Optimizing mixing in channel flows: kinematic aspects associated with secondary flows in the cross-section

McIlhany, K.; Wiggins, Stephen

doi:10.1007/s10404-010-0656-6

Cited by 8 publications

(13 citation statements)

References 16 publications

(33 reference statements)

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“…13,15,and 16) as having a distinct advantage when studying dynamical systems in that they can predict some traits of the dynamics under study without having to perform the costly computational steps of integrating velocity vector fields to obtain trajectories. How efficient are EIs?…”

Section: Computational Efficiencymentioning

confidence: 99%

Eulerian indicators under continuously varying conditions

McIlhany

Wiggins

2012

Physics of Fluids

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In this paper, we extend the notion of Eulerian indicators (EIs) for predicting Lagrangian mixing behavior previously developed for blinking flows to the continuous time setting. We apply the EIs to a study of mixing in a kinematic model of a timedependent double-gyre with five different time dependencies-sinusoidal, sawtooth, square wave, triangular, and noise (which is constructed so that it is also periodic in time). Each of the five velocity fields is described by two parameters; the strength of the time dependence ( ) and the period (T). Based on a trajectory based quality of mixing diagnostic (Danckwerts' normalized variance of concentration) we find that noisy time dependence has the largest region of good mixing in the parameter space and triangular time dependence has parameter values corresponding to the most complete and fastest mixing. These Lagrangian based predictions are confirmed by the EIs (product of the transversality and mobility). Although not every feature of the mixing behavior is captured by EIs, we show that they do in general predict the regions in the parameter space under consideration that correspond to good mixing. Moreover, the EIs offer a factor of 100 computational advantage in exploring the parameter space in comparison with the trajectory based mixing diagnostic. C 2012 American Institute of Physics. [http://dx.

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Section: Computational Efficiencymentioning

confidence: 99%

Eulerian indicators under continuously varying conditions

McIlhany

Wiggins

2012

Physics of Fluids

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“…23 Here, we use the normalized variance of concentration. 7,24,25 Consider a mixture of two separate fluids, which we designate red and blue. The relative concentration of red fluid in some subdomain at some later time is given by…”

Section: Quantifying Mixing: Variance Of Concentrationmentioning

confidence: 99%

“…To date, application of EIs has been limited to assessing and predicting mixing characteristics of "blinking" type flows constructed from combinations of two or three distinct analytically defined velocity fields. 7 At present, only two EIs have been studied extensively, a, the transversality (which will be discussed later), and b, the transverse shear. 6,7 In this paper, we continue our development of EIs by analyzing the mixing characteristics of a two-dimensional, liddriven blinking Stokes flow.…”

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confidence: 99%

“…7 At present, only two EIs have been studied extensively, a, the transversality (which will be discussed later), and b, the transverse shear. 6,7 In this paper, we continue our development of EIs by analyzing the mixing characteristics of a two-dimensional, liddriven blinking Stokes flow. This flow serves as a model for mixing in a three-dimensional, spatially periodic, steady channel flow, where the blinking flow patterns model the two cross-sectional flow patterns that the fluid experiences as it moves down a spatially periodic channel.…”

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confidence: 99%

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Optimizing mixing in lid-driven flow designs through predictions from Eulerian indicators

et al. 2011

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In this paper, we further develop the notion of Eulerian indicators (EIs) for predicting Lagrangian mixing behavior. We employ a two-dimensional "blinking" Stokes flow as a model for mixing in a three-dimensional, spatially periodic channel flow. Each blinking flow alternates two distinct velocity fields that were calculated using a lid-driven cavity model. A new EI termed mobility is introduced to measure how effectively the blinking velocity fields transport fluid throughout the domain. We also calculate the transversality for these flows, which is an EI measuring how much the velocity direction at each point in the domain changes when the velocity fields blink. For the studied flows, we show that although individually the mobility and transversality do not correlate well with mixing as measured by the decay of the variance of concentration, the product of mobility and transversality does correlate well with the decay of the variance of concentration and predicts which combinations of velocity fields will produce the most effective mixing.

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“…However, both these approaches require the knowledge of the particle paths, and hence are computationally intensive. Recently, a new approach to optimize micromixers based on the Eulerian characteristics of the velocity field has been put forward by Wiggins and co-workers 31,34,40,41 .…”

Section: Optimizationmentioning

confidence: 99%

Chaotic mixing in a planar, curved channel using periodic slip

2015

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We propose a novel strategy for designing chaotic micromixers using curved channels confined between two flat planes. The location of the separatrix between the Dean vortices, induced by centrifugal force, is dependent on the location of the maxima of axial velocity. An asymmetry in the axial velocity profile can change the location of the separatrix. This is achieved physically by introducing slip alternatingly at the top and bottom walls. This leads to streamline crossing and Lagrangian chaos. An approximate analytical solution of the velocity field is obtained using perturbation theory. This is used to find the Lagrangian trajectories of fluid particles. Poincare sections taken at periodic locations in the axial direction are used to study the extent of chaos. The extent of mixing, for low slip and low Reynolds numbers, is shown to be greater when Dean vortices in adjacent half cells are counter-rotating. Wide channels are observed to have much better mixing than tall channels; an important observation not made for separatrix flows till now. Eulerian indicators are used to gauge the extent of mixing with varying slip length and it is shown that an optimum slip length exists which maximizes the mixing in a particular geometry.

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Optimizing mixing in channel flows: kinematic aspects associated with secondary flows in the cross-section

Cited by 8 publications

References 16 publications

Eulerian indicators under continuously varying conditions

Eulerian indicators under continuously varying conditions

Optimizing mixing in lid-driven flow designs through predictions from Eulerian indicators

Chaotic mixing in a planar, curved channel using periodic slip

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