Copyright© 1998, American Institute of Aeronautics and Astronautics, Inc. COMPUTATION OF NOISE GENERATION BY TURBULENCE IN INTERNAL FLOWS E. Longattef P. Lafon* Departement Acoustique et Mecanique Vibratoire, Electricite de France, 1, Avenue du General de Gaulle, 92141 Clamart Cedex, France, S. Candel§ Laboratoire EM2C, CNRS, Ecole Centrale Paris 92295 Chatenay-Malabry Cedex, France Abstract Stochastic modelling techniques are currently used to deal with various problems in turbulence. These methods are explored in this article with as objective the computation of the solution of aeroacoustic noise problems. The principle may be described as follows. The mean flow field is first deduced from a RANS cal- culation associated with a turbulence closure scheme like the k — e model. Next, a space-time turbulent field is synthetized stochastically, providing the lo- cal turbulent fluctuations and the associated noise sources. The radiated sound field is then calculated numerically. The present article is structured around the three following points. The aeroacoustic calculation is pre- sented in the first part. The stochastic model of tur- bulence is described in the second part. The last section is devoted to computational methods and to numerical results related to noise generation by dia- phragms placed in ducted flows. Three-dimensional numerical results are compared with experimental data in terms of acoustic levels. Results of calcu- lations are in good agreement with predictions. Introduction In the framework of LighthilFs theory, standard aeroacoustic noise prediction methods rely on an analogy featuring a propagation equation associated with source terms. These formulations require time Copyright ©1998 by the Confederation of European Aerospace Societies. All rights reserved. ^Research Student ^Research Scientist, Member AIAA ^Professor, Member AIAA average or unsteady aerodynamic computation (k —e, LES or DNS) and provide acoustic far-fields. They do not account for all acoustic/mean flow interac- tions. More complex wave operators were derived to describe these interactions allowing extensions to prediction of noise generated by complex free flows. However, application to confined configurations is not straightforward because it requires the determi- nation of adapted Green's functions. Also, most of these methods rely on third order equations, which is not convenient for numerical purposes. Further- more, propagation equations bear acoustic distur- bances and also convective modes, vorticity and en- tropy waves. The stochastic approach used in this article does not feature some weaknesses of the afore-mentioned modellings. It is based on the computation of Eu- ler equations describing the propagation and inclu- ding acoustic source terms associated with turbu- lence. Propagation equations are linearized (or semi- linearized) around a mean field deduced from a time average aerodynamic calculation. Noise sources are expressed in terms of a turbulent velocity field pro- vided by a Stochastic Noise Generation and Radia- tion (SNGR) model. Finally, acoustic fields are de- duced from Euler equations associated with the pre- viously computed mean and turbulent fields. In this article, we describe this method and its applications to three-dimensional confined configu- rations. The first section is devoted to preliminary aerodynamic computations. In the second part, the stochastic model of turbulence and the synthesis of acoustic source terms are presented. Finally, nume- rical methods are described and some results related to noise generation by a diaphragm placed in ducted flows are discussed. 1 American Institute of Aeronautics and Astronautics