Wall-bounded flow over a realistically rough superhydrophobic surface

Direct numerical simulations (DNS) are performed for two wall-bounded flow configurations: laminar Couette flow at $Re=740$ and turbulent channel flow at $Re_{\tau}=180$, where $\tau$ is the shear stress at the wall. The top wall is smooth and the bottom wall is a realistically rough superhydrophobic surface (SHS), generated from a three-dimensional surface profile measurement. The air-water interface, which is assumed to be flat, is simulated using the volume-of-fluid (VOF) approach. The laminar Couette flow is studied with varying interface heights $h$ to understand the effect on slip and drag reduction ($DR$). The presence of the surface roughness is felt up to $40\%$ of the channel height in the wall-normal direction. A nonlinear dependence of $DR$ on $h$ is observed with three distinct regions. The DNS results are used to obtain a nonlinear curve fit for gas fraction $\phi_g$ as a function of $h$, where $\phi_g$ determines the amount of slip area exposed to the flow. A power law linear regression fit is used to obtain $b_{eff}$ as a function of $\phi_g$. For the turbulent channel flow, statistics of the flow field are compared to that of a smooth wall to understand the effects of roughness and $h$. Two interface heights, $h=h_{rms}$ and $h=h_{max}$ are simulated to study their effect on the behaviour of the flow, where $h_{rms}$ and $h_{max}$ are the rms and maximum peak of the roughness heights respectively. Results show that the presence of trapped air in the cavities significantly alters near wall flow physics. The fully wetted roughness increases the peak value in turbulent intensities, whereas the presence of the interface suppresses them. Overall, there exists a competing effect between the interface and the asperities, where the interface suppresses turbulence whereas the asperities enhance them.