| Jiazhong Zhang1, Yan Liu2, Shicheng Fan1, Jingsheng Gao1 |
| 1) School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an 710049, P. R. China 2) School of Mechanical Engineering, Northwestern Polytechnical University, Xi’an 710072, P. R. China |
Abstract: From viewpoint of a dynamic system, the initial study shows that there exist intrinsic spatiotemporal structures in complex unsteady flows, and their topology properties have significant influences on the flow performance. However, due to the complexity of the unsteady flow, the quantitative description and analytical approach of the “intrinsic properties” of the unsteady flow have always been a difficult problem in fluid dynamics and there is no specified method. The results show that the flow separation is the main source of some singular phenomena in flow. Hence, it is important to study the intrinsic flow structures in unsteady separation flows and the criterion, and regulatability of the intrinsic flow structures.
Under such background, the Parabolic Lagrangian Coherent Structures(LCSs) with spatiotemporal properties will be developed to describe and analyze the complex flow structures in the shear layer induced by unsteady separation flows, and the complete intrinsic LCSs modes or basis in such unsteady separation flow including flow separation, vortex, and shear flow, will be given based on the Hyperbolic, Elliptical and Parabolic LCSs. Then, the fundamental spectrum composed of complete LCSs in unsteady separation flow is given, and the universal criterion will be presented following the topology changing of the spectrum in unsteady separation flow. Further, by studying the routes to induce the breaking or changing of original LCSs to others with some excitations, some fine structures, and properties in LCSs of complex unsteady separation flows, such as topology structures of energy transport, will be investigated with the LCSs method presented and Lobe dynamics, and can be used to control or regulate the complex unsteady separation flow in a new way. Finally, as a verification of the above discussions, some examples relevant to unsteady separation flows are presented to illustrate the feasibility and advantages of the analytic method based on dynamic system theories.
As the result, the methods based on complete intrinsic Lagrangian Coherent Structures could be given to describe and analyze the flow structures and dynamics of complex unsteady separation flows quantitatively, and further control the flow with one new and accurate method.