Efficient simulation and characterization of a head-on vortex ring collision

We simulate and analyze the head-on collision between vortex rings at $Re_{\Gamma_0} =$ 4,000. We utilize an adaptive, multi-resolution solver, based on the lattice Green's function, whose fidelity is established with integral metrics representing symmetries and discretization errors. Using the velocity gradient tensor and structural features of local streamlines, we characterize the evolution of the flow with a particular focus on its transition and turbulent decay. Transition is excited by the development of the elliptic instability, which grows during the mutual interaction of the rings as they expand radially at the collision plane. The development of antiparallel secondary vortex filaments along the circumference mediates the proliferation of small-scale turbulence. During turbulent decay, the partitioning of the velocity gradients approaches an equilibrium that is dominated by shearing and agrees well with previous results for forced isotropic turbulence. We also introduce new phase spaces for the velocity gradients that reflect the interplay between shearing and rigid rotation and highlight geometric features of local streamlines. In conjunction with our visualizations, these phase spaces suggest that, while the elliptic instability is the predominant mechanism driving the initial transition, its interplay with other mechanisms, particularly the Crow instability, becomes more important during turbulent decay. Our analysis suggests that the geometry-based phase space may be promising for identifying the effects of the elliptic instability and other mechanisms using the structure of local streamlines. Moving forward, characterizing the organization of these mechanisms within vortices and universal features of velocity gradients may aid in modeling the turbulent cascade.Comment: 34 pages, 11 figure

Extract and Characterize Hairpin Vortices in Turbulent Flows

Hairpin vortices are one of the most important vortical structures in turbulent flows. Extracting and characterizing hairpin vortices provides useful insight into many behaviors in turbulent flows. However, hairpin vortices have complex configurations and might be entangled with other vortices, making their extraction difficult. In this work, we introduce a framework to extract and separate hairpin vortices in shear driven turbulent flows for their study. Our method first extracts general vortical regions with a region-growing strategy based on certain vortex criteria (e.g., $\lambda_2$) and then separates those vortices with the help of progressive extraction of ($\lambda_2$) iso-surfaces in a top-down fashion. This leads to a hierarchical tree representing the spatial proximity and merging relation of vortices. After separating individual vortices, their shape and orientation information is extracted. Candidate hairpin vortices are identified based on their shape and orientation information as well as their physical characteristics. An interactive visualization system is developed to aid the exploration, classification, and analysis of hairpin vortices based on their geometric and physical attributes. We also present additional use cases of the proposed system for the analysis and study of general vortices in other types of flows.Comment: Accepted for presentation at IEEE VIS 2023. The paper will appear in IEEE Transactions on Visualization and Computer Graphic

Vortex detection and tracking in massively separated and turbulent flows

The vortex produced at the leading edge of the wing, known as the leading edge vortex (LEV), plays an important role in enhancing or destroying aerodynamic force, especially lift, upon its formation or shedding during the flapping flight of birds and insects. In this thesis, we integrate multiple new and traditional vortex identification approaches to visualize and track the LEV dynamics during its shedding process. The study is carried out using a 2D simulation of a flat plate undergoing a 45 degree pitch-up maneuver. The Eulerian 1 function and criterion are used along with the Lagrangian coherent structures (LCS) analyses including the finite-time Lyapunov exponent (FTLE), the geodesic LCS, and the Lagrangian-Averaged Vorticity Deviation (LAVD). Each of \h{these} Lagrangian methods \h{is} applied at the centers and boundaries of the vortices to detect the vortex dynamics. The techniques enable the tracking of identifiable features in the flow organization using the FTLE-saddles and -saddles. The FTLE-saddle traces have shown potential to identify the timing and location of vortex shedding, more precisely than by only studying the vortex cores as identified by Eulerian techniques. The traces and the shedding times of the FTLE-saddles on the LEV boundary matches well with the plate lift fluctuation, and indicates a consistent timing of LEV formation, growth, shedding. The formation number and vortex shedding mechanisms are compared in the thesis with the shedding time and location by the FTLE-saddle, which validates the result of the FTLE-saddles and provide explanations of vortex shedding in different aspects (vortex strength and flow dynamics). The techniques are applied to more cases involving vortex dominated flows to explore and expand their application in providing insight of flow physics. For a set of experimental two-component PIV data in the wake of a purely pitching trapezoidal panel, the Lagrangian analysis of FTLE-saddle tracking identifies and tracks the vortex breakdown location with relatively less user interaction and provide a more direct and consistent analysis. For a simulation of wall-bounded turbulence in a channel flow, tracking FTLE-saddles shows that the average structure convection speed exhibits a similar trend as a previously published result based on velocity and pressure correlations, giving validity to the method. When these Lagrangian techniques are applied in a study of the evolution of an isolated hairpin vortex, it shows the connection between primary and secondary hairpin heads of their circulation and position, and the contribution to the generation of the secondary hairpin by the flow characteristics at the channel wall. The current method of tracking vortices yields insight into the behavior of the vortices in all of the diverse flows presented, highlighting the breadth of its potential application

Potential impacts of advanced technologies on the ATC capacity of high-density terminal areas

Advanced technologies for airborne systems (automatic flight control, flight displays, navigation) and for ground ATC systems (digital communications, improved surveillance and tracking, automated decision-making) create the possibility of advanced ATC operations and procedures which can bring increased capacity for runway systems. A systematic analysis is carried out to identify certain such advanced ATC operations, and then to evaluate the potential benefits occurring over time at typical US high-density airports (Denver and Boston). The study is divided into three parts: (1) A Critical Examination of Factors Which Determine Operational Capacity of Runway Systems at Major Airports, is an intensive review of current US separation criteria and terminal area ATC operations. It identifies 11 new methods to increase the capacity of landings and takeoffs for runway systems; (2) Development of Risk Based Separation Criteria is the development of a rational structure for establishing reduced ATC separation criteria which meet a consistent Target Level of Safety using advanced technology and operational procedures; and (3) Estimation of Capacity Benefits from Advanced Terminal Area Operations - Denver and Boston, provides an estimate of the overall annual improvement in runway capacity which might be expected at Denver and Boston from using some of the advanced ATC procedures developed in Part 1. Whereas Boston achieved a substantial 37% increase, Denver only achieved a 4.7% increase in its overall annual capacity

Objective Momentum Barriers in Wall Turbulence

We use the recent frame-indifferent theory of diffusive momentum transport to identify internal barriers in wall-bounded turbulence. Formed by the invariant manifolds of the Laplacian of the velocity field, the barriers block the viscous part of the instantaneous momentum flux in the flow. We employ the level sets of single-trajectory Lagrangian diagnostic tools, the trajectory rotation average and trajectory stretching exponent, to approximate both vortical and internal wall-parallel momentum transport barrier (MTB) interfaces. These interfaces provide frame-indifferent alternatives to classic velocity-gradient-based vortices and boundaries between uniform momentum zones (UMZs). Indeed, we find that these elliptic manifold approximations and MTBs also significantly outperform standard vortices and UMZ interfaces in blocking diffusive momentum transport.Comment: 26 Pages, 14 Figur