Acoustics of permeable media with active internal heat sources

Acoustics of permeable media with active internal heat sources is investigated in this paper. A macroscopic non-homogeneous Helmholtz equation, established by using the two-scale asymptotic method of homogenization, is found to describe the propagation and emission of sound waves in the studied permeable media. We study two classes of permeable materials in which external energy is injected. In one of them, the heat sources act in the material solid skeleton, while in the other class of materials they act in the pore fluid network, with the generalization to the case of heat sources acting in both constituents also provided. The derived macroscopic description shows that the general properties of the effective parameters of the fluid equivalent to the permeable medium are not altered by the internal heat sources. However, these sources determine the non-homogeneous term in the upscaled Helmholtz equation. Through theoretical analyses and analytical models, the key characteristics of acoustic wave propagation and emission in the studied media are illustrated. Additionally, a generalized impedance matching condition, enabling the control of the active apparent sound reflection and absorption coefficients of rigidly backed finite layers of the materials, is first introduced. The results of this work provide fundamental insights on the role of active internal heat sources on the linear long-wavelength acoustics of permeable media and lay the foundation for the development of active thermoacoustic porous materials for acoustic wave control applications.