Quasi-Analytical Solution of Optimum and Maximum Depth of Transverse V-Groove for Drag Reduction at Different Reynolds Numbers

Influence of the stability of boundary vortex on drag reduction induced by transverse V-grooves

Previous studies revealed the skin-friction drag reduction properties induced by transverse grooves. However, the effects of unsteady characteristics of vortices within the grooves on the drag reduction properties have not been investigated. A hypothesis that the unsteady motion of vortices may reduce the friction drag-reduction rate induced by transverse V-grooves is proposed in this paper. To verify this hypothesis, we use the LES (large eddy simulation) method to investigate the flow field in the range of Reynolds number 0.5E5 to 7.5E5 over the different profiles of symmetric V-grooves, whose depths are 0.2 mm and AR's are 0.5, 1, 2, 5, and 8. The results show that the AR (aspect ratio of a transverse groove) affects the stability of boundary vortices, thus driving the variation of total viscous drag and pressure drag. With the increase of AR, the boundary vortices tend to be stable at first and then gradually become unstable. When AR is 2, the boundary vortices are stable within the grooves, corresponding to optimal drag reduction. In this case, the slip velocities induced by boundary vortices are the largest, and the Reynolds shear stress is the least, suggesting that the grooves have the strongest abilities to reduce the total viscous drag. When the stability of the boundary vortices is broken, a larger area containing high pressure and low pressure is formed in the groove, and the difference also becomes greater between the high pressure and low pressure. The results provide improved understandings of the drag reduction mechanism of transverse grooves.