Baker R.C. Flow Measurement Handbook: Industrial Designs, Operating Principles, Performance, and Applications
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11.3 INDUSTRIAL DEVELOPMENTS OF VORTEX-SHEDDING FLOWMETERS 267
separated by 2D from the disturbance should have 5D to the meter. Mottram (1991)
obtained good results using a Mitsubishi conditioner with a different spacing. For a
bend, 90° offset bends, orifice plate with £ = 0.645, and fully open globe valve, his
results were within a band of
±1%
with 5D between the fitting and the conditioner,
2.5D between the conditioner and bluff body, and 2.5D downstream of the bluff
body.
Other mounting constraints are not usual, but pipework must ensure that the
meter runs full.
11.3.9 EFFECT OF PULSATION AND PIPELINE VIBRATION
It is known that vortex meters may be affected by pulsatile flow, particularly where
the pulsating frequency or its harmonics are close to the shedding frequency. The
meter may lock on to the pulsation frequency and give an error (cf. Amadi-Echendu
and Zhu 1992). Some sensing techniques may be more susceptible to error due to
pulsation than others. Some may be designed to select the shedding frequency by
eliminating pulsation or vibration using a push-pull arrangement.
Hebrard et al. (1992) confirmed that pulsations can cause large metering errors.
Pulsations of an amplitude of only a few percent may be sufficient to produce meter-
ing errors, particularly when the frequency
is
near the fundamental or first harmonic
of the shedding frequency. The lock-on frequency is most likely to occur when the
pulsation frequency is twice the vortex-shedding frequency, and lock-on can occur
(Al-Asmi and Castro 1992) even down to pulsation amplitudes of about 2%. Outside
the lock-on range, there can still be significant differences between the shedding
frequency in steady and pulsating flows, and free stream turbulence may increase
the problem.
Manufacturers may suggest that disturbances upstream of an unsteady nature
should be given a wide berth. Malard et al. (1991) found that there was an increase
of about 2% and a decrease in the signal-to-noise ratio when the turbulence intensity
increased from 3.3 to
10.3%.
Their work also confirmed the errors due to pulsatile
flows.
As indicated earlier, sensors are designed to minimize the effect of pipeline vibra-
tion, and the manufacturer should be consulted for information. However, process
noise may cause zero flow signals but may be diagnosed by looking at the raw signal
(Ginesi and Annarummo 1994).
11.3.10 TWO-PHASE FLOWS
Hussein and Owen (1991) found that the correction factor for the vortex meter
for wet steam of high dryness factor is closest to the value x~
1/2
(Figure 11.13). BS
3812:1964 is quite close. Pressure was shown to have little effect on correction
factors. Hussein and Owen (1991) gave the wise advice that an upstream separator is
advisable, and that there are several types giving a value of x >
95%
with reasonably
low pressure loss.
The possibility that the meter might be developed to sense the droplets of wet
steam is an interesting challenge for the signal processing experts.
268
VORTEX-SHEDDING, SWIRL, AND FLUIDIC FLOWMETERS
1.10
U. 1.05
3
1-00
0.95
0.90
0.85
vortex-shedding
meter
BS 3812:1964
0.84 0.88
0.92 0.96
Dryness fraction
x
1.00
Figure
11.13.
Comparison between wet steam correc-
tion factors for vortex meters (after Hussein and Owen
1991).
The meter
has
virtually
the
same
calibration
for
liquid
and gas
flows
and
might therefore
be
expected
to
behave
well
in
two-component flows. However
the published work highlights some severe
problems.
The first
is
that
the
components
are
separated
by
the vortex motion. Hulin
et al.
(1982,
1983)
found that shedding
in ver-
tical water-air flow
was
stable
up to
about
10%
void fraction. They also found that
the
vortices trap bubbles [Figure 2.9(b)] with
an associated decrease
in the
strength
of
the pressure fluctuations. Their later work
on water-oil flows shows some contrasts.
The separation
is
much more complete
for water-air
due
presumably
to the den-
sity difference,
and
this leads
to a
much
narrower vortex emission bandwidth.
The
stability
at oil
concentrations greater than
30%
was notable,
and the
cores
of the
vortices were continuous
oil.
The second
is
that
the
bubbles
may
trigger certain sensors. Baker
and
Deacon
(1983) obtained results suggesting that, even though vortex-shedding continued
with increase
in
void fraction
in a
vertical upward water-air flow, bubble impact
may cause additional pulses. Above
air
volume concentrations
of 1%, the
meter
error increased
by
more than 1%
for
each additional 1%
air
concentration.
A
third problem,
to
which Washington (1989) attributed poor results
in wet
gas,
may
be
slip between
the
components.
A
homogeneous second component
in the
flow may be measured
but
will usually result
in a
loss
of
accuracy due,
in
part,
to the
fact that
the
instrument measures
the
volumetric flow.
11.3.11 SIZE
AND
PERFORMANCE RANGES
AND
MATERIALS
IN INDUSTRIAL DESIGNS
As indicated earlier,
the low end is
limited
by
Reynolds number behavior,
and the
effect
of
Equation (11.1)
is
that,
as the
size increases,
the
frequency becomes very
low
and
makes
the
meter unusable.
Diameter ranges from about
12 to 200 mm or
more
are
quoted
by
various
man-
ufacturers. Flow rates through
the
meters
are up to
about
9 m/s for
liquids
and
75
m/s for
steam
and
gas. Flow ranges
for
liquids
may be
from
a
minimum
of
less
than
1 1/s to a
maximum
of
about
600 1/s and for
gases
15 1/s or
less
to
3,000
1/s or
more.
Range
is of
order
20:1 on gas and
steam
and 10:1 for
liquids
(up to 60:1 is
sometimes given). This creates a constraint with the minimum
Re,
which may inhibit
its application where
the
precise range
is
unknown
or
spans
two
meter sizes.
In
others,
a
smaller-sized meter may
be
necessary
to
cope with
the
range. Overranging
up
to 20% is
generally allowable,
but the low
flow
end may be
more
due to the
strength
of the
signal.
11.3 INDUSTRIAL DEVELOPMENTS OF VORTEX-SHEDDING FLOWMETERS 269
Minimum Reynolds number is variously given as 3,800-5,000, although meters
may be of lower accuracy below 10,000 and upper limits of 500,000 and up to or
greater than
1,000,000
may be given.
Viscosity should be below 8 cP (the viscosity of cooking oils), although it may
be possible to measure with reduced range up to 30 cP (Ginesi and Annarummo
1994).
A low flow cutoff is usually set somewhat below Re = 10,000, and this may
be a disadvantage for some applications.
The temperature range may be from less than -200° to over 400°C. Pressure may
be up to 150 bar or more depending on the transducer. Pressure drop on a meter
of nominal internal diameter equal to the pipe is normally less than about 40 kPa
(6 psi) on water flow.
Pulse rates will vary enormously depending on the size of the meter. For a small
meter of about 20 mm diameter, the rate will be of order 200
pulses/1,
whereas for
a large meter of 300 mm diameter the rate will be of order 0.02
pulses/1.
Response
time may be of order 0.2 s or three shedding cycles for a change to 63% of input.
All this may be affected by resolution problems when combined with poor period
repeatability.
Material of the bluff body is most commonly stainless steel but may be titanium
or another material.
Vortex meters, like turbine meters, are limited at the upper end of their range by
possible cavitation. Casperson (1975) suggested the possibility of hysteresis effects
due to cavitation and the need to avoid operating in this regime. To avoid cavitation
in liquid flows, some manufacturers give a formula of the following type for the
minimum back pressure 5D downstream:
Pgmin = AAp + Bp
v
- p
a
tmos
where Ap is the pressure drop across the meter, p
v
is the saturated liquid vapor
pressure, and p
a
tmos is the atmospheric pressure. A appears to have a value of about
3.0, and B has a value of about 1.3. Ap is of order 1 bar at 10 m/s.
These meters may, also, be subject to compressibility effects.
11.3.12 COMPUTATION OF FLOW AROUND BLUFF BODIES
Some early work obtained good agreement between numerical and experimental
results for Re up to 1,000 for confined two-dimensional flows around rectangular
cylinders (Davis et al. 1984). More recent work by Matsunaga et al. (1990) showed
some impressive computer-generated flow patterns around a trapezoidal body in a
two-dimensional flow. Comparison of Strouhal number obtained computationally
and experimentally agreed quite well at Re > 1,000 but appear to diverge for lower
Re and were less good for
Re
of order 10,000. Figure 11.14 shows the vortex-shedding
mechanism as interpreted by the authors.
Johnson (1990) computed the unsteady laminar flow around a cylinder and ob-
tained agreement within 10% for the Strouhal number in comparison with experi-
mental values for part of the range. Computer simulations by El Wahed et al. (1993)
again obtained good agreement with the experimentally acquired Strouhal number
and indicated that the T-shaped shedder produced the largest vortex.
270 VORTEX-SHEDDING, SWIRL, AND FLUIDIC FLOWMETERS
• Upper flow
(a)
(b)
\—s
(c)
Inlet
flow
(d)
(e)
Figure 11.14. Flow pattern behind shedder: (a) t =
1.2615
s; (b) t =
1.2660
s;
(c) t =
1.2690
s; (d) t =
1.2735
s; (e) t =
1.2765
s (after Matsunaga et al. 1990;
reproduced with permission of Elsevier Science Ltd.).
11.3.13 APPLICATIONS, ADVANTAGES, AND DISADVANTAGES
Furness and Jelffs (1991) sought to make a case for using vortexmeters to measure
flows in and out of refineries rather than depending on tank transfer. Proving, how-
ever, may be problematic due to the poor period repeatability.
11.3 INDUSTRIAL DEVELOPMENTS OF VORTEX-SHEDDING FLOWMETERS 271
Siegwarth (1989) discussed tests on specially designed vortex-shedding meters
for application to very high flow rates of liquid oxygen in the space shuttle main
engine ducts. The details of this work may be of interest to those engaged in vortex
flowmeter design.
The claims of manufacturers for applications include
• liquid flows (e.g., liquid N
2
, CO
2
, O
2
, clean liquids, distilled water, glycol, some
acids,
low viscosity hydrocarbons, benzene, diesel, hydraulic oils, creosote, and
tar),
• gas flows [e.g., steam (superheated and saturated) and various gases including
compressed air, methane, N
2
, and CO
2
], and
• cryogenic applications, but not multiphase applications.
In general Yamasaki (1993) saw the meter as an alternative to the orifice meter,
provided it could cover a similar range of fluid parameters. (One manufacturer claims
that costs are about 50% of those for orifice plates.) The sensing method is the main
constraint to extending parametric range. However, temperature range now allows
its use with superheated steam and liquid natural gas (LNG).
11.3.14 FUTURE DEVELOPMENTS
There is a need to extend the range of the vortex meter, to improve application data
(e.g., installation effects), and to develop the signal processing.
Zanker and Cousins in their work
as
long ago as 1975 foresaw the dual bluff body,
and, no doubt, there is further development possible in the design of these bodies.
They also mentioned annular ring/coaxially mounted bluff bodies, and Takamoto
and Komiya (1981) also proposed such a ring-shaped bluff body that sheds ring
vortices.
Miau and Hsu (1992) surveyed the flow around axisymmetric disks and rings as
vortex shedders, showed the pattern of vortex loops behind a disk, and were par-
ticularly interested in the flow characteristics near the pipe wall, suggesting that
an advantage of the axisymmetric designs is that the sensing can be on the pipe
wall. Axisymmetric vortex-shedding rings intuitively offer an elegant axisymmmet-
ric version of the meter. Tai et al. (1993) discussed optimum size and positioning
and signal-to-noise ratio. Cousins and Hayward
(1993,
cf. Cousins et al. 1989) de-
scribed developments of the vortex ring flowmeter and discussed sensing options.
They made the point that ring vortices are far more stable than those from straight
bluff
bodies.
They suggested that a ring/pipe diameter ratio of 0.4 is about optimum.
They found that the signal-to-noise ratio varies markedly across the pipe and down
the centerline, peaking at 3 to 4 ring widths downstream. They found that the inner
ring vortices give a clearer signal. The provisional design, which appears to be opti-
mal is a double ring with a tail; it appears to give a repeatability of
±0.1%
or better
with only 0.3 velocity head pressure loss.
The combination of electrostatic sensing as described by El Wahed and Sproston
(1991) with ring vortex shedders could be very attractive. The sensor could be in the
wall of the tube or even at various points to give greater intelligence to the meter
and forms of self-monitoring.
272
VORTEX-SHEDDING, SWIRL, AND FLUIDIC FLOWMETERS
11.4 SWIRL METER - INDUSTRIAL DESIGN
This section is concerned with the industrial design of the swirl meter, which has
some fluid behavioral similarities to the vortex whistle (Chanaud 1965). In the whis-
tle,
initial swirl is created by tangential flow into an upstream plenum from which
the helical vortex emerges.
11.4.1 DESIGN AND OPERATION
A
diagram of this type of flowmeter is shown in Figure 11.15. As the flow enters the
meter, inlet guide vanes cause it to swirl.
As
the flow moves through the contraction,
the angular momentum created by the guide vanes is largely conserved, and so the
angular velocity will increase. The vortex filament develops into a helical vortex,
as shown in the diagram, which moves to the outside of the tube. The frequency
with which the helix passes the sensor provides a measure of the flow rate. The
flowmeter section then expands, and the swirling jet at the wall surrounds a region
of reverse flow on the axis. This motion is removed before the fluid leaves the meter
by means of a deswirler. Dijstelbergen (1970) explained the precession as being due
to the increasing pressure in the diffusing section causing a force on the exiting
swirl, which is converted to a lateral momentum change. Ricken (1989) gave further
details of a model to describe the behavior of the meter.
Heinrichs (1991) described a sensing system for a swirl meter in which the rota-
tion is sensed by using two diametrically opposed pressure ports. In the measuring
tube of the swirl meter, a helix-shaped vortex appears, rotating with a frequency
proportional to the volumetric flow rate. In this way, the differential pressure elimi-
nates common mode signals and hence the problem of a high line pressure and flow
Preamplifier
Swirler
Deswirler
Figure 11.15. Swirl flowmeter (after Bailey-Fischer and Porter with their per-
mission).
11.4 SWIRL METER - INDUSTRIAL DESIGN 273
fluctuations. The push-pull arrangement suggests that the range may be extended.
Capacitive sensors seem to be less suitable, whereas the results for piezoelectric ones
are more promising.
11.4.2 ACCURACY AND RANGES
An industrial design has been available for liquids, gases, or steam with vortex ro-
tation frequency obtained using piezosensors. Measurement uncertainty of better
than 1% of rate is claimed by the manufacturer over the upper 80% of the range for
the smaller sizes, with better than 2% for the 10-20% part of the range. For sizes
above 32 mm, uncertainty of better than 1% of rate is possible over the upper 90%
of the range.
Flow ranges are, for liquids, from 0.2 to 2 m
3
/h up to 180 to 1800 m
3
/h and,
for gases, from 5 to 25 m
3
/h up to 1000 to 20,000 m
3
/h. Values for steam should be
obtained from the manufacturer. Turndown for some sizes for liquids is up to about
30:1,
and for gases it is between 5:1 and 20:1. Maximum frequencies range for
liquids from 100 Hz for a 20-mm-diameter meter to 13 Hz for a 400-mm meter and
for gases from 1200 Hz for meters of 20 mm down to 150 Hz for a 400 mm diameter
meter. A 10% overranging is allowed in gases, but in liquids cavitation must be
avoided. Maximum velocity is 6 m/s for liquids and 50 m/s for gases.
For liquids at the top of the flow range, pressure loss can range from about 200
to 400 mbar or more, and for gases the range is from 25 to 70 mbar or more. The
flowmeter is available in designs suitable for hazardous area use.
11.4.3 MATERIALS
The material in contact with the liquid is predominantly stainless steel, except for
the thermistor sensor in gases, which is glass-insulated and epoxy-potted, and the
piezosensor, which is stainless steel or some other material.
11.4.4 INSTALLATION EFFECTS
For bends, contractions, and valves upstream, the recommendation is for 3D straight
pipe before the inlet flange; for bends and expansions downstream, it is ID. How-
ever, a contraction downstream is not permitted. For large radius bends, etc., the
requirements may be further reduced.
The manufacturer appears to claim low sensitivity to fluid pressure, temperature,
and density. Fluid temperature is -40 to 280° C.
Maximum viscosity is 70 mPas. Deposits can cause errors, but it may also tend
to self-clean. Cavitation must be avoided with liquids by ensuring adequate static
pressure.
11.4.5 APPLICATIONS, ADVANTAGES, AND DISADVANTAGES
The meter is recommended by the manufacturer for applications where absolute
reliability with minimum maintenance is essential and is claimed to be suitable for
wet or dirty gases and liquids. Specific applications are water, sludge water, conden-
sate,
acids, solvents, petrochemical raw materials, gasoline, air, CO
2
, natural gas,
ethylene, and steam.
274 VORTEX-SHEDDING, SWIRL, AND FLUIDIC FLOWMETERS
11.5 FLUIDIC FLOWMETER
The third instability we consider is that for the fluidic flowmeter. A diagram of a
typical design is shown in Figure 11.16. The fluidic flowmeter uses the Coanda effect.
If a two-dimensional diffuser has too wide an angle, the flow will separate and attach
to one wall of the diffuser. It may attach to either wall and can be displaced from
one to the other by a suitable disturbance. The fluidic flowmeter introduces such
a disturbance, which causes the flow to oscillate between the diffuser walls at a
frequency proportional to the velocity of flow. There are several parallels with the
vortex meter. Types of sensors used in vortex flowmeters could be applied to this
device. There is likely to be room for design optimization. The flow range may be
wide, and certainly the device looks promising for low flows.
The mechanism by which the flowmeter operates is that the flow, having at-
tached to one wall, passes into a feedback channel. The fluid when it exits from this
channel knocks the main jet to the other side of the diffuser, and the process starts
again. Thus the period is related to the time for the flow to move from the entry
of the flowmeter to the entry of the feedback channel and communicate, via that
channel, to the entry. This time will be inversely proportional to the velocity of flow,
and so the oscillating frequency will be proportional to the flow rate.
11.5.1 DESIGN
Boucher and Mazharoglu (1988) developed one design of fluidic target meter, which
operated down to Re of about 70 but with considerable change in Strouhal number
at low Re. Hysteresis may have a small effect in starting and stopping (cf. Boucher
1995).
Sanderson (1994) described a new fluidic water meter using electromagnetic
sensing. This is a particularly appropriate method with a wide dynamic range and a
linear response to flow rate. It is also usable in a constant magnetic field design due
to the fluctuating nature of the flow. The sensing electrodes were made of stainless
steel, and earthing electrodes were also provided. The magnetic materials considered
for this device included sintered ferrite and bonded and sintered neodymium. The
general configuration is shown in Figure 11.17. Sanderson's preferred arrangement
of magnetic sensor was for the measurement to take place in the main jet with
, Feedback
path
Oscillating
jet
Inlet • ^ '.'.'""" ( •
Outlet
Figure 11.16. Diagram of a fluidic flowmeter (reproduced with permission of
Professional Engineering Publishing).
11.5 FLUIDIC FLOWMETER 275
magnetic material in the diffuser walls giv-
ing a field strength of about 0.3 T. The two
pairs of electrodes were in the side walls act-
ing 180° out of phase in a push-pull arrange-
ment. Over most of its range, the meter
was linear to within ±2% (from about 5 to
500 ml/s). Further linearization was possi-
ble within the electronic circuitry. The me-
ter operated from a 3.6-V lithium battery
with a 10-year lifetime.
Sakai et al. (1989) described a dual sens-
ing system gas flowmeter for domestic use
in Japan. It was designed to operate from
3,000 1/h down to 150 1/h with a piezoelec-
tric differential pressure sensor and seems
to have achieved ±2.5% for 150-600 1/h
and ±1.5% above 600 1/h. For the range
3-1501/h, an integrated circuit thermal sen-
sor was used. This had a heated area with
Magnetic material
Backing piate
Electrode
Figure 11.17. Fluidic flowmeter with magnetic sens-
ing (Sanderson 1994; reproduced with permission of
Elsevier Science Ltd.).
temperature sensor areas on each side of the integrated circuit chip. The character-
istic of this sensor appears to have a varying coefficient, and it is not clear what
final precision was claimed for low flows. Sakai et al. saw the prospect of using one
lithium battery of
5,000
mAh, which would last 10 years in continuous service by
lowering the consumption of the circuits.
Measurement accuracy of a preproduction gas meter on field tests in Japan is
claimed (Yamasaki 1993) to be within ±1.5% of reading with a 30:1 turndown
ratio.
Upper flow limits are defined by the allowable loss in the meter. Computer
simulation was used as an aid in the design.
Nishigaki et al. (1995) used LDA methods to obtain the flow patterns in a flu-
idic gas flowmeter and concluded that the patterns were almost the same across a
Reynolds number range from 291 to 2,160.
The development of a meter for various Japanese gas companies (Aoki et al.
1996,
Sato et al. 1996) has included numerical analysis. It has a more complicated
array of internal bodies with a U-shaped initial target. A 60:1 turndown appeared
to be achieved.
11.5.2 ACCURACY
Okabayashi and Yamasaki (1991) found that accuracy could be improved by
i. optimizing the shapes of the side walls and the position of the target and
ii.
incorporating a flow straightener to make the jet two-dimensional.
They claimed a linearity of ±0.8% of reading within the range 0.15-5.0 m
3
/h
with a repeatability of ±0.2% of reading. The frequency appeared to be about
20 Hz/m
3
/h. Sensing was by a piezoelectric sensor (using a polymer piezoelectric
film) that does not consume power and an amplifier with very low current con-
sumption.
276 VORTEX-SHEDDING, SWIRL, AND FLUIDIC FLOWMETERS
11.5.3 INSTALLATION EFFECTS
It seems likely that these devices will be virtually insensitive to upstream distur-
bance because the inlet duct within the meter will have changed section and will be
equivalent to several diameters. There is also likely to be flow straightening.
11.5.4
APPLICATIONS,
ADVANTAGES, AND
DISADVANTAGES
The prime application of these devices is for utility flows where they meet require-
ments of
• small size,
• large turndown,
• low power, and
• long life without maintenance.
With no moving parts and compact size, these devices should show advantages
over existing meters for utility (water and gas) flows. However, the sensing range will
require capability for large turndown if the fluid turndown range is to be realized.
11.6 OTHER PROPOSED DESIGNS
A wake oscillation was observed by Mair (1965). With an axially symmetric and
streamlined body followed by a disk, the wake gathers in the cavity and puffs out
regularly. With a torpedo-shaped body of diameter D, a coaxial disk of diameter
d, and spacing x downstream of the flat rear of the body, Mair found that with
x/D
~ 0.5 and w/D ~ 0.8 the vortex was trapped between the body and the disk
and resulted in a low drag, whereas for x/D ~ 0.3 and w/D ~ 0.8, a high drag and
oscillation occurred, which he attributed to breathing of the cavity.
Parkinson (1991) described a combination of a venturi nozzle with a folded flu-
idic flowmeter (Figure 11.18). Boucher et al. (1991) also designed a folded version
of the fluidic flowmeter to create a bypass for a venturi meter (cf. Wang et al. 1996).
In this way, the fluidic principle can be applied to pipes in the range 40-150 mm
with turndown ranges of 24:1 to
40:1.
The sensing in the fluidic flowmeter was by
means of a miniature air-flow sensor on a silicon chip based on thermal convection.
Shakouchi (1989) demonstrated an alternative geometry of fluidic meter where
a rectangular jet issues into a larger space. The oscillating vane meter was discussed
in Section 8.8.
11.7 CHAPTER CONCLUSIONS
The vortex meter offers
a
very attractive alternative to the orifice plate for some appli-
cations and gains over the orifice plate by its frequency output and larger turndown.
Its application to dry saturated steam may prove to be one of the most important
contributions of this device. It would be interesting to explore means of sensing, by
impact or by entrainment in the shed vortices, the amount of water in the flow and
thus to obtain a dryness factor.