有三维势流时消声器声学特性预测的有限元法

Finite Element Method for Prediction of Acoustic Characteristics of Silencers with Three-Dimensional Potential Flow

将有限元法应用于预测有三维势流时管道和消声器的声学特性,推导了三维势流中声传播问题的有限元法计算公式,给出了管道和消声器声学特性的计算方法和数值实施过程。与传统的声学有限元法相比,新方法考虑了声学控制方程中气流马赫数二阶小量的影响,因此适用于求解具有较高马赫数亚音速流中的声传播问题。使用三维有限元法首先计算了管道的四极参数,并与一维解析解比较验证了新方法的正确性和精度,然后使用三维有限元法计算双级膨胀腔消声器的传递损失。数值计算结果表明:随着气流马赫数的增加,消声器传递损失曲线向低频方向移动,因而改变了各频率下的消声量。为了精确预测消声器的声学特性,三维势流对管道和消声器内声传播的影响应该加以考虑。

The finite element method（FEM） was applied to predict the acoustic characteristics of ducts and silencers with three-dimensional potential flow.The finite element formulations were derived for the sound propagation in three-dimensional potential flow,and the predictive method and numerical procedure for the acoustic characteristics of ducts and silencers were introduced.Compared to conventional acoustic finite element method,the presented method took into account the second order terms of flow Mach number in the acoustic governing equation,so it was suitable for the cases with higher Mach number subsonic flow.The four-pole parameters of a straight duct were predicted using the presented three-dimensional FEM and were compared with the one-dimensional analytical solutions.The presented method was proved to be valid and accurate.Transmission loss of two-stage expansion chamber silencers was then predicted using the three-dimensional FEM,and the numerical results show that the curves of transmission loss of silencers shift to lower frequency direction as the flow Mach number increasing,causing the attenuation at various frequencies to be changed.In order to predict acoustic characteristics of silencer accurately,the influence of three-dimensional potential flow on the sound propagation in ducts and silencers should be considered.