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.

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

Visualization Studies of a Shear Driven Three-Dimensional Recirculating Flow

1984 ◽  
Vol 106 (1) ◽  
pp. 21-27 ◽  
Author(s):  
J. R. Koseff ◽  
R. L. Street
Keyword(s):  
Cell Structure ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Uniform Density ◽  
Driven Cavity ◽  
Recirculating Flow ◽  
Circulation Cell ◽  
Speed Range ◽  
Main Circulation ◽  
Cavity Width

A facility has been constructed to study shear-driven, recirculating flows. In this particular study, the circulation cell structure in the lid-driven cavity is studied as a function of the speed of the lid which provides the shearing force to a constant and uniform density fluid. The flow is three-dimensional and exhibits regions where Taylor-type instabilities and Taylor-Go¨rtler-like vortices are present. One main circulation cell and three secondary cells are present for the Reynolds number (based on cavity width and lid speed) range considered, viz., 1000–10000. The flows becomes turbulent at Reynolds numbers between 6000 to 8000. The transverse fluid motions (in the direction perpendicular to the lid motion) are significant. In spite of this, some key results from two-dimensional numerical simulations agree well with the results of the present cavity experiments.

Start-up flows in a three-dimensional rectangular driven cavity of aspect ratio 1:1:2 at Re = 1000

2002 ◽  
Vol 450 ◽  
pp. 169-199 ◽  
Author(s):  
J.-L. GUERMOND ◽  
C. MIGEON ◽  
G. PINEAU ◽  
L. QUARTAPELLE
Keyword(s):  
Aspect Ratio ◽  
Three Dimensional ◽  
High Sensitivity ◽  
Viscous Flows ◽  
Reynolds Numbers ◽  
Two Dimensions ◽  
Dimensionless Time ◽  
Driven Cavity ◽  
Start Up ◽  
Initial Evolution

This paper provides comparisons between experimental data and numerical results for impulsively started flows in a three-dimensional rectangular lid-driven cavity of aspect ratio 1:1:2 at Reynolds number 1000. The initial evolution of this flow is studied up to the dimensionless time t = 12 and is found both experimentally and numerically to exhibit high sensitivity to geometrical perturbations. Three different flow developments generated by very small changes in the boundary geometry are found in the experiments and are reproduced by the numerics. This indicates that even at moderate Reynolds numbers the predictability of three-dimensional incompressible viscous flows in bounded regions requires controlling the shape of the boundary and the values of the boundary conditions more carefully than needed in two dimensions.

scholarly journals Application of a Projection Method for Simulating Flow of a Shear-Thinning Fluid

Fluids ◽  
2019 ◽  
Vol 4 (3) ◽  
pp. 124 ◽  
Author(s):  
Masoud Jabbari ◽  
James McDonough ◽  
Evan Mitsoulis ◽  
Jesper Henri Hattel
Keyword(s):  
Projection Method ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Shear Thinning ◽  
Navier Stokes ◽  
Bottom Surface ◽  
Navier Stokes Equations ◽  
Driven Cavity ◽  
Main Vortex

In this paper, a first-order projection method is used to solve the Navier–Stokes equations numerically for a time-dependent incompressible fluid inside a three-dimensional (3-D) lid-driven cavity. The flow structure in a cavity of aspect ratio δ = 1 and Reynolds numbers ( 100 , 400 , 1000 ) is compared with existing results to validate the code. We then apply the developed code to flow of a generalised Newtonian fluid with the well-known Ostwald–de Waele power-law model. Results show that, by decreasing n (further deviation from Newtonian behaviour) from 1 to 0.9, the peak values of the velocity decrease while the centre of the main vortex moves towards the upper right corner of the cavity. However, for n = 0.5 , the behaviour is reversed and the main vortex shifts back towards the centre of the cavity. We moreover demonstrate that, for the deeper cavities, δ = 2 , 4 , as the shear-thinning parameter n decreased the top-main vortex expands towards the bottom surface, and correspondingly the secondary flow becomes less pronounced in the plane perpendicular to the cavity lid.

Alternate Eddy Shedding Set Up by the Nonaxisymmetric Recirculation Zone at the Exhaust of a Cyclone Dust Separator

1998 ◽  
Vol 120 (1) ◽  
pp. 193-199 ◽  
Author(s):  
A. J. Griffiths ◽  
P. A. Yazdabadi ◽  
N. Syred
Keyword(s):  
Recirculation Zone ◽  
Laser Doppler Anemometry ◽  
Reverse Flow ◽  
Three Dimensional ◽  
Time Dependent ◽  
Velocity Measurements ◽  
Flow Zone ◽  
Precessing Vortex Core ◽  
Dust Separator ◽  
Set Up

Two cyclone dust separators with geometric swirl numbers of 3.324 and 3.043 were used to analyze the motion of the complex three-dimensional time dependent motion set up in the free exhaust. A quantitative analysis of the flow was carried out, obtaining time dependent velocity measurements with the use of laser Doppler anemometry (L.D.A.) techniques. The investigations highlighted a eddy or vortex shedding mechanism in two distinct areas of the flow. This was in part caused by a reverse flow zone and a precessing vortex core within the exhaust region of the separator. Changes in the Reynolds number by a factor of 2 were observed to have no effect on the main characteristics of the flow. Some changes were seen in the flow structure with change in swirl number, particularly the size of the reverse flow zone and the position of the large engulfment vortices.

Finite-amplitude solutions in the flow through a sudden expansion in a circular pipe

2011 ◽  
Vol 691 ◽  
pp. 201-213 ◽  
Author(s):  
E. Sanmiguel-Rojas ◽  
T. Mullin
Keyword(s):  
Numerical Simulations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Finite Amplitude ◽  
Time Dependent ◽  
Sudden Expansion ◽  
Numerical Evidence ◽  
Pipe Flows ◽  
Bifurcation Phenomena ◽  
Flow Through

AbstractResults of three-dimensional numerical simulations of the flow through a sudden expansion in a pipe are presented. The axisymmetric state is known to be stable over the range of Reynolds numbers studied, but recent experimental results suggest bifurcation phenomena. A resolution of this dichotomy between calculation and experiment is provided using imperfections to promote the nonlinear development of asymmetric steady states. These lose stability to disordered motion and the boundary between the steady and time-dependent flows has been established over a range of parameters. Moreover, disordered flows are found to co-exist with the axisymmetric regime when the disturbance is removed from the flow. Hence we provide direct numerical evidence for multiplicity of solutions for the axisymmetric expansion problem, which may have relevance to pipe flows.

scholarly journals Three-dimensional flow instability in a lid-driven isosceles triangular cavity

2011 ◽  
Vol 675 ◽  
pp. 369-396 ◽  
Author(s):  
L. M. GONZÁLEZ ◽  
M. AHMED ◽  
J. KÜHNEN ◽  
H. C. KUHLMANN ◽  
V. THEOFILIS
Keyword(s):  
Flow Instability ◽  
Three Dimensional ◽  
Steady Motion ◽  
Reynolds Numbers ◽  
Two Dimensional ◽  
Driven Cavity ◽  
Neutral Curves ◽  
Critical Reynolds Numbers ◽  
Dimensional Instability ◽  
Steady Laminar

Linear three-dimensional modal instability of steady laminar two-dimensional states developing in a lid-driven cavity of isosceles triangular cross-section is investigated theoretically and experimentally for the case in which the equal sides form a rectangular corner. An asymmetric steady two-dimensional motion is driven by the steady motion of one of the equal sides. If the side moves away from the rectangular corner, a stationary three-dimensional instability is found. If the motion is directed towards the corner, the instability is oscillatory. The respective critical Reynolds numbers are identified both theoretically and experimentally. The neutral curves pertinent to the two configurations and the properties of the respective leading eigenmodes are documented and analogies to instabilities in rectangular lid-driven cavities are discussed.

Buoyancy-Induced Flow in a Heated Rotating Cavity

2004 ◽  
Vol 128 (1) ◽  
pp. 128-134 ◽  
Author(s):  
J. Michael Owen ◽  
Jonathan Powell
Keyword(s):  
Laser Doppler Anemometry ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Velocity Measurements ◽  
Turbine Engine ◽  
Rotating Cavity ◽  
Heated Disk ◽  
Induced Flow ◽  
Cooling Air ◽  
Buoyancy Induced Flow

Experimental measurements were made in a rotating-cavity rig with an axial throughflow of cooling air at the center of the cavity, simulating the conditions that occur between corotating compressor disks of a gas-turbine engine. One of the disks in the rig was heated, and the other rotating surfaces were quasi-adiabatic; the temperature difference between the heated disk and the cooling air was between 40 and 100°C. Tests were conducted for axial Reynolds numbers, Rez, of the cooling air between 1.4×103 and 5×104, and for rotational Reynolds numbers, Reϕ, between 4×105 and 3.2×106. Velocity measurements inside the rotating cavity were made using laser Doppler anemometry, and temperatures and heat flux measurements on the heated disk were made using thermocouples and fluxmeters. The velocity measurements were consistent with a three-dimensional, unsteady, buoyancy-induced flow in which there was a multicell structure comprising one, two, or three pairs of cyclonic and anticyclonic vortices. The core of fluid between the boundary layers on the disks rotated at a slower speed than the disks, as found by other experimenters. At the smaller values of Rez, the radial distribution and magnitude of the local Nusselt numbers, Nu, were consistent with buoyancy-induced flow. At the larger values of Rez, the distribution of Nu changed, and its magnitude increased, suggesting the dominance of the axial throughflow.

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.

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