Mixing Analysis in a Lid-Driven Cavity Flow at Finite Reynolds Numbers

Rao, Pradeep; Duggleby, Andrew; Stremler, Mark A.

doi:10.1115/1.4006361

Cited by 8 publications

(3 citation statements)

References 15 publications

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“…As can be seen from Figure , the mixing level increases with the increase of viscosity. A similar result was reported by Rao et al It is also sensitive to the initial tracer injection locations, especially for the low viscosity situations. The periodic boundary movement creates repeating stretching and folding of material lines, which may promote mixing efficiently for a highly viscous system.…”

Section: Resultssupporting

confidence: 86%

Mixing in a soft‐elastic reactor (SER): A simulation study

Xiao

Zhang

et al. 2018

Can J Chem Eng

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Inspired by the animal upper digestion tract, a strategy of developing soft-elastic reactors (SERs) for potential industrial usage has evolved, and is under the framework of bio-inspired chemical engineering. In our laboratory, two basic reactor categories have been experimented upon to explore the parameters influencing SER performance: vertical and horizontal cylindrical reactors. Different from the traditional rigid reactors equipped with solid agitators, SERs mainly triggers mixing through the movement of its elastic wall. The mechanisms of SERs are, however, not yet fully understood due to the limitations in the laboratory work in scale and in the diversity of the working conditions. For the first time we present a numerical study on the mixing behaviour of an SER to reveal its special characteristics as an alternative mixing method difficult to show in laboratory. Two-dimensional situations are analyzed numerically with a successful implementation of a moving mesh method in ANSYS Fluent. The approach allows versatile movement of the reactor wall to be effectively simulated. Systematic investigations were then carried out to investigate the effects of two chosen wall motion modes. The effects of such motion modes have been demonstrated through tracking the evolutions of the flow fields. This work shows room for potential improvements of SERs by devising different wall movements.

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Section: Resultssupporting

confidence: 86%

Mixing in a soft‐elastic reactor (SER): A simulation study

Xiao

Zhang

et al. 2018

Can J Chem Eng

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“…The chaotic lid-driven cavity model 32,33,36,37 is a twodimensional area-preserving flow defined over a 2D vertical cross-section of a rectangular cavity, extending vertically from −b ≤ y ≤ b and horizontally from 0 ≤ x ≤ a. 3) with τ f = 0.96, guaranteeing the existence of a period-three orbit, seen in Fig 6c.…”

Section: A Chaotic Lid-driven Cavity Flowmentioning

confidence: 99%

Ensemble-based topological entropy calculation (E-tec)

Roberts

Sindi

Smith

et al. 2019

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Topological entropy measures the number of distinguishable orbits in a dynamical system, thereby quantifying the complexity of chaotic dynamics. One approach to computing topological entropy in a two-dimensional space is to analyze the collective motion of an ensemble of system trajectories taking into account how trajectories "braid" around one another. In this spirit, we introduce the Ensemble-based Topological Entropy Calculation, or E-tec, a method to derive a lower-bound on topological entropy of two-dimensional systems by considering the evolution of a "rubber band" (piece-wise linear curve) wrapped around the data points and evolving with their trajectories. The topological entropy is bounded below by the exponential growth rate of this band. We use tools from computational geometry to track the evolution of the rubber band as data points strike and deform it. Because we maintain information about the configuration of trajectories with respect to one another, updating the band configuration is performed locally, which allows E-tec to be more computationally efficient than some competing methods. In this work, we validate and illustrate many features of E-tec on a chaotic lid-driven cavity flow. In particular, we demonstrate convergence of E-tec's approximation with respect to both the number of trajectories (ensemble size) and the duration of trajectories in time.arXiv:1809.01005v3 [physics.comp-ph]

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“…Ghadimi et al 13 simulated the flow in a square as well as the L-shaped cavity using fourth-order finite difference method (FDM). Moreover, Rao et al 14 used Poincaré sections and mixing measures in order to study chaotic advection and compute the mixing effectiveness in a rectangular cavity. Kuhlmann et al 15 indicated that 2D flow inside the one-sided lid-driven cavity could lose its exceptionality if another lid was moving parallel or antiparallel to the first moving lid.…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation of three‐sided lid‐driven square cavity

Kamel

Haraz

Hanna

2020

Engineering Reports

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In this article, an incompressible, two-dimensional (2D), time-dependent Newtonian fluid flow in a square cavity is simulated using finite difference method and alternating direction implicit technique. Navier-Stokes equations are solved numerically in stream function-vorticity formulation. In order to verify the numerical solver, the one-sided lid-driven cavity is studied and the results are compared with relevant data in the literature. They were in a very good agreement. Furthermore, two distinguished unexplored cases of the three-sided lid-driven cavity have been investigated. In case (1), the upper and lower walls are translated to the right, while the left wall is translated upward and the right wall remains stationary. Moreover, in case (2), the upper wall is translated to the right but the lower wall is translated to the left, while the left wall is translated downward and the right wall remains stationary. However, stream function and vorticity values in addition to the location of primary and secondary vortices' centers inside the square cavity have been revealed at low and intermediate Reynolds numbers (Re), typically (Re = 100 to 2000). Moreover, the higher the Re, the more main primary vortex approaches the cavity center and the bigger the secondary vortices. K E Y W O R D Sfinite difference method, incompressible flow, lid-driven cavity, Navier-Stokes equations, stream function-vorticity formulation 1 This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.

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Mixing Analysis in a Lid-Driven Cavity Flow at Finite Reynolds Numbers

Cited by 8 publications

References 15 publications

Mixing in a soft‐elastic reactor (SER): A simulation study

Mixing in a soft‐elastic reactor (SER): A simulation study

Ensemble-based topological entropy calculation (E-tec)

Numerical simulation of three‐sided lid‐driven square cavity

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