Enhanced Mixing at Low Reynolds Numbers Through Elastic Turbulence

2011 ◽  
Vol 66 (6-7) ◽  
pp. 450-456
Author(s):  
Chris Goddard ◽  
Ortwin Hess
Keyword(s):  
Turbulent Flow ◽  
Three Dimensional ◽  
Maxwell Model ◽  
Reynolds Numbers ◽  
Cavity Flow ◽  
Driven Cavity ◽  
Low Reynolds Numbers ◽  
Tracer Particles ◽  
Laminar And Turbulent Flow ◽  
Spatio Temporal

A generic nonlinear Maxwell model for the stress tensor in viscoelastic materials is studied under mixing scenarios in a three-dimensional steady lid-driven cavity flow. Resulting laminar and turbulent flow profiles are investigated to study their mixing efficiencies. Massless tracer particles and passive concentrations are included to show that the irregular spatio-temporal chaos, present in turbulent flow, is useful for potential mixing applications. A Lyapunov measure for filament divergence confirms that the turbulent flow is more efficient at mixing

scholarly journals Flow through pipe orifices at low Reynolds numbers

1930 ◽  
Vol 126 (801) ◽  
pp. 231-245 ◽  
Keyword(s):  
Turbulent Flow ◽  
Discharge Coefficient ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Orifice Diameter ◽  
Vortex System ◽  
Low Reynolds Numbers ◽  
Commercial Practice ◽  
Flow Through ◽  
Low Reynolds

Most of the experimental work in connection with the flow of fluids through diaphragm orifices in pipe lines has been directed to the establishment of the orifice as a flow meter, and has been carried out at the velocities of flow commonly encountered in commercial practice. As a result of such research the coefficients relating the volumetric discharge of incompressible fluids to the differential head across an orifice are well known over a large range of high Reynolds numbers. For a particular diameter ratio ( i. e., orifice diameter ÷ diameter of pipe line) the discharge coefficient is nearly constant under conditions of turbulent flow. Over the range from steady to turbulent flow, however, very appreciable variations occur in the value of the discharge coefficient, suggest­ing that the accompanying variations in the nature of the flow through and beyond the orifice will be no less marked. As regards the turbulent flow pattern, an investigation, in which the author collaborated, of the airflow downstream of a flat plate suggests that an orifice in a pipe will in general give rise to a vortex system, probably having some points of resemblance to the well-known Kármán street which is a feature of the two-dimensional flow past a bluff obstacle, but doubtless exhibiting interesting differences arising from the symmetrical and three-dimensional character of the flow through an orifice. At sufficiently low Reynolds numbers, on the other hand, perfect flow free from periodic vorticity will occur. The stages connecting these two extreme conditions present many points of interest not only as regards the nature of the vortex system downstream of the orifice and the conditions of flow covering its inception, but also as regards the accom­panying pressure-velocity relation during the transition.

Initial movement of grains on a stream bed: the effect of relative protrusion

1977 ◽  
Vol 352 (1671) ◽  
pp. 523-537 ◽  
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Threshold Stress ◽  
Reynolds Numbers ◽  
Low Reynolds Numbers ◽  
Laminar And Turbulent Flow ◽  
Small Grains ◽  
Individual Grains ◽  
Initial Movement ◽  
Stream Bed

Shields (1936) found that the dimensionless shear stress necessary to move a cohesionless grain on a stream bed depended only on the grain Reynolds number. He ignored the degree of exposure of individual grains as a separate parameter. This report describes experiments to measure the dimensionless threshold stress and its dependence on grain protrusion, which was found to be very marked. The threshold stress for grains resting on the top of an otherwise flat bed in a turbulent stream was measured and found to be 0.01 –considerably less than previously-reported values of 0.03–0.06 for beds where all grains were at the same level. It is suggested that the new lower value be used in all turbulent flow situations where the bed is of natural sediments or unlevelled material. An hypothesis is proposed that the conventional Shields diagram implicitly contains variation with protrusion between the two extremes of (i) large grains and large Reynolds numbers, with small relative protrusion, and (ii) small grains, low Reynolds numbers, and protrusion of almost a complete grain diameter. In view of this, the extent of the dip in the Shields plot is explicable in that it represents a transition between two different standards of levelling as well as the transition between laminar and turbulent flow past the grains, the range of which it overlaps considerably.

Flow Characteristics Within and Downstream of Spherical and Cylindrical Dimple on a Flat Plate at Low Reynolds Numbers

2004 ◽  
Author(s):  
A. Khalatov ◽  
A. Byerley ◽  
D. Ochoa ◽  
Seong-Ki Min
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Reynolds Numbers ◽  
Flow Patterns ◽  
Flow Features ◽  
Laminar And Turbulent Flow ◽  
Low Reynolds ◽  
Oscillation Frequencies

A comprehensive experimental study has been performed in the U.S. Air Force Academy water tunnel to obtain a better understanding of the complicated flow patterns in shallow dimple configurations (h/D ≤ 0.1), including single cylindrical and spherical dimples, as well as single spanwise rows of dimples. The flow patterns, in-dimple separation zone extent, and bulk flow oscillation frequencies have been measured at low Reynolds number conditions. Three different single dimples and two single rows of dimples have been tested over a range of Reynolds numbers ReD of 3,170 to 23,590 including laminar and turbulent flow patterns downstream of a dimple. To visualize the fine flow features, five different colors of dye were injected through five cylindrical ports machined at locations upstream and inside the dimples. The measured results revealed unsteady and three-dimensional flow features inside and downstream of the dimple. The Reynolds number, dimple shape and the presence of adjacent dimples all play important roles in determining the nature of the flow pattern formation. Some preliminary conclusions regarding the laminar-turbulent flow transition after a dimple are presented.

On End Wall Effects in a Lid-Driven Cavity Flow

1984 ◽  
Vol 106 (4) ◽  
pp. 385-389 ◽  
Author(s):  
J. R. Koseff ◽  
R. L. Street
Keyword(s):  
Three Dimensional ◽  
Symmetry Plane ◽  
Reynolds Numbers ◽  
Cavity Flow ◽  
Thymol Blue ◽  
Major Influence ◽  
Cavity Depth ◽  
Driven Cavity ◽  
Driven Cavity Flow ◽  
Cavity Width

Experiments were conducted in a three-dimensional lid-driven cavity flow to study the effects of the end walls on the size of the downstream secondary eddy. The ratio of cavity depth to cavity width is 1:1. The span of the cavity was varied such that span-to-width ratios of 3:1, 2:1, and 1:1 were obtained. Flow visualization was accomplished by the thymol blue technique, and by rheoscopic liquid illuminated by laser-light sheets, for Reynolds numbers (based on lid speed and cavity width) between 1000 and 10,000. The results indicate that the corner vortices present at the end walls, in the region of the downstream secondary eddy, are a major influence on the size of this eddy. In addition, as the span of the cavity is reduced the size of the downstream secondary eddy at the symmetry plane becomes smaller with increasing Reynolds numbers, for Reynolds numbers greater than 2000.

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

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

Turbulent flow between counter-rotating concentric cylinders: a direct numerical simulation study

2008 ◽  
Vol 615 ◽  
pp. 371-399 ◽  
Author(s):  
S. DONG
Keyword(s):  
Turbulent Flow ◽  
Large Scale ◽  
Outer Cylinder ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Taylor Vortex ◽  
Small Scale ◽  
Mean Flow ◽  
Concentric Cylinders ◽  
High Reynolds

We report three-dimensional direct numerical simulations of the turbulent flow between counter-rotating concentric cylinders with a radius ratio 0.5. The inner- and outer-cylinder Reynolds numbers have the same magnitude, which ranges from 500 to 4000 in the simulations. We show that with the increase of Reynolds number, the prevailing structures in the flow are azimuthal vortices with scales much smaller than the cylinder gap. At high Reynolds numbers, while the instantaneous small-scale vortices permeate the entire domain, the large-scale Taylor vortex motions manifested by the time-averaged field do not penetrate a layer of fluid near the outer cylinder. Comparisons between the standard Taylor–Couette system (rotating inner cylinder, fixed outer cylinder) and the counter-rotating system demonstrate the profound effects of the Coriolis force on the mean flow and other statistical quantities. The dynamical and statistical features of the flow have been investigated in detail.

The two-sided lid-driven cavity: experiments on stationary and time-dependent flows

2002 ◽  
Vol 450 ◽  
pp. 67-95 ◽  
Author(s):  
CH. BLOHM ◽  
H. C. KUHLMANN
Keyword(s):  
Three Dimensional ◽  
Standing Waves ◽  
Reynolds Numbers ◽  
Time Dependent ◽  
Flow State ◽  
Incompressible Fluid Flow ◽  
Velocity Measurements ◽  
Driven Cavity ◽  
Rectangular Container ◽  
Hot Film

The incompressible fluid flow in a rectangular container driven by two facing sidewalls which move steadily in anti-parallel directions is investigated experimentally for Reynolds numbers up to 1200. The moving sidewalls are realized by two rotating cylinders of large radii tightly closing the cavity. The distance between the moving walls relative to the height of the cavity (aspect ratio) is Γ = 1.96. Laser-Doppler and hot-film techniques are employed to measure steady and time-dependent vortex flows. Beyond a first threshold robust, steady, three-dimensional cells bifurcate supercritically out of the basic flow state. Through a further instability the cellular flow becomes unstable to oscillations in the form of standing waves with the same wavelength as the underlying cellular flow. If both sidewalls move with the same velocity (symmetrical driving), the oscillatory instability is found to be tricritical. The dependence on two sidewall Reynolds numbers of the ranges of existence of steady and oscillatory cellular flows is explored. Flow symmetries and quantitative velocity measurements are presented for representative cases.

Cylinder rolling on a wall at low Reynolds numbers

2011 ◽  
Vol 685 ◽  
pp. 461-494 ◽  
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.

Stability of the Lid-Cavity Flow at Low Reynolds Numbers

2021 ◽  
Author(s):  
Nicoleta-Octavia Tanase ◽  
Diana Broboana ◽  
Corneliu Balan
Keyword(s):  
Reynolds Numbers ◽  
Cavity Flow ◽  
Low Reynolds Numbers ◽  
Low Reynolds
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