This document is the property of EADS CCR. It may not be communicated to any third parties and/or reproduced without the prior written consent of EADS CCR and its content may not be disclosed. EADS CCR POTENTIAL ADVECTIVE LINEAR AXISYMETRIC ACOUSTIC CODE PA2R S.DUPREY Département Environnement Simulation Numérique EADS Corporate Research Center Toulouse & Suresnes, France 17 Novembre 2004 Suresnes

This document is the property of EADS CCR. It may not be communicated to any third parties and/or reproduced without the prior written consent of EADS CCR and its content may not be disclosed. EADS CCR INTRODUCTION Principales hypothèses et positionnement scientifique Ecoulement Acoustique Couplage

This document is the property of EADS CCR. It may not be communicated to any third parties and/or reproduced without the prior written consent of EADS CCR and its content may not be disclosed. EADS CCR Gaz parfait adiabatique, isentropique et équation dEuler pour lécoulement total Découplage total écoulement-acoustique, acoustique linéaire et propagation pure Phénomènes potentiels Régime harmonique et sources modales (rayonnement moteur avion) Axisymétrie Equations intégrales Elements volumiques H1-conformes HYPOTHESES PHYSIQUES POSITIONNEMENT SCIENTIFIQUE

This document is the property of EADS CCR. It may not be communicated to any third parties and/or reproduced without the prior written consent of EADS CCR and its content may not be disclosed. EADS CCR FLUIDE PORTEUR EQUATIONS Ecoulement potentiel Equation obtenue à lordre 0 des équations de lécoulement total Flux imposés Liens entre les variables : EDP non linéaire :

This document is the property of EADS CCR. It may not be communicated to any third parties and/or reproduced without the prior written consent of EADS CCR and its content may not be disclosed. EADS CCR FLUIDE PORTEUR THEORIE Formulation variationnelle : Restriction aux régimes subsoniques : Point fixe convergent :

This document is the property of EADS CCR. It may not be communicated to any third parties and/or reproduced without the prior written consent of EADS CCR and its content may not be disclosed. EADS CCR FLUIDE PORTEUR NUMERIQUE Méthode de point fixe numérique inspirée de la théorie Potentiel à létape k calculé par éléments finis H1-conformes Densité et vitesse calculées à létape k+1, constants par éléments Nouvelle matrice assemblée à chaque itération Matrice creuse, symétrique et parallélisée Contrainte de convexité estimée sur chaque élément à chaque itération Formulation axisymétrique

This document is the property of EADS CCR. It may not be communicated to any third parties and/or reproduced without the prior written consent of EADS CCR and its content may not be disclosed. EADS CCR ACOUSTIQUE EQUATIONS acoustique potentielle obtenue à lordre 1 de l écoulement total Condition impédante de type Myers sur les parties traitées Réfraction totale sur les parois rigides non traitées Sources modales au moteur Condition de Sommerfeld à linfini Formulation axisymétrique EDP linéaire à coefficients inhomogènes provenant de lécoulement

This document is the property of EADS CCR. It may not be communicated to any third parties and/or reproduced without the prior written consent of EADS CCR and its content may not be disclosed. EADS CCR ACOUSTIQUE COUPLAGE A LINFINI Formulation variationnelle acoustique continue Discrétisation et rapatriement

This document is the property of EADS CCR. It may not be communicated to any third parties and/or reproduced without the prior written consent of EADS CCR and its content may not be disclosed. EADS CCR ACOUSTIQUE COUPLAGE MODAL Nouvelle base dofs -> modes

This document is the property of EADS CCR. It may not be communicated to any third parties and/or reproduced without the prior written consent of EADS CCR and its content may not be disclosed. EADS CCR ACOUSTIQUE NUMERIQUE Problème volumique discrétisé en éléments finis H1-conformes Assemblage séparé et parallélisé des matrices dinteractions (volumique, modale-volumique,volumique-surfacique, surfacique) Matrice surfacique intégrale pleine Matrice volumique non symétrique et creuse (solveur creux) Complément de Schur (solveur creux) Singularité sur laxe

This document is the property of EADS CCR. It may not be communicated to any third parties and/or reproduced without the prior written consent of EADS CCR and its content may not be disclosed. EADS CCR TECHNICITE

This document is the property of EADS CCR. It may not be communicated to any third parties and/or reproduced without the prior written consent of EADS CCR and its content may not be disclosed. EADS CCR Nombre de Mach Module du potentiel acoustique Partie réelle potentiel acoustique Partie réelle vitesse acoustique selon y Résultats acoustiques sur écoulement potentiel ( ) k=10

This document is the property of EADS CCR. It may not be communicated to any third parties and/or reproduced without the prior written consent of EADS CCR and its content may not be disclosed. EADS CCR Comparaison potentiel-uniforme ( ) k=10 Différence absolue partie réelle potentiel acoustique Différence absolue module du potentiel acoustique Différence relative module du potentiel acoustique

This document is the property of EADS CCR. It may not be communicated to any third parties and/or reproduced without the prior written consent of EADS CCR and its content may not be disclosed. EADS CCR Nombre de Mach Module potentiel acoustique Partie réelle potentielle acoustique Partie réelle vitesse acoustique selon y Résultats acoustiques sur écoulement potentiel ( ) k=40

This document is the property of EADS CCR. It may not be communicated to any third parties and/or reproduced without the prior written consent of EADS CCR and its content may not be disclosed. EADS CCR Différence absolue partie réelle potentielDifférence absolue module potentiel acoustique Différence relative module potentiel Comparaison potentiel-uniforme ( ) k=40

This document is the property of EADS CCR. It may not be communicated to any third parties and/or reproduced without the prior written consent of EADS CCR and its content may not be disclosed. EADS CCR Nombre de Mach Module potentiel acoustique Partie réelle potentielle acoustique Partie réelle vitesse acoustique selon y Résultats acoustiques sur écoulement potentiel ( ) k=10

This document is the property of EADS CCR. It may not be communicated to any third parties and/or reproduced without the prior written consent of EADS CCR and its content may not be disclosed. EADS CCR Différence absolue module potentiel acoustique Différence absolue partie réelle potentiel Différence relative module potentiel Comparaison potentiel-uniforme ( ) k=10

This document is the property of EADS CCR. It may not be communicated to any third parties and/or reproduced without the prior written consent of EADS CCR and its content may not be disclosed. EADS CCR Nombre de Mach Module potentiel acoustique Partie réelle potentielle acoustique Partie réelle vitesse acoustique selon y Résultats acoustiques sur écoulement potentiel ( ) k=40

This document is the property of EADS CCR. It may not be communicated to any third parties and/or reproduced without the prior written consent of EADS CCR and its content may not be disclosed. EADS CCR Différence absolue module potentiel acoustique Différence absolue partie réelle potentiel Différence relative module potentiel Comparaison potentiel-uniforme ( ) k=40

This document is the property of EADS CCR. It may not be communicated to any third parties and/or reproduced without the prior written consent of EADS CCR and its content may not be disclosed. EADS CCR Partie réelle potentielle acoustique Module potentiel acoustique Partie réelle vitesse acoustique selon y Pression fluide Résultats acoustiques sur écoulement potentiel ( ) k=10

This document is the property of EADS CCR. It may not be communicated to any third parties and/or reproduced without the prior written consent of EADS CCR and its content may not be disclosed. EADS CCR Différence absolue module potentiel acoustique Différence absolue partie réelle potentiel Différence relative module potentiel Comparaison potentiel-uniforme ( ) k=10

This document is the property of EADS CCR. It may not be communicated to any third parties and/or reproduced without the prior written consent of EADS CCR and its content may not be disclosed. EADS CCR Pression fluide Module potentiel acoustique Partie réelle potentielle acoustique Partie réelle vitesse acoustique selon y Résultats acoustiques sur écoulement potentiel ( ) k=40

This document is the property of EADS CCR. It may not be communicated to any third parties and/or reproduced without the prior written consent of EADS CCR and its content may not be disclosed. EADS CCR Différence absolue module potentiel acoustique Différence absolue partie réelle potentiel Différence relative module potentiel Comparaison potentiel-uniforme ( ) k=40

This document is the property of EADS CCR. It may not be communicated to any third parties and/or reproduced without the prior written consent of EADS CCR and its content may not be disclosed. EADS CCR Une nacelle plus réaliste

This document is the property of EADS CCR. It may not be communicated to any third parties and/or reproduced without the prior written consent of EADS CCR and its content may not be disclosed. EADS CCR Ecoulement nul constant mode 00-01

This document is the property of EADS CCR. It may not be communicated to any third parties and/or reproduced without the prior written consent of EADS CCR and its content may not be disclosed. EADS CCR Ecoulement potentiel nul à linfini

This document is the property of EADS CCR. It may not be communicated to any third parties and/or reproduced without the prior written consent of EADS CCR and its content may not be disclosed. EADS CCR Ecoulement potentiel nul à linfini mode 00-01

This document is the property of EADS CCR. It may not be communicated to any third parties and/or reproduced without the prior written consent of EADS CCR and its content may not be disclosed. EADS CCR Ecoulement potentiel non nul à linfini

This document is the property of EADS CCR. It may not be communicated to any third parties and/or reproduced without the prior written consent of EADS CCR and its content may not be disclosed. EADS CCR Écoulement potentiel non nul à linfini mode 00-01