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.

中文翻译：

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轴对称充液管道中的模式匹配：法兰散射。

管道的远程超声波测试会沿管壁发送超声波，然后从存在的缺陷中检测出散射。众所周知，管道固定装置和配件（例如法兰）的散射会引起变形并干扰识别缺陷的能力。本文开发了一个理论模型来研究带有弹性壁的充液管道中法兰的散射。使用模式匹配是因为这是一种计算有效的方法，可用于检查管道的较长长度并在区域不连续性上实施适当的轴向连续性条件。最近的一篇文章提出了针对类似问题的模式匹配方法，并且在此证明了对方程的重新铸造对于确保强制实施所有适当的匹配条件是必要的。还将模式匹配预测与替代点配置方法进行比较，以提供独立的基准。演示了模式匹配和点配置之间的极佳一致性，并生成了反射和透射系数，以显示法兰的共振行为，并说明了其影响是重要的，并且与频率密切相关。