A laboratory study of two-dimensional and three-dimensional instabilities in a quasi-two-dimensional flow driven by differential rotation of a cylindrical tank and a disc on the free surface

2004 ◽  
Vol 16 (9) ◽  
pp. 3325-3340 ◽  
Author(s):  
Isao Kanda
Keyword(s):  
Free Surface ◽  
Laboratory Study ◽  
Differential Rotation ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Cylindrical Tank ◽  
Dimensional Flow ◽  
Two Dimensional Flow

Contracting ducts of finite length

1951 ◽  
Vol 2 (4) ◽  
pp. 254-271 ◽  
Author(s):  
L. G. Whitehead ◽  
L. Y. Wu ◽  
M. H. L. Waters
Keyword(s):  
Stream Function ◽  
Finite Length ◽  
Velocity Potential ◽  
Three Dimensional ◽  
Relaxation Method ◽  
Two Dimensional ◽  
Dimensional Flow ◽  
Hodograph Plane ◽  
Two Dimensional Flow ◽  
Working Section

SummmaryA method of design is given for wind tunnel contractions for two-dimensional flow and for flow with axial symmetry. The two-dimensional designs are based on a boundary chosen in the hodograph plane for which the flow is found by the method of images. The three-dimensional method uses the velocity potential and the stream function of the two-dimensional flow as independent variables and the equation for the three-dimensional stream function is solved approximately. The accuracy of the approximate method is checked by comparison with a solution obtained by Southwell's relaxation method.In both the two and the three-dimensional designs the curved wall is of finite length with parallel sections upstream and downstream. The effects of the parallel parts of the channel on the rise of pressure near the wall at the start of the contraction and on the velocity distribution across the working section can therefore be estimated.

Three-dimensional flow in cavities

1963 ◽  
Vol 16 (4) ◽  
pp. 620-632 ◽  
Author(s):  
D. J. Maull ◽  
L. F. East
Keyword(s):  
Static Pressure ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Three Dimensional Flow ◽  
Large Span ◽  
Dimensional Flow ◽  
Pressure Distributions ◽  
Oil Flow ◽  
Two Dimensional Flow

The flow inside rectangular and other cavities in a wall has been investigated at low subsonic velocities using oil flow and surface static-pressure distributions. Evidence has been found of regular three-dimensional flows in cavities with large span-to-chord ratios which would normally be considered to have two-dimensional flow near their centre-lines. The dependence of the steadiness of the flow upon the cavity's span as well as its chord and depth has also been observed.

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.

Vorticity and curvature at a free surface

1998 ◽  
Vol 356 ◽  
pp. 149-153 ◽  
Author(s):  
MICHAEL S. LONGUET-HIGGINS
Keyword(s):  
Free Surface ◽  
Simple Relation ◽  
Surface Curvature ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Dimensional Flow ◽  
Umbilical Point ◽  
Two Dimensional Flow ◽  
Principal Directions ◽  
Component Parallel

For two-dimensional flow there is a simple relation between the vorticity at a stress-free surface and the surface curvature. In this note the relation is generalized to flow in three dimensions. It is shown that in addition to a component of vorticity perpendicular to the flow there is also a component parallel to the direction of flow. The latter vanishes only at an umbilical point or when the flow is in one of the two principal directions of curvature.

Theoretical Aspects of Thrust Vector Control by Secondary Gas Injection in Rocket Nozzles

1968 ◽  
Vol 72 (686) ◽  
pp. 171-177 ◽  
Author(s):  
John H. Neilson ◽  
Alastair Gilchrist ◽  
Chee K. Lee
Keyword(s):  
Vector Control ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Three Dimensional Flow ◽  
Side Force ◽  
Thrust Vector Control ◽  
Dimensional Flow ◽  
Two Dimensional Flow ◽  
Thrust Vector ◽  
Secondary Injection

This work deals with theoretical aspects of thrust vector control in rocket nozzles by the injection of secondary gas into the supersonic region of the nozzle. The work is concerned mainly with two-dimensional flow, though some aspects of three-dimensional flow in axisymmetric nozzles are considered. The subject matter is divided into three parts. In Part I, the side force produced when a physical wedge is placed into the exit of a two-dimensional nozzle is considered. In Parts 2 and 3, the physical wedge is replaced by a wedge-shaped “dead water” region produced by the separation of the boundary layer upstream of a secondary injection port. The modifications which then have to be made to the theoretical relationships, given in Part 1, are enumerated. Theoretical relationships for side force, thrust augmentation and magnification parameter for two- and three-dimensional flow are given for secondary injection normal to the main nozzle axis. In addition, the advantages to be gained by secondary injection in an upstream direction are clearly illustrated. The theoretical results are compared with experimental work and a comparison is made with the theories of other workers.

scholarly journals Volumetric imaging of shark tail hydrodynamics reveals a three-dimensional dual-ring vortex wake structure

2011 ◽  
Vol 278 (1725) ◽  
pp. 3670-3678 ◽  
Author(s):  
Brooke E. Flammang ◽  
George V. Lauder ◽  
Daniel R. Troolin ◽  
Tyson Strand
Keyword(s):  
Three Dimensional ◽  
Flow Patterns ◽  
Wake Flow ◽  
Ring Vortex ◽  
Vortex Wake ◽  
Two Dimensional ◽  
Volumetric Imaging ◽  
Dimensional Flow ◽  
Classic Problem ◽  
Two Dimensional Flow

Understanding how moving organisms generate locomotor forces is fundamental to the analysis of aerodynamic and hydrodynamic flow patterns that are generated during body and appendage oscillation. In the past, this has been accomplished using two-dimensional planar techniques that require reconstruction of three-dimensional flow patterns. We have applied a new, fully three-dimensional, volumetric imaging technique that allows instantaneous capture of wake flow patterns, to a classic problem in functional vertebrate biology: the function of the asymmetrical (heterocercal) tail of swimming sharks to capture the vorticity field within the volume swept by the tail. These data were used to test a previous three-dimensional reconstruction of the shark vortex wake estimated from two-dimensional flow analyses, and show that the volumetric approach reveals a different vortex wake not previously reconstructed from two-dimensional slices. The hydrodynamic wake consists of one set of dual-linked vortex rings produced per half tail beat. In addition, we use a simple passive shark-tail model under robotic control to show that the three-dimensional wake flows of the robotic tail differ from the active tail motion of a live shark, suggesting that active control of kinematics and tail stiffness plays a substantial role in the production of wake vortical patterns.

Extension of the Prandtl–Batchelor theorem to three-dimensional flows slowly varying in one direction

2010 ◽  
Vol 654 ◽  
pp. 351-361 ◽  
Author(s):  
M. SANDOVAL ◽  
S. CHERNYSHENKO
Keyword(s):  
Flow Field ◽  
Small Parameter ◽  
Order Approximation ◽  
Three Dimensional ◽  
Inviscid Limit ◽  
Two Dimensional ◽  
Leading Order ◽  
Dimensional Flow ◽  
Two Dimensional Flow

According to the Prandtl–Batchelor theorem for a steady two-dimensional flow with closed streamlines in the inviscid limit the vorticity becomes constant in the region of closed streamlines. This is not true for three-dimensional flows. However, if the variation of the flow field along one direction is slow then it is possible to expand the solution in terms of a small parameter characterizing the rate of variation of the flow field in that direction. Then in the leading-order approximation the projections of the streamlines onto planes perpendicular to that direction can be closed. Under these circumstances the extension of the Prandtl–Batchelor theorem is obtained. The resulting equations turned out to be a three-dimensional analogue of the equations of the quasi-cylindrical approximation.

A Theory for the Side Force produced in Two-Dimensional Nozzles by Secondary Gas Injection

1968 ◽  
Vol 72 (687) ◽  
pp. 267-274
Author(s):  
John H. Neilson ◽  
Alastair Gilchrist ◽  
Chee K. Lee
Keyword(s):  
Gas Injection ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Three Dimensional Flow ◽  
Side Force ◽  
Dimensional Flow ◽  
Increase With Increase ◽  
Two Dimensional Flow ◽  
Secondary Port ◽  
Theoretical Side

Summary:This work is concerned with the side force produced in rocket nozzles by secondary gas injection. A new theory for determining the side force is presented for two-dimensional flow and this is considered to be an important step towards a theory applicable to three-dimensional flow. The proposed theory is based on a double wedge model for the separated region upstream of the secondary port. The principal feature of the model is that it accounts tor the fact that the angle of the shock wave, originating from the separated region, is observed to increase with increase in secondary mass flow rate. Theoretical side force results are shown to compare favourably with experimental results obtained using two-dimensional nozzles and a comparison is made between the proposed theory and the theories of other workers.

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