Inhalt des Dokuments
MATHEON Projekt B-MI2
This research is carried out in the framework of Matheon supported by Einstein Foundation Berlin.
|Duration||June 2014 - May 2017|
|Head||Dr. Kersten Schmidt|
|Member||Dr. Anastasia Thöns-Zueva|
|Cooperation||Ralf Hiptmair (ETH Zurich)|
Patrick Joly (INRIA Saclay)
Bérangère Delourme (Université Paris 13)
Sébastien Tordeux, Julien Diaz, Juliette Chabassier (INRIA Bordeaux Sud Ouest)
Alexey Chernov (University of Reading)
Lars Enghardt, Friedrich Bake (DLR Berlin)
Carlos Jerez Hanckes (Pontificia Universidad Catolica de Chile)
|Link||MATHEON project webpage|
|Description||The reduction of the excited noise of transportation, especially in gas turbines of airplanes and ships or mufflers of cars, is currently of major public and industrial interest. We aim to describe the effective absorption properties of sound absorbing resonator structures and perforated walls. As the governing equations and structures possess several scales, we study the problems asymptotically. In this project we derive and study approximative boundary and transmission conditions, that take into account the physical phenomena on the small scales inside the holes of the perforated absorber and the boundary layers in their neighbourhood.|
The reduction of the excited noise of transportation, such as in gas turbines of airplanes and ships or engines of cars, is essential and currently of major public and industrial interest. The city of Berlin and its surrounding area with the five companies Siemens Energy, Rolls-Royce, MTU, MAN Diesel & Turbo and ALSTOM (altogether about 8000 employees) are the largest production region of gas turbines in Europe.
Nowadays combustion processes create acoustic sources of higher intensity, which in their turn create acoustic instabilities at particular frequencies and may even harm the live time of the gas turbine. The reduction of noise is obtained by sound absorbing resonator structures in the hull or by perforated walls between the combustion chamber and the chamber for cooling. Understanding the absorption properties of such devices in gas turbines aims to reduce the environmental impact of those conventional energy systems.
By interior friction (viscosity) of real gases tiny acoustic boundary layers close to walls constitute themselves in which the acoustic velocity changes abruptly. These boundary layers and a high number of small holes in perforated walls, or even a high number of resonance chambers below perforated walls, cannot be resolved in direct numerical simulations. Nevertheless, they have an essential influence on the absorption properties.
Viscous boundary layers close to rigid walls
We have introduced the two-scale expansion, which expresses an approximation to the exact solution as a decomposition into far field, which models the macroscopic picture of the solution, and correcting near field in the neighbourhood of the boundary by multiscale analysis.
We have introduced a multi-scale expansion, which expresses an approximation to the exact solution as a decomposition into far field, which models the macroscopic picture of the solution, and correcting near field in the neighborhood of the geometrical singularities by multiscale analysis. This analysis covers the case of thick holes (two-scale expansion), as well as the case of thin holes (three-scale expansion).
Acoustic experiments in the group of L. Enghardt and F. Bake at DLR Berlin show that the noise absorption by perforated walls differs if smaller or larger acoustic amplitudes are used. In addition, an interaction of different frequencies has been observed. To describe these effects we consider the compressible Navier-Stokes equations in time domain. We obtained a frequency domain formulation with the multiharmonic analysis, writing both acoustic velocity and pressure in Fourier transform. We can then decouple the system partly by asymptotic expansion. The limit approximation model has been obtained for frequency 0 and ω (the frequency of the excitation) and is implemented in the numerical C++ library Concepts.