Johnson-Champoux-Allard model in thermoacoustics

Johnson-Champoux-Allard (JCA) model is widely used in acoustics to study sound propagation inside porous material. It is mainly applied for predicting sound absorption of porous materials even if it is used in a variety of applications. In thermoacoustic engine the porous material is the core of the engine because the conversion from heat into mechanical (or acoustical) energy takes place inside it. Depending on the sound field, it is possible to distinguish two categories of the device: standing-wave or travelling-wave engine. The porous material used inside a standing-wave device is called stack whereas in the travelling-wave is called regenerator. The thermal and viscous interactions that occur between the solid and working fluid inside the stack/regenerator are studied by using the spatially averaged viscous and thermal functions f_v and f_k. It is known that, when porous materials have straight pores and regular pore shapes (e.g. circular, rectangular), the viscous and thermal functions have explicit expressions. In many papers, the need for a theoretical modelling of tortuous materials was highlighted as well as in DeltaEC software, where it can be simulated only in the case of regenerator (where the hydraulic radius is much less than the thermal penetration depth) by using a reduction factor to adjust the solid thermal conductance. In Dragonetti et al., the challenge to model tortuous materials has been met by using JCA model. The JCA model requires the knowledge of five parameters as opposed to only one parameter namely the hydraulic radius used to describe stack/regenerator having straight pores. Therefore, this circumstance allows designers to have more degrees of freedom in the choice of materials.