Lagrangian Vortices Interactions Using Large-Eddy Simulation (LES) and Surface Roughness Model—Application for Aircraft Wake Vortices with Crosswind

A new technique for two-dimensional vortex methods is presented. The vorticity field is discretized and represented by vortex blobs. Viscosity and roughness are incorporated into vortex simulations by means of the corrected core-spreading method with LES theory. A deterministic and efficient grid-free method simulates viscous effects by maintaining small vortex core sizes through a splitting algorithm that controls the consistency error. The LES theory also enables the implementation of the roughness model. The effectiveness of this method is shown in calculating vortex interactions and decay in aircraft wakes with crosswind near a rough ground plane. The numerical results of the trajectory of primary vortical structures are compared with experimental data (when possible), suggesting the validity of the method. In general, the control of the roughness height size appears as an important factor to interfere on the trajectory of primary vortical structures in the ground effect with crosswind. The effect of the relative roughness height of ε/Δs = 0.001 shows that the primary vortical structures survive the interaction with the ground plane and can attain a maximum height in the order of 0.95 h (h is the release height of the primary vortical structures) during the loop for crosswind velocity of U∞ = 0.02 at Re = 7650. On the other hand, the combined effects of roughness ε/Δs = 0.001 and of crosswind U∞ = 0.04 at Re = 75,000 indicate that the primary vortical structures attain a maximum height about 0.83 h during the loop, tending to leave the runway faster, with sufficient intensity to disturb a smaller aircraft operating on a parallel runway.

Palavras-chave

corrected core-spreading method, decay in aircraft wakes, Lagrangian vortex method, large-eddy simulation, method of images, surface roughness effects