Thermal behaviour of porous skeletons under oscillatory flow

This study develops a comprehensive methodology for estimating the dynamic thermal behaviour of the solid skeleton in porous materials from analytical, numerical and experimental approaches. Thermal exchange is driven by oscillating fluid flows within the porous material, as seen in acoustic and thermoacoustic applications. The limitations of the commonly assumed isothermal behaviour of the solid skeleton are addressed, emphasizing the impact of the finite thermal capacity of the solid skeleton on its overall dynamic effective volumetric heat capacity. The semi-phenomenological models of Champoux–Allard (CA) and Champoux–Allard–Lafarge (CAL) are used to predict the dynamic thermal behaviour of the solid skeleton of porous materials. Results indicate that while both models effectively predict the frequency-dependent and complex heat capacity ratio, the CAL model outperforms the CA model as geometric complexity increases, such as for configurations encountered in longitudinal pin arrays. Three thermal transport parameters are introduced for the solid geometry: the solid volume fraction φs, the solid thermal characteristic length Λs′ and the solid static thermal permeability k0,s′. A methodology accounting for the calculation of the solid thermal characteristic length Λs′ and the solid volume fraction φs is presented, along with a Poisson problem formulation to estimate the static thermal permeability of the solid phase k0,s′. Numerical simulations for three kinds of microstructural classes of porous media are presented: Three-dimensional cellular structures (foams), tetragonal pin arrays (structured fibrous media), and granular materials. Numerical data reveal that there exist a logarithmic relationship between the thermal permeabilities ratio k0′/k0,s′ and the volume fractions ratio φ/φs. A measurement methodology of the dynamic heat capacity ratio is also presented, addressing intrinsic challenges associated with these measurements.