Abstract Direct numerical simulations (DNS) based on advanced computational aeroacoustic (CAA) methods are conducted to study the acoustic impedance of a uniformly distributed multi-slit liner under grazing incident sound waves at different frequencies and sound pressure levels (SPL), in the absence of mean-flow. The liner consists of a series of fifteen identical slit Helmholtz resonators. Numerical results show that a portion of the slit resonators in the upstream works in a non-linear regime and the others in the downstream work in a linear regime when high intense waves near the resonance are excited. It is a direct evidence that the acoustic impedance is non-uniform and spatially varying over the liner length due to the different local incident sound pressure levels. With the numerical data, two methodologies are adopted to determine the acoustic impedance of the liner, one is referred to as the Prony's method and the other one is based on an inverse method. The impedance value is validated by a time-domain linearized Euler equation (LEE) solver. Numerical results indicate that representing the liner with a homogenized impedance leads to considerable errors in the reconstructed sound fields when the liner experiences a transition from non-linear regime to linear regime. On the other hand, in cases where such a transition is absent, the homogenized constant impedance is adequate to estimate the acoustic response of the liner. Therefore, a spatially piece-wise function is derived and calibrated by the DNS results to take into consideration both the resistance and reactance variation in stream-wise direction. Comparison shows that the prediction of the sound field is improved by the space-dependent impedance boundary.

中文翻译：

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由于内衬管道中的高声强衰减引起的空间变化声阻抗

摘要 基于先进的计算气动声学 (CAA) 方法进行直接数值模拟 (DNS) 以研究均匀分布的多缝衬垫在不同频率和声压级 (SPL) 的掠入射声波下的声阻抗。平均流量。衬垫由一系列 15 个相同的狭缝亥姆霍兹谐振器组成。数值结果表明，当共振附近的强波被激发时，上游的一部分狭缝谐振器工作在非线性状态，而下游的其他部分工作在线性状态。这是一个直接证据，表明由于不同的局部入射声压级，声阻抗在衬垫长度上是不均匀的和空间变化的。有了数字数据，采用两种方法来确定衬管的声阻抗，一种称为 Prony 方法，另一种基于逆方法。阻抗值由时域线性化欧拉方程 (LEE) 求解器验证。数值结果表明，当衬垫经历从非线性状态到线性状态的转变时，用均质阻抗表示衬垫会导致重建声场中的相当大的误差。另一方面，在没有这种转变的情况下，均匀的恒定阻抗足以估计衬垫的声学响应。因此，空间分段函数由 DNS 结果导出和校准，以考虑流向方向上的电阻和电抗变化。