Modeling energy conversion in a tortuous stack for thermoacostic applications

The stack represents the core of standing wave engines since inside it the thermal energy is converted into mechanical energy. Commonly stacks are realized with straight pores whose sections have regular shapes (e.g. circular, rectangular). In these cases the viscous and thermal interactions are described by well-known spatially averaged thermal and viscous functions. Instead, for a materials having tortuous pore, there is a lack in theoretical description of the thermoacoustic phenomenon. This paper deals with the performance of a thermoacoustic engine in which a tortuous porous material is used as stack. The spatially averaged thermal and viscous functions are obtained by classical models used to describe the sound propagation inside a porous material. In particular the Johnson–Champoux–Allard model is considered. It requires the knowledge of five parameters instead of the only hydraulic radius used to describe the standard stack having straight pores (e.g. circular, slit or square pores). The physical meaning of these parameters is explained starting from a straight circular pore and modifying, step by step, the shape of the pore until it becomes tortuous. The proposed functions have been included in the Rott theory and implemented in a numerical procedure. The achieved results are useful to analyse the thermoacoustic performance of a standing wave engine and to understand how the gain factor as well as the viscous and thermal losses inside the stack are affected by the tortuosity. A validation of this procedure is given by comparing the obtained results with ones given by DeltaEC software. This work can be useful to understand the applicability of tortuous porous materials, such as fibrous material as well as open-cell material, for standing wave thermoacoustic engines.