Numerical study on effects of computational domain length on flow field in standing wave thermoacoustic couple

Abstract

For the analysis of thermoacoustic (TA) devices, computational methods are commonly used. In the computational studies found in the literature, the flow domain has been modelled differently by different researchers. A common approach in modelling the flow domain is to truncate the computational domain around the stack, instead of modelling the whole resonator to save computational time. However, where to truncate the domain is not clear. In this study, we have investigated how the simulation results are affected by the computational domain length (ld) when the truncated domain approach is used. For this purpose, a standing wave TA couple which undergoes a refrigeration cycle was considered. The stack plate thickness was assumed to be zero and the simulations were performed for six different dimensionless domain length (ld/λ) varying between 0.029 and 0.180. Frequency and Mach number were taken as 100 Hz and 0.01, respectively, and kept constant for all the cases considered. The mean pressure and the pressure amplitude were taken as 10 kPa and 170 Pa, respectively (Drive ratio of 1.7%). Helium was considered as the working fluid. To assess the accuracy of the simulation results, the pressure distributions across the domain were compared with that of the standing wave. In addition to the pressure variation, the effects of the domain length on the phase delay of the pressure and velocity waves along the stack plate were also investigated. The results showed that with the increasing ld/λ ratio, the simulated pressure distribution compares better with the standing wave pressure distribution. With the lowest ld/λ ratio (0.029) considered, the difference between the amplitudes of the computed pressure distribution and theoretical standing wave pressure distribution was approximately 50 Pa. However, as ld/λ value increases, the simulation results approach to the theoretical standing wave pressure distribution better. The computational results obtained with ld/λ = 0.132 and 0.180, were almost identical with standing wave acoustic field. Hence, it was concluded that the domain length has a significant effect on the accuracy of the computational results when the truncated domain approach is used. It was also observed that for a given TA device and operating parameters, there is a minimum ld/λ value for obtaining reliable results.