# Design of a Noise Mitigation System Using Lightweight Graded Micro-Porous Material
## 1 Introduction
### Non-Acoustic Flow Properties and Calculation Methods  
Non-acoustic flow properties play a key role in characterizing the thermo-viscous behavior of the micro-porous geometry. The three acoustic models JCAL, JCAPL, and PSD specified in the previous subsection require different types and numbers of flow properties. The required flow properties for each acoustic model are listed in Table 1. The calculation or  
Figure 2: Flow chart of MATELYS AlphaCell simulator [35]. estimation of these flow properties is critical for accurate acoustic predictions of a specific material system. There are several works available in the literature that are applied to or limited to monodisperse loose spherical particles. The works of [PERSON] [36] reported a method of predicting the flow properties for monodisperse loose solid spherical glass beads through the packing concept (Face-Centered Cubic (FCC), Body-Centered Cubic (BCC), and Simple Cubic (SC)), and an absorption coefficient for loose solid spherical glass beads was tested using a vertical impedance tube setup for validation. However, the predictive methodology was not very accurate due to the assumptions related to the FCC, BCC, and SC packing structure. This method was limited to monodisperse spherical particles. The works of [PERSON], [PERSON], and [PERSON] [37] established a direct relationship between the acoustic properties, the intrinsic flow properties, and the microstructure of the randomly arranged spherical granular media. Their approach used a Representative Volume Element (RVE) to simulate granular media with random closed packing (RCP) of the monodisperse spherical particles. All the flow property relations were expressed in terms of the particle diameter [37], validated by the vertical tube testing of loose solid spherical glass beads. This method was limited to monodisperse spherical particles. [PERSON], [PERSON], and [PERSON] [31] developed an inverse method that uses acoustic data for measuring and inverting the key non-acoustical flow properties of solid spherical glass beads. A Pade approximation model was used to curve fit experimental data (real and imaginary parts of the reflection coefficient) using the Nelder-Mead function minimization technique [38] in MATLAB to predict the flow properties of the material. Like previous studies, validation was conducted using loose monodisperse solid spherical beads in a vertical tube setup. This method was applied only to monodisperse spherical particles. The gap in the research lies in applying [PERSON]'s PSD model-based inverse method to a material system of smooth-surface polydisperse spherical beads and later extending it to uPHB composite material involving Cenospheres that are nearly spherical, rough surface lightweight particles to calculate the flow properties. Note that the predictive methods of smooth-surface particles do not directly translate to lightweight rough particles like Cenospheres. This study addresses these gaps by introducing an alternative multivariable-fit inverse method based on Glover-JCAL/JCAPL equations (introduced in this work) to calculate the flow properties. This method can be applied to smooth-surface polydisperse spherical beads and uPHB composite material involving rough-surface Cenospheres and a complex pore structure, and it can extend to materials developed from any size and shaped particles. Therefore, a clear understanding of the links between (1) the morphology of the granular micro-porous material that controls the sound flow/dissipation, (2) flow properties, and