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

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CHAPTER

Probes for Local Velocity Measurement

in Liquids and Gases

18.1 INTRODUCTION

We resort to probes for flow measurement for three main reasons:

i. To provide a low cost method of flow monitoring;

ii.

To provide an in situ calibration;

iii.

To obtain fine detail of the flow in the pipe (velocity profile, swirl, and turbu-

lence).

For our present purposes, we shall not consider

(iii).

relevant to fluid mechan-

ics research, mainly uses hot-wire and laser doppler anemometers, and is, therefore,

outside the scope of this book. We will concentrate on work relating to bulk flow

measurement. In situ calibration techniques are covered in Chapter 4. In this chap-

ter we shall consider the various devices that have been used and are commercially

available either as a local flow monitor or as the probe for in situ calibration. How-

ever, before considering these, we need to understand what is being measured.

i. Ideally the probe measures the local velocity and obtains a representative value

of the mean velocity from the shape of the velocity profile. Alternatively, it may

measure the complete profile.

ii.

In practice the probe may be in error because:

• it was calibrated in an approximately uniform profile or on the pipe axis but

will need to measure velocity profiles that result in a significant variation of

velocity across the sensing head;

• it will alter the flow by its presence; and

• the flow pattern will continue to change as the probe head is inserted farther

and farther into the pipe and as it approaches the opposite side of the pipe.

In some cases, these flows may be analyzed theoretically, but in most cases one

would expect to calibrate the probe, and this calibration will be different at the

pipe axis and at the pipe wall.

iii.

The probe will reduce the flow area of the duct by its presence, and the area will

continually decrease as the probe is inserted farther. This blockage will need to

be allowed for. The blockage will also differ between incompressible and com-

pressible fluids.

Our object in using a probe is to obtain the best measure of the local flow rate

that can be obtained. We shall need to remember both the limitations of the probe

427

428 PROBES FOR LOCAL VELOCITY MEASUREMENT IN LIQUIDS AND GASES

and the uncertainty of the relationship between the reading and the mean velocity.

We also need to remember that, to deduce the mean flow rate in the duct, there is

uncertainty in the measurement of the cross-section of the pipe and the blockage

caused by the probe.

The variation on one probe, according to tests by the National Engineering Lab-

oratory in Scotland, suggested that blockage at the center for pipe sizes from 250 to

750 mm ranged between about ±5% and the change as the probe moves from the

center to the wall can be of order 10%.

For any new probe design, there is clearly a need for some careful work as to

a. what velocity the probe is measuring in an ideal uniform flow;

how the signal will change in a real, nonuniform pipe flow, and when close to

the wall; and

c. how the flow in the duct will be altered by the probe and how the local probe

measurement would relate to the flow in the duct if no probe were present.

In Section 2.3 and, specifically, in Table 2.2, we noted that the velocity in a turbu-

lent flow at about the 0.76 radius point (0.24 of

radius in from the wall)

practically

equal to the mean flow in the pipe. So this suggests that the probe should be set at

this point. However, this may result in reduced precision due to the shape of the

flow profile in this region (b), the level of turbulence, and the proximity of the wall.

18.2 DIFFERENTIAL PRESSURE PROBES - PITOT PROBES

Using Equation (2.10), but introducing a factor k for nonideal conditions, we can

obtain the pressure rise when flow comes to rest in the entrance of a pitot tube

(Figure 18.1) as

, Stagnation

pressure

line

Static

tapping

Pitot tube

Figure

18.1.

Separate pitot and static tubes.

Ap=

\kpV

(18.1)

For ideal conditions k = 1. Ap is the dif-

ference between the stagnation pressure at

the mouth of the pitot tube and the static

pressure; in this case, it was obtained with

a wall tapping in the same cross-sectional

plane as the mouth of the pitot tube. The

static pressure at the wall tapping

will

be the

same as the value at the pitot tube assum-

ing that there is no cross flow in the tube.

The measurement assumes that any pres-

sure effects caused by gravity between the

pitot tube entry and the wall tapping will be

equal for both the total and the static mea-

surements and will, therefore, cancel out.

Figure 18.2 shows two forms of pitot-

static tube used to obtain the dynamic pres-

sure or velocity head. Figure 18.2(a) is a

18.2 DIFFERENTIAL PRESSURE PROBES - PITOT PROBES

429

FLOW

1 or 2 rings

STATIC

of 7 holes

TAPPINGS

(b)

Figure 18.2. Two designs of pitot-static tube commended by Bean, both similar to NPL designs

(reproduced from Bean 1971 with permission of ASME): (a) Round-nosed pitot-static tube;

(b) Conical-nosed pitot-static tube.

diagram of

tube recommended by Bean (1971).

National Physical Laboratory (UK)

design appears to differ in that it has an ellipsoidal nose, which is claimed to be less

sensitive to lack of smoothness between the tip and the cylindrical section. Figure

18.2(b) shows an alternative design. Note in Figure 18.2 the coaxial arrangement of

the tubes so that the total pressure is carried in the center of the tube and the static

pressure is carried in the outer annulus. Note also the sensing holes for the static

pressure. Bean (1971) recommends that d should be between about 5 and 8 mm

(re to & in.)-

At low Reynolds number based on the tube diameter (<100) when the effect of

viscosity becomes important, k diverges from unity. Goldstein (1965) gave k values

for conical entry and round-nosed designs in the range

1.020-1.055

at about 0.6 m/s

(Re « 300), a minimum value of k = 0.991 at about 3-3.5 m/s (Re 1,600-1,900), and

a value within about 0.1% of unity for 6-27 m/s (Re 3,000-10,000). Bean (1971)

also reckoned that, for correct alignment (less than 12°), the reading should be

within 0.3%. For further information, the reader is referred to ISO 3966 or Ower

and Pankhurst (1966).

At high velocities in a gas, there are compressibility effects. The simple Equation

(18.1) has to be replaced by one that allows for these effects. Using Equation (2.16)

(2.16)

where M

= pV

/(yp) for a perfect gas, we obtain a modified equation for V

V =

p\(Po\

1)/y

-\p \\p)

(18.2)

Bean (1971) suggested that, below about 15 m/s for air at sea level, there is

negligible difference between this value and that from Equation (18.1) (with k = 1).

430

PROBES FOR LOCAL VELOCITY MEASUREMENT IN LIQUIDS AND GASES

We can see this if we rewrite Equation (18.2) as

If we then use the binomial theorem to expand the inner bracket, we obtain

2y p f

y-\ Ap

y - 1 p \ y p

(18.4)

assuming that we can neglect terms of order (Ap/p)

and greater. This reduces to

2Ap

(18.5)

In neglecting terms of order (Ap/p)

or greater powers, we have neglected terms of

order (\pV

/p)

or greater. If p = 1.3, V = 15 m/s, and p = 10

Pa (1 bar), then the

error resulting from ignoring \pV

/p is of order 0.15%, confirming Bean's value.

One major problem with the pi tot tube

is the effect of unsteady flow on its read-

ing, and because turbulence is very com-

mon in normal industrial flows, the pitot

tube will tend to read high (cf. Goldstein

1936).

MacMillan (1954) discussed the ef-

fects of low Reynolds number and noted

(MacMillan 1957) that in a shear flow there

was an apparent shift in the effective center

of the pitot tube of 0.1 Sd in the direction of

high velocity, where d is the outside diam-

eter of the pitot tube.

One manufacturer offers a device that

is not strictly a pitot tube (Figure 18.3) but

consists of

cylindrical probe with sensing

at the end. The differential pressure result-

ing from the flow acts on a spring-loaded di-

aphragm, the movement of which is sensed

by an inductive displacement transducer.

Bean (1971) refers to designs with upstream

and downstream pointing tubes, (cf. Cutler

1982)

Figure 18.3. Probe-type differential pressure sensor

[reproduced with permission of Laaser (UK)

Ltd.].

18.3 DIFFERENTIALPRESSURE

PROBES-PITOT-VENTURI PROBES

In order to increase the pressure difference

in the pitot tube in low flow rates, the

pitot-venturi has been used. In this device,

the total pressure is compared with a de-

pressed pressure created by the flow at the

18.5 INSERTION TURBINE METER

431

(a)

throat of the venturi. This is shown in

Figure 18.4(a) (Bean 1971). The pressure dif-

ference can be increased even further by us-

ing a double venturi [Figure 18.4(b)]. The

outer venturi causes a reduced pressure at

the outlet of the inner venturi, thus increas-

ing the flow through the inner one and re-

ducing the throat pressure even more.

Another device depending on differen-

tial pressure and having some similarities

to a venturi is the Elliot-Nathan flow tube

illustrated by Hayward (1977c), which ap-

pears to have a sharply converging and di-

verging venturi, in the diverging portion

of which is a hollow cone in which the

downstream pressure is measured. Hayward

commented that it is claimed to have an

outstanding performance. However, strictly

this is a full-bore meter, since its installation

would have to be in a spool piece.

Cairney (1991) described the use of a

bidirectional pitot-venturi inserted into the

bled-steam line of a generating plant in

which there was a possibility of a flow re-

versal due to a major transient in the sys-

tem. The device consisted of two very small venturi meters with axes parallel but

facing opposite directions in which the differential pressure was measured between

the throats. The device was sensitive to Reynolds number and turbulence level.

Figure 18.4. Pitot-Venturis (Bean 1971; reproduced

with permission of ASME): (a) Single venturi; (b)

Double venturi.

18.4 INSERTION TARGET METER

The flow acts on the disk (Figure 18.5), which is supported by a lever. The small

movement of the lever is sensed by an inductive displacement, counterweight, or

magnetic coupling to a pneumatic sensor. Liquid flows can be measured in a range

of about 0.05-4 m/s and gas flows from about 0.6 m/s up to about 5 m/s. It may be

applicable to temperatures up to 500°C. Measurement uncertainty for gas flows is

claimed as ±1.5% measured value.

18.5 INSERTION TURBINE METER

18.5.1 GENERAL DESCRIPTION OF INDUSTRIAL DESIGN

The insertion turbine flowmeter is a small diameter turbine and pickup on the end

of a relatively small diameter probe, usually inserted into the pipe via an isolation

valve. The propeller may be able to cope with velocities for liquids of 0.1-12 m/s or

possibly higher, and for gases of

m/s or less to 50 m/s or possibly more, with a range

432

PROBES

FOR

LOCAL VELOCITY MEASUREMENT

LIQUIDS

AND

GASES

Figure 18.5. Insertion target disk flow probe [repro-

duced with permission

Laaser (UK)

Ltd.].

for

one

probe

about 10:1.

operating

range

much as 100:1 may be quoted

some designs. The turbine probe, shown

Figure 18.6 retracted into the threaded pipe

fitting,

may

have ball bearings, jeweled

pivot, tungsten carbide journal,

other.

Ideally this will result

in a

rotational speed

for

limited range proportional

to the

flow

rate past

the

head. There

likely

to be a

minimum velocity

for

which

the

propeller

will turn

and

another

for

which

it can be

expected

give results within

the

normal

precision.

For

very

low

drag,

the

pickup

may

radiofrequency

other

low

drag

type.

typical manufacturer's specification

follows:

15-30 mm

±0.5-1%

of full scale

0.05-0.25%

10:1

Stainless steel

-200 to 150°C

Diameter of

rotor

Linearity

Repeatability

Turndown

Construction

Temperature

range

The turbine is inserted through

isolation

valve

through-bore type with

clear

concentric opening

diameter depending

on the meter. The complete device consists,

typically,

of a

small stainless steel turbine

the end of the

stainless steel insertion

tube (Figure 18.6). External handles

may

indicate

the

alignment

of the

probe,

and

this should

axial

avoid errors.

insertion Stem

Depth indicator

Seal Clamp

Seal Housing

Turbine Rotor Cage

& Assembly

Pressure Transducer

Tapping

Figure 18.6. Insertion turbine probe showing

the

turbine cage retracted into

the

screwed pipe

fitting (reproduced with permission from Flow Automation (UK) Ltd.). Note: Figure

drawn

for clarity,

not

correct alignment.

18.5 INSERTION TURBINE METER

433

The insertion tube passes through an outer tube, which seals the line pressure.

When this pressure tube is inserted into the valve, the valve can be opened, and the

turbine can be inserted through the valve into the line. Fluid seal mechanisms need

to avoid leakage but allow the probe to be inserted. In high pressure applications,

inappropriate selection can result in the probe's being expelled from the process line,

or at least moved from its set position.

These probes are suitable for water and hydrocarbons, particularly the latter be-

cause of their lubricating properties. They are not likely to be suitable for high ve-

locities or hot water.

If such a probe is to be inserted and used as a single reading device for pipe flow

monitoring, then the position of the probe in the pipe will need to be carefully

considered as discussed earlier.

To obtain a full flow profile, a series of measurements can be made, and the results

can be integrated to obtain the flow rate. There is usually a limit to the proximity to

the pipe wall at which measurements can be made. However, the nonslip condition

at the wall should allow a curve to be fitted for this region. The profile shape thus

determined allows the computation of volumetric flow. In this mode, they are also

used for in situ calibration, although the overall uncertainty is likely to be in the

range

±2-5%.

Various other designs of wall-mounted probe are available for hot-tapping or

fitting into a T-piece in the wall. An example is shown in Figure 18.7. These paddle-

wheel-type probes essentially measure flow near the wall of the pipe, and the deduc-

tion of mean flow in the pipe will be obtained by reference to the manufacturer's

literature.

18.5.2 FLOW-INDUCED OSCILLATION

AND PULSATING FLOW

Small diameter probes at the center of

a pipeline of, say, 2 m diameter or greater,

with high velocity flow, are prone to oscil-

late.

This may appear as a pulsation but can

lead to failure of the support tube in ex-

treme cases.

Ower (1937) developed a theory for a

vane anemometer, showed that it overesti-

mated average air speed, and obtained an

expression for the error. Experiments con-

firmed the theoretical conclusions.

Jepson (1967) investigated the effect

of pulsating flow on current meters and

concluded that fluctuations of the veloc-

ity vector parallel to the mean flow al-

ways cause overestimation, whereas fluctu-

ations perpendicular generally cause under-

registration. He suggested that errors could

be reduced by

Figure 18.7. Paddle-wheel-type flow sensor (repro-

duced with permission of Peek Measurement).

434

PROBES FOR LOCAL VELOCITY MEASUREMENT IN LIQUIDS AND GASES

a. using blades with a large aspect ratio,

making the tip-to-tip diameter small to keep the blade thickness as small as

possible,

c. keeping the blade angle to a minimum, and

d. using low density material for the rotor.

Jepson's paper is a useful source of earlier references on current meters.

18.5.3 APPLICATIONS

Application of turbine probes to large diameter pipe flow measurement should be

undertaken with care, recognizing the need for an integration routine, the blockage

effect caused by the probe, the effect of wall on probe calibration, the errors in

measurement of pipe diameter, and the total uncertainty of final value of flow rate.

Turbine probes have been used in applications such as compressor efficiency and

surge control, pipeline leak detection, odorizers, samplers, and checking through-

put. Some have claimed that this device can be used for custody transfer to mea-

sure with high accuracy and reduce cost by avoiding the purchase, installation, and

15 ins (381mm)

Junction Box

Alignment handle

Positive stem lock

Seal housing

Isolation chamber

Figure 18.8. Mauflo crude oil insertion flowmeter (reproduced with permission

from F.M.A. Ltd.).

18.7 INSERTION ELECTROMAGNETIC PROBES 435

maintenance of a large bore flowmeter. In my opinion this is rarely likely to be

achievable. However, if calibrated in situ, the probe may provide a long term check

on performance, although short term repeatability may not be so good.

Another device has been developed for crude oil flow measurement (Figure 18.8)

and consists of a rotor of up to 140 mm diameter that is capable of coping with wax

and fibrous materials in the flow. For a flow range of 0.15-12 m/s, the uncertainty

is claimed to be about ±0.3% at the top of the range and ±5% at the bottom with a

repeatability of ±0.15%.

Raustein and Fosse (1991) used insertion turbine meters for fuel gas flow mea-

surements and estimated measurement uncertainty as

±2-5%.

They are also used

for flare gas metering where it appears that uncertainty is likely to be in the range

±5-10%.

18.6 INSERTION VORTEX PROBES

commercial vortex-shedding insertion probe, which has been available in the past,

had a rectangular slot in the end of the insertion bar (about 32 mm diameter), and

the bluff body spanned this perpendicular to the axis of the bar. The insertion bar

was retractable and of length up to about 900 mm.

turndown of

20:1

was claimed

with repeatability of

1-1.5%

of reading.

18.7 INSERTION ELECTROMAGNETIC PROBES

Insertion electromagnetic probes have been the subject of considerable develop-

ment, and their performance has been analyzed by Hemp (1995b) and Zhang and

Hemp (1994, 1995) to obtain the sensitivity of its signal to proximity to the wall.

Industrially, it has also advanced in terms of accuracy and of low power usage.

The probe shown in Figure 18.9(a) is claimed by the manufacturer to have a

range up to about 5 m/s, the actual maximum depending on the insertion length

with maximum flow allowed for insertions of 300 mm or less. The accuracy is given

as ±2% of rate or ±2 mm/s, whichever is the greater. Insertion is up to 1 m with

typical materials for wetted parts of stainless steel and PVC. The temperature range

for water is given as 0-60°C. It is designed for local measurement of water velocity.

Figure 18.9(b) shows the installation arrangement (cf. Baird 1993 who described an

insertion probe for pipes of 25-300 mm).

These devices in various forms have been tried out for current flow measurement,

for ships' logs, and for pipe flows for many years. For more references, the reader is

referred to an earlier review by Baker (1983).

One manufacturer offers probes with different sizes of discus-shaped head, in

one case with a spherical head with electrodes projecting radially, and in another

with a ring with electrodes projecting radially inward. The heads are directionally

sensitive and operate at 128 Hz. The measurement uncertainty is claimed as 1% of

reading + 5 mm/s, and the direction is claimed to be better than 5° (cf. Bowden and

Fairbairn 1956).

Another insertion probe, but for axial insertion, was developed for blood flow in

arteries (Mills 1966, cf. Baker 1968).

436

PROBES FOR LOCAL VELOCITY MEASUREMENT IN LIQUIDS AND GASES

(b)

Figure 18.9. Electromagnetic-type insertion probe (reproduced with permission from

ABB

Ltd.):

(a) Pipe insertion probe; (b) Insertion arrangement.

18.8 INSERTION ULTRASONIC PROBES

The doppler ultrasonic principle lends itself to applications as a flow probe, provided

there are sufficient scatterers in the flow; most of the reservations have already been

set out in Chapter 13.

very much more precise instrument, depending on the transit-time principle,

has been developed by Rawes and Sanderson (1997). The device consists of a bar,

with ultrasonic transducers on each end, that is inserted through a fitting in the pipe

wall. Once in, the bar is turned into the flow so that it lies parallel with the pipe axis.

It is then possible to send ultrasonic pulses from one transducer via reflections on

the pipe wall to the other, both up- and downstream. This may lead to quite wide

flow coverage and flow averaging. Its performance, even downstream of disturbing

fittings, appears to be better than ±2.5% for higher flow rates. Figure 18.10 shows

the essentials of this meter.

Olsen (1991) reported on the use of transit-time techniques to measure air veloc-

ity. The frequencies used were 3.1 Hz (sonic) and 40 kHz (ultrasonic). He claimed that

the precision was better than a pitot-static tube and that the small size, simplicity,

and low price compared well with other methods.