Wenbo Duan

On the scattering of elastic waves from a non-axisymmetric defect in a coated pipe

Viscoelastic coatings are often used to protect pipelines in the oil and gas industry. However, over time defects and areas of corrosion often form in these pipelines and so it is desirable to monitor the structural integrity of these coated pipes using techniques similar to those used on uncoated pipelines. A common approach is to use ultrasonic guided waves that work on the pulse-echo principle; however, the energy in the guided waves can be heavily attenuated by the coating and so significantly reduce the effective range of these techniques. Accordingly, it is desirable to develop a better understanding of how these waves propagate in coated pipes with a view to optimising test methodologies, and so this article uses a hybrid SAFE-finite element approach to model scattering from non-axisymmetric defects in coated pipes. Predictions are generated in the time and frequency domain and it is shown that the longitudinal family of modes is likely to have a longer range in coated pipes when compared to torsional modes. Moreover, it is observed that the energy velocity of modes in a coated pipe is very similar to the group velocity of equivalent modes in uncoated pipes. It is also observed that the coating does not induce any additional mode conversion over and above that seen for an uncoated pipe when an incident wave is scattered by a defect. Accordingly, it is shown that when studying coated pipes one need account only for the attenuation imparted by the coating so that one may normally neglect the effect of coating on modal dispersion and scattering.

On the scattering of torsional waves from axisymmetric defects in buried pipelines

This article develops a numerical model suitable for analysing elastic wave scattering in buried pipelines. The model is based on a previous so-called hybrid approach, where a nominally infinite length of pipe is split up into uniform and non-uniform regions. The key challenge for buried structures is in enforcing the appropriate boundary conditions in both the axial and radial directions, which must encompass the entire length of the structure, as well as the surrounding material. Accordingly, the focus of this article is on developing a model suitable for accurately applying these boundary conditions, and so the analysis is restricted here to the study of axisymmetric defects and to an incident sound field that consists of the fundamental torsional mode only. It is shown that this problem may be addressed in a numerically efficient way provided one carefully choses a perfectly matched layer for the surrounding material, and then integrates over this layer using a complex co-ordinate stretching function. This enables the use of mode matching to deliver a convergent system of equations that enforce the appropriate axial and radial boundary conditions.

A hybrid finite element approach to modeling sound radiation from circular and rectangular ducts

A numerical model based on a hybrid finite element method is developed that seeks to join sound pressure fields in interior and exterior regions. The hybrid method is applied to the analysis of sound radiation from open pipes, or ducts, and uses mode matching to couple a finite element discretization of the region surrounding the open end of the duct to wave based modal expansions for adjoining interior and exterior regions. The hybrid method facilitates the analysis of ducts of arbitrary but uniform cross section as well the study of conical flanges and here a modal expansion based on spherical harmonics is applied. Predictions are benchmarked against analytic solutions for the limiting cases of flanged and unflanged circular ducts and excellent agreement between the two methods is observed. Predictions are also presented for flanged and unflanged rectangular ducts, and because the hybrid method retains the sparse banded and symmetric matrices of the traditional finite element method, it is shown that predictions can be obtained within an acceptable time frame even for a three dimensional problem.

Measurement of complex acoustic intensity in an acoustic waveguide

Acoustic intensity is normally treated as a real quantity, but in recent years, many articles have appeared in which intensity is treated as a complex quantity where the real (active) part is related to local mean energy flow and the imaginary (reactive) part to local oscillatory transport of energy. This offers the potential to recover additional information about a sound field and then to relate this to the properties of the sound source and the environment that surrounds it. However, this approach is applicable only to multi-modal sound fields, which places significant demands on the accuracy of the intensity measurements. Accordingly, this article investigates the accuracy of complex intensity measurements obtained using a tri-axial Microflown intensity probe by comparing measurement and prediction for sound propagation in an open flanged pipe. Under plane wave conditions, comparison between prediction and experiment reveals good agreement, but when a higher order mode is present, the reactive intensity field becomes complicated and agreement is less successful. It is concluded that the potential application of complex intensity as a diagnostic tool is limited by difficulties in measuring reactive intensity in complex sound fields when using current state of the art acoustic instrumentation.

Structural Health Monitoring of Above-Ground Storage Tank Floors by Ultrasonic Guided Wave Excitation on the Tank Wall

There is an increasing interest in using ultrasonic guided waves to assess the structural degradation of above-ground storage tank floors. This is a non-invasive and economically viable means of assessing structural degradation. Above-ground storage tank floors are ageing assets which need to be inspected periodically to avoid structural failure. At present, normal-stress type transducers are bonded to the tank annular chime to generate a force field in the thickness direction of the floor and excite fundamental symmetric and asymmetric Lamb modes. However, the majority of above-ground storage tanks in use have no annular chime due to a simplified design and/or have a degraded chime due to corrosion. This means that transducers cannot be mounted on the chime to assess structural health according to the present technology, and the market share of structural health monitoring of above-ground storage tank floors using ultrasonic guided wave is thus limited. Therefore, the present study investigates the potential of using the tank wall to bond the transducer instead of the tank annular chime. Both normal and shear type transducers were investigated numerically, and results were validated using a 4.1 m diameter above-ground storage tank. The study results show shear mode type transducers bonded to the tank wall can be used to assess the structural health of the above-ground tank floors using an ultrasonic guided wave. It is also shown that for the cases studied there is a 7.4 dB signal-to-noise ratio improvement at 45 kHz for the guided wave excitation on the tank wall using shear mode transducers.

Modeling the scattering of elastic waves from defects in buried pipes

Long Range Ultrasonic Testing (LRUT) is a popular non-destructive evaluation technique for identifying defects in pipelines. The method sends an elastic wave down the walls of a pipe and then monitors echoes that arise if the wave is scattered by a defect. The technical challenge of LRUT lies in separating out, and interpreting from coherent and random background noise, those signals that belong to a defect. This becomes particularly challenging when a pipe is buried, because energy in an elastic wave is known to leak out of the pipe walls when it is surrounded by materials such as soil, concrete, or sand. To address this problem it is necessary to develop a better understanding of how elastic waves propagate in buried structures, and so, a finite element based model is introduced here that seeks to analyze the scattering from a defect in a buried pipe in both the frequency and time domain. Results from the implementation of this numerical model for the torsional T(0,1) mode are presented, and the effects...

Complex intensity in circular ducts containing an obstruction

Sound intensity may be defined as a complex quantity in which the real part of the intensity is related to the magnitude of the local mean energy flow, and the imaginary part to the local oscillatory transport of energy. By treating intensity as a complex quantity it is possible to visualise energy flow in a different way and this has the potential to aid in the interpretation of, say, sound fields scattered by objects. Accordingly, the sound field scattered by an object placed in a semi-infinite circular duct is examined here. Experimental measurements of complex intensity are obtained in three (orthogonal) directions using a Microflown intensity probe, and measurements are compared to predictions obtained using a finite element based theoretical model. Comparisons between prediction and measurement are undertaken for both plane wave and multi-modal sound fields and here it is noted that when at least one higher order mode propagates it becomes more difficult to obtain good agreement between prediction a...

Reflection and transmission across partial blockages in fluid‐filled flexible, non‐thin‐walled pipes.

A model is presented for propagation along a flexible pipe whose thickness is not small in comparison with its diameter across a partial blockage with varying sizes and material properties. Comparison is made with Flugge’s well‐known thin‐shell theory for a propagation along a pipe where it is found that the additional computational complexity found in the current model becomes necessary when the thickness of the shell exceeds 10% of the pipe radius. Comparison is also made with experiment both for the propagation characteristics of the pipe and for the reflection from a partial blockage. Two reflection models are presented: a crude area change model with compensation for the mass of the blockage and a more accurate model using high‐order modes and matching to a flexible blockage using co‐location. Reasonable agreement is found for both with the more accurate model, giving better agreement but at the expense of computational efficiency. The work is useful both for blockage detection and for detecting sten...

The Effects of Blockage on the Propagation of Acoustic Waves in the Liquid-Shell Coupled System

The free vibration of a fluid/structure system consisting of a cylindrical blockage submerged in a liquid enclosed by a cylindrical shell is investigated for the purpose of pipe line transportation monitoring. The wavenumbers are obtained and the reflection and transmission characteristics of these waves at the blockage interfaces are investigated theoretically. Reflection and transmission ratios are obtained in the axisymmetric mode, as functions of frequency. High order modes play an important role in the near field of the discontinuity and are taken into account.

Analysis of Leakage Flow and Dynamic Characteristics in Floating Ring Seals for High Pressure Turbopump

Because the solutions based on the numerical integration of the complete Navier-Stokes equations can be very time-consuming, the bulk-flow model was used for calculating the static and the dynamic characteristics of floating ring seals. The bulk-flow model is governed by three partial differential equations on eccentric working conditions with steepest descent method to find the seal’s equilibrium position efficiently. A finite difference scheme has been used to solve the nonlinear governing equations. Compared to Nelson and Nguyen’s Fast Fourier Transform Method, this scheme has better consistency. Perturbation analysis of the flow variables yields a set of zeroth and first-order equations. The SIMPLE algorithm is used to integrate the system of bulk-flow equations. Comparisons of the numerical predictions (lock-up eccentricity ratio, leakage flow rate and rotordynamic coefficients) with Ha’s results, which were formulated using the Fourier series, and experimental data are presented subsequently.Copyright