. A significant increase in friction is observed over the substrate with $\phi_{xy} \approx 1/8$. Coherent structures extracted via POD analysis show qualitative agreement with model predictions.