1,721,033 research outputs found
Wave-based discontinuous Galerkin methods in the frequency domain with application to flow acoustics
No full textExact integration of polynomial-exponential products with application to wave-based numerical methods
No full textWave-based numerical methods often require to integrate products of polynomials and exponentials. With quadrature methods, this task can be particularly expensive at high frequencies as large numbers of integration points are required. This paper presents a set of closed-form solutions for the integrals of polynomial-exponential products in two and three dimensions. These results apply to arbitrary polygons in two dimensions, and for arbitrary polygonal surfaces or polyhedral volumes in three dimensions. Quadrature methods are therefore not required for this class of integrals that can be evaluated quickly and exactly
Discontinuous Galerkin methods with plane waves for time-harmonic problems
No full textA general framework for discontinuous Galerkin methods in the frequency domain with numerical flux is presented. The main feature of the method is the use of plane waves instead of polynomials to approximate the solution in each element. The method is formulated for a general system of linear hyperbolic equations and is applied to problems of aeroacoustic propagation by solving the two-dimensional linearized Euler equations. It is found that the method requires only a small number of elements per wavelength to obtain accurate solutions and that it is more efficient than high-order DRP schemes. In addition, the conditioning of the method is found to be high but not critical in practice. It is shown that the Ultra-Weak Variational Formulation is in fact a subset of the present discontinuous Galerkin method. A special extension of the method is devised in order to deal with singular solutions generated by point sources like monopoles or dipoles. Aeroacoustic problems with non-uniform flows are also considered and results are presented for the sound radiated from a two-dimensional jet
A comparison of impedance boundary conditions for flow acoustics
Full text linkAcoustic liners remain a key technology for reducing community noise from aircraft engines. The choice of optimal impedance relies heavily on the modeling of sound absorption by liners under grazing flows. The Myers condition assumes an infinitely thin boundary layer, but several impedance conditions have recently been proposed to include a small but finite boundary layer thickness. This paper presents a comparison of these impedance conditions against an exact solution for a simple benchmark problem and for parameters representative of inlet and bypass ducts on turbofan engines. The boundary layer thickness can have a significant impact on sound absorption, although its actual influence depends strongly on the details of the incident sound field. The impedance condition proposed by Brambley seems to provide some improvements in predicting sound absorption compared to the Myers condition. The boundary layer profile is found to have little influence on sound absorption<br/
Discontinuous Galerkin methods with plane waves for the displacement-based acoustic equation
No full textSeveral special finite element methods have been proposed to solve Helmholtz problems in the mid-frequency regime, such as the Partition of Unity Method, the Ultra Weak Variational Formulation and the Discontinuous Enrichment Method. The first main purpose of this paper is to present a discontinuous Galerkin method with plane waves (which is a variant of the Discontinuous Enrichment Method) to solve the displacement-based acoustic equation. The use of the displacement variable is often necessary in the context of fluid–structure interactions. A well-known issue with this model is the presence of spurious vortical modes when one uses standard finite elements such as Lagrange elements. This problem, also known as the locking phenomenon, is observed with several other vector based equations such as incompressible elasticity and electromagnetism. So this paper also aims at assessing if the special finite element methods suffer from the locking phenomenon in the context of the displacement acoustic equation. The discontinuous Galerkin method presented in this paper is shown to be very accurate and stable, i.e. no spurious modes are observed. The optimal choice of the various parameters are discussed with regards to numerical accuracy and conditioning. Some interesting properties of the mixed displacement–pressure formulation are also presented. Furthermore, the use of the Partition of Unity Method is also presented, but it is found that spurious vortical modes may appear with this method
Noise sources for duct acoustics simulations: broadband noise and tones
No full textWhile simulating acoustic tones propagating in ducts or waveguides is relatively well established, broadband noise is comprised of a wide range of frequencies and at each frequency the acoustic energy is generally distributed over all the cut-on modes of the duct. Simulating the propagation and absorption of broadband noise is further complicated by the random nature of the sound field. This paper presents a computational method to generate truly broadband, multi-mode noise in a time-domain simulation. This method is equally applicable to the generation of deterministic tones. For broadband noise, we devise a stochastic source that is tailored to radiate a sound field characterized by the cross-correlation between mode amplitudes. This stochastic source allows to compute in a single time-domain simulation the complete spectrum of the broadband multi-mode sound field. Unlike other methods proposed for predicting broadband noise, there is no need to perform several simulations for different realizations. Results are presented for broadband noise alone, as well as for a combination of tones and broadband noise
Mode-matching techniques for sound propagation in lined ducts with flow
No full textThis paper discusses the use of mode-matching techniques to model sound propagation in lined ducts with flow. With no flow mode-matching methods are relatively well established and the continuity of acoustic pressure and axial velocity is generally applied. But with a base flow the behaviour of the solution at the transition between, say, a hard wall and a lined wall is not well understood. For this reason different assumptions can be made on the behaviour of the acoustic field and these lead to different models. This paper presents a comparison of different models and illustrates that significant differences can be observed. A modified mode-matching scheme based on conservation of mass and momentum is proposed. The conservation of sound power is investigated for different matching conditions. Finally, the link between the solutions obtained with mode-matching methods and finite element methods is discussed, and the present analysis can shed some light on the underlying assumptions used in finite element model
Wave-based discontinuous Galerkin methods for the linearized Euler equations in the frequency domain
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Near- to far-field characteristics of acoustic radiation through plug flow jets
No full textThis paper reports a theoretical study of the radiation of sound through jet exhausts. It focuses on the transition from near field to far field by considering the features of the near-field solution and how these features translate to the far field. The main focus of this work is the importance in some cases of lateral waves radiating from the jet. While the presence of lateral waves has long been recognized, there has been no systematic investigation of the practical consequences of these waves in the prediction of sound propagation through round jets. The physical mechanisms involved in the generation of these waves are presented as well as the conditions under which they become significant. Another issue is the possibility of “channeled waves” inside the jet associated with strong sound radiation in the forward arc. This paper also discusses the validity of the far-field approximation when lateral waves are present. It is shown that the standard far-field approximation can be improved by adding correction terms that account for the presence of the lateral waves and channeled waves. The challenge posed to computational aeroacoustics by these near-field effects is also discussed
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