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

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16.3 CHAPTER CONCLUSIONS 397

16.3 CHAPTER CONCLUSIONS

The fuel flow transmitter is an elegant solution but probably suffers, in an age when

mechanical precision is being displaced by solid state, from being a mechanical

rotating device. If the mechanical integrity can be assured and operating life is long

enough, one would expect that sensing of the rotation, torque, and other factors,

with intelligent secondary instrumentation would make it highly accurate.

It is surprising that it has not been exploited for more applications, and even

for gas flow measurement. Presumably the main reason is the preference for a meter

without moving parts.

The logical next step to overcome this would be to move to an oscillating or

vibrating device to achieve the same result. Such devices have been suggested but

may offer little advantage over the Coriolis, which we shall look at next. Any de-

velopments in this device will also be in competition with the rapidly developing

ultrasonic methods that clearly meet many of today's requirements in terms of no

moving parts and predominantly electrical sensors.

The future development of a device such as this, therefore, is unlikely to be

extensive.

CHAPTER

Coriolis Flowmeters

17.1 INTRODUCTION

This is one of the most important recent meter developments, and its application

in the next few years is likely to impinge on many areas of industry. Its importance

is recognized by the main national and international advisory bodies (cf. Mandrup-

Jensen 1990 who described initial work in Denmark on pattern approval and ISO

developments).

17.1.1 BACKGROUND

Plache (1977) makes the interesting point that mass cannot be measured without

applying a force on the system and then measuring the resulting acceleration. This

is a point that I have long considered a possible requirement, and it is certainly

supported in the Coriolis meter.

Possibly the first application of the Coriolis effect for mass flow measurement

was proposed by Li and Lee (1953). The meter is shown in Figure

17.1.

The T-piece

flow tube rotated with the outer casing and was linked to it by a torque tube. As the

flow increased, so the T-piece experienced a displacing torque due to the Coriolis

acceleration, and this was measured from the displacement of the T-piece relative to

the main body.

In the Li and Lee meter, the liquid was forced to move radially, and therefore

a force was applied to it through the tube. This force, in turn, was balanced by an

equal and opposite one applied by the liquid to the tube. The force caused the tube

to twist, and the small rotation was sensed to obtain the mass flow rate.

It is interesting to note that Stoll (1978) made no mention of the technology that

was to revolutionize mass flow measurement. Medlock (1989) referred to several de-

signs that, although not identified as dependent on the Coriolis effect, have a very

similar basis. Macdonald (1983) described the vibrating vane flowmeter, Vsesojuzny

(1976) described the vibrating nozzle flowmeter shown in Figure 17.2 (cf. Hemp's

1994b recent work on vibrating elements). Finnof et al. (1976) described the vibrat-

ing tube flowmeter shown in Figure 17.3.

Tucker and Hayes (1982) analyzed the error in oil flow rate for a vibrating pen-

dulum two-phase flowmeter invented by Rivkin (1978) and its suitability for North

American oil well applications. Reimann et al. (1982) tested a true mass flow meter

(TMFM) on a steam-water loop. This instrument created an angular momentum in

the fluid and then measured the torque needed to remove it. John et al. (1982) built

and tested a TMFM for up to 50-kg/s flows in air-water. They found that it was nearly

398

17.1 INTRODUCTION 399

Figure 17.1. Li and Lee (1953) fast response true mass-rate flowmeter (repro-

duced with the permission of ASME).

A /

Amplitude

detector

-• Density

signal

Set point

Cain

control

Drive

transducer

flow

signal

•

Figure 17.2. Vsesojuzny (1976) vibrating nozzle.

OTT

ill

Figure 17.3. Finnof et al. (1976) vibrating tube.

400

CORIOLIS FLOWMETERS

independent of the flow regime and had an overall measurement uncertainty of less

than ±1.5% of full-scale deflection up to 20% mass fraction of air, although they

observed a shift in the characteristic of

2.5%

for mass fractions of air above 1%. This

was an impressive performance. However the instrument is unlikely to be attractive

for most applications due to the requirement to drive a rotor and the consequent

design and maintenance problems.

Dimaczek et al. (1994) suggested the use of a radial turbine type wheel to create

a Coriolis effect meter for dosing gas-solid flows. They claimed that a measurement

uncertainty of ±1% rate was achieved, and that it was used for flows of coal dust,

quartz sand, feldspar, plastic granulates, and foodstuffs.

Decker's (1960) design can be explained in terms of a modern Coriolis meter.

It appears to have been the meter developed by Finnof et al. (1976, cf. Smith and

Cage 1985), which was first successfully launched into the market in 1976 (Plache

1977,

cf. 1980) according to Medlock (1989). Tullis and Smith (1979) reported early

tests on meters of g, \, and 1 in., which were promising and led to optimism for

wide application of the meters to liquids, gases, and two-phase flows.

17.1.2 QUALITATIVE DESCRIPTION OF OPERATION

My explanation of the operation of these flowmeters will be based on the U-tube

design (Figure 17.4) rather than on the most recent straight tube design, which I

expect to become increasingly common. The theory is essentially the same for both,

but I find it easier to explain for the U-tube flowmeter. We consider one of these

vibrating tubes, and we consider the period of vibration during which it rotates

upward. A simple theoretical treatment is given in Appendix

17.A.1.

Fixed

pipes

Force

on tube

Flow

Sensors

Force

on tube

Figure 17.4. Diagrams of the U-tube meter to show motion of the vibrating tube

and consequent forces during the upward movement (after MicroMotion).

17.1 INTRODUCTION

401

Flow

Magnet

position

sensors

Figure 17.5. Variation of twist with vibration for U-tube meter (reproduced from

MicroMotion's brochure with permission).

Consider first a portion of the fluid moving outward in half of the U-tube. It will

have a certain angular momentum because of the rotation of the tube upward. As it

moves outward and the tube rotates upward, the angular momentum will increase

because the same portion of fluid will be at a greater radius from the hinge and so

will have to move at a greater velocity upward. To achieve this, it is necessary to

apply a force on the portion of fluid in an upward direction. As a result, the portion

of fluid will apply an equal downward force on the pipe. Now consider the other

half of the U-tube where the fluid is moving inward and another portion of fluid.

As this portion moves inward, its angular momentum will be reduced because the

upward velocity of the tube will be less. The tube will therefore have to apply a force

downward on the portion of fluid, and this will, in turn, apply a force upward on

the tube. The result of all this is a force twisting the tube so that the near side is

forced down and the far side is forced up.

The principle of operation is based on the Coriolis acceleration, resulting from

the flow of fluid through the flow tube. However, the motion is vibration rather than

pure rotation. The forces are essentially the same, but are alternating. The vibration

takes place in such a way that one end is essentially stationary, and the other end is

vibrating through an arc. This is illustrated in Figure 17.5.

the tube

rises,

the forces are at their maximum as it passes the midplane, and at

the top of the motion the forces become zero and the twist will cease. As the U-tube

descends, the forces reverse, and the twist reverses so that again at the midplane the

twist is at a maximum. It is then apparent that if the transit time of the two halves

of the U-tube past the midplane are measured, the difference will be related to the

twist in the tube and therefore to the mass flow through the tube.

If we, now, unbend the U-tube so that it forms a straight tube with the vi-

brating drive at the center, each half will "rotate" about its end. If we consider

the center rising, the inlet half will be distorted downward by the Coriolis forces,

and the outlet half will be distorted upward. The sensors at the quarter and three-

quarter positions will sense the lag, rather than the twist, caused by the Coriolis

forces.

402 C0RI0LIS FLOWMETERS

17.1.3 EXPERIMENTAL INVESTIGATIONS

Adiletta et al.

(1993,

cf. Cascetta et al. 1989a, 1989b) described a prototype that

sought to overcome the limitations of commercial instruments' dependence on tube

deformation by

a. a system of rigid tubes,

a separate elastic suspension, and

c. electromagnetic drive and capacitance transducers to infer the twist.

Their design appeared to be affected little by external vibrations.

Sultan (1992) described a single-tube meter of 28-mm OD built for laboratory

experiments. It had a drive coil in the center of the 1410-mm-long straight pipe and

two symmetrically positioned detector coils. For his rig, a change of water tempera-

ture of about 14°C caused a zero flow calibration shift equivalent to about 0.4 m/s

(maximum flow rates tested were about 5.6 m/s). He accounted for this as being

due to differential thermal expansion and the consequent differential characteris-

tics.

This will lead to frequency change. Tube temperature change will also cause

a change in the modulus of elasticity and hence a frequency change. Sultan also

showed that a pump in the flow circuit caused a zero fluctuation due to vibration

equivalent to a flow of about ±0.1 m/s.

Kolahi et

al.

(1994) described a prototype meter with similarities to the MicroMo-

tion meter having two U-tubes. The design was very versatile in terms of component

changes. Optical, capacitive, and inductive sensors could be used. It was also possible

to tune it so as to amplify the torsional amplitude by up to 100 times.

Hagenmeyer et

al.

(1994) reported a design of

single-tube, compact Coriolis me-

ter operating in a hoop mode and claimed that experimental results were promising.

17.2 INDUSTRIAL DESIGNS

The MicroMotion meter was the first to appear in 1981 and resulted from patents

filed in 1975, 1977, and 1978 (cf. Wilier 1978 and Smith 1978). The initial device

consisted of a single U-tube.

recent paper by Tsutsui and Yamikawa (1993) seemed

to be using one tube plus a resonance vibrator as in the early MicroMotion meter.

Twin tubes were introduced in model D in 1983. The main features of this meter

are a single inlet splitting into the two tubes, a drive system to cause the tubes to

vibrate, a pair of sensors to detect the movement of the tubes past the midplane, and

a strong point around which the tubes vibrate in opposition. In some meters, the

outer cover forms a pressure vessel so that, if the tubes fail, the fluid will be contained.

Failure should not be due to fatigue, because manufacturers should design so that

tubes will not fail due to cyclic stressing. Tube failure almost always occurs due to

corrosive stressing.

Several designs followed MicroMotion and a selection of these, some no longer

available, are shown diagrammatically in Figure 17.6 based on my understanding

of the manufacturers' brochures. Apart from those shown [Bopp & Reuther, Dan-

foss,

Endress & Hauser, EXAC, Foxboro, K-Flow, Krohne, MicroMotion, Neptune

(Schlumberger), and Smith], there maybe other manufacturers of this type of meter,

17.2 INDUSTRIAL DESIGNS 403

(a)

Drive

Bopp and

Reuther

Krohne

Drive

(C)

Danfoss

Optical T Optical

sensor A sensor B

Endress

and

Hauser

(i)

Sensor B

MicroMotion

(twin-tube)

MicroMotion

(single-tube)

Drive

(d)

Exac

Neptune

(Schlumberger)

(e)

Foxboro

(k)

Sensor A Drive

Sensor B

Smith

(f)

Nodes

Drive

K-Flow

Nodes

(I)

Sensor A Sensor B

Straight

tube

Figure 17.6. A selection of Coriolis-type mass flowmeters available commercially now or in

the past: (a) Bopp and Reuther; (b) Danfoss; (c) Endress

Hauser; (d) EXAC; (e) Foxboro;

(f) K-Flow; (g) Krohne; (h) MicroMotion (twin-tube); (i) MicroMotion (single-tube); (j) Neptune

(Schlumberger); (k) Smith; (1) Krohne, Endress

Hauser, and others.

such as Heinrichs and Yokogawa. It should be noted that some manufacturers offer

two options.

Most industrial designs in current operation use two parallel wetted tubes or two

tubes in series. The deflection is measured from one tube to the other so that external

404 C0RI0LIS FLOWMETERS

vibrations are largely eliminated and the measured shift between the tubes has the

effect of adding the flows in the two tubes even if the flow split is not equal.

Single-tube versions (e.g., Hussain and Farrant 1994) are beginning to be intro-

duced, and these are likely to be an increasingly attractive option for the future

(Reider and Drahm 1996, Yamashita 1996). At present, these may be offered as a

second design by some manufacturers (cf. Stansfeld et al. 1988, Harrie 1991 for an

earlier design).

17.2.1 PRINCIPAL DESIGN COMPONENTS

Flow Tubes

The deflection of the tubes is sensed from one tube to the other in twin-tube versions

or between tube and outer compensating tube in single-tube versions. This elimi-

nates,

to a large extent, external vibrations. The tubes are mounted to isolate them

from external vibration and are designed to optimize phase shift between sensor

signals and to minimize pressure loss. Wagner (1988) discussed trade-offs for tube

selection. For instance, by lengthening the meter tube, vibration of the tube is easier,

stresses are reduced, and twist and Coriolis force increase. However, this is at the cost

of greater weight and pressure drop.

The problem of corrosion is a reason why some manufacturers use an outer

containment vessel around the vibrating tubes in case of tube failure.

Foxboro has introduced a technique called antiphase excitation, which uses a

double driver system to produce a rotating motion on the tube essentially at the

flattened bottom of the U-tube. In this way, the stresses are greatly reduced because

the vibration is away from the pipe joints. This appears to be similar to the Bopp &

Reuther and the Krohne designs. Watt (1990) described work on the computation

of pipe stresses.

Drive Mechanisms

Drive mechanisms are most commonly electromagnetically excited to oscillate at

the chosen frequency. In some cases, this is the natural (resonant) frequency; in

others, it is a harmonic of the natural frequency. Higher frequencies are claimed to

reduce the effect of external disturbances by introducing free nodes of vibration and

by working farther above the most common surrounding frequencies. The control

circuit then keeps the oscillation at the chosen frequency. For high viscosity or

density, additional power may be required in the drive.

Sensor Types

In meters with twin tubes, the sensor usually measures the displacement between

the two tubes, thus eliminating any common spurious vibrations. One method used

in several designs has a coil on one tube and a magnet on the other. The relative

velocity causes a voltage to be generated in the coil, and, in order to obtain po-

sition, this signal is integrated. Another method (Vogtlin and Tschabold, Endress

& Hauser) is optical and uses an arrangement of photodiodes and a modulating

shutter (Figure 17.7). "Small plates acting as shutters are attached to the tubes

... leaving a defined gap between each pair. The shutter changes as the two tubes os-

cillate in phase opposition. ... Infrared light is beamed from a light-emitting diode

into a sapphire rod with face ground to a 45° angle. Thus the quantity of light is

modulated ... and converted into alternating electric current. ... "

17.2 INDUSTRIAL DESIGNS 405

LED [> -[X— Photodiode

Sapphire rod

Modulator metal sheet

(a)

Temperature sensing is included in

some commercial instruments (e.g., the use

of a platinum resistance thermometer (PRT)

with resistance set to 100 ohms). Nichol-

son (1994) noted that the location of the

temperature sensor within the meter hous-

ing had a significant effect on the pre-

cision with which fluid temperature was

measured. His results suggest discrepancies

ranging up to ±2°C. In Krohne's single

straight tube design, a strain gauge has been

added together with a temperature sensor,

in order to obtain information from the me-

ter for subsequent corrections by the elec-

tronics.

Kalotay (1994) used the pressure drop

through the MicroMotion meter to obtain

a value of viscosity.

Secondary Containment

Some manufacturers design the flow tube

with an outer containment tube so that, in

the event of flow tube failure, the process

fluid is contained (cf. Hussain and Farrant

1994 who quote a bursting pressure of 500

bar with in-house testing up to 300 bar).

Meter Secondary

As indicated earlier, the distortion in the

tube due to Coriolis forces will cause the

two sensors to pass the midplane at differ-

ent times. The phase shift at full-scale flow

may be about

1°.

At zero flow, the phase dif-

ference should be zero, although normally

there is an offset and hence a zeroing rou-

tine.

Figure 17.8(a) shows the block diagram of a signal processing system. The drive

coil vibrates the tube at its natural frequency. Sensing obtains tube velocity, which

is integrated to obtain position and in so doing filtered to remove some noise.

The conversion of the signals is shown in Figure 17.8(b). Position detector signals

are slightly offset, and the effect at zero flow can be seen. A reference current is

integrated during the pulses so that the voltage on the integrator is proportional to

the time period and hence the mass flow.

An alternative is to use a high speed clock to count the time differences. At

maximum flow this is of order 120

/^s.

The minimum measurement must therefore

be less than 10 ns to discriminate at the lowest flow rates.

For their latest designs, MicroMotion claims to achieve a time difference between

the two pick-off signals of about 60 /xs at the top of the range and, with a 100:1

(c)

Figure 17.7. Endress and Hauser modulating shutter

(reproduced with permission): (a) Schematic repre-

sentation of optical sensor; (b) Longitudinal and (c)

cross-sectional construction of the measuring sensor;

A, electromagnetic excitation (coil); B, C, optical de-

tection of the tube oscillations.

406 C0RI0LIS FLOWMETERS

Sensor unit

Frequency output

(a)

Zero flow With flow

Outputs of

integrators

and 49'

Output of

integrator 49

Output of

integrator 49'

Ref.

Sample

Comparator 60

Downcount/

integration

Upcount/

(b)

Figure 17.8. MicroMotion signal processing system (reproduced with permission): (a) Block

diagram; (b) Conversion of signals.

turndown, 0.6 /xs at the bottom of the range. To measure this with an uncertainty

of ±0.4% requires a resolution of about ±2.4 ns.

In another signal processing system (Vogtlin and Tschabold undated), the circuit

keeps equal the amplitudes of the alternating currents, which energize each of the

sensing photodiodes. These are then fed into a differential amplifier.

phase locked

loop (PLL), avoiding phase shift, ensures that the tubes vibrate at resonance, and

hence the density of the fluid is obtained.