# Advances in Riblets Design
## 5 Computational Efforts  
Numerical studies are widely implemented for the investigation of flow properties over riblet surfaces. Although experimental studies offer a good understanding of the flow properties within the boundary layer, numerical methods could be efficient enough to evaluate the behavior of the flow over the riblet surfaces. On this basis, the flow properties are numerically evaluated by use of Direct Numerical Simulations (DNS), Large Eddy Simulation (LES) and Reynolds Average Navier-Stokes equations (RANS). All flow scales would be resolved by the DNS technique, which requires  
Figure 5: (a) Schematic of riblet application by a robot in the laboratory [66]. (b) Automatic application of riblet coating on the aircraft wing [85]. Figure 6: An indication of contactless riblet production [45]. more computational time and therefore remains unpractical for high Reynolds number flows and complex 3D geometries such as aircraft surfaces. In the realm of simulating riblet performance, the DNS method has been the primary choice. However, owing to the computational demands associated with DNS, the vast majority of evaluations are carried out using flat plates, particularly at low Reynolds numbers. Additionally, researchers have extended riblet simulations to include airfoil configurations, which may take the form of 2D extruded shapes or intricate 3D wing geometries. These simulations have employed either DNS or LES techniques. To address the computational challenges posed by these methods, the RANS technique has been used as an alternative approach. Within this context, it is important to note that over the past few decades, numerous flow simulations have been conducted to analyze the performance of riblet geometries. These simulations encompass a wide range of scenarios, starting with basic flat plates and progressing to more complex configurations, including extruded airfoils, wing-body combinations, standard aircraft models, and unmanned aerial vehicles (UAVs). In the following paragraphs, an overview of the research efforts dedicated to the abovementioned categories is presented. Flat plate simulations: Previous DNS numerical investigations in riblet geometries were only devoted to a simple simulation of a flat plate in low Reynolds numbers [78; 79; 121; 122; 123; 124]. [PERSON] et al. [78] investigated drag-reducing configurations by use of DNS for triangular shapes in a fully developed turbulent channel at low Reynolds numbers. The authors indicated the effect of small spacing on the riblet tips wetted area due to the restricting position of longitudinal vortices. A virtual origin was defined at the location of maximum turbulent kinetic energy production, at around \(y^{+}\approx 13\). By increasing the sharpness, the virtual origin moved up and became closer to the riblet tips. They indicated an upward shift in the logarithmic region, and a 5-6% reduction in friction drag was observed for \(s^{+}=20\). The mechanism of lifting streamwise vortices was also investigated by some researchers. [PERSON] et al. [125] carried out DNS to investigate turbulent characteristics and drag reduction in a compressive flat plate flow by comparing vorticity fluctuations and streak structures in the riblet plate and the smooth surface. Streaks are elongated regions in a plane parallel to the wall where the instantaneous velocity over there is below the average. The results showed an upward shift in the longitudinal vortices (see Figure 7), resulting in fewer interactions with the wall and suppression of the intensity in Reynolds shear stress. In a similar study, [PERSON] et al. [78] investigated the size of the vortices and riblets in various 20 and 40 non-dimensional spacing, based on the non-dimensional diameter of vortices (which was roughly located at \(y^{+}\approx 13\)) to indicate the diameter of streamwise cylindrical vortices. Besides two-dimensional riblet families, three-dimensional geometries were also investigated by some researchers. [PERSON] et al.