Wall-induced anisotropy effects on turbulent mixing in channel flow: A network-based analysis

D. Perrone, J. G. M. Kuerten, L. Ridolfi, and S. Scarsoglio

Phys. Rev. E 102, 043109 – Published 27 October 2020

Abstract

Turbulent mixing is studied in the Lagrangian framework with an approach based on the complex network formalism. We consider the motion of passive, noninertial particles inside a turbulent channel simulated at ${Re}_{τ} = 950$ . The time-dependent network is built to evaluate the transfer of tracers between thin wall-parallel layers which partition the channel in the wall-normal direction. By doing so, we are able to assess the spatial and temporal complexities arising from turbulence dynamics and their influence on the mixing process. This approach highlights the effects of small-scale features of turbulent flow structures and also the larger scale effects determined by wall-induced anisotropy. Complex networks, coupled to the Lagrangian description of turbulence, are effective in providing novel insights into inhomogeneous turbulence and mixing.

Received 15 July 2020
Accepted 8 October 2020

DOI:https://doi.org/10.1103/PhysRevE.102.043109

Physics Subject Headings (PhySH)

Community structure Turbulent mixing

Directed networks Weighted networks

Lagrangian particle tracking

Fluid DynamicsNetworks

Authors & Affiliations

D. Perrone ^*

Department of Mechanical and Aerospace Engineering, Politecnico di Torino, 10129 Turin, Italy

J. G. M. Kuerten

Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands

L. Ridolfi

Department of Environmental, Land and Infrastructure Engineering, Politecnico di Torino, 10129 Turin, Italy

S. Scarsoglio

Department of Mechanical and Aerospace Engineering, Politecnico di Torino, 10129 Turin, Italy

^*davide.perrone@polito.it

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Issue

Vol. 102, Iss. 4 — October 2020

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Images

Figure 1
(a) The channel is divided into levels, here identified by the colored bands, and each level is represented by a node of the network. Tracers are marked with their starting levels and are released in a square grid at $x^{+} = 0$ ; as they move across the channel they enter different levels, thus establishing connections from their starting node to the present ones. (b) The network nodes represent the discrete levels of the channel in the same order as reported in panel (a), while links are determined by the exchange of tracers; here links are depicted with thickness proportional to the link weight, i.e., the number of exchanged tracers. As time proceeds, connections between farther and farther levels are established.
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Figure 2
Evolution of the transport matrix. (a) The time $T_{0}^{+}$ at which each link is activated for the first time. (b) The evolution of the network weight matrix and the corresponding distribution of tracers in the channel with their starting location color-coded; in the weight matrices, the start level is labeled with its distance from the nearest wall, while the end level is indicated by the node number. (c) The weight distribution at $τ^{+} = 15200$ and the Poisson distribution corresponding to a mean value of 1.
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Figure 3
Probability density function of tracer distribution after different time lags (solid lines), together with the fitted beta distribution (dashed lines): (a) tracers starting from $y_{0}^{+} = 28.5$ and (b) tracers starting from $y_{0}^{+} = 940.5$ . Both distributions are plotted as a function of the normalized channel height $y^{+} / 2 δ$ . (c) Standard deviation of the tracer distribution, both as measured (solid lines) and as obtained from the fitted beta distribution (dotted lines); (d) $α$ and $β$ parameters of the Beta distribution for two different levels.
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Figure 4
(a) Mean degree $〈 k 〉$ ; (b) standard deviation of the ingoing and outgoing degree. (c) Ingoing degree, $k^{IN}$ , and (d) outgoing degree, $k^{OUT}$ , shown for all levels and $τ^{+} \in [0, 10000]$ .
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Figure 5
(a) Weighted link length $D_{w, i}^{+, OUT} / D_{0}$ , averaged for each node and corresponding to outgoing links; (b) mean temporal duration of each link $〈 T_{l}^{+} 〉$ (the highest values are found for end levels 1 and 100); (c) Trend line of the mean centripetal acceleration versus link duration.
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Figure 6
(a) The modularity of the network is shown for different times and decomposed into the contributions given by the near-wall (top and bottom) and all the central communities together. (b) Partitioning for three different times is shown: for very short times, two near-wall regions are present, while in the channel core there is a large number of small communities, which we all indistinctly show in gray; for intermediate times, only the near-wall communities remain (the core region presents no community structure and is shown in white); in the end, all communities break up and no modular structure can be identified (only small communities are present, shown in gray; still, their contribution to the modularity is negligible).
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