Numerische Methoden zur Simulation von Schallerzeugung und Ausbreitung in Strömungen um komplexe zwei- und dreidimensionale Geometrien

Abstract

In der Aeroakustik breiten sich die elastischen Wellen vom Entstehungsort der Quelle zum Beobachter mit Schallgeschwindigkeit aus. Ziel ist es, den Ort der Quellenstehung und die Entstehungsmechanismen zu bestimmen und durch aktive und passive Maßnahmen die Quellstärke zu reduzieren und neue Technologien zur Minderung des Lärms zu entwickeln. Zur Bestimmung des Schallfeldes kann die Akustische Analogie angewendet werden. Mit Hilfe der Akustischen Analogie ist es möglich, das Strömungsfeld und das Akustikfeld getrennt voneinander zu untersuchen. Im ersten Schritt wird das Strömungsfeld mit numerischen Methoden bestimmt. Anschlie"send werden die aeroakustischen Quellen mit Hilfe von numerischen oder experimentellen Methoden bestimmt. Liegt das Strömungsfeld sowie das Quellfeld vor, so kann die Schallausbreitung mit Hilfe von numerischen Methoden berechnet werden. Die numerischen Quellgenerierungsmethoden werden anhand der analytischen Lösung des korotierenden Wirbelpaares untersucht. Das Beamforming Verfahren ist ein messtechnisches Verfahren zur Lokalisierung von Schallquellen. Das Beamforming Verfahren verwendet die gemessenen Mikrophondaten und liefert auf einer Fokusebene die gesuchten Schallquellen. Die Bestimmung von Schallquellen in Windkanälen ist jedoch nicht ohne weiteres möglich, da sich die Schallsignale durch ein inhomogenes Strömungsfeld bewegen. Mit Hilfe eines neuen Korrekturalgorithmus kann das Beamforming Verfahren im Windkanal eingesetzt werden.

Die Berechnung des Schallfelds, welches im Allgemeinen eine große Ausdehnung hat, benötigt genaue numerische Verfahren, da sonst die numerischen Fehler zu ungenauen Ergebnissen führen. In dieser Arbeit werden Finite Differenzen und Finite Volumen Verfahren hoher Ordnung hergeleitet und bei der Berechnung der Schallausbreitung um Tragflügelprofile eingesetzt. Mit Hilfe der vorgestellten Verfahren wurden am Tragflügel des Flugzeugs Airbus A320 Lärmminderungsmaßnahmen entwickelt und in zahlreichen Windkanalmessungen nachgewiesen. Zudem tragen die hier entwickelten Verfahren dazu bei, das Schallfeld mit höherer Genauigkeit zu bestimmen und somit bei der Entwicklung neuer Tragflügelkonzepte einzusetzen.

In Aeroacoustics, elastic waves propagate with the speed of sound from the point of development to the observer. The aim of aeroacoustics is to determine the point of development of the sound waves as well as its development mechanism. With this information it is possible to reduce the source strength with active and passive measures and to develop new technologies to reduce aerodynamically generated noise. The determination of the sound field can be performed with the so called Acoustic Analogy. With this it is possible to separate the flow and acoustic fields and to analyse them individually. The calculation of the source terms can be performed using numerical methods from the flow field or experimentally with the Microphone-Array-measurement technique. The determination of a sound field can be performed with the acoustic analogy. With this acoustic model the flow field and the acoustic field can be analysed individually. The first step is the simulation of the flow field. Next, the calculation of the source terms can be performed using either a numerical source model or experimentally with the microphone array measurement technique. In the last step, the simulation of sound propagation can be done with the existing flow and acoustic field. The numerical method for the modelling of the sound sources requires an incompressible flow field. This model is investigated using the analytical solution of the co-rotated vortex pair. Beamforming is a signal processing technique which makes it possible to determine the sound sources from experimental data. The method uses multiple microphone signals to determine the sound sources on the so called focus plane. The determination of sound sources in wind tunnels has complications, because the sound signals propagate through an inhomogeneous flow field. With a new correction algorithm it is possible to consider the influence of the flow to acoustics. The correction algorithm uses a iterative Newton method. The validation of the method is done by acoustical measurements of a loudspeaker in flow and by acoustical measurements of the wing of the Airbus A320. Beamforming is a signal processing technique which makes it possible to determine the sound sources from experimental data. The method uses multiple microphone signals to determine the sound sources on the so called focus plane. The determination of sound sources in wind tunnels is complicated, because the sound signals propagate through an inhomogeneous flow field. With a new correction algorithm, it is possible to consider the flow influence to acoustics. The correction algorithm uses an iterative Newton method and considers the influence of the geometry of the wind tunnel and the position of the microphones. The validation of the algorithm is performed with a loudspeaker in a flow field. The modified Beamforming method is used for the localisation of sound sources of a model of the Airbus A320 in wind tunnels. The calculation of the sound field, which generally has a great dimension, requires highly accurate numerical methods. Otherwise the numerical errors in the solution of the linearized Euler equations delivers inaccurate results. The increasing of either the accuracy or the order means an increase in the number of the calculation operations and computing time. In this work high order Finite Difference and Finite Volume methods are derived. The high order Finite Volume method uses the new Natural Neighbour method for calculating the variable values at the cell sides. The Natural Neighbour method uses the Taylor polynomial to calculate the partial derivatives on structured and unstructured two and three dimensional grids. It becomes necessary to solve an overdetermined equation system with the Cholesky decomposition. With this procedure the sound propagation around complex geometries can be calculated with high accuracy and without oscillations. The computation time in the calculation of sound propagation around complex geometries can be improved by combining the Finite Difference and Finite Volume methods. In this case, the Finite Volume method is used around the complex geometry and the integral Finite Difference method is used a few cells away from the surface. With this approach it is possible to reduce the computing time without a loss of accuracy Using the methods described above, noise reduction measures on the wing of the Airbus A320 were developed and demonstrated in numerous array measurements in wind tunnels. Furthermore with these methods it is possible to compute the sound field with an increased degree of accuracy for the development of new airfoil concepts. With these methods noise reduction measures on the wing of the Airbus A320 were developed and demonstrated in numerous wind tunnel measurements. Furthermore, with these methods it is possible to compute the sound field with a higher degree of accuracy for the development of new airfoil concepts.