Abstract
The transport and sound absorption properties of random close packings of monodisperse spherical particles are explored following a multiscale approach. First, the discrete element method is used to simulate the free fall of the monodisperse particles in a bounded domain to create virtual samples that are representative of real samples. Different particle diameters ranging from 1 to 16 mm are studied. From the virtual samples, representative volume elements (RVEs) are defined. Local partial differential equations governing the transport properties are numerically solved on the RVEs. From the discretized RVEs and the numerical solutions, eight transport properties (porosity, tortuosity, and viscous and thermal static tortuosities, permeabilities, and characteristic lengths) are derived. Micro-macro relationships between these properties and the particle diameter are developed. They are validated against experimental measurements of the open porosity and sound absorption coefficients. The relationships are used to analyze the salient sound absorption features of such media, notably the resonant sound absorption behavior. Expressions allowing identification of the optimal particle diameter for a given thickness, or conversely, the optimal thickness for a given particle diameter, for achieving 100% absorption at the first resonant absorption are derived.
Highlights
On each representative volume elements (RVEs), the steady-state Stokes problem, the inertial flow problem, and the steady-state heat conduction problem presented in Sec
This paper explored the transport and sound absorption properties of random close packings (RCPs) of monodisperse spherical particles, and its salient acoustic features
A multiscale approach was proposed to develop micro-macro relationships to predict the macroscopic properties of these granular media based solely on the diameter of the spherical particles of these media
Summary
These particles may be of the same shape and of the same diameter, or of different shapes and of different diameters. A fluid, like air, fills the interstices between the particles. Under acoustic excitations, they behave as rigid-frame open-cell porous media that can be represented as equivalent fluid media. An equivalent fluid medium is typically defined by transport properties, often called the non-acoustic or macroscopic parameters. In the eight-parameter model of Johnson-Champoux-Allard-PrideLafarge (JCAPL) (formed by Eqs. 5.50, 5.51, 5.56, and 5.57 of Ref. 1), the transport properties are the open porosity, the tortuosity (at infinite frequency), and the viscous and thermal characteristic lengths, tortuosities, and permeabilities
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