Direct Numerical Simulation of Fully-Developed Turbulent Channel Flow with Slip Boundary Condition on One of the Walls

In this study, the results of a direct numerical simulation of turbulent drag reduction in a channel flow by hydrophobic coating at a nominal shear Reynolds number of Reτ = 180 are reported. Slip condition is imposed on the lower wall whereas the upper wall has no-slip condition. For this purpose, the use is made of a numerical simulation of three-dimensional, time-dependent Navier-Stokes equations for the incompressible flow of a Newtonian fluid. Finally, statistical quantities of turbulent flow (specifically the mean velocity profile, the root-mean-square of velocity fluctuations in different directions and the Reynolds shear stress are shown and discussed. The results confirm that by increasing the amount of slip on the lower wall, the bulk velocity passing through the channel increases. Also, the variation of root-mean-square of velocity fluctuations shows a similar behavior in the vicinity of the upper wall. But, their general trend is different in the proximity of the lower wall. Moreover, a change in the shape of the Reynolds shear stress profile from a minimum close to the lower wall towards a maximum close to the upper wall is observed.