Eventos Anais de eventos
COBEM 2023
27th International Congress of Mechanical Engineering
The study of the development of aircraft wakes near a ground plane through a Lagrangian approach
Submission Author:
Marília Vidille , SP
Co-Authors:
Marília Vidille, Paulo Guimarães de Moraes, Luiz Antonio Alcântara Pereira, Alex Bimbato
Presenter: Marília Vidille
doi://10.26678/ABCM.COBEM2023.COB2023-0067
Abstract
This work aims to simulate the behaviour of vortices detached from airplane wings and their interaction with a ground plane using a lagrangian method. The phenomenon occurs during take-off and landing procedures and may cause accidents in airports. The lagrangian computational technique used is the discrete vortex method, whereby the vorticity field is represented by Lamb discrete vortex, whose objective is to solve the vorticity transport equation, obtained from the Navier-Stokes and continuity equations. To reduce the complexity of the solution, the viscous splitting algorithm is used, which simulates the advection and diffusion processes separately, but at the same time step of the numerical simulation. To simulate the diffusion, the random walk method is used. According to this method, random numbers are generated to count the radial and circumferential displacements of the discrete particles. To simulate the advection, it is necessary to know the velocity field in the position occupied by each Lamb discrete vortex and it is composed of three parcels: the incident flow, the solid boundary and the discrete vortex cloud contributions. The solid boundary is represented by a source panel method to satisfy the impermeability boundary condition and a discrete vortex is positioned in the neighbourhood of each panel, at each time step of the numerical simulation, to satisfy the no-slip condition. The vortex-vortex interaction is the more onerous part of the velocity field calculation, because its computational costs, using the Biot-Savart law, are proportional to Z^2, where Z is the number of particles in the computational domain. The increase in the number of particles because of the vorticity generation makes the CPU time high and the simulation prohibitive. Therefore, an accelerator algorithm based on the fast multipole method is implemented to avoid this. The principle of this algorithm is to divide the computational domain into square boxes to enable more interactions among boxes than interactions among particles. The numerical results are compared with experimental ones and show that the use of the fast multipole method makes the simulations viable, well reproducing the vortices trajectory, even when the vorticity field is discretized using a large number of vortex particles.
Keywords
Aircraft Wakes, Accelerator Algorithm, fast multipole method, panel method, Lagrangian description
