Direct numerical simulation of optimal Taylor-couette flow and turbulent boundary layer over a divergent convergent superhydrophobic surface

Abstract

The direct numerical simulation (DNS) of optimal Taylor-Couette flow, turbulent boundary layer over a superhydrohobic surface and turbulent pipe flow were implemented. In the optimal condition the maximum transport of the angular velocity was achieved mainly by the convective transport. The momentum source (positive turbulent inertia) contribution to the angular velocity flux was larger than the momentum sink (negative turbulent inertia). The study of the velocity-vorticity correlations revealed the dominant contribution of vorticity stretching to the skin friction which was maximum for the optimal condition. The turbulent flow over superhydrophobic surfaces one with the straight patterns and two with divergent and convergent patterns ($P_x = 16W_z$ and $P_x = 32W_z$) were studied. The gas fraction for all was 0.5. $P_x = 32W_z$ gave 21% more drag reduction than the straight SHS due to the manipulation of the secondary flow in the y-z plane and turbulence structure. The secondary flow is in the form of streamwise vortices. Over $P_x = 32W_z$ these vortices were diminished. The ejection and sweep motions and vortical structure over $P_x = 32W_z$ were weaker. The vortex stretching had largest contribution to the skin friction and drag reduction. The reverse flow which corresponded to the negative wall shear stress was studied in turbulent pipe flow. The origin of this flow was a lateral vortex in the buffer layer. The flow statistics around these regions were determined by conditional averaging. Above them the flow was accelerated due to the larger wall-normal gradient of Reynolds shear stress. The reverse flow regions induced larger ejection locally which manifested the lateral and streamwise movement of the low speed flow. The largest contribution to the skin friction was by the wall normal gradient of spanwise vorticity. These regions lied under the negative (very) large scale motions more frequently.