Computational fluid dynamics simulation of a thermoacoustic refrigerator

The thermal interactions between the stack plates and their neighboring gas particles within the thermal penetration depth in a thermoacoustic resonator convert acoustic energy into heat energy in the process of standing thermoacoustic refrigeration systems. Few numerical approximations describe the flow behavior and energy flux density in standing devices, but almost no simulation results are available for the fully coupled continuity of Navier-Stokes and energy equations. Here, we report a two-dimensional computational fluid dynamics simulation of the nonlinear oscillating flow behavior in a helium-filled half-wavelength thermoacoustic refrigerator. The finite volume method is used, and the solid and gas domains are represented by large numbers of quadrilateral and triangular elements. The calculations assume a periodic structure to reduce the computational cost and apply the dynamic mesh technique to account for the adiabatically oscillating wall boundaries. The simulation uses an implicit time integration of the full unsteady compressible flow equations with a conjugate heat transfer algorithm (ANSYS FLUENT). A typical run involves 12,000 elements and a total simulation time of 5 s. Simulation results for drive ratios range Dr = 0.28%-2% are compared to both linear theory and a low Mach number model, and show good agreement with the experimental values. A maximum cooling effect of 3° is predicted at a non-dimensional wave number kx = π/4, measured from the resonator rigid end. This simulation provides an interesting tool for understanding the bulk and microstructural flow behavior and the associated nonlinear acoustic streaming in thermoacoustic refrigerators, by characterizing and optimizing their performance and building computational fluid dynamics models of thermoacoustic devices.