Non-dimensional parameters controlling the behaviour of oscillaltory flows around stacks of parallel plates in thermoacoustic devices

In thermoacoustic engines and coolers, a compressible fluid undergoes an oscillatory motion around a solid body to facilitate an energy transfer between heat and acoustic waves. The solid body often takes a form of a stack of parallel plates. The oscillatory flow leads to interesting vortex shedding processes at the end of stack, which impacts the performance of the thermoacoustic device due to possible modification of heat transfer processes. There have been many works, experimental and numerical, dedicated to studies of the fluid flow around stacks, both for dimensions representative for realistic devices and using scaled-up arrangements, to obtain a better insight into the flow processes. Depending on the plate thickness, plate spacing and the fluid displacement amplitude, a series of distinct vortex shedding flow patterns are identified. These are either related to a breakup of thin elongated shear layers, or von Karman-like shedding (typical for bluff bodies in steady flows). However, the broad parameter space and the flow physics, which is still not very well understood, make the comparisons between various configurations and flow conditions difficult. Subsequently it is difficult to devise appropriate criteria for the design of stacks. The present work is an effort to find a unified approach to studying the oscillatory flow phenomena around stacks. Firstly, the Navier-Stokes equation is normalized for this particular type of flow, and a group of potential controlling parameters is identified. Secondly, based on the data available from existing literature and our own experiments, the complex phenomena of the oscillatory flow around a stack are discussed in some detail using the likely non-dimensional controlling parameters. Conclusions and suggestions for future work are drawn.