Using Lagrangian Coherent Structures to Analyze Fluid Flows

Abstract

In computational sciences several tools are being employed to study the nature of physical systems. In case of fluid flow post processing techniques like streamlines, vectors and contours etc are in use. These techniques help in understanding the nature of flow and its properties. Each of these post processing techniques mentioned are based on Eulerian methods and have certain inherent deficiencies pertaining to the amount of information they can convey about certain aspects of fluid flow. Lagrangian Coherent Structures (LCS) on the other hand use Lagrangian data for analysis purposes. LCS are generated used Finite Time Lyapunov exponent fields which in turn depict the rate of expansion or contraction of the trajectories around a certain point. LCS act as the transport barriers across which there is approximately zero mass flux. This property means that LCS can be applied to problems related to separation and reattachment in fluid flow and find virtual boundaries inside flows. Present work is concerned with application of LCS to HVAC systems and LP turbines. In HVAC systems LCS can be used to identify the virtual boundaries in fluid flow. This helps in indication of regions where mixing of particles occurs and also where particles are stagnated. This type of study is useful in analyzing air flows in locations like data centers and operation theaters. The outcome of this study can be used to improve the energy efficiency as well as patient or server well being. The second application of LCS is analysis of transition in a LP turbine. Designers of modern high altitude gas turbines are faced with the challenge of reducing weight for improvement in efficiency. An obvious solution is reduction in the number of low pressure turbine blades. This however entails increase in aerodynamic loading on remaining blades. High altitude operation also means that the gas turbine is operating at a low Reynolds Number regime. These two conditions result in transition and separation occurring on the suction side of the turbine blades. In some situations a separation bubble is formed on the suction surface. A study that predicts the process of transition and separation is very important as even small pressure disturbances upstream of the blade can have an effect on the overall efficiency of the system. Different techniques of feature detections are used to simulate the process. Most widely used are the Eulerian techniques such as the ones involving modeling using RANS, DNS and LES. Both the DNS and LES techniques are widely used for research purposes but they do 8 not have many practical usages due to certain constraints involved. RANS on the other hand is more practical and models have been developed to simulate transition using these. Apart from these Eulerian techniques flow features can also be investigated using Lagrangian methods. A Lagrangian Coherent Structures (LCS) technique has been used in current thesis to simulate transition and separation on a low Reynolds's number T106A LP turbine blade. First a code is developed to generate LCS using FTLE field. This code is validated using the benchmarking double gyre problem. A CFD simulation has been conducted using RANS and its results are used to generate the LCS. These LCS are then studied to identify transition patterns and vortex shedding downstream of the turbine blade.