Numerical study on influence of protrusion heights on Reynolds stress and viscous stress variations in turbulent vortical structures

Analysing the influence mechanism of the riblet protrusion height on turbulent drag components is more beneficial in organising the vortical structure over the riblet surface. Therefore, the Large Eddy Simulation (LES) is used to investigate the vortex structure over the riblet surface with different protrusion heights. Then, the variations of Reynolds stress and viscous shear stress in a turbulent channel are analysed. As a result, the drag reduction rate increases from 3.4% when the riblets are completely submerged in the turbulent boundary layer to 7.9% when the protrusion height is 11.2. Further analysis shows that the protrusion height affects the streamwise vortices and the normal diffusivity of spanwise and normal vortices, thus driving the variation of Reynolds stress. Compared with the smooth surface, the vorticity strength and the number of streamwise vortices are weakened near the wall but increase in the logarithmic layer with increased protrusion height. Meanwhile, the normal diffusivity of spanwise vorticity decreases with the increase of protrusion height, and the normal diffusivity of normal vorticity is the smallest when the protrusion height is 11.2. Moreover, the protrusion height affects the velocity gradient of the riblet tip and riblet valley, thus driving the variation of viscous shear stress. With the increase of protrusion height, the velocity gradient of the riblet tip increases dramatically but decreases in the riblet valley.