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

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13.2 TRANSIT-TIME FLOWMETERS

317

Downstream

pulse

Figure 13.3. Diagram to explain transit-time measurement.

Upstream

pulse

We obtain from Equation (13.4), assuming V is constant across the pipe,

_ nD

7tD

(13.5)

It is important to appreciate the value of the times involved in these measure-

ments. If the flowmeter is to discriminate to better than 1%, we may define E(Af)

as At/100, and for two meters, we obtain the values in Table 13.1 (Baker 1988/9).

Table 13.1 highlights the problem of the very small time differences we need to

measure in the transit-time flowmeter. For the smaller tube, this is to better than

1 ns. However, one advantage of this system is that any echoes or standing waves

have time to die down, another advantage is that the same path can be used for each

direction of the pulse, and, finally, the individual measurements can be used as a

tolerance check to ensure that spurious measurements are rejected (Scott 1984).

An alternative way to eliminate sound speed is the sing-around method

(Figure 13.4) discussed by Suzuki et al. (1975, cf. 1972). In this method, each of

the paths, upstream and downstream, is operated in such a way that when the pulse

is received by the receiving transducer, it triggers a new pulse from the transmitting

transducer. Thus the frequency of pulses is dependent on the velocity of sound and

Table 13.1.

Diameter

(mm)

100

300

Transit-time meter times

(*U

+ <d)/2 (s) At(s)

io-

3 x 10~

3 x IO-

E(At) (s)

io-

3 x IO-

6 = 45°, V = 1 m/s, and c is taken as 1430 m/s, the value

for water at 4°C.

318 ULTRASONIC FLOWMETERS

of the flow. We find that the frequency of

pulses is given by

2XV/L

(13.6)

which has the virtue of relating V to the

frequency difference without requiring the

value of c, the sound speed. Again we can

obtain typical values for the frequencies

from Table 13.2 (Baker 1988/9). Making the

approximation that V

constant across the

pipe,

we obtain

(13.7)

Figure 13.4. Diagram

explain sing-around system.

The limitation of the sing-around

method relates more to the very low fre-

quencies and the long time periods needed

to achieve sufficient accuracy. To achieve

1% uncertainty, we shall need to have a measuring period of greater than 1 s for the

most favorable of the cases in Table 13.2.

Timing can also be achieved in some cases by obtaining the phase shift between

the two arriving waves to obtain the time difference (Baker and Thompson 1975).

Other problems such as standing waves and spurious transmission paths that cannot

be gated out may need to be considered in relation to any of the methods chosen.

Unwanted reflections within the pipe and their effect on the measurement uncer-

tainty may be reduced by the use of higher frequencies. These attenuate reflections,

but they also attenuate the signal. Cunningham and Astami (1993) produced curves

of upper and lower frequency limits against pipe diameter for various reflection set-

tling times. The upper limit ensures that signal attenuation is not too great, whereas

the lower limit is to ensure that attenuation of reflections is sufficient. They reckoned

that the received signal should be at least 30% of that transmitted.

An alternative approach, rather than measuring the value of c, is to use the

fact that c

= l/(k

p) for a particular liquid and that c

= yp/p for a particular gas

[Equation (13.A.3)]. For a liquid,

XpV

7ZD

(13.8)

Table 13.2. Sing-around meter frequencies

Diameter V=lm/s V=10m/s

(mm)

100

300

45°,

water

V =

4°C.

10,

m/s

(Hz)

117

372

and

Af (Hz)

3.3

cis taken

as 1,430

fu (Hz)

10,162

3,387

m/s,

the value

100

for

(Hz)

13.2 TRANSIT-TIME FLOWMETERS 319

Table 13.3. y for various gases from Haywood (1968)

Type of Gas Mean

(number Examples Value Value

atoms)

Gases

of 7 of7

Monatomic

Diatomic

3-5 atoms

3 atoms

5 atoms

8-9 atoms

8 atoms

9 atoms

Argon

Air

Nitrogen

Oxygen

Carbon dioxide

Methane

Ethane

Propylene

Based on number of atoms.

1.67

1.40

1.31

1.19

1.15

1.67

1.40

1.29

1.17

where the adiabatic compressibility would need to be known and, because it varies

with temperature, would need to include some temperature compensation. For a gas,

^ 2pXV

$Xq

(13.9)

thus relating the mass flow rate of a gas to the time difference, the pressure of the

gas,

and the geometry of the flow tube. Table 13.3 gives values of y, and a flowmeter

using this method would need a selection switch for the type of gas in addition to

the pressure measurement facility.

An alternative method to obtain the mass flow is to obtain the density from

the value of the impedance discussed earlier. Guilbert and Sanderson (1996a) have

described such an ultrasonic mass flowmeter, which combines a fairly standard

configuration of ultrasonic flowmeter with an impedance density cell, in which

the impedance of the liquid is obtained through the interface between the liq-

uid and a material that divides the cell into compartments. The material selected

was polyamide/imide. They also used the time between reflected signals to ob-

tain the sound speed in the divider and hence its impedance (cf. Chapman and

Etheridge (1993) who described the evolution of the ultrasonic flowmeters for gas

measurement).

13.2.3 EFFECT OF FLOW PROFILE AND USE OF MULTIPLE PATHS

The preceding simple analysis has assumed that the flow profile is uniform. In fact, if

we allow for varying velocity along the path of the ultrasonic beam, Equation (13.4)

may be rewritten in the form

2Xt

(13.10)

320

ULTRASONIC FLOWMETERS

Figure 13.5. Acoustic beam positions

(T,

top of

pipe,

indicates possible preferred orientation in

liquid flow): (a) Diametral path; (b) Mid radius paths; (c) Four path; (d) Reflex mode with W

path; (e) Reflex mode with two V paths; (f) Reflex mode with triangular path.

where V

is the mean velocity along the path of the beam, since the flowmeter aver-

ages velocity along the path of the beam. In general, this average does not correspond

to the area average of the velocity required for an ideal flowmeter. Unfortunately, for

circular pipes with paths crossing the diameter [Figure 13.5(a)], the mean velocity

along the path gives too heavy an emphasis to the flow at the center of the pipe. This

implies that change of profile from laminar to turbulent and through the turbulent

range will affect the calibration. It is easy to show (Kritz 1955) that the effect of

integrating a laminar profile across a diameter of the pipe causes a signal about 33%

high due to the overweighting that the velocities near the axis receive, compared

with a uniform profile. Through the turbulent range, using the 1/n power law (see

Chapter 2) for a Re number variation between 10

and 10

, a variation of about

occurs. Apart from Kritz, others have provided calibration factors (Kivilis and

Reshetnikov 1965, Del Grosso and Spurlock 1957). Thus for a meter that is con-

structed this way, there is an inherent variation in calibration factor, which cannot

be wholly allowed for in the transmitter circuitry due to Reynolds number depen-

dence on factors other than velocity only. Scott (1984) made the point that a change

in viscosity from 1 to 10 cP causes a change in profile, which will account for a 1%

error.

One way to improve this is to offset the paths from the axis [Figure 13.5(b)], in

which case a position at about the mid radius is found to be a good compromise

(Appendix 13.A.2). Baker and Thompson (1975) showed the effect of offset paths

(Figure 13.6) for varying Reynolds number on the signal with the paths offset at

0.5R, 0.505R, and 0.523R from the axis. This shows that a position of 0.523R is ideal

for the turbulent range, whereas 0.505R is probably a reasonable compromise for

13.2 TRANSIT-TIME FLOWMETERS 321

error

Figure 13.6. Calculated values of the percentage error against Reynolds number for three posi-

tions of the acoustic paths (after Baker and Thompson 1975).

the whole Reynolds number range. They also suggested that the meter should have

low sensitivity to swirl and to flows that have symmetry of size but opposite sense

about the axis.

Hastings (1968, 1970) used four paths [Figure 13.5(c)] and selected their posi-

tions so that a Gaussian Quadrature integration (a numerical method for integrat-

ing general curves, which is similar but more complicated than Simpson's rule - see

Appendix 13.A.2) could be used to give a correct mean velocity signal for profiles

that are formed from polynomials of seventh power or less. Again the experimental

evidence since these early papers confirms the quality of the integration achieved

and the potential accuracy of the design.

Using the velocity measured on multiple paths, Vaterlaus (1995) gave the fol-

lowing positions for multiple paths and the weight to be given to each:

Planes

Distance from

center plane

±0.520

±0.774

±0.339

±0.861

Weight

0.5

0.444

0.277

0.326

0.174

The value given for two paths agrees well with Baker and Thompson (1975).

Taylor and Cassidy (1994) quoted weightings for four planes, which, to three

signif-

icant figures, agreed with these (cf. Pannell et al. 1990 on a generalized approach to

positioning chordal paths).

322 ULTRASONIC FLOWMETERS

variation on the positioning of the paths uses internal reflection of the beams to

allow transmitter and receiver to be on the same side of the pipe [Figures 13.5(d, e)].

This is known as reflex mode. This can be either V with one reflection or W with

three reflections. It can also be used to create subtle reflections, which essentially give

the path position the benefits of off-axis integration [Figure 13.5(f)] and multiple

paths around the pipe to give even better integration of the profile. An example

of this results in the paths lying on an equilateral triangle if viewed axially down

the pipe, thus using the midradius point but also covering a large area of the tube

(Drenthan and Huijsmans 1993).

Jackson et al. (1989) developed an ultrasonic flowmeter using one transmitting

transducer and a lens system made of Perspex, which produced a diverging ultra-

sound beam detected by three widely spaced receiving transducers. The chords of the

three paths are all designed to be of different lengths and angles. In the test meter, a

further path was used across the flow to obtain the sound speed. It is not obvious that

this design contributes significantly to the normal design with three complete paths

or, indeed, the designs using reflecting beams to obtain off-diametral paths. The ad-

vantage of reciprocating paths is that the sound speed is obtained using the mean.

Jackson et al.

(1991,

cf. 1989) described a three-path meter where the path an-

gles were chosen to obtain information about the flow profile. The paths were in a

diametral plane and with chordal paths on each side at angles of 44° and 52° to the

diametral plane. For axisymmetric profiles, performance was of order 2%. Asymme-

try was detected unless there was a symmetry about the diametral plane, but precise

flow measurement with asymmetry was not obtained.

Van Dellen (1991) of Daniel Industries, Inc., demonstrated compensation by

using multiple paths. Such designs allow self-checking routines where speed of sound

is compared and successive measurements can be used.

Multipath meters are an option for hydroelectric turbine efficiency measure-

ment. Lowell and Walsh (1991) reported on the use of eight eight-path crossed plane

meters and concluded that ±0.5% uncertainty of flow rate could be achieved with

appropriate relative positioning of acoustic plane and upstream fittings.

Sanderson and Hemp (1981) also mention the use of a wide beam to average the

flow

rate.

Hemp (1982) has developed the concept of weight vectors (cf. Appendix 13.A.3)

and in a more recent paper (Hemp 1997) showed a weight function distribution for

point transducers (which, in practice, would presumably need to be small area) in

a circular pipe. This indicated that the meter was most sensitive to flow near the

transducers.

See Smith and Morfey 1997 on the effect of beam bending due to velocity vari-

ation across the pipe.

13.3 TRANSDUCERS

One of the most important features of the mechanical design of the meter is the

transducer and its mounting. This must achieve

• efficient transmission and reception of acoustic signals through the interface,

13.3 TRANSDUCERS 323

• negligible acoustic transmission through the body of the flowmeter,

• accurate and permanent positioning,

• no adverse effects due to operating fluid, and

• trouble-free performance.

Transducers fall into a number of categories, and these will be worth bearing in

mind in the following discussion:

Factory installed Wetted transducers - open cavity

Nonwetted transducers - open cavity

Nonwetted transducers - filled cavity

Note: For any of these, the spool piece may be factory wet calibrated. Only the

first is suitable for gases.

Retrofit Wetted transducers - open cavity

Nonwetted transducers - open cavity

Note: Only in situ calibration is possible. Dry calibration by very careful

measurement may be acceptable.

Clamp-on Nonwetted transducers - transmission through pipe wall

Note: Wet calibration is virtually impossible. This transducer is not suitable

for gases.

Figure 13.7 shows some typical mounts for transducers. Figure 13.7(a) shows a

wetted transducer in an angled mounting block. The crystal emits a pencil of sound

through perpendicular interfaces, and it is not therefore refracted. Figure 13.7(b)

shows an alternative arrangement with mounts perpendicular to the tube and trans-

ducer with an angled end in which the crystal is mounted. If the liquid is aggressive

or particle laden, some form of window may be required. In this case, the transducer

may be mounted as shown in Figure 13.7(c), where a metal window is used but

where all interfaces remain perpendicular to the beam. The cavity is a source of flow

disturbance and solid deposit. Both may cause signal failure or flow measurement

errors.

Figure 13.7(d) has the cavity smoothed off with a filler of some sort such as

an epoxy. Ideally, this filler should have an acoustic refractive index similar to the

liquid, thus keeping refraction to a very low value, and the bending of the acoustic

ray on crossing the interface will be small. However, changes of fluid or tempera-

ture may introduce errors. An important advantage of the mounts shown in Figures

13.7(a, b) is that alternative transmission around the tube wall and outside the fluid

is reduced, and in practice the transducer mount can be made to absorb it. With

the mounting systems in Figures 13.7(c, d), the signal processing must discriminate

between the fluid-borne signal and the spurious signals around the wall of the tube.

Sanderson and Hemp (1981) gave some details of ways to increase the bandwidth of

the piezoelectric plate.

Figure 13.7(e) shows a clamp-on system in which the transducer mount

entirely

external to the tube and may be mounted on existing tube. Here the problems of

the type found in the mounts shown in Figures 13.7(c, d) are greatly increased.

For very small pipe sizes, the limitations of pipe diameter and consequent short

pulse times can be overcome by a flow tube and transducer mounting system of the

324 ULTRASONIC FLOWMETERS

(b)

(d)

(e)

Figure 13.7. Transducer mounts (cf. Baker 1988/9): (a) In line - wetted; (b) Angled - wetted;

(e) Clamp-on transducer with crystal embedded in the mount; (f) In-line transmission for small

tubes with either wetted or protected transducers.

type shown in Figure 13.7(f). The flow enters a section of tube in which the acoustic

beam is axial, and hence there is no limitation on the separation of transducers apart

from those resulting from the application.

For gases, it is essential that the transducers are in contact with the fluid and so

are mounted as shown in Figures 13.7(a, b) or possibly Figure 13.7(f).

13.5 SIGNAL PROCESSING AND TRANSMISSION 325

To overcome the impedance mismatch, a low impedance transducer was re-

ported (Collings et al. 1993). When used in a meter, it allowed natural gas flows

of 0.013-8 m

/h with a temperature range of —13 to 47°C and is claimed to have

significant advantages over current domestic meters.

It should also be remembered that for high pressure service the transducers must

be flanged to the correct line pressure (rather than screwed). Transducers that project

into the tube may avoid attenuation and other problems due to air collection within

the pockets. To reduce turbulence caused by the transducer cavities on a 20-mm-ID

ultrasonic flowmeter for gas, nets have been placed to create a wall that transmitted

the ultrasound (Hakansson and Delsing 1992).

Lynnworth (1988) suggested the use of new types of wetted and clamp-on buffer

rods to allow for extreme temperature (e.g., ±200°C) such as might occur in wetted

use in cryogenics or in the flow of quench oil in a carbon steel pipe at 260°C.

13.4 SIZE RANGES AND LIMITATIONS

Single- and twin-path designs may be available for liquids in 80-2,000 mm diameter

or greater, although very large sizes may be retrofit applications. The arrangement

for small tubes is likely to be for 10-80 mm.

When retrofitting, there is always a tolerance on the pipe dimensions, both di-

ameter and wall thickness, which will affect the deduction of mean flow from ul-

trasound path velocity, and the measurement needs to take account of the actual

separation of transducers (Scott 1984). For instance, in a carbon steel pipe with a

100-1,000 mm diameter, the tolerance may be

±1%

on diameter and ±10% on wall

thicknesses of 3-5 mm. In addition, erosion, corrosion, and painting of the pipe

makes it improbable that the error can be reduced below 0.5%. Manufacturers may

offer retrofit for one, two, or four paths, which with precise internal measurement

should be capable of high accuracy.

13.5 SIGNAL PROCESSING AND TRANSMISSION

As indicated earlier, the measurement system essentially requires the ability to mea-

sure very small time periods, or periods to very high precision. This increment could

be of order 10~

(a nanosecond), which Sanderson and Hemp (1981) pointed out

was comparable with the (then) propagation delays and rise times of the fastest

commercially available logic. Clearly the technology in this area is moving rapidly,

and the problems encountered in small time measurement, phase comparison, or

sing-around are finding new solutions.

Tables 13.1 and 13.2 have identified the design requirements for the signal pro-

cessing, namely,

• for transit-time meters to measure timed differences to better than 10~

s (one

nanosecond) and

• for sing-around meters to measure frequency differences to better than, say,

0.03 Hz for 1% discrimination in a 300-mm tube with V = 1 m/s.

326 ULTRASONIC FLOWMETERS

To achieve this, various clock circuits have been used. In an early commercial

meter, a ramped voltage system provided a time measure. In addition, there are

problems in ensuring that the zero-pass, or whatever part of the wave is used, is

consistent between transmitters and receivers. Szebeszcyk (1994) discussed some

aspects of the design of the ultrasonic flowmeter and transducers, use of first zero

crossing of the signal, optimum thickness of matching layers, etc.

Vaterlaus (1995) described a time measurement system with two counters. One

counter N

was clocked during the measuring period by a stable quartz oscillator with

a frequency f

—

64 MHz, whereas the other counted the number of samples N

. A

start pulse initiated the measurement by activating the two counters and triggering

the ultrasonic pulse emission. During the measurement period r = 30 ms, every

pulse received caused a new pulse to be emitted. The two counts N

and N

were

used to calculate the propagation time from

It appeared that x was obtained precisely from N

/f; hence, provided x ended

after a complete value of N

, it was possible to obtain the transit time as

/(N

and a resolution of 60 ps in 116 /xs was claimed.

Advantages claimed were:

• Velocity resolution was to 0.8 mm/s.

• Precision depended on the stability of the oscillator.

• Jitter in digital logic was averaged.

Another solution to the timing problem (Pavlovic et al. 1997) appeared to use

a. a transmitted pulse in two halves, the first at one amplitude and the second at

twice the amplitude, presumably allowing more precise timing edges;

the downstream and upstream times were then given by

= N

T+ Ar

ta = N

T + Ar

where N

and N

were the whole number of counter periods of a 2.2-MHz square

wave train obtained from a 17.7-MHz oscillator through a divider by 8 and were

obtained by standard counter methods;

c. Ard and Ar

were measured through the phase difference between transmission

and received signals, and a two-stage measurement system using a coarse and

fine approach. An integrator was used to obtain Aid and Ar

The effects of error due to temperature on pipe diameter, recesses, delays in

electronics, and transducers were also addressed.

Because such short times are being measured, system designs need to address de-

lays in the cables, transducers, and converter (Scott 1984). Time delays of microsec-

onds could lead to errors if the head is calibrated on water for use on oil (±1.5%), or

if the temperature of the water changes by 10°C (±0.1%). Further delays are caused

in the window, or in the transmission through the wall, ranging from about 3 /is to

about 15 /xs. These delays will also be dependent on the choice of materials.

Hemp (1988, 1998) has proposed a reciprocity approach to the elimination of

zero instability. This requires that the transducers are driven, say, by a voltage pulse,