Bi WenPing, Pagneux Vincent, Lafarge Denis, Aurégan Yves
Laboratoire d'Acoustique de l'Université du Maine, UMR CNRS 6613, Le Mans Cedex 9, France.
J Acoust Soc Am. 2007 Jul;122(1):280-90. doi: 10.1121/1.2736785.
An efficient method is proposed for modeling time harmonic acoustic propagation in a nonuniform lined duct without flow. The lining impedance is axially segmented uniform, but varies circumferentially. The sound pressure is expanded in term of rigid duct modes and an additional function that carries the information about the impedance boundary. The rigid duct modes and the additional function are known a priori so that calculations of the true liner modes, which are difficult, are avoided. By matching the pressure and axial velocity at the interface between different uniform segments, scattering matrices are obtained for each individual segment; these are then combined to construct a global scattering matrix for multiple segments. The present method is an improvement of the multimodal propagation method, developed in a previous paper [Bi et al., J. Sound Vib. 289, 1091-1111 (2006)]. The radial rate of convergence is improved from O(n(-2)), where n is the radial mode indices, to O(n(-4)). It is numerically shown that using the present method, acoustic propagation in the nonuniform lined intake of an aeroengine can be calculated by a personal computer for dimensionless frequency K up to 80, approaching the third blade passing frequency of turbofan noise.
提出了一种用于模拟无流非均匀衬里管道中时谐声传播的有效方法。衬里阻抗在轴向分段均匀，但在周向变化。声压以刚性管道模式和一个携带阻抗边界信息的附加函数展开。刚性管道模式和附加函数是先验已知的，从而避免了难以计算的真实衬里模式的计算。通过匹配不同均匀段之间界面处的压力和轴向速度，为每个单独的段获得散射矩阵；然后将这些散射矩阵组合起来构建多段的全局散射矩阵。本方法是对先前论文[Bi等人，《声学学报》289，1091 - 1111（2006）]中开发的多模传播方法的改进。径向收敛速率从O(n(-2))提高到O(n(-4))，其中n是径向模式指数。数值结果表明，使用本方法，航空发动机非均匀衬里进气道中的声传播可以由个人计算机计算到无量纲频率K高达80，接近涡轮风扇噪声的第三叶片通过频率。
