Effect of texture randomization on the slip and interfacial robustness in turbulent flows over superhydrophobic surfaces

Superhydrophobic surfaces demonstrate promising potential for skin friction reduction in naval and hydrodynamic applications. Recent developments of superhydrophobic surfaces aiming for scalable applications use random distribution of roughness, such as spray coating and etched process. However, most of previous analyses of the interaction between flows and superhydrophobic surfaces studied periodic geometries that are economically feasible only in lab-scale experiments. We conduct direct numerical simulations of turbulent flows over randomly patterned interfaces considering a range of texture widths $w^+\approx 4-26$, and solid fractions $\phi_s=11\%$ to $25\%$. Slip and no-slip boundary conditions are implemented in a pattern, modeling the presence of gas-liquid interfaces and solid elements. Our results indicate that slip of randomly distributed textures under turbulent flows are about $30\%$ less than those of surfaces with aligned features of the same size. In the small texture size limit $w^+\approx 4$, the slip length of the randomly distributed textures in turbulent flows is well described by a previously introduced Stokes flow solution of randomly distributed shear-free holes. By comparing DNS results for patterned slip and no-slip boundary against the corresponding homogenized slip length boundary conditions, we show that turbulent flows over randomly distributed posts can be represented by an isotropic slip length in streamwise and spanwise direction. The average pressure fluctuation on gas pocket is similar to that of the aligned features with the same texture size and gas fraction, but the maximum interface deformation at the leading edge of the roughness element is about twice larger when the textures are randomly distributed.