Description
The objective of the proposed work is to develop a network-based framework to control vortex dominated fluid flows. To achieve the goals outlined in this project, we will perform a computational study using network analysis and graph theory to uncover connectivity among vortices and among coherent fluid flow structures. With the connectivity of flow structures revealed, we will examine both local and global interactions, such as how one structure influences others. We will then develop novel network-based fluid flow control techniques, extending graph-theoretic control strategies to our models. In the proposed study, three main modeling approaches are considered: (1) vortex interaction models, (2) modal interaction models, and (3) recurrent network models; as well as their hybrid models. These models will provide a path to formulate graph theoretic multi-agent based feedback control techniques which will identify driver and follower nodes (flow structures). Modeling and control efforts will be computationally verified in three broadly categorized incompressible flow problems of (1) discrete point vortex dynamics, (2) two-dimensional low-Reynolds number wake flows, and (3) three-dimensional moderate/high-Reynolds number wake flows. Sparsified-dynamics and reduced-order modeling techniques will play an important role in scaling algorithms to handle the big data associated with higher Reynolds number problems. Advanced flow control using network analyses will enable practical engineering goals including lift increase, drag reduction, and improved robustness, which are critical to improve performance and efficiency in various aerospace applications. We anticipate that the use of network analysis will be transformative in how we examine and manipulate nonlinear interactions and energy transfers in complex fluid flows.