中文摘要：

流管实验装置是测量有流动情况下航空发动机消声短舱内声衬声阻抗的主要装置。本文发展了一种解析的模态匹配方法进行在平均流有声衬条件下矩形流管中声传播的计算。用同伦方法求解特征值问题，并与用环绕积分求解的结果进行比较。声场通过轴向阻抗间断面的声压和声质点速度积分相等计算。第一个算例是无流动、硬壁、有限长、考虑端口反射的情况，并与北航流管实验台测量数据进行了对比；第二个算例为有流动情况下有限长声衬管道不考虑端口反射的声场计算，它与文献中NASA流管实验结果和CAA计算结果符合得很好。

英文摘要：

Flow duct facility is a main device to measure the impedance of the liners on nacelle of aeroengine with flow. A analytical mode matching method is developed for the sound propagation through rectangular flow duct with mean flow and with lining. The eigenvalue problem is solved by homotopy method and compared with that by wind-number integral method. The acoustic field is calculated through the integral equality of acoustic pressure and velocity at the axial impedance discontinuous planes. The first case is for a finite duct of hard wall without flow and considering reflection on inlet/outlet, the results are compared with the experimental data obtained from BUAA flow duct facility. The second case considers finite lined duct with flow, no reflection on inlet/outlet, the results agree well with the data from NASA flow duct facility and CAA calculation in references.