Existing models of extended-tube liners are mainly applicable to the normal-incidence case, and the influence of the grazing-flow effect is often ignored. In the current paper, an impedance model is developed based on the transfer matrix method, and the grazing-flow effect on the surface impedance is taken into account in terms of the end corrections. The validity of the model is examined on a flow-duct facility, and the liner impedances are obtained from an impedance eduction method. The proposed model shows a reasonable agreement with the educed data, and better accuracy is found in terms of the transmission loss. Geometric parameters including the length of the extended tube and the grazing-flow speed are then investigated. It is found that the frequency for maximum attenuation is shifted to lower frequencies for a longer extended tube, but it is less sensitive to the grazing-flow speed. The effects of the sound pressure level and nonlinearities are also investigated.

现有的加长管内衬模型主要适用于正常入射情况，往往忽略了掠流效应的影响。在本文中，基于传递矩阵法建立了阻抗模型，并在端部修正方面考虑了掠流对表面阻抗的影响。该模型的有效性在一个流动管道设施上进行了检验，并通过阻抗推导方法获得了衬管阻抗。所提出的模型与导出的数据显示出合理的一致性，并且在传输损耗方面具有更好的准确性。然后研究几何参数，包括延伸管的长度和掠流速度。发现对于更长的延伸管，最大衰减的频率移至较低频率，但它对放牧流速不太敏感。还研究了声压级和非线性的影响。