A level set-based model for performance prediction of superhydrophobic surfaces

The drag reduction (DR) capabilities of superhydrophobic surfaces (SHS) hinge on their reduced wettability, which is intrinsically linked to the morphology of the air-water interface. Accurate prediction of the topology and stability of this interface is vital. In this study, we employ a variational level set methodology (Alame et al. 2020) in a novel approach to characterize and predict the hydrodynamic performance of SHS. A parallel, highly scalable 3D solver for determining the equilibrium interface topology of realistic SHS is developed; the proposed model encapsulates the properties of the equilibrium interface, its correlation with DR, surface characteristics, and flow dynamics. We have established correlations between the skin friction coefficient for various SHS under different flow scenarios and the properties of their interfaces, as well as the substrate characteristics. This methodology offers a powerful tool for optimizing SHS design for enhanced drag reduction in practical applications. The results are validated against SHS with both canonical structured roughness and realistic roughness over a range of Re_H.