Iacobello, Giovanni

Kuerten, J. G. M.

Ridolfi, Luca

Scarsoglio, Stefania

English

Giovanni Iacobello

Stefania Scarsoglio

J. G. M. Kuerten

Luca Ridolfi

PORTO@iris (Publications Open Repository TOrino - Politecnico di Torino)

04 August 2020POLITECNICO DI TORINORepository ISTITUZIONALEComplex network characterization of Lagrangian mixing in a turbulent channel flow / Iacobello, Giovanni; Scarsoglio,Stefania; Kuerten, J. G. M.; Ridolfi, Luca. - ELETTRONICO. - 9(2019). ((Intervento presentato al convegno 9th EuropeanPostgraduate Fluid Dynamics Conference tenutosi a Ilmenau (Germany) nel July, 16-19, 2019.OriginalComplex network characterization of Lagrangian mixing in a turbulent channel flowPublisher:PublishedDOI:Terms of use:openAccessPublisher copyright(Article begins on next page)This article is made available under terms and conditions as specified in the  corresponding bibliographic description inthe repositoryAvailability:This version is available at: 11583/2748072 since: 2019-08-20T13:19:18ZEuropean Mechanics SocietyEPFDC 2019, July 16th - 19th, Ilmenau, GermanyComplex network characterization of Lagrangianmixing in a turbulent channel flowGiovanni Iacobello1, Stefania Scarsoglio1, Hans Kuerten2 and Luca Ridolfi31Department of Mechanical and Aerospace Engineering, Politecnico di Torino, Turin, Italy2Department of Mechanical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands3Department of Environmental, Land and Infrastructure Engineering, Politecnico di Torino, Turin, ItalyKeywords: Turbulence mixing, Lagrangian analysis, Complex networksAbstractTurbulent mixing plays a fundamental role in several natural phenomena and practical ap-plications, due to its effectiveness to enhance transport [1, 2]. Here we propose a complexnetwork-based approach to study turbulent mixing from a Lagrangian viewpoint [3]. Amongdifferent research areas in which network science has been exploited, turbulence represents anemerging field of application, so that complex networks offer a novel perspective on the turbu-lence dynamics. In our work, a direct numerical simulation (DNS) of a fully-developed turbu-lent channel flow was employed at a (frictional) Reynolds number Reτ = Huτ/ν = 950, whereuτ is the friction velocity, H is the half-channel height and ν is the kinematic viscosity [4]. Aset of 100×100 fluid particles was uniformly released at the initial time in the plane (y+,z+) atx+ = 0 (e.g., see figure 1(a)), where the streamwise, wall-normal and spanwise coordinates are(x+,y+,z+), respectively. Particles were grouped into Ny = 100 wall-normal levels, and parti-cle positions were tracked for a total time T = 15200ν/u2τ . In order to build the network, eachnode was associated with a wall-normal level, while connections between particle pairs wereestablished based on their spatial proximity (see figure 1). Specifically, two particles are con-nected if their Euclidean distance (at each time) is sufficiently small; the proximity boundary isrepresented by an ellipsoid with semi-axis values that are proportional to the average pairwisedistance between all particles (see figure 1(b)). In this way, since the pairwise distance betweenparticles depends on time, we obtain a time-varying network made up of Nt = T/∆t = 3200graphs. Specifically, each node in the graphs comprises a set of Nz = 100 particles, and eachlink is weighted to quantify the interaction strength between particle pairs in each node.Nz particlesx+z+y+(x = 0; t0)t1y+z+Ny levelst2Mean flowdirection(a) (b)particletrajectoryFigure 1: Sketch of the set-up, in which particles and connections are depicted as colouredspheres and black lines, respectively [3]. (a) Particles initially released from a uni-formly spaced grid at x+ = 0; (b) particle connections at different times, where theellipsoids represent the proximity boundaries of each particle.The structure of the resulting time-varying network captures non-trivial insights into the effectsof turbulence on particle dynamics, as it emerges from the different patterns in the weight ma-trices,Wi, j (see figure 2). More in detail, network metrics are able to reveal the extent to whichEPFDC 2019, July 16th - 19th, Ilmenau, Germanyboth the mean flow advection and wall-normal turbulent mixing affect the particle dispersion.By doing so, we extract two time scales corresponding to the dominant advection regime, i.e.t+ < 400 (see figure 2(b-c)), and the asymptotic Taylor’s regime of dominant vertical mixing,i.e. t+ > 5000 (see figure 2(e-f)) [3]. Moreover, through the network analysis it is possible tocharacterize the effect of the mean shear on particle dispersion, as well as the appearance of ex-treme events (i.e., mixing between particles initially far in space) [3]. Based on present findings,Lagrangian-based networks can pave the way for a systematic network-based investigation ofturbulent mixing, thus extending the level of information of classical statistics.Nodest +=2327.5Nodest +=15195.5Nodest +=5201.25Nodest +=0Nodest +=190 t +=427.5Nodes(a) (c)(b)(e)(d) (f)Wi,jWi,jWi,jWi,jWi,jWi,jFigure 2: Representation of the time-varying network as weight matrices, Wi, j, for node pairs(i, j). Colorbars indicate the weight intensity of each link in the networks [3].References[1] Dimotakis, P.E. (2005) Turbulent mixing. Annual Review of Fluid Mechanics, 37, 329-356.[2] Sreenivasan, K.R., and Schumacher, J. (2010) Lagrangian views on turbulent mixing ofpassive scalars. Philosophical Transactions of the Royal Society A, 368(1916), 1561-1577.[3] Iacobello, G., Scarsoglio, S., Kuerten, J.G.M., and Ridolfi, L. (2019) Lagrangian networkanalysis of turbulent mixing. Journal of Fluid Mechanics, 865, 546-562.[4] Kuerten, J.G.M., and Brouwers, J.J.H. (2013) Lagrangian statistics of turbulent chan-nel flow at Reτ = 950 calculated with direct numerical simulation and Langevin models.Physics of fluids, 25(10), 105108.

Complex network characterization of Lagrangian mixing in a turbulent channel flow

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Complex network characterization of Lagrangian mixing in a turbulent channel flow

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