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 previous analyses of the interaction between flows and superhydrophobic surfaces studied periodic geometries that are economically feasible only in laboratory-scale experiments. In order to assess the drag reduction effectiveness as well as interfacial robustness of superhydrophobic surfaces with randomly distributed textures, we conduct direct numerical simulations of turbulent flows over randomly patterned interfaces considering a range of texture widths w(+) approximate to 4-26, and solid fractions phi(s) = 11%-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 is about 30% less than those of surfaces with aligned features of the same size. In the small texture size limit w(+) approximate to 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 a 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 as large when the textures are randomly distributed. The presented analyses provide insights on implications of texture randomness on drag reduction performance and robustness of superhydrophobic surfaces.