Asymptotic method for deriving an aeroacoustic model in a flow duct

Article type: Research Article

Authors: Destuynder, Philippe

Affiliations: Chaire de Calcul Scientifique, Département de Mathématiques, Conservatoire National des Arts et Métiers, 292 rue Saint Martin, Paris 75003 E-mail: [email protected]

Abstract: The goal of this paper is to derive a fluid-structure model from a three-dimensional formulation and using an asymptotic method. The mechanical model that we consider is a flow duct, a part of which is flexible. This part can be assimilated to a shell or a membrane structure and a smart device is located on it in order to control the vibrations induced by the flow inside the duct. This control model is known to be challenging and no realistic controllability result has been obtained as far as a three-dimensional model is considered. But it can be derived for one-dimensional model. It is the reason why we are interested in this paper to analyze the links between the three-dimensional model and a limit one, assuming that the duct is quite long compared to its radius. The basic tool is a scaling method in the transverse section of the duct.

Keywords: aeroacoustic, fluid-structure, asymptotic method, error analysis

Journal: Asymptotic Analysis, vol. 46, no. 3-4, pp. 299-323, 2006