A numerical investigation on stack sides thermo-gas dynamic in a large amplitude standing wave thermoacoustic engine

Abstract

The non-linear unsteady thermal field of a standing wave thermoacoustic engine (SWTE) was investigated using a finite volume computational code in a two-dimensional domain. The transient interaction between temperature and pressure fields and the level of non-linearity especially close to and out of stack plates are studied in 3 cases with different hot heat exchanger (HHX) temperatures of 700,500,450 K and ambient heat exchanger with constant temperature of 300 K. The results show regions with extremum temperatures far different from our understanding of the linear theory of thermoacoustic and the second law of thermodynamics. The gasdynamic field (pressure oscillations) close but out of the stack plates, approached its saturated single harmonic quasi-steady state in a short time (less than 0.3 s), but afterward the thermal field starts and keeps a non-sinusoidal temperature variation. Particle tracking through a Lagrangian analysis revealed that the difference of the thermodynamic cycles for particles that cross a particular region adjacent to the heat exchangers leads to these non-harmonic patterns. Furthermore, in case 1 with HHX temperature and drive ratio of 700 K and 18.2%, respectively, time-averaged temperature extremums with –23 K and +49 K differences (in comparison to AHX and HHX, respectively) were found in the final quasi-steady-state solution. The temperature differences become less considerable when the Drive ratio decreases. For the low temperature close to the AHX, Hybrid Eulerian-Lagrangian analysis, and temperature-entropy diagrams were used to explain this strange physics of generation of extremum temperatures. Thermo-acoustic cycles for ten gas parcels are analyzed to show that parcels in the resonator section visiting shortly the AHX (or HHX) region are responsible for this phenomenon. The thermodynamic cycle for different particles, including interactions of the gas-dynamic field with the thermal field, are analyzed with different tools to justify its strange physics. It is concluded that linear theories do not observe important phenomena in thermoacoustic engines with high-pressure amplitudes. A similar logic holds for the formation of a hot temperature region out of the HHX side of the stack.