Axisymmetric semi-analytical finite elements for modelling waves in buried/submerged fluid-filled waveguides

Abstract

Efficient and accurate predictions of wave propagation are a vital component of wave-based nondestructive interrogation techniques. Although a variety of models are available in the literature, most of them are suited to a particular wave type or a specific frequency regime. In this paper we present a multi-wave model for wave propagation in axisymmetric fluid-filled waveguides, either buried or submerged in a fluid, based on the semi-analytical finite elements. The cross-section is discretised with high-order spectral elements to achieve high efficiency, and the singularities resulting from adopting a Lobatto scheme at the axis of symmetry are handled appropriately. The surrounding medium is modelled with a perfectly matched layer, and a practical rule of choice of its parameters, based only on the material properties and the geometry of the waveguide, is derived. To represent the fluid and the solidfluid coupling, an acoustic SAFE element and appropriate coupling relationships are formulated. The model is validated against both numerical results from the literature and experiments and the comparisons show very good agreement. Finally, an implementation of the method in Python is made available with this publication.

Guided wave propagation in cylindrical ducts with elastic walls enclosing a fluid moving with a uniform velocity

“…This illustrates the complexity of this type of coupled guided wave problem and this is behaviour that has been shown before [13]. Of course, it is also well known that the compressional modes never cross one another in the dispersion curves of a lossless system, and instead they avoid crossing, or veer apart, as the energy is transferred between the fluid and the structure [12,21].…”

“…Both analytic and numerical methods have been developed, see for example the commercial code DISPERSE®, which uses an analytic solution for the coupled problem [19]. More recently, alternative numerical approaches have been developed, including the wave finite element method [20], and the semi analytic finite element (SAFE) method [21]. These numerical models have been applied to liquid filled pipes and demonstrate that large numbers of eigenmodes can readily be obtained.…”

“…The analysis is restricted to circular ducts as this simplifies the problem and enables a focus on modal behaviour. External fluid loading is also neglected, although this can be included if necessary, see for example Kalkowski et al [21] and Duan et al [22]. In this article, a uniform mean flow is assumed for the fluid as this is generally accepted to provide a good approximation in duct acoustics [1]; however, the numerical approach presented in the next section is sufficiently general to include shear layers if desired, although the addition of viscosity will significantly complicate the finite element analysis for the acoustic wave equation.…”

A Comprehensive Review of Acoustic Methods for Locating Underground Pipelines

“…Alternatively, finite-element methods are commonly used to model the wave propagation in buried pipe systems. Relevant research can be found in [79]. Recent studies have shown that the fluid-dominated wave can radiate effectively into surrounding soil, based on which the location of buried pipes can be inferred through monitoring the ground surface vibration using for example geophones [69].…”

“…Alternatively, finite-element methods are commonly used to model the wave propagation in buried pipe systems. Relevant research can be found in [79].…”