Model for Frequency Dependence of Thermal Permeability in Order to Quantify the Effects of Thermal Exchange on Wave Propagation in Multi Layered Porous Medium

Abstract

The ability to quantify and predict the energy absorption/transmission characteristics of multi-layered porous medium is imperative if one is involved in the automotive, launch vehicle, commercial aircraft, architectural acoustics, petroleum exploration, or even in modeling human tissue. A case in point, the first four aforementioned fields rely on effective Noise and Vibration (NV) development for their commercial success. NV development requires the setting of NV targets at different system levels. The targets are then translated to Transmission Loss (TL), Insertion Loss (IL), and absorption (Alpha) performance for the multi-layered porous materials being utilized. Thus, it behooves to have a thorough understanding of the physics behind the energy dissipating mechanism of the material that entails the effects of the fluid meandering through the pores of the material and its interaction with the structural skeleton. In this section of the project the focus is on the thermal interchange that occurs within the porous medium. Via the acoustic modeling at the micro/macro level it is shown how this thermal exchange affects the acoustic compressibility within the porous material. In order to obtain a comprehensive approach the ensuing acoustic modeling includes the effects due to relaxation process, thus bulk viscosity and instantaneous entropy functions (effects due to vibration of diatomic molecules of air) are incorporated into the equation. The instantaneous entropy functions are explained by means of the Boltzmann's distribution, partition function, and quantum states. The concept of thermal length and its connection to thermal permeability is clarified. Lastly, the results for TL calculations employing the aforementioned thermal exchange into the Transfer Matrix Method with finite size How to cite this paper: Teagle-Hernandez, A., Ohtmer, O. and Nguyen, D. (2019) Model for Frequency Dependence of Thermal Permeability in Order to Quantify the Effects of Thermal Exchange on Wave Propagation in Multi Layered Porous Medium.

Mathematical Modeling of Porous Medium for Sound Absorption Simulations II: Wave Propagation and Interface Conditions

“…In [2] the concepts of tortuosity, viscous length, and viscous permeability are explained. The thermal interchange is described in Teagle, et al [3]. In [3], the mathematical description of the thermal energy dissipated by the thermal boundary layer is explained along with the relaxation process.…”

“…The thermal interchange is described in Teagle, et al [3]. In [3], the mathematical description of the thermal energy dissipated by the thermal boundary layer is explained along with the relaxation process. This thermal exchange changes the acoustic bulk modulus of the porous medium and thus the speed of sound inside the porous layer.…”