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This article is excerpted from D. Wadlow, Chapter 28.4 Turbine and vane flowmeters, In J.G. Webster (ed.), The Measurement, Instrumentation and Sensors Handbook, Boca Raton, FL: CRC Press, Dec. 1998, and is reproduced here by kind permission of CRC Press, LLC.
This article describes the applications, performance characteristics, mode and theory of operation, calibration, installation and maintenance procedures and the design and construction of axial turbine flowmeters, including two dual rotor axial turbine designs, propeller meters and spirometers. The article also includes descriptions of insertion axial turbines and multi-jet turbines.
The modern axial turbine flowmeter, when properly installed and
calibrated, is a reliable device capable of providing the highest
accuracies attainable by any currently available flow sensor for
both liquid and gas volumetric flow measurement. It is the product
of decades of intensive innovation and refinements to the original
axial vaned flowmeter principle first credited to Woltman in 1790,
and at that time applied to measuring water flow. The initial
impetus for the modern development activity was largely the increasing
needs of the US natural gas industry in the late 1940's and 50's
for a means to accurately measure the flow in large diameter,
high pressure, interstate natural gas lines. Today, due to the
tremendous success of this principle, axial turbine flowmeters
of different and often proprietary designs are used for a variety
of applications where accuracy, reliability and rangeability are
required in numerous major industries besides water and natural
gas including oil, petrochemical, chemical process, cryogenics,
milk and beverage, aerospace, biomedical and others.
Figure 1. Longitudinal section of an axial turbine flowmeter depicting the key components. The flowmeter body is usually a magnetically transparent stainless steel such as 304. Common end-fittings include face flanges (depicted), various threaded fittings and tri-clover fittings. The upstream and downstream diffusers are the same in bi-directional meters, and generally supported by 3 or more flat plates, or sometimes tubular structures, aligned with the body and which also act as flow straighteners. The relative size of the annular flow passage at the rotor varies among different designs. Journal rotor bearings are frequently used for liquids, while ball bearings are often used for gases. Magnetic reluctance pickups (depicted) are frequently used. Others types include mechanical and modulated carrier pickups. (1) End fitting - flange type shown; (2) Flowmeter body; (3) Rotation pickup - magnetic reluctance type shown; (4) Permanent magnet; (5) Pickup coil wound on pole piece; (6) Rotor blade; (7) Rotor hub; (8) Rotor shaft bearing - journal type shown; (9) Rotor shaft; (10) Diffuser support and flow straightener; (11) Diffuser; (12) Flow conditioning plate (dotted) - optional with some meters.
Figure 1 is a schematic longitudinal section through the axis of symmetry depicting the key components of a typical meter. As one can see, the meter is an inline sensor comprising a single turbine rotor, concentrically mounted on a shaft within a cylindrical housing through which the flow passes. The shaft or shaft bearings are located by end supports inside suspended upstream and downstream aerodynamic structures called diffusers, stators or simply cones. The flow thus passes through an annular region occupied by the rotor blades. The blades, which are usually flat but may be slightly twisted, are inclined at an angle to the incident flow velocity and hence experience a torque which drives the rotor. The rate of rotation, which can be up to several X 104 RPM for smaller meters, is detected by a pickup, which is usually a magnetic type, and registration of each rotor blade passing infers the passage of a fixed volume of fluid.
Axial turbines perform best when measuring clean, conditioned,
steady flows of gases and liquids with low kinematic viscosities
(below about 10-5 m2s-1, 10 cSt,
although they are used up to 10-4 m2s-1,
100 cSt), and are linear for subsonic, turbulent flows. Under
these conditions the inherent mechanical stability of the meter
design gives rise to excellent repeatability performance. Not
including the special case of water meters, which are described
later, the main performance characteristics are:
0.1%
of reading for liquids and 0.25%
for gases with up to 0.02%
for high accuracy meters. Typical linearities, (before electronic
linearization), are between 0.25%
to 0.5%
of reading for liquids and 0.5%
and 1.0%
for gases. High accuracy meters have linearities of 0.15% for
liquids and 0.25% for gases, usually specified over a 10:1 dynamic
range below maximum rated flow. Traceability to NIST (National
Institute of Standards and Technology) is frequently available
allowing one to estimate the overall absolute accuracy performance
of a flowmeter under specified conditions. Under ideal conditions,
absolute accuracies for optimum designs and installations can
come close to the accuracy capabilities at the NIST, which are
stated as 0.13%
for liquid flows and 0.25%
for air.
There are two approaches described in the current literature for analyzing axial turbine performance. The first approach describes the fluid driving torque in terms of momentum exchange, while the second describes it in terms of aerodynamic lift via airfoil theory. The former approach has the advantage that it readily produces analytical results describing basic operation, some of which have not appeared via airfoil analysis. The latter approach has the advantage that it allows more complete descriptions using fewer approximations. However, it is mathematically intensive and leads rapidly into computer generated solutions. One prominent pioneer of the momentum approach is Lee [1] who, using this approach, later went on to invent one of the few, currently successful, dual rotor turbine flowmeters, while Thompson and Grey [2] provided one of the most comprehensive models currently available using the airfoil approach, which for instance, took into account blade interference effects. In the following, I have used the momentum exchange approach to highlight the basic concepts of the axial turbine flowmeter.
In a hypothetical situation, where there are no forces acting
to slow down the rotor, it will rotate at a speed which exactly
maintains the fluid flow velocity vector at the blade surfaces.
Figure 2. Vector diagram for a flat-bladed axial turbine rotor. The difference between the ideal (subscript i) and actual tangential velocity vectors is the rotor slip velocity and is caused by the net effect of the rotor retarding torques. This gives rise to linearity errors and creates swirl in the exit flow. V incident fluid velocity vector; VE exit fluid velocity vector;exit flow swirl angle due to rotor retarding torques;
blade pitch angle, same as angle of attack for parallel flow;
rotor angular velocity vector; r rotor radius vector; F flow induced drag force acting on each blade surface; c blade chord; s blade spacing along the hub; c/s rotor solidity factor.
Figure 2 is a vector diagram for a flat bladed rotor with a blade
pitch angle equal to .
Assuming that the rotor blades are flat and that the velocity
is everywhere uniform and parallel to the rotor axis, then referring
to figure 2:
When one introduces the total flow rate this becomes:
where 
is the 'ideal' rotational speed, Q is the volumetric flow rate,
A is the area of the annular flow cross section and 
is now the root-mean-square of the inner and outer blade radii,
(R, a). Eliminating the time dimension from the left hand side
quantity reduces it to the number of rotor rotations per unit
fluid volume, which is essentially the flowmeter K factor specified
by most manufacturers. Hence, according to Eq. (2), in the ideal
situation the meter response is perfectly linear and determined
only by geometry. (In some flowmeter designs the rotor blades
are helically twisted to improve efficiency. This is especially
true of blades with large radius ratios, (R/a). If the flow velocity
profile is assumed to be flat, then the blade angle in this case
may be described by tan
=constant X r. This is sometimes called the 'ideal' helical blade.)
In practice, there are instead a number of rotor retarding torques
of varying relative magnitudes. Under steady flow the rotor assumes
a speed which satisfies the following equilibrium:
Referring again to figure 2, the difference between the actual
rotor speed, r,
and the ideal rotor speed, 
,
is the rotor slip velocity due to the combined effect of all the
rotor retarding torques as described in Eq. (3), and as a result
of which the fluid velocity vector is deflected through an exit
or swirl angle, .
Denoting the radius variable by r, and equating the total
rate of change of angular momentum of the fluid passing through
the rotor to the retarding torque, one obtains:
which yields:
where 
is the fluid density and NT is the total
retarding torque. Combining Eqs. (1) and (4) and rearranging,
yields:
The trends evident in Eq. (5) reflect the characteristic decline
in meter response at very low flows and why lower friction bearings
and lower drag pickups tend to be used in gas versus liquid applications
and small diameter meters. In most flowmeter designs, especially
for liquids, the latter three of the four retarding torques described
in Eq. (3) are small under normal operating conditions compared
with the torque due to induced drag across the blade surfaces.
As shown in figure 2, the force, F, due to this effect
acts in a direction along the blade surface and has a magnitude
given by:
where CD is the drag coefficient and S
is the blade surface area per side. Using the expression for drag
coefficient corresponding to turbulent flow, selected by Pate
et al. [3] and others, this force may be
estimated by:
where Re is the flow Reynolds number based on the blade chord
shown as dimension c in figure 2. Assuming
is small compared with ,
then after integration, the magnitude of the retarding torque
due to the induced drag along the blade surfaces of a rotor with
n blades is found to be:
Combining Eqs. (7) and (5), and rearranging yields:
Eq. (8) is an approximate expression for K factor because it neglects
the effects of several of the rotor retarding torques, and a number
of important detailed meter design and aerodynamic factors, such
as rotor solidity and flow velocity profile. Nevertheless, it
reveals that linearity variations under normal, specified operating
conditions are a function of certain basic geometric factors and
Reynolds number. These results reflect general trends which influence
design and calibration. Additionally, the marked departure from
an approximate 
(actually
via
Re in Eq.(6)) dependence of the fluid drag retarding torque on
flow properties under turbulent flow, to other relationships under
transitional and laminar flow, gives rise to major variations
in the K factor versus flow rate and media properties for low
flow Reynolds numbers. This is the key reason why axial turbine
flowmeters are generally recommended for turbulent flow measurement.
Axial turbine flowmeters have a working dynamic range of at least
10:1 over which the linearity is specified. The maximum flow rate
is determined by design factors related to size versus maximum
pressure drop and maximum rotor speed. The minimum of the range
is determined by the linearity specification itself. Due to small,
unavoidable, manufacturing variances, linearity error curves are
unique to individual meters and are normally provided by the manufacturer.
However, although recommended where possible, the conditions of
the application cannot usually and need not necessarily duplicate
those of the initial or even subsequent calibrations. This has
pivotal importance in applications where actual operating conditions
are extreme or the medium is expensive or difficult to handle.
Figure 3. A typical single rotor axial turbine linearity error, or calibration, curve for a low viscosity fluid showing the main alternative presentations in current use. Higher accuracy specifications usually correspond to a 10:1 flow range down from Qmax, while extended operating ranges usually correspond to reduced accuracies. The hump in the depicted curve is a characteristic feature caused by flow velocity profile changes as Re approaches the laminar region. This feature varies in magnitude between meters. Sensitivity and repeatability performance degrades at low Re. Percent registration is only used with meters which have mechanical pickups. All other meters have a K factor. UVC and Re calibrations remain in effect at different known media viscosities provided Re or f/v stays within the specified range. Re is referenced to the connecting conduit diameter and is less within the flowmeter. The Re range shown is therefore approximate and can vary by an order of magnitude depending on the meter. Linearity error may also be expressed in terms of Strouhal number (fD/V) versus Re (VD/v) or Roshko number (fD2/v ), when instead D is a flowmeter reference diameter, [4].
Figure 3 depicts a typically shaped calibration curve of linearity
versus flow rate expressed in terms of multiple alternative measures,
various combinations of which may be found in current use. The
vertical axis thus represents either the linearity error as a
percentage of flow rate, a K factor expressed in terms of the
number of pulses from the rotation sensor output per volume of
fluid or the deviation from 100% registration; the latter only
applying to flowmeters with mechanical pickups. The horizontal
axis may be expressed in terms of flow rate in volume units/time,
Reynolds number, (Re), or pulse frequency (from the rotation sensor
for non-mechanical) divided by kinematic viscosity, (f/v),
in units of Hz per m2s-1 , (Hz/cSt or Hz/SSU;
10-6 m2s-1 = 1 centistoke 
31.0
seconds Saybolt Universal), and where kinematic viscosity is the
ratio of absolute viscosity (u) to density. Calibrations
are preferably expressed versus Re or f/v, which
is proportional to Re. The hump shown in the curve is a characteristic
frequently observed at lower Re and is due to velocity profile
effects. K factor versus f/v calibration curves are specifically
called universal viscosity curves (UVC) and for most meters are
available from the manufacturer for an extra charge. A key utility
of UVC is that where media type and properties differ significantly
from those of the original calibration, accuracies much greater
than the overall linearity error can still readily be obtained
via the flowmeters UVC if the kinematic viscosity of the application
is known. An alternative, advanced calibration technique [4],
is to provide response in terms of Strouhal number versus Re or
Roshko number. This approach is not widely adopted, but it is
particularly relevant to high accuracy and extreme temperature
applications because it further allows correct compensation for
flowmeter thermal expansion errors.
The accuracy of axial turbine flowmeters is reduced by unconditioned flow, especially swirl. An installation incorporating flow conditioners along with specific upstream and downstream straight pipe lengths is generally recommended, [5]. Some axial turbine flowmeters can be purchased with additional large flow straighteners that mount directly ahead of the flowmeter body or conditioning plates which are integral to the body. The manufacturer is the first source of information regarding installation. Errors due to flow velocity pulsations are another concern, particularly in certain gas installations. However no standard technique for effectively counteracting this source of error has yet been adopted. Periodic maintenance, testing and recalibration is required because the calibration will shift over time due to wear, damage or contamination. For certain applications, especially those involving custody transfer of oil and natural gas, national standards, international standards and other recommendations exist which specify the minimum requirements for turbine meters with respect to these aspects, [6, 7, 8, 9, 10].
There are numerous, often proprietary, designs incorporating variations
in rotors, bearings, pickups and other components in format and
materials which are tailored to different applications. Meter
bodies are available with a wide range of standard end-fittings.
Within application constraints, the primary objective is usually
to optimize the overall mechanical stability and fit in order
to achieve good repeatability performance. Design for performance,
application and manufacture considerations impact every internal
component, but most of all the rotor with respect to blade shape
and pitch, blade count, balance and rigidity versus, drag, stress
and inertia, bearings with respect to precision versus friction,
speed rating and durability and rotation pickup versus performance
and drag.
Most low radius ratio blades are machined flat, while high ratio
blades tend to be twisted. The blade count varies from about 6
to 20 or more depending on the pitch angle and blade radius ratio
so that the required rotor solidity is achieved. Rotor solidity
is a measure of the 'openness' to the flow such that higher solidity
rotors are more highly coupled to the flow and achieve a better
dynamic range. The pitch angle, which primarily determines the
rotor speed, is typically 30o to 45o but
may be lower in flowmeters designed for low density gas applications.
Rotor assemblies are usually a close fit to the inside of the
housing. In large diameter meters the rotor often incorporates
a shroud around the outer perimeter for enhanced stability. Also,
since large meters are often used for heavy petroleum products,
via selection of a suitable wall clearance, the fluid drag resulting
from this clearance gap is often designed to offset the tendency
at high media viscosities for the meter to speed up at lower Reynolds
numbers. The materials of construction range from non magnetic
to magnetic steels to plastics.
Stainless steel ball bearings tend to be used for gas meters and
low lubricity liquids such as cryogenic liquids and freon, while
combination tungsten carbide or ceramic journal and thrust bearings
are often considered best for many other liquid meters depending
on the medium lubricity. Fluid bearings (sometimes called 'bearingless'
designs) are often used in conjunction with the latter, but also
sometimes with gases, for reducing the drag. They operate by various
designs which use flow induced forces to balance the rotor away
from the shaft ends. Bearing lubrication is either derived from
the metered medium or an internal or external system is provided.
The more fragile, jeweled pivot bearings are also used in certain
gas applications and small meters. Sanitary meters may incorporate
flush holes in the bearing assembly to meet 3A crack and crevice
standards.
The most common types of rotation sensor are magnetic, modulated carrier and mechanical, while optical, capacitative and electrical resistance are also used. In research, a modulated nuclear radiation flux rotation sensor for use in certain nuclear reactors has also been reported, [11, 12]. Mechanical pickups, which sometimes incorporate a magnetic coupling, are traditional in some applications, can have high resolution and one advantage that they require no electrical power. However the pickup drag tends to be high. The magnetic and modulated carrier types utilize at least a coil in a pickup assembly which screws into the meter housing near the rotor. In magnetic inductance types, which are now less common, the blades or shroud carry magnetized inserts, and signals are induced in the coil by the traversing magnetic fields. In the more prevalent magnetic reluctance type, an example of which is schematically depicted in figure 1, the coil is wrapped around a permanent magnet or magnet pole piece in the pickup assembly which is mounted next to a high magnetic permeability bladed rotor (or machined shroud). The latter is then typically made of a magnetic grade of stainless steel such as 416, 430 or 17-4Ph. As the rotor turns, the reluctance of the magnetic circuit varies producing signals at the coil. In the more expensive modulated carrier types, the rotor need only be electrically conductive. The coil is part of a radio frequency, (RF), oscillator circuit and proximity of the rotor blades changes the circuit impedance giving rise to modulation at a lower frequency which is recovered. The RF types have much lower drag, higher signal levels at low flow and can operate at temperatures above the Curie point of typical ferromagnetic materials. They are preferred for wide dynamic range and high temperature applications. Bi-directional flowmeters, usually have two magnetic pickups to determine flow direction. This is useful, for example, in the monitoring of container filling and emptying operations often encountered in sanitary applications. Multiple magnetic pickups are also used in some designs to provide increased measurement resolution. Regarding output, various pulse amplifiers, totalizers, flow computers for gas pressure and temperature correction, along with 4-20 mA and other standard interface protocols, are available to suit particular applications. As an example of advanced transmitters, at least one manufacturer provides a real-time, miniature, reprogrammable, 'smart' transmitter which is integrated into the pickup housing along with a meter body temperature sensor, for full viscosity compensation and UVC linearization. These are for use in dedicated applications, such as airborne fuel management, where the medium viscosity-temperature relationship is known.
Certain applications have uniquely different design requirements and solutions, and two are discussed separately in the following.
Propeller meters are used in either municipal, irrigation or waste
water measurement. Although in some designs propeller and turbine
meters look almost identical and operate on the same axial rotor
principle, this type of flowmeter is currently commercially and
officially, [13, 14],
distinguished as a separate category distinct from the axial turbine.
Diameters of up to 2440 mm (96'') are available. The flow rate
capacity of a 1800 mm (72") diameter propeller meter is up
to about 25,000 m3/hr, (110,000 gpm). Typical accuracies
are 2%
of reading. A primary requirement is ruggedness, and it is in
the designs most suited to harsh environments that the formats
are most distinctive. Rotor and pickup assemblies are generally
flanged to the housing and removable. The rotors have large clearances,
are often cantilevered into the flow, and supported via a sealed
bearing without stators. The rotors are typically made of plastic
or rubber and carry as few as 3 highly twisted, high radius ratio
blades. Pickups are always mechanical and frequently have magnetic
couplings.
Monitoring spirometers measure the volumes of gas flows entering and leaving the lungs and may also be incorporated in ventilator circuits. Diagnostic spirometers are used to monitor the degree and nature of respiration. With these a clinician may determine patient respiratory condition by various measures and clinical maneuvers. Low cost, light weight, speed of response and patient safety are major considerations. Measurement capabilities include the gas volume of a single exhalation and also the peak expiratory flow for diagnostic types, measured in liters and liters per second, respectively. Various technologies are used. However, the Wright respirometer, named after the original inventor [15], today refers to a type of hand-held monitoring spirometer which utilizes a special type of tangential turbine transducer with a two bladed rotor connected to a mechanical pickup and a dial readout for the volume. These particular spirometers are routinely used by respiratory therapists for patient weaning and ventilator checking. Other axial turbine based flowmeters are available for ventilation measurements involving, for example, patient metabolics measurements. One axial turbine based diagnostic spirometer made by Micro Medical, Ltd utilizes an infrared, optical pickup and has a battery powered microprocessor controlled display. In these medical devices, rotors tend to be plastic with a large blade radius ratio. Flow conditioning is minimal or absent. The meters are typically accurate to a few percent of reading. In the U.S. spirometers are designated as class 2 medical devices and as such certain FDA approvals are required concerning manufacture and marketing. In the EU they are class IIb medical devices under a different system and other approvals are required.
Dual rotor axial turbines have performance features not found in single rotor designs.
In 1981 Lee et al. [16] were issued a US patent for a self-correcting, self-checking dual rotor turbine flowmeter which is currently manufactured exclusively by Equimeter, Inc. and sold as the Auto-Adjust. This is a high accuracy flowmeter primarily intended for use on large natural gas lines where even small undetected flow measurement errors can be costly. It incorporates two closely coupled turbine rotors which rotate in the same direction. The upstream rotor is the main rotor and the second rotor, which has a much shallower blade angle, is the sensor rotor. Continuous and automatic correction of measurement errors due to varying bearing friction is achieved by calculating the flow rate based on the difference between the rotor speeds. As shown in figure 2 and discussed in the theory section, the flow exit angle is due to the net rotor retarding torque. If this torque increases in the main rotor, thereby reducing its speed, the exit angle increases and the speed of the sensor rotor is then also reduced. The meter is also insensitive to inlet swirl angle, because the swirl affects both rotor speeds in the same sense and the effect is then subtracted in the flow calculation. The meter also checks itself for wear and faults by monitoring the ratio of the two rotor speeds and comparing this number with the installation value, [17].
A dual rotor liquid flowmeter, invented by Ruffner et al. [18],
was introduced by Exact Flow, LLC. It is offered as a high accuracy
flowmeter, (up to 0.1%
linearity and 0.02%
repeatability), which has an extraordinarily wide dynamic range
of 500:1 with a single viscosity liquid. This flowmeter had early
commercial success in fuel flow measurement in large jet engine
test stands where the wide dynamic range is particularly useful,
[19]. The meter comprises two, closely
and hydraulically coupled rotors which rotate in opposite directions.
Due to the exit angle generated by the first rotor, the second
rotor continues to rotate to much lower flow rates compared with
the first.
A differential pressure producing flowmeter such as a venturimeter
in series with a turbine is known to be a technically appropriate
and straightforward method for measuring the volumetric and mass
flow rates of some fine, solid aerosols. However, this section
highlights a current research area in the application of axial
rotor turbine meters to a range of industrial flow measurement
problems where gas/liquid, two phase flows are encountered. Customarily
turbine meters are not designed for and cannot measure such flows
accurately. Errors of the order 10% arise in metering liquids
with void fractions of around 20%. Such flows are normally measured
after gas separators. Although this problem is not restricted
to these industries, the current main impetuses for the research
are the direct measurement of crude oil in offshore multiphase
production systems, the measurement of water/steam mixtures in
the cooling loops of nuclear reactors and the measurement of freon
liquid-vapor flows in refrigeration and air conditioning equipment.
Several techniques investigated so far use an auxiliary sensor.
This may either be a void fraction sensor or a pressure drop device
such as a venturimeter or drag disk, of which the pressure drop
approach appears to be technically more promising, [20,
21]. Also from a practical standpoint,
gamma densitometers for measuring void fraction are additional
and expensive equipment and not for instance, well adapted for
use in undersea oil fields. Two techniques currently studied do
not require an auxiliary in-line sensor. The first uses the turbine
meter itself as the drag body and combines the output of the turbine
with that of a small differential pressure sensor connected across
the inlet and outlet regions. This technique requires a homogenizer
ahead of the turbine and measurement accuracies of 3%
for the volumetric flow rates of both phases have recently been
reported for air/water mixtures up to a void fraction of 80%,
[22]. The second technique is based entirely
on analysis of the turbine output signal and has provided significant
correlations of the signal fluctuations with void fraction. Accuracies
of water volumetric flow rate measurement of 2%
have been reported when using air/water mixtures with void fractions
of up to 25%, [23].
These flowmeters comprise a small axial rotor mounted on a stem
which is inserted radially through the conduit wall, often through
a shut-off valve. They measure the flow velocity at the rotor
position from which the volumetric flow rate is inferred. They
are an economical solution to flow measurement problems where
pipe diameters are high and accuracy requirements are moderate,
and also may be technically preferred where negligible pressure
drop is an advantage, as in high speed flows. They are typically
more linear than insertion tangential turbine flowmeters and compete
also with magnetic and vortex shedding insertion flowmeters. They
are available for the measurement of a range of liquids and gases,
including steam, similar to the media range of full bore axial
turbines, and have a similarly linear response. The rotors, which
are usually metal but can be plastic, typically have diameters
of 25 mm to 51 mm (1'' to 2''). They can be inserted into pipes
with diameters ranging from 51 mm to 2032 mm (2'' to 80''). Velocity
measurement ranges cover 0.046 m.s-1 to 91 m.s-1,
(9 fpm to 18,000 fpm) for gases and 0.03 m.s-1 to 30
m.s-1 (6 fpm to 6000 fpm) for liquids. Dynamic ranges
vary between 10:1 and 100:1. The maximum flow rate measurement
capacity in a 1836 mm (72'') diameter pipe can be as high as nearly
56,500 m3/hr, (about 250,000 gpm). Since these devices
are local velocity sensors, calculating the volumetric flow rate
requires a knowledge of the area velocity profile and the actual
flow area. Flow conditioning is therefore particularly important
for accurate volumetric measurements, while radial positioning,
which is a further responsibility of the user, must be according
to the manufacturer's recommendation, which can either be centerline,
one third of the diameter, 12% of the diameter or determined by
'profiling'. Quick [24] discusses operation
and installation for natural gas measurement. Although linearities
or 'accuracies' may be quoted up to 1%
of velocity, achieving the same accuracy for the volumetric flow
rate, although possible, may be difficult or impractical. In this
respect a unique dual rotor design, exclusive to Onicon, Inc.,
and primarily used for chilled water flow measurement in HVAC
systems, requires less flow conditioning than single rotor designs.
It comprises two rotors which rotate in opposite directions. The
output is based on the average rotor speed. Any flow swirl present
due to poor flow conditioning changes the speed of rotation of
each rotor by the same but opposite amounts. Swirl induced error
is thus virtually absent in the averaged output. Also, flow profile
sampling is improved over that of a single rotor. The devices
are calibrated using a volumetric prover and the specified accuracy
of 2%
of reading is for volumetric flow rate rather than velocity. This
is the total error and includes an allowance for dimensional variations
in industry standard pipes.
These are linear, volumetric flowmeters designed for liquids measurements
and comprise a single, radial-vaned impeller, vertically mounted
on a shaft bearing within a vertically divided flow chamber, sometimes
called a distributor. The impeller is often plastic and may even
be neutrally buoyant in water. There are various designs, however
typically both chambers access a series of radially distributed
and angled jets. The lower chamber jets connect to the flowmeter
input port and distribute the flow tangentially onto the lower
region of the impeller blades, while the upper series, which is
angled oppositely, allow the flow to exit. The flow pattern within
the flow chamber is thus a vertical spiral and the dynamic pressure
drives the impeller to track the flow. This design gives the meters
good sensitivity at low flow rates. Due to the distribution principle
the meters are also insensitive to upstream flow condition. Impeller
rotation pickups are always mechanical, often magnetically coupled,
and frequently also connect with electric contact transmitters.
They are primarily used in water measurement including potable
water measurement for domestic and business billing purposes and
in conjunction with energy management systems such as hot water
building or district heating, and to a much lesser extent in some
chemical and pharmaceutical industries for dosing and filling
systems involving solvents, refrigerants, acids and alkalis with
absolute viscosities less than 4.5 mPa.s, (0.045 Poise). Available
sizes range from 15 mm to 50 mm. Dynamic ranges lie between 25:1
and 130:1 and flow measurement ranges cover 0.03 to 30 m3/hr,
(0.13 to 130 gpm). Measurement linearities range between 1%
to 2%,
with typical repeatabilities of 0.3%.
Operating temperatures range from normal to 90oC (200oF)
and maximum operating pressures are available up to 6.9 MPa, (1000
psi). A number of potable water measurement systems come with
sophisticated telemetry options which allow remote interrogation
by radio or telephone. For potable water applications in the U.S.
these meters normally comply with the applicable AWWA standard,
[25], while in Europe EEC, DIN and other
national standards apply.
In the author's opinion, there is also another type of vaned flowmeter
which could be classified as a type of multi-jet turbine. This
type comprises an axially mounted, vaned impeller with an upstream
element which imparts a helical swirl to the flow. The transducer
is typically a small, low cost, sometimes disposable, plastic
component, and is usually designed for liquids, (but also to lower
accuracies, gases), low flow rate measurements, (down to 50ml/min).
The dynamic range is high and accuracies range up to 0.5%.
Goss [26] describes one particular design
in current use. Specialized applications cover the pharmaceutical,
medical and beverage industries.
However anachronistic intricate mechanical sensors may appear amidst current everyday high technology, there are fundamental reasons why axial turbines are likely to experience continued support and development rather than obsolescence, especially for in-line applications requiring in the region of tenth percent volumetric accuracy. Mechanical coupling is the most direct volume interaction for a flowing fluid, which is why mechanical meters historically developed first and continue to be the most accurate and reliable types of flowmeters for so many different fluids. Other, non-mechanical, perhaps higher technology, or newer approaches thus face high demands for accurate compensation to render such less directly volume-coupled techniques as generally accurate, or more accurate. This is because the error in each corrected factor or assumption in an indirect technique contributes to the overall error. The technology of high accuracy flowmeters continues to be driven by applications, such as the custody transfer of valuable oil and natural gas, which demand high accuracy and reliability. There is a continuing demand for accurate and reliable water flowmeters. By reason of long proven field experience, turbine and other vane type devices have become one of a few broadly accepted techniques in many major applications such as these where the demands for flow sensors is significant or growing.
1. W. F. Z. Lee, and H. J. Evans, Density effect and Reynolds number effect on gas turbine flowmeters, Trans. ASME, J. Basic Eng., 87 (4): 1043-1057, 1965.
2. R. E. Thompson, and J. Grey, Turbine flowmeter performance model, Trans. ASME, J. Basic Eng., 92 (4): 712-723, 1970.
3. M. B. Pate, A. Myklebust, and J. H. Cole, A computer simulation of the turbine flow meter rotor as a drag body, Proc. Int. Comput. in Eng. Conf. and Exhibit 1984, Las Vegas: 184-191, NY, NY: ASME, 1984.
4. P. D. Olivier, and D. Ruffner, Improved turbine meter accuracy by utilization of dimensionless data, Proc. 1992 Nat. Conf. Standards Labs. (NCSL) Workshop and Symp.: 595-607, 1992.
5. ISA-RP 31.1, Specification, installation and calibration of turbine flowmeters, Research Triangle Park, NC: ISA, 1977.
6. ANSI/ASME MFC-4M-1986 (R1990), Measurement of gas flow by turbine meters, NY, NY:ASME.
7. API MPM, Ch. 5.3, Measurement of liquid hydrocarbons by turbine meters, 3rd Ed., Washington, DC:API (Amer. Petroleum Inst.), 1995.
8. AGA Transmission Meas. Committee Rep. No. 7, Measurement of fuel gas by turbine meters, Arlington, VA:AGA (Amer. Gas Assoc.), 1981.
9. Int. Recommendation R32, Rotary piston gas meters and turbine gas meters, Paris, Fr.: OIML (Int. Organization of Legal Metrology), 1989.
10. ISO 9951:1993, Measurement of gas flow in closed conduits - turbine meters, Geneva, Switz.: Int. Organization for Standardization, (also available ANSI), 1993.
11. T. H. J. J. Van Der Hagen, Proof of principle of a nuclear turbine flowmeter, Nucl. Technol., 102 (2): 167-176, 1993.
12. K. Termaat, W. J. Oosterkamp, and W. Nissen, Nuclear turbine coolant flow meter, U.S. Patent 5,425,064, 1995.
13. AWWA C704-92, Propeller-type meters for waterworks applications, Denver, CO: Amer. Water Works Assoc., 1992.
14. ANSI/AWWA C701-88, Cold water meters - turbine type, for customer service, Denver, CO: Amer. Water Works Assoc., 1988.
15. B. M. Wright, and C. B. McKerrow, Maximum forced expiratory flow rate as a measure of ventilatory capacity, Brit. Med. J.: 1041-1047, 1959.
16. W. F. Z. Lee, R. V. White, F. M. Sciulli, and A. Charwat, Self-correcting self-checking turbine meter, U.S. Patent 4,305,281, 1981.
17. W. F. Z. Lee, D. C. Blakeslee, and R. V. White, A self-correcting and self-checking gas turbine meter, Trans. ASME, J. Fluids Eng., 104: 143-149, 1982.
18. D. F. Ruffner, and P. D. Olivier, Wide range, high accuracy flow meter, U.S. Patent 5,689,071, 1997.
19. D. F. Ruffner, Private communication, 1996.
20. A. Abdul-Razzak, M. Shoukri, and J. S. Chang, Measurement of two-phase refrigerant liquid-vapor mass flow rate - part III: combined turbine and venturi meters and comparison with other methods, ASHRAE Trans.: Research 101 (2): 532-538, 1995.
21. W. J. Shim, T. J. Dougherty, and H. Y. Cheh, Turbine meter response in two-phase flows, Proc. Int. Conf. Nucl. Eng. - 4, 1 part B: 943-953, NY, NY:ASME, 1996.
22. K. Minemura, K. Egashira, K. Ihara, H. Furuta, and K. Yamamoto, Simultaneous measuring method for both volumetric flow rates of air-water mixture using a turbine flowmeter, Trans. ASME, J. Energy Resources Technol., 118: 29-35, 1996.
23. M. W. Johnson, and S. Farroll, Development of a turbine meter for two-phase flow measurement in vertical pipes, Flow Meas. Instrum., 6 (4): 279-282, 1995.
24. L. A. Quick, Gas measurement by insertion turbine meter, Proc. 70th Int. School Hydrocarbon Meas., OK, 1995. (Available E. Blanchard, Arrangements Chair, Shreveport, LA, 318 868 0603.)
25. ANSI/AWWA C708-91, Cold-water meters, multi-jet-type, Denver, CO: Amer. Water Works Assoc., 1991.
26. J. Goss, Flow meter, U.S. Patent 5,337,615, 1994.
27. C. R. Sparks, Private communication, 1996.
D. W. Spitzer (ed.), Flow measurement, Research Triangle Park, NC: ISA, 1991, is a popular 646 page practical engineering guide of which four chapters concern turbine flowmeters, sanitary flow meters, insertion flow meters and custody transfer issues.
A. J. Nicholl, Factors affecting the performance of turbine meters, Brown Bov. Rev., 64 (11): 684-692, 1977, describes some basic design factors not commonly discussed elsewhere.
J. W. DeFeo, Turbine flowmeters for measuring cryogenic liquids, Adv. Instrum. Proc., 47 pt.1: 465-472, ISA, 1992, provides guidance for a less frequently discussed application in which axial turbines perform well.
ATS Standardization of spirometry, 1994 Update, Am. J. Respir. Care Med. 152: 1107-1136, 1995, is the latest version of the official US guideline for spirometry generated by the American Thoracic Society.
M. D. Lebowitz, The use of expiratory flow rate measurements in respiratory disease, Ped. Pulmonology, 11: 166-174, 1991, provides a review of the diagnostic usefulness of PEFR using portable spirometers.
W. M. Jungowski, and M. H. Weiss, Effects of flow pulsation on a single-rotor turbine meter, Trans. ASME, J. Fluids Eng., 118 (1): 198-201, 1996.
C. R. Sparks, and R. J. McKee, Method and apparatus for assessing and quantifying pulsation induced error in gas turbine flow meters, U.S. Patent 5,481,924, 1996, assigned to the Gas Research Institute, Chicago, is a potential solution to the accurate measurement of pulsating gas flows which will require engineering development and a high performance rotation sensor [27].
K. Ogawa, S. Ito, C. Kuroda, Laminar-turbulent velocity profile transition for flows in concentric annuli, parallel plates and pipes, J. Chem. Eng. Japan, 13 (3): 183-188, 1990, provides mathematical descriptions of velocity profiles.
J. Lui, B. Huan, Turbine meter for the measurement of bulk solids flowrate, Powder Technol. 82: 145-151, 1995, describes theory and experiments relating to a very simple design for a unique application, namely the volumetric measurement of plug flows of sands in a pipe.