Characterization of Two-phase Turbulent Flows

Turbulent dispersed flows manifest in a wide variety of industrial and environmental settings. To accurately predict and control these dynamical systems, improved models, grounded in physical insights, are imperative. This thesis is an endeavour to address this need. It consolidates the findings reported in three distinct scientific manuscripts, written by the thesis author in collaboration with researchers from the Technical University of Denmark, the Otto Von Guericke University in Magdeburg and the University of Illinois at Urbana-Champaign. While the manuscripts feature the introduction of a Lagrangian formulation of the Proper Orthogonal Decomposition (POD), and demonstrate the statistical method as a tool for obtaining novel physical insights, this thesis contains additional details, that have otherwise been omitted. Moreover, it offers potential applications and outlines future studies required for further advancements.

A significant part of the thesis is dedicated to the application of POD for the analysis of turbulent flows laden with inertial particles of various densities. The application is particularly relevant for non-stationary flows, where the limitations of the more commonly applied Fourier transform are pronounced. Indeed, by examining the POD modes extracted for both the carrier and dispersed phases in particle-laden decaying homogeneous isotropic turbulence, it is evident that Fourier modes do not optimally represent the temporal dynamics of either phase. In the context of response functions, which represent the spectral relation between the two phases, the limitations are further exemplified, whereas the efficacy of the Lagrangian formulation of POD is demonstrated. These observations are discussed at length in the journal publications [P1] and [P2] (refer to the Appendix for the full length articles). Adding to this, the Lagrangian POD is here proposed as a tool for denoising particle trajectories measured in experiments. Applied to a synthetic data set, where Gaussian noise is added to simulated particle trajectories, the method is shown as a viable approach to attenuating noise, and a heuristic for the procedure is provided. Finally, in the context of particle-laden turbulence, Lagrangian POD is proposed as a method for analyzing particle separation, with potential applications to the modal characterization of cluster dynamics.

Where the analysis outlined above largely focuses on the global particle dynamics, the second main application of Lagrangian POD, studied in this thesis, centers on more localized dynamics. Specifically, the interface-oscillations of droplets immersed in turbulence are decomposed to reveal both spatially and temporally dependent features. The temporal features are shown to closely resemble those of the surrounding fluid (see full length article [P4] in the Appendix), indicating that the fluid dynamics may be inferred from the droplet dynamics, and vice versa. Moreover, by studying the temporal POD expansion coefficients, patterns of the statistical evolution of the droplet shape are deduced. Conversely, the spatial decomposition reveals a symmetry between POD modes and spherical harmonic functions, which have historically been applied for the analysis of droplet oscillations.

The case studies examined in the present work serve as a reference point for future investigations into the intricacies of (turbulent) dispersed flows. The author of this thesis is hopeful that the methods outlined herein will play a contributing role in extracting deeper insights in subsequent studies.