Large-eddy simulations of the flow around a three-element wing

Abstract

This work presents a numerical study of the turbulent flow around the 30P30N three-element high-lift wing. A Wall-Modeled Large-Eddy Simulation (WMLES) is used at a Reynolds number of Re = 5×106 and an angle of attack (AoA) of 8 ◦ . The use of high-lift devices such as slats and flaps is essential during takeoff and landing in order to increase lift at low flight speeds. However, these devices generate complex unsteady flow features, including shear layer instabilities, recirculation bubbles and laminar-to-turbulent transition, that are challenging to capture accurately using traditional low-fidelity models. The 30P30N configuration, developed by McDonnell-Douglas, is widely used in experimental and numerical studies as a benchmark geometry for high-lift aerodynamics and aeroacoustics. While most previous research has been conducted at moderate Reynolds numbers (Re ≤ 1.7×106 ) using RANS or hybrid RANS/LES approaches, this work applies WMLES at a more realistic Reynolds number, closer to actual operational conditions. The simulation is performed using a high-order, low-dissipation spectral element solver (SOD2D) and three progressively refined high-order hexahedral meshes are used to study mesh sensitivity. The results show that the numerical setup is able to capture key aerodynamic phenomena such as leading-edge suction peaks, turbulent boundary layer development and wake structures behind the flap. The analysis of the skin friction coefficient (Cf) indicates that the flow remains mostly attached throughout the airfoil surface, with localized regions of weak separation in the slat and flap coves. Instantaneous velocity fields and Q-criterion isosurfaces reveal coherent vortical structures and shear layer instabilities, in agreement with reference data. The aerodynamic coefficients obtained are consistent with literature values, supporting the accuracy and physical relevance of the simulation. In conclusion, this study demonstrates the ability of WMLES to predict complex, high-Reynolds-number flow behavior in multi-element airfoils with a good balance between computational cost and fidelity. It validates the use of high-order meshes in combination with wall modeling and shows that, with appropriate mesh resolution, WMLES can accurately capture both global aerodynamic performance and local flow details. This work establishes a solid foundation for future research and optimization in the field of high-lift aerodynamics under realistic flight conditions.