Chaotic mixing in a bounded three-dimensional flow

2000 ◽  
Vol 417 ◽  
pp. 265-301 ◽  
Author(s):  
G. O. FOUNTAIN ◽  
D. V. KHAKHAR ◽  
I. MEZIĆ ◽  
J. M. OTTINO
Keyword(s):  
Laser Sheet ◽  
Three Dimensional ◽  
Vertical Axis ◽  
Operating Conditions ◽  
Chaotic Advection ◽  
Base Case ◽  
Dimensional System ◽  
Three Dimensional Flow ◽  
Dimensional Flow ◽  
Moderate Reynolds Number

Even though the first theoretical example of chaotic advection was a three-dimensional flow (Hénon 1966), the number of theoretical studies addressing chaos and mixing in three-dimensional flows is small. One problem is that an experimentally tractable three-dimensional system that allows detailed experimental and computational investigation had not been available. A prototypical, bounded, three-dimensional, moderate-Reynolds-number flow is presented; this system lends itself to detailed experimental observation and allows high-precision computational inspection of geometrical and dynamical effects. The flow structure, captured by means of cuts with a laser sheet (experimental Poincaré section), is visualized via continuously injected fluorescent dye streams, and reveals detailed chaotic structures and chains of high-period islands. Numerical experiments are performed and compared with particle image velocimetry (PIV) and flow visualization results. Predictions of existing theories for chaotic advection in three-dimensional volume-preserving flows are tested. The ratio of two frequencies of particle motion – the frequency of motion around the vertical axis and the frequency of recirculation in the plane containing the axis – is identified as the crucial parameter. Using this parameter, the number of islands in the chain can be predicted. The same parameter – using as a base-case the integrable motion – allows the identification of operating conditions where small perturbations lead to nearly complete mixing.

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

2017 ◽  
Vol 825 ◽  
pp. 631-650 ◽  
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.

Three-Dimensional-Flow Theories for Axial Compressors and Turbines

1948 ◽  
Vol 159 (1) ◽  
pp. 255-268 ◽  
Author(s):  
A. D. S. Carter
Keyword(s):  
Three Dimensional ◽  
Axial Compressor ◽  
Physical Nature ◽  
Secondary Flows ◽  
Operating Conditions ◽  
Tip Clearance ◽  
Three Dimensional Flow ◽  
Axial Compressors ◽  
Dimensional Flow ◽  
Blade Row

It has long been known that the energy losses occurring in an axial compressor or turbine cannot be fully accounted for by the skin-friction losses on the blades and annulus walls. The difference, usually termed secondary loss, is attributed to miscellaneous secondary flows which take place in the blade row. These flows both cause losses in themselves and modify the operating conditions of the individual blade sections, to the detriment of the overall performance. This lecture analyses the three-dimensional flow in axial compressors and turbines, so that, by appreciation of the factors involved, possible methods of improving the performance can readily be investigated. The origin of secondary flow is first examined for the simple case of a straight cascade. The physical nature of the flow, and theories which enable quantitative estimates to be made, are discussed at some length. Following this, the three-dimensional flow in an annulus with a stationary blade row is examined, and, among other things, the influence of radial equilibrium on the flow pattern is noted. All physical restrictions are then removed, and the major factors governing the three-dimensional flow in an actual machine are investigated as far as is possible with existing information, particular attention being paid to the influence of a non-uniform velocity profile, tip clearance, shrouding, and boundary layer displacement. Finally the various empirical factors used in design are discussed, and the relationships between them established.

Three-dimensional flow field around and downstream of a subscale model rotating vertical axis wind turbine

2016 ◽  
Vol 57 (3) ◽  
Author(s):  
Kevin J. Ryan ◽  
Filippo Coletti ◽  
Christopher J. Elkins ◽  
John O. Dabiri ◽  
John K. Eaton
Keyword(s):  
Flow Field ◽  
Wind Turbine ◽  
Three Dimensional ◽  
Vertical Axis ◽  
Vertical Axis Wind Turbine ◽  
Three Dimensional Flow ◽  
Dimensional Flow

Development of a Two-Dimensional Computational Fluid Dynamics Approach for Computing Three-Dimensional Honeycomb Labyrinth Leakage

2004 ◽  
Vol 126 (4) ◽  
pp. 794-802 ◽  
Author(s):  
Dong-Chun Choi ◽  
David L. Rhode
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Three Dimensional ◽  
Labyrinth Seal ◽  
Operating Conditions ◽  
Two Dimensional ◽  
Cfd Model ◽  
Resource Requirement ◽  
Three Dimensional Flow ◽  
Dimensional Flow

A new approach for employing a two-dimensional computational fluid dynamics (CFD) model to approximately compute a three-dimensional flow field such as that in a honeycomb labyrinth seal was developed. The advantage of this approach is that it greatly reduces the computer resource requirement needed to obtain a solution of the leakage for the three-dimensional flow through a honeycomb labyrinth. After the leakage through the stepped labyrinth seal was measured, it was used in numerically determining the value of one dimension (DTF1) of the simplified geometry two-dimensional approximate CFD model. Then the capability of the two-dimensional model approach was demonstrated by using it to compute the three-dimensional flow that had been measured at different operating conditions, and in some cases different distance to contact values. It was found that very close agreement with measurements was obtained in all cases, except for that of intermediate clearance and distance to contact for two sets of upstream and downstream pressure. The two-dimensional approach developed here offers interesting benefits relative to conventional algebraic-equation models, particularly for evaluating labyrinth geometries/operating conditions that are different from that of the data employed in developing the algebraic model.

Unsteady Three-Dimensional Flow Phenomena in an Axial Flow Pump at Different Operating Points

2008 ◽  
Author(s):  
Friedrich-Karl Benra ◽  
Hans Josef Dohmen
Keyword(s):  
Three Dimensional ◽  
Axial Flow ◽  
Flow Fields ◽  
Operating Conditions ◽  
Three Dimensional Flow ◽  
Design Point ◽  
Part Load ◽  
Dimensional Flow ◽  
Axial Flow Pump ◽  
Flow Pump

In highly loaded axial flow pumps considerable changes of the flow behavior are known when altering the flow rate from design point operation to part load operation. The flow structure which is changing from stable operating conditions to stalled flow conditions has been investigated experimental by Kosyna and Stark. The measured results are compared to results obtained by numerical simulations in a previous paper of the authors. Time dependent three dimensional flow fields in this axial flow pump have been investigated by unsteady Reynolds averaged Navier-Stokes simulations. The time resolved flow fields are compared to the time averaged results of the measurements for the design point and also for part load operating conditions. The change in the vortex structure induced by the tip leakage flow is investigated in detail for different conditions of operation. Also the part load recirculation vortex dominating the rotor tip flow at deep stall conditions as well as the cross passage vortex is visualized by evaluating the numerical results.

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