## 1 Introduction
[17] studied the compressible flow over a wing, and observed how spanwise forcing affects the shock wave to yield large reduction of the total drag of the aircraft. The availability of a boundary condition to faithfully simulate in a RANS the presence of riblets on the surface of a solid body of complex shape is thus becoming extremely attractive. The standard no-slip condition at a solid wall can be extended to a partial-slip one, which is useful to describe specific physical situations (e.g., flow over superhydrophobic surfaces). Riblets are amenable to such a description; their slip length is related to the protrusion height concept [3; 4; 5]. In particular, [PERSON] in [5] defined the longitudinal and transverse protrusion heights, which identify the virtual origin for the streamwise and spanwise velocity profiles, and realised that the only meaningful non-arbitrary quantity is their difference. Later, he also introduced [18] a linearised boundary condition for generic roughness and the protrusion heights for various roughness types to be adopted in DNS. He also demonstrated that the difference \(\Delta t\) between the two riblets protrusion heights corresponds to the slip length \(\lambda\). [PERSON] et al. [19] later discussed how the slip length \(\lambda^{+}\) expressed in viscous units is equivalent to the upward displacement \(\Delta U^{+}\) of the mean velocity profile in the logarithmic region; here, \(\lambda^{+}=\lambda u_{\tau}/\
u\), where \(\
u\) is the kinematic viscosity, \(u_{\tau}=\sqrt{\tau_{w}/\rho}\) is the friction velocity, \(\rho\) is the density, and \(\tau_{w}\) is the (local) shear stress. The value of the slip length \(\lambda\) depends upon the shape and size of the riblets cross-section. [PERSON] et al. [4] found that the largest drag reduction for riblets of different shapes was obtained when \(s^{+}\), the spanwise period of the riblets, is in the range 10-20. [PERSON] and [PERSON] [1] tested alternative scalings to find whether drag reduction can be linked to a single geometric parameter that captures the importance of riblet spacing and their cross-sectional shape as well. Data for different riblets were found to best collapse when plotted against a dimensionless length scale \(l_{g}^{+}\) derived from the cross-sectional area \(A_{g}\) of the groove, and defined as \(l_{g}^{+}=(A_{g}^{+})^{1/2}\). For riblets of various geometries, the best performance was consistently found at \(l_{S}^{+}\approx 10.5\). For optimal triangular riblets, \(l_{S}^{+}=10.5\) corresponds to a unitary shift \(\Delta U^{+}\), which coincides with the one reported in previous studies [15; 20; 21]. Recently, [PERSON] et al. [22] have been able to compute the slip length for other riblets shapes, i.e., with trapezoidal and blade cross-sections. The goal of this paper is to present the implementation of a slip-length boundary condition for riblets, and to use it in a set of RANS simulations to assess the drag reduction capabilities of riblets when installed on a fixed-wing UAV, for which endurance is of capital importance. Indeed, over the years, riblets have been studied either at low speed over plane walls, or in transonic flow conditions for aeronautical applications, especially for medium- or long-range commercial passenger aircraft. Such studies, carried out both numerically [10; 23] and experimentally [24; 25; 26; 27; 28], provide interesting results for aircraft operating in a range of chord-based Reynolds numbers up to \(Re_{\infty}=3\times 10^{7}\). In contrast, the low-speed aircraft considered in the present work has a cruise speed of 22 m/s with \(Re_{\infty}=5\times 10^{5}\). This paper describes the implementation into an incompressible CFD solver of a slip-length wall boundary condition, similar to that described in ref. [21], to compute the drag reduction achievable with riblets of optimal dimensions. The computational model is validated against configurations of increasing complexity, and eventually applied to a realistic use case.