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 When
a fluid stream encounters a rock or another obstruction, it
separates moves around the object and flows downstream. At the
point of contact, eddy currents or vortex swirls are formed
alternately on either side of the object. This creates a local
increase in pressure and a local decrease in velocity on one
side of the obstruction. Meanwhile, it creates a local decrease
in pressure and a local increase in velocity on the other side
of the object. After shedding a swirl from one side, the process
is reversed and a vortex or a swirl is shed from the other side.
The frequency of this alternating shedding process is proportional
to the velocity of the flowing stream as it passes the point
of contact.
In the vortex shedding flow meter, the flow path is obstructed
by a bluff body (or strut) that creates the vortex swirl.
In 1912, Theodor Von Karman pioneered early bluff body design
in vortex metering development. This led to later awareness
that sharp-edged bluff bodies (struts) improve the strength
and consistency of vortex shedding. Therefore, we now refer
to a series or pattern of vortex swirls as "a Von Karman
vortex street".The rate of vortex shedding is detected
by an ultrasonic, electronic, or fiber optic sensor that monitors
the changes in the vortex pattern, or Von Karman vortex street
downstream from the bluff body, transmitting a pulsating output
signal to external readouts or data acquisition equipment. There
are no moving parts in a vortex shedding flow meter. The average
fluid velocity is proportional to the frequency of vortex shedding
and the width of the bluff body (strut). This proportionality
is defined as the Strouhal number, which is dimensionless.
Therefore: St = fdv
Where:
St = Strouhal Number
f = Frequency of Vortex Shedding
d = Width of Bluff Body
v = Average Fluid Velocity
The
actual width of a bluff body within a specific vortex meter
is fixed, therefore, a constant. The frequency of vortex shedding
is linearly proportional to the average flowing velocity over
a wide range of Reynolds numbers. Today, most vortex shedding
flow meters operate accurately at Reynolds numbers from 10,000
up to 10,000,000.
The vortex shedding flow meter is a volumetric flow meter. Therefore,
to define the mathematics of vortex metering, we must first
define the following relationships of volumetric flow.
Q = Av
Where: Q = Volumetric Flow Rate
v = Average Fluid Velocity
A = Cross Sectional Area of Flow Path
If a Strouhal number is substituted for average fluid velocity
(" v "), it becomes
Q = fdA
St
Since the Strouhal number, and bluff body width, and the cross
sectional area of the flow meter are all constants (which is
defined as "K"), the equation becomes;
Q = f
K
Similar to other frequency-producing flow meters, such as the
turbine meter, this "K" factor can be defined as pulses
per unit volume, such as pulses per gallon, pulses per liter,
pulses per cubic foot. Therefore, all that is needed is a defined
pulse per unit time to indicate the flow rate such as GPM, lpm,
or ft/sec.
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