用放射性衰变布朗运动,根据Biot理论计算饱和多孔介质气体的动态体积模量

IF 1 3区 物理与天体物理 Q4 ACOUSTICS Acta Acustica Pub Date : 2023-01-01 DOI:10.1051/aacus/2023034
Denis Lafarge, Navid Nemati, Stéphane Vielpeau
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引用次数: 0

摘要

我们提出了一种新的随机模拟方法来确定气体的长波有效动态体积模量,例如环境空气,饱和多孔介质具有相对任意的微观几何形状,即简单到足以保证Biot的简化,即流体和固体运动在孔隙尺度上是准不可压缩运动。该仿真方法基于两个不同物理问题之间的数学同构。其中之一是在生物理论背景下的气体和固体之间的傅里叶热交换问题。另一类是扩散-分解控制问题,考虑扩散粒子在孔隙体积中发生放射性衰变和孔壁瞬间衰变的布朗运动。通过适当选择衰减时间和扩散系数,提出了确定扩散粒子平均寿命的随机算法,直接给出了饱和流体的有效表观模量。我们展示了它如何导致纯几何随机结构来确定一些几何参数。在验证了该算法对圆柱形圆孔的影响后,说明了该算法对用于噪声控制的纤维材料的有效性。结果与含孔隙空间三个纯几何参数的有效模量模型吻合良好:静态热渗透率除以孔隙度、静态热弯曲度和热特征长度。
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Brownian motion with radioactive decay to calculate the dynamic bulk modulus of gases saturating porous media according to Biot theory
We present a new stochastic simulation method for determining the long-wavelength effective dynamic bulk modulus of gases, such as ambient air, saturating porous media with relatively arbitrary microgeometries, i.e., simple enough to warrant Biot’s simplification that the fluid and solid motions are quasi-incompressible motions at the pore scale. The simulation method is based on the mathematical isomorphism between two different physical problems. One of them is the actual Fourier heat exchange problem between gas and solid in the context of Biot theory. The other is a diffusion-disintegration-controlled problem that considers Brownian motion of diffusing particles undergoing radioactive-type decay in the pore volume and instant decay at the pore walls. By appropriately choosing the decay time and the diffusion coefficient, the stochastic algorithm we develop to determine the average lifetime of the diffusing particles, directly gives the effective apparent modulus of the saturating fluid. We show how it leads to purely geometric stochastic constructions to determine a number of geometrical parameters. After validating the algorithm for cylindrical circular pores, its power is illustrated for the case of fibrous materials of the type used in noise control. The results agree well with a model of the effective modulus with three purely geometric parameters of the pore space: static thermal permeability divided by porosity, static thermal tortuosity, and thermal characteristic length.
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来源期刊
Acta Acustica
Acta Acustica ACOUSTICS-
CiteScore
2.80
自引率
21.40%
发文量
0
审稿时长
12 weeks
期刊介绍: Acta Acustica, the Journal of the European Acoustics Association (EAA). After the publication of its Journal Acta Acustica from 1993 to 1995, the EAA published Acta Acustica united with Acustica from 1996 to 2019. From 2020, the EAA decided to publish a journal in full Open Access. See Article Processing charges. Acta Acustica reports on original scientific research in acoustics and on engineering applications. The journal considers review papers, scientific papers, technical and applied papers, short communications, letters to the editor. From time to time, special issues and review articles are also published. For book reviews or doctoral thesis abstracts, please contact the Editor in Chief.
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