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

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13.11 CORRELATION FLOWMETER 347

pattern

for

channel

will

found

to be

displaced

time

from that

for

channel

A. From this,

simple

deduce that

the

flow has taken time

move

distance

V=—

(13.12)

Correlating

the two

signals requires some

complex electronics.

The

fluctuation

the

signal must

adequate,

and for

this

rea-

son,

will probably need

to be

created

ar-

tificially

upstream disturbance

in the

flow, if heavy turbulence, bubbles, second

phase,

etc., are

absent naturally.

The

math-

ematical concept

cross correlation

de-

fined by

the

equation (Keech

1982)

(r)

limr-oo

~ /

y(t)x(t

+ x)dt

Transmitters

(13.13)

where

x{t)

and y(t) are the

upstream

and

downstream signals, respectively. The value

of time delay

corresponding

to the max-

imum

(r) provides

measure

of the

Flow

(a)

Receiver

A Receivers

Receiver

•-»*"*

Time

A iv.

••

Time

(b)

Figure

13.12.

Correlation

flowmeter:

(a)

Diagram

the

geometry;

(b)

Traces from channels

and

flow transit time between

the two

beams

spaced

apart.

The

calculation

of the

integral

Equation (13.13)

achievable

with modern computation.

The

problem

is to do it

cheaply

and

fast.

For

instance,

sufficient precision may

achievable by using only the polarity

the signal, and by

cutting the signal into sufficiently small bits

fixed

size,

but

by varying polarity,

the

integration

may be

simplified

and

speeded

without significant loss

precision.

(However,

see

Yang

and

Beck 1997.)

has

found

particular niche

multiphase flows where

the

disturbance

the

signal will be substantial. However, Keech (1982) suggested that some form

valida-

tion

needed because

the

system

can

give incorrect estimates

velocity: spurious

noise

can

give

correlation, decay

disturbances

at low

flows, other movement

such

cavitation-generated shock waves

intense pressure waves,

and

oscillatory

flows. Multichannel devices

may

overcome some

these effects.

13.11.2 INSTALLATION EFFECTS

Paik

et al.

(1994) used clamp-on transducers with

1-MHz

crystals,

35°

wedges,

and

2D or 3D

spacing

some tests

installation effects. Their baseline tests

were with

120D

upstream straight pipe.

The

errors found

them

are

shown

Table

13.9.

There may be other experimental studies

installation effects

which

am not

aware,

but

because this

is the

only data provided

this book,

should probably

used with caution.

348 ULTRASONIC FLOWMETERS

Table 13.9. Error in signal due to upstream fittings

Diameters Upstream

Fitting 5 10 20 30

Single elbow -7% -4% (-2%) (-2%)

Double elbow

out-of-plane -2 to -4% +5% +2 to 6% 0 to 4%

Double elbow

in-plane -6% -5% -2% -2%

() possible scatter.

13.11.3 OTHER PUBLISHED WORK

King (1988; cf. King et al. 1988 and Sidney et al. 1988a, b) mentioned the develop-

ment of an ultrasonic cross-correlation meter for multiphase flow at the National

Engineering Laboratory, Scotland, in collaboration with Moore, Barrett, and Red-

wood. This development undoubtedly exploits one of the most important applica-

tions of this technique, and increasingly sophisticated electronics should allow more

information about the flow components and their velocities to be deduced.

Coulthard and Yan (1993c) provided one of the many reviews of correlation

flowmeters. They review results for two-phase mixtures:

Solids and liquids Satisfactory operation

Oil and gas At void fractions up to 25% and velocities

up to 7 m/s scatter of results was ±4.5%

without mixing and ±2% with mixing

Single-phase gas and liquid are also usable but may need a bluff body to enhance

the signal.

Xu et al. (1994) described a clamp-on ultrasonic cross-correlation flowmeter for

liquid-solid two-phase flows, with brief indications of how the various components

operate. Calibrations of these meters against an electromagnetic meter gave differ-

ences of about ±5% for a 0.4% by weight paper pulp flow and about ±3% for a crude

oil flow.

Recent work by Battye (1993) suggested measurement uncertainty over 10:1

of ±2% with 0.5% scatter, but that temperature variation in the acoustic path, if

not allowed for, might reduce linearity. Other work by Kim et al. (1993a) suggested

±2.2%

or for clamp-on

±2.8%.

very recent paper by Yang and Beck (1997) claimed

that, with a highly intelligent cross-correlator, a measurement accuracy of 1% could

be achieved.

Lemon (1995) discussed a technique referred to as acoustic scintillation flow mea-

surement; it appears to refer to, or be related to, cross-correlation flow measurement

using the disturbances caused to the ultrasonic beams in traversing the flow.

It should be remembered that even though cross-correlation has been used with

ultrasonics and included here for that reason, it has much wider application. Chen

et al. (1993) reported work using two pairs of radiation sensors. Their application

was to medium-consistency pulp in the paper industry. Flows approach Newtonian

13.12 OTHER ULTRASONIC APPLICATIONS

349

at high rates but at low flows behave more like a plug with a laminar annulus of

continuous pure liquid between plug and wall. As flow increases, the annulus flow

becomes turbulent with lower consistency suspension. Eventually complete plug

disruption takes place. Flow rates in industry are typically 0.3-3 m/s. The correlation

can be based on inhomogeneities, floes in the annulus, or temperature changes, and

precision of 2.5% may be possible.

Beck and Plaskowski (1987) have given a full statement on this topic.

13.11.4 APPLICATIONS, ADVANTAGES, AND DISADVANTAGES

The cross-correlation ultrasonic flowmeter appears to require a significant distur-

bance in the flowing fluid. Where the disturbance is due to multiphase flow, the

meter comes into its own and provides one of the few types that can satisfacto-

rily deal in a nonintrusive way with such flows. Its current price may make it less

attractive for normal applications, but it is more in line with the overall costs of

applications such as oil well monitoring.

13.12 OTHER ULTRASONIC APPLICATIONS

Flowmeters could be designed to make use of the beam sweeping caused by the flow.

These have been proposed, but I am not aware of any that use only this principle.

Figure 13.13 shows a beam crossing the flow approximately at right angles but being

swept sideways due to the fluid motion. On the receiving side of the flow passage,

two or more sensors measure the strength of the received signal at each sensor and so

allow the electronics to deduce the deflection due to the flow. The angular deflection

is given by

tan/3 = -

and the deflection on the receiving wall will be

(13.14)

(13.15)

Ultrasonic sensing is also used in open channel flowmeters, flumes, and weirs to

sense the level of the upstream surface from which is deduced the flow rate (Herschy

1995).

Position of

beam with no flow

Position of

beam with flow

Figure 13.13. Flowmeter concept using beam sweeping.

350 ULTRASONIC FLOWMETERS

In vortex meters, one method of sensing the oscillation of the shedding is ultra-

sound, which is disturbed by the vortices and provides a signal that can be used to

extract the frequency of shedding.

Coulthard and co-workers have also suggested using the vortex-shedding com-

bined with a correlation-sensing system to obtain flow measurement. It should be

noted in this technique that vortices may move faster than the fluid.

Teufel et al. (1992) described a new technique for measuring the profile in pipes

and applied it to oscillating flows. The object of the paper was to compare LDV and

the new ultrasonic velocity profile sensor. They saw the techniques as complemen-

tary, and it is possible that the second may offer an industrial approach where profile

determination is important.

Olsen (1991) described tests of what appeared to be an anemometer using sonic

and ultrasonic signals and allowing velocities in a wind tunnel to be measured in

three directions simultaneously.

Joshi (1991) describes a surface-acoustic-wave (SAW) flow sensor. The oscillation

frequency is temperature dependent, and so if the element is heated above ambient

and placed in the flowing gas, the frequency will be flow-rate dependent.

Guilbert et al. (1996) used a pulse of heat through the pipe wall to mark the

liquid, and the passing of the marked liquid was sensed by an ultrasonic beam using

the transit time across the pipe for cold and hot liquid.

13.13 CHAPTER CONCLUSIONS

One feature of ultrasonic flowmeters is the large amount of information avail-

able from the system, but not completely used, which will give indication of op-

erating changes or problems. In my earlier book (1988/9), I suggested that ultra-

sonic technology might develop a clamp-on meter (possibly a master meter) that

sensed:

• wall thickness,

• the quality of the inside of the tube,

• the turbulence level,

• profile from a range-gated doppler system,

• flow measurement from a transit-time system,

• correlation to provide information about a second phase,

• density from the impedance and sound speed, and

• condition (self) monitoring.

Such a device could measure diameter and other pipe details and could program

a much simpler device for permanent installation at the site.

Some of these features now appear together. Sanderson and Torley (1985) com-

bined wall thickness and some dimensional and condition monitoring, with intelli-

gent control. Range-gated doppler has been exploited in medical applications. Birch

and Lemon (1995) discussed the use of doppler on multiple paths with range gating

to obtain profiles of flows in open channels and discharges. A commercial device

may allow operation in both transit-time and doppler modes. Correlation has been

13.A.1 SIMPLE PATH THEORY 351

used for multiphase oil and gas flow measurement. Guilbert et al. (1996) have used

the device for mass flow measurement. Lynnworth (1990) has found that the phase

velocity of flexural waves in the wall of small diameter pipes was dependent on the

density of the liquid inside. As the technology becomes more widely accepted, the

microprocessor control is likely to become more powerful and to introduce multiple

facilities.

The extraordinary success in developing instruments for domestic gas measure-

ment, which are within the tight budget for the utilities, operate off a battery with

years or more of life, and have sophisticated external communication ability, will,

with little doubt, provide precursors of much more in this area.

Perhaps the ultrasonic flowmeter is the realistic rival to the Coriolis meter in gas

mass flow measurement, at lower cost, and of greater versatility.

Much development work continues as shown by the preceding references. Bragg

and Lynnworth (1994, cf. Lynnworth 1989, 1994) proposed the use of a single port

with two axially spaced transducers. As an example, they suggested that a spacing

of 60 mm axially for a velocity of 1 m/s and a sound speed of 343 m/s would result

in a l-/xs transit-time difference or a 10-ns resolution (i.e., 1%). To avoid cross-talk

between the transducers, they investigated O-rings of various materials and found

that silicone was highly attenuating.

The application at which this is aimed is firstly noncombustible gases, in which

category some stack gases fall.

They also suggested that two angled transducers in the same port can transmit

and receive a signal that forms a triangular path in the pipe cross-section and thus

senses swirl. Lynnworth et al. (1994) also developed a profile-measuring method

using the one port with either a traversing reflector or a series of fixed reflectors.

Ultrasonics combined with other methods (e.g., Guilbert et al. 1996) such as

thermal marking may provide new scope.

Another interesting development is the insertion meter of Rawes and Sanderson

(1997) discussed in Chapter 18, which could revolutionize in situ calibration in

liquids and gases.

This is such a powerful technology that it is starting to be seen as capable of

meeting fiscal demands for metering liquid hydrocarbons; therefore, limits of its

precision and reasons for baseline instability need to be understood urgently.

APPENDIX

13. A

Simple Mathematical Methods and Weight Function

Analysis Applied to Ultrasonic Flowmeters

13.A.1 SIMPLE PATH THEORY

Transit-Time

Figure 13.2 provides a diagram on which to base the mathematics. We can work in

terms of trigonometric functions or dimensions.

352 ULTRASONIC FLOWMETERS

We start with the downstream-going wave and note that its speed will be greater

than the sound speed by the component of the flow in the direction of the path.

This component is VcosO. The distance to be traveled is D cosec 0, where D is the

pipe diameter so that the time taken for the downstream wave to travel from the

transmitter to the receiver is

t* = ^ (13.A.1)

A similar expression for the upstream wave time t

Dcosec0

, „

A rtX

= (13.A.2)

c-Vcos<9

We can now obtain the difference between these two wave transit times (Figure 13.3)

At=t

-t

Dcosec0

c-VcosO c+VcosO

DcosecO/c DcosecO/c

V V

1 cos 0

H— cos 0

c c

Combining the two fractions on the right-hand side over a common denominator

and ignoring terms in (V/c)

, we obtain

IVDcotO

/I*A^

At = (13.A.3)

Thus we see that, provided we know the speed of sound, we can find the value of V

from the time difference and the geometry of the meter. The requirement to know

the value of

is not difficult if we measure, as well as the time difference, the actual

transit times each way and take the mean t

. We can make the approximation

£ = (t

- At/2)(td + At/2)

= t

*d + At(t

- *d)/2 - (At)

= t

*d + At(At)/2 - (At)

+ (At)

tuta

(13.A.4)

where, using values in Table 13.1, we have neglected a term of about 10~

. We can

now replace c

by L

td and cot# by X/D. We can then rewrite Equation (13.A.3)

^ (13.A.5)

From this, we can obtain Equation (13.5).

13.A.2 USE OF MULTIPLE PATHS TO INTEGRATE FLOW PROFILE 353

Sing-Around

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 of the flow.

We can obtain the period between pulses from Equations (13.A.1) and (13.A.2), and

the pulse frequency will be the inverse of the period, or for the downstream-going

pulses

c+ VcosO

f _ (13.A.6)

Dcosec<9

v ;

A similar expression for the upstream pulse train is

. c- VcosO

/u = (13.A.7)

' Dcosec6>

If we now take the difference between these frequencies, we obtain

2f cos6>sin6>

Vsin20/D

(13.A.8)

We can write this in terms of dimensions, since 2cos#

sinO

= 2DX/L

, as

Af =

2VX/L

(13.A.9)

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 can obtain Equation (13.7).

13.A.2 USE OF MULTIPLE PATHS TO INTEGRATE FLOW PROFILE

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

allow for varying velocity along the path of the ultrasonic beam, Equation (13.A.3)

may be rewritten in the form of an integral

V(y)dy

long

(

The flowmeter obtains the average velocity, V

, along the path of the beam.

354

ULTRASONIC FLOWMETERS

For integration along the chord shown

in Figure 13.A.I,

2cot0

At =

(13.A.11)

If the path is on the diameter, two

extremes of laminar profile and uniform

profile yield a At ratio for equal volumetric

flows of 4:3. Thus an ultrasonic flowmeter

with diametral sensing has an intrinsic cal-

ibration shift across the laminar-turbulent

profile change approaching 33%.

Baker and Thompson (1975, 1978) showed the improvement possible by using

approximately midradius transducers and recalculating Equation

(13.A.

11)

for values

of h

a/2. By using the approximate expression for the turbulence velocity profile

Figure 13.A.I. Geometry of the pipe cross-section for

chordal integration.

•H)

1/w

(13.A.12)

where n varies with Reynolds number as

Re 4 x 10

2.3 x 10

1.1 x 10

2.0 x 10

to 3.2 x 10

17 6.0 6.6 7.0 8.8 10

the signal variation can be obtained as in Figure 13.6.

The basis for using more than two paths lies in the mathematics of numerical

integration. Linked to the name of Gauss, it can be shown that a polynomial of the

form

f{f)

d t

cst

• • •

2n+1

can be precisely integrated as

f(t)dt = A

f(fy) +

f ft) + A

f(t

) +

• • •

+ A

(13.A.13)

Or a polynomial of degree In + 1 or less can be correctly integrated by an ex-

pansion such as in Equation (13.A. 13) provided the constants A

and the positions

are correctly chosen. It is also possible to show that an integral can be rearranged

to the interval -1 to +1. Thus with four positions and with suitable weighting, the

integral of a polynomial of up to order seven can be correctly evaluated.

It is as a result of considerations such as these, and possible refinements based

on likely profiles in the flow, that weightings for multiple paths (cf. Vaterlaus 1995)

have been obtained.

13.A.4 DOPPLER THEORY 355

13.A.3 WEIGHT VECTOR ANALYSIS

Hemp (1982) has developed the ideas from electromagnetic flowmeter theory for

ultrasonic flowmeters. As in the case of electromagnetic flowmeters, the condition

for an ideal flowmeter, one where the signal is independent of flow profile, is

VxW =

(13.A.14)

and Hemp obtained a flow signal expression using his reciprocal theory of

±(U$

- U^I = 2 f V

•

WdV (13.A.15)

where the negative sign is for electromagnetic and/or magnetostrictive transduc-

ers and the positive one for electrostatic and/or piezoelectric, I is the driving cur-

rent,

L/j

(2)

and U^ are the received voltages, and V

is the undisturbed flow. The

weight vector is then given in terms of p

the mean density in the meter and v

the

acoustic field for two distinct cases (1) and (2) when opposite transducers transmit

W = p

Hemp suggested that a flowmeter in a rigid-walled duct with plane wave modes,

a meter with radial transmission, and a meter with a large area transmission (e.g.,

the industrial design for small pipes) are approaching ideal configurations.

In addition to the fundamental weight vector [Equation (13.A.

16)],

it is possible

to define weight vectors for phase shift and amplitude shift (in sine wave operation)

and for pulse operation (Hemp 1998).

13.A.4 DOPPLER THEORY

Figure 13.11 is a diagram of the effect. A wave approaches a particle moving with

velocity component v in the direction of the acoustic wave, which has a velocity

c, and is reflected. The velocity remains at c relative to the medium after reflection

because sound speed is not affected by frequency (within reasonable limits). But the

period between two waves being reflected will not be k

/c. The wave will hit the

particle at a velocity c-v, and so peaks will hit the particle every k

/(c - v) seconds.

But successive peaks will make contact with the moving particle at different particle

positions, so the second peak will hit the particle k

/(c - v) seconds after the first

but will then need to travel k

V/(c

—

v) to reach the starting point of the first peak.

This additional travel takes k

V/c(c - v) seconds. So the time between peaks is r

given by

ktl + v/c (13.A.17)

c 1-v/c

K }

356 ULTRASONIC FLOWMETERS

Expanding Equation (13.A.17) using the binomial theorem, the frequency of the

reflected wave f

becomes (ignoring ^)

Hence, the frequency shift

f is given by

(13.A.19)