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Etude mathématique et numérique de la propagation acoustique d'un turboréacteur

Stefan Duprey 1, 2
2 CORIDA - Robust control of infinite dimensional systems and applications
IECN - Institut Élie Cartan de Nancy, LMAM - Laboratoire de Mathématiques et Applications de Metz, Inria Nancy - Grand Est
Abstract : This thesis deals with the industrial problem of modelisation and
numerical simulation of the acoustic radiation from fan duct air entry. The physical
hypothesis subsequent to the industrial framework give way to a simplified
model of linear acoustic propagation upon a non linear potential flow. Engine
modal noise source modelisation requires acoustic boundary conditions through
a Dirichlet-Neumann operator. Existence and uniqueness of the global mathematical
problem (a convected Sommerfeld condition is added) of the potential
and local perturbation from a uniform flow are prooved. A discrete coupling
between the volumic acoustic potential (finite volumic elements) and its elliptic
normal derivate (boundary finite element) through an integral equation is
exhibed. Computing code is validated analytically and comparatively. Original
results are described and prove the necessity to consider the nonlinearity of the
flow by differences greater than 5 dBs in the far field acoustic diagrams. Optimal
positionning of the radiating surface and the plugability of the fast multipole
method make this coupling unmissable. Simplified potential-linear model, even
if its range of validity is restricted to the fan duct air entry, gets his whole interest
as a brick in a global domain decomposition code. By the way, let's mention
the achievement of a natural axisymetric finite element and an alternative method
to the calculus of the non linear flow by a fixed point method.
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Contributor : Antoine Henrot <>
Submitted on : Wednesday, May 9, 2007 - 10:42:31 AM
Last modification on : Friday, February 26, 2021 - 3:22:03 AM
Long-term archiving on: : Wednesday, April 7, 2010 - 1:19:44 AM


  • HAL Id : tel-01746556, version 2



Stefan Duprey. Etude mathématique et numérique de la propagation acoustique d'un turboréacteur. Mathématiques [math]. Université Henri Poincaré - Nancy 1, 2006. Français. ⟨NNT : 2006NAN10185⟩. ⟨tel-01746556v2⟩



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