Uncertainty Quantification of Drag Reduction over Superhydrophobic Surfaces by Unified Parameterizing Structure Spacing

Abstract

Superhydrophobic surfaces (SHS) have demonstrated significant potential in reducing turbulent drag by introducing slip conditions through micro-structured geometries. While previous studies have examined individual SHS configurations such as post-type, ridge-type, and transverse ridge-type surfaces, a unified analysis that connects these patterns through geometric parameterization remains limited. In this study, we propose a systematic framework to explore the drag reduction characteristics by varying the streamwise and spanwise spacing ($d_1, d_2$) of post-type patterns, effectively encompassing a range of SHS geometries. High-fidelity direct numerical simulations (DNS) were performed using NekRS, a GPU-accelerated spectral element solver, to resolve incompressible turbulent channel flows over these SHSs. To account for variability in the geometric parameters and quantify their influence, we construct a surrogate model based on polynomial chaos expansion (PCE) using Latin hypercube sampling (LHS) method. The resulting model enables efficient uncertainty quantification (UQ) and sensitivity analysis, revealing the relative importance of $d_1$ and $d_2$ in drag reduction performance. This unified UQ framework provides both predictive capability and design guidance for optimizing SHS configurations under uncertain geometric conditions.