# Design of a Noise Mitigation System Using Lightweight Graded Micro-Porous Material
## 1 Introduction
### Granular Materials
Moreover, the concept of controlling the microstructure through grading appropriate particle sizes, processing the material as a continuous system without creating interfaces between gradations, and demonstrating this concept by achieving an engineered combination of sound absorption and transmission loss across a broad frequency range is original, novel, and innovative. Granular ceramic hollow microbubbles are one of the best choices [24]. Readily available hollow microbubbles that are the byproducts of coal-burning electric power plants are used. The chosen hollow microbubbles are Censopheres commercially available and supplied by SphereOne--called Extendospheres--with a broad varying particle-size distribution. The rationale for selecting these particles lies in the fact that they are lightweight and nearly spherical, with a surface roughness that can improve sound energy dissipation by enhancing friction (sound energy converted to heat) and tortuosity (a dimensionless property of porous material--the ratio of the effective flow path length to the length of the material or medium). These features of the hollow microbubbles can help develop a noise-mitigating micro-porous material system by controlling the particle size, thereby controlling the pore size and their distribution within the material, such that one can engineer a targeted acoustic response. We previously developed a new novel particle surface coating processing technique using Censopheres and a phenolic high-char binder; a detailed description of the processing and development of the micro-porous material is described in reference [25], and the properties of the same are summarized here. The developed material is non-flammable and multifunctional (it can withstand high temperatures up to 311 \({}^{\circ}\)C, is structural and noise mitigating) and lightweight (bulk density \(<\) 0.45 g/cc), with a good compression strength of 0.86 to 3 MPa (for different particle-size groups), a high glass transition temperature (T\({}_{\rm g}\)) of 311 \({}^{\circ}\)C, a coefficient of linear thermal expansion (CTE) of 5.16 ppm/\({}^{\circ}\)C that is small, indicating it is a ceramic material (ensuring dimensional stability), and a low thermal conductivity of 0.1062 W/m \({}^{\circ}\)C (thermally isotropic), and it is referred to as a micro-porous hollow bubble composite material (\(\mu\)PHB) [25]. Furthermore, the material offers a 3D fluid flow that can enhance sound energy dissipation relative to 1D or 2D flow [26] technologies (for example, traditional Single Degree of Freedom systems (SDOFs)). This is the first time the concept of a lightweight granular micro-porous material has been developed for aircraft engine noise mitigation, where the interest is in an acoustic liner of a thickness of 50 mm and noise mitigation in a broad frequency range over 500 Hz. In acoustic material design, in addition to developing porous materials, tools to test and predict acoustic responses are also critical. We need suitable acoustic models to make predictions of acoustic response, and for making these predictions, we need transport parameters, referred to as non-acoustic fluid flow properties (either by measurements or calculation by predictive methodologies), in this work. Henceforth, non-acoustic flow properties will be referred to as flow properties.