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 from3.4% 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.

On the tip sharpness of riblets for turbulent drag reduction

It is commonly known that riblets with sharper tip generally have better turbulent drag reduction capacity,which,however,poses great challenges for manufacturing and makes the riblets vulnerable to tip erosion.In this study,we show that a scalloped riblet which is not as sharp in the tip as corresponding triangular riblet with same height-width ratio,nevertheless has a larger protrusion height,a quantity solely depending on the riblet shape and calculated through a boundary element algorithm in this study,and thus a higher projected drag reduction rate.In addition,it is found that,when subjected to tip rounding,this scalloped riblet performs better in terms of protrusion height than corresponding parabolic riblet,which indicates stronger resilience to riblet tip erosion.With the class of scalloped riblets,designed by smoothly connecting two third-order polynomials and thus the tip sharpness and valley curvature can be well defined,it is revealed that two mechanisms,one for the valley curvature at the viscous limit and one for the tip sharpness at infinite deep limit,determine the protrusion height,and thus the projected drag reduction capacity.Direct numerical simulations are then carried out to investigate controlled boundary layer transition with the scalloped riblet of width s+=20 and 5+=60.A 7.8%drag reduction in the turbulent region is found for the smaller riblet with a preferable transition delay,while for the larger riblet transition is promoted and drag is increased in the turbulent region.It is also found that the area fraction of high drag region around the riblet tips is basically the same for the two cases.Surprisingly,even higher drag is found around the tip region for the smaller drag-reducing riblets.On the other hand,a much smaller drag coefficient is found in the valley of the smaller riblet,which results in the reduction of turbulent drag.It is thus inferred that the issue of sharp riblet tip,that hard to manufacture and deteriorate substantially when subjected to tip erosion,could be mitigated by optimization of the riblet geometry.