适用于时域计算的多自由度宽频阻抗模型研究

Study on the multi-freedom broadband impedance model for time-domain simulations

旨在建立通用且适定的宽频阻抗模型用于时域数值模拟计算。基于扩展的Helmholtz共振腔阻抗模型,通过引入共轭复数极点-残值对有理分式组合的方式,提出了一种新型多自由度宽频阻抗模型,并证明了该模型的适定性。频域内阻抗边界条件通过傅里叶反变换的方法转换为宽频时域阻抗边界条件,时域模拟采用递推算法快速实现。分别采用二维和三维标准问题对该宽频阻抗模型及相应的时域边界条件进行校核,数值解和参考解一致。研究结果表明所提出的多自由度阻抗模型能够描述声衬宽频特性,相应的宽频时域阻抗边界条件可以精确预测宽频阻抗表面声传播问题。

The purpose of this paper is to construct a general broadband impedance model which is suited for predicting acoustic propagation problems in time domain. A multi-freedom broadband impedance model for sound propagation over impedance surfaces is proposed and the corresponding time domain impedance boundary condition is presented. Basing on the Extended Helmholtz resonator, the multi-freedom impedance model is constructed through combing with a sum of rational functions with general complex-conjugate pole-residue pairs and it is proved that the impedance model is well-posed. The impedance boundary condition can be implemented into a computational aeroacoustics solver by a recursive convolution technique which results in a fast and computationally efficient algorithm. The two dimensional and three dimensional benchmark problems are selected to validate the accuracy of the current impedance model and time domain simulations. The numerical results are in good agreement with the reference solutions. It is demonstrated that the proposed impedance model can be used to describe the broadband characteristics of acoustic liners. And the corresponding time domain impedance boundary condition is viable and accurate for the prediction of sound propagation over broadband impedance surfaces.