Acoustic streaming and its modeling in a traveling-wave thermoacoustic heat engine

Abstract

variable-area resonator with the hot and ambient heat-exchangers (HHX, AHX) and the regenerator (REG) located at one end enclosed in a coaxial annular tube. Heat-transfer in the heat-exchangers is modeled via source terms which drive the local gas temperature towards the imposed temperature. Turning on the sources terms generates a finite-amplitude perturbation that is amplified until a limit cycle is reached. Simulations have been carried out for HHX temperatures in the range 460K ‐ 500K and an AHX temperature of 300K. Acoustic nonlinearities are detectable from the early stages of operation in the form of streaming. Complex system-wide streaming flow patterns rapidly develop and control the operation of the device in the nonlinear stages. A solution decomposition based on sharp-spectral filtering is adopted to extract the wave-induced Reynolds stresses and energy fluxes at the limit cycle. The key processes involved are traveling-wave streaming in the feedback inertance, periodic vortex roll-up around the edges of the annular tube and near-wall acoustic shear-stresses in the variable-area sections of the resonator. The first drives the mean advection of hot fluid away from the HX/REG (Gedeon streaming), causing heat leakage. The latter is contained by introducing an AHX2 (creating a thermal buffer tube, or TBT) resulting in the saturation of acoustic energy growth in the system. A simplified numerical model is adopted todirectly simulate acoustic streaming as an axially symmetric incompressible flow driven by the acoustic wave-induced stresses. Key features such as the intensity of Gedeon streaming are correctly predicted. The evaluation of the nonlinear energy fluxes reveals that the efficiency of the device deteriorates with the drive ratio and that the acoustic power in the TBT is balanced primarily by the mean advection and thermoacoustic heat transport. Thermoacoustic Stirling heat engines (TASHE) are devices that can convert heat into acoustic power with very high efficiencies. This potential is due to the absence of moving parts and relative simplicity of the components. This results in low manufacturing and maintenance costs making these systems an attractive alternative for clean and effective energy generation. The core energy conversion process occurs in the regenerator ‐ a porous metallic block, placed between a hot and a cold heat-exchanger, sustaining a mean temperature gradient in the axial direction. Acoustic waves propagating through it (with the right phase) can be amplified via a thermodynamic process resembling a Stirling cycle. Most designs explored up to the mid 1980’s were based on acoustic standing waves and had efficiencies typically less than 5%. A significant breakthrough was made by Ceperley (1979) 5 who showed that traveling-waves can extract acoustic energy more efficiently, leading to the concept of traveling-wave TASHE, currently used today 2 . In this configuration the generated acoustic power is in part resupplied to the regenerator via some form of feedback loop and in part directed towards a resonator for energy extraction. This design is the focus of the present study. Improving the technology behind TASHEs is still of particular interest in the last decade with research efforts being made worldwide (see Garrett (2004) 6 for a review). A recent breakthrough, for example, has been made by Tijiani and co-workers 16 who designed a traveling-wave TASHE achieving a remarkable overall efficiency equal to 49% of the Carnot limit. Current design choices for TASHEs, however, are not informed by an accurate description of the underlying fluid mechanics. In particular state-of-the-art prediction capabilities and technological design can significantly benefit from a direct modeling of the nonlinear, system-wide, three-dimensional processes limiting the efficiencies of such devices.