Numerical investigation of the drag reduction effect in turbulent channel flow by superhydrophobic grooved surfaces

Superhydrophobic surfaces (SHSs) are considered to be a promising technology for achieving skin-friction drag reduction. Development of more efficient techniques for simulating the turbulent boundary layer on SHSs continues to be a subject of interest. In this study, numerical simulations were carried out to capture near-wall behaviours due to the effect of the SHS on wall-bounded flows. To achieve this, high- to intermediate-fidelity turbulence models including Reynolds-averaged Navier-Stokes, detached eddy simulation and large eddy simulation were utilized. With regard to slip conditions, the well-known Navier slip velocity method was used over the SHS. For validating the numerical solutions, the slip velocity and skin friction over the SHS were compared with the experimental output. Results showed that the velocity profile and Reynolds stresses on the SHS were comparable to the reported results. Then, the developed models were further extended to investigate the drag reduction effect of SHSs with rectangular grooves. The subsequent results showed that the combination of superhydrophobicity and rectangular grooves led to a better performance with a maximum drag reduction of 46.1%. This is due to the surface slip caused by the SHS and the secondary vortex effect created by the grooves. Our results revealed that Reynolds stresses of the slippery grooved surface were higher than those of the case in which a shear-free condition was employed for the grooved surface. More importantly, the numerical results indicate the previous assumption of the shear-free condition is inaccurate for the geometrically simplified grooved SHSs. Therefore, geometry modifications rather than an overly simplified shear-free boundary condition should be applied in computational fluid dynamics simulations for SHSs with grooves or other complex structures.