# Advances in Riblets Design
## 5 Computational Efforts
[121] investigated three-dimensional shark skin replicated geometries in a channel flow by DNS. The authors reported that secondary flow generation within the turbulent boundary layer resulted in an increase in skin friction drag. [PERSON] et al. [38] demonstrated the possibility of drag reduction by riblets of about 10%. The authors studied the effectiveness of triangular riblets with various sizes in a fully developed channel flow. Drag reduction was analyzed by changing spacing and height for different riblet tip angles. They also conducted a comparison with experimental results and demonstrated that at \(s^{+}<20\), the drag reduction is in their optimum values for \(Re_{\tau}=186\). [PERSON] et al. [123] studied turbulent flow over riblets by directly integrating the equations of motion, modeling the damping effect of crossflow velocity fluctuations and displacement of turbulent quantities by use of LES. Although LES effectively simulated the larger scales of the flow, it still required a substantial amount of computational resources. [PERSON] et al. [32] reported that the average vortex diameter is in the order of 20-45 of non-dimensional diameter, for Reynolds number values of 2500-13,000. Results showed both drag decrease and increase in the wide range of non-dimensional spacing. Theyapplied the theory of cylindrical vortices to investigate the continuous and segmented riblets, by replicating them from shark skin. Impeding cross-flow motions by riblet surfaces has also been investigated by researchers. [PERSON] et al. [78] pointed out that the reduction in the crossflow velocity vector is a result of the reduction in Reynolds shear stress. In a similar study, [PERSON] et al. [126] carried out time-dependent models of the viscous wall region with \(y^{+}\approx 40\). Their studies reveal that lateral displacement of the flow towards the surface would be limited by riblets and, as a consequence, would lower the values of momentum in the riblet valleys. The effect of applying riblets in the laminar to turbulent transition region was investigated by [PERSON] et al. [127]. The authors investigated the effect of riblets installed on a flat plate with Zero Pressure Gradient (ZPG) by use of the Mono Integrated LES for streamwise aligned riblets amplification of T-S waves in laminar-turbulent transition observed for both K-type and oblique transition. In the process of transition, three main configurations are \(\Lambda\)-, hairpin vortex and turbulent breakdown. It resulted in the \(\Lambda\)-vortex structures in the K-type transition becoming weakened but not delayed by weak spanwise disturbances, while turbulent breakdown was delayed in the oblique transition. Since the microstructure geometries over the surface require numerical simulations in high Reynolds numbers, DNS and LES methods are unpractical due to the high computational costs; a number of research studies are implemented by making modifications to turbulent models. This approach would more simply simulate riblet surfaces rather than exactly capturing all the flow scales inside the boundary layer [58; 69; 70; 126; 128]. The rough surface was an idea applied by [PERSON] et al. [58]. The authors developed a numerical formulation in the turbulent model to sensitize to riblet geometries. The model contains two steps: (1) the first step was mainly developed according to the previous experimental data in triangular and semicircular grooves, with the related shifting of streamwise velocity over the surface; (2) in the second step, turbulent models were modified according to their contribution to the logarithmic region. The study looked at the effectiveness of their solution for Spalart-Allmaras and k-\(\omega\) models in the domains where experimental data was available, while the lack of experimental data decayed the quality of the results. Moreover, the accuracy of the results was reduced by adding pressure gradients and crossflows. Figure 7: Streamlines distribution in smooth and riblet surfaces normal to the flow direction [125].