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.

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.

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

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.

Numerical Simulation of Incompressible Laminar Flow over Three-Dimensional Rectangular Cavities

2004 ◽  
Vol 126 (6) ◽  
pp. 919-927 ◽  
Author(s):  
H. Yao ◽  
R. K. Cooper ◽  
S. Raghunathan
Keyword(s):  
Reynolds Number ◽  
Incompressible Flow ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Cavity Flow ◽  
External Flow ◽  
Cavity Flows ◽  
Recirculating Flow ◽  
Deep Cavity ◽  
Shallow Cavity

This paper presents results of investigations of unsteady incompressible flow past three-dimensional cavities, where there is a complex interaction between the external flow and the recirculating flow inside the cavity. A computational fluid dynamics approach is used in the study. The simulation is based on the solution of the unsteady Navier-Stokes equations for three-dimensional incompressible flow by using finite difference schemes. The cavity is assumed to be rectangular in geometry, and the flow is assumed to be laminar. Typical results of computation are presented, showing the effects of the Reynolds number, cavity geometry, and inflow condition on the cavity flow fields. The results show that high Reynolds numbers, with deep cavity and shallow cavity flows can become unsteady with Kelvin-Helmholtz instability oscillations and exhibiting a three-dimensional nature, with Taylor-Go¨rtler longitudinal vortices on the floor and longitudinal vortex structures on the shear layer. At moderate Reynolds numbers the shallow cavity flow is more stable than deep cavity flows. For a given Reynolds number the flow structure is affected by the thickness of the inflow boundary layer with a significant interaction between the external flow and the recirculating flow inside the cavity.

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.

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.

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 three-dimensional dielectric electrohydrodynamic convection between two plates

2012 ◽  
Vol 696 ◽  
pp. 228-262 ◽  
Author(s):  
A. Kourmatzis ◽  
J. S. Shrimpton
Keyword(s):  
Spatial Data ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Energy Budgets ◽  
Turbulent Regime ◽  
Scalar Flux ◽  
Wide Range ◽  
Scalar Variance

AbstractThe fundamental mechanisms responsible for the creation of electrohydrodynamically driven roll structures in free electroconvection between two plates are analysed with reference to traditional Rayleigh–Bénard convection (RBC). Previously available knowledge limited to two dimensions is extended to three-dimensions, and a wide range of electric Reynolds numbers is analysed, extending into a fully inherently three-dimensional turbulent regime. Results reveal that structures appearing in three-dimensional electrohydrodynamics (EHD) are similar to those observed for RBC, and while two-dimensional EHD results bear some similarities with the three-dimensional results there are distinct differences. Analysis of two-point correlations and integral length scales show that full three-dimensional electroconvection is more chaotic than in two dimensions and this is also noted by qualitatively observing the roll structures that arise for both low (${\mathit{Re}}_{E} = 1$) and high electric Reynolds numbers (up to ${\mathit{Re}}_{E} = 120$). Furthermore, calculations of mean profiles and second-order moments along with energy budgets and spectra have examined the validity of neglecting the fluctuating electric field ${ E}_{i}^{\ensuremath{\prime} } $ in the Reynolds-averaged EHD equations and provide insight into the generation and transport mechanisms of turbulent EHD. Spectral and spatial data clearly indicate how fluctuating energy is transferred from electrical to hydrodynamic forms, on moving through the domain away from the charging electrode. It is shown that ${ E}_{i}^{\ensuremath{\prime} } $ is not negligible close to the walls and terms acting as sources and sinks in the turbulent kinetic energy, turbulent scalar flux and turbulent scalar variance equations are examined. Profiles of hydrodynamic terms in the budgets resemble those in the literature for RBC; however there are terms specific to EHD that are significant, indicating that the transfer of energy in EHD is also attributed to further electrodynamic terms and a strong coupling exists between the charge flux and variance, due to the ionic drift term.

scholarly journals Steady flow separation patterns in a 45 degree junction

2000 ◽  
Vol 411 ◽  
pp. 1-38 ◽  
Author(s):  
C. ROSS ETHIER ◽  
SUJATA PRAKASH ◽  
DAVID A. STEINMAN ◽  
RICHARD L. LEASK ◽  
GREGORY G. COUCH ◽  
...  
Keyword(s):  
Flow Separation ◽  
Stokes Equations ◽  
Bypass Graft ◽  
Three Dimensional ◽  
Symmetry Plane ◽  
Axial Flow ◽  
Reynolds Numbers ◽  
Secondary Flows ◽  
Measured Velocity ◽  
Curved Tube

Numerical and experimental techniques were used to study the physics of flow separation for steady internal flow in a 45° junction geometry, such as that observed between two pipes or between the downstream end of a bypass graft and an artery. The three-dimensional Navier–Stokes equations were solved using a validated finite element code, and complementary experiments were performed using the photochromic dye tracer technique. Inlet Reynolds numbers in the range 250 to 1650 were considered. An adaptive mesh refinement approach was adopted to ensure grid-independent solutions. Good agreement was observed between the numerical results and the experimentally measured velocity fields; however, the wall shear stress agreement was less satisfactory. Just distal to the ‘toe’ of the junction, axial flow separation was observed for all Reynolds numbers greater than 250. Further downstream (approximately 1.3 diameters from the toe), the axial flow again separated for Re [ges ] 450. The location and structure of axial flow separation in this geometry is controlled by secondary flows, which at sufficiently high Re create free stagnation points on the model symmetry plane. In fact, separation in this flow is best explained by a secondary flow boundary layer collision model, analogous to that proposed for flow in the entry region of a curved tube. Novel features of this flow include axial flow separation at modest Re (as compared to flow in a curved tube, where separation occurs only at much higher Re), and the existence and interaction of two distinct three-dimensional separation zones.

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