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 ISTITUZIONALETemporal network-based analysis of turbulent mixing / Iacobello, Giovanni; Scarsoglio, Stefania; Kuerten, J. G. M.;Ridolfi, Luca. - ELETTRONICO. - 7(2018), pp. 396-399. ((Intervento presentato al convegno International Conference onComplex Networks and Their Applications tenutosi a Cambridge, UK nel December 11-13, 2018.OriginalTemporal network-based analysis of turbulent mixingPublisher: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: 11583/2721702 since: 2018-12-27T14:56:29ZCOMPLEX NETWORKS 2018Temporal network-based analysis of turbulent mixingGiovanni Iacobello1, Stefania Scarsoglio1, J.G.M. Kuerten2, and Luca Ridolfi31 Department of Mechanical and Aerospace Engineering, Politecnico di Torino, Turin, Italygiovanni.iacobello@polito.it,2 Department of Mechanical Engineering, Eindhoven University of Technology, Eindhoven,The Netherlands3 Department of Environmental, Land and Infrastructure Engineering, Politecnico di Torino,Turin, Italy1 IntroductionComplex network-based tools have been recently attracting a lot of interest in the analy-sis of fluid flows. So far, most of the research has focused on geophysical flows [1], twophase flows [2], as well as turbulent flows [3, 4]. In particular, the investigation of fluidflows from a Lagrangian point of view – i.e., by tracing particle trajectories during themotion – has recently been explored [5, 6]. However, particle trajectories are typicallyexploited to build static networks, thus losing transient information on the flow dynam-ics. In this work, we propose a temporal network-based approach [7–9] for the study ofturbulent mixing, that fully captures the temporal evolution of particle dynamics.2 Data description and network buildingA turbulent channel flow was simulated through a direct numerical simulation at Reτ =Huτ/ν = 950 and performed for a time T+ = Tuτ/ν = 15200 with a time step ∆ t+ =4.75, where H is the half-channel height, uτ is the friction velocity and ν is the kine-matic viscosity [10]. A set of 100×100 fluid particles were initially arranged at x+ = 0on a uniformly spaced grid in the plane (y+,z+) (see Fig. 1(a)), where (x+,y+,z+)are the streamwise, wall-normal and spanwise coordinates, respectively. Particles weregrouped into N = 100 levels, li, according to their y+ value at the initial time t+ = 0(see Fig. 1(a)). Trajectories of the particles are then computed over time.If two particles are sufficiently close to each other at a given time, then a connec-tion is established between them. Specifically, a particle A is connected to a particle Bif A lies inside a reference ellipsoid centred in B, and vice versa (by symmetry). Forexample, in Fig. 1(b) the trajectories of two particles A and B and their correspond-ing reference ellipsoids are shown. The corresponding time-sequence of connectionsbetween A and B is illustrated in Fig. 1(c). The ellipsoid was geometrically anchoredand centred to each particle location and it was chosen as reference geometry to takeinto account the anisotropy of the flow. Since the average Euclidean distance betweenparticles increases in time (mainly due to the streamwise dispersion), the semi-axes ofthe ellipsoid were set to grow proportionally to the average distance in each direction.As particles follow the turbulent motion, their relative distance changes in time, thusparticles belonging to different levels generate different time-sequences of connections.x+y+Wallt3t1t2Timet0 t3t2t1BA(a) (b)(c)Levels, liy+z+Initial setup - t0WallBAt4t7t6t5t8t10t9Fig. 1. (a) Sketch of the initial arrangement of particles at x+ = 0. Different colors highlight dif-ferent levels. (b) Example of trajectories (black lines) of two particles A and B and their referenceellipsoids. (c) Time-sequence of the connections between particles A and B shown in panel (b)(the corresponding sampling time is highlighted by the red dashed box).Therefore, we modelled the turbulent particle dynamics by means of a weighted time-varying network [9], Wi, j(t+), in which nodes correspond to levels, li (i.e., groups ofparticles initially at the same y+). At each time, the weight of a link between two nodes(i, j) – i.e., two levels – is equal to the total number of connections shared by particlesbelonging to levels li and l j . By doing so, a time-varying network of NT = 3200 undi-rected weight matrices (each one of size 100× 100) is obtained, that is able to capturethe temporal effects of turbulent mixing and flow advection on particle dynamics.3 ResultsSince Wi, j(t+) embeds the information of the modelled particle dynamics, the weightmatrices at three representative times are shown in Fig. 2(a), where colors indicate theintensity of the weight, i.e., the number of connections between each pair of levels. Att+ = 0, the weight matrix displays a band structure corresponding to the initial arrange-ment, where nodes close in space are strongly linked each other. As time increases, theweight matrix changes structure: a three-square pattern of highWi, j(t+) values emerges,as a consequence of turbulent dispersion, while turbulent mixing enables the activationof links between initially distant levels (e.g., levels 20 and 90). Finally, for large times(t+ = 15200) the turbulent mixing dominates the particle dynamics, approaching anasymptotic behaviour, where particles are well-mixed independently from their start-ing level. Consequently, the resulting weight matrix does not show any clear pattern.The change in the particle dynamics is also highlighted by a different network topol-ogy of Wi, j(t+). This is shown in Fig. 2(b), where the change in the network topologyas function of time is evident. In particular, at t+ = 900 the nodes tend to cluster intothree groups in analogy with the three-square pattern in Fig.2(a). This pattern is lost att+ = 15200, in which the network topology appears as a random layout. From a cen-trality perspective, the analysis of the average strength over time is able to highlightand discern characteristic advection-mixing regimes in a straightforward way. Hence,the main advantage of the proposed approach is its ability to fully incorporate the infor-mation about particle dynamics into the weight matrices, at any time.(a)(b)t + = 0 t + = 900 t + = 15200100501Fig. 2. (a) Weight matrices of the time-varying network at three representative times. The colorbarindicates the intensity of the links. (b) Visualization of the networks reported in panel (a). Nodesare colored with their level (see colorbar), while link intensity is colored in grey-scale (stronglinks are in black, weak links are in light-grey).Summary. In this work, the turbulent mixing in a channel flow is investigated througha Lagrangian approach. A set of fluid particles is traced in time, where each particlebelongs to a level corresponding to its initial wall-normal coordinate. By exploitingthe pairwise distance between particles, a weighted time-varying network is built inwhich nodes represent levels, and the link weight is equal to the number of connectionsbetween each pair of levels. Different particle dynamics are found to result into differentnetwork topologies and link weight patterns. In this way, it is possible to entirely capturethe features of the turbulent mixing and geometrize the evolution of the particle swarm.References1. Donner, R. V., Herna´ndez-Garcı´a, E., Ser-Giacomi, E.: Introduction to Focus Issue: Complexnetwork perspectives on flow systems. Chaos 27(3), 035601 (2017).2. Gao, Z., Jin, N.: Flow-pattern identification and nonlinear dynamics of gas-liquid two-phaseflow in complex networks. Phys. Rev. E, 79(6), 066303 (2009).3. Charakopoulos, A.K.,Karakasidis, T.E.,Papanicolaou, P.N.,Liakopoulos, A: The applicationof complex network time series analysis in turbulent heated jets. Chaos, 24(2), 024408 (2014)4. Iacobello, G., Scarsoglio, S., Kuerten, J. G. M., Ridolfi, L. Spatial characterization of turbu-lent channel flow via complex networks. Phys. Rev. E, 98(1), 013107 (2018).5. Ser-Giacomi, E., Rossi, V., Lo´pez, C., Herna´ndez-Garcı´a, E.: Flow networks: A characteri-zation of geophysical fluid transport. Chaos, 25(3), 036404 (2015)6. Padberg-Gehle, K., Schneide, C.: Network-based study of Lagrangian transport and mixing.Nonlinear Proc. Geoph., 24(4), 661 (2017).7. Braha, D., BarYam, Y.: From centrality to temporary fame: Dynamic centrality in complexnetworks. Complexity, 12(2), 59-63 (2006).8. Hill, S. A., Braha, D.: Dynamic model of time-dependent complex networks. Phys. Rev. E,82(4), 046105 (2010).9. Holme, P., Saramki, J.: Temporal networks. Phys. Rep., 519(3), 97-125 (2012).10. The use of supercomputer facilities was provided by NWO, Physical Sciences.

Temporal network-based analysis of turbulent mixing

https://iris.polito.it/retrieve/handle/11583/2721702/223462/Iacobello_CNA2018_CAMERA.pdf

Temporal network-based analysis of turbulent mixing

Abstract

Similar works

Full text

Available Versions

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