Prediction of effective properties and sound absorption of random close packings of monodisperse spherical particles: Multiscale approach.

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.