Page 52 - Fluid mechanics, heat transfer, and mass transfer

FLOW PHENOMENA 29

& When considering a long circular cylinder, the fre-
quency of vortex shedding is given by the empirical
formula
f vs D 0 =V c ¼ 0:198½1 ð19:7=N Re ފ; ð2:21Þ

where f vs is the vortex shedding frequency (Hz), D 0 is
FIGURE 2.8 Vortex street phenomenon.
the diameter of the cylinder, and V c is the flow
velocity.
essentially a measure of the ratio of inertial to viscous & This formula will generally hold good for the range
5
forces in the flow. 250 < N Re < 2 10 .
7
& Over a large N Re range (47 < N Re < 10 for circular . What is Strouhal number?
cylinders), eddies are shed continuously from each & The dimensionless parameter, f vs D 0 /V c , is known as
side of the body, forming rows of vortices in its wake. the Strouhal number.
The alternation leads to the core of a vortex in one & Studies have shown that insects such as bees borrow
row being opposite to the point midway between two
energy from thevortices that form around their wings
vortex cores in the other row, giving rise to the
during flight. Vortices inherently create drag. Insects
distinctive pattern shown in Figure 2.8. Ultimately,
can recapture some of this energy and use it to
the energy of the vortices is consumed by viscosity as
improve speed and maneuverability. Insects rotate
they move further downstream and the regular pat-
their wings before starting the return stroke, and
tern disappears.
thewings are lifted by the eddies of air created on the
& When a vortex is shed, an unsymmetrical flow pattern
downstroke. The high-frequency oscillation of
forms around the body, which therefore changes the insect wings means that many hundreds of vortices
pressure distribution. This means that the alternate are shed every second. However, this leads to a
shedding of vortices can create periodic lateral forces symmetric vortex street pattern, unlike the ones
on the body in question, causing it to vibrate. If the shown above.
vortex shedding frequency is similar to the natural & Flow across a tube produces a series of vortices in the
frequency of a body or structure, it causes resonance. downstream wake formed as the flow separates al-
It is this forced vibration that, when at the correct ternately from the opposite sides of the tube.
frequency, causes telephone or power lines to hum,
& This alternate shedding of vortices produces alter-
the antennae on a car to vibrate more strongly at
nating forces that occur more frequently as the
certain speeds, and it is also responsible for the
velocity of flow increases.
fluttering of Venetian blinds as the wind passes
& For a single cylinder, the tube diameter, the flow
through them.
velocity, and the frequency of vortex shedding can be
& Periodic forcing set up in this way can be highly
described by the dimensionless Strouhal number.
undesirable and hence it is important for engineers to
& For single cylinders, the vortex shedding Strouhal
account for the possible effects of vortex shedding
number is a constant with a value of about 0.2.
when designing a wide range of structures, from
submarine periscopes to industrial chimneys. In or- & Vortex shedding occurs in the range of Reynolds
6
5
der to prevent the unwanted vibration of such cylin- numbers 100 to 5 10 and greater than 2 10 . The
drical bodies, a longitudinal fin can be fitted on the gap is due to a shift of the flow separation point of the
downstream side, which, as long as it is longer than vortices in this intermediate transcritical Reynolds
the diameter of the cylinder, will prevent the eddies number range.
from interacting, and consequently they remain at- & Vortex shedding also occurs for flow across tube
tached. Obviously for a tall building or mast, the banks. The Strouhal number is no longer a constant,
relative wind could come from any direction. For this but varies with the arrangement and spacing of the
reason, helical projections that look like large screw tubes. There is less certainty that there is a gap in the
threads are sometimes placed at the top, which vortex shedding Reynolds number.
effectively create unsymmetrical three-dimensional & Vortex shedding is fluid mechanical in nature and
flow, thereby discouraging the alternate shedding of does not depend on any movement of the tubes. For a
vortices. given arrangement and tube size, the frequency of
& A vortex street phenomenon is illustrated in the vortex shedding increases as the velocity
Figure 2.8. increases.