Towards numerical simulation of components of thermoacoustic devices with commercial CFD software: implementation of impedance boundary conditions and application to four different studies

摘要

Thermoacoustic engines promise to be a cost effective and reliable alternative to traditional Stirling engines, as the function of the piston is fulfilled by an acoustic wave. For the design and development of thermoacoustic devices, the one-dimensional thermoacoustic equations are commonly used. However, to further improve the performance of these devices a better understanding of the flow field and the acoustic losses inside of thermoacoustic components is required. To gain further insight, commercial Computational Fluid Dynamics (CFD) software is used in this thesis, as CFD allows revealing the entire flow field with all its physical quantities in the respective component of the thermoacoustic device. Reducing the numerical study to individual components of thermoacoustic devices is only possible with dedicated acoustic boundary conditions. As these boundary conditions are not yet readily available in commercial CFD packages, their implementation into ANSYS Fluent is included within the scope of this work. The boundary conditions are validated successfully in one- and two-dimensional cases against analytical solutions from the low-reduced frequency approximation. Furthermore, the analytical solutions are used in order to derive the optimal numerical parameters for thermoacoustic simulations and to give general rules of thumb for the spatial and time discretization. In a second step these parameters are applied to the simulations of four different thermoacoustic cases in order to show that CFD can lead to a better understanding of phenomena that are not incorporated in the one-dimensional thermoacoustic equations.The first investigated component is the thermal buffer tube. Its aim is to provide thermal insulation between the hot heat exchanger and the secondary ambient heat exchanger while transmitting the acoustic power out of the hot zone. However, due to the interaction of the acoustic wave with the temperature gradient, a two-dimensional steady mass flux called acoustic streaming occurs, which leads to undesired thermal losses. Using the implemented ideal heat exchanger boundary condition, the two-dimensional streaming field inside the thermal buffer tube is revealed and the influence of the wall properties on the streaming pattern is estimated. The temperature field resulting from the different streaming patterns as well as the repercussions on the acoustic properties are shown. The second investigated component is the U-bend that feeds back the acoustic wave in a traveling wave device. In the scope of reducing the size of the thermoacoustic devices, the bend becomes increasingly sharp, introducing additional losses and reflection as well as a velocity component in the cross-direction, which is expected to influence nearby components such as heat exchangers. The influence of the geometric parameters of the bend on the flow field are investigated in this thesis. The deviations from the analytical solution are revealed and for even sharper bends the onset of vortex generation is given. In general, this study shows the strength of numerical CFD simulations in thermoacoustics, as a large geometric parameter space could be investigated, leading to an in-depth understanding of the underlying flow phenomena. The subsequent study in this thesis makes the link between the one-dimensional thermoacoustic equations and the full time domain CFD, as it shows how the accuracy of the results from the one-dimensional equations can be increased when data from CFD is used. In this work the thermoacoustic functions, which incorporate the three-dimensional effects in the one-dimensional thermoacoustic equations, are calculated from CFD for a reduced model of a stacked screen regenerator, leading to more realistic values of the thermoacoustic functions. It is shown that the arrangement of the screens has an effect on the heat transfer inside the regenerator, while the viscous effects stay the same. This study shows that not only large components like bends and the thermal buffer tube can be successfully simulated with CFD, but so can small scale geometries like the ones inside the regenerator. In the last thermoacoustic study within this work, the entrance effects in a stacked screen regenerator are investigated for different geometric variations. The mean temperature profile due to the non-linear entrance effects and the heat pumped at the end of the stacked screen regenerator are calculated. Furthermore, a one-dimensional time dependent heat equation is used in order to predict the changes in mean temperature. In this one-dimensional time dependent heat transfer equation the thermal thermoacoustic function is used in order to estimate the heat transfer coefficient between the regenerator and the fluid. The results compare well with the CFD results. It can be concluded from the four studies conducted within this thesis that the simulation of components of thermoacoustic devices with commercial CFD is possible and that they will contribute to a better understanding of the flow phenomena inside of the respective components. This work paves the way towards the in-depth investigation of other components within the field of thermoacoustics using CFD.