Baker R.C. Flow Measurement Handbook: Industrial Designs, Operating Principles, Performance, and Applications

Подождите немного. Документ загружается.

11.3 INDUSTRIAL DEVELOPMENTS OF VORTEX-SHEDDING FLOWMETERS 257

for a 3-in. (75-mm) meter in air over a 360:1 turndown (with a lower Reynolds

number of 10

) and showed that scatter was of order ±1% over the range. A major

problem in achieving this size of turndown is how to sense at the varying level

of signal. If velocity changes by

100:1,

then pressure head variation due to the

velocity will change by 10

:1.

Goujon-Durand (1995) confirmed that a minimum

Reynolds number of Re = 30,000 is probably necessary to avoid serious increase in

nonlinearity. Takahashi and Itoh (1993) showed a slight decrease in Strouhal number

(about 2%) from Re = 20,000 to Re = 50,000 for heavy oil, water, and air.

Inkley et al. (1980) obtained data to show the small effect of temperature change

through viscosity and density on the meter. Change of liquid and liquid viscosity

appears to have caused calibration shifts of order

0.5%.

If the meter is designed close

to the minimum in Figure 11.4(a), any variation due to temperature expansion will

be minimized. The major change was due to cavitation. The authors agreed with

White et al. (1974) that a universal curve should be obtainable and foreshadowed

the work of Takamoto and Terao (1994) and, no doubt, others.

11.3.2 BLUFF BODY SHAPE

Figure 11.6 shows the effect of body shape on the optimum value of w/D and also

shows that the K factor decreases from the value for circular bluff bodies. The trun-

cated triangular or trapezium shape appears to be best if length to width is in the

range 1.2 to 1.5. The rectangular body with length to width about 0.6 may have

strong shedding.

Lucas and Turner (1985) confirmed that a splitter plate attached to the bluff body

improved signal quality, which, presumably, is the reason for the T and truncated

triangular body shapes.

El Wahed and Sproston (1991) experimented with various bluff body shapes

in air. The sensing used a modulated signal from naturally occurring flow-induced

streaming currents. The shedder shapes are shown in Figure 11.7. The shedders had

end plates to create two-dimensional conditions. The main conclusions were that

the best position for the sensor was attached to the front face of the bluff body and

that:

1000

800

600

£00

200

CIRCULAR CROSS-SECTION

EQUILATERAL TRIANGULAR

•EASTECH DESIGN

KI DESIGN

0-1 02 03 0A 0-5 06

w/D

Figure 11.6. Optimum w/D for various body shapes (from Zanker and Cousins

1975;

reproduced

with permission from NEL).

258

VORTEX-SHEDDING, SWIRL, AND FLUIDIC FLOWMETERS

Figure 11.7. Shedder shapes tested by El Wahed

and Sproston (1991) (reproduced with permission of

Elsevier Science Ltd.).

• the cylinder with a slit was slightly bet-

ter than the solid cylinder (cf. Igarashi

1986);

• the rectangular shedder produced a high

signal-to-noise ratio suggesting that the

body produced a large drag, which in

turn encouraged the vortex to sweep

across the rear face, reinforcing and sta-

bilizing the shedding; and

• the T-shaped shedder was the best, sug-

gesting that the tail helps control the

shedding and produces a high signal-to-

noise ratio, which is approximately con-

stant throughout the entire range.

Figure 11.8 shows the cross-section of various bluff body shapes that have been

used in flowmeters. Bentley and Nichols (1990) suggested that, for a thin plate, the

vortex field is much farther downstream than for

square.

The shape in Figure 11.8(g)

may result in a considerable amplification of the vortex strength and hence of the

pressure variation.

There appear to be mixed views on the use of composite shapes (cf. Majumdar

and Gulek 1981 and Herzl 1982). The conditions for optimum shedding from dual

bodies (Bentley and Benson 1993) relate to

• the thickness-to-width ratio of the two bodies;

• the spacing of the bodies; and

• the positions of maximum vorticity.

For dual bluff bodies, the movement of the boundary layer through the gap is

essential for vortex enhancement. There are two options (Bentley et al. 1996) for

position of a second bluff body: either the second body is far enough away for

there to be shedding from both, or the second is less than a critical spacing, which

(a)

(d)

(f) (g)

(h)

Figure

11.8.

Diagrams of cross-section of bluff bodies (some after Yamasaki 1993

and some from manufacturers' brochures).

11.3 INDUSTRIAL DEVELOPMENTS OF VORTEX-SHEDDING FLOWMETERS 259

leads to shedding taking place downstream of both, with greater shedding stability.

Bentley et al. identified certain spacing, which appears to be preferable, but the

small size of the spacing between bodies may present a problem in small meter

sizes.

It is interesting to note that the dual bluff body

essentially providing a feedback

path between the two bodies of fixed dimensions and so, presumably, defining the

volume needed to fill the feedback path and the time in a more stable way, hence the

greater stability. Tests by Bentley and co-workers suggested that this is still further

enhanced by introducing a throat in the gap, by making the downstream body a

double wedge with the vertex pointing upstream.

Some manufacturers' designs allow the replacement of the sensor without clos-

ing down the line. One that uses a dual bluff body (essentially a triangular shape

followed by a piezoelectric sensor mounted outside the flow line on a symmetrical

wing airfoil that senses the downstream pressure variations) provides for the piezo

crystal's accessibility during operation.

Turner et al. (1993) proposed a new body shape (cf. Zanker and Cousins 1975) for

vortex-shedding flowmeters, consisting of a cylinder split across its lateral diameter,

with a concave rear surface. They claim a high signal-to-noise ratio and an almost

constant Strouhal number over a wide Reynolds number range. Miau et al. (1993)

described a T-shaped vortex shedder consisting of a trapezoidal bar of fixed shape,

with a rear plate whose length can be varied. The optimum length of plate was found

to be in the range

1.56-2.0

times the width of the vortex shedder. They obtained a

turndown ratio of about 17:1.

One manufacturer (at least) offers a triple body. The outer bodies (cylinders)

create the vortex street, and the center body senses the

vortices.

It should give similar

performance for flow in both directions.

11.3.3 STANDARDIZATION OF BLUFF BODY SHAPE

Takamoto and Terao (1994) have taken a basic design of bluff body of the truncated

triangle type (Figure 11.8b). Figure 11.9 shows the essential dimensions, and the pa-

per sets out the tolerance on these and the tolerance with which the body should be

set. Thus, a selection of the dimensions and tolerances (rounded to reduce significant

figures in some cases) are given in Table

11.1.

The alignment refers to the orientation

of the bluff body relative to the axis of the pipe. The perpendicularity is relative to

the pipe diameter. This is a very interesting development, which appears to stem

Table 11.1. Selection of dimensions and approximate permitted error for a

standard flowmeter

Dimension

Value

Maximum

error

Effect on

^-factor (%)

w/D

0.28

0.1%

0.13

H/D

0.35

0.7%

0.09

h/D

0.03

6.6%

0.13

L/D

0.912

0.15%

0.08

19°

0.4°

0.05

Alignment

0°

0.5°

0.05

Perpendicularity

0°

0.3°

0.06

Refer to the original paper by Takamoto and Terao (1994) for precise values.

260 VORTEX-SHEDDING, SWIRL, AND FLUIDIC FLOWMETERS

(b)

Figure 11.9. Diagram to show the main dimensions for a proposed standard

(after Takamoto and Terao 1994): (a) Cross-section of bluff body; (b) Cross-

section of pipe.

mainly from Japan. It is interesting to note that the flow area is close to that for

an orifice of p = 0.65. In their tests, the value of H/D ranged from 0.20 to 0.40

for w/D = 0.28, and the Strouhal number varied by about 8% for this range. Their

results also suggest that H/D = 0.35 results in a Strouhal number, which only varies

by about 1% for a range of Reynolds number from 2 x 10

to 10

11.3.4 SENSING OPTIONS

A major limitation of the meter is the transducer; consequently, various sensing

methods have been tried, and all have advantages and disadvantages. Some of these

methods include:

11.3 INDUSTRIAL DEVELOPMENTS OF VORTEX-SHEDDING FLOWMETERS 261

• Ports in the sides of a bluff body as in Figure 11.8 (a, b) leading to a transverse

duct, which allows movement of fluid to be sensed by an internal hot wire or a

thermistor;

• Temperature variation to sense changes by attaching thermistors to the upstream

face of a bluff body such as that in Figure 11.8(b) or Figure 11.8(d);

• Pressure on lateral (electrical capacitance) diaphragms that deflect [Fig-

ure 11.8(e)];

• Pressure on a small diaphragm in the side of the bluff body [Figure 11.8(f)];

• Pressure sensed through ports in the sides of the bluff body [as for Figures

11,8(b,

d)], or downstream of the bluff body in the fluid or in a symmetrical wing

airfoil. The pressure changes create very small bending of a sensitive element (at

low flows the tip may be moving by as little as 3 x 10~

m). This movement can

either be measured by strain gauge or by capacitive methods.

• Flexure of whole or part of the bluff body [Figure 11.8(h)] measured with strain

gauges;

• Flexure of the whole bluff body sensed by strain gauges in the end supports of

the body;

• A shuttle ball in an internal cavity in the bluff body linked by ports to the fluid,

with movement sensed by magnetic induction [Figure 11.8(b)]; and

•

beam of ultrasound, crossing the flow downstream of the bluff body, modulated

by the vortex shedding.

Pressure is the most common variable to be sensed, evidenced by: ports in the

bluff body, pressure sensor built into the bluff body surface, flexible diaphragm,

forces on the body, movement of a shuttle in the body. Thermal sensors are also

used, built into the body and affected by fluid flows. Fluids should be clean and

noncorrosive.

A new design of meter using ultrasonic sensing appears to operate successfully.

Optical sensing may offer a further alternative (e.g., in the form of optical fibers in

the bluff body).

Takahashi and Itoh (1993) described a design that used the alternating lift on

the shedder, which is sensed through two piezoelectric elements [Figure 11.10(a)].

By using two sensors, effects due to vibration of the pipeline are reduced. A stable

zero is created by using the strength of the vortex-shedding signal (proportional to

) and creating a low flow cutoff when this does not tally with the value of V from

the vortex-shedding frequency. Another arrangement is shown in Figure 11.10(b);

here the vortices lead to a small flexural movement of a section of the shedder

bar, and a piezoelectric element inside the sensor senses this minute movement.

Figure 11.10(c) shows the position of a sensor bar, which can be inserted into or

placed downstream of the shedder body.

Herzog (1992) used optical fibers within the bluff body of a vortex-shedding

flowmeter to sense the frequency. One fiber appears to have been subject to the

transverse forces through ports in the body, whereas the other was totally en-

closed. The bending of the first fiber caused changes to the quality and inten-

sity of the light, and both speckle pattern and intensity were used to obtain the

frequency (cf. Hisham Marshad and Irvine Halliday 1994 and also Wen Dong-Xu

1990).

262 VORTEX-SHEDDING, SWIRL, AND FLUIDIC FLOWMETERS

Leadwires

Pipe Line (body)

Direction of Flow

(a)

Piezoelectric

Sensor Element

Figure 11.10. Commercial designs of flowmeter

sensing systems: (a) Basic construction and vortex

shedder bending moment diagram showing signal

components 5 and noise components N (repro-

duced with permission of Yokogawa Europe B.V.);

(b) Shedder bar/sensor operation (reproduced with

permission of Fisher-Rosemount Ltd.); (c) Sensor

positions (reproduced with permission of Bailey-

Fischer and Porter).

Sensor

(c)

Sproston et al. (1990) experimented with electrostatic sensing, and in later tests

El Wahed and Sproston (1991) used electrostatic sensors as shown in Figure

11.11,

either in the

walls,

behind the body, or on the front face of the

body.

The mechanism,

on which this sensing is based, is that charge is produced in flows (flow-induced

streaming currents), and so its variation can be used to measure flow variation. The

experiments were in air.

11.3 INDUSTRIAL DEVELOPMENTS OF VORTEX-SHEDDING FLOWMETERS

263

Piezoelectric elements may be sensitive

to pipe vibration and degrade the signal-

to-noise ratio. Stiffening the meter body,

using filtering and

low cutoff (Kawano

et al. 1992) may partially overcome these

problems.

Figure 11.12 shows a block diagram for

a signal converter.

11.3.5 CROSS CORRELATION AND

SIGNAL INTERROGATION METHODS

Coulthard and Yan (1993a) suggested the

use

the vortex wake

as a

tracer

for

use with cross-correlation techniques. The

bluff bodies that were used presented a low

blockage to flow and appeared to give sim-

ilar accuracy to those of vortex-shedding

frequency measurement. This presumably

indicates that the cross-correlation tech-

nique is capable of the same discrimination

as the frequency measurement electronics.

Coulthard and Yan (1993b) investigated

the effect of various bluff body shapes but

found little difference between them (how-

ever, cf. Terao et al. 1993).

Amadi-Echendu et al. (1993) described

a further piece of work to analyze the raw

signal from a flowmeter, in this case

vortex

'///////

V//////////////777.

V77///////////Y7

Figure

11.11.

Electrostatic sensor positions

(El

Wahed and Sproston

1991;

reproduced with permis-

sion of Elsevier Science Ltd.).

Electronics module

Piezoelectric

sensor

Anti-aliasing

filter

Analog-to-

digital signal

conversion

Galvanic

isolation

'-z

Digital

tracking

filter ASIC

Galvanic

isolation

Microprocessor

• Transmitter

configuration

• Temperature

correction

• Diagnostics

• Rerange

Display

• 8 digit

• Engineering

units

• Configurable

I • configurable

Pulse

Digital

communication

Digital-to-

analog signal

conversion

Figure 11.12. Block diagram of electronics module for commercial flowmeter (after Fisher-

Rosemount Ltd.).

264 VORTEX-SHEDDING, SWIRL,

AND

FLUIDIC FLOWMETERS

flowmeter,

ascertain information beyond pure flow information.

It is not

clear

from this paper

the

extent

which this will

possible. Clearly condition moni-

toring from this source would

very valuable. However, there

is a

need

link

the

frequency data

closely

possible

to the

physical effects

that

the

changes

can

be intelligently used

(cf.

Section 10.2.16

and a

note

Chapter

21).

11.3.6 OTHER ASPECTS RELATING TO DESIGN AND MANUFACTURE

Itoh

and

Ohki (1993) claimed (as does

one

manufacturer) a vortex flowmeter design,

which obtains mass flow rate

using

the

lift

on the

central body divided

by the

frequency

pulsation. This depends

on the

assumption that

the

lift coefficient

and

the

Strouhal number

are

both constant

that

the

lift

proportional

to pV

and

the

frequency

proportional

to V. As a

result,

the

ratio

proportional

p V

(cf.

Yamasaki 1993).

Miller

al. (1977) gave some impressively consistent

factors from

the

produc-

tion process showing random uncertainty

in K of

order ±0.8%

for

50-mm meters,

±0.4%

for

75-mm meters,

and

±0.3%

for

100-mm meters.

11.3.7 ACCURACY

Typical performances

meters currently available

are

given as: repeatability, about

±0.2%

rate; linearity, better than

±1%

for a

turndown ratio

of up to

40:1

for

liquids

and

up to 30:1 for

gases.

For

liquids

higher flow rates,

the

uncertainty appears

in the

range

0.5-1%

rate.

At low

flow rates,

it is the

same range

values

but as

a percentage

full-scale deflection.

The

change will

be at

about

Re =

20,000, with

a minimum value

of Re of

about 4,000

and

upper limit

about

7 x 10

. The

type

of transducer

may

affect

the low

flow limit.

For gases

and

steam,

the

uncertainty appears

to be in the

range

1-1.5% of

rate,

but with

Re <

20,000 likely

increase uncertainty.

Temperature variation

likely

affect precision,

and

compensation

may be

included (e.g., 0.3%/50°C).

Cousins

has

commented that

it is

necessary

collect

large number

pulses

to achieve good repeatability

due to

variation

10-20%

in the

shedding period.

a consequence, long integration times should

expected.

11.3.8 INSTALLATION EFFECTS

Table

11.2

shows

the

change

error

for

increasing installation lengths (Takamoto

et al. 1993b). Some

the results suggest that

the

error does

not

always decrease with

spacing.

The

worst case

has

been used, from

the

results

four meters.

Mottram (1991) commented that

'The

difficulties

deciding what should be

the

minimum straight pipe length between

given type

flowmeter

and a

particular

upstream pipe fitting

are

notorious. Even when

the

geometry

standardized,

as is

the case

for the

sharp edged orifice,

the

issue

still controversial. This

is due to the

typical shape

of the

envelope enclosing

the

experimental results

for the

calibration

shift plotted against

the

straight pipe length separating

the

meter from

the

upstream

fitting. Minimum straight lengths may differ by

factor

two."

Mottram

;

s tests were

for

vortex meter with

area ratio approximately equivalent

to a ft = 0.6

orifice

11.3 INDUSTRIAL DEVELOPMENTS

VORTEX-SHEDDING FLOWMETERS

265

Table 11.2. Results from Takamoto

al. (1993b) that appear

give

the

worst

case uncertainty (rounded

up to the

first decimal place)

various spacings

2x Bend

(%)

10D

20D

30D

Bend

90° (%)

1.9

0.6

0.4

0.3

Same

Plane

2.1

0.7

0.4

0.2

90°

Plane

2.1

1.1

0.8

0.6

Reducer

(%)

0.9

0.7

0.3

Expander

(%)

4.2

1.4

0.3

Gate Valve Open (%)

100%

0.3

0.4

0.3

50%

5.1

1.5

0.5

0.4

area ratio. We compare

Table 11.3 Mottram's

and

Takamoto

al.'s (1993b) values

for

the

vortex installation lengths

and

those from

ISO 5167 for

orifice meters with

= 0.6 and £ = 0.75.

Mottram gave

general rule that vortex sensitivity

was

similar

that

for a

high beta ratio orifice plate. This would appear

to be a

reasonable working rule

thumb from his results

and

close agreement with Ginesi and Annarummo (1994)

who suggested using

the 0.7

beta ratio lengths. However, Mottram's comment that

minimum lengths

may

differ

by a

factor

of two is

borne

out by

Takamoto

et al.'s

(1993b) results.

Further results from Mottram

and

Rawat (1988) (using

rectangular bluff body

and hot-wire anemometer probe

detect

the

vortices) suggested that pipe wall

roughness, presumably resulting

profile changes,

can

cause 3% variation

cali-

bration

(cf.

Witlin 1979).

compare manufacturers' requirements, they are fairly consistent

suggest-

ing

downstream although

least

one

suggests

10D, but for

upstream spacing,

Table 11.3. Installation lengths (diameters) between upstream fitting

and

meter

for

changes within

0.5% compared with spacing

for

orifice

2x Bend

Bend Same 90°

90° Plane Plane Reducer

Gate Valve Open

Expander 100%

50%

—

Orifice

zero additional uncertainty

= 0.6 18 26 48 9

Vortex

55 60

Vortex

13 12 43 14

Orifice

- ±

0.5% additional uncertainty

= 0.75 18 21 35 11

Orifice

zero additional uncertainty

= 0.75 36 42 70 22

Mottram's (1991) meter with blockage equivalent

to £ = 0.6.

Takamoto

et al.'s

(1993b).

266 VORTEX-SHEDDING, SWIRL, AND FLUIDIC FLOWMETERS

Table 11.4. Installation requirements (in

manufacturers' literature compared with

90° bend or T

bends

in same plane

in perpendicular planes

Reducer

Expander

Valve

Downstream spacing

Orifice

(3 =

(±0%)

diameters) as indicated in

orifice plate requirements

0.6

Vortex

10-20

20-25

30-40

10-20

10-40

20-50

5-10

Orifice

= 0.75

(±0.5%)

Globe valve fully open.

they give values as in Table

11.4.

These are, again, compared with orifice spacings, for

p = 0.6 ratio orifice (zero additional uncertainty) and p = 0.75 ratio orifice

(±0.5%

additional uncertainty).

Apart from the valve, the values in Table 11.4 suggest that to take the greater of

the spacings for a p = 0.6 orifice with zero additional uncertainty and for a ft = 0.75

orifice with ±0.5% additional uncertainty might provide a rule of thumb for other

fittings. There appears to be a more severe effect due to reducers and expanders,

about which some manufacturers are clearly cautious. Further, although this is in

line with Takamoto et al. (1993b), it does not cover the more pessimistic results

of Mottram (1991), and for safety we may need to accept his guidance that the

installation distance should be that for zero additional uncertainty with p = 0.75

(or 0.8), accepting Mottram's factor-of-two observation.

Manufacturers have warned against the protrusion of gaskets into the flow up-

stream and adjacent pipe bores of different size to the meter. The inlet pipe should

be free of weld beads and thermometer pockets and should be smooth; the pipework

should be aligned with the meter. Takahashi and Itoh (1993) suggested \% error for

installation in a pipe of different bore to the meter, and one manufacturer gives the

effect as less than 0.6% for a step of 4-10% greater than the flowmeter ID resulting

from the pipe schedule.

Cousins (1977) commented on the severe effect of swirl in changing the cali-

bration and even in suppressing the shedding and suggested at least 50D upstream

spacing from the source of the swirl for a swirl angle of 10° and more spacing for

larger angles. However, Laneville et al. (1993) showed that, for swirl indices (Q =

injected swirling flow rate/total flow rate) less than 0.3, the vortex-shedding signal

quality from a vortex flowmeter with trapezoidal body is equivalent to the zero swirl

case,

and the frequency is still within about 2% of the swirl free value for a spacing

18D downstream of the swirl generator. These apparently differing results will call

for caution.

Pressure taps downstream should be 2D to 7D, and temperature taps should

be ID to 2D downstream of the pressure ones. A flow straightener of 2D length