Peripheral mixing of passive scalar at small Reynolds number

Mixing of a passive scalar in the peripheral region close to a wall is investigated by means of accurate direct numerical simulations of both a three-dimensional Couette channel flow at low Reynolds numbers and a two-dimensional synthetic flow. In both cases, the resulting phenomenology can be understood in terms of the theory recently developed by Lebedev & Turitsyn (Phys. Rev. E, vol. 69, 2004, 036301). Our results prove the robustness of the identified mechanisms responsible for the persistency of scalar concentration close to the wall with important consequences in completely different fields ranging from microfluidic applications to environmental dispersion modelling.

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Flow in two-sided lid-driven cavities: non-uniqueness, instabilities, and cellular structures

Journal of Fluid Mechanics ◽

10.1017/s0022112096004727 ◽

1997 ◽

Vol 336 ◽

pp. 267-299 ◽

Cited By ~ 95

Author(s):

H. C. KUHLMANN ◽

M. WANSCHURA ◽

H. J. RATH

Keyword(s):

Three Dimensional ◽

Reynolds Numbers ◽

Two Dimensional ◽

Single Vortex ◽

Low Reynolds Numbers ◽

Dimensional Flow ◽

Two Dimensional Flow ◽

The Difference ◽

Convective Cells ◽

Highly Strained

The steady flow in rectangular cavities is investigated both numerically and experimentally. The flow is driven by moving two facing walls tangentially in opposite directions. It is found that the basic two-dimensional flow is not always unique. For low Reynolds numbers it consists of two separate co-rotating vortices adjacent to the moving walls. If the difference in the sidewall Reynolds numbers is large this flow becomes unstable to a stationary three-dimensional mode with a long wavelength. When the aspect ratio is larger than two and both Reynolds numbers are large, but comparable in magnitude, a second two-dimensional flow exists. It takes the form of a single vortex occupying the whole cavity. This flow is the preferred state in the present experiment. It becomes unstable to a three-dimensional mode that subdivides the basic streched vortex flow into rectangular convective cells. The instability is supercritical when both sidewall Reynolds numbers are the same. When they differ the instability is subcritical. From an energy analysis and from the salient features of the three-dimensional flow it is concluded that the mechanism of destabilization is identical to the destabilization mechanism operative in the elliptical instability of highly strained vortices.

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A numerical and experimental study of transition processes in an obstructed channel flow

Journal of Fluid Mechanics ◽

10.1017/s0022112094003484 ◽

1994 ◽

Vol 260 ◽

pp. 185-209 ◽

Cited By ~ 40

Author(s):

E. P. L. Roberts

Keyword(s):

Numerical Simulation ◽

Shear Layer ◽

Three Dimensional ◽

Reynolds Numbers ◽

Stability Study ◽

Two Dimensional ◽

Mean Velocity ◽

Cross Sectional ◽

Low Reynolds Numbers ◽

Steady And Unsteady Flows

Incompressible Newtonian flow in a two-dimensional channel with periodically placed sharp edged baffles has been studied both by numerical simulation and by experimental flow visualization. The flow was observed to be steady and symmetric at low Reynolds numbers, with recirculating eddies downstream of each baffle. At a critical Reynolds number (based on channel width and cross-sectional mean velocity) of approximately 100 the flow became asymmetric and unsteady. This transition to unsteadiness led to an eddy shedding regime, with eddies formed and shed successively from each baffle. A stability study suggested that the mechanism for transition to unsteady flow is a Kelvin–Helmholtz instability associated with the shear layer formed downstream of the sharp edged baffles. The frequency of the unsteadiness is, however, dependent on the full flow field, and not only the shear layer characteristics. Experimental observations show that the instability is followed by a secondary transition to three-dimensional disordered flow. Experimentally observed flows in the two-dimensional regime were found to be in close agreement with the numerical simulation for both the steady and unsteady flows.

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3D simulation of emulsion flow using the boundary element method on the heterogeneous computational systems

Proceedings of the Mavlyutov Institute of Mechanics ◽

10.21662/uim2012.1.028 ◽

2012 ◽

Vol 9 (1) ◽

pp. 142-146

Author(s):

O.A. Solnyshkina

Keyword(s):

Boundary Element Method ◽

Boundary Element ◽

Three Dimensional ◽

Reynolds Numbers ◽

Problem Size ◽

Low Reynolds Numbers ◽

Infinite Domains ◽

The Matrix ◽

Computational Systems ◽

Element Method

In this work the 3D dynamics of two immiscible liquids in unbounded domain at low Reynolds numbers is considered. The numerical method is based on the boundary element method, which is very efficient for simulation of the three-dimensional problems in infinite domains. To accelerate calculations and increase the problem size, a heterogeneous approach to parallelization of the computations on the central (CPU) and graphics (GPU) processors is applied. To accelerate the iterative solver (GMRES) and overcome the limitations associated with the size of the memory of the computation system, the software component of the matrix-vector product

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A Code for Simulating Heat Transfer in Turbulent Channel Flow

Mathematics ◽

10.3390/math9070756 ◽

2021 ◽

Vol 9 (7) ◽

pp. 756

Author(s):

Federico Lluesma-Rodríguez ◽

Francisco Álcantara-Ávila ◽

María Jezabel Pérez-Quiles ◽

Sergio Hoyas

Keyword(s):

Heat Transfer ◽

Stokes Equations ◽

Three Dimensional ◽

Turbulent Channel Flow ◽

Passive Scalar ◽

Direct Numerical Simulations ◽

Time Dependent ◽

Navier Stokes ◽

Thermal Flow ◽

Navier Stokes Equations

One numerical method was designed to solve the time-dependent, three-dimensional, incompressible Navier–Stokes equations in turbulent thermal channel flows. Its originality lies in the use of several well-known methods to discretize the problem and its parallel nature. Vorticy-Laplacian of velocity formulation has been used, so pressure has been removed from the system. Heat is modeled as a passive scalar. Any other quantity modeled as passive scalar can be very easily studied, including several of them at the same time. These methods have been successfully used for extensive direct numerical simulations of passive thermal flow for several boundary conditions.

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Bifurcation Characteristics of Flows in Rectangular Sudden Expansion Channels

Volume 1: Symposia, Parts A and B ◽

10.1115/fedsm2005-77098 ◽

2005 ◽

Cited By ~ 2

Author(s):

Francine Battaglia ◽

George Papadopoulos

Keyword(s):

Reynolds Number ◽

Laminar Flow ◽

Critical Reynolds Number ◽

Three Dimensional ◽

Reynolds Numbers ◽

Expansion Ratio ◽

Sudden Expansion ◽

Two Dimensional ◽

Effective Expansion ◽

Three Dimensional Simulations

The effect of three-dimensionality on low Reynolds number flows past a symmetric sudden expansion in a channel was investigated. The geometric expansion ratio of in the current study was 2:1 and the aspect ratio was 6:1. Both experimental velocity measurements and two- and three-dimensional simulations for the flow along the centerplane of the rectangular duct are presented for Reynolds numbers in the range of 150 to 600. Comparison of the two-dimensional simulations with the experiments revealed that the simulations fail to capture completely the total expansion effect on the flow, which couples both geometric and hydrodynamic effects. To properly do so requires the definition of an effective expansion ratio, which is the ratio of the downstream and upstream hydraulic diameters and is therefore a function of both the expansion and aspect ratios. When the two-dimensional geometry was consistent with the effective expansion ratio, the new results agreed well with the three-dimensional simulations and the experiments. Furthermore, in the range of Reynolds numbers investigated, the laminar flow through the expansion underwent a symmetry-breaking bifurcation. The critical Reynolds number evaluated from the experiments and the simulations was compared to other values reported in the literature. Overall, side-wall proximity was found to enhance flow stability, helping to sustain laminar flow symmetry to higher Reynolds numbers in comparison to nominally two-dimensional double-expansion geometries. Lastly, and most importantly, when the logarithm of the critical Reynolds number from all these studies was plotted against the reciprocal of the effective expansion ratio, a linear trend emerged that uniquely captured the bifurcation dynamics of all symmetric double-sided planar expansions.

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Experimental studies of the laminar separation bubble on a two-dimensional airfoil at low Reynolds numbers

10.2514/6.1980-1440 ◽

1980 ◽

Author(s):

S. BATILL ◽

T. MUELLER

Keyword(s):

Separation Bubble ◽

Experimental Studies ◽

Reynolds Numbers ◽

Laminar Separation Bubble ◽

Two Dimensional ◽

Laminar Separation ◽

Low Reynolds Numbers ◽

Low Reynolds

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Cellular flow in a partially filled rotating drum: regular and chaotic advection

Journal of Fluid Mechanics ◽

10.1017/jfm.2017.393 ◽

2017 ◽

Vol 825 ◽

pp. 631-650 ◽

Cited By ~ 5

Author(s):

Francesco Romanò ◽

Arash Hajisharifi ◽

Hendrik C. Kuhlmann

Keyword(s):

Three Dimensional ◽

Reynolds Numbers ◽

Chaotic Advection ◽

Two Dimensional ◽

Rotating Drum ◽

Three Dimensional Flow ◽

Dimensional Flow ◽

Heteroclinic Connection ◽

Two Dimensional Flow ◽

Chaotic Streamlines

The topology of the incompressible steady three-dimensional flow in a partially filled cylindrical rotating drum, infinitely extended along its axis, is investigated numerically for a ratio of pool depth to radius of 0.2. In the limit of vanishing Froude and capillary numbers, the liquid–gas interface remains flat and the two-dimensional flow becomes unstable to steady three-dimensional convection cells. The Lagrangian transport in the cellular flow is organised by periodic spiralling-in and spiralling-out saddle foci, and by saddle limit cycles. Chaotic advection is caused by a breakup of a degenerate heteroclinic connection between the two saddle foci when the flow becomes three-dimensional. On increasing the Reynolds number, chaotic streamlines invade the cells from the cell boundary and from the interior along the broken heteroclinic connection. This trend is made evident by computing the Kolmogorov–Arnold–Moser tori for five supercritical Reynolds numbers.

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Cylinder rolling on a wall at low Reynolds numbers

Journal of Fluid Mechanics ◽

10.1017/jfm.2011.331 ◽

2011 ◽

Vol 685 ◽

pp. 461-494 ◽

Cited By ~ 8

Author(s):

Alain Merlen ◽

Christophe Frankiewicz

Keyword(s):

Three Dimensional ◽

Reynolds Numbers ◽

Navier Stokes ◽

Navier Stokes Equation ◽

Flow Around A Cylinder ◽

Low Reynolds Numbers ◽

Initial Location ◽

Upstream Pressure ◽

Small Reynolds Numbers ◽

Onset Of Cavitation

AbstractThe flow around a cylinder rolling or sliding on a wall was investigated analytically and numerically for small Reynolds numbers, where the flow is known to be two-dimensional and steady. Both prograde and retrograde rotation were analytically solved, in the Stokes regime, giving the values of forces and torque and a complete description of the flow. However, solving Navier–Stokes equation, a rotation of the cylinder near the wall necessarily induces a cavitation bubble in the nip if the fluid is a liquid, or compressible effects, if it is a gas. Therefore, an infinite lift force is generated, disconnecting the cylinder from the wall. The flow inside this interstice was then solved under the lubrication assumptions and fully described for a completely flooded interstice. Numerical results extend the analysis to higher Reynolds number. Finally, the effect of the upstream pressure on the onset of cavitation is studied, giving the initial location of the phenomenon and the relation between the upstream pressure and the flow rate in the interstice. It is shown that the flow in the interstice must become three-dimensional when cavitation takes place.

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