A method to calculate finite-time Lyapunov exponents for inertial particles in incompressible flows

Garaboa-Paz, Daniel; Pérez‐Muñuzuri, V.

doi:10.5194/npg-22-571-2015

Cited by 13 publications

(9 citation statements)

References 25 publications

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“…Clustering of inertial particles has also been investigated using FTLE for compressible flows [39]. Modifications to the standard FTLE calculation have also been proposed for inertial particle calculations [19].…”

Section: B Previous Work Investigating Inertial Particles With Dynammentioning

confidence: 99%

Lagrangian coherent structures and inertial particle dynamics

2016

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In this work we investigate the dynamics of inertial particles using finite-time Lyapunov exponents (FTLE). In particular, we characterize the attractor and repeller structures underlying preferential concentration of inertial particles in terms of FTLE fields of the underlying carrier fluid. Inertial particles that are heavier than the ambient fluid (aerosols) attract onto ridges of the negative-time fluid FTLE. This negative-time FTLE ridge becomes a repeller for particles that are lighter than the carrier fluid (bubbles). We also examine the inertial FTLE (iFTLE) determined by the trajectories of inertial particles evolved using the Maxey-Riley equations with nonzero Stokes number and density ratio. Finally, we explore the low-pass filtering effect of Stokes number. These ideas are demonstrated on two-dimensional numerical simulations of the unsteady double-gyre flow.

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Section: B Previous Work Investigating Inertial Particles With Dynammentioning

confidence: 99%

Lagrangian coherent structures and inertial particle dynamics

2016

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“…We specify an unsteady velocity field v that has seen extensive use as a testbed for LCS analysis [142,143,109,144,1,145,38,146,102,77,147,78,79,148,76,88]: the double gyre flow as introduced by Shadden et al [75]. The velocity v = (v 1 , v 2 ) takes the form where the function h is defined by…”

Section: Passive Scalar Advectionmentioning

confidence: 99%

Generalized Lagrangian coherent structures

Balasuriya

Ouellette

Rypina

2018

Physica D: Nonlinear Phenomena

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The notion of a Lagrangian Coherent Structure (LCS) is by now well established as a way to capture transient coherent transport dynamics in unsteady and aperiodic fluid flows that are known over finite time. We show that the concept of an LCS can be generalized to capture coherence in other quantities of interest that are transported by, but not fully locked to, the fluid. Such quantities include those with dynamic, biological, chemical, or thermodynamic relevance, such as temperature, pollutant concentration, vorticity, kinetic energy, plankton density, and so on. We provide a conceptual framework for identifying the Generalized Lagrangian Coherent Structures (GLCSs) associated with such evolving quantities. We show how LCSs can be seen as a special case within this framework, and provide an overarching discussion of various methods for identifying LCSs. The utility of this more general viewpoint is highlighted through a variety of examples. We also show that although LCSs approximate GLCSs in certain limiting situations under restrictive assumptions on how the velocity field affects the additional quantities of interest, LCSs are not in general sufficient to describe their coherent transport.

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“…For inertial particles in unsteady flow, separation is frequently studied with the finite-time Lyapunov exponent [Sha05, HY00], which measures the separation due to a small perturbation of the seed position [PD09,SH09]. Garaboa-Paz and Pérez-Muñuzuri [GPPMn15] studied separation in the full phase space, and Sagristà et al [SJJ * 17] viewed the separation in the position and velocity subspace using multi-dimensional stacking. They studied n-body problems and did not observe the influence of the variation of the particle size, which was studied by Günther and Theisel [GT15], keeping the seed velocity constant.…”

Section: Related Work In Visualizationmentioning

confidence: 99%

Visualizing the Phase Space of Heterogeneous Inertial Particles in 2D Flows

Rojo

Groß

Günther

2018

Computer Graphics Forum

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µm300 µm diameter dp y t min max density x y t x y r x y |v| Figure 1: Our coordinated visualizations of inertial particle motion give insights into size-dependent separation, clustering and attraction. The left image shows the individual particle trajectories of a continuous range of differently-sized particles in space-time, which can become cluttered. Thus, the second visualization displays the trajectory density, which reveals clustering regions and easier conveys an impression of the general motion. The trajectories of differently-sized particles are clearly separated in the third view. The motion of inertial particles is governed by a size-dependent attracting manifold. The last view focuses on a selection of trajectories and displays for each the distance to the attracting manifold by connecting the trajectories to the closest curve on the manifold. As shown here, heavy particles generally converge slower due to their momentum and inertia. Here, in the BORROMEAN flow with dp = 100 µm (•), dp = 200 µm (•) and dp = 300 µm (•). AbstractIn many scientific disciplines, the motion of finite-sized objects in fluid flows plays an important role, such as in brownout engineering, sediment transport, oceanology or meteorology. These finite-sized objects are called inertial particles and, in contrast to traditional tracer particles, their motion depends on their current position, their own particle velocity, the time and their size. Thus, the visualization of their motion becomes a high-dimensional problem that entails computational and perceptual challenges. So far, no visualization explored and visualized the particle trajectories under variation of all seeding parameters. In this paper, we propose three coordinated views that visualize the different aspects of the high-dimensional space in which the particles live. We visualize the evolution of particles over time, showing that particles travel different distances in the same time, depending on their size. The second view provides a clear illustration of the trajectories of different particle sizes and allows the user to easily identify differences due to particle size. Finally, we embed the trajectories in the space-velocity domain and visualize their distance to an attracting manifold using ribbons. In all views, we support interactive linking and brushing, and provide abstraction through density volumes that are shown by direct volume rendering and isosurface slabs. Using our method, users gain deeper insights into the dynamics of inertial particles in 2D fluids, including size-dependent separation, preferential clustering and attraction. We demonstrate the effectiveness of our method in multiple steady and unsteady 2D flows.

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A method to calculate finite-time Lyapunov exponents for inertial particles in incompressible flows

Cited by 13 publications

References 25 publications

Lagrangian coherent structures and inertial particle dynamics

Lagrangian coherent structures and inertial particle dynamics

Generalized Lagrangian coherent structures

Visualizing the Phase Space of Heterogeneous Inertial Particles in 2D Flows

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