Pressure drop measurements over anisotropic porous substrates in channel flow

Abstract 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 ( $$\kappa _{xx}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>κ</mml:mi> <mml:mrow> <mml:mi>xx</mml:mi> </mml:mrow> </mml:msub> </mml:math> , $$\kappa _{yy}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>κ</mml:mi> <mml:mrow> <mml:mi>yy</mml:mi> </mml:mrow> </mml:msub> </mml:math> , and $$\kappa _{zz}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>κ</mml:mi> <mml:mrow> <mml:mi>zz</mml:mi> </mml:mrow> </mml:msub> </mml:math> ). 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 $$\frac{\kappa _{xx}}{\kappa _{yy}} \in [0.035,28.6]$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mfrac> <mml:msub> <mml:mi>κ</mml:mi> <mml:mrow> <mml:mi>xx</mml:mi> </mml:mrow> </mml:msub> <mml:msub> <mml:mi>κ</mml:mi> <mml:mrow> <mml:mi>yy</mml:mi> </mml:mrow> </mml:msub> </mml:mfrac> <mml:mo>∈</mml:mo> <mml:mrow> <mml:mo>[</mml:mo> <mml:mn>0.035</mml:mn> <mml:mo>,</mml:mo> <mml:mn>28.6</mml:mn> <mml:mo>]</mml:mo> </mml:mrow> </mml:mrow> </mml:math> . 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 ( $$\hbox {Re}_b \in [500,4000]$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mtext>Re</mml:mtext> <mml:mi>b</mml:mi> </mml:msub> <mml:mo>∈</mml:mo> <mml:mrow> <mml:mo>[</mml:mo> <mml:mn>500</mml:mn> <mml:mo>,</mml:mo> <mml:mn>4000</mml:mn> <mml:mo>]</mml:mo> </mml:mrow> </mml:mrow> </mml:math> ). 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 ( $$\sqrt{\kappa _{yy}}^+&gt; 0.4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:msqrt> <mml:msub> <mml:mi>κ</mml:mi> <mml:mrow> <mml:mi>yy</mml:mi> </mml:mrow> </mml:msub> </mml:msqrt> <mml:mo>+</mml:mo> </mml:msup> <mml:mo>&gt;</mml:mo> <mml:mn>0.4</mml:mn> </mml:mrow> </mml:math> ) 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. Graphical abstract