Analysis of Stable and Unstable Manifolds in Fluid Flows Using Lagrangian Coherent Structures

Abstract

In dynamical systems, regions containing similar dynamics can be identified and their boundaries visualized using Lagrangian Coherent Structures (LCS). In fluid flows, LCS can be approximated as virtual boundaries dictating the structure of flow. Current study makes use of LCS to simulate two cases for fluid flows; flow features around the turbine blade and a ventilation system. Detection of LCS will present a useful technique of providing an insight into coherent structures on the suction surface and vortex formation downstream of the blade. The performance of the low pressure turbine is significantly affected by the laminar separation bubble that forms on the suction surface and it is hence very important to capture the details of the associated flow features. This information can in turn help in the examination of procedures developed for their control. A T106 LP turbine blade is selected for the purpose of present study. A numerical simulation is performed using Transition SST model. The results of the computational study are validated using experimental and other computational studies. Information from the CFD study is then used to generate LCS. Different flow features are indentified and their evolution with time is observed. LCS help describe the process of vortex formation and are related to the flow topology. LCS associated with the separation bubble are discussed. A second case of ventilation inside a two dimensional domain is considered. LCS are used to depict the effect of ventilation systems with changing inlet air velocity angles. Study of ventilation using LCS show the patterns of fluid flow inside the domain and can be useful in design of HVAC systems by identifying real time location of virtual walls inside the domain.