Pressure drop measurements over anisotropic porous substrates in channel flow

Previous theoretical and simulation results indicate that anisotropic porous materials have the potential to reduce turbulent skin friction in wall-bounded flows. This study experimentally investigates the influence of anisotropy on the drag response of porous substrates. A family of anisotropic periodic lattices was manufactured using 3D printing. Rod spacing in different directions was varied systematically to achieve different ratios of streamwise, wall-normal, and spanwise bulk permeabilities ( \(\kappa _{xx}\) ${\kappa }_{\mathit{xx}}$ , \(\kappa _{yy}\) ${\kappa }_{\mathit{yy}}$ , and \(\kappa _{zz}\) ${\kappa }_{\mathit{zz}}$ ). The 3D printed materials were flush-mounted in a benchtop water channel. Pressure drop measurements were taken in the fully developed region of the flow to systematically characterize drag for materials with anisotropy ratios \(\frac{\kappa _{xx}}{\kappa _{yy}} \in [0.035,28.6]\) $\frac{{\kappa }_{\mathit{xx}}}{{\kappa }_{\mathit{yy}}}\in [0.035,28.6]$ . Results show that all materials lead to an increase in drag compared to the reference smooth wall case over the range of bulk Reynolds numbers tested ( \(\hbox {Re}_b \in [500,4000]\) ${\text{Re}}_b\in [500,4000]$ ). However, the relative increase in drag is lower for streamwise-preferential materials. We estimate that the wall-normal permeability for all tested cases exceeded the threshold identified in previous literature ( \(\sqrt{\kappa _{yy}}^+> 0.4\) ${\sqrt{{\kappa }_{\mathit{yy}}}}^{+}>0.4$ ) for the emergence of energetic spanwise rollers similar to Kelvin–Helmholtz vortices, which can increase drag. The results also indicate that porous walls exhibit a departure from laminar behavior at different values for bulk Reynolds numbers depending on the geometry.