Andreas Hüppe

SPECTRAL FINITE ELEMENTS FOR COMPUTATIONAL AEROACOUSTICS USING ACOUSTIC PERTURBATION EQUATIONS

This paper addresses the application of the spectral finite element (FE) method to problems in the field of computational aeroacoustics (CAA). We apply a mixed finite element approximation to the acoustic perturbation equations, in which the flow induced sound is modeled by assessing the impact of a mean flow field on the acoustic wave propagation. We show the properties of the approximation by numerical benchmarks and an application to the CAA problem of sound generated by an airfoil.

A hybrid approach to the computational aeroacoustics of human voice production

The aeroacoustic mechanisms in human voice production are complex coupled processes that are still not fully understood. In this article, a hybrid numerical approach to analyzing sound generation in human voice production is presented. First, the fluid flow problem is solved using a parallel finite-volume computational fluid dynamics (CFD) solver on a fine computational mesh covering the larynx. The CFD simulations are run for four geometrical configurations: both with and without false vocal folds, and with fixed convergent or convergent–divergent motion of the medial vocal fold surface. Then the aeroacoustic sources and propagation of sound waves are calculated using Lighthill’s analogy or acoustic perturbation equations on a coarse mesh covering the larynx, vocal tract, and radiation region near the mouth. Aeroacoustic sound sources are investigated in the time and frequency domains to determine their precise origin and correlation with the flow field. The problem of acoustic wave propagation from the larynx and vocal tract into the free field is solved using the finite-element method. Two different vocal-tract shapes are considered and modeled according to MRI vocal-tract data of the vowels /i/ and /u/. The spectra of the radiated sound evaluated from acoustic simulations show good agreement with formant frequencies known from human subjects.

STABLE MATCHED LAYER FOR THE ACOUSTIC CONSERVATION EQUATIONS IN THE TIME DOMAIN

In recent years the development of free field radiation conditions in the time domain has become a topic of intensive research. Perfectly matched layer (PML) approaches for the frequency domain are well known. In the time domain, on the other hand, they suffer in many cases from highly increased complexity and instabilities. In this paper, we introduce a PML for the conservation equations of linear acoustics. The used formulation requires three auxiliary variables in 3D and circumvents thereby convolution integrals and higher order time derivatives. Furthermore, we prove the weak stability of the proposed formulation and show their good absorption properties by means of numerical examples.

Modeling and Finite Element Formulation for Acoustic Problems Including Rotating Domains

A finite element formulation for the efficient numerical simulation of sound in computational domains, including rotating regions, is presented. The mathematical description is based on an arbitrary Lagrangian–Eulerian framework and results in a convective wave equation for the scalar acoustic potential. Numerically, the capability of nonconforming grids is explored by applying a Nitsche-type mortaring between stationary and rotating regions. The formulation can be applied to classical acoustics (stagnant fluid) as well as moving fluids in the case of aeroacoustics. The validation with the analytical solution of a rotating point source in three dimensions demonstrates the accuracy and robustness of the developed numerical scheme. Additionally, the convergence study shows that the intersection mesh operations needed in the nonconforming setting do not deteriorate the accuracy of the numerical solution.

A Numerical Investigation of the Laminar Instability Multi-Tonal Noise of Aerofoils

In the frame of applied aeroacoustics the numerical prediction of the aerofoil selfgenerated noise is key issue for a number of applications in aeronautics, vehicle industry and wind energy. Aerofoil airborne noise has been widely approached in several studies and well characterized for a number of flow conditions. Nevertheless there are still many cases where it is not yet completely clear how the flow noise is generated. The objective of this paper is to perform a deep and accurate analysis of the noise generated by laminar instabilities of the boundary layer arising for Reynolds numbers ranging approximately between 0.6M and 1.1M. The test-case chosen is the NACA 0012 aerofoil which has been investigated by means of transient RANS aerodynamic simulations coupled with the Ffowcs Williams and Hawkings acoustic analogy and a Finite Element based approach to Lighthill’s equation for the acoustic computations. Numerical sound pressure spectra have been compared to experimental data achieving a very good agreement for different flow speeds and Angles of Attack. The numerical simulations performed have been able to capture the sharply peaked multi-tonal acoustic phenomena which arise from the flow instabilities evolving within the boundary layer proving the high potentialities of such numerical approaches in the frame of the applied aeroacoustics.

On the importance of strong fluid-solid coupling with application to human phonation

An advanced finite element (FE) method is presented and applied to simulate the fluid-solid-acoustic interaction in human phonation. We apply an arbitrary-Lagrangian-Eulerian (ALE) method, which allows coupling of the Eulerian fluid field with the Lagrangian mechanical field. Thereby, we investigate strong and weak (sequential staggered) coupling schemes for flow and structural mechanics. The acoustic field is computed by acoustic perturbation equations to account for convection and refraction effects of the sound in the flow region. For our application – the human phonation – we can assume a low Mach number flow and therefore use a hybrid aeroacoustic approach, which just consider a forward coupling from the flow to the acoustic field.

Acoustic perturbation equations and Lighthill's acoustic analogy for the human phonation

In speech, air is driven through the larynx by compression of the lungs. Thereby, air flows through the glottis which forces the vocal folds to oscillate which in turn results in a pulsating air flow. This air flow is the main source of the generated sound-the phonation. The acoustic wave then passes through the vocal tract, which acts as a filter modulating the propagated sound leaving the mouth. We model the fluid-structure-acoustic interaction with a so called hybrid approach. The air flow in the larynx, together with a prescribed vocal fold motion, is simulated with help of the open source solver OpenFOAM. Based on the resulting fluid field, acoustic source terms and the wave propagation is calculated within the finite element solver CFS++. Two methods are available to choose from, Lighthills acoustic analogy and an aeroacoustic analogy based on a perturbation ansatz. Additionally, the simulation domain is extended by a realistic but geometrical fixed vocal tract and connected to a propagation region. The different acoustic approaches are compared, by analysing the acoustic pressure in the glottis (source region) and outside the vocal tract. Moreover, to illustrate the effects of the vocal tract an alternative geometry is used for comparison.

Computational Aeroacoustics for Rotating Systems with Application to an Axial Fan

A hybrid aeroacoustic formulation, which is well suited for the computation of rotating systems, is presented. It is based on a decomposition of flow (incompressible part) and acoustic (compressibl...

Finite-Elemente-Verfahren für mechatronische Systeme

ZusammenfassungDie Entwicklung von mechatronischen Systemen erfordert die Verfügbarkeit von entsprechenden CAE (Computer Aided Engineering) Werkzeugen, da die Herstellung von einzelnen Prototypen sehr kostenintensiv ist. Dabei führt die physikalische/mathematische Modellierung dieser Systeme zu gekoppelten, partiellen Differentialgleichungen, deren effiziente numerische Lösung eine große Herausforderung darstellt. In diesem Bereich kann die Finite-Elemente-Methode als das universellste numerische Verfahren bezeichnet werden, welches auch in den meisten kommerziellen Simulationsprogammen zum Einsatz kommt.Dieser Beitrag diskutiert die Herausforderungen und den Einsatz von Finite-Elemente-Methoden für die effiziente Entwicklung von mechatronischen Systemen. Dabei werden grundlegende Koppelstrategien zwischen den einzelnen physikalischen Feldern, neueste Ansätze wie nichtkonforme Gittermethoden sowie Elemente höherer Ordnung besprochen. Anhand von zwei praktischen Beispielen – Elektrothermik in Leistungshalbleitern und Lärmberechnung eines Lüfters – wird die Wichtigkeit der Weiterentwicklung von Finite-Elemente-Methoden demonstriert, um dieses Werkzeug für die Analyse und Optimierung von komplexen mechatronischen Systemen effizient einsetzen zu können.AbstractThe development of mechatronic systems heavily relies on CAE (Computer Aided Engineering) tools, since the fabrication of prototypes is quite expensive. Thereby, the physical/mathematical modeling of such systems results in coupled, partial differential equations (PDEs), and their efficient numerical solution is a main challenge. The Finite-Element (FE) method can be seen as a universal solution approach, which is applied in most commercial software programs.This paper focuses on the challenges and requirements for FE-methods to efficiently simulate mechatronic systems. Thereby, we discuss coupling strategies between the individual physical fields, latest developments as non-conforming grid techniques and higher order finite elements. We present two practical applications—electro-thermal simulation of power semiconductors, and the noise generation of vents as used in air-conditioning systems—to demonstrate the importance of developing new and highly efficient FE methods, which can handle the complexity of mechatronic systems.

Coupling Acoustic Perturbation Equations and Pierce Wave Equation for Computational Aeroacoustics

We present a currently developed approach for computational aeroacoustics (CAA). Thereby, we model the acoustic field in the region of the main acoustic sources by acoustic perturbation equations (unknowns are the acoustic pressure and particle velocity) and in all other regions by the convective acoustic wave equation according to Pierce (unknown is the acoustic scalar potential). This approach allows us to correctly obtain the acoustic pressure in regions of flow by fully taking into account refraction and convection effects. The acoustic perturbation equations as well as Pierce equation are solved by the Finite Element (FE) method. To guarantee the physical interface conditions for acoustic waves, we couple the equations along the common interface by a Mortar-FE ansatz. Numerical computations for the NACA 0012 aerofoil demonstrate both the reduction of computational time and the practical applicability of the developed CAA scheme.