A gas-kinetic scheme (GKS) based on an unstructured grid is applied to simulate the evolution of the fluid motions in exponential variable cross-section resonators. The effects of the acoustic field intensity on the oscillatory pressure, velocity, temperature, and flow streaming structure were investigated numerically, and the model was validated. The results demonstrate that the geometry and driving strength are the main factors affecting the final performance of the system. For the quasi-linear and moderate non-linear cases in optimum exponential tube, the periodic generation, evolution, and shedding of vortices in flow fields are associated with the storage and release of energy, which is the transmission mode of the third type of direct current (DC) flow, and its driving mechanism is attributed to the asymmetrical pressure and temperature. Meanwhile, some new physical characteristics were also discovered for the highly non-linear case, e.g., the disorder and unsteadiness of the flow direction accomplished with turbulent flow streaming structures. The secondary flow is manifested as multiscale, irregular and unsteady vortices throughout the tube. The smallest increment of pressure and velocity amplitude occurs concurrently with the biggest increment of temperature amplitude. These evidences suggest that there is an optimal driving strength, even for a good configuration tube, with which the maximum efficiency can be obtained.
Shear deformation effect in non-linear analysis of composite beams of variable cross section
