Effects of Acoustic and Fluid Dynamic Interactions in Resonators
Authors:   , Antao Dion Savio , Farouk Bakhtier 
Published: July 2021

Thermoacoustic refrigeration systems have gained increased importance in cryogenic cooling technologies and improvements are needed to increase the efficiency and effectiveness of the current cryogenic refrigeration devices. These improvements in performance require a re-examination of the fundamental acoustic and fluid dynamic interactions in the acoustic resonators that comprise a thermoacoustic refrigerator. A comprehensive research program of the pulse tube thermoacoustic refrigerator (PTR) and arbitrarily shaped, circular cross-section acoustic resonators was undertaken to develop robust computational models to design and predict the transport processes in these systems. This effort was divided into three main focus areas: (a) studying the acoustic and fluid dynamic interactions in consonant and dissonant acoustic resonators, (b) experimentally investigating thermoacoustic refrigeration systems attaining cryogenic levels and (c) computationally studying the transport processes and energy conversion through fluid-solid interactions in thermoacoustic pulse tube refrigeration devices. To investigate acoustic-fluid dynamic interactions in resonators, a high fidelity computational fluid dynamic model was developed and used to simulate the flow, pressure and temperature fields generated in consonant cylindrical and dissonant conical resonators. Excitation of the acoustic resonators produced high-amplitude standing waves in the conical resonator. The generated peak acoustic overpressures exceeded the initial undisturbed pressure by two to three times. The harmonic response in the conical resonator system was observed to be dependent on the piston amplitude. The resultant strong acoustic streaming structures in the cone resonator highlighted its potential over a cylindrical resonator as an efficient mixer. Two pulse tube cryogenic refrigeration (PTR) devices driven by a linear motor (a pressure wave generator) were designed, fabricated and tested. The characterization of the systems over a wide range of operating conditions helped to better understand the factors that govern and affect the performance of the PTR. The operating frequency of the linear motor driving the PTR affected the systems performance the most. Other parameters that resulted in performance variations were the mean operating pressure, the pressure amplitude output from the linear motor, and the geometry of the inertance tube. The effect of the inertance tubes geometry was controlled by a single parameter labeled the inertance. External/ambient conditions affected the performance of the cryocoolers too. To prevent the influence of the ambient conditions on the performance, a vacuum chamber was fabricated to isolate the low temperature regions of the PTR from the variable ambient atmosphere. The experiments provided important information and guidelines for the simulation studies of the PTR that were carried out concurrently. A time-dependent high fidelity computational fluid dynamic model of the entire PTR system was developed to gain a better understanding of internal interactions between the refrigerant fluid and the porous heat-exchangers in its various components and to facilitate better design of PTR systems based on the knowledge gained. The compressible forms of the conservation of mass, momentum and energy equations are solved in the gas and porous media (appropriate estimation of fluid dynamics in heat-exchangers) regions. The heat transfer in the porous regions is governed by a thermal non-equilibrium heat transfer model that calculates a separate gas and solid temperature and accounts for heat transfer between the two. The numerical model was validated using both temporal and quasi-steady state results obtained from the experimental studies. The validated model was applied to study the effects of different operating parameters (frequency, pressure and geometry of the components) on the PTRs performance. The simulations revealed interesting steady-periodic flow patterns that develop in the pulse tube due to the fluctuations caused by the piston and the presence of the inertance tube. Similar to the experiments, the simulations provided important information that help guide the design of efficient PTR systems.