The analytical and phenomenological sensitivity study of the flow-induced instabilities about a hinged circular cylinder with a splitter plate

Abstract

This thesis investigates the origin of flow-induced instabilities and their sensitivities in a flow over a rotationally flexible circular cylinder with a rigid splitter plate. A linear stability and sensitivity problem are formulated in the two-dimensional Eulerian frame by considering the geometric nonlinearity arising from the translations and rotational motion of an arbitrary geometry (cross-sectional structure's shape), which is not present in the stationary or purely translating stability methodology. This nonlinearity needs careful and consistent treatment in the linearised problem, particularly when considering the Eulerian frame of reference adopted in this study and not so widely considered. Considering the one degree of freedom problem of the rotationally flexible circular cylinder with a rigid splitter plate, two types of instabilities arising from the fluid-structure interaction are found. The first type of instability is the stationary symmetry-breaking mode, which was well reported in previous studies. This instability exhibits a strong correlation with the length of the recirculation zone. A detailed analysis of the instability mode and its sensitivity reveals the importance of the flow near the tip region of the plate for the generation and control of this instability mode. The second type is an oscillatory torsional flapping mode, which has not been well reported. This instability typically emerges when the length of the splitter plate is sufficiently long. Unlike the symmetry breaking mode, it is not so closely correlated with the length of the recirculation zone. However, the sensitivity analysis also reveals the crucial role played by the flow near the tip region in this instability. Finally, it is found that many physical features of this instability are reminiscent of those of the flapping (or flutter instability) observed in a flow over a flexible plate or a flag, suggesting that these instabilities share the same physical origin. The sensitivity analysis of both the symmetry breaking and flapping instability is also compared to the results obtained from a stationary circular cylinder fitted to a splitter plate of the same lengths. Physically meaningful analogies are noted between the sensitivity regions of the three instabilities.