The scattering of torsional guided waves from Gaussian rough surfaces in pipework

In older sections of industrial pipework there are often regions of general corrosion that typically have a Gaussian thickness distribution. During guided wave inspection this corrosion causes an increase in the background noise and a significant attenuation of the inspection wave. These effects are investigated in this paper through finite element modelling of the interaction of torsional guided waves with rough surfaces in pipes. Pipes of different diameter and rough surface profile are modelled and it is found that the attenuation of waves is explained by significant mode conversion and scattering within the rough surface. This mode conversion is greatest when the non-axisymmetric modes to which energy is scattered are close to the cutoff frequency or when the ratio of surface correlation length to wavelength is around 0.2-0.25. Mode conversion increases with increasing surface roughness and is a strong function of frequency-diameter product, with larger pipes causing more mode conversion. When this mode conversion occurs the energy is lost mostly to those waves with a displacement profile closest to the original torsional inspection wave. Resulting attenuation of the inspection signal can be severe; for example a mean wall thickness loss of 28% can cause 2.7 dB/m attenuation in a pulse-echo configuration.