Mode matching in axisymmetric fluid-filled pipes: Scattering by a flange

Long range ultrasonic testing of pipelines sends an ultrasonic wave along a pipe wall and then detects scattering from defects present. It is well known that scattering by pipe fixtures and fittings, such as a flange, can cause distortion and interfere with the ability to identify defects. This article develops a theoretical model to investigate scattering from a flange in a fluid-filled pipe with elastic walls. Mode matching is used as this is a computationally efficient way to examine long lengths of pipe and for enforcing the appropriate axial continuity conditions over area discontinuities. A recent article presented a mode matching approach for a similar problem, and it is demonstrated here that a re-casting of the equations is necessary to ensure all of the appropriate matching conditions are enforced. Mode matching predictions are also compared with an alternative point collocation approach in order to provide an independent benchmark. Excellent agreement between mode matching and point collocation is demonstrated, and reflection and transmission coefficients are generated in order to show the resonant behaviour of a flange and illustrate that its influence is significant and strongly frequency dependent.