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ABSTRACT: The problem of non-uniqueness (NU) of the solution of exterior acoustic problems when using the boundary element method (BEM) is well known. Methods like the Burton-Miller technique or the CHIEF method are used to solve this challenge at the expense of more complex procedures for handling hypersingular integrals and/or higher computing times due to higher complexity of the algorithm or additional equations. The dual surface method, commonly used for electromagnetic problems, was adapted for acoustic radiation and scattering problems. The basic principles of methods to solve the NU problem are outlined and results for different models and solution procedures are presented, taking into account quality, solution time, and the numerical advantages when using iterative solvers.
The Journal of the Acoustical Society of America 05/2013; 133(5):3517. · 1.55 Impact Factor
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ABSTRACT: The Multi-Level Fast Multipole Method (MLFMM) allows the computation of acoustical problems based on the Boundary Element Method (BEM) where the discretized models of the corresponding structures may consist of a huge number of elements.
The required multipole expansion order of the so-called translation operator increases significantly with higher frequency and larger dimensions of the model considered. If this order reaches a value of about 80-90, depending on the cluster distance, one can hardly achieve reasonable results due to numerical inaccuracies of the Hankel functions and high memory requirements for the unit sphere integrations.
This problem can be avoided by combining the MLFMM with a so-called source clustering method (SCM) that replaces the translation operator at these high orders or large cluster distances by a summation method, which considers the interactions between the relevant points of the source - and target cluster.
The article explains the basic principles of both methods and presents the first results obtained, taking into account quality and solution time.
DAGA/AIA 2013, Merano, Italy; 03/2013
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ABSTRACT: The frequency dependent backscattering of an obstacle can be calculated by means of different numerical methods. The use of classical methods like the conventional BEM or FEM leads to high computing times in combination with large memory requirements due to the re-quired discretization efforts in the higher frequency range.
Classical high-frequency approximation procedures like the Kirchhoff- or the Plane-Wave-method reduce the calculation time at the expense of imprecise solutions.
This paper will present the results of a new approach which combines the advantages of all the above mentioned methods using alternative ansatz functions. This approach allows it to use a discretization which needs just one element per wavelength. So in comparison with the common rule of thumb of six elements per wavelength even much larger problems and/or higher frequencies can be calculated.
19th International Congress on Sound and Vibration (ICSV19), Vilnius, Lithuania; 07/2012
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ABSTRACT: Numerical simulations for estimating the transmission loss of plates can be an important alternative to measurements when there is no access to transmission loss test facilities. Furthermore, parametric studies and design changes can be made easily and faster. This work presents a method to calculate the transmission loss of plates placed between a source and a receiver room using an iterative approach. The sound radiation due to the vibration of the plates is solved with a Boundary Element formulation while the motion of the plate is determined using a Finite Element formulation with the sound pressure as the exciting force. The starting point is the blocked pressure approximation. The real pressure on the plate and its displacement are obtained after some iterations. If no damping in the plate is considered, poor or no convergence is expected at the resonant frequencies of the plate. This problem is avoided introducing some damping in the plate as well as in its fixation (boundary). With this approach, the use of existing techniques to accelerate the calculations that are already developed for the BEM, e.g. the Fast Multipole Method and for the FEM, e.g. the Model Order Reduction can be directly applied without needing to adapt them to this specific problem.
The Journal of the Acoustical Society of America 04/2012; 131(4):3271. · 1.55 Impact Factor
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ABSTRACT: The Multi-Level Fast Multipole Method (MLFMM) allows the computation of acoustical problems based on the Boundary Element Method (BEM) where the discretized models of the corresponding structures may consist of a huge number of elements. The required calculation time and the memory requirements are much less when compared with conventional methods because the algorithm uses a level-based composition of the potentials from different point sources to acoustic multipoles, which highly accelerates the computation of the matrix-vector-products required for iterative solvers. A multi-level single-order variation of the algorithm was extended to a multi-level adaptive-order version, which was analyzed and optimized with respect to quality, performance and parallelization issues. The iterative solvers used with the MLFMM will be combined with appropriate preconditioners for reducing the number of iterations and improving the performance. The insights gained will be presented using different test cases and the results achieved will be compared with analytical solutions and results of conventional BEM- and FEM-based calculations.
The Journal of the Acoustical Society of America 04/2012; 131(4):3512. · 1.55 Impact Factor
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Martin Ochmann
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ABSTRACT: The transient sound field caused by a Dirac delta impulse function above an infinite locally reacting plane can be calculated by applying the inverse Fourier transform of the corresponding half-space Green's function in frequency domain. As a starting point, the representation given by Ochmann [J. Acoust. Soc. Am. 116(6), 3304-3311 (2004)] is used, which consists of discrete and continuous superposition of point sources. For a locally reacting plane with masslike character and also with pure absorbing behavior, it is possible to express the resulting impulse response in closed form. Such a result is surprising, because corresponding formulations in the frequency domain are not available yet. Hence, the first main result is the closed form solution Eq. (22) for an impulse response over an infinite plane with a pure imaginary impedance. The second main result is the closed form solution Eq. (53) for an impulse response over an infinite plane with a pure real impedance. As a particular application of both main results, a convolution technique is used for deriving formulas for point sources with a general time dependency. For special signals like an exponentially decaying time signal or a triangular shaped impulse, the resulting sound field can be presented in terms of elementary functions.
The Journal of the Acoustical Society of America 06/2011; 129(6):3502-12. · 1.55 Impact Factor
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ABSTRACT: The bistatic and monostatic numerical calculation of the pressure scattered from structures composed of elastic materials and possibly filled with another material is one of the main purposes for the detection of underwater objects. For this reason, the sound pressure scattered from spherical objects placed in and filled with fluid will be calculated in the frequency domain. The results of an in-house developed BEM-package which supports single and multiple fluid-structure-interactions will be compared with analytical solutions based on spherical wave functions and with results of commercial BEMFEM applications. Performance optimizations of the calculation process for the uncoupled rigid and coupled monostatic case as a result of using a parallelized matrix creation and solution with a specific variant of the direct solving process will be presented. We will also compare results for a cubic structure, placed in water above a finite plane boundary, with an equivalent half-space solution that incorporates a suitable half-space Green's function and could be used for fast approximations in the mid- and high-frequency range.
The Journal of the Acoustical Society of America 05/2009; 125(4):2733. · 1.55 Impact Factor
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ABSTRACT: The present work addresses the calculation of the radiated sound power spectrum in the far field of open or enclosed flames based on the application of the dual reciprocity boundary element method (DRBEM). The focus of this work is the development of a technique that allows a good representation of the sound field, assuming that the sound sources originated by the combustion are known. Following the acoustic analogy approach, the sound radiation of open flames can be evaluated by a volume integral over the equivalent acoustic source terms in the combustion zone. The DRBEM allows replacing the volume integral by a series of surface integrals. The technique is applied to the theoretical model of a spherical flame. The accuracy of the DRBEM model can be studied by comparing it with available analytical solutions for the sound radiation of this flame type. For enclosed flames, the DRBEM is used to calculate the sound propagation in the region of temperature gradients that appears at the exhaust of the combustion chamber. The sensitivity of the radiated sound field to this adjacent inhomogeneous temperature field is investigated. The non-uniqueness problem of the boundary integral equation method is tackled by the Burton and Miller approach. The DRBEM allows an effective determination of the radiated acoustic field because it can take into account inhomogeneities and satisfies automatically the radiation condition at infinity.
Acta Acustica united with Acustica 04/2009; 95(3):448-460. · 0.57 Impact Factor
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ABSTRACT: In this paper, the application of the Equivalent Source Method (ESM) and the acoustical Boundary Element Method (BEM) for the prediction of the noise generated by an open diffusion flame is investigated. These acoustical methods have been coupled with a Large Eddy Simulation (LES) of the turbulent flow, which simulates the flow and combustion processes in a source region in the vicinity of the flame. Among the hybrid methods which are being used to predict the sound produced by turbulent flow, the ESM and BEM have the advantage that only one acoustic variable must be known at a surface surrounding the source zone (fewer data has to be processed) and that the far field can be directly computed. The sound power generated from two open diffusion flames have been calculated with both the ESM and the BEM, using the velocity distribution over cylindrical control surfaces, which enclose the source region. The results of the calculations are presented and compared with the measured sound power of the same flames. For one configuration good agreement between measurement and simulation at low and middle frequencies is obtained. Possible reasons for the differences for the other configuration will be discussed.
Acta Acustica united with Acustica 06/2008; 94(4):514-527. · 0.57 Impact Factor
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ABSTRACT: The far field pressure of a turbulent flame can be determined using the standard boundary element method (BEM) if the sound pressure or its derivative is known at a closed surface (control surface) surrounding the flame, as long as the medium outside the control surface is homogeneous. If temperature gradients are present, the homogeneous Helmholtz equation is no more valid. In that case, the wave equation can be rewritten in form of an inhomogeneous Helmholtz equation with a source term that depends also on the unknown pressure. Using the "Dual Reciprocity BEM" the integral form of this wave equation can be solved involving only surface integrals, so that the sound field can still be computed from field values at the control surface. The cases under study consider a volume of hot gas with a temperature distribution that is prescribed or obtained from a CFD simulation. The influence of the temperature gradients on the sound field can be evaluated by comparison of characteristic quantities like sound power and radiation patterns, with and without temperature gradient.
The Journal of the Acoustical Society of America 06/2008; 123(5):3405. · 1.55 Impact Factor
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ABSTRACT: The Boundary-Element-Method is a powerful tool for the simulation of sound radiation and scattering. Classically, it was developed for the free 3D-space, but it can be modified easily for half-space solutions as long as the half-space is delimited by a perfectly rigid or soft plane. In this case, the Green's function, the core of the BEM, can be derived from a simple image source ansatz, which however cannot be used for a more general impedance boundary condition. The alternative, an additional discretisation of a finite but large part of the plane leads to an enormous increase of the size of the set of equations. In this presentation, an appropriate Green's function will be introduced, which is able to describe the sound propagation above an impedance plane and is suitable for an implementation into a BEM code. It bases on the superposition of sound sources with complex source points. The numerical evaluation of this Green's function will be presented along with several test cases including sound radiation from burning flames above ground and tire-road noise. The computational costs of the developed "Complex-Source-Point-BEM" (CBEM) in comparison with a classical BEM together with a discretisation of the impedance plane will be discussed.
The Journal of the Acoustical Society of America 06/2008; 123(5):3418. · 1.55 Impact Factor
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ABSTRACT: Based on a BEM-BEM-coupling method, the scattered pressure from elastic objects placed in water and partially buried in the sediment is calculated. For this reason, a special variant of the boundary element method (BEM) is implemented. It contains a pre- and a postprocessor with 3D visualization, in order to define the geometry of the scattering objects in the interface layer between fluid and sediment and the parameters needed for characterizing the fluid and the elastic material. The solver is able to perform numerical calculations in a multiple parallel manner. For the solution of the underlying system of linear equations, we use different kinds of approximate and direct solution techniques. Simple acoustical exterior problems, for example, the sound scattering by elastic solid cylinders and spheres placed in a fluid are treated by the BEM-BEM-coupling method. The results will be compared with analytical solutions or solutions obtained from other numerical methods.
The Journal of the Acoustical Society of America 06/2008; 123(5):3757. · 1.55 Impact Factor
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ABSTRACT: Based on the Helmholtz integral equation, a boundary element method in time domain (TD-BEM) can be formulated. Because of instability issues, this method is rarely used in numerical acoustics. The stability and accuracy of the method for exterior radiation problems is investigated using some simple examples. A connection between the internal resonances of the closed structure and the instable behaviour of the method is assumed, but it is mathematically unproven. Numerical evidence of this connection is presented. Because of the sparse structure of the resulting system matrix, the use of iterative solvers is advantageous. The performances of different solvers are compared with respect to stability and numerical costs. For testing purposes, the acoustic radiation from an open turbulent flame is calculated and compared with results of a frequency domain BEM calculation.
The Journal of the Acoustical Society of America 06/2008; 123(5):3530. · 1.55 Impact Factor
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Martin Ochmann
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ABSTRACT: The sound field caused by a monopole source above an impedance plane can be calculated by using a superposition of equivalent point sources located along a line in the mirror space below the plane. Originally, such an approach for representing the half-space Green's function was described by Sommerfeld at the beginning of the last century, in order to treat half-space problems of heat conduction. However, the representation converges only for masslike impedances and cannot be used for the more important case of reflecting planes with springlike surface impedances. The singular part of the line integral can be transformed into a Hankel function, which shows that surface waves are contained in the whole solution. Unfortunately, this representation suffers from the lack of validity at certain receiver points and from restrictions on wave number and impedance range to ensure the necessary convergence. The main idea of the present method is to use also a superposition of equivalent point sources, but to allow that these sources can be located at complex source points. The corresponding form of the half-space Green's function is suitable for both masslike and springlike surface impedances, and can be used as a cornerstone for a boundary element method.
The Journal of the Acoustical Society of America 01/2005; 116(6):3304-11. · 1.55 Impact Factor
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ABSTRACT: This paper addresses the calculation of the sound radia-tion of turbulent flames into the acoustic far field based on a coupling of a Large Eddy Simulation (LES) and the Boundary Element method (BEM). The numerical aspects of the coupling, including the choice of a cou-pling interface, data sampling at coarsened grids and Fourier Transform of the coupling variables from time to frequency domain, are surveyed. The simulation re-sults for the radiated sound power of an open turbu-lent non-premixed jet flame are compared to measured data. The influence of ground effects on the sound ra-diation is briefly discussed. Considering a second con-figuration, where a region of temperature gradients rep-resents the exhaust of a combustion chamber, the Dual Reciprocity Boundary Element Method (DRBEM) is ap-plied for the simulation of the sound propagation in a non-homogeneous medium. The sensitivity of the radi-ated sound field to this adjacent inhomogeneous temper-ature field is investigated. As the results show, the pre-sented hybrid approach is able to predict effectively the sound radiation of flames and the DRBEM still expands the possibilities of the hybrid methodology for the numer-ical simulation of combustion noise.
03/2005;
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ABSTRACT: The Source Simulation Technique is a general tool for calculating the sound radiation or scattering from complex-shaped structures into the three-dimensional space. The basic idea of the method consists in replacing the structure by a system of acoustical sources placed in the interior of the structure. By definition, these source functions have to satisfy the Helmholtz equation and the radiation condition. For solving the radiation or scattering problem completely or approximately, the source system also has to fulfil or minimize the boundary conditions on the surface of the body. In most cases, spherical wave functions e.g. monopoles, dipoles, quadrupoles etc. with different source locations are used as sources, since they can be calculated easily. If the coordinates of the source positions are shifted from real values into the complex plane, the corresponding monopoles show a similar behaviour like surface waves or possess a distinctive directivity pattern, depending on the values of the imaginary parts of their coordinates. Therefore, by adding such complex source point solutions to the system of equivalent sources, a strongly focused sound field should be computed in a more efficient and stable way. The capacity of the extended source simulation technique is investigated and represented by applying it to calculate the sound field radiated from a circular baffled piston.
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ABSTRACT: Equivalent sources have been successfully used to calculate the sound radiation and the sound scattering from solid bodies lying in a homogeneous medium without flow. For the field determination an acoustic boundary condition at the body surface must be known. In an earlier work, the application of this method to compute the sound radiation of open turbulent flames was investigated in order to extend the range of use of this basic method to aero-thermoacoustic problems. It was assumed that outside a region surrounding the flame, the flow and temperature gradient had strongly decayed and approximate homogeneous conditions existed. The necessary data at a control surface (Kirchhoff surface) surrounding the combustion zone was delivered by an incompressible Large Eddy Simulation (LES). Measurements carried out of two simulated flame configurations showed that while the spectrum of one flame was well reproduced, the spectrum of the second flame was satisfactorily matched only in some positions. In the present work, additional calculations are made trying to explain and reduce these differences, for example, calculations using different control surfaces, using open surfaces and including a constant background flow. The results obtained are presented and discussed.
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ABSTRACT: brick, piscoya, ochmann]@tfh-berlin.de , Peter.Koeltzsch@ias.et.tu-dresden.de In the German research project "Combustion noise", simulation tools for combustion noise are in development [3]. This is a complex task taking into account that it involves both the noise generation due to the processes in the reactive zone (i.e. turbulent flow and combustion) as well as the propagation of sound waves through a turbulent region to the surrounding medium. Due to its complexity, a direct numerical simulation (DNS) is not possible and hybrid methods have to be applied. The use of the Equivalent Source Method (ESM) coupled to a incompressible Large-Eddy-Simulation (LES) to compute the sound field of open flames is one of the subjects that are being investigated by the research project. The LES provides velocity data from the flow field on a control surface, which entirely encloses the combustion zone and with the ESM it is possible to determine the acoustic field outside this control surface by evaluating the surface data. In the course of the research project, the sound radiation of open flames of three different types was investigated, i.e. non-premixed jet flames (H3 and HD), which are benchmark flames of the TNF workshop [2], a non-premixed swirled flame (TD1) and a premixed swirled flame (TECFLAM). Previous results for the H3 and HD-flame are published in [1], [4], [8]. Details for the used ESM, like positioning and characteristics of the equivalent sources can be found in [9] and [10], the LES approach is described in detail in [5-7]. In the present work, the focus lies on a comparison of the characteristics of the sound radiation of the investigated flames. With the ESM, the sound power and the directivity of the radiated sound field for selected frequencies were determined. Fig.1 shows the radiated sound power level of the HD-, H3-, TD1-and TECFLAM-flame. In case of the first three flames (HD, H3 and TD1), also measurements of the sound power were done. For the HD flame, the resulting sound power is in good agreement with the measured spectra. For the H3-and TD1-flame, the measurement results differ significantly from the simulation results. Though H3-and TD1-flame are very different types of flames (jet vs. swirled flame), the characteristics of the measured and simulated spectra are very similar, also with respect to the discrepancies between measurement and simulation. The LES-model for the simulation of non-premixed swirled flames is currently in progress and an improvement of the results is expected for the future. The sound level spectrum of the the premixed swirled flame (TECFLAM-flame) shows a minimal decrease of the sound power with increasing frequency compared to the other flames. A comparative measurement of the radiated sound power for this flame is not available yet. All flames show a uniform radiation at low and middle frequencies up to about 250 Hz. At higher frequencies the directivity is focusing in direction of the flame axis for the jet flames and TD1. For the TECFLAM-flame, the focus is directed perpendicular to the flame axis with increasing frequency – radiation pattern of jet flame and swirl flame are nearly "orthogonal"! Fig.2 shows the directivity at a frequency of 2000 Hz for the four investigated flames, where the mentioned characteristics in the higher frequency range can be observed. In the presentation details of the flame's simulation will be given and the drawbacks and opportunities of the simulation process will be discussed.
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