# Advances in Riblets Design
## 5 Computational Efforts
Airfoil geometry simulations: [PERSON] et al. [129] employed the LES method to analyze the Eppler E374 airfoil under specific conditions: a free stream Mach number of 0.2, angle of attack of \(3^{\circ}\) and Reynolds number of \(2\times 10^{5}\). Triangular riblets were positioned from 30% to 99% of the airfoil's chord length and the numerical trip was located at 13% of the chord. The airfoil model and computational grid are illustrated in Figure 8. The computational results, both with and without trip, closely matched the experimental data. The authors demonstrated that implementing triangular riblets leads to an increase in mean flow velocity in the streamwise direction and also effectively suppresses the Reynolds stress and pressure power spectrum density over most of the upper surface of the airfoil. Wing body simulations: [PERSON] et al. [69] investigated two models for estimating riblets performance. The turbulent model and slip length were based on the boundary conditions and introduced according to the k-\(\omega\) turbulent model. The authors introduced the concept of slip-length as a representation of the tangent to the wall velocity components. Increasing the slip-length value leads to an upward shift of the log-law, indicating changes in the velocity profile near the wall. [PERSON] et al. [70] applied the RANS equations for riblet geometries by considering them as a singular roughness problem and by modifying the Wilcox boundary condition in which the boundary condition for \(\omega\) in the k-\(\omega\) turbulence model for rough walls was modeled as a function of non-dimensional riblets cross-section area [57], introducing the \(l_{\delta}^{+}\) value. They evaluated the effectiveness of micro-grooves on a flat plate, transonic airfoil, and standard NASA Common Research Model (CRM). Results showed the effect of riblets height on the optimum operation of riblet geometries. The effect of riblet height on a wing body with Natural Laminar Flow (NLF) was also investigated [69]. By imposing a transition line on the wing and setting the turbulence model's production terms to zero in the laminar zone, the NLF conditions were established. Riblets were then introduced in the turbulent zones of the wing body. The study found that the installation of riblets at various heights resulted in a significant reduction in drag. The drag reduction was particularly prominent during cruise conditions, with higher riblet heights demonstrating better drag reduction performance. Figure 9 depicts that the choice of riblet height plays a crucial role in optimizing the aerodynamic efficiency of NLF wing bodies. Figure 8: Computational grid of the airfoil and riblet [125]. UAVs simulation; the impact of riblets on a fixed wing, low-speed UAV investigated by [PERSON] et al. [37]. The authors utilized RANS and incorporated the riblet geometry as a homogenized boundary condition on a smooth surface at a free stream speed of 22 m/s. They made a virtual shift in wall units on the non-slipping wall parameter, by introducing a dimensionless upward adjustment to the streamwise velocity profile. This shift effectively exploited the presence of riblets through a slip boundary condition. After testing this approach on both flat plate and NACA 0012 airfoil, the authors demonstrated that applying riblets across the entire surface of the UAV model resulted in a drag reduction of approximately 3%. Alternatively, by applying riblets only to the upper side of the wings, they achieved a drag reduction of approximately 1.7%. This means that by covering just around 29% of the total surface with riblets, one can achieve significant drag reduction, thereby reducing the cost of implementation and maintenance. In another study carried out by [PERSON] et al. [130], research was conducted on the HCUAV RX-1, a medium-altitude, long-endurance, fixed-wing UAV prototype. The researchers implemented a modification in surface roughness similar to the approach used by [PERSON] et al. [70] that considers the riblet surface as a singular roughness problem.