Wave Scattering from Step Discontinuities in a Water Pipeline Waveguide: Analytical Modeling and Discontinuity Material Influence

Step discontinuities, which are formed in pipeline repair and maintenance, will introduce additional wave scattering in the pipeline diagnosing work. Therefore, an analytical model is established in this paper to investigate the longitudinal wave scattering from a step discontinuity and the influence of discontinuity material on the scattering characteristics in water pipelines. In the model, axial wavenumber, displacement and stress profiles of the unblemished pipeline and discontinuity sections are calculated by a multi-layered cylindrical waveguide model. To concatenate these sections and predict the overall influences of the discontinuity, the mode matching method is applied by enforcing the flexible axial boundary conditions with an extended bi-orthogonality relation. Based on the established model, numerical calculations are carried out to investigate the reflection/transmission characteristics when discontinuity material and attenuation are considered. Both finite element method (FEM) software and laboratory experiments are also conducted for modeling verification: the maximum root mean square errors of the predicted reflection and transmission coefficients are 0.01 and 0.1 compared with FEM and experiment results, respectively. It indicates the proposed model is accurate in predicting the wave scattering from a step discontinuity in a water pipeline with the influence of discontinuity material accounted for. In addition, this pure analytical model introduces advantages in computational cost when modeling long pipelines compared with existing FEM packages.