ISO TR 3313:2018 download

05-20-2021 comment

ISO TR 3313:2018 download.Measurement of fluid flow in closed conduits Guidelines on the effects of flow pulsations on flow-measurement instruments.
I Scope
ISO TR 3313 defines puLsating flow, compares It with steady flow, indicates how it can be detected, and describes the effects it has on orifice plates, nozzles or Venturi tubes, turbine and vortex tlowmeters when these devices are being used to measure fluid flow in a pipe. These particular llowmeter types feature in ISO TR 3313 because they are amongst those types most susceptfluie to pulsation effects, Methods for correcting the flowmeter output signal for errors produced by these effects are described for those flowmeter types for which this Is possible, When correction Is not possible, measures to avoid or reduce the problem are Indicated. Such measures include the Installation of pulsation damping devices and/or choice of a flowmeter type which is less susceptible to pulsation effects.
ISO TR 3313 applies to flow In which the pulsations are generated at a single source which is situated either upstream or downstream of the primary element of the llowmeter. Its applicability Is restricted to conditions where the flow direction does not reverse In the measuring section but there is no restriction on the waveform of the flow pulsatlon The recommendations within this document apply to both liquid and gas flows although with the latter the validity might be restricted to gas flows in which the density changes In the measuring section are small as Indicated for the particular type of Ilowmeter under discussion.
2 Normative references
There are no normative references In this document.
3 Terms and definitions
For the purposes of ISO TR 3313v, the following terms and definitions apply.
ISO and IEC maintain ternilnological databases for use In standardization at the following addresses:
Note 3 to entry: Unless otherwise stated In ISO TR 3313 the term pulsatlng flow is always used to desrlbe periodic pukating flow.
4 Symbols and subscrIpts
4.1 Symbols
A area
Ag area of the throat of a Venturi nozzle
turbine blade aspect ratio
hr. Cr amplitude of the rth harmonic component in the undamped or damped pulsation
B bfp/qv, dimensionless dynamic response parameter
b turbine flowmeter dynamic response parameter
C turbine blade chord length
C contraction coefficient
CD discharge coefficient
C,, velocity coefficient
c speed of sound
D internal diameter of the tube
d throat bore of orifice, nozzle or Venturi tube
residual en-or in time-mean flowrate when calculated using the quantity ,J
Er total error In the time-mean flowrate
f turbine flowmetcr output signal, proportional to volumetric flowrate
pulsation frequency
fr resonant frequency
vortex-shedding frequency
H harmonic distortion factor
Ho Hodgson number
1 moment ol Inertia
lit. Ir moments of inertia of turbine rotor and fluid contained in rotor envelope respectively
kID relative roughness of pipe wall
1, turbine blade length
effective axial length
Impulse line length for differential pressure (DP) measurement device
maximum allowable uncertainty in the indicated flowrate due to pulsation at the flowmeter
maximum allowable relative error a, 2ufp angular pulsation frequency
4.2 SubscrIpts and superscripts
pulsation source
measured under pulsating flow conditions, possibly damped measured under pulsating flow conditions helore damping
RMS root mean square
measured under steady flow conditions
(over-bar) the time-mean value
measuring sections
fluctuating component about mean value.
5 Description and detection of pulsating floi
5.1 Nature of pipe flows
Thily steady pipe flow is only round in Ia r conditions which can normally only exist when the pipe Reynolds number, Re, is below abo Most industrial pipe flows have higher Reynolds numbers and are turbulent which mea th cy are only statistically steady. Such flows contain continual Irregular and random 0 ct quantities such as velocity, pressure and temperature. Nevertheless, If the conditions are I a those which are typical ci fully developed turbulent pipe flow and there is no periodic puls io e provisions of such standards as ISO 5167 (all parts) apply.
The magnitude of the turbulent fluctuations increases with pipe roughness, and this Is one of the reasons why ISO 5167 (all parts) stipulates a maximum allowable relative roughness, kID, of the upstream pipe for each type of primary device covered by ISO 5167 (all parts).
ISO 5167 (all parts), however, cannot be applied to flows which contain any periodic flow variation or pulsation.
5,2 Threshold between steady and pulsating flow
5.2.1 General
If the amplitude of the periodic flowrate variations is sufficiently small there should not be any error in the indicated llowrate greater than the normal measurement uncertainty. It is possible to define amplitude threshokls for both differential pressure (DP) type (lowmeters and turbine flowmeters without reference to pulsation frequency. It Is also possible to do this for vortex flowmeters but extreme caution Is necessary If even the smallest amplitude Is known to be present In the flow.
For DP-type flcwmcters, the threshold Is relevant when slow-response DP cells are being used. In the case of turbine flowmeters, the threshold value is relevant when there is any doubt about the ability of the rotor to respond to the periodic velocity Iluctuations. In the case of a vortex flowmeter the pulsation frequency relative to the vortex-shedding Frequency is a much more important parameter than the velocity pulsation amplitude.
5.2.2 Differential pressure (DP) type flowmeters
The threshold can be defined in terms of the velocity pulsation amplitude such that the flow can be treated as steady if
where U is the instantaneous bulk-mean axial velocity such that
UU’+U (2)
U’ is the periodic velocity fluctuation:
ü is the time-mean value.
The threshold in terms olthe equivalent OP pulsation amplitude is
0l0 (3)
where hp,, Is the instantaneous differential pressure across the tappings of the phmary device such that
=Sp+p’, (4)
Is the time-mean value:
—r p
Is the periodic differential pressure fluctuation.
To determine the velocity pulsation amplitude it is necessary to use one of the techniques described in £S such as laser Doppler or thermal anemomerry. To determine the OP pulsation amplitude it is necessary to use a last-response OP sensor and to observe the rules governing the design of the complete secondary instrumentation system as described In 6J..i.
Theoretical considerations are covered in Annex A.
S.2.3 Turbine flowmeters
At a given velocity pulsation amplitude a turbine flowmeter tends to read high as the frequency of pulsation increases and exceeds the frequency at which the turbine rotor can respond faithfully to the velocity fluctuations. The positive systematic error reaches a plateau value depending on the amplitude and thus the threshold amplitude can be defined such that the resulting maximum systematic error Is still within the general measurement uncertainty. For example, if the overall measurement uncertainty Is greater than or equal to 0,5 % then it can be assumed that a systematic error due to pulsation of 0,1 % or less has negligible effect on the overall measurement uncertainty.
Techniques such as laser Doppler and thermal anemometry can be used to determine the velocity pulsation amplitude. If the how meter output Is a pulse train at the blade passing frequency and lithe rotor inertia is known, then signal analysis can be used to determine the flow pulsation amplitude as described in 2.
5.2.4 Vortex flowmeters
A vortex hlowmeter is subject to very large pulsation errors when the vortex-shedding process locks in to the flow pulsation. There is a danger of this happening when the pulsation frequency is near the vortex-shedding frequency. At a sufficiently low amplitude, locking-in does not occur and flow-metering errors due to pulsation are negligible. This threshold amplitude, however, Is only about 3 % of the mean velocity and Is comparable to the velocity turbulence amplitude. The consequences of not detecting the pulsation or erroneously assuming the amplitude Is below the threshold can be very serious. This Issue Is discussed further In f3.
5.3 Causes of pulsation
Pulsation occurs commonly in industrial pipe flows. It might be generated by rotary or reciprocating positive displacement engines, compressors, blowers and pumps. Rotodynamic machines might also induce small pulsation at blade passing frequencies. Pulsation can also be produced by positive- displacement flowmeters. Vibration, particularly at resonance, of pipe runs and flow control equipment Is also a potential source of flow pulsation, as are periodic actions of flow controllers, e.g. valve “huntlng and governor oscillations. Pulsation might aLso be generated by flow separation within pipe fIttings, valves, or rotary machines (e.g. compressor surge).
Flow pulsation can also be due to hydrodynamic oscillations generated by geometrical features of the flow system and multiphase flows (e.g. slugging), Vortex shedding from bluff bodies such as thermometer wells, or trash grids, or vortex-shedding flowmeters fail into this category. Self-excited flow oscillations at tee-branch connections are another example.
5.4 Occurrence of pulsating flow conditions in industrial and laboratory flowmeter installations
In industrial flows, there is often no obvious indication of the presence of pulsation, and the associated errors, because of the slow-response times and heavy damping of the pressure and flow instrumentation commonly used. Whenever factors such as those indicated in 5,3 are present, there is the possibility of flow pulsation occurring, It should also be appreciated that pulsation can travel upstream as well as downstream and thus possible pulsation sources could be on either side of the flowrneter installation. however, amplitudes might be small and, depending on the distance from pulsation source to flowmetcr, might be attenuated by compressibility effects (In both liquids and gases) to undetectable levels at the Ilowmeter location. Pulsation frequencies range from fractions of a hertz to a few hundred hertz: pukation amplitudes relative to mean flow vary from a few percent to 100 % or larger. At low percentage amplitudes the question arises of discrimination between pulsation and turbulence.
Flow pulsation can be expected to occur In various situations In petrochemical and process Industries, natural gas distribution flows at end-user locations and Internal combustion engine flow systems. Flow- metering calibration systems might also experience pulsation arlsin from, for exampLe, rotodynamic pump blade passing effects and the effects of rotary positive-displacement flowmeters.
5.5 Detection of pulsation and determination of frequency amplitude and waveform
5.5.1 General
if the presence of pulsation Is suspected then there are various techniques available to determine the flow pulsation characteristics.
5.5.2 CharacterIstics of the ideal pulsation sensor
The ideal sensor would be non-intrusive, would measure mass ilowrate, or bulk flow velocity, and would have a bandwidth from decihertz to several kilohertz. The sensor would respond to both liquids and gases and not require any supplementary flow seeding. the technique would not require optical transparency or constant fluid temperature. The sensor would be uninfluenced by pipe wall material. transparency or thickness. The device would have no moving parts, its response would be linear, its calibration reliable and unaffected by changes In ambient temperature.
5.5.3 Non-IntrusIve techniques OptIcal: laser Doppler anemometry (IDA)
This technology is readily available, but expensive. Measurement of point velocity on the tube axis allows an estimate only of bulk Ilow pulsation amplitude and waveform but, for constant frequency pulsation. accurate frequency measurements can be made. Optical access to an optically transparent fluid is either by provision of a transparent tube section. or insertion of a probe with flbre•optlc coupling. With the exception of detecting low frequency pulsation, supplementary seeding of the flow would probably be required to produce an adequate bandwidth. LDA characteristics are comprehensively described in Reference [21. Acoustic: Doppler shift; transit time
Non-intrusive acoustic techniques are suitable for liquid flows only, because for gas flows there is poor acoustic-impedance match between the pipe wall and flowing gases. For the externally mounted transmitter and receiver, usually close-coupled to the tube wall, an acoustically transparent signal path is essential. The Doppler shift technique might require flow seeding to provide adequate scattering. instruments for point velocity measurements are available which, as for the IDA. provide only an estimate of bulk flow pulsation amplitude and waveform. Moreover. Doppler-derived ‘instantaneous” full-velocity profile instrumenisiJl allow much closer estimates of bulk flow pulsation characteristics. Tiansit-time instruments measure an average velocity, most commonly along a diagonal path across the flow. All acoustic techniques are limited in bandwidth by the requirement that reflections from one pulse of ultrasound should decay before transmission of the next pulse. Many commercial instruments do not provide the signal processing required to resolve unsteady flow components. An Investigation by Hakanssonlll on a transit time, lntrusive’type ultrasonic flowrneter for gases subjected to pulsating flows showed that only small shifts In the calibration took place and that these were attributable to the changing velocfty profile. Electromagnetic Ilowmeters
When the existing flowmeter installation is an electromagnetic device, then, if it is of the pulsed d.c. field type (likely macimum d.c. pulse frequency a few hundred hertz), there is the capability to resolve flow pulsation up to frequencies approximately five times below the excitation frequency. This technique is only suitable for liquids with an adequate electrical conductivity. It provides a measure of bulk flow pulsation, although there is some dependence upon velocity profile shape5.
5.5.4 Insertion devices Thermal anemometry
The probes used measure point velocity, and relatively rugged (e.g. fibre-film) sensors arc available for industrial flows. These probes generally have an adequate bandwidth, but the amplitude response is inherently non-linear. As with other point velocity techniques, pulsation amplitude and waveform can only be estimated. Estimates of pulsation velocity amplitude relative to mean velocity may be made without calibration. The RMS value of the fluctuating velocity component can be determined by using a true RMS flowmeter to measure the fluctuating component of the linearized anemometer output voltage. Mean-sensing RMS flowmeters should not be used as these only read correctly for sinusoidal waveforms. Accuratr frequency measurements from spectral analysis can be made for constant frequency pulsation.
Applications are limited to clean, relatively cool, non-flammable and non-hostile fluids. Cleanness otfiow is very important; even nominally clean flows can result in rapid fouling of probes with a consequent dramatic loss of response. A constant temperature flow Is desirable although a slowly varying fluid temperature can be accommodated. Other techniques
Insertion versions of both acoustic and electromagnetic flowmeters are available. Transit-time acoustic measurements can he made In gas flows when the transmitter and receiver are directly coupled the flowll, although this might require a permanent insertion. Again there Is the limitation of a lack of commercially available instrumentation with the necessary signal processing to resolve time-varying velocity components.
Insertion electromagnetic flowmeiers are not widely available and are subject to the same bandwidth limitations as the tube version. due to the maximum sampling frequency of the signal.
5.5.5 SIgnal analysIs on existing flowmeter outputs: software tools OrifIce plate with last-response OP sensor
A last-response secondary measurement system Is capable of correctly following the time-varying pressure difference produced by the primary Instrument provided the rules given In 6J.32 can be Followed, In principle, a numerical solution of the pressure difference/flow relationship derived from the quasi-steady temporal inertia model, Formula (,A..11). would then provide an approximation to the Instantaneous flow. The square-root error would not be present, although other measurement uncertainties (e.g. C0 variations, compressibility effects) produced by the pulsation would be. Successive numerical solutions would then provide an approximation to the flow as a function of time and, hence, amplitude and waveform information. Frequency Information can be determined directly from the measured pressure difference. At the time of publication of this document, there Is no software tool described for this implementation. Turbine flowmeter
The raw signal from a turbine flowmeter Is in the form of an approximately sinusoidal voltage with a level which varies with the flow but is usually in the range 10 mV to I V peak to peak. In most installations this signal Is amplified and converted to a stream ci pulses. The extraction of information about the amplitude and waveform of any flow pulsation from the variations In the frequency of this pulse train depends on the value of the dynamic response parameter of the flowmeter. Flowmeter manufacturers do not normally specify the response parameter icr their flowmeters, and the measurements which would be necessary to determine it are unlikely to be possible on an existing I lowmeter installation. However, the dependency of the parameter on the geometry of the turbine rotor and on the fluid density is discussed in 2.L4. and the range of values which have been found for typical flowmeters is presented In Table I
The response ola turbine flnwmeter to flow pulsation Is discussed In £1.1. It can range from the ability to follow the pulsation almost perfectly (medium to large flowmeters In liquid flows) to an almost total inability to follow the pulsation (small to medium flowmeters in gas flows with moderate to high frequencies of pulsation). This latter condition is a worst case for a turbine Ilowmeter installation because not only does the flowmeter output not show significant pulsation but if the flow pulsation Is of significant magnitude, the apparently steady flowmeter output Is not a correct representation of the mean how. If this condition Is suspected, other means of measuring the flow pulsation should be employed.
In any particular installation, the first step in an attempt to interpret a turbine flowmeter output should be to take the best available estimate of the flowmeter response parameter and using the results summarized In ZJ.. to estimate the general nature of the flownieter response. In the Interpretation of any observable fluctuations in the turbine flowmeter output, unevenness In the spacing of the turbIne blades can give the appearance of flow pulsation at the rotor frequency, Unevenness In blade spacing might be a result either of damage caused by the passing of a solid through the flowmerer or of manufacturing tolerances. Unevenness alas much as 3 % or 4% in the blade spacing has been observed
in a number oF installations. A procedure for processing a turbine flowmeter output signal to remove the effect of uneven blade spacing is given in Ajrnex.C.
If preliminary estimates of the Frequency of any pulsation in the flowmeter output and the general nature of the ulowmeter response combine to suggest that the amplitude of pulsation In the llowmeter output Is being attenuated by limited Ilowmcter response. it might be possible to correct the output. Two possible methods of correction have been described by Checsewright et aLIZI and by Atk1nsonLl; both are summarized in Annex C. Within the constraints of the uncertainty about the value of the flowmeter response parameter, this procedure can yield estimates of the amplitude and waveform of the flow pulsation. Vortex flowmeter
The vortex (lowmeter output can be used for instantaneous flow measurements, and hence amplitude and waveform information, in a range restricted to pulsation frequencies less than 2,5 $ of the lowest mean-flow vortex-shedding frequency. Limited Information can be obtained at higher pulsation frequencies but, in order to avoid the substantial flowmeter errors which can arise from the shedding frequency becoming locked-in to the pulsation frequency (see the pulsation frequency should be less than 25 % of the mean-flow shedding frequency. The detection of pulsation frequencies substantially above the mean-flow shedding frequency can be achieved by spectral analysis. The pulsation frequency is indicated by a local peak in the power spectrum.
6 Measurement of the mean flowrate of a pulsating flow
6.1 Orifice plate, nozzle, and Venturi tube
6.1.1 Description of pulsation effects and parameters Square-root error
For steady flow, the flowrate through a restriction such as an orilice plate is proportional to the square-root of the differential pressure measured between upstream and downstream tappings, The relationship is given by The temporal inertia term is also a function of the geometry of the restriction and the axial distance between the pressure tappings, arid thus the coefficient Ki contains L, an effective axial length of the primary device.
In pulsating how the velocity profiles upstream and through the restriction arc varying cyclically and. thus. I(i and K2 are varying cyclically and even their time-mean values are not necessarily equal to the steady (low values, except when pulsation amplitudes and frequencies are small. Discharge coefficients
In steady flow, the discharge coefficients of all the different types of primary device are dependent on the velocity profile of the approaching flow. The orifice plate tends to be particularly sensitive to variations In velocity profile because of the et contraction effect. A flatter than normal velocity profile increases the contraction effect and consequently reduces the discharge coefficient. A velocity profile which Is more peaked than normal has the opposite effect.
In pulsating flow, the instantaneous velocity profile is varying throughout the pulsation cycle. The degree of variation Is dependent on the velocity pulsation amplitude, the waveform and the pulsation Strouhal number. As a consequence, the instantaneous discharge coefficient also depends on the phase.
angle in the pulsation cycle, the pulsation amplitude, the waveform and the Strouhal number. At the time of publication of this Document it is not possible to relate mathematically the instantaneous discharge coefficient to the pulsation parameters.
The practical approach to the calculation of a fiowrate In pulsating flow conditions Is to use a constant value of the discharge coefTlcient, preferably the value used In steady flow conditions. This approach gives accurate results for low amplitude and low frequency pulsation In incompressible flow and limiting values of the relevant parameters defined n L2.3. Residual errors due to temporal inertia effects and variations in discharge coefficient increase with pulsation amplitude and frequency as shown by Galan et aLll.
6.1.2 Flowmeters using slow-response DP sensors LimitIng conditions of applicability
For a slow-response PP sensor (upper frequency limit of about 1 Hz) then, at best, the time-mean differential pressure is indicated. The corresponding Indicated mean flowrates derived from
— 1/2
(ip) include both the square-root and temporal-inertial effect errors. Conditions limiting applicability are those which prevent the secondary measurement system producing a correct time- mean pressure signal. These Include distortion of the pressure waveform or phase relationship In either of the two lines connecting tappings to the sensor. These effects arise from boundary friction, finite gas volumes and non-linear damping. In addition, the connecting line length should be restricted to prevent resonance due to this length being equal to the pulsation quarter-wavelength. This resonance occurs at a frequencf,., given hyf, c/(41). In practice minimum connecting line length is restricted by physical size of primary and secondary instrumentation and associated valve assemblies, Al the time of publication of this Document, it is not possible to define a threshold level of negligible pulsation applicable to all designs olsecoodary device. However, It is possible to recommend a number oldesign rules. Design of llowmeter secondary Instrumentation
For devices used to Indicate the time-mean differential pressures In pulsating flow conditions, the design rules are as follows.
a) The bore of the pressure tapping should be uniform and not too small, I-e. 3 mm. Piezometer rings should not be used.
b) Distance between pressure tappings should be small compared with the pulsation wavelength.
c) The tube connecting the pressure tappings to the manometer should be as short as possible and of the same bore as the tappings. A tube length near the pulsation quarter-wavelength should not be used.
d) For gas-filled secondary systems, sensor cavities or other discrete volumes should be as small as possible.
e) For liquid-filled secondary systems, gas bubbles should not be trapped in the connecting tube or sensing device; thus vent points are required.
f) Damping resistances in the connecting tubes and sensing element should be linear. Throttle cocks should not be used.
g) The device time constant should be about 10 times the period of the pulsation cycle.
h) When the above rules cannot be observed, the secondary device might be effectively isolated from pulsation by the Insertion of Identical lInear-resistance damping plugs into both connecting tubes. as close as possible to the pressure tappings.
Observance of the rules listed in items a) to h) for a slow-response device cannot eliminate the square- root error but merely reduces the error in the measurement of the time-mean differential pressure.
Thus the percentage additional uncertainty for pulsating flow Is equal to 100 Erand should be added to the uncertainty calculated for steady flow, lithe Strouhal number for the pulsation is less than 0,02. the percentage additional uncertainty may be reduced to SO ET.
6.1.3 Flowmeters using fast-response DP sensors LimitIng conditions of applicability
If the nme-varying difference can he faithfully followed by the secondary measurement system and the square-root of its signal averaged, then the simple square-root error is eliminated for the indicated time-mean flowrate, The conditions limiting applicability are those which prevent the secondary measurement system from producing a correct instantaneous differential pressure signal. In addition to the factors given in 6J..L1, there Is the need to avoid dynamic distortion due to the secondary measurement system resonant frequency being too close to the pulsation frequency. For gas-filled systems, the limiting resonance Is commonly that due to the connecting line length being close to the pulsation quarter-wavelength, rather than the resonant frequency of the transmitter or transducer alone. For liquid-filled systems, the limiting resonance might be either that due to the coupled stiffness of the sensor and inertial properties of the liquid-filled connecting lines, or it might be the quarter- wavelength resonant frequency, depending on the system geometry. The presence of gas bubbles in a liquid-filled system can have a dramatic effect upon the resonant frequencyllOl. DesIgn of flownieter secondary Instrumentation
For design of a fast-response secondary measurement system, a DP transmitter or transducer with very small internal volume and high natural frequency Is required. Rule a) of applies for gas-filled systems, and rules, b). d). and e) of 6L2.2 and the following apply.
a) The mechanical and electronic frequency limits of the secondary measurement system should be at least ten times greater than the pulsation frequency.
b) Connecting tube lengths should be as short as possible and the pressure path length from tapping to sensor should be less than 10% of the pulsation quarter-wavelength.
c) For liquid-filled secondary systems the bore of the connecting tubes should be greater than or equal to 5 mm to avoid Inertial effects reducing the resonant frequency.
d) Connecting tubes, fittings and valves should be of the same bore
e) The secondary device should be geometrically identical on both upstream and downstream skies.
f) Secondary devices for liquids should not have any gas bubbles trapped In the connecting lines or the device Itself; thus vent points are necessary. EstImation of correction (actors and measurement uncertainties due to pulsation
Assuming that the fast-response DP sensor Is used in conjunction with a signal processor which generates an output proportional to the square-root of the instantaneous differential pressure, the systematic error due to the square-root effect” is eliminated. There are some additional uncertainties due to pulsation, however, which can be estimated as follows.
Provided that the frequency response of the entire secondary system, including the connecting tubes, fittings and DP sensor, can be proved by experiment to be flat from 0 to lOf (wherefp Is the fundamental pulsation frequency), the additional percentage uncertainty may be taken as.
As indtcated in LU. ET can be estimated using Formula (19). LZGI or L211 provided thai the flow can be regarded as incompressible. This is th€ case  0,99.
Systematic errors In (he secondary measurement system arise from pressure wave distortion effects In connecting lines and from resonance effects due either to connecting line quarter.waveiength resonance or connecting line plus sensor cavity resonance. Because these errors are strongly dependent upon secondary system geometry and the fluid, it Is not possible to give general results for error estimation. Details of these effects and suggested correction procedures are given by ClarkfJ&l and Batros et al.LUl.
614 Pulsation damping
6.14.1 Adequate damping criteria for gs flow General
Pulsation In gases or vapours can be damped by a combination of volumetric capacity and throttling placed between the pulsation source and the flowmetrr (see Figure 1). The volumetric capacity can Include the volume of any receivers and the pipeline itself, provided that the axial lengths Involved are short compared with the pulsation wavelength. The throttling can be provided by the flowmeter itself and can be augmented by valves and other fittings. The frictional pressure losses in the pipeline can also contribute towards the throttling effect. The straight pipe length between the flowmeter and any additional throttling device should he in accordance with the installation requirements of the appropriate part 01 ISO 5167. Care should be taken that the selected throttling device does not create hydrodynamlc oscillations. Further work on pulsation damping criteria Is gIven In Annex B.
In ISO TR 3313 more attention is paid to single-receiver damping systems than to divided-receiver systems because it is possible to present a simple mathematical representation of an adequate damping criterion for the former but not for the latter,6.2 Turbine flowmeters
62.1 DescrIption of pulsation effects and parameters General
A turbine flowmetcr comprises a freerunnlng, axial flow, turbine rotor, which for steady flow has a closely linear relationship between the rotational speed and the volume flowrate. The rotational speed is usually obtained by detecting the passage of blade tips past a pickup mounted on the casing. Some flowmeters use the pickup from only one of the blades per revolution but the additional resolution obtained by using the signal from all the blades is often important when there are pulsation effects. When subjected to a time-dependent flow, the inertia of the rotor (and possibly of the fluid contained within the rotor envelope) can cause the rotor speed to lag behind the steady state condition In an accelerating flow and to exceed It In a decelerating flow. The Influence of a decelerating flow Is greater than that of an acceleratIng one so that the mean speed of a flowmcter subjected to pulsation can be greater than that corresponding to the mean flowrate. In extreme cases the error can be more than 25 % of the indicated flow. General relationship between metering error and pulsation parameters
The I lowmeter error depends on the amplitude and waveform of the pulsation, the mean flowrate, the density of the fluid and the design characteristics of the turbine rotor, Including Its moment of inertia. The transient behaviour olthe flowmeter can be described by
where 6(a) varies smoothly from a value of I at a O to a value of 1.6 at a = 0,5.
For some applications the above criteria might be unduly conservative because the quantity of interest Is the mean flaw rather than the Instantaneous flow. The assumption dq / dt — df / cit • which Is made above, removes the asymmetry between accelerating and decelerating flows so that Formulae (33) and L34) cannot be used to estimate the error in the mean flow. There is no simple analytical expression for the error in the mean flow. For sinusoidal pulsation in a (low pressure) gas flaw Atkinsnnllil has made extensive computations of the flowmeter response and has confirmed his results by experimental measurements. A summary of this work Is given for information In Annex C where FigurcC,1 shows the relative mean-flow error as a function of a and B(= bf /qv). DetermInation of the dynamic response parameter
There are two main ways in which the value of the response parameter can be obtained; one Is by experiment via a step response test and the other is by the use of one of the many analytic formulae which have appeared in the literature. The biter are discussed in 62.1.4.
FormulaUij shows that the response ala fiowmeier to a step change in the flow can be divided into two parts. Firstly, there will be a change in the f)owmeter speed to accommodate any Influence of the fluid Inertia term. Secondly, there will be first order (esponential) transition to the new condition. For gas flows, the first of these parts is small and occurs very rapidly compared with the second. For liquid flows, the rapidity of change which is required to constitute a step (S 100 ps) is such that there have not been any step response tests made with liquids. It seems likely, however, that If such tests were made. the two parts of the response might overlap.
carried out In a wind tunnel by Al Asmi and CastrolZlll indicates that the bluff body shapes associated with the largest locking-in flowrate range are those normally selected by flowmeter manufacturers to give the strongest and most regular vortex signals. Ii was also found that the locking-in tlowrate range tended to increase as blockage ratio was increased to the values typically found in commercial vortex Ilowmeters.
When the pulsation frequency is much higher than the vortex-shedding frequency there Is no obvious locking-in but shifts In the Strouhal number, and the resulting departure from the steady flow calibration, can still be of the order of ±10%.
6.3.12 Threshold pulsation amplitudes
The critical flow pulsation amplitude is that which is ust sufficient to cause locking-in to occur when the pulsation frequency is around twice the vortex-shedding frequency. If the flow pulsation amplitude Is less than this critical or threshold value there is no significant shift In Strouhal number, and therefore no significant deviation from the steady-flow calibration.
Available data both from tests in a low turbulence intensity wind-tunnellZQi and from experiments In a pipe flow riglZll indicate that the critical or threshold flow pulsation amplitude is in the region of 3 % of the mean-flow velocity. These data indicate that the threshold value Is independent of bluff body shape and blockage ratio (bluff body frontal area as a fraction of the pipe cross-sectional area].
As the critical velocity pulsation amplitude Is of the same order as the velocity turbulence amplitude sophisticated techniques are necessary to detect the pulsation and measure Its amplitude. It Is suggested that a fast-response velocity sensor such as a hot wire or hot film probe. Inserted in the pipe Immediately upstream of the vortex flowmeter location, should be used to determine whether or not there is any pulsation present at a frequency and amplitude which might cause locking-in. It is necessary to apply band-pass liltering to exclude turbulence components outside the vortex-shedding frequency range. If no filtering Is employed, there isa danger that any pulsation might be masked by the velocity turbulence noise.
Unless It can be demonstrated by the above or similar technique that the velocity pulsation amplitude UM5 /U Is less than 3 %, it should be assumed that a vortex flowmeter is liable to locking-in if the pulsation frequency is In a range from 25% of the lowest to at least twice the maximum vortex-shedding frequency. Frequency limit for quasi-steady behaviour
The available experImental data are restrIcted to conditions where the velocity pulsation amplitude /U does not exceed 20 %. These data Indicate that quasi-steady behaviour can be assumed provided that the pulsation frequency Is less than 25 % of the vortex-shedding frequency at the lowest
flow velocity. Ic. quasi-steady behaviour II UH5 /U 0.2 and <0,25.
6.3.2 MinimIzing pulsation effects
The sensitivity of a vortex flowmeter to pulsation Is such that it would only be sensible to select this flowmeter type if there was either no pulsation present or if the pulsation frequency was less than 25% of the lowest vortex-shedding frequency. The vortex-shedding frequency is inversely proportional to the bluff body diameter. Thus, it might be possible to select a vortex flowmeter with a small bluff body diameter (low blockage ratio) to raise the shedding frequency. Insertion vortex flowmerers have very much smaller bluff bodies than full line-size flowmeters.
6.3.3 EstImation of measurement uncertainties
It Is only possible to make an estimate ol measurement uncertainty If vortex-shedding frequencies are derived from spectral analysis of the raw signal from the vortex sensor and when:
a) quasi-steady conditions exist,fv/fp <0,25;
b) pulsation frequencies are much higher than twice the maximum shedding frequency.
In the first case data only exist at velocity pulsation amplitudes less than 20 % and these indicate a measurement uncertainty of about 1 %.
In the second case, even if there is no obvious locking-in, experimental data exist at velocity pulsation amplitudes between 10 % and 20 % that indicate that there could still be errors in the indicated flowrate of the order of 10 %.

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