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Simplified vortex methods to model wake vortex roll-up in real-time simulations for fuel-saving formation flight

Spark, Henrik; Luckner, Robert

FG Flugmechanik, Flugregelung und Aeroelastizität

One possibility for reducing fuel consumption is to fly in the upwind field of the wake vortex generated by an aircraft that is flying ahead. Migratory birds use this principle. Manually flying an aircraft at the point of optimal fuel reduction is not suited for routine flight operations as the pilot workload is excessively high. Hence, an autopilot function has to carry out this task. For designing the autopilot, a flight mechanical simulation with a wake vortex velocity model is required that has the ability to calculate the vortex-induced velocity fields. This paper contributes to the choice of a real-time simulation method for modelling vortex-induced velocities that the wake vortex of a leading aircraft generates and that the trailing aircraft shall use during fuel-saving formation flight.Two different wake vortex velocity models are introduced and compared during steady, horizontal flight. One model is based on the Lifting Line Method (LLM) and the other on the unsteady Vortex Lattice Method (VLM). Both models are able to calculate the wake vortex roll-up phase for arbitrary lift distributions, whereas the commonly used Single Horseshoe Vortex Model (SHVM) ignores the near-field roll up. The differences in the induced upwind distribution and vortex filament position are analysed for coarse spatial and temporal discretisation that the real-time constraint requires. Despite the more stringent simplifications of LLM, both methods yield similar filament positions and similar velocity fields for the same discretisation of the lifting surfaces. Finally, the influence of the discretisation parameters is discussed and parameter values are recommended for using VLM and LLM in real-time flight simulations.