1,720,975 research outputs found
A study of aliasing error in DGM solutions to turbofan exhaust noise problems
No full textHighly non-uniform flows such as shear layers are an intrinsic feature of turbofan exhaust noise problems. Modeling the sound radiation from turbofan exhausts with the linearized Euler equations raises the issue of accurately representing strongly spatially-varying mean flows numerically, while ensuring that numerical solutions are not polluted by spurious solutions such as aliasing errors. This paper investigates the behavior of aliasing instabilities in time domain solutions obtained by the discontinuous Galerkin method. A model exhaust noise problem is studied to demonstrate the growth of unphysical temporal instabilities. A new fully-discrete dispersion analysis technique is developed that permits non-uniform mean flows. The dispersion analysis is used to study the spectral behavior of aliasing instabilities and the impact of polynomial order on their formation and growth. The results of this study indicate that aliasing errors are largely absolute instabilities which build up in the solution over time and are highly sensitive to the polynomial order
On the performance of high-order fem for solving large-scale industrial acoustic problems
No full textOpen data for paper "Efficient implementation of high-order finite elements for Helmholtz problems"
No full textThis repository contains the open data associated with the journal paper titled "Efficient implementation of high-order finite elements for Helmholtz problems" by Hadrien Be?riot, Albert Prinn and Gwe?nae?l Gabard published in the International Journal for Numerical Methods in Engineering.
The DOI of this paper is 10.1002/nme.5172.
See also the ePrints page http://eprints.soton.ac.uk/384370.</span
A comparison of high-order polynomial and wave-based methods for Helmholtz problems
No full textThe application of computational modelling to wave propagation problems is hindered by the dispersion error introduced by the discretisation. Two common strategies to address this issue are to use high-order polynomial shape functions (e.g. hp-FEM), or to use physics-based, or Trefftz, methods where the shape functions are local solutions of the problem (typically plane waves). Both strategies have been actively developed over the past decades and both have demonstrated their benefits compared to conventional finite-element methods, but they have yet to be compared. In this paper a high-order polynomial method (p-FEM with Lobatto polynomials) and the wave-based discontinuous Galerkin method are compared for two-dimensional Helmholtz problems. A number of different benchmark problems are used to perform a detailed and systematic assessment of the relative merits of these two methods in terms of interpolation properties, performance and conditioning. It is generally assumed that a wave-based method naturally provides better accuracy compared to polynomial methods since the plane waves or Bessel functions used in these methods are exact solutions of the Helmholtz equation. Results indicate that this expectation does not necessarily translate into a clear benefit, and that the differences in performance, accuracy and conditioning are more nuanced than generally assumed. The high-order polynomial method can in fact deliver comparable, and in some cases superior, performance compared to the wave-based DGM. In addition to benchmarking the intrinsic computational performance of these methods, a number of practical issues associated with realistic applications are also discussed
Finite element simulation of noise radiation through shear layers
No full textPredicting sound propagation through the jet exhaust of an aero-engine presents the specific difficulty of representing the refraction effect of the mean flow shear. This is described in full in the linearised Euler equations but this model remains rather expensive to solve numerically. The other model commonly used in industry, the linearised potential theory, is faster to solve but needs to be modified to represent a shear layer. This paper presents a way to describe a vortex sheet in a finite element model based on the linearised potential theory. The key issues to address are the continuity of pressure and displacement that have to be enforced across the vortex sheet, as well as the implementation of the Kutta condition at the nozzle lip. Validation results are presented by comparison with analytical results. It is shown that the discretization of the continuity conditions is crucial to obtain a robust and accurate numerical model
A high-order finite element method for the linearised Euler equations
Full text linkSound propagation in complex non-uniform mean flows is an important feature of turbofan exhaust noise radiation. The Linearised Euler Equations are able to represent the strong shear layer refraction effects on the sound field, as well as multiple length scales. Frequency domain solvers are suitable for tonal noise and considered a way to avoid linear instabilities, which may occur with time domain solvers. However, the classical Finite Element Method suffers from dispersion error and high memory requirements. These shortcomings are particularly critical for high frequencies and for the Linearised Euler Equations, which involve up to five unknowns. In this paper, a high-order Finite Element Method is used to solve the Linearised Euler Equations in the frequency domain in order to overcome those issues. The model involves high-order polynomial shape functions, unstructured triangular meshes, numerical stabilisation and Perfectly Matched Layers. The acoustic radiation from a straight circular semi-infinite hard-wall duct with several mean flow configurations is computed. Comparisons with analytic solutions demonstrate the method accuracy. The acoustic and vorticity waves are well represented, as well as the refraction of the sound field across the jet shear layer. The high-order approach allows to use coarse meshes, while maintaining a sufficient accuracy. The benefits in terms of memory requirements are significant when compared to standard low-order Finite Element Method
Impedance modelling of acoustically treated circumferential grooves for over-tip-rotor fan noise suppression
No full textExperimental investigation of Over-Tip-Rotor circumferential groove liners has shown potential for fan noise suppression in turbofan engines whilst providing minimal penalty in fan aerodynamic performance. The validation of Over-Tip-Rotor liner analytical prediction models against published experimental data requires the modelling of an equivalent impedance for such acoustic treatments. This paper describes the formulation of two analytical groove impedance models as semi-locally reacting liners, that is locally reacting in the axial direction and non-locally reacting in the azimuthal direction. The models are cross-verified by comparison with high-order FEM simulations, and applied to a simplified Over-Tip-Rotor configuration consisting of multiple grooves excited by a monopole point source located close to the grooved surface
Performance of the DGM for the linearized Euler equations with non-uniform mean-flow
Full text linkA dispersion analysis of the fully-discrete, nodal discontinuous Galerkin method (DGM) for the solution of the time-domain linearized Euler equations (LEE) is performed. Two dispersion analysis methods are developed, considering both uniform and non-uniform mean-flow effects. Convergence studies are performed for the dispersion, dissipation, and nodal solution errors of the acoustic, entropy, and vorticity modes. The accuracy and stability of the DGM are analyzed in the context of aeroacoustic applications, and guidelines are proposed for the choice of optimal discretizations. Computational costs are estimated for a model problem and related to the choice of the element size, polynomial order, and time step. Results indicate that temporal error can become a dominant source of error for high accuracy requirements and long distance wave propagation. The stability of the scheme is analyzed for a shear layer mean flow profile. Aliasing-type errors are found to contribute to the formation of numerical instabilities which are further strengthened by increases in the polynomial order
Implementation of a vortex sheet in a finite element model based on potential theory for exhaust noise predictions
No full textPredicting sound propagation through the jet exhaust of an aero-engine presents the specific difficulty of representing the refraction effect of the mean flow shear. This is described by the linearised Euler equations, but this model remains rather expensive to solve numerically. The other model commonly used in industry, the linearised potential theory, is faster to solve but needs to be modified to represent a shear layer. This paper presents a way to describe a vortex sheet in a finite element model based on the linearised potential theory. The key issues to address are the continuity of pressure and displacement that have to be enforced across the vortex sheet, as well as the implementation of the Kutta condition at the nozzle lip. Validation results are presented by comparison with analytical results. It is shown that the discretization of the continuity conditions is crucial to obtain a robust and accurate numerical model
A performance study of high-order finite elements and wave-based discontinuous Galerkin methods for a convected Helmholtz problem
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