# A new approach about mathematic and numerical modeling in aeroacoustic with Goldstein equations and application in aeronautics

Event type:

Thesis defence

Event name:

Thèse de Antoine Bensalah

Start at:

july 06, 2018

Place:

ENSTA salle 2.2.34 à 14h30

Contact:

Responsible team:

Title:

A new approach about mathematic and numerical modeling in aeroacoustic with Goldstein equations and application in aeronautics

Detail:

We work on the computation of the acoustic waves radiated from an aircraft engine during flight. The main topics is aeroacoustics, that is to study the propagation of the acoustic perturbations within a flowing fluid. We assume that this carrier flow is known, in practice coming from a computational fluid dynamic code for instance. We consider a system of equations equivalent to the linearized Euler model, called Goldstein model. This model can be seen as a perturbation of the convected Helmholtz equation, which is well-know both theoretically and numerically. The Goldstein model reduces to this convected Helmholtz equation when the carrier flow is potential. The perturbation is characterised by the addition of a new unknown, called hydrodynamic one, satisfying a transport equation. This unknown allows to take into account the complex coupling between acoustic and hydrodynamic effects present because of the vorticity of the fluid. It is located only where the vorticity of the carrier flow does not vanish. These areas are quite restricted in general, limited around the aircraft engine. Therefore, the potential model is often used, assuming that the error is small. In particular, Airbus already has an efficient industrial computation tool for solving the Helmholtz convected equation. The final aim of this thesis is the integration of the numerical resolution in the Airbus Group code, named ACTIPOLE, of the Goldstein equations in time harmonic domain, to take into account the vortical part of the flow previously neglected. The additional computational cost should be reasonable because the new unknown lies only on a limited part of the domain. Therefore the transport equation introduces only a moderate number of extra degrees of freedom to the problem. As far as we know, the Goldstein model has not been much studied in aeroacoustic, this is why it is necessary to analyze its main mathematical properties to build an efficient numerical scheme. Finally, we plan to take into account the uncertainties of the data, here the carrier flow. Indeed, in practice, the carrier flow is computed by a CFD (computational fluid dynamic) code and therefore is affected by errors due to the numerical resolution. It is then interesting and important to take into account the uncertainties of the data when studying a model dealing with realistic flow (vortical) which cannot be known exactly.