Wave Envelope Elements Research Articles

TRANSIENT WAVE ENVELOPE ELEMENTS FOR WAVE PROBLEMS

A novel family of infinite wave envelope elements is described which can be used in conjunction with conventional finite elements to model the transient wave equation in unbounded regions. The elements are obtained by applying an inverse Fourier transformation to a mapped wave envelope formulation in the frequency domain. The discrete transient equations obtained in this way can be applied to two-dimensional and three-dimensional problems without restriction, being valid over a full range of excitation frequencies. The effectiveness and accuracy of the method is demonstrated in application to simple test cases which involve the calculation of transient sound fields generated by pulsating spheres and cylinders excited from rest in an unbounded region. Test solutions are compared to analytic solutions and to finite element solutions obtained by using large computational grids which extend beyond the region influenced by the transient disturbance.

On the use of variable order infinite wave envelope elements for acoustic radiation and scattering

The use of the variable order infinite wave envelope element to model acoustic radiation and scattering problems is investigated. Different acoustic modeling aspects are focused upon. These involve the modeling of acoustic wave propagation above infinite homogeneous impedance planes, different methods to prescribe acoustic sources and alternative postprocessing procedures. Special attention is given to limitations encountered for this finite element based modeling of wave propagation in unbounded domains. The limitations are assessed by analyzing the higher-order multipoles of the axisymmetric pulsating rigid sphere.

Improved Finite Element Modeling of the Turbofan Engine Inlet Radiation Problem

Improvements have been made in the finite element model of the acoustic radiated field from a turbofan engine inlet in the presence of a mean flow. The problem of acoustic radiation from a turbofan engine inlet is difficult to model numerically because of the large domain and high frequencies involved. A numerical model with conventional finite elements in the near field and wave envelope elements in the far field has been constructed. By employing an irrotational mean flow assumption, both the mean flow and the acoustic perturbation problem have been posed in an axisymmetric formulation in terms of the velocity potential, thereby minimizing computer storage and time requirements. The finite element mesh has been altered in search of an improved solution. The mean flow problem has been reformulated with new boundary conditions to make it theoretically rigorous. The sound source at the fan face has been modeled as a combination of positive and negative propagating duct eigenfunctions. Therefore, a finite element duct eigenvalue problem has been solved on the fan face and the resulting modal matrix has been used to implement a source boundary condition on the fan face in the acoustic radiation problem. In the post processing of the solution, the acoustic pressure has been evaluated at Gauss points inside the elements and the nodal pressure values have been interpolated from them. This has significantly improved the results. The effect of the geometric position of the transition circle between conventional finite elements and wave envelope elements has been studied and it has been found that the transition can be made nearer to the inlet than previously assumed.

A Variable Order Infinite Acoustic Wave Envelope Element

A new infinite wave envelope element for analyzing acoustic radiation and scattering problems in an unbounded domain is presented. The element is based on a finite to infinite geometry mapping and a wave representation within the shape function. It allows for the specification of an arbitrary number of acoustic degrees of freedom in the radial infinite direction, yielding a 1/ r″ expansion for the proper modelling of the amplitude decay. Both two-dimensional and axisymmetric problems are presented to show the use and accuracy of this nth order infinite wave envelope element. Numerical results are compared with analytical and boundary element solutions.

Mapped Wave Envelope Elements for Acoustical Radiation and Scattering

Wave envelope elements provide an alternative to boundary element methods for the solution of exterior wave problems. Applications to date have been to axisymmetric geometries and have involved the use of large, but finite, wave envelope meshes compatibly matched to denser, near field meshes of conventional elements. In the present paper the wave envelope idea is extended by the inclusion of an element mapping, taken directly from infinite element methodology, and by modifications to the residual formulation. Taken in conjunction, these two measures permit the outer boundary of the wave envelope region to be moved to infinity while preserving the boundedness of the acoustic mass and stiffness integrals. The present formulation is developed initially with reference to a simple one-dimensional model and is then applied in two and three dimensions. Comparisons between computed results and those obtained from analytic solutions, where applicable, and from boundary element codes demonstrate the effectiveness of the method.

Wave envelope elements for acoustical radiation in inhomogeneous media

This paper reviews applications of the wave envelope, finite element method to linear acoustical wave propagation. A detailed formulation is given for the particular case of acoustical radiation from a sound source embedded in a region of significant temperature variation. Results are presented for the case of sound propagating along a heated pipe and radiating from an unflanged exhaust. Measured and computed transmission losses are shown to be in close agreement. Although the formulation is presented in the context of acoustical propagation it applies equally well to other wave propagation problems which involve the solution of inhomogeneous, Helmholtz type equations. The analysis presented in this paper and all applications to date are for the axisymmetric case

Wave envelope and finite element approximations for turbofan noise radiation in flight

Calcul approche par elements finis et enveloppes des ondes pour le bruit rayonne en vol par un turboreacteur double flux

A finite element, wave envelope formulation for acoustical radiation in moving flows

An axisymmetric finite element model is presented for the prediction of radiation patterns generated by stationary acoustical sources in moving flows. The acoustical field is represented in an outer region by wave envelope elements which incorporate some features of ray acoustical behaviour. These are compatibly matched to a conventional finite element mesh in a region close to the generating mechanism. Results are presented for problems involving vibrating cylinders and spheres in subsonic mean flows. Good agreement is established between computed and exact solutions.

Wave envelope and infinite element schemes for fan noise radiation from turbofan inlets

Finite element models are presented for the calculation of radiated fan noise in the vicinity of turbofan inlets. The models involve the use of conventional axisymmetric finite elements in an inner region close to the inlet. The far field is represented by infinite elements or wave envelope elements. Theory and results are presented for the case with no mean flow. Comparisons of computed data with analytic solutions and measured values establish the utility of both the infinite element and wave envelope element schemes. The wave envelope scheme is shown to be effective also in the far field. Both schemes use meshes which are much sparser than would be required in conventional numerical discretizations and may be applied to real inlet configurations at modest computational cost.

Wave envelope and infinite elements for acoustical radiation

AbstractFinite element models are presented for the calculation of near and far field acoustical radiation. These models are applied to the specific problem of fan noise radiation from axisymmetric turbofan inlets. In all cases conventional acoustic finite elements are used within an inner region close to the inlet. The far field is represented by infinite elements or wave envelope elements. Theory and results are presented for the case with zero mean flow. Comparisons of computed data with analytic solutions and measured values establish the utility of both the infinite element and wave envelope element schemes in determining the near field values of acoustical pressure. The wave envelope scheme is shown to be effective also in the far field. Both schemes use meshes an order of magnitude more sparse that would be required in conventional numerical discretizations, and may consequently be applied at modest computational cost.