16. Creeping flow past two circles side-by-side.
The Reynolds number is 0.01, and the gap between the cylinders is 0.2
their diameter. Aluminum dust in glycerine shows that there is no-apparent
separation. Taneda 1979, J. Phys. Soc. Jpn.,46, 1935-1942.
17. Circle in slow linear
shear near a plate.
The cylinder is 0.1 diameter from the plate,or
0.2 diameter from its hydrodynamic image, which is actual
ly visible as an
optical image. The Reynolds number is 0.011 based on the shear rate.Large
recirculating eddies form because the glycerine must stick to the plate,
in contrast to the photograph above, where it flows along the symmetry plane.
Taneda 1979, J. Phys. Soc. Jpn., 46, 1935-1942.
Laminar separation from a curved wall.
Air bubbles i
n water show the separation of a laminar
boundary layer whose Reynolds number is 20,000 based on distance from the
leading edge (not shown). Because it is free of bubbles, the boundary layer
appears as a thin dark line at the left. It separates tangentially near
the start of the convex surface, remaining laminar for the distance to which
the dark line persists, and then becomes unstable and turbulent. ONERA
photograph, Werlé 1974, Le Tunnel Hydrodynamique au Servicede
la Recherche Ae
rospatiale, Publ. No. 156, ONERA, France.
Turbulent separation over a rectangular block on a plate.
The step height is large compared with the thickness
of the oncoming laminar boundary layer. The flow is effectively plane, so
that the recirculating region ahead of the step is closed, whereas in the
corresponding three-dimensional flow it is op
en and drains around the sides,ONERA
photograph, Werlé 1974, Le Tunnel Hydrodynamiqueau Service
de la Recherche Aerospatiale, Publ. No. 156, ONERA, France.
Circular cylinder at R=9.6.
Here, the flow has clearly separated to form a pair of recirculating eddies.
The cylinder is moving through a tank of water containing aluminum powder,
and is illuminated by a sh
eet of light below the free surface.Extrapolation
of such experiments to unbounded flow suggests separation at R=4 or 5, whereas
most numerical computations give R=5 to 7. Photograph by Sadatoshi Taneda.
41. Circular cylinder at R=13.1.
The standing eddies become elongated in the flow directional the speed increases.
Their length is found to increase linearly with Reynolds number until the
flow becomes unstable above R=40. Taneda 1956a, J. Phys. Soc. Jpn.,
42.Circular cylinder at R=26.
The downstream distance to the cores of the eddies also increases linearly
with Reynolds number. However, the lateral distance between the cores appears
to grow more nearly as the square root. Photograph by Sadatoshi Taneda.
47. Circular cylinder at R=2000.
At this Reynolds number one may properly speak of a boundary layer. It is
laminar over the front, separates, and breaks up into a turbulent wake.
The separation points, moving forward as the Reynolds number is increased,
have now attained their upstream limit,ahead of maximum thickness. Visualization
is by air bubbles in water. ONERA pho
tograph, Werlé Gallon
1972, Aeronaut. Astronaut.,no. 34, 21-33.
Circular cylinder at R=10,000.
At five times the speed of the photograph at the
top of the page, the flow pattern is scarcely changed. The drag coefficient
consequently remains almost constant in the range of Reynolds number spanned
by these two photographs. It drop
s later when the boundary layer becomes
turbulent at separation. Photograph by Thomas Corke and Hassan Nagib.
The sphere is falling steadily down the axis of a tube filled with oil,
but here so large that the influence of the walls is negligible.Magnesium
cuttings are illuminated by a sheet of light, which casts the shadow of
the sphere. Archives de l'Académie de
s Sciences de Paris, Payard
Coutanceau 1974, C.R. Acad. Sci. Ser. B,
53. Sphere at R=118.
The wake grows more slowly in axisymmetric than
plane flow. These photographs have shown that the length of the recirculating
region is proportional to the logarithm of the Reynolds number, whereas
ws linearly with Reynolds number for a cylinder. Aluminum dust shows
the flow of water. Taneda 1956a, J. Phys. Soc. Jpn., 11, 302-307.