| Biography | |
|---|---|
 Prof. Mabrouk Ben Tahar University of Technology of Compiègne, France |
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| Title: Finite element approach for aeroacoustics problems based on an Eulerian–Lagrangian description: Galbrun’s equation | |
| Abstract: This presentation reviews our developments and applications of Computational AeroAcoustics (CAA) to acoustic propagation on subsonic non-potential mean flows, using a nonstandard linear wave equation, established by Galbrun in 1931 (LGE). Galbrun’s equation describes exactly the same physical phenomenon such as the linearized Euler’s equations (LEE) but is derived from an Eulerian–Lagrangian approach written only in term of the Lagrangian perturbation of the displacement. This equation has interesting properties and offers a good alternative to the Linearized Euler Equations (LEE). Indeed, only acoustic displacement is involved (even in non-homentropic cases). The equation provides exact expressions for acoustic intensity and energy. Also, the boundary conditions are easily expressed because acoustic displacement, whose normal component is continuous, appears explicitly, which avoid the use of Myers’ condition. The governing equations are presented and a comparison will be made with LEE. Galbrun’s equation is solved using a finite element method. However, with standard finite element, the direct displacement-based variational formulation gives some erroneous solutions. A mixed finite element (pressure-displacement), satisfying the inf-sup condition, is proposed to avoid this problem. Using the finite element method with an irregular mesh provides the flexibility for real industrial applications. A particular issue such as the boundary conditions, impedance conditions, transparent boundary conditions in infinite domain and energy equation are discussed. In unbounded domain, an accurate and efficient modified perfectly matched layer (PML) is proposed. Lined boundary walls described by the Biot’s model has been developed. A complex Laplace transform scheme is used to study the time dependent variables. Finally, the proposed model is compared with some measured data and benchmark problems. The comparison shows a good agreement, which validates it. | |
| Biography: Mabrouk Ben Tahar, Full Professor, the University of Technology of Compiègne - France, holds a Ph.D. degree (1981) and Doctor of Science (docteur ès-sciences) (1991) from the University of Technology of Compiègne. He was appointed to the University of Technology of Compiègne in 1982, and from 2000 was a full professor in the mechanical engineering department. He also served as a Head of the Acoustic group (2000-2017) and a Head of the doctoral school in mechanical engineering. He is a Fellow of the French Society of Acoustic (SFA) and the French Mechanical Association (AFM). He was a visiting researcher/professor at the Institute of Sound and Vibration (ISVR), Laval University Quebec-Canada, Technical University of Denmark, the Sherbrook University Canada, the Institute of Vibration, Shock & Noise, the Shanghai Jiao Tong University, Mohammadia Engineering School, the Mohammed V University, Rabat-Morocco, Engineering School of Monastir-Tunisia, Engineering School of Gabès-Tunisia and Engineering School of Adelaide university. His primary research focuses on the numerical methods in acoustic and aeroacoustics (CAA). The major focus has been the numerical approach of aeroacoustics using Galbrun’s equation. He has supervised more than twenty Ph.D. students, published more than 40 scientific articles, and more than 100 international and national conferences. | |
