scholarly journals Symmetry-breaking waves and space-time modulation mechanisms in two-dimensional plane Poiseuille flow

2020 ◽  
Vol 5 (9) ◽  
Author(s):  
Roger Ayats ◽  
Alvaro Meseguer ◽  
Fernando Mellibovsky
Keyword(s):  
Symmetry Breaking ◽  
Poiseuille Flow ◽  
Breaking Waves ◽  
Space Time ◽  
Two Dimensional ◽  
Plane Poiseuille Flow ◽  
Time Modulation ◽  
Dimensional Plane

scholarly journals Optimal mixing in two-dimensional plane Poiseuille flow at finite Péclet number

2014 ◽  
Vol 748 ◽  
pp. 241-277 ◽  
Author(s):  
D. P. G. Foures ◽  
C. P. Caulfield ◽  
P. J. Schmid
Keyword(s):  
Scalar Field ◽  
Poiseuille Flow ◽  
Peclet Number ◽  
Passive Scalar ◽  
Two Dimensional ◽  
Plane Poiseuille Flow ◽  
Péclet Number ◽  
Dimensional Plane ◽  
Scalar Variance ◽  
Optimal Mixing

AbstractWe consider the nonlinear optimisation of the mixing of a passive scalar, initially arranged in two layers, in a two-dimensional plane Poiseuille flow at finite Reynolds and Péclet numbers, below the linear instability threshold. We use a nonlinear-adjoint-looping approach to identify optimal perturbations leading to maximum time-averaged energy as well as maximum mixing in a freely evolving flow, measured through the minimisation of either the passive scalar variance or the so-called mix-norm, as defined by Mathew, Mezić & Petzold (Physica D, vol. 211, 2005, pp. 23–46). We show that energy optimisation appears to lead to very weak mixing of the scalar field whereas the optimal mixing initial perturbations, despite being less energetic, are able to homogenise the scalar field very effectively. For sufficiently long time horizons, minimising the mix-norm identifies optimal initial perturbations which are very similar to those which minimise scalar variance, demonstrating that minimisation of the mix-norm is an excellent proxy for effective mixing in this finite-Péclet-number bounded flow. By analysing the time evolution from initial perturbations of several optimal mixing solutions, we demonstrate that our optimisation method can identify the dominant underlying mixing mechanism, which appears to be classical Taylor dispersion, i.e. shear-augmented diffusion. The optimal mixing proceeds in three stages. First, the optimal mixing perturbation, energised through transient amplitude growth, transports the scalar field across the channel width. In a second stage, the mean flow shear acts to disperse the scalar distribution leading to enhanced diffusion. In a final third stage, linear relaxation diffusion is observed. We also demonstrate the usefulness of the developed variational framework in a more realistic control case: mixing optimisation by prescribed streamwise velocity boundary conditions.

A two-dimensional-three-component model for spanwise rotating plane Poiseuille flow

2019 ◽  
Vol 880 ◽  
pp. 478-496 ◽  
Author(s):  
Shengqi Zhang ◽  
Zhenhua Xia ◽  
Yipeng Shi ◽  
Shiyi Chen
Keyword(s):  
Reynolds Number ◽  
Poiseuille Flow ◽  
Reynolds Shear Stress ◽  
Streamwise Velocity ◽  
Channel Height ◽  
Neutral Stability ◽  
Two Dimensional ◽  
Plane Poiseuille Flow ◽  
Rotation Numbers ◽  
3C Model

Spanwise rotating plane Poiseuille flow (RPPF) is one of the canonical flow problems to study the effect of system rotation on wall-bounded shear flows and has been studied a lot in the past. In the present work, a two-dimensional-three-component (2D/3C) model for RPPF is introduced and it is shown that the present model is equivalent to a thermal convection problem with unit Prandtl number. For low Reynolds number cases, the model can be used to study the stability behaviour of the roll cells. It is found that the neutral stability curves, critical eigensolutions and critical streamfunctions of RPPF at different rotation numbers ($Ro$) almost collapse with the help of a rescaling with a newly defined Rayleigh number $Ra$ and channel height $H$. Analytic expressions for the critical Reynolds number and critical wavenumber at different $Ro$ can be obtained. For a turbulent state with high Reynolds number, the 2D/3C model for RPPF is self-sustained even without extra excitations. Simulation results also show that the profiles of mean streamwise velocity and Reynolds shear stress from the 2D/3C model share the same linear laws as the fully three-dimensional cases, although differences on the intercepts can be observed. The contours of streamwise velocity fluctuations behave like plumes in the linear law region. We also provide an explanation to the linear mean velocity profiles observed at high rotation numbers.

Lateral Migration of Large and Small Droplets Suspended in Channel Flow

2013 ◽  
Author(s):  
Masato Makino ◽  
Masako Sugihara-Seki
Keyword(s):  
Numerical Simulation ◽  
Channel Flow ◽  
Poiseuille Flow ◽  
Size Difference ◽  
Two Dimensional ◽  
Lateral Migration ◽  
Plane Poiseuille Flow ◽  
Surface Tensions ◽  
Segregation Behavior ◽  
The Mean

In order to investigate the effect of the size differences between suspended particles on the segregation behavior in channel flow of multicomponent suspensions, we conduct a two-dimensional numerical simulation for suspensions of fluid droplets of two different sizes subjected to a plane Poiseuille flow. The large and small droplets are assumed to have equal surface tensions and equal internal viscosities. The temporal evolutions of the lateral positions of the large and small droplets relative to the channel centerline are computed for various size ratios and area ratios of the large and small droplets. It is found that the small droplets tend to migrate toward the channel walls with increasing fraction of the large droplets and that the mean lateral positions of the large droplets are always closer to the channel centerline compared to the mean lateral positions of the small droplets, which represent the margination of the small droplets and the segregation of the droplets caused by the size difference. These trends are enhanced as the size ratio of large and small droplets is increased.

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