# Design of a Noise Mitigation System Using Lightweight Graded Micro-Porous Material
## 4 Concluding Remarks  
This research work demonstrated the design, development, and validation of a noise mitigation system employing lightweight micro-porous material derived from the phenolic binder and coal-burned fly ash, specifically Cenospheres--a mineral waste from electrical power plants. An establishment of predictive methods to determine the flow properties of the uPHB composite materials is achieved in this study. To begin with, the pore-size distribution (PSD) model-based inverse method, previously verified only for monodisperse spherical particles, was applied to polydisperse smooth spherical beads for the first time and validated with experimental data. However, this method yielded inconsistent flow properties and is unreliable for uPHB composite materials. A novel multivariable-fit inverse method, based on the G-JCAL/JCAPL method, was introduced to calculate the flow properties that are crucial for predicting acoustic responses--sound absorption and transmission loss. The method was validated for both smooth-surface polydisperse spherical glass beads and uPHB composite materials, showing reliability in predictions across varying geometries and particle sizes. Utilizing the flow properties of uPHB composite materials, a graded pore-size distribution uPHB composite material suitable for turbine engine acoustic liners was designed using MATELYS AlphaCell predictive analyses. Two selected graded uPHB composite material combinations were fabricated, normal incidence impedance tested, and the acoustic predictions were validated experimentally. The specific conclusions are as follows:  
* The proposed multivariable-fit inverse method based on the G-JCAL/JCAPL method is valid for calculating the flow properties of JCAL/JCAPL acoustic models. The method is robust and can be applied to both smooth and rough surface particles;
* The study confirmed that the flow properties are unique for the given particle-size distribution if the least dimension of the specimen geometry is greater than 10 times the mean particle size. Further, the same flow properties can predict transmission loss for any geometry for a specific particle size group uPHB composite material;  
Figure 19: Validation of predictions with experimental transmission versus frequency for a graded (L\({}_{\text{37.5}}\), M\({}_{\text{37.5}}\), S\({}_{\text{25}}\)) μPHB composite material. * The acoustic responses from the \(\upmu\)PHB composite materials demonstrate that a graded pore-size distribution system (large to small pore size) is needed to achieve the design condition of both absorption coefficient and transmission loss. This was validated through analyses and tests of graded \(\upmu\)PHB composite material systems;
* The developed graded \(\upmu\)PHB composite material met the design objective of achieving an absorption coefficient \(\geq\)0.50 and transmission loss \(\geq\)20 dB over a broad frequency range above 500 Hz. This design technology was used to build a 4-foot inner diameter, 9-inch axial length, and 2-inch thick acoustic liner to test on NASA-GRC's ANCF low-speed test bed at the Turbomachinery Lab at the University of Notre Dame. The TRL 3-4 test was successful. Conceptualization, B.K. and K.S. ; methodology, B.K. ; software, B.K. ; validation, B.K. ; formal analysis, B.K. ; investigation, B.K. ; resources, K.S. ; data curation, B.K. ; writing--original draft preparation, B.K. ; writing--review and editing, K.S. and B.K. ; visualization, B.K. and K.S. ; supervision, K.S. ; project administration, K.S. and B.K. ; funding acquisition, K.S. All authors have read and agreed to the published version of the manuscript. This research was funded by the NASA Glenn Research Center, Cleveland, Ohio, United States, contract numbers 80 NSSC20P1055 P00003 and 80 NSSC21P0133 under the Advanced Air Vehicle Program. Not Applicable. The original data presented in the study are openly available through the specified link below.