Direct numerical simulation (DNS) is performed for two wall-bounded flow configurations: laminar Couette flow at and turbulent channel flow at , where 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 two flow cases are studied with varying interface heights to understand its effect on slip and drag reduction . For the laminar Couette flow case, the presence of the surface roughness is felt up to of the channel height in the wall-normal direction. Nonlinear dependence of on is observed with three distinct regions. A nonlinear curve fit is obtained for gas fraction as a function of , where determines the amount of slip area exposed to the flow. A power law fit is obtained from the data for the effective slip length as a function of and is compared to those derived for structured geometry. 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 . Four cases are simulated ranging from fully wetted to fully covered and two intermediate regions in between. Scaling laws for slip length, slip velocity, roughness function and are obtained for different penetration depths and are compared to past work for structured geometry. is shown to depend on a competing effect between slip velocity and turbulent losses due to the Reynolds shear stress contribution. Presence of trapped air in the cavities significantly alters near-wall flow physics where we examine near-wall structures and propose a physical mechanism for their behaviour. The fully wetted roughness increases the peak value of turbulent intensities, whereas the presence of the interface suppresses them. The pressure fluctuations have competing contributions between turbulent pressure fluctuations and stagnation due to asperities, the near-wall structure is altered and breaks down with increasing slip. Overall, there exists a competing effect between the interface and the asperities, the interface suppresses turbulence whereas the asperities enhance them. The present work demonstrates DNS over a realistic multiphase SHS for the first time, to the best of our knowledge.
Bibliographical noteFunding Information:
This work was supported by the United States Office of Naval Research (ONR) MURI (Multidisciplinary University Research Initiatives) program under grant N00014-12-1-0874 managed by Dr K.-H. Kim. Computing resources were provided by the Minnesota Supercomputing Institute (MSI). We are grateful to Professor W. Choi at University of Texas Dallas and Professor G. H. McKinley at MIT for providing us with the scanned surface data used in the present work. The authors would like to thank Dr P. Kumar and Dr Y. Li for their helpful discussions and suggestions.
© 2019 Cambridge University Press.
- drag reduction
- multiphase flow
- turbulence simulation