Three-dimensional, time-varying flow has been a significant research subject for decades. A long-term goal of the ongoing research in the turbulence community has been to develop an improved understanding of the dynamically-evolving vortex structure and organization in turbulent boundary layers. Such improved understanding requires the development and validation of accurate and robust numerical models of flow under complex conditions, and has the potential to enable the development of effective strategies to predict and control vortex generation and organization, which has influential practical impact in many industries.
The focus of this work is on understanding and visualizing the dynamics of three-dimensional flows. The primary objective is to study the relationship of various attributes in the flows, to relate multiple variables to the structure of turbulence and to correlate the evolution of vortex structures among all vortices' lifecycles. While many methods have been proposed for defining and visualizing vortices in 3D flow data, little attention has been devoted to the problem of robustly ensuring that the identified regions accurately correspond to individual vortex structures, as opposed to containing entangled clusters of closely spaced and potentially intertwined vortices. The success of efforts to effectively analyze unsteady flows at the level of individual structures critically depends on this ability.
This dissertation presents innovative methods for achieving the primary research objective of overcoming the limitations of current methods for vortex definition and feature extraction in 3D turbulent flows. Multi-variate visualization of 3D turbulent flow data provides efficient schemes for effectively conveying multiple scalar and vector quantities and their relationships within identified target regions. The LIC glyph approach allows the detailed characteristics of important scalar variables such as vorticity magnitude, swirl strength and velocity magnitude, as well as vector properties such as direction and orientation, to be understood both individually and in relationship to each other throughout a complex flow. This contribution is critical in the feature identification process.
Two novel approaches are proposed for pursuing our efforts to achieve a robust segmentation of a 3D turbulent flow dataset into individual vortex regions. The first approach is based on the intuition that while any single scalar measure may not provide enough information, by itself, to robustly define an appropriate segmentation of a composite region into individual vortices, it is possible that better results can be achieved by considering multiple, non-redundant, local scalar and vector measures in combination. A careful mathematical analysis of the interrelationships between swirl and vorticity is derived to show how these measures can be used together to resolve ambiguities in structure identification that cannot be as successfully determined using either measure alone. In a second, different approach to the problem, we introduce a novel method for automatically detecting potential compound structures in an initial segmentation of a flow and coherently partitioning the constituent components. This method is based on the combined use of vortex core lines and hierarchical region identification. The datasets used in this research were obtained from a direct numerical simulation of a turbulent channel flow by Zandonade and Moser.
Finally, we have applied our segmentation and tracking schemes to a time-varying experimentally acquired flow dataset to effectively visualize the dynamic and irregular evolution of a three-dimensional vortex ring. The vortex structures in this data consist of a tilted primary vortex ring and two opposite vertical streams, which branch irregularly with the perturbed fluids. A full analysis and visualization approach successfully identifies each individual vortex and consistently highlights significant structures, corresponding to well-correlated flow features, over time.
In summary, this dissertation introduces approaches to effectively depict the physical attributes, distribution, orientation and strength of vortex structures within both numerically simulated and experimentally acquired turbulent flow data. Investigations of the relationships between multiple variables in the data have assisted the development of two novel algorithms for the identification and segmentation of individual vortices within compound regions. Finally, through the application of our feature tracking methods to time-varying vortex rings, we have successfully demonstrated the ability of our methods to achieve reasonable segmentation results across a wide range of input data types, and to enable tracking coherent structures over time.
University of Minnesota Ph.D. dissertation. May 2011. Major: Computer science. Advisor:Victoria Interrante. 1 computer file (PDF); xvii, 164 pages, appendix p. 159-164.
Effectively identifying and segmenting individual vortices in 3D turbulent flow..
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