flow handbook - Académie de Bordeaux · PDF fileFlow Handbook Chapter 1: Basic ... it may be single-phase (clean gas, water or oil) or multi-phase ... the numerous flow metering...

Flow Handbook

Chapter 1:Basic properties of fluids ............... 2

Chapter 2:Positive displacement meters ........ 8

Chapter 3:Inferential meters ........................ 12

Chapter 4:Oscillatory flow meters ............... 17

Chapter 5:Differential pressure meters ........ 24

Chapter 6:Electromagnetic flow meters ....... 35

Chapter 7:Ultrasonic flow meters ................ 45

Chapter 9:Open channel flow measuring ..... 60

Chapter 10:Common installation practices .... 66

Chapter 11:Bibliography ................................ 69

Over the past 50 years, the importance of flow measure-ment has grown, not only because of its widespread usefor accounting purposes, such as the custody transfer offluid from supplier to consumer, but also because of itsapplication in manufacturing processes. Throughout thisperiod, performance requirements have become morestringent—with unrelenting pressure for improvedreliability, accuracy, lincariiy, repeatability and rangeability.

These pressures have been caused by major changes inmanufacturing processes and because of several dramaticcircumstantial changes, such as an increase in the cost offuel and raw materials and the need to minimise pollution.Industries involved in flow measurement and controlinclude:

• food and beverage• medical• mining and metallurgical• oil and gas transport• petrochemical• pneumatic and hydraulic transport of solids• power generation• pulp and paper• water distributionFluid properties can vary enormously from industry toindustry. The fluid may be toxic, flammable, abrasive, radio-active, explosive or corrosive; it may be single-phase (cleangas, water or oil) or multi-phase (for example, slurries, wetsteam, unrefined petroleum, or dust laden gases). The pipecarrying the fluid may vary from less than 1 mm to manymetres in diameter. Fluid temperatures may vary from closeto absolute zero to several hundred degrees centigrade,and the pressure may vary from high vacuum to manyatmospheres.

Because of these variations in fluid properties and flowapplications, many flow meter techniques have beendeveloped: each suited to a particular area. However, ofthe numerous flow metering techniques that have beenproposed in the past, only a few have found widespreadapplication and no one single flow meter can be used forall applications.

Why measure flow?There is of course no single answer. Most flow measure-ments are concerned with either how much is produced orhow much is used. Flow measurement is also used inprocess control for flow control, blending, and batching.Lastly, it is concerned with custody transfer (fiscal and legalmetering).

Basic fluid propertiesOne of the most important primary properties of a fluid(liquid or gasj is its viscosity—its resistance to flow or toobjects passing through it. Conceptually, viscosity mightbe thought of as the ‘thickness’ of a fluid. In essence it isan internal frictional force between the different layers ofthe fluid as they move past one another. In a liquid, this isdue to the cohesive forces between the molecules whilstin a gas it arises from collisions between the molecules.

Different fluids possess different viscosities: treacle is moreviscous than water and gearbox oil (SAE 90) is more viscousthan light machine oil (for example 3-in-l). A comparisonof various fluids is shown in Table 1.1.

Table 1.1:Comparison of the viscosities of various fluids

If ihe fluid is regarded as a collection of moving plates, one on top of theother, then when a force is applied Lo the fluid, shearing occurs and theviscosity is a measure of the resistance offered by a layer betweenadjacent plates.

Figure 1.1 shows a thin layer of fluid sandwiched betweentwo flat metal plates of area A—the lower plate is stationaryand the upper plate moves with velocity v. The fluid directlyin contact with each plate is held to the surface by theadhesive force between the molecules of the fluid and thoseof the plate. Thus the upper surface of the fluid moves atthe same speed v as the upper plate whilst the fluid incontact with the stationary plate remains stationary. Sincethe stationary layer of fluid retards the flow of the layerjust above it and this layer, in turn, retards the flow of thenext layer, the velocity varies linearly from zero to V, asshown.

Figure 1.1:When a thin layer of fluid is sandwiched between two flat metal plates,shearing occurs and the upper surface of the fluid moves at the samespeed as the upper plate whilst the fluid in contact with the stationaryplate remains stationary

The relative force acting on the layers is called the shearstress (the force per unit area). In Figure 1.1, the fluidflows under the action of the shear stress due to the motionof the upper plate. It is also clear that the lower plate exertsan equal and opposite shear stress to satisfy a ‘no-slip’condition at the lower stationary surface.

It follows, therefore, that at any point in the flow, thevelocity at which me layers move relative to each other,referred to as the shear rate, is directly proportional to theshear stress:

where µ is the viscosity—the ratio of shear stress and shearrate.

Chapter 1: Basic properties of fluids

Shear rate = ∝ Shear stressor: Shear stress = µ. Shear rate

Fluid Temperature (°C) Viscosity µ (Pa.s)

Molasses 20 100Glycerine 20 1.5Engine oil (SAE 10) 30 0.2Milk 20 5.0 x 10-3

Blood 37 4.0 x 10-3

Water 0 1.8 x 10-3

Ethyl alcohol 20 1.2 x 10-3

Water 20 1.0 x 10-3

Water 100 0.3 x 10-3

Air 20 0.018 x 10-3

Water vapour 100 0.013 x 10-3

Hydrogen 0 0.009 x 10-3

These days, viscosity is expressed as absolute or dynamicviscosity measured in Pascal-Seconds (Pa.s).

Formerly, viscosity was expressed as relative viscosity—the ratio of Ihe liquid’s absolute viscosity with respect tothe viscosity of water. Here, the unit of measurement wasthe centipoise (cPj or. in the case of gases, micropoise (U.PJ

where:

1 Pa.s = 1000cPAs shown in Figure 1.2, the viscosity of a fluid dependsstrongly on temperature and generally decreases when thetemperature increases. Gases, however, show the oppositebehaviour andtheviscosity increases for increasingtemperature.

Figure 1.2:The viscosity of fluids depends strongly on temperature

Subsequently, Table 1.1 lists the viscosity of various fluidsat specified temperatures—with the viscosity of liquids suchas motor oil, for example, decreasing rapidly as temperatureincreases.

The viscosity of“ a fluid also depends on pressure but,surprisingly, pressure has less effect on the viscosity ofgases than on liquids.

A pressure increase from 0 to 70 bar fin air) results in anapproximate increase of 5% in viscosity. However, withmethanol, for example, a 0 to 15 bar increase results in a10-fold increase in viscosity. Some liquids are more sensitiveto changes in pressure than others.

Viscosity related to the density of a fluid is termed thekinematic viscosity. Kinematic viscosity is given by:

v = U./P where:

v = kinematic viscosity measured in m2/s u, = dynamicviscosity measured in Pa.s p = density of the liquid (kg/m3)

Kinematic viscosity was formerly measured in centistokes(cSt) where: 1 m2/s= 106cSt

Non-Newtonian fluidsMost fluids used in engineering systems exhibit Newtonianbehaviour in that, for a given value of pressure andtemperature, the shear stress is directly proportional tothe shear rate. Thus, if the shear stress is plotted againstshear rate the result is a straight line passing through theorigin (Figure 1.3).

Certain fluids, however, do not exhibit this behaviour.

Examples include: tar. grease, printers’ inks, colloidalsuspensions, hydrocarbon compounds with long-chainmolecules and polymer solutions. In addition, some fluids,called viscoelastic fluids, do not immediately return to acondition of zero shear rale when stress is removed.

The ideal plasticThe so-called Ideal plastics or Bingham fluids exhibit alinear relationship between shear stress and shear rate.However, such substances only flow after a definite yield

Figure 1.3:The sheaf stress plotted against shaar rate for 3 number of materials.Fur Newtonian materials the shear stress plotted against shear rateresults in a straight line passing through the origin

point has been exceeded (Figure 1.3). When at rest, thesematerials possess sufficient rigidity to resist shear stressessmaller than the yield stress. Once exceeded, however, therigidity is overcome and the material flows in much thesame manner as a Newtonian fluid.

Examples of materials exhibiting this type of behaviourinclude: tar; chewing gum; grease: slurries; sewage slugs;and drilling muds.

PseudoplasticA pseudoplastic substance, such as printer’s ink, ischaracterised by polymers and hydrocarbons which possesslong-chain molecules and suspensions of asymmetricparticles. Although exhibiting a zero yield stress, therelationship between shear stress and shear rate is non-linear and the viscosity decreases as the shear stressincreases.

DilatantDilatant materials also exhibit a non-linear relationshipbetween shear stress and shear rate and a zero yield stress.However, in this case, the viscosity increases as the shearstress increases. This type of behaviour is found in highlyconcentrated suspensions of solid particles. At low ratesof shear, the liquid lubricates the relative motion of adjacentparticles, thereby maintaining relatively low stress levels.As the shear rate increases, the effectiveness of thislubrication is reduced and the shear stresses are increased.

Velocity profilesOne of the most important fluid characteristics affectingflow measurement is the shape of the velocity profile inthe direction of flow.

Chapter 1: Basic properties of fluids

Ideal profileIn a friction less pipe in which there is no retardation ai thepipe walls, a ilat ‘ideal1 velocity profile would result (Figure1.4) in which all the fluid particles move at the samevelocity.

Laminar flowWe have already seen, however, that real fluids do not ‘slip’at a solid boundary but are held to the surface by theadhesive force between the fluid molecules and those ofthepipe. Consequently, at the fluid/pipe boundary, there is no

relative motion between the fluid and the solid.

Figure 1.4: A flat‘ideal’ velocity profile

At low flow rates the fluid particles move in straight linesin a laminar manner—each fluid layer flowing smoothlypast adjacent layers with no mixing between the fluidparticles in the various layers. As a result the flow velocityincreases from zero, at the pipe walls, to a maximum valueat the centre of the pipe and a velocity gradient existsacross the pipe. The shape of a fully developed velocityprofile lor such a laminar flow is parabolic, as shown inFigure 1.5, with the velocity at the centre equal to twicethe mean flow velocity. Clearly, it“ not corrected for, thisconcentration of velocity at the centre of the pipe cancompromise the flow computation.

Figure 1.5: A laminar‘parabolic’ velocityprofile

Turbulent flowOne of the earliest investigators into fluid flow was OsborneReynolds (1842-1912) who conducted a number ofexperiments using what is now termed a Reynold’sinstrument, a device that injects ink into the flow stream(Figure 1.6).

Figure 1.6: Reynold’sinstrument injects inkinto the flow streamto observe the flowregime (courtesyFisher Rosemount)Figure 1.7:Transition fromlaminarthrough toturbulent flow

For a given pipe and liquid, as the flow rale increases, thelaminar path of an individual particle of fluid is disturbedand is no longer straight. This is called the transitionalstage (Insure 1.7). As the velocity increases further theindividual paths start, to intertwine and cross each otherin a disorderly manner so that thorough mixing of the fluidtakes place. This is termed turbulent flow. Since the flow

velocity is almost constant in all of the pipe cross section,the velocity profile for turbulent flow is flatter than forlaminar flow and thus closer approximates the ‘ideal’ or‘one dimensional’ ficj-w (Figure 1.8).

Figure 1.7:Transition fromlaminar through toturbulent flow

Figure 1.8:A turbulent velocityprofile

Reynolds numberThe onset of turbulence is often abrupt and to be able topredict the type of flow present in apipe, for any application,use is made of the Reynolds number, Re—a dimensionlessnumber given by:

Re =

Where:ρ = density of fluid (kg/m3)µ = viscosity of fluid (Pa.s)ν = mean flow velocity (m/s)d = diameter of pipe (m)

Irrespective of the pipe diameter, type of fluid or velocity.Reynolds showed that the flow is:

Laminar: Re <2000

Transitional: Re =2000-4000

Turbulent: Re >4000

From the foregoing it is seen that, in addition to viscosity,Re also depends on density. Since most liquids are prettywell incompressible, the density varies only slightly withtemperature.

Chapter 1: Basic properties of fluids

ρ ν dµ

However, for gases, the density depends strongly on thetemperature and pressure in which (for ideal gas):

PV= mRT

where:

P = pressure (Pa)

V = volume of the gas (m3)

T = temperature (K)

m = number of moles

R = universal gas constant (8,315 J/(mol.K))

Since:

p = m/V = P/RT

Most gases may be considered ideal at room temperaturesand low pressures. Both.laminar and turbulent flow profilesrequire time and space to develop. At an entrance to apipe, the profile may be very flat—even at low Re. And itmay stay laminar, for a short time, even at high Re.

Disturbed flow profilesObstructions in a pipe, such as bends, reducers, expanders,strainers, control valves, and T-pieces, can all affect theflow profile in a manner that can severely affectmeasurement accuracy. Such disturbcdllow, whichshouldnot be confused with turbulent flow, gives rise to anumber of effects that include:

• swirl—fluid rotation about the pipe axis• vortices—areas of swirling motion with high local

velocity which are often caused by separation or asudden enlargement in pipe area

• asymmetrical profile—see Figure 1.9• symmetrical profile with high core velocity—

caused by a sudden reduction in pipe area

Figure 1.9:Asymmetric flowprofile due todisturbed flow

Ultimately the flow profile will be restored by the naturalmixing action of the fluid particles as the fluid movesthrough the pipe. However, the effect of such disturbancescan have an important bearing on accuracy for as much as40 pipe diameters upstream of the measuring device. Figure1.10 shows the ongoing disturbance in a pipe following asimple elbow.

Figure 1.10:Ongoing disturbance in a pipe following a simple elbow

Chapter 1: Basic properties of fluidsFlow measurementIn flow measurement a number of parameters can be usedto describe the rate at which a fluid is flowing:

Volumetric flow rateThe volumetric flow rate, Q, represents the total volume offluid

flowing through a pipe per unit of time and is usuallyexpressed in litres per second 1/sJ or cubic metres perhour (mVh). The measurement of volumetric How rate ismost frequently achieved by measuring the mean velocityof“ a fluid as it travels through a pipe of known crosssectional area A (Figure I.I I). Thus:

Q = V⋅ A

Figure 1.11:The volumetric flow rate, Q, represents the total volume of fluid

VelocityThe term velocity is often used loosely to describe the speedat which the fluid passes a point along the pipe. Inreality, most modern flow meters measure either the pointvelocity or the mean velocity.

Point velocityThe point velocity is the flow velocity in a localised regionor point in the fluid and is generally of little use in practice.Tt is used mainly in research to determine, for example,velocity profiles or flow patterns.

Mean flow velocityThe mean flow velocity, v can be obtained by measuringthe volumetric flowrate, Q, and dividing it by the cross-sectional area of the pipe, A:

v =

Alternatively, if the velocity profile is known the mean flowvelocity can be obtained by averaging the velocity overthe velocity profile, giving equal weighting to equal annularregions.

An example of the calculation of the mean velocity of theflow conduit by area-weighting point-velocitymeasurements is illustrated in Figure 1.12. As shown, anumber of velocity bands are scaled across the cross-sectional area of a 320 mm diameter conduit.

Figure 1.12:Example of areaweighted techniquefor determining themean velocity of afluid

QA

Chapter 1: Basic properties of fluidsThe mean velocity can be determined using standardaveraging techniques in which the velocities of each bandare summed and then divided by the number of bands:

In the area-weighted technique, the scaled areas, velocitiesand products of each area, times its local velocity, aretabulated for each velocity band (Table 1.2). The area-weighted mean velocity is calculated by summing thevelocity-area products, and dividing the sum of the cross-sectional area of the flow conduit.

Table 1.2:Calculations for determining area-weighted mean velocity

Mass flow rateMost chemical reactions are largely based on their massrelationship and, consequently, to control the process moreaccurately, it is often desirable to measure the mass flowof the product. The mass flow rate, W, gives the total massof fluid flowing at any given time. A knowledge of volumeflow rate, Q and the fluid density, p, determines the massflow rate from:

W = Q.⋅ p (kg/s)Some flow meters, such as Coriolis meters, measure themass flow directly. However, in many cases, mass flow isdetermined by measuring the volumetric flow and thedensity and then calculating the mass flow as shown above.Sometimes the density is inferred from the measurementof the pressure and temperature of the fluid. This type ofmeasurement is referred to as the inferred method ofmeasuring mass flow.

Multi-phase flowsFor multi-phase flows, the mass or volume flow rate ofone of the constituents is often of interest. For example, inthe case of slurry, the mass flow rate of the solid phase isusually the required variable.

Flow range and rangeabilityWhilst there is considerable confusion regarding basicterminology, nowhere is this more evident than in thedifference between the terms flow range, turndown ratio,span, and rangeability.

Flow rangeThe flow range is simply the difference between themaximum and minimum flow rate over which a meterproduces acceptable performance within the basic accuracyspecification of the meter. This is illustrated in Figure 1.13.

For flow meters that exhibit a minimum flow rate, the flowrange is thus the interval from the minimum flow rate tothe maximum flow rate. If the meter does not exhibit aminimum flow rate, the flow range is the interval fromzero flow to maximum flow.

Figure 1,13:The flow range is the difference between the maximum and minimum flowrate over which a meter produces acceptable performance within thebasic accuracy specification of the meter

Turndown ratioThe turndown ratio is the ratio of the maximum flow rateto the minimum flow rate for a measuring range that iswithin a stated accuracy. For example, the measuring rangeof a magnetic flow meter might be 0.3 m/s to 12 m/s withinan accuracy of 0.3%. This would be stated as having a 40:1turndown ratio (0.3 %). In addition the measuring rangemight extend from 0.2 m/s to 12 m/s within an accuracyof 0.5%. In this case the turndown ratio is 60:1 (0.5%). It istherefore meaningless to express the turndown ratiowithout a specified accuracy.

SpanThe term span relates to the flow meter output signals andis the difference between the upper and lower range valuesassigned to the output signal.

For example, for a Coriolis meter with a 4-20 mA analogoutput, the upper and lower range values might be assignedas:

Lower range value:0 mA = 0 kg/h

Upper range value:20 mA = 5000 kg/hThe span is therefore the difference between the two values,ie 5000 - 0 = 5000 kg/h. The minimum span is the lowestflow rate able to produce full-scale output and the maximumspan is equal Lo the maximum range of the sensor.

RangeabilityRangeanility is a measure of how much the flow range ofan instrument can be adjusted and is defined as the ratioof the maximum How range (maximum span) and theminimum span. The term rangeability is often confusedwith turndown ratio and users should be careful as to whatis meant when the terms are used.

AccuracyThe accuracy of a flow meter is the maximum deviationbetween the meter’s indication and the true value of theflow rate or the total flow. Accuracy, also referred to asuncertainty, is the interval within which the true value ofthe measured quantity can be expected to lie within a statedprobability (generally taken to be 95 % unless otherwisespecified).

VAV

= = 108.25VA + V

B + V

C + V

D

4

Band Radius Velocity Area Vn ⋅⋅⋅⋅⋅ An

(cm) (cm/s) (cm)

A 4.0 130 50.26 6533B 8.0 120 150.80 18096C 12.0 107 251.33 26892D 16.0 76 351.86 26741

Total 804.25 78262

Chapter 1: Basic properties of fluidsIt includes the combined errors due to linearity, hysterisisand repeatability and can be expressed in any one of“ threeways: as a percentage of span; as a percentage of a rate; oras a percentage of the upper range value.

To illustrate this difference, consider three flow meters:one with an accuracy of ±1% of span; one with an accuracyof ± \% of a reading; and one with an accuracy of ± 1 % ofURL (Upper Range Limit). The URL is defined as the highestflow rate that a meter can be adjusted to measure whilstthe Upper Range Value (URV) is defined as the highest flowrate that the meter is adjusted to measure. Each meter hasa URL of 100 1/min, and is calibrated 0 to 50 l/min.

For the percentage of span instrument, the absolute erroris determined at the 100 % span reading, and then used todetermi ne the accuracy at lower flow rates. Since the spanis 501/min the absolute error would be ± I % of 50, or±0.51/min. The accuracy of the meter at 50 1/min wouldbe 50 1/min ±0.5 1/min. or±l %. At 25 1/min the accuracywould be 25 1/min ±0.5 1/min, or ±2 % (Figure 1.14). Forthe percentage of reading instrument, the absolute erroris determined at the actual reading, and varies with flowrate. The absolute error at 501/min is ± 1 % of 50, or ±0.51/min. The absolute error at 251/min is ± I %of25,or±0.25 1/min. This means the meter has a constant accuracy of ±1 %at all readings (Figure L15).

Figure 1.14: In the percentage of span instrument, the absolute error isdetermined at the 100 % span reading, and then used to determine theaccuracy at lower flow rates

Figure 1.15: In the percentage of reading instrument, the absolute erroris determined at the actual reading, and varies with flow rate

Figure 1.16: In the percentage of URL instrument, the absolute error isdetermined at the URL and then used to determine the accuracy at lowerflow rates

For the percentage of URL instrument, the absolute erroris determined at the URL and then used to determine theaccuracy at lower flow rates. The absolute error would be±1 %of 100, or ± 1 1/min. The accuracy of the meter at 50l/inin would be 50 1/min ±1 1/min, or ±2 %. The accuracyat 25 1/min would be 25 1/min at ± I 1/min, or ±4 % (Figure1.16). In the above example, two of the three meters wouldhave the same accuracy, ±1 %, when calibrated at the URL,100 1/min. Percentages of rate meters are generallypreferred when operating over a wide flow rate range.

Positive displacement meters (sometimes referred to asdirect volumetric totalisers) all operate on the generalprinciple where defined volumes of the medium areseparated from the flow stream and moved from the inletto the outlet in discrete packages.

Totalising the number of packages provides the totalvolume passed and the total volume passed in a given timeprovides the flow rate, for example, litres/min.

Because they pass a known quantity, they are ideal forcertain fluid batch, blending and custody transferapplications.

They give accurate information and are generally used forproduction and accounting purposes.

There are many different configurations of positivedisplacement meters and this chapter discusses some ofthemost popular types.

Sliding vaneUsed extensively in the petroleum industry for gasolineand crude oil metering, the sliding vane meter is one ofthe highest performance liquid positive displacementmeters. In its simplest form it comprises a rotor assemblyfitted with four spring-loaded sliding vanes so that theymake constant contact with the cylinder wall (Figure 2.1),The rotor is mounted on a shaft which is eccentric to thecentre of the meter chamber.

Chapter 2: Positive displacement metersThe disadvantages of the sliding vane meter are:

• suitable for clean liquids only• limitations due to leakage• high unrecoverable pressure loss

Oval gear metersOval gear flow meters comprise two identical precisionmoulded oval rotors which mesh together by means ofgear teeth around the gear perimeter. The rotors rotate onstationary shafts which are fixed within the measuringchamber (Figure 2.2).

Figure 2.1:Sliding vane positive displacement meter comprising a rotor assemblyfitted with four spring-loaded sliding vanes

As liquid enters the measuring chamber the pressure onthe exposed portion of vane 1 causes the rotor to turn.While the rotor turns on its shaft, vane 2 moves to seal offthe inlet port—rotating to occupy the position formerlyoccupied by vane 1.

This process is repeated, without pulsations, as the vanesmove around the measuring chamber—with ‘packets’ offluid trapped and passed to the outlet manifold as discreteknown quantities of fluid.

A mechanical counter register or electronic pulse counteris attached to the shaft of the rotor so that flow volume isdirectly propoitional to shaft rotation.

Close tolerances and carefully machined profiles of thecasing ensure the blades are guided smoothly through themeasuring crescent to give high performance.

Advantages of the sliding vane meter are:

• suitable for accurately measuring small volumes• high accuracy of ± 0.2%.• high repeatability of ± 0.05%• turndown ratio of 20:1• suitable for high temperature service, up to 180°C• pressures up to 7 MPa• not affected by viscosity

Figure 2.2:Construction of the oval gear meter (courtesy Fisher Ftosemount)

The meshed gears seal the inlet from the outletflow,developing a slight pressure differential across the meterthat results in movement of the oval rotors.

When in the position shown in Figure 2.3(a), Gear A receivestorque from the pressure difference while the net torqueon Gear B is zero, (b) Gear A drives Gear B. (c) As Gear Bcontinues to rotate, it traps a defined quantity of fluid until,in this position, the net torque on Gear A is zero and GearB receives torque from the pressure difference, (d) Gear Bdrives Gear A and a defined quantity of fluid is passed tothe outlet. This alternate driving action provides a smoothrotation of almost constant torque without dead spots.

Figure 2.3:Principle of the oval gear meter: (a) Gear A receives torque from thepressure difference while the net torque on Gear B is zero, (b) GearA drives Gear B. (c) As Gear B continues to rotate it traps a definedquantity of fluid until, in this position, the net torque on Gear A is zeroand Gear B receives torque from the pressure difference, (d) GearB drives Gear A and a defined quantity of fluid is passed to the outlet

Chapter 2: Positive displacement metersWith flow through the meter, the gears rotate and trapprecise quantities of liquid in the crescent shapedmeasuring chambers. The total quantity of flow for onerotation of the pair of oval gears is four times that of thecrescent shaped gap and the rate of flow is proportional tothe rotational speed of the gears. Because the amount ofslippage between the oval gears and the measuringchamber wall is minimal, the meter is essentially unaffectedby changes in viscosity and lubricity of the liquids.

An output shaft is rotated in direct proportion to the ovalgears by means of a powerful magnetic coupling. Oval gearmeters find widespread use in the measurement of solvents,with close tolerances ensuring that leakage is minimised.

The major disadvantage of this meter is that the alternatedriving action is not constant and, as a result, the meterintroduces pulsations into the flow.

Further, the viscosity of the fluid can affect the leakage orslip flow. If the meter is calibrated on a particular fluid, itwill read marginally higher should the viscosity increase.

Newer designs of this type of meter use servomotors todrive the gears. These eliminate the pressure drop acrossthe meter and the force required to drive the gear. Thisapplies mainly to smaller sized meters and significantlyincreases the accuracy at low flows.

Advantages of the oval gear meter are:

• high accuracy of ± 0.25%• high repeatability of ± 0,05%• low pressure drop of less than 20 kPa• high operating pressures, up to 10 MPa• high temperatures, up to 300°C• wide range of materials of constructionThe disadvantages of the oval gear meter are:

• pulsations caused by alternate drive action• accuracy dependent on viscosity

Lobed impellerSimilar in operation to the Oval meter, the lobed impellertype meter (Figure 2.4) is a non-contact meter comprisingtwo high precision lobed impellers which are gearedexternally and which rotate in opposite directions withinthe enclosure. For each revolution four measured ‘cups’ ofthe fluid are transferred through the meter with an accuracyof up to 0,2% under controlled conditions. The lobedimpeller meter is suitable for a wide range of fluids rangingfrom LPG through to tar in the ranges 41 to 200 kl/hr,process temperatures up to 300 °C, and pressures up to 10MPa.

Figure 2.4:Lobed impellermeter (courtesyTokico Ltd)

Oscillating pistonThe oscillating or rotating piston meter consists of astainless steel housing and a rotating piston as shown inFigure 2.5. The only moving part in the measuring chamberis the oscillation piston which moves in a circular motion.

Figure 2.5:Basic layout ofoscillating orrotating pistonmeter

To obtain an oscillating motion, movement of the piston isrestricted in two ways. First, the piston is slotted verticallyto accommodate a partition plate which is fixed to thechamber. This plate prevents the piston from spinningaround its central axis and also acts as a seal between theinlet and outlet ports of the chamber. Second, the pistonhas a central vertical pin which confines the piston’smovement to a circular track, which is part of the chamber.

Differential pressure across the meter causes the piston tosweep the chamber wall in the direction of flow—displacingliquid from the inlet to the outlet port in a continuousstream.

The openings for filling and discharging are located in itsbase and thus in Figure 2.6 (a), areas 1 and 3 are bothreceiving liquid from the inlet port (A) and area 2 isdischarging through the outlet port (B).

Figure 2.6:Oscillating or rotating piston meter showing principle of operation

In Figure 2.6 (b), the piston has advanced and area 1, whichis connected to the inlet port, has enlarged. Area 2, whichis connected to the outlet port, has decreased, while area3 is about to move into position to discharge through theoutlet port.

In Figure 2.6(c), area 1 is still admitting liquid from theinletport, while areas 2 and 3 are discharging through the outletport. In this manner known discrete quantities of themedium have been swept from the inlet to the outlet port.

The rotating piston meter is particularly suitable foraccurately measuring small volumes and its advantagesare:

• accuracy of ± 0.5%• performance largely unaffected by viscosity (from

heating oil to paste)

Chapter 2: Positive displacement metersDisadvantages of the oscillating piston meter are:

• leakage and maximum permissible pressure loss

Nutating discThe term nutation is derived from the action of a spinningtop whose axis starts to wobble and describe a circularpath as the top slows down.

In a nutating disc type meter the displacement element isa disc that is pivoted in the centre of a circular measuringchamber (Figure 2.7). The lower face of the disc is alwaysin contact with the bottom of the chamber on one side,and the upper face of the disc is always in contact with thetop of the chamber on the opposite side.

The chamber is therefore divided into separatecompartments of known volume.

Figure 2.7:Nutating disc meter in which the displacement element is a disc pivoted inthe centre of a circular measuring chamber

Liquid enters through the inlet connection on one side ofthe meter and leaves through an outlet on the other side—successively filling and emptying the compartments andmoving the disc in a nutating motion around a centre pivot.A pin attached to the disc’s pivot point drives the countergear train.

Although there are inherently more leakage paths in thisdesign, the nutating disk meter is also characterised by itssimplicity and low-cost.

It tends to be used where longer meter life, rather thanhigh performance, is required, for example, domestic waterservice. The meter is also suitable for use under hightemperatures and pressures.

Figure 2.8:Physical construction ofthe axial radial fluted‘Birotor’ meter (courtesyFisher Rosemount)Figure 2.9:Operation of the axialradial fluted ‘Birotor’meter (courtesy FisherRosemount)

Fluted rotor metersThe axial and radial fluted rotor meters work on the sameprincipal.

The axial fluted rotor meter (Figure 2.8) makes use of twoaluminium spiral fluted rotors working within the samemeasuring chamber - with the rotors maintained in aproperly timed relationship with one another by helicalgears.

As the product enters the intake of the measuring unitchamber, (Figure 2.9) the two rotors divide the volumebeing measured into segments; momentarily separatingeach segment from the flowing inlet stream and thenreturning them to the outlet of the measuring unit chamber.

During this ‘liquid transition1, the segments of flow arecounted and the results are transferred to a totalisingcounter or other flow recording device by means of a geartrain.

In the radial fluted rotor meter, Figure 2.70, two speciallyshaped hydraulically unbalanced rotors are maintained ina properly timed relationship by helical gears. The rotorsare neither in metal-to-metal contact with one another norwith the housing in which they rotate. Again, as shown, asthe product enters the intake of the measuring unit chamberthe two rotors divide the volume being measured intosegments; momentarily separating each segment from theflowing inlet stream and then returning them to the outletof the measuring unit chamber.

Figure 2.10:Operation of the radial fluted ‘Birotor’ meter (courtesy Fisher Rosemount)

Wet-type gas metersThe wet-type gas meter (Figure 2.11) comprises a gas-tightcasing containing a measuring drum, with four separatecompartments, mounted on a spindle that is free to revolve.The casing is filled to approximately 60% of its of volumewith water or light oil.

Under normal operation the gas passes through themeasuring drum so that each compartment of the drummust, in turn, be emptied of water and filled with gas—thus forcing the drum to rotate. In an alternativearrangement the gas is introduced into the space abovethe water in the outer casing and then passes through thedrum to the outlet of the meter.

The calibration of the measuring drum (ie the quantity ofgas passed for each revolution) is determined by the heightof the water in the casing. Consequently, the normalcalibration point

Chapter 2: Positive displacement meters

Figure 2.11:The wet-type gas meter

is a shown by a water level indicating point that is visiblein the site box located on the side of the meter casing. Thespindle on which the measuring drum is mounted isconnected through gears to record the quantity of gaspassing through the meter. Such meters are available incapacities ranging from 0.25 to 100 dm-3 with accuracydown to ±0.25%

General summaryBecause of their high accuracy, positive displacementmeters are used extensively in liquid custody transferapplications where duty is applicable on such commoditiesas petrol, wines, and spirits. In use. some of the followingapplication limitations should be noted:

• owing to mechanical contact between the componentparts, wear and tear is aproblem. In general, herefore,positive displacement meters are primarily suited toclean, lubricating and non-abrasive applications

• in some cases, filters (down to 10 urn) may berequired to filter debris and clean the fluid before themeter. Such filters require regular maintenance. Ifregular maintenance is not carried out, the addedpressure drop may need to be considered

• their working life depends on the nature of the fluidbeing measured, especially with regard to solidsbuild-up and medium temperature

• positive displacement meters are an obstruction tothe flow path and consequently produce anunrecoverable pressure loss

• because many positive displacement meters have thesame operating mechanisms as pumps, they may bedriven by a motor and used as dosing or meteringpurnps

• one of the drawbacks of the positive displacementmeter is its high differential pressure loss. This,however, may be reduced by measuring the differen-tial pressure across the meter and then driving it witha motor that is controlled by a feedback system

• positive displacement meters are limited at high andlow viscosities. Errors can occur due to leakage(slippage) around the gears or pistons. Slippage maybe reduced by using viscous luids which have theability to seal the small clearances. However, if thefluid is too viscous it can coat the inner chambers ofthe meter and reduce the volume passed—causingreading errors. Thus, whilst low viscosities limit theuse at low flows (due to increased slippage), highviscosities limit the use at high flows due to the highpressure loss

• if slippage does occur, and is calibrated for, it canchange with temperature as the viscosity varies

• positive displacement meters can be damaged byoverspeeding

• in certain cases (for example, the oval gear meter)positive displacement meters give rise to pulsations,which may inhibit the use of this type of meter incertain applications

• positive displacement meters are used primarily forlow volume applications.

Chapter 3: Inferential metersInferential meters, loosely referred to as ‘turbine meters1,are indirect volumetric totalisers, in which packages of theflowing media are separated from the flow stream andmoved from the input to the output. However, unlike thepositive displacement meter, the enclosed volume is notgeometrically defined.

Inferential meters have rotor-mounted blades in the formof a vaned rotor or turbine which is driven by the mediumat a speed proportional to the flow rate. The number ofrotor revolutions is proportional to the total flow and ismonitored by either a gear train or by a magnetic or opticalpick-up.

Competing with the positive displacement meter foraccuracy and repeatability, the turbine flow meter is usedextensively in custody transfer applications on suchproducts as crude oil or petroleum.

Turbine metersAvailable in sizes from 5 to 600 mm, the turbine meterusually comprises an axially mounted bladed rotorassembly (the turbine) running on bearings and mountedconcentrically within the flow stream by means of upstreamand downstream support struts (Figure 3.1). The supportassembly also often incorporates upstream anddownstream straightening sections to condition the flowstream. The rotor is driven by the medium (gas or liquid)impinging on the blades.

Figure 3.1:The turbine meter consists of a bladed rotor suspended in the flow stream.Upper and lower straightening vanes are normally included (courtesyFisher Rosemount)

The simplest method of measuring the rotor speed is bymeans of a magnet, fitted within the rotor assembly, whichinduces a single pulse per revolution in an externallymounted pick-up coil. To improve the resolution, theexternally mounted pick-up coil is integrated with apermanent magnet and the rotor blades are made of amagnetically permeable feiTous material. As each bladepasses the pick-up coil, it cuts the magnetic field producedby the magnet and induces a voltage pulse in the coil.

To improve the resolution even further, especially in largeturbine meters (200 mm and above) where the rotoroperates at much lower angular velocities, small magneticbars are inserted in a non-magnetic rim that is fitted aroundthe blades. This modification can improve the pulseresolution by as much as ten times.

K-factorThe number of pulses produced per unit volume is termedthe K-factor. Ideally, the meter would exhibit a linearrelationship between the meter output and the flow rate—a constant K-factor, In reality, however, the driving torqueof the fluid on the rotor is balanced by the influence ofviscous, frictional and magnetic drag effects.

Since these vary with the flow rate, the shape of the K-factor curve (Figure 3.2) depends on viscosity, flow rate,bearing design, blade edge sharpness, blade roughnessand the nature of the flow profile at the rotor leading edge.In practice, all these influences have differing effects onthe meter linearity and thus all turbine meters, even fromthe same manufacturing batch, should be individuallycalibrated.

The linear relationship of the K-factor is confined to a flowrange of about 10:1—sometimes extending up to 20:1.

Figure 3.2:The K-factor (the meter ‘constant’) should, ideally, be flat. The actualplot exhibits a drop off at low flow rates and a viscosity hump

At low flows, the poor response of the meter is due tobearing friction, the effect of fluid viscosity and magneticdrag on the rotor due to the use ofamagneticpick-off. It ispossible to extend the lower limit of the meter’s responseby using, for example, a radio pick-off coupled with theuse of high quality rotor bearings. The humping section ofthe curve flattens as the viscosity decreases—with resultantincrease in accuracy.

Selection and sizingAlthough turbine meters are sized by volumetric flow rate,the main factor that affects the meter is viscosity.

Typically, larger meters are less affected by viscosity thansmaller ones. This would indicate that larger meters arepreferred; in fact the opposite is true. By using a smallermeter, operation is more likely to occur towards themaximum permitted flow rate, and away from the non-linear ‘hump1 response at low flows.

Turbine meters are specified with minimum and maximumlinear flow rates which ensure the response is linear andthe other specifications are met. For good rangeability, itis recommended that the meter be sized so the maximumflow rate of the application is about 70% to 80% of that ofthe meter.

Application limitationsIn liquids, the maximum flow rate is usually limited by theeffect of cavitation. This occurs when the system pressurefalls to a point at which the liquid itself, and/or the dissolvedgases in the liquid, ‘boils-off at critical points in the meter

Chapter 3: Inferential meterswhere hydrodynamic forces cause a low pressure region.Cavitation can be avoided by retaining a sufficiently highback pressure and by keeping the pressure loss throughthe meter at a minimum. Because the rotor, stator,measuring pipe and bearings all come in contact with themedium, the meter’s resistance to aggressive fluids dependson the materials from which it is constructed. Generallythe measuring pipe, rotor and stator are fabricated fromstainless steel, while the bearings are made of ceramicmaterials suchas aluminium oxide, or PTFE used inconjunction with metal or other materials.

Density changes have little effect on the meters’ calibration.Because turbine meters rely on the flow impinging on therotor blades, they absorb some pressure. As a result, thepressure drop is typically around 20 to 30 kPa at themaximum flow rate and varies depending on the flow rate.

AdvantagesBecause the rotation of the turbine is measured by non-contact methods, no tapping points are required in thepipe. The result is that, depending on pipe diameter andmaterials of construction, pressures of up to 64 MPa canbe applied.

When properly installed and maintained, turbine metersare capable of high accuracy (± 0,5 % of flow over a 10:1range) and excellent repeatability (±0,05 %). They alsoexhibitawide flow capacity range (from 4 litres/min— 800kilolitres/min).

Temperature limitations are imposed only by the limitationsof the materials of construction, and turbine flow meterscan operate in high process media temperatures (up to600 °C) and low temperatures (cryogenic fluids down to -220 °C). The advantages can be summarised as follows:

• suitable for pressures up to 64 MPa• high accuracy (up to ± 0,2 % of flow)• excellent repeatability (± 0,05 %)• wide rangeability up to 20:1• wide range of temperature applications from -220 to

600 °C• able to measure non-conductive liquids• capability of a heat measuring device• suitable for low flow rates

DisadvantagesThe main limitation of a turbine meter is that because ithas a moving part (the rotor), it is subject to wear.Consequently, it is unsuited to dirty fluids and requiresregular maintenance and calibration to maintain itsaccuracy. Another disadvantage is that because the K-factordepends on the viscosity, the viscosity of the liquid mustbe known and each meter must be calibrated for itsapplication—especially at low flow rates.

Turbine meters are not suitable for use with high viscosityfluids since the high friction of the fluid causes excessivelosses leading to excessive non-recoverable pressure losses.The disadvantages of turbine meters can be summarisedas follows:

• unsuitable for high viscous fluids• viscosity must be known• 10 diameter upstream and 5 diameter downstream

of straight pipe is required• ineffective with swirling fluids• only suitable for clean liquids and gases ; . ...• pipe system must not vibrate

• specifications critical for measuring range andviscosity

• subject to erosion and damage• relatively expensive

Woltman metersThe Woltman meter, used primarily as a water meter, issimilar in design to the turbine meter. The essentialdifference is that the measurement of rotation is carriedout mechanically using a low friction gear train connectingthe axle to the totaliser.

Figure 3.3: Horizontal turbine Woltman meter

The Woltman meter is available in two basic designs —one with a horizontal turbine (Figure 3.3) and one with avertical turbine (Figure 3.4). The vertical design offers theadvantage of minimal bearing friction and therefore a highersensitivity resulting in a larger flow range. Whilst thepressure drop of the vertical turbine meter is appreciablyhigher, because of the shape of the flow passage, it is widelyused as a domestic water consumption meter.

Figure 3.4: Vertical turbineWoltman meter

In many designs, an adjustable regulating vane is used tocontrol the amount of deflection and thus adjust the meterlinearity.

Propeller type flow metersIn the propeller type flow meter (Figure 3.5) the body ofthe meter is positioned above the flow path and only thepropeller is in the flow line.

With the bearings outside of the main flow, the effects ofcontamination from dirty liquids are eliminated or reducedto a minimum. The use of a three-bladed propeller withlarge clearances between each blade, enables particles insuspension to pass with ease and, in addition, thetransmitter and all working parts can be removed and

Figure 3.7:A Tee-mount flow sensorsuitable for pipe sizesranging from 10 to 100mm (courtesy GLIInternationa!)

Other versions are available for use with welded-on pipethreads that allow the same meter to be used on pipe sizesranging from 75 mm to 2.5 m diameter. This techniquealso allows its use in a ‘hot tap’ mode whereby it may beremoved and replaced on high pressure lines without theneed for a shutdown.

Another form of the impeller type meter, the Pelton wheelturbine (Figure 3.8) is able to measure extremely low flowrates down to 0,02 litres/min, coupled with a turn-downratio of up to 50:1.

Figure 3.8:Cross-section of Pelton wheel system

The incoming low velocity fluid is concentrated into a jetthat is directed onto a lightweight rotor suspended on jewelbearings. The rotational speed is linear to flow rate and isdetected by means of ferrite magnets, located in the rotortips, which induce voltage pulses in a sensing coil. Onedrawback is that the nozzle can cause a rather largepressure drop.

Application limitationsAs with turbine meters, most such sensors employ multipleblades with a permanent magnet embedded in each blade.A pick-up coil in the sensor acts as a generator stator—generating an electrical pulse each time the blade passesnear it. The use of such a magnetic pick-up, however, hassome serious drawbacks. Firstly, the signal is susceptibleto interference by extraneous magnetic fields in the vicinityof the coil. In addition, ferrous contamination, present inmany industrial applications, causes particles to beattracted to the magnets in each blade. This not only affectssensor accuracy, but can impede or stop the impeller from

Chapter 3: Inferential metersreplaced in a few minutes, without breaking the pipeline.Another advantage of this type of meter is thatmanufacturing costs are significantly reduced. On thenegative side performance is correspondingly lower withthe linearity typically ±2% and repeatability typically ±1%of full scale.

Figure 3.5: Propellertype flow meter with themeter body positionedabove the flow path andonly the propeller in thef/ow line (courtesyRhodes & Son)

Impeller metersAs opposed to the vane-axial blades of turbine-type models,the rotating blades ofimpeller-type sensors areperpendicular to the flow—making them inherently lessaccurate than turbine sensors. However, their typical 1%accuracy and excellent repeatability makes them ideal formany applications.

Impeller sensors are especially suitable for measuring flowrates of low-viscosity liquids that are low in suspendedsolids over line velocities of between 0.15 and 10 m/s(Figure 3.6).

Figure 3.6:Reading versus velocity for a typical impeller type meter

At lower flow rates, the fluid cannot maintain the forceneeded to overcome bearing friction, impeller mass inertiaand fluid drag. At flow rates above 10 m/s, cavitation canoccur and cause readings to increase more than the increasein flow velocity. As velocity continues to increase undercavitation conditions, the reading eventually decreases withrespect to true velocity.

The most common form ofimpeller-type meter is the in-line insertion format in which the main bearing is locatedout of the main flow stream and thus provides only aminimal pressure drop. Figure 3.7 illustrates a Tee-mountflow sensor suitable for pipe sizes ranging from 10 to 100mm.

Chapter 3: Inferential meters

Figure 3.9:The problem of magnetic drag may be overcome through the use of a Hall-effect transducer that picks up the signal from magnets embedded in theimpeller blades (courtesy FTE)

rotating. Further, at low flows, the magnetic attractionbetween each rotating blade and the pick-up coil increasesthe force required to turn the impeller—resulting in poorlinearity.

One method of overcoming this problem is shown in figure3.9 in which permanent magnets embedded in the impellerblades pass close to a Hall-effect transducer.

Another method of overcoming the problem is throughthe use of a non-magnetic ferrite rods embedded in theimpeller blades. Although the ferrites are not magnetic,they form a low permeable path for a magnetic field.

As shown in Figure 3.10, the pickup comprises a compositetransmitting and sensing coil. In the absence of a ferriterod the magnetic coupling is loose and the signal producedby the receiving coil is small. However, in the presence ofa ferrite rod, the magnetic coupling is strong, resulting ina much larger output signal.

Figure 3.10:in the absence of a ferrite rod the magnetic coupling is loose and thesignal produced by the receiving coil is small. When a ferrite rod ispresent, the magnetic coupling is strong resulting in a much larger outputsignal (courtesy GLI Internationa!)

Because permanent magnets are not used, there is nomagnetic drag and no accumulation of magnetic particleslo degrade the accuracy or cause clogging.

Installation recommendationsTo reap the benefits of high accuracy the followinginstallation practices should be observed:

• at least 10 pipe diameters of straight approach and 5pipe diameters of straight outlet piping are required

• turbines should never be subjected to a swirling flow• flow must not contain any solids—especially fibre• do not exceed the measuring range• a turbine for liquids should never be subjected to gas

flow (danger of over-speeding)• never clean with compressed air

Chapter 4: Oscillatory flow metersOscillatory flow measurement systems involve threeprimary metering principles: vortex, vortex swirl(precession) and Coanda effect. Tn all three, the primarydevice generates an oscillatory motion of the fluid whosefrequency is detected by a secondary measuring device toproduce an output signal that is proportional to fluidvelocity.

Vortex flow metersVortex flow meters for industrial flow measurement werefirst introduced in the mid-1970s but the technology waspoorly applied by several suppliers. As a result, thetechnology developed a bad reputation and a number ofmanufacturers dropped it. Since the mid-1980s many ofthe original limitations have been overcome and vortexflow metering has become a fast growing flow technology.

Vortex meters are based on the phenomenon known asvortex shedding which takes place when a fluid (gas, steamor liquid) meets a non-streamlined obstacle—termed a bluffbody. Because the flow is unable to follow the definedcontours of the obstacle, the peripheral layers of the fluidseparate from its surfaces to form vortices in the lowpressure area behind the body (Figure 4.1). These voiticesare swept downstream to form a so-called Karman VortexStreet. Vortices are shed alternately from either side of thebluff body at a frequency that, within a given Reynoldsnumber range, is proportional to the mean flow velocity inthe pipe.

Figure 4.1:The Karman vortex street—with vortices formed on alternate sides in thelow pressure area of bluff body

In vortex meters, the differential pressure changes, thatoccur as the vortices are formed and shed, are used toactuate the sealed sensor at a frequency proportional tothe vortex shedding.

Formation of vorticesAt low velocities—the laminar flow region (Figure 4.2(a))—the fluid flows evenly around the body without producingturbulence. As the fluid velocity increases the fluid tendsto shoot past the body, leaving a low pressure region behindit (Figure 4.2(5)). As the fluid velocity increases even further,this low pressure region begins to create a flow pattern asshown in Figure 4.2(c)—the beginning of the turbulent flowregion. The action momentarily relieves the pressure voidon one side of the low pressure region and the fluid formsinto a vortex. The interaction of the vortex with the mainstream fluid releases it from the surface of the body and ittravels downstream. Once released, the low pressure regionshifts towards the other rear side of the body to formanother vortex. This process is repeated, resulting in therelease of vortices from alternate sides of the bluff bodyas illustrated in Figure 4.1.

Figure 4.2: Formationof vortices: (a) laminarflow region with fluidflowing evenly aroundthe body; (b) at highervelocities a low pressureregion starts to formbehind the bluff body;and (c) beginning ofturbulent flow regionand formation of vortex

Vortex shedding occurs naturally throughout nature andcan he observed in the whistling tone that the windproduces through telephone wires or in a flag waving froma flagpole. Because the flagpole acts as a bluff body, vortexshedding occurs. As the wind speed increases the rate ofvortex shedding increases and causes the flag to wavefaster.

Strouhal factorIn 1878 Strouhal observed that the frequency of oscillationof a wire, set in motion by a stream of air, is proportionalto the flow velocity. He showed that:

f =

where:f = vortex frequency (Hz)d = diameter of the bluff body (m)v = velocity of liquid(m/s)St = Strouhal factor (dimensionless)

Unlike other flow sensing systems, because the vortexshedding frequency is directly proportional to flow velocity,drift is not a problem as long as the system does not leaveits operating range. Further, the frequency is unaffectedby the medium’s density, viscosity, temperature, pressureand conductivity, as long as the Reynolds number (Re) stayswithin defined limits. Consequently, irrespective of whetherthe meter is used for measuring steam, gas or liquids, itwill have virtually the same calibration characteristic andthe same meter factor— although not necessarily over thesame volumetric flow velocity ranges.

Figure 4.3:Relationshipbetween Strouha!factor andReynolds numberfor both a roundand a delta bluffbody (courtesyEndress + Hauser)

St. v

d

Chapter 4: Oscillatory flow metersIn reality, the Strouhal factor is not a constant but, asillustrated in Figure 4.3, varies with the shape of the bluffbody and the Reynolds number. The ideal vortex flow rneterwould, therefore, have a bluff body shape that features aconstant Strouhal number over as wide a measuring rangeas possible.

Meters based on this relationship are shown to have alinearity of better than ±0.5 % over a flow range of as highas 50: 1 for liquids and 100:1 for gases. The limits aredetermined at the low-end by viscosity effects and at theupper end by cavitation or compressibility.

Another major advantage of the vortex meter is that it hasa constant, long-term calibration that does not involve anyin-service adjustment or tuning. For a given size and shapeof bluff body, the vortex shedding frequency is directlyproportional to flow rate.

Shedder designsMeters differ only in the shape of the bluff body and in thesensing methods used—with each manufacturer claimingspecific advantages. Some of the bluff body shapes areshown in Figure 4.4.

Tests have shown that changes in the dimensions of thebluff body have a negligible effect on calibration. Forexample, tests with a rectangular bluff body indicate thatwith a body-to-meter bore ratio of 0.3, the body width canvary by as much as ±10 % to produce a change in the meterfactor of < 0.4 %. Similarly, radiussing the edges of thebluff body by as much as 4 mrn will not cause the calibrationto deviate outside the standard accuracy band.

(Compare this with an orifice plate where radiussing thesharp edge of the orifice by as little as 0.4 mm produces areading inaccuracy of approximately 4%.) The major benefitof this insensitivity to dimensional changes of the bluffbody is that the vortex meter is virtually unaffected byerosion or deposits.

Figure 4.4:Various bluff body shapes: (a) round: (b) rectangular; and (c) two-partrectangular; (d) Tee-bar; (e) delta-shaped (courtesy Endress + Hauser)

CylindricalEarly bluff bodies were cylindrical. However, as theboundary layer changes from laminar to turbulent, thevortex release point fluctuates backwards and forwards,depending on the flow velocity. The frequency,subsequently, is not exactly proportional to velocity. Asaresult, use is made of bluff bodies with a sharp edge thatdefines the vortex shedding point.

Rectangular bodiesFollowing the cylindrical body, the rectangular body wasused for many years. However, current research indicatesthat this body shape produces considerable fluctuation inlinearity in varying process densities.

Rectangular two-part bodiesIn this configuration, the first body is used to generate thevortices and the second body to measure them. The two-part body generates a strong vortex (hydraulicamplification) that requires the use of less complicatedsensors and amplifiers. On the negative side, the pressureloss is almost doubled.

Delta-shaped bodiesThe delta-shaped shedder has a clearly defined vortexshedding edge and tests (including those carried out byNASA) indicate that the delta shape provides excellentlinearity. Accuracy is not affected by pressure, viscosity orother fluid conditions. Many variations of the Delta shapeexist and are in operation.

Delta-shaped two-part bodiesClaimed to combine the best features of moderntechnology, here, the delta-shaped bluff body generatesthe vortices and the second body is used to measure them.

Tee-shaped barAlso claimed to combine the best features of the delta-shapedbody with a high hydraulic amplification.

SensorsSince the shedder bar is excited by kinetic energy, theamplitude of the vortex signal depends on the dynamicpressure of the fluid:

pd = ½ ρ v²where:pd = dynamic pressureρ = fluid densityv = velocity

As shown, the sensor amplitude is thus proportional tothe fluid density and to the square of the velocity (Figure4.5).

Consequently, the dynamic sensitivity range of the vortexsensor needs to be quite large. For a turn-down ratio of1:50 in flow velocity, the magnitude of the vortex signalwould vary by 1:2500. This leads to small signal levels atthe low end of the measuring range.

Figure 4.5:Amplitude as a function of velocity and process density

Chapter 4: Oscillatory flow metersWhile the vortex shedding frequency decreases as the sizeof the bluff body or meter increases, the signal strengthfalls off as the size decreases—thus generally limiting themeter size to within the range 15 to 200 mm bore.

There are several methods for measuring vortex frequency,but there is no sensor currently available which will suit alloperating conditions.

Many vortex meters use non-wetted, external sensorsconnected to internal parts that move or twist due to vortexshedding. Formerly, this technology was plagued bysensitivity to pipeline vibration which produces a similarmotion to vortex shedding when there is no flow in thepipe and can cause an erroneous output at zero flow.However, modern instruments have largely overcome thisproblem and systems as illustrated in Figure 4.6 areinsensitive to vibrations in each axis up to at least 1 gcovering the frequency range up to 500 Hz.

Figure 4.6: Use of separatemechanically balanced sensorpositioned behind the bluffbody (courtesy Endress +Hauser)

Thermal sensingThermal sensors (Figure 4.7) make use of electrically heatedthermistors (heat-sensitive semi-conductor resistors) witha high temperature coefficient and a rapid time response.As the vortices are shed, on alternate sides of the fluffbody, heat is convected away from the preheatedelements—resulting in a change in resistance that is inphase with the shedding frequency.

Depending on their location, the thermistors are sensitiveto dirt and are generally incapable of withstandingtemperature shocks. In addition, the upper frequency limit500 Hz precludes their use with small diameter pipes (forexample, 25 mm) particularly with gas where vortexfrequencies of 3300 Hz or more can be encountered.

Mechanical sensorsSometimes called a shuttle ball sensor, a magnetic ball ordisc moves from side to side, under the influence of thevortices, along a lateral bore that connects both sides ofthe bluff body (Figure 4.8). This movement is detected bya magnetic pickup.

Figure 4.7:Basic configuration of thermal sensor (courtesy Endress + Hauser)

Figure 4.8:Shuttle ball or disc sensor (courtesy Endress + Hauser)

The main problems with this sensor are that it is easilyblocked by dirt and in saturated steam the movement ofthe ball or disc can be slowed by condensation.

Further, condensed water can cause the ball or disc toadhere to one side or other.

Capacitive sensorsIn the form illustrated in Figure 4.9, stainless steeldiaphragms are welded onto the sides of the bluff bodyand the assembly filled with oil and sealed. Since the oil isincompressible it fully supports the diaphragms againsthigh static pressure. However, under the influence of anasymmetric differential pressure, as occurs during vortexshedding, the diaphragms deflect and the oil transfersthrough the internal port from one side to the other. Whenthe diaphragms deflect there is a change in the capacitancebetween the diaphragms and the electrodes— one sideincreases and the other decreases.

Figure 4.9:The vortices act on two diaphragms. As the diaphragms deflect the oiltransfers through the internal ports from one side to the other— changingthe capacitance between the diaphragms and the electrodes (courtesyEndress + Hauser)

Since the capacitance is inversely proportional to thedistance between the electrodes and directly proportionalto the plate area, pressure differences can be used to varythe plate overlap area or the electrode distance. Moderncapacitive sensors are available for use with superheatedsteam for temperatures up to 426°C.

Piezoelectric sensorLike the capacitive sensor, the alternating vortices, shedon each side of the shedder, act on two diaphragmsmounted on each side of the sensor. In this case, (Figure4.10) the flexing motion is coupled to a piezoelectric sensor,outside the flow line, which senses the alternating forcesand converts them to an alternating signal.

Chapter 4: Oscillatory flow metersFigure 4.10: Use ofpiezoelectric sensorpositioned outside the Howline (courtesy FisherFtosemount)

The piezo elements produce a voltage output that isproportional to the applied pressure. Whilst piezoceramicmaterials produce a high output for a given pressure (ahigh ‘coupling factor’) they have a limited operatingtemperature range (about 250 °C). The piezoelectric materialLithium Niobate (LiNbO,) offers only medium couplingfactors but can be operated at temperatures above 300 °C.

Generally, piezoelectric materials are unsuitable fortemperatures below -40 °C since below this point, thepiezoelectric effect becomes too small.

Because the piezoelectric element produces an output thatis affected by movement or acceleration, it is also sensitiveto external pipe vibration. This problem can be overcomeby using a second piezoelectric element to measure thevibration and use it in a compensating circuit to ensurethat only the clean vortex shedding frequency is obtained.

Strain gauge sensorsThe vortices created by the bluff body cause the body itselfto be mechanically displaced by small amounts—of theorder of 10 (im. This elastic movement can be detectedusing strain gauges attached directly or indirectly to thebluff body. Movement of the body produces a change inresistance of the strain gauges.

The main drawbacks of this technology are the uppertemperature limitation of the strain gauges (about 120°C)and the fact that diameters above 150 mm are sensitive tovibration.

Ultrasonic sensingAn ultrasonic detector system (Figure 4.11) makes use ofan ultrasonic transmitter and receiver placed behind thebluff body. The vortices modulate die ultrasonic beam andthe resultant output is the vortex signal. This sensor systemhas a good turndown ratio and, since there is no massassociated with the sensor that would experience a force

Figure 4.11:Generalconfiguration ofthe ultrasonicsensor (courtesyEndress +Hauser)

under vibration, the sensor is virtually vibrationinsensitive. The main problem associated with thistechnique is that extraneous sound sources canaffect measurements.Application guidelines for vortex flow metering*In general, a voitex shedding flow meter works well onrelatively clean low viscosity liquids, gases and steam toobtain specified accuracy.

ViscosityThe pipe Reynolds number should be above 30 000minimum. This means vortex meters can only be used onlow viscosity liquids. Highly viscous fluids (>3 Pa.s (30cP)) and slurries are not recommended applications. As arule of thumb, the viscosity should be 0.8 Pa.s (8 cP) orless (a viscosity of 0.8 Pa.s would correspond to cookingoil). Higher viscosity fluids can be metered, but at theexpense of rangeability and head loss.

Low flowThe voitex meter cannot measure flow down to zero flowsince, at low flow rates, vortex shedding becomes highlyirregular and the meter is totally inaccurate. This generallycorresponds to a Reynolds number between 5 000 and 10000 and therefore depends on the pipe diameter and thefluid viscosity. Forwater, typical minimum velocity flow ratevalues would vary from about 2.4 m/s for a 15 DN pipe to0.5 m/s for a 300 DN pipe.

Whilst the minimum Reynolds number requirement imposesa limitation on the usability of the vortex meter, this is nota serious limitation for many applications. For example,water flow in line sizes 25 DN and higher generallycorresponds to Reynolds numbers in the tens of thousandsto hundreds of thousands. Gas and steam applicationsgenerally correspond to Reynolds numbers in the lowhundreds of thousands to the millions.

Most voitex meters include a low flow cut-in point, belowwhich the meter output is automatically clamped at zero(for example, 4 mA for analog output).

For many applications the low flow cut-off point does notpose a problem. However, it can be a serious drawback forapplications that see low flows during start-up andshutdown operations (ie, flows much lower than normalconditions, often by a factor of 10 or more). While usersmay not want to measure flow accurately during such times,they may want to get some indication of flow. The vortexmeter is not a good choice for such an application.

Batching operationsVortex meters may or may not be suitable for typicalbatching applications involving intermittent (on/off) flow—especially if the pipe does not remain full at zero flow. Thevortex meter will not register flow as the fluid acceleratesfrom zero to the low flow cut-in value, and again when theflow decelerates from the low flow cut-in value to zero.This lost flow may or may not create a significant errordepending on the dynamics of the system, and the size ofthe batch being measured. In addition, the vortex metercan only measure flow in one direction. Any back flowthrough the meter (for example, the result of turning

* These application guidelines have been compiled from a series of notessupplied by Krohne

Chapter 4: Oscillatory flow metersa pump off) will not be measured and will not be deductedfrom the registered batch total. One way to minimise errorson intermittent flows is to install check valves with thevortex meter on horizontal lines to keep the line full duringzero flow conditions.

RangeabilityNote that in vortex meters, rangeability is fixed for a givenapplication and meter size. Although it depends on thespecific application it is generally > 20:1 on gases andsteam, and >10:1 on liquids. A 50 mm vortex metertypically has a flow range of 1 to 15 1/s on water (15:1rangeability). If we need to measure over the range 0.5 to3 1/s there is nothing that can be done to the 50 DN meterto allow it to measure a lower range and it would benecessary to use a 25 DN meter. For this reason, vortexmeters are sized to the desired flow range, rather than tothe nominal pipe diameter. To get the proper rangeability(Figure 4.12), it is often necessary to use a smaller diametermeter than the nominal diameter of the pipe.

Figure 4.12:Use of reducer and expander to obtain the correct rangeability(courtesy Krohne)

When buying a flow meter, the instrument engineer oftendoes not know the exact flow range and has to make aneducated guess. Since vortex meter rangeability is fixedfor a given line size by the process conditions, a metersized on an educated guess may not meet the processconditions.

Consequently if the user does not have a good ‘ball park’figure in regard to rangeability it is often better to opt fora more forgiving technology such a magnetic flow meter.

Process noiseProcess noise from pumps, compressors, steam traps,valves, etc., may cause the meter to read high, by triggeringa higher than expected frequency output from the sensor,or by indicating a false flow rate when the system is atzero flow. Process noise is generally not a problem onliquids because the sensor’s signal-to-noise ratio is at amaximum. However, gases and steam produce a muchweaker sensor signal, which may not be as easilydiscernible from process noise at low flow.

Process noise cannot be quantified before the meter isinstalled and, therefore, it should always be assumed thatsome process noise exists. It can be eliminated using built-in noise filtering circuitry. However, this raises the thresholdvalue of the low flow cut off. Thus, the more filtering usedto eliminate process noise, the less the net rangeability ofthe meter. To avoid this, vortex flow meters need to besized properly to ensure a desired rangeability and thereare two general sizing guidelines that should be followed:

i the user Upper Range Value (URV)mustnot be lessthan20% of the meter Upper Range Limit (URL) JVote:URL is the highest flow rate that a meter can beadjusted to measure whilst the URV is the highestflow rate that a meter is adjusted to measure. TheURV will always be equal to or lower than the URL

ii the minimum desired flow rate must be > 2 times thevalue of the meter’s low flow cut-in rate

AccuracyVortex meter accuracy is based on the known value of themeter factor (K-factor), determined from a water calibrationat the factory. Accuracy for liquids is typically stated as ±0.5% of flow rate for Reynolds numbers above 30 000.

Water calibration data cannot precisely predict K-factorvalues for gases and steam, which can flow at Reynoldsnumbers well outside the test data range. For this reason,gas and steam accuracy is typically stated as ±1.0% of flowrate for Reynolds numbers above 30 000.

Long term accuracy depends on the stability of the internaldimensions of the flow tube and shedder body. Onlysignificant changes in these dimension’s (due to corrosion,erosion, coatings, etc) can affect accuracy with time. Whilstvortex meter K-factors can only be determined by wetcalibration, the dimensions of the flow tube inside diameterand bluff body thickness can be used as a ‘flag’ to determineif recalibration is necessary. Prior to installation, inspectthe flow tube and carefully measure and record the tworeference dimensions. After a period of time in service,the meter can be removed, cleaned, and re-measured. Themeter does not require recalibration if there has been nosignificant change in the two reference dimensions.

Effects of erosionAlthough vortex shedding flow meters are primarilydesigned for measuring the flow of clean liquids and gases,they can still be used if small amounts of foreign matterare present. Since there are no moving parts, or ports withactive flow, there is little concern for erosion, physicaldamage or clogging. The effect of erosion on the salientedges of the bluff body is small and often poses nosignificant accuracy degradation.

Low density gasesMeasuring gas flows can be a problem when the processpressure is low (ie low density gases) because a vortexproduced under such conditions does not have a strongenough pressure pulse to enable a sensor to distinguish itfrom flow noise. For such applications, minimummeasurable flow becomes a function of the strength of thepressure pulse (a function of the product of fluid densityand the square of fluid velocity) rather than Reynoldsnumber. Low-density gases can be measured with a vortexmeter; however, minimum measurable flow may correspondto a high fluid velocity, and rangeability may be significantlyless than 20:1.

OrientationVortex meters can be installed vertically, horizontally or atan angle. However, for liquid measurements the meter mustbe full at all times. The meter should also be installed toavoid formation of secondary phases (liquid, gas or solid)in the internal sensor chambers.

Pressure dropIf the inside meter diameter is the same as the nominaldiameter of the process piping (ie a 50 DN meter is used ina 50 DN line), then the pressure drop will normally be lessthan 40 kPa on liquid flow at the URL (usually in the 14 to20 kPa range at the user’s URV). However, when downsizingthe vortex meter to achieve a desired rangeability, theunrecoverable pressure loss through the meter is increased.

It must be ensured that this increased pressure loss is not

Chapter 4: Oscillatory flow meters

enough to cause a liquid to flash or cavitate within thepipe. Flashing and cavitation have an adverse effect onmeter accuracy, and can cause damage to the meter itself.

Multi-phase flowMeasurement of two- or three-phase flow (for example,water with sand and air, or ‘wet1 steam with vapour andliquid) is difficult and if multi-phase flow is present thevortex meter will not be as accurate.

Because the vortex meter is a volumetric device, it cannotdistinguish which portions of the flow are liquid and whichportions of the flow are gas or vapour. Consequently, themeter will report all the flow as gas, or all the flow asliquid, depending on the original configuration of thedevice. Thus, for example, if the meter is configured tomeasure water in litres, and the actual water has someentrained air and sand mixed in, a litre registered by themeter will include the water, air and sand that is present.Therefore if the area of interest were the amount of water,a reading from the meter would be consistently high, basedon the proportions of air and sand present. A user thereforewould need to separate the phases prior to metering orlive with this inherent error.

SteamWater converts from its liquid phase to its vapour phase (steam) at its boiling point of 100 °C at atmospheric pressure,rising as the system pressure increases.

Steam that is fully vaporised, but has not been heated to a temperature above the boiling point temperature, is calledsaturated steam. Steam that is fully vaporised and heated to temperature above the boiling point is called superheatedsteam.

Steam that is not fully vaporised is called wet steam. The percentage, by weight, of the water droplets in wet steamis known as the percentage moisture, and subtracting the percentage moisture from i 00 gives the percentage qualityof the steam.

The measurement of ‘wet’ low quality steam is possible with a vortex meter — depending on the distribution of theliquid phase within the steam. Ideally, the secondary phase should be homogeneously dispersed within the primaryphase (Figure 4.13). This tends to be the case with low amounts of secondary phase due to the high velocities andturbulence produced by the meter.

However, for low quality steam the distribution of the liquid phase within the steam may be stratified. In horizontalpipes the water phase travels continuously along the bottom of the pipe and the vapour phase travels as a continuousstream along the top. Here, the best installation for the vortex meter would be in a horizontal line with the shcdderpositioned in the horizontal plane (Figure 4.14 courtesy Krohne).

In vertical pipes the trend is towards ‘slug’ flow in which the water phase travels as discontinuous slugs down thepipeline, suspended between the vapour phase (Figure 4. IS).

Again, however, users should be aware that the meter will, at best, measure the total volume and performance willnot be to standard specifications. Most meters cannot make a measurement if slug flow exists and many meters willbe destroyed by slug flow.

Figure 4.13:Homogeneous distribution of ‘wet’ towquality steam (courtesy Krohne)

Figure 4.14:Recommended installation for ‘wet’, low qualitysteam with stratified flow in horizontal pipes

Figure 4.15:‘Slug’ flow in vertical pipes (courtesyKrohne)

Material build-upFluids that tend to form coatings arc bad applications forvortex meters. Coating build-up on the bluff body willchange its dimensions, and therefore, the value of the K-factor.

Piping effectsThe specification for vortex meter accuracy is based on awell-developed and symmetrical fluid velocity profile, freefrom distortion or swirl, existing in the pipe. The mostcommon way to prevent errors is to provide sufficientlengths of straight, unobstructed pipe, upstream anddownstream of the meter, to create a stable profile at themeter site.

Generally, vortex meters require similar amounts ofupstream and downstream pipe runs to orifice plates,turbine meters and ultrasonic meters. Vortex meters arenot usually recommended for ‘tight’ piping situations, withlimited runs of straight pipe, unless repeatability is moreimportant than accuracy.

Typical manufacturers’ recommendations are shown inFigure 4.16, when flow conditioners are not being used.

Chapter 4: Oscillatory flow meters

Figure 4.16:Typical manufacturers’ recommendations for straight pipe lengths(courtesy Fisher Rosemount)

Most performance specifications are based on usingschedule 40 process piping. This pipe should have aninternal surface free from mill scale, pits, holes, reamingscores, bumps, or other irregularities for a distance of 4diameters upstream, and 2 diameters downstream of thevortex meter. The bores of the adjacent piping, the meter,and the mating gaskets must be carefully aligned to preventmeasurement errors.

For liquid control applications, it is recommended that thevortex meter be located upstream of the control valve fora minimum of 5 diameters. For gas or steam controlapplications, it is recommended that the vortex meter belocated a minimum of 30 diameters downstream of thevalve. The only exception to this rule is for butterfly valves.In this instance the recommended distances are increasedto 10 diameters for liquids, and 40 to 60 diameters forgases and steam.

Mass measurementPressure and/or temperature measurements are generallyused in conjunction with a vortex meter measurement whenthe user wants an output in mass.

• pressure taps should be located 3.5 to 4.5 diametersdownstream of the meter

• the temperature tap should be located 5 to 6diameters downstream of the meter, and the smallestpossible probe is recommended to reduce thechances of flow disturbance

Avoiding problemsThe following guidelines will help prevent application andmeasurement problems with a vortex meter and ensurepremium performance;

• improper configuration• improper sizing• insufficient upstream/downstream relaxation piping• improper meter orientation• partially full piping• accumulation of secondary phase (gas, liquid or solid)

inside the meter• improper temperature/pressure taps• flows below Reynolds numbers of 30000• flows below the low flow cut-in• process noise (at low flows or zero flow)• presence of multiple phases

Vortex precessionThe ‘Swirlmeter1, a patented technology withmanufacturing rights ceded to Bailey-Fischer & Porter, isbased on the principle known as vortex precession.

The inlet of the Swirlmeter (Figure 4.17) uses guide vanes,whose shape is similar to a turbine rotor, to force the fluidentering the meter to spin about the centreline. Thisswirling flow then passes through a venturi, where it isaccelerated and then expanded in an expansion chamber.

The expansion changes the direction of the axis aboutwhich the swirl is spinning—moving the axis from a straightto a helical path. This spiralling vortex is called vortexprecession. A flow straightener is used at the outlet fromthe meter. This isolates the meter from any downstreampiping effects that may affect the development of thevortex.

Figure 4.17Basic principle of a vortex precession Swirlmeter (courtesy Bailey-Fischer &Porter)

Above a given Reynolds number, the vortex precessionfrequency, which lies between 10 and 1500 Hz and ismeasured with a piezoelectric sensor, is directlyproportional to the flow rate. Although the Swirlmeter canbe used with both gases or liquids, it finds its mainapplication as a gas flow meter.

A major advantage of the vortex precession technique overthai of vortex shedding is thatithas amuch lowersusceptibility to the flow profile and hence only threediameters of straight line are required upstream of themeter. Tn addition, the Swirlmeter features: linear flowmeasurement; rangeability between 1:10 and 1:30; nomoving parts; and installation at any angle in the pipeline.

Because of the higher tolerance in manufacture of this typeof meter, it is more expensive than comparative meters.

Fluidic flow metersThe fluidic flow meter is based on the wall attachment or‘Coanda’ effect. Wall attachment occurs when a boundarywall is placed in proximity to a fluid jet—causing the jet tobend and adhere to the wall.

This effect is caused by the differential pressure across thejet, deflecting it towards the boundary (Figure 4.18). Hereit forms a stable attachment to the wall, which is littleaffected by any downstream disturbances.

In the fluidic meter (Figures 4.19 and 4.20), the flow streamattaches itself to one of the walls—with a small portion ofthe flow fed back through a passage to a control port(Figure 4.19).

Chapter 4: Oscillatory flow metersFigure 4.18:Explanation of theCoanda effect—resulting in stableattachment of theflow stream to thewall

This feedback, diverts the main flow to the opposite sidewall where the same feedback action is repeated (Figure4.20).

The result is a continuous oscillation of the flow betweenthe sidewalls of the meter body whose frequency is linearlyrelated to the fluid velocity. Flow in the feedback passagecycles between zero and maximum which is detected by abuilt-in thermistor sensor.

The main benefit offered by the fluidic meter is thatfeedback occurs at much lower Reynolds numbers and itmay thus be used with fairly viscous media. In addition,since a fluidic oscillator has no moving parts to wear withtime, there is no need for recalibration during its expectedlifetime. Other benefits include: rugged construction, highimmunity to shock and pipe vibration and high turndownratio.

The main drawback of the fluidic oscillator is its relativelyhigh pressure loss and its poor performance at low flowrates.

Figure 4.19:Once attached to one side of the wall a feedback passage diverts a portionof stream back onto the main flow (courtesy Moore Products)

Figure 4.20:Main stream is diverted to the other wall by virtue of the feedback controlaction, and the procedure is then repeated (courtesy Moore Products)

Chapter 5: Differential pressure metersDifferential pressure flow meters encompass a wide varietyof meter types which includes: orifice plates, venturi tubes,nozzles, Dall tubes, target meters, Pitot tubes and variablearea meters. The measurement of flow using differentialpressure is still the most widely used technology.

One of the features of the differential flow meter, sometimesreferred to as a ‘head’ meter, is that flow can be accuratelydetermined from: the differential pressure; accuratelymeasurable dimensions of the primary device; andproperties of the fluid. Thus, an important advantage ofdifferential type meters over other instruments is that theydo not always require direct flow calibration. In addition,they offer excellent reliability, reasonable performance andmodest cost.

Another advantage of orifice plates in particular, is thatthey can be used on liquid or gas applications with littlechange.

Basic theoryDifferential pressure flow rate meters are based on aphysical phenomenon in which a restriction in the flowline creates a pressure drop that bears a relationship to theflow rate. This physical phenomenon is based on two well-known equations: the equation of continuity and Bernoulli’sequation.

Consider the pipe in Figure 5.1 which rapidly convergesfrom its nominal size to a smaller size followed by a shortparallel sided throat before slowly expanding to its fullsize again. Further, assume that a fluid of density p flowingin the pipe of area Ap has a mean velocity v, at a linepressure Pr It then flows through the restriction of area A,,where the mean velocity increases to v2 and the pressurefalls to P,.

Figure 5.1:Basic definition of terms

The equation of continuity states that for an incompressiblefluid the volume flow rale, Q, must be constant. Very simply,this indicates that when a liquid flows through a restriction,to allow the same amount of liquid to pass (to achieve aconstant flow rate) the velocity must increase (Figure 5.2).

Mathematically:

Q = v1A1 = V2A2

where: v1 and v2 and A1 and A2 are the velocities and cross-sectional areas of the pipe at points 1 and 2 respectively.

In its simplest form, Bernoulli’s equation states that understeady flow conditions, the total energy (pressure + kinetic+ gravitational) per unit mass of an ideal fluid (ie one witha constant density and zero viscosity) remains constantalong a flow line.

Figure 5.2:To allow the same amount of liquid to pass the velocity must increase ie Q= v1A1 = v2A2

P/p + v²/2+ gz = K

where:

P =the pressure at a pointv =the velocity at that point .P =the fluid densityg =the acceleration due to gravityz =the level of the point above some arbitrary horizontal

reference plane

Thus, in the restricted section of the flow stream, the kineticenergy (dynamic pressure) increases due to the increase invelocity and the potential energy (static pressure) decreases.The difference between the static pressures upstream andthe pressure at or immediately downstream of therestriction can be related to flow by the followingexpression:

where:Q = flow ratek = constantCd = discharge coefficientAP = differential pressure (P1 - P2)P = density of fluid

The discharge coefficient Cd is a function of the diameterratio, the Reynolds number Re, the design of the restriction,the location of the pressure taps and the friction due topipe roughness. Reference texts and standards are availablethat list typical values and tolerances for Cd under certainflows in standard installations.

The foregoing formula highlights two major limitationsthat are applicable to all differential pressure systems:

• the square root relationship between differentialpressure (AP) and flow (Q) severely limits the turn-down ratio of such techniques to a maximum of 5:1

• if density (p ) is not constant, it must be known ormeasured. In practice, the effect of density changes isinsignificant in most liquid flow applications andneed only be taken into account in the measurementof gas flow.

A third limitation of meters based on differential pressuremeasurement is that, as shown in Figure 5.3, they create apermanent pressure loss. This ‘head’ loss depends on thetype of meter and on the square of the volume flow (Figure5.4).

Chapter 5: Differential pressure meters

Figure 5.3:Defining the ‘head’ loss

Figure 5.4:The permanent ‘head’loss for variousmeasurementtechniques. The orificeplate produces themost drop whilst theDall tube causes theleast (courtesy KentInstruments)

Gas flowVapour or gas flow through a restriction differs from liquidflow in that the pressure decrease in the throat isaccompanied by a decrease in density. Thus, for the massflow to remain constant, the velocity must increase tocompensate for the lower density. The result is that theformula for gas flow is slightly modified by the addition ofthe term Y:

Here, Y is termed the upstream expansion factor that isbased on the determination of density at the upstream ofthe restriction. Tables and graphs are available for theexpansion factor as a function of the pressure ratio acrossthe restriction and the specific heat of the gas (BS 1042).Alternatively the expansion factor may be calculated bystandard equations listed in BS 1042. The mass flow ratefor both liquids and gases is found by multiplying thetheoretical mass flow equation by the expansion factor andthe appropriate discharge coefficient.

Orifice platesThe orifice plate is the simplest and most widely useddifferential pressure flow measuring element and generallycomprises a metal plate with a concentric round hole(orifice) through which the liquid flows (Figure 5.5). Anintegral metal tab facilitates installation and carries detailsof the plate size, thickness, serial number, etc. The plate,usually manufactured from stainless steel, Monel, or

Figure 5.5:Concentric orifice plate withintegral metal tab

phosphor bronze, should be of sufficient thickness towithstand buckling (3-6 mm). The orifice features a sharpsquare upstream edge and, unless a thin plate is used, abevelled downstream edge.

A major advantage of the orifice plate is that it is easilyfitted between adjacent flanges that allow it to be easilychanged or inspected (Figure 5.6).

Figure 5.6:Orifice plate fitted between adjacent flanges

It is commonly assumed that, since the orifice is essentiallyfixed, its performance does not change with time. In realitythe orifice dimensions are extremely critical and althoughthe uncertainty may be as low as 0,6% for a new plate, thismeasurement accuracy is rapidly impaired should the edgeof the orifice bore become worn, burred or corroded.

Figure 5.7:Errors Incurred as a result of wear and contamination on the orifice plate.Independent tests carried out by Florida Gas Transmission Co (courtesyDieterich Standard)

Chapter 5: Differential pressure metersIndeed, damaged, coated or worn plates that have not beenexamined for some time can lead to dramatic measurementuncertainties as shown in Figure 5.7. Even radiussing thesharp edge of the orifice by as little as 0.4 mm produces areading inaccuracy of approximately 4%. Although acorrectly installed new plate may have an uncertainty of0,6%, most orifice meters measure flow only to an accuracyof about ± 2 to 3%. This uncertainty is due mainly to errorsin temperature and pressure measurement, variations inambient and process conditions and the effects of upstreampipework.

An adaptation of the sharp, square edge is the quadrantedge orifice plate (also called quarter circle and round edge).As shown in Figure 5.8 this has a concentric opening witha rounded upstream edge that produces acoefficient ofdischarge that is practically constant for Reynolds numbersfrom 300 to 25 000, and is therefore useful for use withhigh viscosity fluids or at low flow rates.

Figure 5.8:The quadrantedge orificeplate with aroundedupstream edge

The radius of the edge is a function of the diameters ofboth the pipe and the orifice. In a specific installation thisradius may be so small as to be impractical to manufactureor it can be so large that it practically becomes a flownozzle. As a result, on some installations it may benecessary to change maximum differentials or even pipesizes to obtain a workable solution for the plate thicknessand its radius.

Orifice plate configurationsAlthough the concentric orifice (Figure 5.9 (a)) is the mostfrequently used, other plate configurations are used;

Eccentric

Figure 5.9:Various types of orifice plate configurations: (a) concentric; (b) eccentric;and (c) segmental

In the eccentric bore orifice plate (Figure 5.9 (b)), the orificeis offset from the centre and is usually set at the bottom ofthe pipe bore. This configuration is mainly used inapplications where the fluid contains heavy solids that

might become trapped and accumulate on the back of theplate. With the orifice set at the bottom, these solids areallowed to pass. A small vent hole is usually drilled in thetop of the plate to allow gas, which is often associatedwith liquid flow, to pass. Eccentric plates are also used tomeasure the flow of vapours or gases that carry smallamounts of liquids (condensed vapours), since the liquidswill carry through the opening at the bottom of the pipe.

The coefficients for eccentric plates are not as reproducibleas those for concentric plates, and in general, the errorcan be three to five times greater than on concentric plates.

Segmental orifice platesThe opening in a segrnental orifice plate (Figure 5.9 (c) isa circular segment—comparable to a partially opened gatevalve. This plate is generally employed for measuringliquids or gases that carry non-abrasive impurities, whichare normally heavier than the flowing media such as lightslurries, or exceptionally dirty gases.

Tapping pointsThe measurement of differential pressure requires that thepipe is ‘tapped’ at suitable upstream (high pressure) anddownstream (low pressure) points. The exact positioningof these taps is largely determined by the application anddesired accuracy.

Vena contracta tappingBecause of the fluid inertia, its cross-sectional areacontinues to decrease after the fluid has passed throughthe orifice. Thus its maximum velocity (and lowest pressure)is at some point downstream of the orifice—at the venacontracta. On standard concentric orifice plates these tapsare designed to obtain the maximum differential pressureand are normally located one pipe diameter upstream andat the vena contracta — about !/2-pipe diameterdownstream (Figure 5.10).

Figure 5.10:For maximum differential pressure the high pressure tap is located onepipe diameter upstream and the low pressure tap at the vena contracta—about ‘/s-pipe diameter downstream

The main disadvantage of using the vena contracta tappingpoint is that the exact location depends on the flow rateand on the orifice size—an expensive undertaking if theorifice plate size has to be changed.

Vena contracta taps should not be used for pipe sizes under150 mm diameter because of interference between theflange and the downstream tap.

Pipe tapsPipe taps (Figure 5.11) are a compromise solution and arelocated 2'/2 pipe diameters upstream and 8 pipe diametersdownstream. Whilst not producing the maximum availabledifferential pressure, pipe taps are far less dependent onflow rate and orifice size.

Chapter 5: Differential pressure meters

Figure 5.11:Pipe taps are far less dependent on flow rate and orifice size and arelocated 2'/s pipe diameters upstream and 8 x pipe diameters downstream

Pipe taps are used typically in existing installations, whereradius and vena contracta taps cannot be used. They arealso used in applications of greatly varying flow since themeasurement is not affected by flow rate or orifice size.Since pipe taps do not measure the maximum availablepressure, accuracy is reduced.

Flange tapsFlange taps are used when it is undesirable or inconvenientto drill and tap the pipe for pressure connections. Flangetaps are quite common and are generally used for pipesizes of 50mm and greater. They are typically located25 mm either side of the orifice plate (Figure 5.12).

Figure 5.12:Flange taps are located 25 mm either side of the orifice plate

Flange taps are not used for pipe diameters less than 50mm, as the vena contracta starts to become close to and,possibly, forward of the downstream tapping point.

Usually, the flanges, incorporating the drilled pressuretappings, are supplied by the manufacturer. With the tapsthus accurately placed by the manufacturer the need torecalculate the tapping point, when the plate is changed,is eliminated.

Corner tapsSuitable for pipe diameters less than 50 mrn, corner tapsare an adaptation of the flange lap (Figure 5.13) in whichthe tappings are made to each face of the orifice plate. Thetaps are located in the corner formed by the pipe wall andthe orifice plate on both the upstream and downstreamsides and require the use of special flanges or orifice holdingrings.

Orifice plates—generalAt the beginning of this chapter it was stated that animportant feature of differential type meters is that flowcan be determined directly—without the need forcalibration. This is particularly true for the orifice platewhere there is a comprehensive range of standard designsthat require no calibration.

Figure 5.13:Comer tap Is made toeach face of theorifice plate

The major advantages are: simpie construction;inexpensive; robust; easily fitted between flanges; nomoving parts; large range of sizes and opening ratios;suitable for most gases and liquids as well as steam; wellunderstood and proven and price does not increasedramatically with size.

Disadvantages include: high permanent pressure loss ofhead (Figure 5.4), from 32 % to 70% or more; inaccuracy,typically 2 to 3%; low turn-down ratio—typically from 3 to4:1; accuracy is affected by density, pressure and viscosityfluctuations; erosion and physical damage to the restrictionaffects measurement accuracy; viscosity limits measuringrange; requires straight pipe runs to ensure accuracy ismaintained; pipeline must be full (typically for liquids);output is not linearly related to flow rate.

Application limitationsThe inaccuracy with orifice type measurement is due mainlyto process conditions and temperature and pressurevariations. Ambient conditions and upstream anddownstream piping also affect the accuracy because ofchanges to the pressure and continuity of flow.

Standard concentric orifice plate devices should not be usedfor slurries and dirty fluids, or in applications where thereis a high probability of solids accumulating near the plate.Half-circle or eccentric bores can be used for theseapplications.

Venturi tube metersThe venturi tube (Figure 5.14) has tapered inlet and outletsections with a central parallel section, called the throat,where the low pressure tapping is located.

Figure 5.14:The venturi tube has tapered inlet and outlet sections with a centralparallel section (courtesy Fisher Rosemount)

Chapter 5: Differential pressure metersGenerally, the inlet section, which provides a smoothapproach to the throat, has a steeper angle than thedownstream section. The shallower angle of thedownstream section reduces the overall permanentpressure loss by decelerating the flow smoothly and thusminimising turbulence. Consequently, one of the mainadvantages of the venturi tube meter over other differentialpressure measuring methods is that its permanent pressureloss is only about 10 % of the differential pressure (Figure5.4). At the same time, its relatively streamlined form allowsit to handle about 60 % more flow than, for example, thatof an orifice plate.

The venturi tube also has relatively high accuracy: betterthan ± 0,75 % over the orifice ratios (d/D) of 0,3 to 0,75.This order of accuracy, however, can only be attained aslong as the dimensional accuracy is maintained.Consequently, although the venturi tube can also be usedwith fluids carrying a relatively high percentage of entrainedsolids, it is not well suited for abrasive media.

Although generally regarded as the best choice of adifferential type meter for bores over 1000 mm, the majordisadvantage of the venturi type meter is its high cost —about 20 times more expensive than an orifice plate. Inaddition, its large and awkward size makes it difficult toinstall since aim bore venturi is 4 - 5 m in length.

Although it is possible to shorten the length of the divergentoutlet section by up to 35%, thus reducing the highmanufacturing cost without greatly affecting thecharacteristics, this is at the expense of an increasedpressure loss.

The advantages are: less significant pressure drop acrossrestriction; less unrecoverable pressure loss; requires lessstraight pipe up and downstream.

The disadvantages are that it is more expensive and it isbulky so it requires large section for installation.

Venturi and flow nozzle meters

Venturi nozzleThe venturi nozzle is an adaptation of the standard venturithat makes use of a ‘nozzle’ shaped inlet (Figure 5.15), ashort throat and a flared downstream expansion section.Whilst increasing the permanent pressure loss to around25 % of the measured differential pressure of the standardventuri, the venturi nozzle is cheaper, requires less spacefor installation, and yet still retains the benefits of highaccuracy (± 0,75%) and high velocity flow.

Flow nozzleThe flow nozzle (Figure 5.16) is used mainly in high velocityapplications or where fluids are being discharged into theatmosphere. It differs from the nozzle venturi in that itretains the ‘nozzle’ inlet but has no exit section.

Figure 5.15: Theventuri nozzle is anadaptation of thestandard venturiusing a ‘nozzle’shaped inlet

Figure 5.16:The flow nozzle Is used mainly in high velocity applications (courtesyFisher Rosemount)

The main disadvantage of the flow nozzle is that thepermanent pressure loss is increased to between 30% to80% of the measured differential pressure—depending onits design. Offsetting this disadvantage, however, accuracyis only slightly less than for the venturi tube (± 1 % to 1,5%) and it is usually only half the cost of the standard venturi.In addition it requires far less space for installation and,because the nozzle can be mounted between flanges or ina carrier, installation and maintenance are much easier thanfor the venturi.

The Dall tubeAlthough many variations of low-loss meters have appearedon the market, the best known and most commerciallysuccessful is the Dall tube (Figure 5.17).

Figure 5 .17:The Dall tube low-loss meter

The Dall tube is virtually throatless and has a short steepconverging cone that starts at a stepped buttress whosediameter is somewhat less than the pipe diameter. Followingan annular space at the ‘throat’, there is a diverging conethat again finishes at a step.

A maj or feature of the Dall tube is the annular spacebetween the ‘liner’ and tube into which the flowing mediapasses to provide an average ‘throat’ pressure. With aconventional venturi, upstream and throat tappings aretaken at points of parallel flow where the pressures acrossa cross section are constant. If the streamlines were curvedthe pressure would not be constant over the cross sectionbut would be greater at the convex surface and less at theconcave surface.

Chapter 5: Differential pressure metersIn the Dall tube, the upstream tapping is taken immediatelybefore the buttress formed by the start of the convergingcone, where the convex curvature of the streamlines is ata maximum.

At the ‘throat’, where there is an immediate change fromthe converging to diverging section, the ‘throat’ tapping isthus taken at the point of maximum concave curvature.This means that a streamlined curvature head is added tothe upstream pressure and subtracted from the ‘throat’pressure and the differential pressure is considerablyincreased. Thus, for a given differential head the throatcan be larger—reducing the head loss.

Because of the annular gap, no breakaway of the liquidfrom the wall occurs at the throat and the flow leaves the‘throat’ as a diverging jet. Since this jet follows the walls ofthe diverging cone, eddy losses arc practically eliminated,while friction losses are small because of the short lengthof the inlet and outlet sections. The main disadvantagesare: high sensitivity to both Reynolds number and cavitationand manufacturing complexity.

Target metersThe target flow meter is, in effect, an ‘inside out’ orificeplate used to sense fluid momentum. Sometimes called adrag disc or drag plate, the target meter usually takes theform of a disc mounted within the line of flowing fluid(Figure 5.18). The flow creates a differential pressure forceacross the target and the resultant deflection is transmittedto a flexure tube—with strain gauge elements mountedexternal to the flowing medium indicating the degree ofmovement.

Figure 5.18:The target flow meter—an ‘inside out’ orifice plate

The major advantages of the target rneter include: abilityto cope with highly viscous fluids at high temperatures(hot tarry and sediment-bearing fluids): free passage ofparticles or bubbles; and no pressure tap or lead lineproblems.

Disadvantages include: limited size availability; limited flowrange; and high head loss.

Pilot tubesThe Pitot tube is one of the oldest devices for measuringvelocity and is frequently used to determine the velocityprofile in a pipe by measuring the velocity at various points.

In its simplest form the Pitot tube (Figure 5.19) comprisesa small tube inserted into a pipe with the head bent so thatthe mouth of the tube faces into the flow. As a result, a

small sample of the flowing medium impinges on the openend of the tube and is brought to rest. Thus, the kineticenergy of the fluid is transformed into potential energy inthe form of a head pressure (also called stagnationpressure).

Mathematically this can be expressed by applying Bernoulli’sequation to a point in the small tube and a point in the freeflow region.

Figure 5.19:Basic Pitot tubeillustrating principle ofoperation

From Bernoulli’s general equation:

P1 + ½ pv12 + pgh1= P2 + ½ pv2

2 + pgh2

we can write:

Ph/p + 0 + gh1 = Ps/p + v2/2 + gh2

where:

p = static pressurep = stagnation pressurev = liquid velocityg = acceleration due to gravityh1 and h2 = heads of the liquid at the static and stagnationpressure measuring points respectively

If h1 = h2 then:

Because the Pitot tube is an intrusive device and some ofthe flow is deflected around the mouth, a compensatoryflow coefficient Kp is required. Thus:

For compressible fluids at high velocities (for example.> 100 m/s in air) a modified equation should be used.

By measuring the static pressure with a convenient tapping,the flow velocity can he determined from the differencebet ween the head pressure and the static pressure. Thisdifference, measured by a differential pressure cell, providesa measurement of flow that, like a conventional differentialpressure measurement, obeys a square root relationshipto pressure. Low flow measurement at the bottom end ofthe scale is thus difficult to achieve accurately.

A problem with this basic configuration is that the flowcoefficient K depends on the tube design and the locationof the static tap. One means of overcoming this problem isto use a system as shown in Figure 5.20 that makes use ofa pair of concentric tubes—the inner tube measuring thefull head pressure and the outer tube using static holes tomeasure the static pressure.

Chapter 5: Differential pressure metersBoth these designs of Pitot tube measure the point velocity.However it is possible to calculate the mean velocity bysampling the point velocity at several points within thepipe.

Figure 5.20:Integrated Pitot tube system in which the inner tube measures the headpressure and the outer tube uses static holes to measure the staticpressure

Alternatively, provided a fully developed turbulent profileexists, a rough indication of the average velocity can beobtained by positioning the tube at a point three-quartersof the way between the centreline and the pipe wall.

Point averagingAnother method of determining the average velocity is witha point averaging Pitot tube system (Figure 5.21).

Figure 5.21:Multiport ‘Annubar’Pitot averaging system(courtesy DieterichStandard)

Essentially, this instrument comprises two back-to-backsensing bars, that span the pipe, in which the up- anddownstream pressures are sensed by a number of criticallylocated holes. The holes in the upstream detection bar arearranged so that the average pressure is equal to the valuecorresponding to the average of the flow profile.

Because the point at which the fluid separates from thesensor varies according to the flow rate (Figure 5.22)extreme care must be taken in positioning the staticpressure sensing holes. One solution is to locate the staticpressure point just before the changing separation point.

Figure 5.22:Variation in flow velocity can affect point of separation and thedownstream static pressure measurement

Figure 5.23:‘Shaped’ bluff body establishes a fixed separation point (courtesy DieterichStandard)

Alternatively, a ‘shaped’ sensor (Figure 5.23) can be usedto establish a fixed point where the fluid separates fromthe sensor. These multi-port averaging devices, commonlycalled ‘Annubars’ after the first design, are used mainly inmetering flows in large bore pipes—particularly water andsteam. Properly installed, ‘Annubar1 type instruments havea repeatability of 0,1% and an accuracy of 1% of actualvalue.

Although intrusive, averaging Pitot type instruments offera low pressure drop and application on a wide range offluids. Because they average the flow profile across thediameter of the pipe bore, they are less sensitive to theflow profile than, for example, an orifice plate and can beused as little as 2l/2 pipe diameters downstream of adiscontinuity. On the negative side, the holes are easilyfouled if used on ‘dirty1 fluids.

On a conventional integrated Pitot tube, the alignment canbe critical. Misalignment causes errors in static pressuresince a poll facing slightly upstream is subject to ‘part’ ofthe stagnation or total pressure. A static port facing slightlydownstream is subjected to a slightly reduced pressure.

ElbowIn applications where cost is a factor and additional pressureloss from an orifice plate is not permitted, a pipe elbowcan be used as a differential pressure primary device. Elbowtaps have an advantage in that most piping systems haveelbows that can be used.

If an existing elbow is used then no additional pressuredrop occurs and the expense involved is minimal. Theycan also be produced in-situ from an existing bend, andare typically formed by two tappings drilled at an angle of45° through the bend (Figure 5.24). These tappings providethe high and low pressure tapping points respectively.

Whilst 45" tappings are more suited to bi-directional flowmeasurement, tappings at 22.5° can provide more stableand reliable readings and are less affected by upstreampiping.

A number of factors contribute to the differential pressurethat is produced and, subsequently, it is difficult to predictthe exact flow rate accurately.

Chapter 5: Differential pressure metersSome of these factors are:

• force of the flow onto the outer tapping• turbulence generated due to cross-axial flow at the

bend• differing velocities between outer and inner radius of

flow• pipe texture• relationship between elbow radius and pipe diameter

Generally, the elbow meter is only suitable for highervelocities and cannot produce an accuracy of betterthan 5% .

However, on-site calibration can produce more accurateresults, with the added advantage that repeatability is good.

Although the elbow meter is not commonly used, it isFigure 5.24:Elbow metergeometry

underrated since its low cost, together with its applicationafter completion of pipework, can be a major benefit forlow accuracy flow metering applications.

Suitable applications would include plant air conditioning,cooling water metering, site flow checkpoints possibly withlocal indicators and check flow applications, where the costof magnetic meters is prohibitive.

For installation, it is recommended that the elbow beinstalled with 25 pipe diameters of straight pipe upstreamand at least 10 pipe diameters of straight pipe downstream.

TroubleshootingOne of the most common inaccuracies induced indifferential pressure flow meters is not allowing enoughstraight pipe. When the flow material approaches andpasses some change in the pipe, small eddies are formedin the flow stream. These eddies are localised regions ofhigh velocity and low pressure and can start to formupstream of the change and dissipate further downstream.

Flow meter sensors detect these changes in pressure andconsequently produce erratic or inaccurate readings forflow rate.

Variable area metersThe variable area flow meter is a reverse differentialpressure meter used to measure the flow rate of liquidsand gases.

Operating principleThe instrument generally comprises a vertical, tapered glasstube and a weighted float whose diameter is approximatelythe same as the tube base (Figure 5.25).

Figure 5.25: Basicconfiguration of avariable area flowmeter (courtesyBrooks Instruments)

In operation, the fluid or gas flows through the invertedconical tube from the bottom to the top, carrying the floatupwards. Since the diameter of the tube increases in theupward direction the float rises to a point where the upwardforce on the float created by differential pressure acrossthe annular gap, between the float and the tube, equalsthe weight of the float.

As shown in Figure 5.25, the three forces acting on thefloat are:

• constant gravitational force W• buoyancy A that, according to Archimedes’ principle,

is constant if the fluid density is constant• force S, the upward force of the fluid flowing past the

float For a given instrument, when the float isstationary, W and A are constant and S must also beconstant. In a position of equilibrium (floating state)the sum offerees S + A is opposite and equa! to W andthe float position corresponds to a particular flowrate that can be read off a scale.

A major advantage of the variable area flow meter is thatthe flow rate is directly proportional to the orifice area that,in turn, can be made to be linearly proportional to thevertical displacement of the float. Thus, unlike mostdifferential pressure systems, it is unnecessary to carryout square root extraction. The taper can be ground togive special desirable characteristics such as an offset ofhigher resolution at low flows. In a typical variable areaflow meter, the flow q can be shown to be approximatelygiven by:

where:

q = flowC = constant that depends mainly on the floatA = cross-sectional area available for fluid flow past

the float p = density of the fluidIndicated flow, therefore, depends on the density of thefluid which, in the case of gases, varies strongly with thetemperature, pressure and composition of the gas. It ispossible to extend the range of variable area flow metersby combining an orifice plate in parallel with the flow meter.

Chapter 5: Differential pressure metersFigure 5.26:Float centring in which a slottedfloat head rotates andautomatically centres itselfFloats

A wide variety of float materials, weights, and configu-rations is available to meet specific applications.

The float material is largely determined by the mediumand the flow range and includes: stainless steel, titanium,aluminium, black glass, synthetic sapphire, polypropylene,Teflon, PVC, hard rubber, monel, nickel and Hastelloy C.

Figure 5.27: Float centringin which the float is centredby three moulded ribsparallel to the tube axis

Float centring methodsAn important requirement for accurate metering is thatthe float is exactly centred in the metering tube. One ofthree methods is usually applied:

i Slots in the float head cause the float to rotate andcentre itself and prevent it sticking to the walls of thetube (Figure 5.26. This arrangement first led to theterm ‘Rotameter’, a registered trademark of KDGInstruments Ltd, being applied to variable area flowmeters. Slots cannot be applied to all float shapesand, further, can cause the indicated flow to becomeslightly viscosity dependent.

ii Three moulded ribs within the metering tube cone(Figure 5.27), parallel to the tube axis, guide the floatand keep it centred. This principle allows a variety offloat shapes to be used and the metering edgeremains visible even when metering opaque fluids.

Figure 5.28: Float iscentred by (a) fixedcentre guide rod; or (b)guide rod attached to thefloat (courtesy Bailey-Fischer & Porter)

iii A fixed centre guide rod within the metering tube(Figure 5.28 (a)) is used to guide the float and keep itcentred. Alternatively, the rod may be attached to thefloat and moved within fixed guides (Figure 5.28 (b)).The use of guide rods is confined mainly toapplications where the fluid stream is subject topulsations Hkely to cause the float to ‘chatter’ andpossibly, in extreme cases, break the tube. It is alsoused extensively in metal metering tubes.

Figure 5.29:(a) ball float: (b) rotating (viscosity non-immune) float; (c) viscosityimmune fioat; and (d) float for low pressure losses (courtesy Bailey-FischerS Porter)

Float shapesThe design of the floats is confined to four basic shapes(Figure 5.29):

• ball float• rotating (viscosity non-immune) float• viscosity immune float• float for low pressure losses

Bail floatThe ball float (Figure 5.29 (a)) is mainly used as a meteringelement for small flow meters—with its weight determinedby selecting from a variety of materials. Figure 5.30 showsthe effect of viscosity on the flow rate indication. Since itsshape cannot be changed, the flow coefficient is clearlydefined (1) and, as shown, exhibits virtually no linearregion. Thus, any change in viscosity, due often to smallchanges in temperature, results in changes in indication.

Chapter 5: Differential pressure metersFigure 5.30: Viscosityeffect for various floatshapesfcourtesy Bailey-Fischer & Porter)

Rotating floatRotating floats (Figure 5.29 (b)) are used in larger sizedmeters and are characterised by a relatively narrow linear(viscosity-immune) region as shown in Figure 5.30 (2).

Viscosity immune floatThe viscosity immune float (Figure 5.29 (c) is appreciablyless sensitive to changes in viscosity and is characterisedby a wider linear region as shown in Figure 5.30 (3).Although such an instrument is unaffected by relativelylarge changes in viscosity, the same size meter has a span25% smaller than the previously described rotating float.

Low pressure loss floatFor gas flow rate metering, light floats (Figure 5.29 (d)’)with relatively low pressure drops can be used. The pressuredrop across the instrument is due, primarily, to the floatsince the energy required to produce the metering effectis derived from the pressure drop of the flowing fluid. Thispressure drop is independent of the float height and isconstant.

Further pressure drop is due to the meter fittings(connection and mounting devices) and increases with thesquare of the flow rate. For this reason, the design requiresa minimum upstream pressure.

Metering tubeThe meter tube is normally manufactured from borosilicateglass that is suitable for metering process mediumtemperatures up to 200 °C and pressures up to about 2 - 3MPa. Because the glass tube is vulnerable to damage fromthermal shocks and pressure hammering, it is oftennecessary to provide a protective shield around the tube.

Variable area meters are inherently self-cleaning since thefluid flow between the tube wall and the float provides ascouring action that discourages the build-up of foreignmatter. Nonetheless, if the fluid is dirty, the tube canbecome coated— affecting calibration and preventing thescale from being read. This effect can be minimised throughthe use of an in-line filter.

In some applications use can be made of an opaque tubeused in conjunction with a float follower. Such tubes canbe made fromsteel, stainless steel, or plastic. By using afloatwith a built-in permanent magnet, externally mounted reed-relays can be used to detect upper and lower flow limitsand initiate the appropriate action.

The temperature and pressure range may be considerablyextended (for example, up to 400 °C and 70 MPa) throughthe use of a stainless steel metering tube. Again, the floatcan incorporate a built-in permanent magnet that is coupled

to an external field sensor that provides a flow reading ona meter.

In cases where the fluid might contain ferromagneticparticles that could adhere to the magnetic float, a magneticfilter should be installed upstream of the flow meter.Typically (Figures. 31) such a filter contains bar magnets,coated with PTFE as protection against corrosion, arrangedin a helical fashion.

ConclusionGenerally, variable area flow meters have uncertaintiesranging from 1% to 3% of full scale. Precision instrumentsarc, however, available with uncertainties down to 0,4% offull scale.

Figure 5.31: Typicalmagnetic filter(courtesy Krohne)

The variable area meter is an exceptionally practical flowmeasurement device. Its advantages include:

• wide range of applications• linear float response to flow rate change• 10 to 1 flow range or turndown ratio• easy sizing or conversion from one particular service

to another• ease of installation and maintenance• simplicity• low cost• high low-flow accuracy (down to 5 cm3/ min)• easy visualisation of flow Its disadvantages are:• limited accuracy• susceptibility to changes in temperature, density and

viscosity• fluid must be clean, no solids content• erosion of device (wear and tear)• can be expensive for large diameters• operates in vertical position only• accessories required for data transmissionDifferential pressure transmitters

Tn modem process control systems, measurement ofdifferential pressure is normally carried out by a differentialpressure transmitter whose role is to measure thedifferential pressure and convert it to an electrical signalthat can be transmitted from the field to the control roomor the process controlling system.

As illustrated in Figure 5.32, most industrial differentialcells make use of i solation diaphragms that isolate thetransmitter. Movement of the isolation diaphragms istransmitted via the isolating fluid (for example, silicon fluid)to the measuring diaphragm whose deflection is a measureof the differential pressure.

Chapter 5: Differential pressure meters

Figure 5.32:Basic construction of a iioating ceil capacitive differential pressure sensorin which movement of the isolation diaphragms is transmitted via theisolating fluid (for example, silicon fluid) to the measuring diaphragmwhose deflection is a measure of the differential pressure (courtesy FujiElectric)

Measurement of the deflection of the measuring diaphragmmay be carried out by a number of methods includinginductance, strain gauge, and piezoelectric. However, themost popular method of measuring differential pressure,adopted by a large number of manufacturers, is the variablecapacitance transmitter.

As shown, the upstream and downstream pressures areapplied to isolation diaphragms on the high and lowpressure sides, which are transmitted to the sensingdiaphragm, which forms a movable electrode. As theelectrode changes its

distance from the fixed plate electrodes, this results in achange in capacitance.

Capacitance based transmitters are simple, reliable,accurate (typically 0.1 % or better), small in size and weight,and remain stable over a wide temperature range. The mainadvantage of the capacitive transmitter is that it is extremelysensitive to small changes in pressure—down to 100 Papressure.

Other manufacturers (including Honey well) make extensiveuse of the piezoresistive element, in which piezoresistorsare diffused into the surface of a thin circular wafer of N-type silicon and the diaphragm is formed by chemicallyetching a circular cavity—with the unetched portionforming a rigid boundary and surface. Such silicon-on-insulator devices are now capable of providing continuousoperation at temperatures up to 225 °C at pressures of upto 7 MPa.

Multivariable transmittersAt the beginning of this chapter it was shown that thedifferential pressure can be related to flow by theexpression:

In practice this expression is inadequate—especially inapplications involving, for example, the mass flow of sleam.The most commonly used expression (AIME) for mass flowof liquids, gases and steam is:

where:

Qm = mass flow rateN = units factorCd = discharge coefficientEv = velocity of approach factorY1 = gas expansion factor (= 1 for liquid)d = bore diameterAP = differential pressurep = density of fluidUsing this equation, the approach has been to make use ofthree separate transmitters to measure differential pressure,static pressure and temperature to infer the mass flow. Asshown in Figure 5.33 the density of a gas may be deducedfrom the measurement of static pressure and temperaturecombined with the entry of certain known constants: i.e.the compression factor, gas constant, molecular weight,and fluid constant.

Figure 5.33:Computation of fully compensated mass flow requires the measurement ofDP, static pressure and temperature (courtesy Fisher Rosemount)

In recent years both Honeywell and Fisher-Rosemount havedeveloped a single transmitter solution that makessimultaneous measurement of differential pressure, staticpressure and temperature and provides the on-boardcomputation.

Apart from providing tremendous cost savings in purchaseprice as well as installation, such multivariable transmittersprovide accurate mass flow measurements of process gases(combustion air and fuel gases) and steam, whethersaturated or superheated. Other applications include: DPmeasurement across filters and in distillation columnswhere the user is concerned with the static pressure andtemperature measurements to infer composition; and inliquid flow rate applications where density and viscositycompensation is required due to large temperature changes.

Special transmittersContinued emphasis on safely shut-down systems in thepetrochemical industries has lead to the development of anew ‘Critical’ high availability transmitter from Moore whichprovides complete hardware and software redundancy;comprehensive self testing and primary and secondarycurrent sources to ensure safe fault indication. Thesecapabilities allow a single ‘Critical’ transmitter to be installedwhere two conventional transmitters are usually installedon a critical application or two ‘Critical’ transmitters to beinstalled where three conventional transmitters are requiredin a safety shutdown system.

Chapter 6: Electromagnetic flow metersElectromagnetic flow meters, also known as ‘Magflows’ *or ‘Magmeters’, have been in widespread use for over 40years and were the first modern meters with no movingparts and zero pressure drop.

Measuring principleThe principle of the EM flow meter is based on Faraday’slaw of induction which states that if a conductor is movedthrough a magnetic field a voltage that is proportional tothe velocity of the conductor will be induced in it.

Referring to Figure 6. /, if the conductor of length (1) ismoved through the magnetic field with a magnetic fluxdensity (B) at a velocity (v), then a voltage will be inducedwhere:

6 = B.l.v and:e = induced voltage (V)B = magnetic flux density (Wb/m2)I = length of conductor (m) v = velocity of conductor

(m/s)

Figure 6.1:Illustration of Faraday’s Law of electromagnetic induction

In the electromagnetic flow meter (Figure 6.2) a magneticfield is produced across a cross-section of the pipe—withthe conductive liquid forming the conductor (Figure 6.3).Two sensing electrodes, set at right angles to the magneticfield, are used to detect the voltage which is generatedacross the flowing liquid and which is directly proportionalto the flow rate of the medium.

It can be seen that since v is the flow rate (the parameterto be measured) the generated voltage is limited by thelength of the conductor (the diameter of the pipe) and theflux density. In turn, the flux density is given by:

B = µ.Hwhere:

m = permeabilityH = magnetising field strength (ampere-turns/m)

Because the permeability of the magnetic circuit is largelydetermined by the physical constraints of the pipe (theiron-liquid gap combination), the magnetic flux density B(and hence the induced voltage) can only be maximised byincreasing H—a function of the coil (number of windingsand its length) and the magnetising current.

“The term ‘Magflo’ is a proprietary name used by DanfossInstrumentation.

Figure 6.2:Basic principle of the electromagnetic flow meter

Figure 6.3:The conductive liquid forms the conductor in contact with the electrodes

ConstructionBecause the working principle of the electromagnetic flowmeter is based on the movement of the conductor (theflowing liquid) through the magnetic field, it is importantthat the pipe carrying the medium (the metering tube)should have no influence on the field. Consequently, toprevent short circuiting of the magnetic field, the meteringtube must be manufactured from a non-ferromagneticmaterial such as stainless steel or nickel-chromium.

LinersIt is equally important that the signal voltage detected bythe two sensing electrodes is not electrically short circuitedthrough the tube wall. Consequently, the metering tubemust be lined with an insulating material. Such materialshave to be selected according to the application and theirresistance to chemical corrosion, abrasion, pressure andtemperature (Tab!e 6.1).

Chapter 6: Electromagnetic flow meters

Table 6.1: Commonly used magnetic flow meter liner materials

Material General Corrosion Abrasion Temperature Pressure limitresistance resistance limit °C (bar)

Teflon PTFE Warm deformable Excellent Fair 180 40resin with excellent anti-stickproperties and suitable forfood and beverage

Teflon PFA Melt-processable resin with Excellent Good 180 40better shape accuracy,abrasion resistance andvacuum strength than PTFE

Polyurethane Extreme resistance to wear Wide range Excellent 50 250and erosion but not suitablefor strong acids or bases

Neoprene Combines some of the Wide range Good to excellent 80 100resistance to chemicalattack of PTFE with a gooddegree of abrasion resistance

Hard rubber Inexpensive — finds its main Fair to excellent Fair 95 250(Ebonite) application in the water and

waste water industries

Soft rubber Mainly used for slurries Fair Excellent 70 64

Modified Developed for harsh Very high Good 200 Yield strengtphenolic environments containing of pipe

H2S/CO

2 concentrations

and acids

Fused Highly recommended for Excellent Excellent 180 40aluminium very abrasive and/oroxide corrosive applications

Teflon PTFEA warm deformable resin, Teflon PTFE is the most widelyused liner material. Characteristics include:

• high temperature capability (180°C)• excellent anti-stick characteristics to reduce build-up• inert to a wide range of acids and bases• approved in food and beverage applications

Teflon PFATeflon PFA is a melt-processable resin that offers:• a better shape accuracy than PTFE• better abrasion resistance

• better vacuum strength because of the ability toincorporate stainless steel reinforcement

Polyurethane .......Teflon PTFE/PFA does not have adequate erosion resistancefor certain applications and, often, the best choice whenextreme resistance to wear and erosion is required ispolyurethane. Other characteristics include:

• cannot be used with strong acids or bases• cannot be used at high temperatures since its

maximum process temperature is 40 °C

A long historyThe first reported attempt to use Faraday’s laws ofelectromagnetic induction to measure flow, was in 1832, in anexperiment conducted by Michael Faraday himself.

With the aim of measuring the water flow of the River Thames,Faraday lowered two metal electrodes into the river fromW aterloo bridge. Both electrodes were then connected to agalvanometer which was intended to measure the inducedvoltage produced by the flow of water through the earth’smagnetic field.

The failure of Faraday to obtain any meaningful results wasprobably due to electrochemical interference and polarisationof the electrodes.

It was left to a Swiss Benedictine monk, Father BonaventuraThuriemann OSB, who had lived and worked in the Benedictinemonastery in Engelberg since 1929, to lay the foundations ofthis flow measuring technology. With the publication of hisscientific work, ‘A method of electrically measuring the rate offluids’ in 1941, Father Bonaventura was the first to show that,by proper application of Faraday’s law of induction, it waspossible to measure the volume flows of liquids in pipes.

The reason that hismeasuring principle was notimmediately developed lies inthe fact that the electronicmeasuring equipment of theday was insufficient to do thejob, Breakthrough to ageneral acceptance inindustry arrived in the mid1970s when progress inelectronics made it possibleto produce a low voltage,interference free, measuringamplifier that was sufficientlysensitive and drift free.

Father Bonaventura neverthought fo commercialise hisdiscovery. But, as is so oftenthe case in technologicalhistory, others were quick tosee the advantages andacted accordingly.

Neoprene• resistant to chemical attack• good degree of abrasion resistance• temperature of 80 °C

Hard rubber (Ebonite)• inexpensive general purpose liner• wide range of corrosion resistance• main application in the water and waste water

industries

Soft rubber• relatively inexpensive• high resistance to abrasion• main application in slurries

Modified phenolicDeveloped by Turbo Messtechnik for harsh environmentscontaining H,,S/CO7 concentrations and acids. This is apowder based line with high-resistant fillers and organicpigments; it is suitable for high temperatures (200 °C) andhigh pressures.

Fused aluminium oxideHighly recommended for abrasive and/or corrosiveapplications and suitable for high temperatures up to 180°C,this line is used extensively in the chemical industry.

ElectrodesThe electrodes, like the liners, are in direct contact withthe process medium and again the materials of constructionmust be selected according to the application and theirresistance to chemical corrosion, abrasion, pressure andtemperature.

Figure 6.4: The electrodeseal is maintained throughthe use of five separatesealing surfaces and a coilspring (courtesy FisherRosemount)

Commonly used materials include: 316 stainless steel,platinum/ rhodium, Hastelloy C, Monel and tantalum.

One of the main concerns is the need to ensure that thereis no leakage of the process medium. In the constructiondesign shown in Figure 6.4, the electrode seal is maintainedthrough the use of five separate sealing surfaces and a coilspring. However, to ensure that the overall integrity of thesystem is maintained, even if a process leak should occurpast the liner/ electrode interface, the electrodecompartment can also be separately sealed. Usually ratedfor full line pressure, such containment ensures that in theevent of a leak, no contamination of the field coils occurs.

Where heavy abrasion or contamination of the electrodesmight occur, many manufacturers offer the option of fieldreplaceable electrodes (Figure 6.5).

Fouling of the electrodes by insulating deposits can

Figure 6.5:Field replaceable electrode (courtesy Fisher Rosemount)

Figure 6.6: To developmost of the electrodepotential (e) across theinput impedance (Rl) of themeter amplifier the Rlneeds to be at least 1000times higher than themaximum electrodeimpedance Rs

considerably increase the internal resistance of the signalcircuit This would change the capacitive coupling betweenthe field coils and signal circuitry.

ConductivityThe two main characteristics of the process medium thatneed to be considered are its conductivity and its tendencyto coat the electrode with an insulating layer. As shown inFigure 6.6; to develop most of the electrode potential (e)across the input impedance (R.) of the meter amplifier, andto minimise the effectLiquid Conductivity

(mS/cm)Carbon tetrachloride at 18°C 4x10-12

Toluene 10-8

Kerosene 0.017Aniline at 25°C 0.024Soya bean oil 0.04Distilled water 0.04Acetone at 25CC 0.06Phosphorous 0.4Benzole alcohol at 25 °C 1.8Acetic acid (1% solution) 5.8 x102

Acetic acid (10% solution) 16 x 102

Latex at 25°C 5x 103

Sodium silicate 24X103

Sulphuric acid (90% solution) 10.75 x 104

Ammonium nitrate (10% solution) 11 x 104

Sodium hydroxide (10% solution) 31 x104

Hydrochloric acid (10% solution) 63x104

Table 6.2:Conductivities of some typical fluids

of impedance variations due to changes in temperature,the R. needs to be at least 1000 times higher than themaximum electrode impedance Rs.

Chapter 6: Electromagnetic flow meters

Chapter 6: Electromagnetic flow metersModern high input impedance amplifiers are available inthe range 1013 to 1014 Ω. Consequently, with an amplifierhaving, for example, an input impedance of 1013Ω, the errordue to impedance matching is less than 0,01% and a changein electrode impedance from 1 to 1000 MΩ will effect thevoltage by only 0,001%.

The electrode impedance depends on fluid conductivityand varies with the size of the metering tube. In older acdriven instruments the minimum conductivity of the fluidusually lay between 5 - 20 µS/cm. However, modern acinstruments employ a variety of technologies, includingcapacitively coupled meters that can be used on liquidswith conductivity levels down to 0,05 µS/cm or even lower.In some applications, coating of the electrodes is cause forconcern and, over the years, a number of solutions havebeen offered including a mechanical scraper assembly andultrasonic cleaning.

Figure 6.7. If the electrode isisolated by encrustation (a) a60 V ac voltage is appliedacross the electrodes andelectrolytic action starts toform micropomus pathsthrough the isolating ‘barrier’(b). As these paths becomeprogressively larger, theisolating barrier starts to breakaway from the electrode (c)

A solution offered by Turbo Messtechnik employselectrolytic electrode cleaning. If one or more of theelectrodes becomes isolated by gaseous slugs, sticky mediaor encrustation (Figure 6.7 (a)); the instrument detects theabnormally low conductivity and applies 60 V ac voltageacross the electrodes. After approximately one minute theelectrolytic action starts to form microporous paths throughthe isolating ‘barrier’ (Figure 6.7(b)). As thesepaths becomeprogressively larger, the isolating barrier starts to breakaway from the electrode (Figure 6.7 (c)) to reestablishcontact with the process medium. A 2.5 minute cycle isusually sufficient for normal flow sensing.

Most refinery products, and some organic products, haveinsufficient conductivity to allow them to be metered usingelectromagnetic flow meters (Table 6.2).

It should be noted that the conductivity of liquids can varywith temperature and care should be taken to ensure thatthe performance of the liquid in marginal conductivityapplications is not affected by the operating temperatures.Most liquids have a positive temperature coefficient ofconductivity. However, negative coefficients are possiblein a few liquids.

Capacitive coupled electrodesThe foregoing solutions do not solve the problemof’electrode coating’ in which an insulating depositeffectively isolates the electrodes. These insulating depositsare often found in the paper manufacturing industry andin sewage treatment applications where grease and proteinconglomerates can develop into thick insulating layers.

In the capacitive coupled flow meter developed by Bailey-

Figure 6.8:

The electrodes have been areplaced by capacitive platesburied in the liner

Fisher & Porter, the electrodes, which are normally wettedby the process liquid, have been replaced by capacitiveplates buried in the liner (Figure 6.8). The capacitance isdeveloped when the liquid film of the medium beingmeasured acts as one of the plates; the meter lining actsas the dielectric; and the second capacitive plate is formedby the metallic electrode which is embedded in the tubeliner.

Figure 6.9: Capacitive electrodes formed by two large plates bonded tothe outside of a ceramic flow tube

In an alternative solution offered by Krohne, the electrodestake the form of two large plates bonded to the outside ofa ceramic flow tube (Figure 6.9) —with the pre-amplifermounted directly on the flow tube. Capable of use withliquids with conductivity levels down to 0,05 µS/cm thecapacitive coupled magnetic flow meter features: no gapsor crevices, no risk of electrode damage due to abrasion;no leakage; and no electrochemical effects.

Field characterisationThe purpose of a flow meter is to measure the true averagevelocity across the section of pipe, so that this can be relateddirectly to the total volumetric quantity in a unit of time.The voltage generated at the electrodes is the summationof the incremental voltages generated by each elementalvolume of cross-section of the flowing fluid as it crossesthe electrode plane with differing relative velocities.

Initially, designs assumed the magnetic field to behomogeneous over the measured cross-section and lengthof the pipe to achieve precise flow measurement. However,early

Chapter 6: Electromagnetic flow metersFigure 6.10: For a givenvelocity (v) the mediumflowing at position A t doesnot generate the samevoltage signal as thatflowing position A2(courtesy Endress +Hauser)

Figure 6.11:Weighting factordistribution inelectrode plane(Rummel andKetelsen)

Figure 6.12:The three most common forms of magnetic fields: (a) the homogeneousfield in which B is constant over the entire plane (b) a ‘characterised field’in which B increases in the x-direction but decreases in the y-direction; and(c) the modified field in which B increases in the x-direction but is constantin the y-direction

investigators showed that, for a given velocity, the mediumdoes not generate the same voltage signal in the electrodesat all points. Thus, for a given velocity (v) the mediumflowing at position A! (Figure 6.10) does not generate thesame voltage signal as that flowing in position A,.

Rummel and Ketelsen plotted the medium flowing atvarious distances away from the measuring electrodes(Figure 6.11) and showed how these contribute in differentways towards the direction of the measuring signal. Thisshows that a flow profile that concentrates velocity in thearea of one electrode will produce eight times the outputof that at the pipe centre— leading to errors that cannot beoverlooked.

One solution to this problem is to use a non- homogeneousfield that compensates for these non-linear concentrations.Subsequent to his research, Ketelsen designed a magneticflow meter that made make use of a ‘characterised field’.

As distinct from the homogeneous field in which themagnetic flux density (B) is constant over the entire plane(Figure 6.12 (a)), the ‘characterised field’ is marked by anincrease in B in the x-direction and a decrease in the y-direction (Figure 6.l2(b)). Because commercial exploitationof this design is limited in terms of a patent in the name ofB. Ketelsen, assigned to Fischer & Porter GmbH, a ‘modifiedfield’ has been developed in which the lines of magneticflux, at any place in the electrode-plane, are characterisedby an increase in B in the x-direction, from the centre tothe wall, and constancy in the y-direction (Figure 6.12 (c)).This ‘modified field1 is, therefore, a compromise betweenthe ‘characterised field’ and the ‘homogeneous field1.

Figure 6.13: Distribution of the flux density across the diameter of theflow tube: (a) with a mathematically defined field; and (b) with a non-defined field, caused by the presence of magnetite, the field becomesdistorted (courtesy Krohne)

Magnetite compensationAs seen, with the electromagnetic flow meter it is essentialto maintain the cross-sectional field density in amathematically defined manner—irrespective of themedium. Figure 6.13 (a) shows how the field strength mightbe characterised across the cross-section of the flow tube,whilst Figure 6.13 (b) shows how the field can be distortedby the presence of magnetic material such as magnetitewithin the liquid medium.

In a typical magnetite compensation system the cross-seclional field density is measured using four speciallyconstructed coils. With the coils wound in phase, and in

Figure 6.14: (a) with no magnetite the output V remains constant; (b)with the presence of magnetite the output V will increase or decrease(courtesy Krohne)

the absence of magnetite (Figure 6.14 (a)), the distribution

Chapter 6: Electromagnetic flow metersof the field will generate a constant voltage in each coil toproduce an output (V). However, the presence of magnetite(Figure 6.14 (b)) distorts the field so as to change the voltagegenerated in each coil and thus increase or decrease theoutput. When added to the output of the current measuringcircuit, this variation can be used to control the gain of theflow signal amplifier.

Although the magnetite compensated flow meter can bepre-calibrated fairly accurately, based on many years ofgathered data, final calibration is usually required on-site.Depending on the magnetite concentration, a typical systemaccuracy of better than 3 % can be achieved—a more thanacceptable figure for a medium that had formerly beenconsidered beyond the capabilities of conventional EM flowmeasurement.

A final point lo consider when measuring a mediumcontaining magnetite is that the magnetic field of the flowmeter will attract the magnetic particles. With time, thiswill form a screening layer on the flow meter lining.Consequently, to prevent the layer from forming, theminimum flow speed of the medium should be 2,5 m/s.

Measurement in partially filled pipesA fundamental requirement for accurate volumetric flowmeasurement is that the pipe be full. Given a constantvelocity then, as the fill level decreases, the inducedpotential at the electrodes is still proportional to the mediavelocity. However, since the cross sectional area of themedium is unknown it is impossible to calculate thevolumetric flow rate.

Figure 6.15:How meter installed in(a) an invert or (b) a U-section can often ensurethat the meter remainsfull when the media pipeis only partially full(courtesy Bailey-Fischer+ Porter)

In the water utility industry where large bore flow metersare used and the hydraulic force is based on gravity, theoccurrence of a partially filled pipe, due to low flow, isquite frequent.

Although this problem can be solved by installing the flowmeter at the lowest point of the pipeline in an invert or U-section (Figure 6.15), there are still many situations whereeven the best engineering cannot guarantee a full pipe—thus giving rise to incorrect volume readings.

One answer to this problem would be to determinethecross-sectional area and thus calculate the volumetricflow.

In the solution offered by Bailey-Fischer & Porter in its Parti-MAG, two additional electrode pairs are located in the lowerhalf of the meter to cater for partial flow rate measurementsdown to 10%. In addition, the magnetic field is switchedsuccessively from a series to a reverse coil excitation. The

series excitation mode (Figure 6. 16) corresponds to theexcitation mode for a conventional meter. As a result ofthis field, a voltage that is related to the medium velocityis induced in the electrode pairs.

Figure 6.16: The seriesexcitation modecorresponds to theexcitation mode for aconventional meter(courtesy of Bailey-Fischer& Porter)

Figure 6.17: In thereverse excitation modethe induced voltages inthe upper and lowerhalves of the meter are ofequal magnitude butopposite sign (courtesy ofBailey-Fischer & Porter)

In the reverse excitation mode (Figure 6. 17) the inducedvoltages in the upper and lower halves of the meter are ofequal magnitude but opposite sign. Thus, in a full pipe thepotential would be zero at the electrode pair E1 and somedefinite value at the electrode pairs E2 and Ev As the levelfalls, the signal contribution from the upper half decreaseswhile that from the lower half remains the same—resultingin a change in the potential at the various electrode pairsthat can be related directly to the change in medium level.Microprocessor technology is then used to compute thecross-sectional area and thus the volumetric flow.

A slightly different scheme is used in Krohne’ s TTD ALFLUXmeter. This instrument combines an electromagnetic flowmeter with an independent capacitive level measuringsystem. The electromagnetic flow measuring sectionfunctions like a conventional electromagnetic flow meter,using a single set of electrodes that is placed near thebottom of the pipe as shown in Figure 6.18. In this manner,even when the filling level falls

Figure 6.18: The twosensing electrodes arepositioned so that theelectrodes are stillcovered when thefilling level falls to lessthan 10% of the pipediameter (courtesyKrohne)

Chapter 6: Electromagnetic flow metersFigure 6.19: The levelmeasuring section makes useof insulated transmission anddetection plates embedded inthe flow meter (courtesyKrohne)

to less than 10% of the pipe diameter, the electrodes arestill covered and capable of providing a flow velocity-relatedoutput. The level measuring section makes use of a systemof insulated transmission and detection plates embeddedin the flow meter liner (figure 6../9) in which the change incapacitive coupling is proportional to the wetted cross-section. Using these two measured values it is now possibleto compute the actual volumetric flow (Figure 6.20) from:

Q = v.Awhere:

Q = volumetric flowv = velocity-related signalA = wetted cross-sectional area

Figure 6.20: Thevolumetric flow is computedusing the two measuredvalues of velocity and cross-sectional area (courtesyKrohne)

Empty pipe detectionIn many cases, measurement of partially filled pipes is notrequired. Nonetheless, to draw attention to this situation,many meters incorporate an ‘Empty Pipe Detection’ option.In the most common system (Figure 6.21) a conductivityprobe, mounted on top of the pipe, senses the presence ofthe conductive medium. If the medium clears the sensor,due to partial filling of the pipe, the conductivity falls andan alarm is generated.

An alternative scheme is to use a high frequency currentgenerator acrosstheflowmeter sensing probes. Becausenormal flow measurement uses relatively low frequencies,the high frequency signal used to measure the conductivityis ignored by the flow signal amplifier. ‘Empty PipeDetection’ is not only used to indicate that the volumereading is incorrect. For example, in a two-line standbysystem, one line handles the process and the other line isused for standby. Since the standby line does not containany of the process medium, the flow meter

Figure 6.21:Conductivity probe for empty pipe detection

sensing electrodes are ‘open circuit’ and the amplifier outputsignal will be subject to random drifting. The resultantfalsely generated inputs to any process controllers,recorders, etc, connected to the system will give rise tofalse status alarms. Here, the ‘Empty Pipe Detection’ systemis used to ‘freeze’ the signal to reference zero.

Another application for ‘Empty Pipe Detection’ is to preventdamage to the field coils. Magnetic flow meters based on a‘pulsed dc’ magnetic field, generate relatively low powerto the field coils —typically between 14 and 20 VA. This isusually of little concern regarding heat generation in thefield coils. However, flow sensors based on ‘ac generated1magnetic fields, consume power in excess ofafewhundredVA. Toabsorb the heat generated in the fieldcoils, a medium is required in the pipe to keep thetemperature well within the capability of the field coilinsulation. An empty pipe will cause overheating andpermanent damage to the field coils and, consequently,this type of flow meter requires an ‘Empty Pipe Detection’system to shut down the power to the field coils.

Insertion metersAs shown in Figure 6.22, in-line insertion magnetic flowmeters are installed using a flange, welded to the flowtube, with the measuring section penetrating into themedium flow.

Figure 6.22:In-line insertion magnetic flow meter suitable for pipe sizes ranging

from 100 to 2000mm (courtesy Arad Ltd. Daliaj

In the meter illustrated in Figure 6.23, both the field coilsand electrodes are contained within the insertion probeand the voltage is measured between the centra! electrodeand the outer casing of the probe.

Typically such devices are available for measurement inthe range 0,3 m/s to 10 m/s at pressures to 16 bar andprocess medium temperatures to 150°C.

Chapter 6: Electromagnetic flow meters

Figure 6.23:Both the field coils and electrodes are contained within the insertion probeand the voltage is measured between the centra/ electrode and the outercasing of the probe

Measuring accuracies range down to 1 to 2 % dependingon the application. This technique also allows its use in a‘hot tap’ mode whereby it may be removed and replacedon high pressurelines without the need for a shutdown. Aunique adaptation of the insertion probe is shown in Figure6.24 in which the coils and electrodes form a singleencapsulated unit. Designed specifically for the water andwastewater industries, the UniMag eliminates the need fora liner since the meter, in effect, comprises two separateinsertion devices. Since the flow tube itself forms part ofthe magnetic circuit, the magnetic field is concentrated toa far higher extent than is normally found with a resultantincrease in the signal-to-noise ratio.

Figure 6.24: The coilsand electrodes form asingle encapsulated unitand the flow metercomprises two separate‘insertion’ devices andeliminates the need for aliner (courtesy Isco)

Field excitationThe metallic electrodes in contact with the flowing liquidform a galvanic element that creates an interferingelectrochemical dc voltage. This voltage depends on thetemperature, the flow rate, the pressure and the chemicalcomposition of the liquid as well as on the surface conditionof the electrodes. In practice, the voltage between the liquidand each electrode will be different—giving rise to anunbalanced voltage between the two electrodes.

To separate the flow signal from this interfering dc voltage,an ac excitation field is used—allowing the interfering dcvoltage to be separated easily from the ac signal voltageby capacitive or transformer coupling.

ac excitationThe ac electromagnetic flow meter is a relatively low costsystem with an accuracy of around 1 to 2%. Its majoradvantage is that it produces a strong magnetic field—resulting in a high signal amplitude. This makes itparticularly useful for use with problem media such as paperpulp and mining slurries. The relatively high frequency of

50 Hz also results in more samples per second ofmeasurement to produce an averaged signal that,theoretically, improves the signal representation of flowrate.

There are however many disadvantages. The 50 Hz supplyderived from the mains power has a superimposed voltageerror which is in phase with the flow signal. This is as aresult of eddy currents flowing in the conductive parts ofthe pipe and in the medium.

The eddy currents produced in the medium itself shouldcancel and the error can be factory-tuned to an acceptablelevel. However, in many sewage and waste waterapplications it is often found that, at low flow rates, layersof different density and conductivity are formed. As aconsequence the eddy current distribution that is createdby the time derivative of the induction, is completelydeformed and interference voltages, which cannot be fullysuppressed in the converter, are produced.

Another major disadvantage of ac excitation is its highpower consumption—often of the order of 1 kVA or more.

While ac electromagnetic flow meters have been usedsuccessfully for many years, the use of an alternating fieldexcitation make them susceptible to both internal andexternal sources of error. A further problem with mainsderived ac excitation is that it is impossible to separatethe signal voltage from external interference voltages.Interference voltages can be transferred by either capacitiveor inductive coupling from heavy-current carrying cableslaid in proximity to the signal cable. Although theseinterference voltages may be largely suppressed by multiplescreening of the signal cable, they might not he completelyeliminated.

In addition, stray currents from other systems areoccasionally carried by the pipeline and/or the flowingmedia that generate voltages at the electrodes that cannotbe distinguished from the signal voltage.

These interference voltages require a manually operatedzero control adjustment and make it necessary to stop theflow in order to check the setting.

The pulsed dc fieldOriginally hailed as a general solution to all of the problemsencountered using ac excitation, pulsed dc excitationconsiderably improves zero stability with powerconsumptions of 20 VA or less. However, because themagnetising current and hence the fundamental signalvoltage is generally lower, the signal quality when usedwith pulp or slurries is usually unacceptable. Further, theexcitation frequency of most pulsed dc systems is typically10 times less than that of ac excitation systems.

The pulsed dc field is designed to overcome the problemsassociated with ac and dc interference. In the pulsed dcmeter, the dc field is periodically switched on and off atspecific intervals. The electrochemical dc interferencevoltage is stored when the magnetic field is switched offand then subtracted from the signal, representing the sumof the signal voltage and interference voltage when themagnetic field is switched on.

Figure 6.25 illustrates the voltage at the sensors in whichthe measured voltage V^ is superimposed on the spuriousunbalanced offset voltage Vu. By taking (and storing)samples during the periods A and B, the mean value Vrmay be obtained by algebraic subtraction of the two values:

Chapter 6: Electromagnetic flow metersVm = (Vu + Vm ) - Vu

This method assumes that the value of the electrochemicalinterference voltage remains constant during the measuringperiod between the samples A and B.

Figure 6.25:The voltage at the sensors in which the measured voltage Vm issuperimposed on the spurious unbalanced offset voltage Vu

However, if the interference voltage changes serious errorsare likely to occur. Figure 6.26 shows the unbalanced offsetvoltage as a steadily increasing ramp. Here, the error is ashigh as the amount by which the unbalanced voltage haschanged during the measuring periods A and B, and couldresult in an induction error of as much as 100 %.

One way to overcome this problem is by a method of linearinterpolation as illustrated in Figure 6.27. Prior to themagnetic induction, the unbalanced voltage A is measured.During the magnetic induction phase the value B (which isthe sum of unbalanced voltage and flow signal) is measuredand then, after magnetic induction, the changed unbalancedvoltage C is measured.

Figure 6.26:With the unbalanced offset voltage a steadily increasing ramp, the error isas high as the amount by which the unbalanced voltage has changedduring the measuring periods A and B

The mean value (A + C)/2 of the balanced voltage prior toand after magnetic induction is electronically produced andsubtracted from the sum signal measured during magneticinduction. So, the exact flow signal;

Vm = B-(A +C)/2is free from the unbalanced voltage. This method correctsthe amplitude of the dc interference voltage and also itschange, with respect to time.

Figure 6.27:The unbalanced voltage A is measured prior to the magnetic induction;the value B (the sum of unbalanced voltage and flow signal) is measuredduring the induction phase; and the changed unbalanced voltage C ismeasured after magnetic induction

Bipolar pulse operationAn alternative method of compensation (shown in Figure6.28), uses analternating (orbipolar) dc pulse. Under idealor reference conditions, the values of V1 and V2 would beequal and would both have the value Vm the measured value.Thus:

V1 - V2 = (Vm) - (-Vm) - 2Vm

Now, if the zero or no-flow signal is off-set by an unbalancedvoltage in, for example, a positive direction (Figure 6.29),then:

V1 = Vu + Vm

and

V2 = Vu - Vm

and

V1 - V2 = (Vu +Vm ) - (Vu - Vm ) = 2Vm

Again, linear interpolation methods may be applied,illustrated in Figure 6.30, where five separate samples aretaken during each measurement cycle. A zero potentialmeasurement is taken when the cycle commences; a secondmeasurement at the positive peak; a third at zero potential;a fourth at negative peak and finally another zeromeasurement on completion of the cycle. The result, inthis case, will be:

2Vm = (V1-(Z1+Z2)/2-(V2-Z2 + Z3)/2)

Figure 6.28:Bipolar pulse compensation under ideal or reference conditions

Chapter 6: Electromagnetic flow meters

Figure 6.29:Bipolar pulse compensation eliminates error due to unbalanced offsetvoltage

Meter sizingGenerally the size of the primary head is matched to thenominal diameter of the pipeline. However, it is alsonecessary to ensure that the flow rate of the medium liesbetween the minimum and maximum full scale ranges ofthe meter. Typical values of the minimum and maximumfull scale ranges are 0,3 and 12 m/s respectively.

Figure 6.30:Bipolar pulse compensation with linear interpolation

Experience has also shown that the optimum flow velocityof the medium through an electromagnetic flow meter isgenerally 2 to 3 m/s — depending on the medium. Forexample, for liquids with a solids content, the flow velocityshould be between 3 to 5 m/s to prevent deposits and tominimise abrasion.

Knowing the volumetric flow rate of the medium in, forexample, cubic metres per hour, and knowing the pipediameter, it is easy to calculate and thus check to see if theflow velocity falls within the recommended range. Mostmanufacturers supply nonograms or tables that allow usersto ascertain this data at a glance.

Occasionally, in cases where the calculated meter size needsto be smaller than that of the medium pipe size, a transitionusing conical sections can be installed. The cone angleshould be 8° or less and the pressure drop resulting fromthis reduction can, again, be determined frommanufacturers’ tables (Figure 6.31).

ConclusionThe electromagnetic (EM) flow meter is regarded by manyusers as the universal answer to more than 90% of all flowmetering applications. Some of the many benefits offeredby the EM flow meter include:

• no pressure drop• short inlet/outlet sections (5D/2D)

Figure 6.31:Conical section used to cater for reduced meter size

• relationship is linear (not square root)• insensitive to flow profile changes (laminar to turbu-

lent) including many non-Newtonian liquids• unaffected by variations in density, viscosity,

pressure, temperature, and (within limits) electricalconductivity

• reliable — no moving parts• turn-down ratio of 30:1 or better• inaccuracy of better than ±0,5% of actual flow overfull

range• no recalibration requirements• bi-directional measurement• no taps, or cavities• no obstruction to flow• not limited to clean fluids• high temperature capabilities• high pressure capabilities• volumetric flow• can be installed between flanges• can be made from corrosion resistance materials at

low cost On the down side, the main limitations ofthe magnetic flow meter include:

• oniy suitable for conductive liquids• not suitable for gases• not suitable for entrapped air, foam or two-phase

fluids• pipeline must normally be full• egress and/or entrapment of process medium can

occur at electrodes

Chapter 7: Ultrasonic flow metersUltrasonic FLOW meters, suitable for liquids and gases, havebeen available for more than twenty years and are currentlythe only truly viable non-intrusive measuring alternativeto the electromagnetic flow meter.

Unfortunately, although originally hailed as a panacea forthe flow measurement industry, lack of knowledge and poorunderstanding of the limitations of early instruments(especially the Doppler method) often led to its use inunsuitable applications.

Nonetheless, the ultrasonic meter is probably the onlymeter capable of being used on large diameter pipes (above3 m bore) at reasonable cost and performance (around 1%).

In essence there are three basic principles used in ultrasonicmetering: the Doppler method; the time-of-flight method;and the frequency difference method.

Doppler methodDoppler flow meters are based on the Doppler effect—thechange in frequency that occurs when a sound source andreceiver move either towards or away from each other. Theclassic example is that of an express train passing througha station. To an observer standing on the platform the soundof the train appears to be higher as the train approachesand then falls as the train passes through the station andmoves away. This change in frequency is called the Dopplershift.

In the Doppler ultrasonic flow meter, an ultrasonic beam(usually of the order of 1 to 5 MHz) is transmitted, at anangle, into the liquid (Figure 7.1). Assuming the presenceof reflective particles (dirt, gas bubbles or even strongeddies) in the flow stream, some of the transmitted energywill be reflected back to the receiver. Because the reflectiveparticles are moving towards the sensor, the frequency ofthe received energy will differ from that of the transmittedfrequency (the Doppler effect).

Figure 7.1:In the Doppler ultrasonic flow meter, an ultrasonic beam is

transmitted, at an angle, into the liquid

This frequency difference, the Doppler shift, is directlyproportional to the velocity of the particles.

Assuming that the medium velocity (v) is considerably lessthan the velocity of sound in the medium (C), the Dopplerfrequency shift (Af) is given by:

where f is the transmitted frequency. From this it can beseen that the Doppler frequency, Af, is directly proportionalto flow rate.

The velocity of sound in water is about 1500 m/s. If thetransmitted frequency is 1 MHz, with transducers at 60°,then for a medium velocity of 1 m/s the Doppler shift is

around 670 Hz. Since this technique requires the presenceof reflecting particles in the medium, its use in ultra-cleanapplications or, indeed, in any uncontaminated medium,is generally precluded. Although some manufacturers claimto be able to measure ‘non-aerated’ liquids, in reality suchmeters rely on the presence of bubbles due to micro-cavitation originating at valves, elbows or otherdiscontinuities.

For a particle to be ‘seen’, it needs to be larger thanapproximately V10 of the wavelength of the acousticfrequency in the liquid. In water, a 1 MHz ultrasonic beamwould have a wavelength of about 1,5 mm so particleswould need to be larger than 150 |im to reflect adequately.

Whilst air, oil particles and sand are excellent sonicreflectors, the presence of too many particles can attenuatethe signal so that very little of the signal reaches the receivertransducer.

Probably the single biggest drawback of this technology isthat in multiphase flows, the particle velocity may bearlittle relationship to the medium velocity. Even in single-phase flows, because the velocity of the particles isdetermined by their location within the pipe, there may beseveral different frequency shifts—each originating atdifferent positions in the pipe. As a result, the Dopplermethod often involves a measurement error of 10 % ormore.

Figure 7.2:Insertion type Doppler probe (courtesy Dynasonics)

In the insertion type probe shown in Figure 7.2, thereflective area is to a large extent localised and the potentialsource of errors is thereby reduced.

Generally, however, Doppler meters should not beconsidered as high performance devices and are costeffective when used as flow monitors. They work well ondirty fluids and typical applications include sewage, dirtywater and sludge. Doppler meters are sensitive to velocityprofile effects and temperature.

Transit time metersThe ultrasonic transit time measuring method is based onthe fact that, relative to the pipe and the transducers, theflow velocity will reduce the propagation speed of anultrasonic pulse travelling against the medium flow.

Figure 7.3:In the transit time meter two transducers (A and B) act alternately asreceiver and transmitter

Chapter 7: Ultrasonic flow metersSimilarly, the fluid velocity increases the speed ofpropagation of the pulse travelling downstream. Thedifference between these two transit times can be relateddirectly to the flow velocity.

In practice, the meter comprises two transducers (A and B)mounted at an angle to the flow and with a path length, L(Figure 1.3)— each acting alternately as receiver andtransmitter. The transit time of an ultrasonic pulse, fromthe upstream to the downstream transducer, is firstmeasured and then compared with the transit time in thereverse direction.

Mathematically:

where:

TAB = upstream travel timeTBA = downstream travel timeL = path length through the fluidC = velocity of sound in mediumv = velocity of mediumThe difference in transit time ∆T is:Since the velocity of the medium is likely to be much lessthan the velocity of sound in the medium itself (15 m/scompared to 1500 m/s), the term v2 cos2 θ will be verysmall compared with C2 and may be ignored for all practicalflow velocities. Thus:

This shows that the flow velocity v is directly proportionalto the transit time difference ∆T.

It also illustrates that v is directly proportional to C2 (thesquare of the speed of sound) which will vary withtemperature, viscosity and material composition.Fortunately, it is possible to eliminate the variable C2 fromthe equation:

and mean transit time,

Then:

and

now, substituting in [1]: A74L2

Since both the length L and the angle 9 arc likely to remainconstant it is only necessary to calculate the sum anddifference of the transit times to derive the flow rateindependent of the velocity of sound in the medium.

As distinct from Doppler meters, transit time meters workbetter on clean fluids and typical applications include: water,clean process liquids, liquefied gases and natural gas pipes.The accuracy of measurement is determined by the abilityof the instrument to measure the transit time accurately.In a 300 mm diameter pipe, for example, with thetransducers set at 45°, and the medium flowing at 1 m/s,the transit time is about 284 p,s and the time difference ATis less than 200 ns. This means that to measure the velocitywith a full-scale accuracy of 1%, time must be measureddown to 2 ns at the very least. With smaller diameter pipes,the measurement accuracy would therefore need to be inthe picosecond range.

Obviously, with longer path lengths, this stringent timemeasurement requirement becomes easier to meet.Performance thus tends to be better with large bore pipes,and providing multiple traverses as illustrated in Figure7.4 can increase the path length.

Figure 7.4:Increasing the path length using a double traverse, single V path on thecentre line

These arrangements are frequently used for gasmeasurement in lines and gas flow measurement. Thedouble traverse, single path flow meter is frequently usedfor low-cost liquid measurement and accurate real-timemeasurement of hazardous and non-hazardous gas flowsin lines from 100 to 900 mm DN.

The ‘U’-form meter as shown in Figure 7.5can he used forvery low flows.

Figure 7.5:The ‘U’-form meter can be used for very low flows

Chapter 7: Ultrasonic flow meters

Figure 7.6:Average velocity along an ultrasonic path

Flow profileThe average velocity along an ultrasonic path (Figure 7.6)is given by:

where:

D = pipe internal diameter

X = distance across the pipe

Thus, with a single path across the flow, the average flowis made up of the sum of the instantaneous velocities ateach point across the diameter of the pipe. The transit timemeter thus provides a picture of the total flow profile alongthe path of the beam.

However, the validity of the measurement can only be reliedon if the flow profile is not subject to an asymmetric velocityprofile or symmetric swirl. In addition it is important toknow the flow profile. If, for example, the flow profile isnot fully developed, then, as shown in Figure 7.7, thelaminar-to-turbulent error can be up to 33%.

Figure 7.7:A single path produces a iaminar-to-turbulent error up to 33% (courtesyKrohne)

Using a dual path as shown in Figure 7.8, the laminar-to-turbulent error can be reduced to 0,5%.

An alternative method is shown in Figure 7.9. Here, internalreflectors used to impart a helical path to a single beamdevice result in high accuracy measurement for a wide flowrange, from laminar to turbulent and even in the transitionalregion.

Figure 7.8:A dual path reduces the iaminar-to-turbulent error to 0.5% (courtesyKrohne)

Figure 7.9:Single beam withhelical path produceshigh accuracymeasurement for awide flow range fromlaminar to turbulent(courtesy Siemens)

In the Krohne multi-channel custody-transfer ultrasonic flowmeter, ten sensors form five measurement paths locatedin the cross-section of the flow tube (Figure 7.10).

Figure 7.10: Fivemeasurement pathsprovide a measurementthat is essentiallyindependent of the flowprofile (courtesy Krohne)

This approach provides a wealth of information on the flowprofile (Figure 7.11) in laminar and in turbulent flowconditions, and provides highly accurate flow even in thepresence of non-symmetric flow profiles and swiri—thusproviding a measurement that is essentially independentof the flow profile—with accuracies to 0,15% andrepeatability to 0,02%.

Chapter 7: Ultrasonic flow meters

Figure 7.11:Determination of the flow profile (courtesy Krohne)

Another advantage of multiple measurement channels isthe obtained redundancy.

Frequency differenceThe frequency difference or ‘sing-around’ flow meter makesuse of two independent measuring paths—each with atransmitter (A and A’) and a receiver (B or B’) (Figure 7.12).Each measuring path operates on the principle that thearrival of a transmitted pulse at a receiver triggers thetransmission of a further pulse. As a result, a pair oftransmission frequencies is set up—one for the upstreamdirection and another for the downstream direction. Thefrequency difference is directly proportional to the flowvelocity.

Figure 7.12:‘Sing-around’ flow meter makes use of two independent measuring pathseach with a transmitter (A and A’) and a receiver (B or B’)

Thus:

and:

The frequency difference AF is given by: 2 v cos 9

and:

The main advantage of this system is that because thefrequency difference is directly proportional to flow, nomaths function is required. Further, the measurement isindependent of the velocity of sound in the medium.

Clamp on instrumentsTransducers that are damped externally to the walls of thepipe provide portable non-intrusive flow measurementsystems that can be installed within a few minutes tovirtually any pipe (Figure 7.13). Pipe materials include:metal, plastic, ceramic, asbestos cement and internal andexternally coated pipes.

Figure 7.13:Clamp-on transducers must take into account the thickness and materialof construction of the pipe wall (courtesy Fuji Electric)

Clamp-on transducers are also often used in permanentinstallations that cannot justify a permanent in-line meter,but nonetheless require period metering.

Because the ultrasonic pulses must traverse the pipe walland any coatings, the thicknesses must be known. Inaddition, the presence of deposits on the inside pipe surfacewill affect the transmitted signal strength and, therefore,performance.

Despite these obstacles modern clamp-on ultrasonicmeters, incorporating microprocessor technology thatallows the transducer mounting positions and calibrationfactors to be calculated for each application, providemeasuring accuracies of 1 to 3%—depending on theapplication.

Figure 7.14:By selecting a transmission frequency that excites a natural acousticwaveguide mode of the pipe, the pipe itself becomes the launching point ofthe acoustical signal and allows a much wider signal beam to betransmitted from one transducer to the other (courtesy ControlotronCorporation)

In conventional designs, a change in the characteristics ofthe liquid, which affects the speed of sound, will have adirect effect on the refraction angle. With sufficient changein the refraction angle, the signal from one transducer willnot be received by the other. This limitation is overcomewith the wide beam approach (Figure 7.14) in which the

Chapter 7: Ultrasonic flow meterspipe wall is incorporated into the signal transmissionsystem. During set-up, the meter selects a transmissionfrequency that excites a natural acoustic waveguide modeof the pipe to induce a sonic wave, which travels axiallydown the pipe wall. Tn this way the pipe itself becomesthe launching point of the acoustical signal and allows amuch wider signal beam to be transmitted from onetransducer to the other. The result is that any change inthe refraction angle will have negligible effect on thestrength of the received signal.

Velocity of sound measurementBecause ultrasonic meters measure volumetric flow whichis, in most cases, not relevant for plant operation purposes,their output is correlated to mass flow—assuming a fixedactual density (reference density) under operatingconditions. Consequently, deviations in density will causea misreading in mass flow, which is inversely proportionalto the deviation compared with the reference density.

Since the velocity of sound is a characteristic property of afluid, its measurement, in conjunction with the temperatureand pressure of the fluid, can be used as a measure/indication of:

• actual flowing density• concentration (for example, for fluids consisting of

two distinctive components)• molecular weight (when pressure, temperature, Cp/

Cv ratio and compressibility are known)Furthermore, since deviations of the velocity of soundsignal/range will indicate a change in fluid composition,its output may thus be used as an ‘interface detector’—alerting operators to different plant operating conditionsand/or feed stock changes or changes in composition forexample, contamination in heavy crude.

Since the signal strength will also be measured, deviationsin signal strength could indicate viscosity changes, anincreased level of solids (crystal formation, catalyst carryover) and/or bubbles (flashing-off of dissolved gases underchanged pressure/ temperature conditions) in the fluid. Inthe Krohne five beam meter, this is carried a stage further.Because the five beams also determine the flow profile,the meter is able to infer the Reynolds number. Thusequipped with data regarding the flow velocity (V) the pipediameter (D) and the density, the instrument can derivethe kinematic viscosity (|l).

Factors influencing the velocity of sound

Except in carbon dioxide gas service, the velocity of soundis independent of the ultrasonic frequency. Generally thevelocity of sound:

• increases with increasing density• decreases with increasing temperature for liquids• increases with increasing temperature for gasesAn important exception is water which has a discontinuityin its relationship between velocity of sound andtemperature. For water below a temperature of 74 °C, thevelocity of sound will increase with increasing temperatureand decrease if the temperature increases above 74°C.

Beam scatteringAs indicated, beam scattering/dispersion may occur if thefluid contains too many particles (crystals, catalystparticles). As soon as the fluid ceases to be single phase,beam scattering may occur under bubble flow or mist flowconditions.

At the frequency and intensity of the ultrasonic energytypically used in industrial applications, propagationthrough liquids may be up to distances of 10 m. However,the same energy will only propagate a few millimetres inair. Therefore,

evenly distributed air bubbles will disperse the energy byreflection from the liquid/air boundaries and causesignificant attenuation (Figure 7.15). The generally acceptedupper limit for entrained gases is about 1 % by volume,and for solids about 1 to 5%.

Figure 7.15:Sound propagation in a mixed medium

Bubble flow could appear with liquids operating close totheir boiling point where only a marginal pressure decreasecould cause the liquid to evaporate and form bubbles.

Another flashing-off phenomenon (not as well recognisedas boiling-offl occurs if gas is dissolved in liquid. Generally,as the pressure decreases or the temperature rises, thedissolved gas can no longer be contained in the liquid andwill flash-off until a new equilibrium is reached.

Typical examples of gases soluble in liquid are:

• H2S in water• H2S in D1PA (diisopropylamine)• CO2 in water• C02 in methanolTo minimise or prevent bubble flow, the meter should bemoved to a location in the line with a higher pressure, forexample, downstream of a pump. In immiscible mixtures(for example, water/oil) beam scattering should be avoidedby thorough upstream agitation to ensure that no largedroplets (oil droplets in water or water droplets in oil) arepresent at the meter section.

Product layering may also introduce beam scattering andshould be avoided by proper mixing. Product layeringoccurs not just as a result of poorly mixed products, but atlocations where cold and hot streams are mixed.

Layering will most likely occur directly downstream of atie-in of a cold stream with a hot stream, of the sameproduct, as a result of density differences. To avoid productlayering, the fluid should be thoroughly mixed upstreamof the meter using reducers (d/D - 0.7) or static mixers.

Upstream/downstream piping requirementsTurbulence or even the swirling of the process fluid canaffect the ultrasonic signals. In typical applications the flowneeds to be stable to achieve good flow measurement.Typically, sufficient straight pipe up- and downstream ofthe transducers does this. The straight section of piperequired upstream and downstream depends on the typeof discontinuity and varies for gas and liquid as shown inTables 7.1 and 7.2.

Chapter 7: Ultrasonic flow meters

Classification Upstream Downstream

90° bend

Tee

Diffuser

Reducer

Valve

Pump

Table 7.1:Minimum straight line pipe lengths for general purpose liquid measurement (courtesy Fuji Electric)

Chapter 7: Ultrasonic flow meters

Classification Upstream Downstream

90° bend

Valve

Fan

Pump

Table 7.2:Minimum straight line pipe lengths for general purpose gas measurement (courtesy Fuji Electric)

Chapter 8: Mass flow measurementMost chemical reactions are based largely on their massrelationship. Consequently, by measuring the mass flowof the product it is possible to control the process moreaccurately. Further, the components can be recorded andaccounted for in terms of mass.

Mass flow is a primary unit of flow measurement and isunaffected by viscosity, density, conductivity, pressure andtemperature. As a result it is inherently more accurate andmeaningful for measuring material transfer.

Traditionally, mass flow has been measured inferentially.Electromagnetic, orifice plate, turbine, ultrasonic, venturi,vortex shedding, etc, all measure the flow of the mediumin terms of its velocity through the pipe (for example,metres per second). However, because the dimensions ofthepipe are fixed, we can also determine the volumetricflow rate (for example, litres per second). Further, bymeasuring density and multiplying it by the volumetricflow rate, we can even infer the mass flow rate. However,such indirect methods commonly result in serious errorsin measuring mass flow.

Coriolis mass flow metersPossibly the most significant advance in flow measurementover the past few years has been the introduction of theCoriolis mass flow meter. Not only does this technologyallow mass flow to be measured directly but Coriolis metersare readily able to cope with the extremely high densitiesof, for example, dough, molasses, asphalt, liquid sulphur,etc, found in many industries.

The Coriolis forceThe Coriolis meter is based on the Coriolis force—sometimes, incorrectly, known as gyroscopic action.

Consider two children, Anne and Belinda, seated on arotating platform. Anne is situated mid-way between theaxis and the outer edge of the platform while Belinda isseated at the outer edge itself (FigureS.l). If Annenowthrowsa ball directly to Belinda, Belinda will fail toreceive the ball!

Figure 8.1:If Anne throws a bait directly to Belinda, Belinda will fail to receive theball due to the Coriolis effect

The reason will have nothing to do with Anne’s ability tothrow a straight ball (we’ll assume she’s a perfect pitcher)or Belinda’s ability to catch a ball (we’ll assume she’s aperfect catcher). The reason is due to what is termed theCoriolis effect.

What Anne has ignored is that although the platform isrotating at a constant angular speed (co) she and Belindaare moving at different circular or tangential speeds.

Indeed, the further you move away from the axis, the fasteryour speed, and the tangential speeds of each are directlyproportional to the radius ie:

v = r.ϖwhere:

v = tangential velocityr = radiusϖ = angular speed

In this case, Belinda at the edge of the platform will have atangential speed twice that of Anne (Figure 8.2). Thus, whenAnne throws the ball radially outwards towards Belinda,the ball initially has the velocity (v) radially outwards and atangential velocity VA due to the rotation of the platform. IfBelinda had this same velocity VA the ball would reach herperfectly. But Belinda’s speed (vB) is twice that of VA. Thuswhen the ball reaches the outer edge of the platform itpasses a point which Belinda has already passed and sopasses behind her.

Figure 8.2:Belinda at the edge of the platform will have a tangential speed twice thatof Anne and thus the ball’s tangential speed needs to be accelerated fromVA to VB

Consequently, to move the ball from Anne to Belinda itstangential speed needs to be accelerated from VA to VR.This acceleration is a result of what is termed the Coriolisforce, named after the French scientist who first describedit, and is directly proportional to the product of the massin motion, its speed and the angular velocity of rotation:

Fcor = 2mϖvwhere:

Fcor = Coriolis forcev = tangential velocityϖ = angularspeedm = the mass of the ball

Looking at this from another point, if we could measurethe Coriolis force and knowing the tangential velocity andthe angular speed, we could determine the mass of theball.

How does this relate to mass measurement of fluids?

Consider a simple, straight liquid-filled pipe rotating aroundaxis A, at an angular velocity ϖ (Figure 8.3). With no actualliquid flow, the liquid particles move on orbits equivalentto their distance r from the axis of rotation. Thus, at distancer1, the tangential velocity of a particle would be r1.ϖ whilstat double the distance r2, the tangential velocity wouldalso double to r2ϖ.

Chapter 8: Mass flow measurement

Figure 8.3:As the liquid flows away from the axis A, each mass particle will beaccelerated by an amount equivalent to its movement along the axis froma low to a higher orbital velocity

If the liquid now flows in a direction away from the axis A,at a flow velocity v, then as each mass particle moves, forexample, from r( to r2 it will be accelerated by an amountequivalent to its movement along the axis from a low to ahigher orbital velocity. This increase in velocity is inopposition to the mass inertial resistance and is felt as aforce opposing the pipe’s direction of rotation—ie it willtry to slow down the rotation of the pipe. Conversely, if wereverse the flow direction, particles in the liquid flowmoving towards the axis are forced to slow down from ahigh velocity to a lower velocity and the resultant Coriolisforce will try to speed up the rotation of the pipe.

Thus, if we drive the pipe at a constant torque, the Coriolisforce will produce either a braking torque or an acceleratingtorque (depending on the flow direction) that is directlyproportional to the mass flow rate.

Although the possibility of applying the Coriolis effect tomeasure mass flow rate was recognised many years ago, itis little more than twenty years since the first practicaldesign was devised. During this development period, manypipe arrangements and movements have been devised—with the major drawback of early systems lying in theirneed for rotational seals. This problem was overcome byusing oscillatory rather than rotational movement.

A practical systemOne of the simplest arrangements that incorporates all thepositive features of a Coriolis-based mass flow meter isillustrated in Figure 8.4. Here, a tubular pipe, carrying the

Figure 8.4:A pipe, formed in a loop, is vibrated around the z axis so that the straightparts of the pipe, A-B and C-D, oscillate on the arcs of a circle

liquid, is formed in a loop and vibrated around the z axis.The straight parts of the pipe, A-B and C-D, oscillate on thearcs of a circle and without any flow will remain parallel toeach other throughout each cycle.

If a liquid now flows through the tube in the directionshown, then the fluid particles in section A-B will movefrom a point with a low rotary velocity (A) to a point with ahigh rotary velocity (B). This means that each mass particlemust be accelerated in opposition to the mass inertialresistance. This opposes the pipe’s direction of rotationand produces a Coriolis force in the opposite direction.Conversely, in section C-D, the particles move in theopposite direction—from a point with a high rotary velocity(C) to a point with a low rotary velocity (D).

The resultant effect of these Coriolis forces is to delay theoscillation in section A-B and accelerate it in section C-D.As a result section A-B tends to lag behind the undisturbedmotion whilst section C-D leads this position.

Figure 8. 5 shows a practical arrangement in which twotubes are vibrated in opposition to each other. Figure 8. 6shows the oscillatory motion applied to a single tube whilstFigure 8.7 shows the forces acting on the tube in whichthere is fluid flow. As a result, the complete loop is twistedby an amount that is directly and linearly proportional tothe mass flow rate of the fluid (Figure 8.8) — with thetwisting moment lent to the pipe arrangement beingmeasured by sensors.

Figure 8.5:Typical arrangement of a Coriolis type instrument (courtesy Micro Motion)

Figure 8.6:Oscillatory motion applied to a single tube (courtesy Micro Motion)

Because of this twisting motion, one of the major designfactors of the oscillating tube is to prevent the pipefracturing because of stress ageing. Here, computersimulation has given rise to a geometric design for thick-walled tubes that does not expose them to bending stressbut to torsional strain applied evenly to the cross-sectionof the tube.

A further factor in reducing stress fractures is to limit theoscillation amplitude to approximately 1 mm which, in anoptimally designed system, would be about 20 % of themaximum permitted value. Thus, because the distortioncaused by the Coriolis forces is about 100 times smaller (amagnitude of about 10 (im) a measurement resolution of ±0,1 % amounts to only a few nanometres.

Chapter 8: Mass flow measurement

Figure 8.7:Forces acting on the tube as a result of fluid flow (courtesy Micro Motion)

Figure 8.8:The complete loop is twisted by an amount that is directly and linearlyproportional to the mass flow rate of the fluid (courtesy Micro Motion)

Although the possibility of stress fractures occurring issmall, consideration must be given to the fact that a stressfracture could occur — resulting in the release of the processmedium. As a result, considerable attention has been paidto secondary containment of the process medium.

It should be noted that secondary containment does notnecessarily match the maximum process pressurespecifications. Thus, for example, whilst the measuringtube and flanges may be suitable for up to 400 bar, ormore, the secondary containment may only be rated up toa pressure of 100 bar.

Multiple phase flowWhile fundamentally suitable for both gaseous and liquidmedia, in practice the Coriolis technique is really onlysuitable for those gases with mass flow rates typical ofliquid medium. These are generally only obtained with highdensity gases.

Mixtures with low admixtures of finely injected gas inliquids or fine grain solid admixtures, react almost like asingle phase liquid in that the admixtures merely alter thedensity. A Coriolis mass measurement is thus still effective.

At higher levels of non-hornogeneity, two problem areasoccur. First, a non-homogenous mixture results in anirregular fluctuating density and, thus, a constantlyfluctuating resonant frequency that can put the system outof phase.

A second problem is that the Coriolis method assumes thatall particles of the medium are accelerated on orbits inaccordance with the movement of the pipes. With highproportions of gas, particles in the middle of the pipe willno longer complete the movement of the pipe. Conversely,the Coriolis forces of the mass particles in the centre ofthe pipe will no longer affect the pipe walls. The result isthat the measuring value will be systematically reduced.

Most Coriolis-based systems can still tolerate an air-watergas volume of between 4 and 6%. However, because thebehaviour of liquid-gas mixtures depends on the

distribution of bubbles, and on the materials involved, thesefigures cannot simply be transferred to other mixtures.With liquids having a lower surface tension than water, forexample, considerably higher proportions of gas can betolerated.

The conditions for solids in water are a great deal morefavourable and many good systems can toleratesuspensions of fine grain solids of up to 20% in waterwithout any difficulty.

Density measurementThe measurement of mass flow by the Coriolis meter is,fundamentally, independent of the density of the medium,However, the resonant frequency of the oscillating pipewill vary with density — falling as the density increases. Inmany instruments this effect is used to provide a directmeasurement of density by tracking the resonant oscillationfrequency.

The temperature of the pipe system changes with thetemperature of the measured medium and alters itsmodulus of elasticity. This alters the oscillation frequencyand the flexibility of the loop system. Thus, the temperaturemust be measured as an independent quantity and usedas a compensating variable. The temperature of the mediumis, therefore, also available as a measured output.

Loop arrangementsThere are many different designs of Coriolis mass flowmeter, in the majority of which the primary sensor involvesan arrangement of convoluted tubes through which themeasured fluid flows.

In any arrangement which requires the tube to be bent toform the desired convolutions, the outside wall is stretchedand becomes thinner while the inner wall becomes thicker.This distortion will vary from one tube to another and,when the flow meter requires two such convoluted tubes,it becomes difficult to balance them dimensionally anddynamically.

Furthermore, if the fluid to be measured is abrasive, thisalready weakened part of the flow meter is likely to beseverely stressed. Abrasive material can also cause erosionthat will change the stiffness of the resonant elements andso cause measurement errors.

In the parallel loop arrangement (Figure 8.9) the flow issplit at the inlet to follow parallel paths through the twosections. The advantage of this is that the total cross-sectional area of the flow path is the sum of the cross-sections of both pipes. At the same time, since each pipehas a relatively small cross section it may be designed tohave a high flexibility — thus increasing the sensitivity tothe Coriolis effect.

A disadvantage of this arrangement is that the action ofsplitting andthenre-combiningthe flow introduces asignificant pressure drop. Furthermore, the flow may notbe divided equally, in which case an unbalance isgenerated—especially if solids or gases are entrained inthe liquid flow. The same reasoning applies if the balanceof the split is disturbed by partial or complete blockage ofone section—again leading to measurement errors. Thebalance may also be disturbed by separation of thecomponents in a two-phase flow, such as air or solidsentrained in liquid flow. A similar problem exists with shear-sensitive fluids. The use of a flow splitter is prohibited inClean-in-Place (C1P) and Steam-in-Place (SIP) applicationssince it is never certain that both tubes are clear. Further,

Chapter 8: Mass flow measurementthe splitter arrangement prohibits the use of a cleaning‘pig’.

Figure 8.9:Parallel loop arrangement with flow splitter

In the serial arrangement (Figure 8.10) the total length ofthe pipe is considerably greater due to the second loopand must therefore have a larger cross-sectional area toreduce the pressure loss. This, however, leads to increasedrigidity that makes it less sensitive to the Coriolis effect atlow flow rates. At high flow rates there is less pressuredrop, and the pipe is easier to clean.

Straight through tubeThe development of a straight through tube mass flowmeter, without any loops or bends, is based on the factthat a vibrating tube, fixed at its ends, also has a rotationalmovement about the fixed points and thereby generates aCoriolis force.

In the first of such designs, (shown in Figure 8.11) twotubes are vibrated at their resonant frequency. Infraredsensors are placed at two exactly defined locations at theinlet and outlet of the pipe to detect the phase of the pipeoscillation. At zero flow the oscillation of the system is inphase (Figure 8.12). When liquid flows into the system theflowing medium is accelerated on the inlet (Figure 8.13)and decelerated on the outlet (Figure 8.14) and theoscillation of the system is out of phase. The measuredphase difference is proportional to mass flow.

Figure 8.10:Serial loop arrangement

In comparison with the ‘looped’ type Coriolis mass flowmeter, the straight through pipe obviously offers a muchlower pressure loss and since it has no bends or loops, it iseasier to clean. Although this design avoids many of theproblems associated with the convoluted tube meter, theflow splitter still causes a pressure drop and an unbalancecan occur due to partial or complete blockage of onesection. In more recent years several manufacturers haveintroduced single straight-tube designs with no bends orsplitters. Currently these are limited to a maximum pipediameter of 50 mm.

Figure 8.11:Two tubes are vibrated at their resonant frequency with sensors placed attwo exactly defined locations at the inlet and outlet of the pipe to detectthe phase of the pipe oscillation

Figure 8.12:At zero flow the oscillation of the system is in phase (courtesy Endress +Hauser)

Figure 8.13:When liquid flows into the system the flowing medium is accelerated onthe inlet (courtesy Endress + Hauser)

Figure 8.14:The flowing medium is decelerated on the outlet and the oscillation of thesystem is out of phase (courtesy Endress + Hauser)

Chapter 8: Mass flow measurementSummary of Coriolis mass measurement

AdvantagesCoriolis meters provide direct, in-line and accurate massflow measurements of both liquids and gases. Accuraciescan be as high as 0,1% for liquids and 0,5% for gases.The measurement is independent of temperature, pressure,viscosity, conductivity and density of the process’s medium.Mass flow, density and temperature can be accessed fromone sensor. They can also be used for almost any applicationirrespective of the density of the process medium.Measurements range from less than 5 g/m to more than350 tons/hr, whilst densities can be measured down to aslittle as 0,0005 g/cc.For critical control, mass flow rate is the preferred methodof measurement and, because of their accuracy, Coriolismeters are becoming common for applications whichrequire tight control. Apart from custody transferapplications, they are used for chemical processes andexpensive fluid handling.

DisadvantagesOn the downside, despite tremendous strides in thetechnology, Coriolis meters are still expensive and manymodels are affected by vibration. Further, currenttechnology limits the upper pipeline diameter to 150 mmand secondary containment can be an area of concern.

Thermal mass flow metersThermal mass flow measurement, which dates back to the1930’s, is a quasi-direct method, suited, above all, tomeasuring gas flow. Thermal mass flow meters infer theirmeasurement from the thermal properties of the flowingmedium (such as specific heat and thermal conductivity)and are capable of providing measurements which areproportional to the mass of the medium.In the ranges normally encountered in the process industry,the specific heat c of the gas is essentially independent ofpressure and temperature and is proportional to densityand therefore to mass.The two most common ways of measuring flow usingthermal techniques are to measure the rate of heat lossfrom a heated body in the flow stream; or to measure therise in temperature of the flowing medium when it is heated.

Heat loss or ‘hot wire’ methodIn its simplest form, this method, sometimes referred to ascalorimetric, comprises a hot body (a heated wire,thermistor, or Resistance Temperature Detector) placed inthe main stream of the flow (Figure 8.15). According to thefirst law of thermodynamics, heat may be converted intowork and vice versa. Thus, the electrical power (I2R)supplied to the sensor is equal to the heat convected awayfrom it.Since the molecules (and hence mass) of the flowing gasinteract with the heated boundary layer surrounding thevelocity sensor and convect away the heat, the electricalpower supplied to the sensor is a direct measure of themass flow rate. The rate of heat loss of a small wire isgiven by:

P = hA (Tw - Tf)where:

P = heat loss in wattsTw = wiretemperatureT = fluid temperatureA = surface area of the wireh = heat transfer coefficient

Figure 8.15:Basic schematic of ‘hot wire’ method

The heat transfer coefficiency depends on the wiregeometry, the specific heat thermal conductivity anddensity of the fluid as well as the fluid velocity in thefollowing way: Typically the heat transfer coefficient isgiven by:

where C1 and C2 are constants that depend on the wiregeometry and gas properties. The term indicates thatthe output of the hot wire flow meter is related to theproduct of density and velocity, which can be shown to beproportional to mass flow rate.

In practice, this device can be used only if the mediumtemperature is constant, since the measured electricalresistance of the hot wire cannot determine whether thechange in resistance is the result of a change in flow speedor of a change in medium temperature. To solve thisproblem the temperature of the medium must be used as areference value and a second temperature sensor immersedin the flow to monitor the medium temperature and correctfor temperature changes (Figure 8.16). The mass measuringRTD has a much lower resistance than the temperatureRTD and is self heated by the electronics. In a constanttemperature system, the instrument measures PR andmaintains the temperature differential between the twosensors at a constant level.

Complete hot wire mass flow meters (Figure 8.17) areavailable for pipes up to 200mm diameter(sizeDN200).Above this size, insertion probes, which incorporate acomplete system at the end of a rod, are used.

The main limitation of this methodis thatbyits very’point’measurement, it is affected by the flow profile within thepipe as well as by the medium viscosity and pressure.Further, since the measurement is determined by thethermal characteristics of the medium, the system must

Figure 8.16:A second ‘temperature sensor’ monitors the gas temperature and

Chapter 8: Mass flow measurementbe calibrated for each particular gas—with each mass flow/temperature sensor pair individually calibrated over itsentire flow range.

The measured value itself is primarily non-linear andrequires relatively complex conversion. On the positiveside, however, this inherent non-linearity is responsible forthe instrument’s wide rangeability (1000:1) and low speedsensitivity (60 mm/s).

Figure 8.17:Typical in-line hot wiremass flow meter (courtesySierra Instruments Ltd)

Such instruments also have a fast response to velocitychanges (typically 2 seconds) and provide a high levelsignal, ranging from 0,5 to 8W over the range 0 to 60 m/s.

One of the .limitations of many conventional hot wiresystems is that they soon reach their performance limitswhen higher mass flow speeds need to be detected. Thethermal current into the medium depends on the flow speedand thus a constant heat input would mean that when theflow speed is low there would be abuild-up of heat and acorresponding temperature increase. And at high flowspeeds the temperature differential would be around zero

To overcome this problem, the heat input can be adaptedto the flow speed. This is achieved in the sensor shown inFigure 8.18 which consists of a high thermal-conductiveceramic substrate upon which are deposited a thick filmheating resistor (Rh) and two temperature-dependent thickfilm resistors (T1and T2) (Figure 8.19).

Figure 8.16:Sensor consists of a high thermal-conductive ceramic substrate uponwhich are deposited a thick film heating resistor and two temperature-dependent thick film resistors (courtesy Weber Sensors Group)

Figure 8.19:As the process medium flowsalong the front of the ceramicsubstrate the thermal currentproduced by the heatingresistor forms a temperaturegradient

As the process medium flows along the front of the ceramicsubstrate the thermal current produced by the heatingresistor forms a temperature gradient as illustrated in Figure8.19. The temperature differential between the two resistorsis then used to regulate the current controlling the heatingresistor.

Temperature rise methodIn this method, the gas flows through a thin tube in whichthe entire gas stream is heated by a constantly poweredsource — with the change in temperature being measuredby RTDs located upstream and downstream of the heatingelement (Figure 8.20). Because of heat requirements thismethod is used for low gas flows.

Here, the mass flow rate qm is:

The main disadvantages of this method is that it is onlysuitable for low gas flows; the sensors are subject to erosionand corrosion; and the multiple tapping points increasechances of leakage.

Figure 8.20:Basic schematic of ‘temperature rise’ method

where:

Chapter 8: Mass flow measurementExternal temperature rise methodAn alternative arrangement places the heating element andtemperature sensors external to the pipe. In thearrangement shown in Figures 8.21 and 8.22, the heatingelements and temperature sensors are combined so thatthe RTD coils are used to direct a constant amount of heatthrough the thin walls of the sensor tube into the gas. Atthe same time, the RTD coils sense changes in temperaturethrough changes in their resistance.

The main advantage of this method is that it provides non-contact, non-intrusive sensing with no obstruction to flow.

Capillary-tube meterIn a typical capillary-tube thermal mass flow meter themedium divides into two paths, one (m2) through thebypass and the other (rrij) through the sensor tube (Figure8.23).

As the name implies, the role of the bypass is to bypass adefined portion of the flow so that a constant ratio of bypassflow to sensor flow (mjm.^ is maintained. This conditionwill only apply iftheflowin the bypass is laminar so thatthe pressure drop across the bypass is linearly proportionalto the bypass flow. An orifice by pass, for example, hasnon-laminar flow so that the ratio of total flow to sensorflow is non-linear.

One solution lies in the use of multiple disks or sinteredfilter elements. Another solution is the bypass element usedby Sierra (Figure 8.24) which consists of a single machinedelement having small rectangular passages with a highlength-to-width ratio. This element provides pure laminarflow and is easily removed and cleaned.

With a linear pressure drop (P1- P2) maintained across thesensor tube, a small fraction of the mass flow passesthrough the sensor tube. The sensor tube has a relativelysmall diameter and

Figure 8.21:Thermal flow meter with external elements and heater

Figure 8.22:In the capillary tube meter the RTD coils are used to direct a constantamount of heat through the thin walls of the sensor tube into the gas(courtesy Sierra Instruments)

Figure 8.23:A typical capillary-tube thermal mass flow meter (courtesy SierraInstruments)

a large length-to-diameter ratio in the range 50:1 to 100:1—both features being characteristic of capillary tubes.

These dimensions reduce the Reynolds number to a levelless than 2 000 to produce a pure laminar flow in whichthe pressure drop (Pl - P2) is linearly proportional to thesensor’s mass flow rate (mj). In operation, the long length-to-diameter ratio of the tube ensures that the entire cross-section of the stream is heated by the coils— with the massflow carrying heat from the upstream coil to thedownstream coil. This means the first law ofthermodynamics can be applied in its simplest form.

This method is largely independent of the flow profile andthe medium viscosity and pressure. It means that the flowcalibration for any gas can be obtained by multiplying theflow calibration for a convenient reference gas by a constantK-factor. K-factors are now available for over 300 gases,giving capillary-tube meters almost universal applicability.

Although the output is not intrinsically linear with massflow, it is nearly linear over the normal operating range.Accurate linearity is achieved with multiple-breakpointlinearisation (for example at 0,25,50,75 and 100% of fullscale). In addition to its applicability to very low gas flows,the capillary tube method can also be used for larger flowsby changing the bypass to effect a higher or lower value ofthe bypass ratio (ir^/nij).

Liquid mass flowAlthough the main application of the thermal mass flowmeter lies with gases, the same technology can also beapplied to the measurement of very low liquid flows, for

Figure 8.24:Single machined elements having small rectangular passages with a highlength-to-width ratio provide pure laminar flow and are easily removedand cleaned (courtesy Sierra instruments)

Chapter 8: Mass flow measurement

Figure 8.25:A typical liquid thermal mass flow meter (courtesy Brookes-Rosemount)

example, down to 30 grams/hour. A typical meter is shownin Figure 8.25. Here, die inlet and outlet of the sensor tubeare maintained at a constant temperature by a heat sink —with the mid-point of the sensor tube heated to a controlledlevel for example, 20°C above the temperature of the inlet-outlet heat sink. These two locations, together with theflow tube, are mechanically connected by a thermallyconductive path.

In this manner, the flowing fluid is slightly heated andcooled along the sensor zones, 1 and 2 respectively, tocreate an energy flow perpendicular to the flow tube. TwoRTDs (T, and T2), located at the mid-point of the sensortube determine the temperature difference. Thistemperature difference is directly proportional to the energyflow and is, therefore, directly proportional to the massflow times the specific heat of the fluid.

Chapter 9: Open channel flow measurementIn many applications, liquid media are distributed in openchannels. Open channels are found extensively in waterirrigation schemes, sewage processing and effluent control,water treatment and mining beneficiation.

The most commonly used method of measuring flow in anopen channel is through the use of an hydraulic structure(known as a primary measuringdevice) which changes thelevel of the liquid. By selecting the shape and dimensionsof the primary device (a form of restriction) the rate offlow through or over the restriction will be related to theliquid level in a known manner. In this manner, a secondarymeasuring element may be used to measure the upstreamdepth and infer the flow rate in the open channel.

To ensure that the flow rate can be expressed as a functionof the head over the restriction, all such structures aredesigned so that the liquid level on the upstream side israised to make the discharge independent of thedownstream level. The two primary devices in general useare the weir and the flume.

The weirA weir (Figure 9.1 is essentially a dam mounted at rightangles to the direction of flow, over which the liquid flows.

Figure 9.1:A basic weir—essentially a dam mounted at right angles to the directionof flow

The dam usually comprises a notched metal plate—the threemost commonly used being the rectangular weir, thetriangular (or V-notch) weir and the trapezoidal (or Cipolletti)weir—each with an associated equation for determiningthe flow rate over the weir that is based on the depth ofthe upstream pool. The crest of the weir, the edge or surfaceover which the liquid passes, is bevelled—with a sharpupstream corner. The depth (h) of the flow over the crestof the weir (Figure 9.2) is

Figure 9.2:For accurate flow measurement, the nappe should have sufficient fall

known as the ‘head’ and is usually measured some distanceupstream of the plate (>4 x h) where the ‘draw-down’ effectis minimal. For the associated equation to hold true andaccurate flow measurement to be determined, thestreamofwater leaving the crest (the nappe), should have sufficientfall (Figure 9.2). This is called free or critical flow, with airflowing freely beneath the nappe so that it is aerated.Should the level of the downstream water rise to a pointwhere the nappe is not ventilated, the discharge rate willbe inaccurate and dependable measurements cannot beexpected.

Figure 9.3:Rectangular weir (a) with nocontraction; and (b) withlateral contraction

Rectangular weirThe rectangular weir was the earliest type in use and dueto its simplicity and ease of construction is still the mostpopular.

In its simplest form (Figure 9.3 (a)), the weir extends acrossthe entire width of the channel with no lateral contraction.The discharge equation (head versus flow rate) of such arestriction, without end contractions, is:

q = k L h1.5

where:q = flow ratek = constantL = length of cresth = the head measured upstream a distance of

> 4 x headGenerally, this means that for a 1% change in flow, therewill be a 0,7% change in the level.

A problem with rectangular weirs without contraction isthat the air supply can become restricted and the nappeclings to the crest. In such cases a contracted rectangularweir (Figure 9.3 (b)) is used where end contractions reducethe width and accelerate the channel flow as it passes overthe weir and provides the needed ventilation. In this casethe discharge equation of such a restriction, with endcontractions, becomes:

q = k (L-0,2h) h1’5 where:q = flow ratek = constant (how is k evaluated)L = length of cresth = the head

The rectangular weir can handle flow rates in the range1:20 from about 0 - 15 1/s to 10 000 Vs or more (3m crestlength).

Chapter 9: Open channel flow measurementTrapezoidal (Cipolletti) weirIn the trapezoidal type of weir (Figure 9.4) the sides areinclined to produce a trapezoidal opening. When the sidesslope one horizontal to four vertical the weir is known as aCipolletti weir and its discharge equation (head versus flowrate) is similar to that of a rectangular weir with no endcontractions:

q = k L h1.5

The trapezoidal type of weir has the same flow range as arectangular weir.

Figure 9.4:The trapezoidal or Cipolletti weir

Triangular or V- notch weirThe V-notch weir (Figure 9.5) comprises an angular v-shaped notch—usually of 90°—and is well suited to lowflows.

A major problem with both the rectangular and trapezoidaltype weirs is that at low flow rates the nappe clings to thecrest and reduces the accuracy of the measurement. In theV-notch weir, however, the head required for a small flowis greater than that required for other types of weirs andfreely clears the crest— even at small flow rates.

The discharge equation of the V-notch weir is given by:

q = k h2.5

where:

q = flow ratek = constanth - the head

This equates to a 0,4 % change in height for a 1 % changein flow. V-notch weirs are suitable for flow rates between 2and 100 I/s and, for good edge conditions, provide anaccuracy of 2-3%. Higher flow rates can be obtained byplacing a number of triangular weirs in parallel. The mainproblem with the V-notch is that it is easily blocked bydebris.

Figure 9.5:The triangular or V- notch weir

Application limitationsThere is a high unrecoverable pressure loss with weirs.This may not be a problem in most applications, however,with the operation of a weir, the flow must clear the weiron departure. If the liquid is not free flowing and there isback pressure obstructing the free flow, then the level overthe weir is affected and, therefore, the level and flowmeasurement. Apart from their simple operation weirs havea good rangeability—capable of detecting high and lowflows.

On the negative side weirs have a high pressure loss andencourage the build-up of silt.

The flumeThe second class of primary device in general use is theflume (Figure 9.6). The main disadvantage of flow meteringwith weirs is that the water must be dammed, which maycause changes in the inflow region. Further, weirs sufferfrom the effects of silt build-up on the upside stream. Incontrast, a flume measures flow in an open channel in whicha specially shaped flow section restricts the channel areaand/or changes the channel slope to produce an increasedvelocity and a change in the level of the liquid flowingthrough it.

Figure 9.6:Basic flume in which a specially shaped flow section produces an increasedvelocity and a change in the liquid level

Major benefits offered by the flume include: a higher flowrate measurement than for a comparably sized weir; a muchsmaller head loss than a weir; and better suitability forflows containing sediment or solids because the high flowvelocity through the flume tends to make it self-cleaning.

The major disadvantage is that a flume installation istypically more expensive than a weir.

Flume flow considerationsAn important consideration in flumes is the state of theflow. When the flow velocity is low and is due mainly togravity, it is called tranquil or sub-critical. Under theseconditions, to determine the discharge rate, it is necessaryto measure the head in both the approach section and inthe throat.

As the flow velocity increases and the inertial forces areequal to or greater than the gravitational force, the flow istermed critical orsupercritical. For both critical andsupercritical states of flow, a definitive head/dischargerelationship can be established and measurement can bebased on a single head reading.

Venturi flume metersOriginally developed in India by Messrs. Inglis and Crump

Chapter 9: Open channel flow measurementof the Indian Irrigation Service, the rectangular venturiflume (Figure 9.7), with constrictions at the side, is themost commonly used since it is easy to construct. Normallyconsisting of a converging section, a throat section, and adiverging section, standardisation was brought about bythe BST in publication BS 3680 of 1981, Part 4a.

Figure 9.7:Rectangular venturi flume with constrictions at the side

In addition, the throat cross-section can also be trapezoidalor U-shaped. Trapezoidal flumes are more difficult to designand construct, but they provide a wide flow range withlow pressure loss. A U-shaped section is used where theupstream approach sectionis alsoU-shapedandgives highersensitivity— especially at low (tranquil) flows.

Although the theory of operation of flumes is morecomplicated than that of weirs, it can be shown that thevolume flow rate through a rectangular Venturi flume isgiven by:

q = k h 1.5 where:q = the volume flowk = constant determined by the proportions of the flumeh - the upstream fluid depth

Measurement is taken at a point three to four times themaximum head upstream of the inlet.

Parshall venturi flume

Developed in the USA in the 1920’s by R. Parshall for use inthe waste water industry, the Parshall Venturi Flume (Figure9.8) differs from conventional flat bottomed venturi flumesin that it incorporates a contoured or stepped floor thatensures the transition from sub-critical to supercritical flow.As shown, the floor is parallel over the inlet section andthen slopes down through the throat section and rises againthrough the discharge stage. This allows it to function overa wide operating range with only a single headmeasurement. The Parshall Venturi flume also has betterself-cleaning properties and relatively low head loss.

Parshall Venturi flumes are manufaetured in a variety offixed sizes and are usually made of glass fibre reinforcedpolyester. Users can install them in existing channels.

Because of its slightly changed shape, the dischargeequation of the Parshall Venturi flume changes slightly to:

Figure 9.8:The Parshall Venturi Flumeincorporates a contouredor stepped floor

q = k hn where:q = flow rateh = the headk and n are constants determined by theproportions of the flume

Generally, the exponent n varies between 1.522 and 1.607,determined mainly by the throat width.

Application limitationsProviding excellent self cleaning properties, the venturiflume has replaced the weir in most applications, and theParshall flume is, at present, possibly the most accurateopen channel flow measuring system with flow ranges from0.15 to 4000 litres/s.

Advantages include: reliable and repeatable measurements;no erosion; insensitive to dirt and debris; low head pressureloss; and simple operation and maintenance. However it ismore expensive than the rectangular Venturi flume andmore difficult to install.

Palmer BowlusThe Palmer Bowlus flume (Figure 9.9) was developed inthe USA in 1936 for use in waste water treatment and itsname derives from the inventors, Messrs. Palmer andBowlus. As shown it comprises a U-sectioned channel witha trapezoidal throat section and a raised invert. Its mainadvantage is its ability to match up to circular pipes and itcan be fitted inside existing pipes in special applications.Flow ranges from 0.3 to 3500 litres/s.

Khafagi flumeSimilar to the Venturi flume the Khafagi flume (Figure 9.10)does not have a parallel throat section. Instead, the throat

Figure 9.9:The Palmer Bowlus flume comprises a U-sectioned channel with atrapezoidal throat section and a raised invert (courtesy Neupiast)

Chapter 9: Open channel flow measurementsection is that point at which the inlet section meets thecurve of the divergent discharge section. The floor ishorizontal throughout its length. Flow range is from 0.25to 1500 litres/s.

Figure 9.10:The Khafagi flume does not have a parallel throat section

Level measurementA weir or a flume restrict the flow and generate a liquidlevel which is related to flow rate. A secondary device istherefore required to measure this level. Several measuringmethods exist:

UltrasonicsThe most popular method is ultrasonic level measurement.This makes use of a transducer, located above the channel,which transmits a burst of ultrasonic energy that is reflectedfrom the surface of the water (Figure 9.11). The time delayfrom the transmitted pulse to the received echo is convertedinto distance and hence determines the liquid level.

Figure 9.11:Ultrasonic levelmeasurement uses atransducer mounted abovethe channel, whichtransmits a burst ofultrasonic energy that isreflected from the liquidsurface (courtesyMilltronics)

Ultrasonic sensors have no contact with the liquid; are easyto install; require minimal maintenance; and are not affectedby grease, suspended solids, silt, and corrosive chemicalsin the flow stream. Modern ultrasonic systems are capableof providing high level measuring accuracies (down to ±0,25%).

Most ultrasonic instruments incorporate built-inlinearisation in which a wide range of differentcompensating curves are stored in the instrument’smemory. During commissioning of the system, users maythen access the correct curve— depending on the type anddimensions of the weir or flume. Manufacturers of fibre-glass flumes are also able to provide suitable linearisationsoftware tailored to the dimensions of their primary devices.

Float measurementFloat measurement is a direct measurement method inwhich the height of the float is proportional to the water

level (Figure 9.12). As illustrated, this height is mechanicallytransmitted via a cable and pulley to rotate a mechanicalcam. The profile of the cam is contoured according to thespecific level-flow rate relationship of the primarymeasuring device being used and thus the position of thecam follower is proportional to flow rate. Alternatively, themechanical movement may be electrically linearised andconverted to a standardised output signal. This method isseldom used and is difficult to calibrate.

Figure 9.12:Float-operated flow meter (courtesy Isco Inc.)

Floats are not only affected by changes in ambient airtemperature, they are also subject to build up of greaseand other deposits that can alter the immersion depth ofthe float and thus affect the measured value. They generallyrequire the use of a stilling well and, since this method hasmoving parts that are subject to wear, periodic maintenanceand repair is required.

Capacitive measuring systemsThe principle of capacitive level measurement is based onthe change in capacitance between an insulated probeimmersed in the liquid and a grounding plate or tube whichis also in contact with the liquid (Figure 9.13).

Figure 9.13:Insulated probe and grounding plate form a capacitor—with the liquidacting as the dielectric (courtesy Endress + Hauser)

The PVC- or Teflon-coated probe and the grounding plateform the plates of a capacitor and the liquid forms thedielectric. As the liquid level changes, it alters the dielectricconstant of the capacitor and, therefore, its capacitance.By measuring the capacitance a reading can be obtained

Chapter 9: Open channel flow measurementand directly related to level and flow.

The main advantages of this system are that there are nomoving parts; no mains power is required at the measuringpoint; and the distance between the probe and the controlroom can be up to 600 m.

The main disadvantage is that accuracy is affected bychanges in the characteristics of the liquid. Further, despitethe very smooth surface of the Teflon or PVC coating, wastewater containing grease can still lead to deposits on themeasuring probe which affect the measured value.

Hydrostatic pressure measurementThis method makes use of a submerged sealed pressuretransducer to measure the hydrostatic pressure of the liquidabove it (Figure 9.1.4). The hydrostatic pressure is the forceexerted by a column of water above a reference point andis proportional to the height.

The transducer comprises a membrane which is firmlyattached to the channel wall—with an oil fill transmittingthe pressure on the membrane to a capacitive meteringcell. Submerged pressure transducers are not affected bywind, steam, turbulence, floating foam and debris, or bydeposits or contamination.

However, because they are submerged, the transducersmay be difficult to install in large channels with high flow,and may

Figure 9.14:Hydrostatic pressure measurement uses a submerged sealed pressuretransducer to measure the hydrostatic pressure of the liquid above it

require periodic maintenance in flow streams with highconcentrations of suspended solids or silt. Further, accuracymay be affected by changes in the temperature of theprocess medium.

Bubble injectionLike the submerged pressure transducer, the bubbleinjection method or ‘bubbler’ measures the hydrostaticpressure of the liquid (Figure 9.IS). The system comprisesa pressure transducer connected to a ‘bubble tube’ whichis located in the flow stream and whose outlet is at thelowest point.

Air or other gas, at a constant pressure, is applied to thetube so that bubbles are released from the end of the bubbletube at a constant rate. The pressure measured by thetransducer, which is required to maintain the bubble rate,is proportional to the liquid level.

Figure 9.15:Bubble injection system (courtesy Baiiey-Fischer + Porter)

Because the pressure transducer is not in contact with thefluid, it is not subject to chemical or mechanical attack. Inaddition, the cost of providing explosion proof protectionis minimal. When used in channels with high concentrationsof grease, suspended solids or silt, bubblers may requireoccasional maintenance—although periodic air purges ofthe bubble tube minimise this problem. Additionalmaintenance is also required to regenerate desiccators thatprevent moisture from being drawn into the air system ofa babbler.

Chapter 10: Common installation practicesIn non-fiscal and non-custody transfer applications, flowmeters are rarely calibrated and are often left in situ for 10or more years without any thought to their accuracy.Further, in too many instances, the initial installation isoften so poorly undertaken, without any regard to basicinstallation practices, that it is highly unlikely that the meterin question ever met the manufacturer’s stated accuracy.The data supplied by most manufacturers is based onsteady flow conditions and installation in long straight pipesboth upstream and downstream of the meter. In practice,most meter installations rarely meet these idealisedrequirements—with bends, elbows, valves, T-junctions,pumps and other discontinuities all producing disturbancesthat have an adverse effect on meter accuracy.Both swirl and distortion of the flow profile can occur—either separately or together. Research has shown that swirlcan persist for distances of up to 100 pipe diameters froma discontinuity whilst in excess of 150 pipe diameters canbe required for a fully developed flow profile to form.

Environmental influencesThe most important feature of a flow meter is that it shouldbe sensitive to flow and as insensitive to environmentalinfluences as possible. The most important environmentalinfluences include:

Fluid temperature

The temperature range of the fluid itself will varyconsiderably

depending on the industry in which it is to be used:

• food industry: 0 to 130°C to withstand CIP (cleaningin place)

• industrial steam, water, gases: 0 to 200 °C• industrial superheated steam: up to 300 °C• industrial outdoor usage: down to -40 °C• cryogenics: down to -200 °C

Pressure pulsationsPressure pulsations can be a problem when measuringliquids since, after they are created, they travel a long waydown the pipeline without being significantly damped. Invortex meters, for example, such symmetrical pulsationscould be detected as a vortex signal.

The insensitivity to such ‘common mode’ pressurefluctuations should, therefore, be at least 15 Pa. Differential

Figure 10.1:A number of flow conditioners or straighteners are available for use in theupstream line to minimise the effects of disturbances

pressure flow measurement systems can be susceptible tocommon mode pressure variations if the connection

systems on either side of the differential pressure cell arenot identical and as short as possible.

VibrationVibration is present on any piece of pipework in industryand is of particular significance in Coriolis and vortexmeters. The vortex frequencies for gas, for example, lie inthe range 5 to 500 Hz. Consequently, vibration inducedsignals in this range cannot be fully filtered out. Wherepossible, therefore, the sensor itself should be insensitiveto pipe vibration.

Flow conditioningWhile the effect of most flow disturbances can be overcomethrough the use of sufficient straight pipe length, upstreamof the meter, this is not always practical. In such cases usecan be made of one of a number of flow conditioners orstraightening vanes or pipes. (Figure 10.1). Straightenersare effective in eliminating swirl and helping to restoregrossly distorted flow profiles. However they cannot,generally, provide the mixing action of fluid layers requiredto normalise a velocity profile and some length of straightpiping is still required downstream of the conditioner toprovide the necessary mixing action.For example, a Vortab Flow Conditioner is 3 diameters long,and requires 4 diameters of straight pipe between it andthe meter. This reduces the total upstream pipe run(including the flow conditioner) to just 7 diameters for anyupstream disturbance. Folded vane and fin typestraightening vanes are normally used on gases whilst thetubular type is normally used on steam or liquids. It isusually recommended that vanes be installed only inextreme cases after all other alternatives have beenexhausted.There is always a danger of straightening vanes comingloose in the flow line and causing serious damage toexpensive equipment. They should be installed as securelyas possible and should be used only for applications wheremoderate line velocities, pressures and temperatures exist.

General installation recommendationsTo ensure reliable flow meter operation, the followingchecklist will minimise problems:• install the meter in the recommended position and

attitude• ensure the measuring tube is completely filled at all

times• when measuring liquids, ensure there is no air or

vapour in the liquid• when measuring gases, ensure there are no liquid

droplets in the gas• to minimise the effects of vibration support the

pipeline on both sides of the flow meter• if necessary, provide filtration upstream of the meter• protect meters from pressure pulsations and flow

surges• install flow control or flow limiters downstream of the

meter• avoid strong electromagnetic fields in the vicinity of

the flow meter• where there is vortex or corkscrew flow, increase

inlet and outlet sections or install flow straighteners• install two or more meters in parallel if the flow rate

is too great for one meter• allow for expansion of the pipework and make sure

there is sufficient clearance for installation andmaintenance work

• where possible provide proving connections

Chapter 10: Common installation practicesdownstream of the meter for regular in-situcalibrations

• to enable meters to be removed for servicing withoutstation shutdown, provide a by-pass line

Figures 10,2 to 10.7 illustrate a number of recommendedinstallation practices laid down specifically forelectromagnetic flow meters. The same principles alsoapply to most other flow metering devices.

TorquingThe role of a gasket is to form a sandwich between theflanges and ensure that the medium flowing through themeter is safely contained.

Figure 10.2:Preferred locations. Since air bubbles collect at the highest point on a piperun, installation of the meter at this point could result in faultymeasurements. The meter should not be installed in a downpipe where thepipe may be drained (courtesy Krohne)

Figure 10.3:In a horizontal pipe run, the meter should be installed in a slightly risingpipe section (courtesy Krohne)

Figure 10.4:Where there is an open discharge, install the meter in a low section of thepipe (courtesy Krohne)

Figure 10.5:In long pipes, always install shutoff valves downstream of the flow meter(courtesy Krohne)

Figure 10.6: Never install a flow meter on the pump suction side(courtesy Krohne)

Figure 10.7:Where a downpipe is 5 m lower than the main inlet pipe, install an airvalve at the highest point (courtesy Krohne)

If the flange bolts are not tightened enough the gasket willleak. If over-tightened, the gasket may become deformed—resulting in a leakage. More seriously, many gaskets (forexample, an O-ring) are recessed, as shown in Figure ]0.8,and are normally tightened until a metal-to-metal contactoccurs. In this case over-tightening can cause deformationof the flanges—leading to possible damage to the meteritself. Ceramic liners, in particular, have been prone todamage through over-tightening as their mechanicalcharacteristics are quite different from metals.

Figure 10.8:Recessed gaskets are normally tightened until a metal-to-metal contactoccurs (courtesy Endress + Hauser)

During commissioning or replacement of a meter, the flangebolts should be tightened only when the maximum processtemperature is reached. Conversely, meters should bedisconnected when the temperature is below 40°C to avoidthe risk of damaging the surface of the gasket.

If a flange connection leaks, despite the fact that the boltsare tight, then they should NOT BE TIGHTENED ANYFURTHER. Loosen the bolts opposite the leak and tightenthe bolts by the leak. If the leak persists, then the sealshould be checked for foreign objects trapped in between.

The torque values given in Table 10.1 are based on greasedbolts and serve as guidelines only since they depend onthe material from which the bolts are manufactured.

EarthingTo ensure measuring accuracy and avoid corrosion damageto the electrodes of electromagnetic flow meters, the sensorand the process medium must be at the same electricalpotential. This is achieved by earthing the primary head aswell as the pipeline by any one or more of a number ofmethods including: earthing straps, ground rings, liningprotectors and earthing electrodes.

Chapter 10: Common installation practices

Torque values DIN in Nm

DN PN Bolts Klingerite Soft rubber PTFE

15 40 4xM12 1520 4xM12 25

25 4xM12 25 5 3332 4xM16 40 “ 5340 4xM16 50 8 6750 4xM16 64 “ 8465 16 4xM16 87 11 11480 8xM16 53 “ 11100 “ 8xM16 65 15 7025 8xM16 80 22 85150 8xM20 110 14 103200 12xM20 108 22 140

30 1374853

250 12xM20 104/125 29/56 139/166300 12xM20 191/170 39/78 159/227350 16xM20 141/193 39/79 188/258400 16xM24 191/245 59/111 255/326450 10/16 20xM24 170/251 58/111 227/335500 20xM24 197/347 70/152 262/463600 “ 20xM27 261/529 107/236 348/706700 24xM27 312/355 122/235 “800 24xM30 417/471 173/330900 28xM30 399/451 183/3491000 28xM33 513/644 245/470

Table 10.1:Torque values based on greasedbolts for various gaskets (courtesyEndress + Hauser)

Figure 10.10:Earthing for conductive unlined and lined pipe with lining protectors(courtesy Fisher Rosemount)

Figure 10.12:Earthing for conductive lined pipe with earthing rings (courtesy FisherRosemount)

Figure 10.9:Earthing for conductive unlined pipe and conductive pipe with earthingelectrode (courtesy Fisher Rosemount)

Figure 10.11:Earthing for non-conductive pipe with earthing rings (courtesy FisherRosemount)

Chapter 10: Common installation practices

Figure 10.13:Earthing for non-conductive lined pipe with earthing electrodes (courtesyFisher Rosemount)

Improper earthing is one of the most frequent causes ofproblems in installations. If the earthing is not symmetrical,earth loop currents give rise to interference voltages—producing zero-point shifts. Figures 10.9 to 10.13 showthe most effective earthing configurations.

Figure 10.14:Cathodic protection installations (Courtesy Fisher Rosemount)

It is essential in cathodic protection installations to ensurethat there is an electrical connection between the two pipingruns using earthing rings or electrodes. It is also essentialthat no connection is made to earth.

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Electronic Reprint ofMike Crabtree’s Flow Handbook - 2nd editionIssued November 2000