Force and velocity fluctuations over rough foils at moderate Reynolds numbers

Abstract Surface roughness modifies the flow dynamics over static surfaces and can significantly affect the instantaneous generation of lift and drag. This study presents force and flow measurements on NACA0012 foils covered with simple, commercially available spherical-cap roughness elements. We varied the roughness area coverage relative to the propulsive area from 0% (smooth) to 35% (mid-rough) and 70% (full-rough). Our experiments survey an angle of attack and a Reynolds number range of $$-2^\circ \le \alpha \le 20^\circ$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>-</mml:mo> <mml:msup> <mml:mn>2</mml:mn> <mml:mo>∘</mml:mo> </mml:msup> <mml:mo>≤</mml:mo> <mml:mi>α</mml:mi> <mml:mo>≤</mml:mo> <mml:msup> <mml:mn>20</mml:mn> <mml:mo>∘</mml:mo> </mml:msup> </mml:mrow> </mml:math> and 10,000 $$\lessapprox Re \lessapprox$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>⪅</mml:mo> <mml:mi>R</mml:mi> <mml:mi>e</mml:mi> <mml:mo>⪅</mml:mo> </mml:mrow> </mml:math> 55,000, respectively. Within this parameter space, surface roughness leads to small alterations in time-averaged statistics of lift and drag. In contrast, it leads substantial changes in unsteady force and flow behavior. Specifically, surface roughness reduces lift fluctuations, up to $$\sim 60\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>∼</mml:mo> <mml:mn>60</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> , due to decreased pressure fluctuations on the foil surface. This reduction is accompanied by a modest decrease in time-averaged lift coefficient and an increase in time-averaged drag coefficient. Drag fluctuations increase by up to $$\sim 30\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>∼</mml:mo> <mml:mn>30</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> , except near stall, where both lift and drag fluctuations decrease. Roughness also mitigates flow separation, as indicated by reduced velocity fluctuations and a delayed stall onset in the $$C_L(\alpha )$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>C</mml:mi> <mml:mi>L</mml:mi> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>α</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> curves. These results show that surface roughness influences not only time-averaged statistics but also the instantaneous response of lift, drag, and flow fields. Our findings offer insights into the hydrodynamic function of shark-skin-inspired surfaces and demonstrate how simple, distributed roughness can provide passive control of boundary layer behavior and flow separation.