Gradient Based Optimization of Superhydrophobic Surface Geometry for Drag Reduction

Through chemical treatment and nano- to microscale geometric design, surfaces can be made to achieve superhydrophobicity. Submerged superhydrophobic surfaces (SHSs) can obtain significant drag reduction in channel flow experiments, compared to a smooth regular surface. A plausible explanation is that SHSs are capable of trapping air pockets between the liquid and the solid surface, thereby inducing a slip velocity in the streamwise direction and reducing the wall shear stress.

This work extends our past research in which a semi-empirical model has been developed and validated for modelling the friction coefficient of SHSs with random roughness characteristics in channel flows at bulk Re numbers between 5000 and 50000. The model describes a power law relationship between Cf and the bulk Reynolds number, with coefficients dependent on six parameters that characterize the statistical roughness properties of the SHS.

Using the surface parameters as design variables, subjected to inequality bounds set by manufacturable limits, this work builds a gradient-based constrained optimization framework to seek the optimal values of the SHS roughness parameters that maximize drag reduction across the relevant range of Re. Having obtained the optimal roughness parameter values, we then explore surface geometric designs that possess the desired values, expressed as a roughness height function expanded by various basis functions.