Roncen R, Fellah Z E A, Lafarge D, Piot E, Simon F, Ogam E, Fellah M, Depollier C
ONERA/Département Multi-Physique pour l'Énergétique, Université de Toulouse, Toulouse, F-31055, France.
Laboratoire de Mécanique et d'Acoustique, Centre National de la Recherche Scientifique, Unité Mixte de Recherche 7031, Aix-Marseille Universite, Centrale Marseille, Marseille Cedex 20, F-13402, France.
J Acoust Soc Am. 2018 Dec;144(6):3084. doi: 10.1121/1.5080561.
In this article, a modeling extension for the description of wave propagation in porous media at low-mid frequencies is introduced. To better characterize the viscous and inertial interactions between the fluid and the structure in this regime, two additional terms described by two parameters and are taken into account in the representation of the dynamic tortuosity in a Laurent-series on frequency. The model limitations are discussed. A sensitivity analysis is performed, showing that the influence of and on the acoustic response of porous media is significant. A general Bayesian inference is then conducted to infer, simultaneously, the posterior probability densities of the model parameters. The proposed method is based on the measurement of waves transmitted by a slab of rigid porous material, using a temporal model for the direct and inverse transmission problem. Bayesian inference results obtained on three different porous materials are presented, which suggests that the two additional parameters are accessible and help reduce systematic errors in the identification of other parameters: porosity, static viscous permeability, static viscous tortuosity, static thermal permeability, and static thermal tortuosity.
本文介绍了一种用于描述中低频下多孔介质中波传播的建模扩展。为了更好地表征该区域中流体与结构之间的粘性和惯性相互作用，在频率的洛朗级数中表示动态曲折度时，考虑了由两个参数描述的两个附加项。讨论了模型的局限性。进行了敏感性分析，结果表明这两个参数对多孔介质声学响应的影响很大。然后进行了一般贝叶斯推断，以同时推断模型参数的后验概率密度。所提出的方法基于对刚性多孔材料板传输的波的测量，使用直接和反向传输问题的时间模型。给出了在三种不同多孔材料上获得的贝叶斯推断结果，这表明这两个附加参数是可获取的，并且有助于减少其他参数（孔隙率、静态粘性渗透率、静态粘性曲折度、静态热渗透率和静态热曲折度）识别中的系统误差。
