Journal ArticleDOI
Kinematical studies of the flows around free or surface-mounted obstacles; applying topology to flow visualization
TLDR
In this paper, the authors show that the zero-shear-stress points on the surface and on the obstacle must be such that the sum of the nodes and the saddles of the saddle must satisfyAbstract:
In flows around three-dimensional surface obstacles in laminar or turbulent streamsthere are a number of points where the shear stress or where two or more component,s of the mean velocity are zero. In the first part of this paper we summarize and extend the kinematical theory for the flow near these points, particularly by emphasizing the topological classification of these points as nodes or saddles. We show that the zero-shear-stress points on the surface and on the obstacle must be such that the sum of the nodes ΣN and the sum of the saddles Σs satisfy
\[
\Sigma_N -\Sigma_S = 0.
\]
If the obstacle has a hole through it, such as a passageway under a building,
\[
\Sigma_N -\Sigma_S =-2.
\]
If the surface is a junction between two pipes,
\[
\Sigma_N -\Sigma_S =-1.
\]
We also consider, in two-dimensional plane sections of the flow, the points where the components of the mean velocity parallel to the planes are zero, both in the flow and near surfaces cutting the sections. The latter points are half-nodes N′ or half-saddles S′. We find that
\[
(\Sigma_N +{\textstyle\frac{1}{2}}\Sigma_{N^{\prime}}-(\Sigma_{S^{\prime}}+{\textstyle\frac{1}{2}}\Sigma_{S^{\prime}}) = 1-n,
\]
where n is the connectivity of the section of the flow considered.In the second part new flow-visualization studies of laminar and turbulent flows around cuboids and axisymmetric humps (i.e. model hills) are reported. A new method of obtaining a high resolution of the surface shear-stress lines was used. These studies show how enumerating the nodes and saddle points acts as a check on the inferred flow pattern.Two specific conclusions drawn from these studies are that:
for all the flows we observed, there are no closed surfaces of mean streamlines around the separated flows behind three-dimensional surface obstacles, which con-tradicts most of the previous suggestions for such flows (e.g. Halitsky 1968);the separation streamline on the centre-line of a three-dimensional bluff obstacle does not, in general, reattach to the surface.read more
Citations
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Journal ArticleDOI
Topology of Three-Dimensional Separated Flows
Murray Tobak,David J. Peake +1 more
TL;DR: In this article, the authors define a small number of singular points (nodes, saddle points, and foci) that characterize the patterns on the surface and on particular projections of the flow (e.g., the crossflow plane).
Journal ArticleDOI
The Flow Around Surface-Mounted, Prismatic Obstacles Placed in a Fully Developed Channel Flow (Data Bank Contribution)
R. Martinuzzi,Cameron Tropea +1 more
TL;DR: In this paper, the flow field around surface-mounted, prismatic obstacles with different spanwise dimensions was investigated using the crystal violet, oil-film and laser-sheet visualization techniques as well as by static pressure measurements.
Journal ArticleDOI
Experiments on stably and neutrally stratified flow over a model three-dimensional hill
J. C. R. Hunt,William H. Snyder +1 more
TL;DR: In this paper, the authors describe the flow structure observed over a bell-shaped hill with height h (the profile of which is the reciprocal of a fourth-order polynomial) when it was placed first in a large towing tank containing stratified saline solutions with uniform stable density gradients and second in an unstratified wind tunnel.
Journal ArticleDOI
Turbulent flow over hills and waves
Stephen E. Belcher,J. C. R. Hunt +1 more
TL;DR: A review of the mechanisms that control neutrally stable turbulent boundary-layer flow over hills and waves, their relative magnitudes, and how they exert their greatest effects in different regions of the flow can be found in this article.
Journal ArticleDOI
Post-stall flow control on an airfoil by local unsteady forcing
TL;DR: In this article, the authors used a Reynolds-averaged two-dimensional computation of a turbulent flow over an airfoil at post-stall angles of attack, and showed that the massively separated and disordered unsteady flow can be effectively controlled by periodic blowing-suction near the leading edge with low-level power input.
References
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Book
An Introduction to Fluid Dynamics
TL;DR: The dynamique des : fluides Reference Record created on 2005-11-18 is updated on 2016-08-08 and shows improvements in the quality of the data over the past decade.
Book
Theory of Ordinary Differential Equations
TL;DR: The prerequisite for the study of this book is a knowledge of matrices and the essentials of functions of a complex variable as discussed by the authors, which is a useful text in the application of differential equations as well as for the pure mathematician.
Journal ArticleDOI
Viscous and resistive eddies near a sharp corner
TL;DR: In this paper, it was shown that when either or both of the boundaries is a rigid wall and when the angle between the planes is less than a certain critical angle, any flow sufficiently near the corner must consist of a sequence of eddies of decreasing size and rapidly decreasing intensity.
Journal ArticleDOI
The flow around a surface-mounted cube in uniform and turbulent streams
Ian P. Castro,A. G. Robins +1 more
TL;DR: In this article, an experimental investigation of the flow around surface mounted cubes in both uniform, irrotational and sheared, turbulent flows is described, and comparisons with the somewhat sparse measurements of previous workers are made and the relevance of recent theoretical attempts to describe the flow, as opposed to numerical calculation techniques to predict it, is briefly discussed.
Related Papers (5)
The flow around a surface-mounted cube in uniform and turbulent streams
Ian P. Castro,A. G. Robins +1 more
The Flow Around Surface-Mounted, Prismatic Obstacles Placed in a Fully Developed Channel Flow (Data Bank Contribution)
R. Martinuzzi,Cameron Tropea +1 more