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The application of sonic (critical flow) nozzles in the gas industry
The application of sonic (critical flow) nozzles in the gas industry P. H. WRIGHT Engineering Services Department, Gas & Fuel Corporation of Victoria, 1 136 Nepean Highway, Highett, Victoria 3190, Australia
Sonic (critical flow venturi) nozzles have been used by some organizations as calibration standards for the accuracy testing of gas meters and have sometimes been used as flow transfer standards in inter-laboratory comparisons, but their routine application has been limited, possibly due to the lack of practical guidelines. The implementation of ISO 9300:1990 'Measurement of gas flow by means of critical flow venturi nozzles" is discussed in relation to the practical application of flow-calibrated nozzles. Working equations applicable to meter accuracy testing are presented. The high level of repeatability of sonic nozzles has been demonstrated by nozzle inter-comparison work using a 'Wheatstone bridge" technique in this laboratory and at the Australian National Measurement Laboratory. Considerations in the practical application of the bridge technique are presented in relation to nozzles used for gas meter testing. Keywords: sonic nozzles; critical flow venturi; nozzle intercomparison
Nomenclature Cross-sectional area of the venturi nozzle throat Discharge coefficient Critical flow factor Molar mass Absolute stagnation pressure at nozzle inlet Absolute static pressure at nozzle inlet Mass flow rate Volume flow rate Universal Gas Constant Nozzle throat Reynolds number Absolute stagnation temperature at nozzle inlet Absolute static temperature at nozzle inlet Length of time of a meter test Calibration factor for critical flow venturi nozzle Volume of gas passed by the meter under test Compressibility factor Differential pressure across bridge
Introduction
Conditions at meter under test Conditions at nozzle inlet Standard conditions Conditions under discussion
The Gas & Fuel Corporation of Victoria, Australia, uses critical flow venturi nozzles (usually referred to as sonic nozzles in the gas industry) as the flow standards for virtually all routine gas meter accuracy certification testing. Critical flow nozzles have been used by a limited number of other organizations as calibration standards for the accuracy testing of gas meters 1' 2, and have sometimes been used as transfer standards in interlaboratory comparisons ~. The lack of a recognized international standard has meant that sonic nozzles as flow measurement standards for the routine calibration of gas flow meters used for customer billing has not achieved general implementation and acceptance. The publication of ISO 9300:1990 'Measurement of gas flow by means of critical flow Venturi nozzles '4 should help correct this situation. This paper aims at providing guidelines for the practical application of ISO 9300 to the use of flow-calibrated nozzles for gas meter accuracy testing. ISO 9300 only provides for calculated flow rates to an uncertainty of no better than ---0.5%, whereas it is possible to calibrate individual nozzles to much better than that ~. The high level of repeatability of sonic nozzles has been demonstrated by nozzle intercomparison work (using a bridge method) both in this laboratory and at the Australian National Measurement Laboratory. Nozzle comparisons to -+0.01% have been quoted 5.
0955-5986/93/020067-05 ~) 1993 Butterworth-Heinemann Ltd
Flow Meas. Instrum., 1993 Vol 4 No 2
A, C C, M Po Pl
qM qv R Red
To Wl
t~ ts
v~ Z Ap
Subscripts m n s x
67
P. H. Wright- The application of sonic nozzles in the gas industry
Sonic (critical flow) nozzles Sonic nozzles or critical flow venturi nozzles are converging/diverging flow restrictions in which the total pressure differential is kept sufficiently high that the gas flow accelerates to the critical velocity (the local sonic velocity) at the throat. The flow into the nozzle is independent of the downstream pressure conditions provided the pressure differential is above that necessary to ensure critical flow. Critical flow nozzles thus lend themselves to the precise setting of flow rates as constant inlet conditions lead to constant upstream flow.
Critical flow nozzles in the Gas & Fuel Corporation The Gas & Fuel Corporation of Victoria uses critical flow venturi nozzles as the flow standards for virtually all routine gas meter accuracy certification testing. The testing equipment includes a range of facilities as below: [] A large industrial gas meter test facility from 6 to 5600 m 3 h -1 with 11 critical flow nozzles used to test meters from 80 mm to 450 mm pipe sizes. This facility has been in use for 10 years. [] A light industrial gas meter test facility from 2.4 to 30 m 3 h -1 with six critical flow nozzles (built using PVC pressure pipe to simplify manufacture) which has been used for over five years. [] 24 automated domestic meter test rigs 6 from 1.2 to 6 m 3 h -1 which have been in continuous use for over six years
temperature and pressure uncertainty can never be better than -+0.5%. This level of uncertainty is generally unacceptable for flow measurement standards to be used for the calibration of other flow meters. It is known from experiments of the type conducted at the C.S.I.R.O. National Measurement Laboratory, Sydney, Australia, that the repeatability of critical flow venturi nozzles is orders of magnitude better than this s, 7, 8 Although ISO 9300:1990 allows for calculation of the flow, direct calibration of critical flow venturi nozzles is preferred, as the inherent high repeatability of the nozzles allows the measurement from a primary standard to be transferred to meters being calibrated with minimal introduced uncertainties. Many gas meters used for customer billing purposes are calibrated on a volume flow basis. A critical flow venturi nozzle is essentially a volume flow device in that the volume flow through the nozzle is constant (to a first approximation) regardless of the pressure. The application of critical flow nozzles to the calibration of gas meters requires the mass flow equations of the ISO standard to be converted to a volume flow basis. The mass flow from ISO 9300 is (to a first approximation) proportional to the absolute pressure upstream of the nozzle: q m --
A,CC, Po (RTo/M) lj2
(1)
The discharge coefficient (C) represents the effects of the non-isentropic and non-one-dimensional flow in the boundary layer of the nozzle. The volume flow equivalent of equation (1) is
All testing is carried out with atmospheric air using the test rooms as the constant pressure and temperature supplies and critical flow being maintained in the flow nozzles via suction from a variety of blower/pump units. All the test facilities use computers to control all the necessary data acquisition, control and calculation functions. Experience to date with these test facilities indicates that critical flow venturi nozzles are highly repeatable and stable flow standards. Observed small changes in calibrated flow through these nozzles are more indicative of changes in the calibration and reference standards (bell or piston provers).
The ISO 9300 standard does not directly address the issue of directly calibrated nozzles and appropriate working equations have been developed and are shown below. The application of ISO 9300 to directly calibrated nozzles is significant, as the calculation of nozzle flows from the standard can be no better than -+0.5% (95% confidence level) whereas directly calibrated nozzles can have an uncertainty of better than 0.1% (95% confidence level).
ISO 9300:1990
Nozzle calibration specification
ISO 9300:1990 'Measurement of gas flow by means of critical flow venturi nozzles' specifies the geometry and method of use of critical flow venturi nozzles used to determine the mass flow rate of a gas flowing through the system. It also gives the information necessary for calculation of the flow rate and its associated uncertainty. The ISO 9300:1990 standard refers to the calculation of gas (mass) flow in relation to the inlet conditions of the nozzle and the throat diameter of the nozzle. The nozzles referred to are of the toroidal inlet/conical outlet form. The discharge coefficient of these standard form nozzles is quoted as having a -+0.5% relative uncertainty at the 95% confidence limit. Thus the calculated total uncertainty including
The calibration (size) of a flow-calibrated nozzle is usually referred to the flow rate at some nominated standard condition. The calibration is sometimes referred to as a 'standard time '9. The standard time, ts, used by the American Meter Company is the time required, in seconds, to pass one cubic foot of dry air through the nozzle under critical flow at an inlet pressure of 24.696 psia and an inlet temperature of 60.0 °F. The 24.696 psia relates to the American Meter Company practice of calibrating the nozzles at a 10 psig inlet pressure. The calibration factor (standard time) used in this laboratory is the time required, in seconds, to pass one cubic metre of dry air through the nozzle under critical flow at an inlet total (stagnation) pressure of 101.325 kPa
68
Flow Meas. Instrum.,
1993 Vol 4 No 2
qv = A,CC,Z
(2)
P. H. Wright- The application of sonic nozzles in the gas industry absolute and an inlet stagnation temperature of 20.0 °C. The quoted standard conditions relate to the nominal calibration conditions and are similar to the normal conditions of use of the nozzles ~°. Regardless of the specification used, the aim is to provide calibrating laboratories with an unambiguous statement of the reference conditions for the calibration of the critical flow venturi nozzles. If the conditions of the calibration are known, then that calibration can be used as the basis for flow calculations at other flowing conditions. The nozzle calibration should, wherever possible, be similar to the conditions of use of the nozzle so that the required corrections to the flow will be small or in many cases can be neglected. Another method for specifying the flow capacity or size of a critical flow nozzle is to calculate the effective diameter of the nozzle throat from the results of a flow calibration as the flow under various conditions can be calculated from that. In practice, such calculations can be quite involved and prone to error.
Application of ISO 9300 to flow-calibrated nozzles Using the previously quoted critical flow nozzle volume flow equation with the concept of a standard time or calibration factor, ts, the following equations are developed. For chosen standard conditions:
1
tRTost 1/2
t~ = q,,s = A,CsC,sZs \ M s /
(RTo×I u2
(4)
where the subscript x indicates a parameter under conditions of the flow measurement in the nozzles. To convert a nozzle calibration to volume flow with different gas flow conditions, the following relation applies:
1C×C,xZ×(MsTo×l 1/2 qvx - t~ CsC,s Zs \Mx Tos/
(5)
(6)
is the same as the ratio of the relative densities (sometimes referred to as specific gravities) of different gases. This term becomes unity if the nozzle calibration gas and the gas being measured have the same composition. It should be noted that the difference in properties of dry air and atmospheric air (which contains water vapour) must be taken into consideration. In many practical applications, where nozzles are used to determine flow at conditions close to the nozzle calibration conditions, the approximate expression shown below is often more than satisfactory.
1 iMs T×lU2 (7)
This simplified equation contains parameters which can usually be determined relatively easily. This equation
(8)
t~,Tn \Mn TJ J
Tmt
t 2 [Pn
Pm \minTs/
n
tsn \Tnl
J
(9)
The ratio of molecular weights (or relative densities) at the meter is the same as at the nozzles, so that factor can be brought outside the summation. Meter accuracy tests are conducted by running the meter under test at a constant flow rate using one or more calibrated nozzles in parallel and measuring the time taken for the meter to pass a chosen quantity of gas. The volume actually passed by the meter can be calculated as below.
Trn( Ms / 1'2
Vm=tVpm\mmT~J
The ratio
MJM×
Pm n
where n refers to the nozzle number. The equation can be rewritten to reduce calculation time as below: q,.,,~
qvx = A,C×C,xZ, \ M× /
t,
q~m
(3)
For other conditions:
qvx =
also assumes that the pipe sizing is large enough that the static and stagnation temperatures and pressures respectively are essentially the same, which is the case for nozzle throat to pipe diameter ratios of 0.3 or greater at atmospheric pressure. The calibration of gas meters is usually achieved by connecting the outlet of the meter under test via pipe work to the inlet(s) of one or more nozzles in parallel. This arrangement effectively ensures that the flow rate of the meter under test is kept constant if the inlet pressure to the meter is kept constant. In the above arrangement the flows through each of the nozzles can be summed to determine the total flow through the meter under test. This summation can be carried out with virtually no increase in overall uncertainty, as the percentage uncertainty of each nozzle flow leads to the same percentage uncertainty in the total flow. To enable the summation of the flows, the flow through each of the nozzles must be corrected to some reference condition. For the accuracy testing of gas meters the most convenient reference point is the conditions prevailing at the meter under test. Thus the summation of the flows through a meter under test can be described by the following equation:
[nt,t"q
~n t~n \Tnn/ J
(10)
The volume actually passed by the meter is compared with the volume indicated by the meter for the same period to determine the meter error. It is usual to time an integral number of revolutions of the meter test dial and use this time as the total test time in the above equation. The determination of meter error thus becomes a comparison of actual and indicated volume flow rates.
Sonic nozzle bridge intercomparison The intercomparison of critical flow venturi nozzles allows the flow calibration of one nozzle to be transferred to another with the minimum increase in uncertainty. The technique relies on pipe work and critical flow venturi nozzles arranged in the gas flow equivalent of an electrical Wheatstone bridge. Sonic nozzles become the equivalent of electrical resistors
Flow Meas. Instrum.,
1993 Vol 4 No 2
69
P. H. Wright- The application of sonic nozzles in the gas industry and pressure and mass flow become the equivalent of voltage and electrical current respectively. A schematic diagram of a sonic nozzle bridge is shown in Figure 1. The downstream nozzles must have a larger capacity than the upstream nozzles to pass the larger volume flow resulting from the pressure drop across the upstream nozzles. The actual pressure drops across arms 1 and 2 (and the corresponding increase in volume flow) depend on the ratio of volume flow capacities of the nozzles in arms 1 and 3, and 2 and 4, respectively. The technique relies on a suitable choice of nozzles and the existence of sufficient total pressure drop to ensure critical flow in all the sonic nozzles. It should be noted that although single nozzles are shown in arms 1, 3 and 4 of the diagram, the arms could be made up from combinations of nozzles in parallel. The pressure differential between the inlets of the nozzles in arms 3 and 4 is very sensitive to changes in the volume flow rates of any of the nozzles in the bridge, particularly if the bridge is nearly 'balanced', that is, if the differential pressure Ap is small. Thus if a known combination of nozzles in (say) arm 2 is replaced by an unknown nozzle, the difference in flow can be determined with precision because of the sensitivity of the differential pressure measurement Ap to changes in the nozzle flows. The bridge technique works with best uncertainty if the flow rate of the unknown nozzle and the (total) flow rate of the calibrated nozzle(s) are within 5% or better of each other. Tests at the Australian National
~ Suppl.y
I. AFm
Arm 2
or
1 Unknown sonic nozzte
Reference sonic nozzte(s)
I
\ Arr~ 3
Arm 4
)
I
Exhaust
Figure l Sonic nozzle bridge for intercomparison of sonic nozzles 70
Flow Meas. Instrum.,
1993 Vol 4 No 2
Measurement Laboratory indicate that the bridge technique can be developed to allow intercomparisons to better than 0.01%~. Within the Gas & Fuel Engineering Services Department gas flow laboratory relatively simple apparatus has been used to calibrate nozzles with air flow rates up to 90 m 3 h -1 with less than 0.05% increase in uncertainty. This increase in uncertainty is added to the uncertainty of the reference nozzle(s). The bridge technique allows large critical flow nozzles to be calibrated against combinations of smaller nozzles in parallel. This means that nozzles which are outside the capacity range of available calibration facilities can be calibrated, traceable via the bridge technique back to the available calibration facility.
Practical sonic nozzle sequences Test stations for accuracy testing of large gas meters usually have a range of critical flow venturi nozzles which can be used in a variety of combinations to provide a wide range of available testing gas flows. As an example, a station with six nozzles in a binary sequence can provide 63 different flow rates, ranging from the flow of the smallest nozzle to the sum of the flows though all the nozzles. In large meter test stations, which may have 10 to 20 available nozzles, the calibration of the larger nozzles may cause difficulties because of the large facilities required for measurement of large flow rates. The original set of nozzles in the largest of the Gas & Fuel Corporation test stations were originally calibrated overseas, as there were no facilities of appropriate size and uncertainty in Australia. It was considered desirable to be able to provide calibration traceability to local measurement standards in the future, possibly by the bridge technique. A second set of nozzles was required, as the meter testing rig could not be out of use during the potentially timeconsuming recalibration. To use the bridge technique for calibrating large nozzles it is necessary to use two or more nozzles whose total flow is close to the nozzle to be calibrated. This implies that if nozzles in a calibration station are arranged in a binary sequence it will be necessary to create a separate 'dummy' set of nozzles to allow each nozzle to be calibrated against two of the next smaller size in parallel s . To reduce costs, the second set of nozzles for the Gas & Fuel Corporation large meter test facility was designed such that the sizing lent itself to simple application of the bridge calibration technique without the necessity for the manufacture of duplicate nozzles which would not be required for the test station. The sequence is such that at the high flow rate end of the sequence the flow rate of each nozzle is close to the sum of the flow rates of the next three smaller nozzles. This means that using the sonic nozzle bridge technique it should be feasible to pass upwards through the sequence calibrating each nozzle by comparison with the sum of the three below it. The smaller nozzles in the sequence would be calibrated directly using conventional flow calibration techniques, such as bell or piston provers. The flow rate ratio between nozzles is 1.839 to 1
P. H. Wright - The application of sonic nozzles in the gas industry for each nozzle to be the equivalent to the sum of the three next smaller nozzles in the sequence. Other choices for how many nozzles should be the equivalent of the next larger nozzle did not seem as practical. It is found that using two nozzles results in a large number of nozzles being required to cover the desired flow range of a test station. Using the summation of four (or more) nozzles requires a more cumbersome bridge and the steps between nozzles are not that different from the case of using three nozzles. The choice of a regular sequence of nozzles can also overcome another problem with the practical application of the bridge technique, namely the requirement of suitable capacity nozzles for the remaining arms of the bridge. The nozzle one size step up from the nozzle being calibrated can be used as the nozzle in the arm of the bridge downstream of the nozzle being calibrated. This downstream nozzle does not need to be calibrated for this application. The two nozzles used to provide the reference arms on the bridge (arms 1 and 3 in Figure 1) can be chosen from adjacent nozzles in the sequence not required on the measurement side of the bridge. Thus the bridge technique only requires the manufacture of one extra nozzle, one step larger than the largest one required for the meter test rig. The above technique assumes that the three smallest nozzles can be precisely calibrated against some reference standard and that there are at least eight nozzles in the sequence. The sequence can be chosen so that each of the larger nozzles is not exactly the sum of the flow rates of the next three smaller nozzles, so that the range of flow rates available will not be reduced by having exactly duplicate flows. Conclusions
Critical flow venturi nozzles have proved to be highly repeatable gas flow standards. The acceptance of critical flow nozzles as the preferred technique for the routine accuracy testing and certification of gas flow meters will be assisted by the publication of ISO 9300:1990 and the acknowledgement that the limiting factor in the uncertainty of the application of these nozzles is the uncertainty in the actual flow calibration of the nozzles. The equations provided in this paper will allow
the application of directly calibrated nozzles to gas meter testing within the framework of ISO 9300. The application of the bridge technique means that the precision of nozzle calibrations from small reference standards such as bell provers can be transferred to higher flows, without the necessity for larger standards. Acknowledgements
The author wishes to thank Thiam Wee Chua who carried out a great many tests on the sonic nozzle bridge and lan Dollery who carried out much of the uncertainty analysis in the applications of sonic nozzles. The author also wishes to thank the Gas & Fuel Corporation of Victoria for permission to publish this work. References
1 Wright, P. H. The application of sonic nozzlesto the automated accuracy testing of gas flow meters In 'Proc. International Conference on Flow Measurement', 20-23 August, Melbourne, Australia (1985) 152-156 2 Aschenbrenner,A. Ein Pr6fstandfiJr Grol3gasz~hlermit ~iberkritischen D~isenals Normalger~te (A test stand for large-scale gas meters, with supercritical nozzles as standard instrument) PTBBericht, PTB-Me-24October (1979) 3 Aschenbrenner,A. Calibration of the new test rig for large gas meters of the Physikalisch-Technische Bundesanstalt. In 'Proc. Flomeko Conference', D6sseldorf, VDI Berichte 768 (1989) 4 ISDO 9300: 1990(E) Measurement of gas flow by means of critical flow Venturi nozzles, International Organization for Standardization, Geneva (1990) 5 Caw,W. A. and Prowse, D. B. A proposed calibration hierarchy for gas flow In 'National Seminar on Flow Measurement in Australia', 9-10 March, National Measurement Laboratory, Sydney (1987) 6 Wright, P. H. Sonic nozzles as gas meter calibration standards In 'Proc. 1986 IICASymposiumon CustodyTransfer', Melbourne 27 February (1986) 7 Caw, W. A., Bryant, N. W. and Bell, G. A. Analogue of the Wheatstone Bridge using critical flow nozzles In 'Australasian Hydraulics and Fluid Mechanics Conference', Adelaide (1977) 605-607 8 Bignell, N. Measurements with a sonic-nozzle bridge In Proc. Australasian Instrumentation and Measurement Conference', Adelaide, 14-I 7 November (1989) 312-315 9 Schroyer,H. R. Sonic nozzles in distribution metering. Pipeline and Gas J. D137-D141, December (1975) 10 Wright, P. H. Automated calibration of critical flow reference nozzles In AustralasianInstrumentationand MeasurementConference, Adelaide, 14-17 November (1989) 238-242
Flow Meas. Instrum.,
1993 Vol 4 No 2
71
Sonic (critical flow venturi) nozzles have been used by some organizations as calibration standards for the accuracy testing of gas meters and have sometimes been used as flow transfer standards in inter-laboratory comparisons, but their routine application has been limited, possibly due to the lack of practical guidelines. The implementation of ISO 9300:1990 'Measurement of gas flow by means of critical flow venturi nozzles" is discussed in relation to the practical application of flow-calibrated nozzles. Working equations applicable to meter accuracy testing are presented. The high level of repeatability of sonic nozzles has been demonstrated by nozzle inter-comparison work using a 'Wheatstone bridge" technique in this laboratory and at the Australian National Measurement Laboratory. Considerations in the practical application of the bridge technique are presented in relation to nozzles used for gas meter testing. Keywords: sonic nozzles; critical flow venturi; nozzle intercomparison
Nomenclature Cross-sectional area of the venturi nozzle throat Discharge coefficient Critical flow factor Molar mass Absolute stagnation pressure at nozzle inlet Absolute static pressure at nozzle inlet Mass flow rate Volume flow rate Universal Gas Constant Nozzle throat Reynolds number Absolute stagnation temperature at nozzle inlet Absolute static temperature at nozzle inlet Length of time of a meter test Calibration factor for critical flow venturi nozzle Volume of gas passed by the meter under test Compressibility factor Differential pressure across bridge
Introduction
Conditions at meter under test Conditions at nozzle inlet Standard conditions Conditions under discussion
The Gas & Fuel Corporation of Victoria, Australia, uses critical flow venturi nozzles (usually referred to as sonic nozzles in the gas industry) as the flow standards for virtually all routine gas meter accuracy certification testing. Critical flow nozzles have been used by a limited number of other organizations as calibration standards for the accuracy testing of gas meters 1' 2, and have sometimes been used as transfer standards in interlaboratory comparisons ~. The lack of a recognized international standard has meant that sonic nozzles as flow measurement standards for the routine calibration of gas flow meters used for customer billing has not achieved general implementation and acceptance. The publication of ISO 9300:1990 'Measurement of gas flow by means of critical flow Venturi nozzles '4 should help correct this situation. This paper aims at providing guidelines for the practical application of ISO 9300 to the use of flow-calibrated nozzles for gas meter accuracy testing. ISO 9300 only provides for calculated flow rates to an uncertainty of no better than ---0.5%, whereas it is possible to calibrate individual nozzles to much better than that ~. The high level of repeatability of sonic nozzles has been demonstrated by nozzle intercomparison work (using a bridge method) both in this laboratory and at the Australian National Measurement Laboratory. Nozzle comparisons to -+0.01% have been quoted 5.
0955-5986/93/020067-05 ~) 1993 Butterworth-Heinemann Ltd
Flow Meas. Instrum., 1993 Vol 4 No 2
A, C C, M Po Pl
qM qv R Red
To Wl
t~ ts
v~ Z Ap
Subscripts m n s x
67
P. H. Wright- The application of sonic nozzles in the gas industry
Sonic (critical flow) nozzles Sonic nozzles or critical flow venturi nozzles are converging/diverging flow restrictions in which the total pressure differential is kept sufficiently high that the gas flow accelerates to the critical velocity (the local sonic velocity) at the throat. The flow into the nozzle is independent of the downstream pressure conditions provided the pressure differential is above that necessary to ensure critical flow. Critical flow nozzles thus lend themselves to the precise setting of flow rates as constant inlet conditions lead to constant upstream flow.
Critical flow nozzles in the Gas & Fuel Corporation The Gas & Fuel Corporation of Victoria uses critical flow venturi nozzles as the flow standards for virtually all routine gas meter accuracy certification testing. The testing equipment includes a range of facilities as below: [] A large industrial gas meter test facility from 6 to 5600 m 3 h -1 with 11 critical flow nozzles used to test meters from 80 mm to 450 mm pipe sizes. This facility has been in use for 10 years. [] A light industrial gas meter test facility from 2.4 to 30 m 3 h -1 with six critical flow nozzles (built using PVC pressure pipe to simplify manufacture) which has been used for over five years. [] 24 automated domestic meter test rigs 6 from 1.2 to 6 m 3 h -1 which have been in continuous use for over six years
temperature and pressure uncertainty can never be better than -+0.5%. This level of uncertainty is generally unacceptable for flow measurement standards to be used for the calibration of other flow meters. It is known from experiments of the type conducted at the C.S.I.R.O. National Measurement Laboratory, Sydney, Australia, that the repeatability of critical flow venturi nozzles is orders of magnitude better than this s, 7, 8 Although ISO 9300:1990 allows for calculation of the flow, direct calibration of critical flow venturi nozzles is preferred, as the inherent high repeatability of the nozzles allows the measurement from a primary standard to be transferred to meters being calibrated with minimal introduced uncertainties. Many gas meters used for customer billing purposes are calibrated on a volume flow basis. A critical flow venturi nozzle is essentially a volume flow device in that the volume flow through the nozzle is constant (to a first approximation) regardless of the pressure. The application of critical flow nozzles to the calibration of gas meters requires the mass flow equations of the ISO standard to be converted to a volume flow basis. The mass flow from ISO 9300 is (to a first approximation) proportional to the absolute pressure upstream of the nozzle: q m --
A,CC, Po (RTo/M) lj2
(1)
The discharge coefficient (C) represents the effects of the non-isentropic and non-one-dimensional flow in the boundary layer of the nozzle. The volume flow equivalent of equation (1) is
All testing is carried out with atmospheric air using the test rooms as the constant pressure and temperature supplies and critical flow being maintained in the flow nozzles via suction from a variety of blower/pump units. All the test facilities use computers to control all the necessary data acquisition, control and calculation functions. Experience to date with these test facilities indicates that critical flow venturi nozzles are highly repeatable and stable flow standards. Observed small changes in calibrated flow through these nozzles are more indicative of changes in the calibration and reference standards (bell or piston provers).
The ISO 9300 standard does not directly address the issue of directly calibrated nozzles and appropriate working equations have been developed and are shown below. The application of ISO 9300 to directly calibrated nozzles is significant, as the calculation of nozzle flows from the standard can be no better than -+0.5% (95% confidence level) whereas directly calibrated nozzles can have an uncertainty of better than 0.1% (95% confidence level).
ISO 9300:1990
Nozzle calibration specification
ISO 9300:1990 'Measurement of gas flow by means of critical flow venturi nozzles' specifies the geometry and method of use of critical flow venturi nozzles used to determine the mass flow rate of a gas flowing through the system. It also gives the information necessary for calculation of the flow rate and its associated uncertainty. The ISO 9300:1990 standard refers to the calculation of gas (mass) flow in relation to the inlet conditions of the nozzle and the throat diameter of the nozzle. The nozzles referred to are of the toroidal inlet/conical outlet form. The discharge coefficient of these standard form nozzles is quoted as having a -+0.5% relative uncertainty at the 95% confidence limit. Thus the calculated total uncertainty including
The calibration (size) of a flow-calibrated nozzle is usually referred to the flow rate at some nominated standard condition. The calibration is sometimes referred to as a 'standard time '9. The standard time, ts, used by the American Meter Company is the time required, in seconds, to pass one cubic foot of dry air through the nozzle under critical flow at an inlet pressure of 24.696 psia and an inlet temperature of 60.0 °F. The 24.696 psia relates to the American Meter Company practice of calibrating the nozzles at a 10 psig inlet pressure. The calibration factor (standard time) used in this laboratory is the time required, in seconds, to pass one cubic metre of dry air through the nozzle under critical flow at an inlet total (stagnation) pressure of 101.325 kPa
68
Flow Meas. Instrum.,
1993 Vol 4 No 2
qv = A,CC,Z
(2)
P. H. Wright- The application of sonic nozzles in the gas industry absolute and an inlet stagnation temperature of 20.0 °C. The quoted standard conditions relate to the nominal calibration conditions and are similar to the normal conditions of use of the nozzles ~°. Regardless of the specification used, the aim is to provide calibrating laboratories with an unambiguous statement of the reference conditions for the calibration of the critical flow venturi nozzles. If the conditions of the calibration are known, then that calibration can be used as the basis for flow calculations at other flowing conditions. The nozzle calibration should, wherever possible, be similar to the conditions of use of the nozzle so that the required corrections to the flow will be small or in many cases can be neglected. Another method for specifying the flow capacity or size of a critical flow nozzle is to calculate the effective diameter of the nozzle throat from the results of a flow calibration as the flow under various conditions can be calculated from that. In practice, such calculations can be quite involved and prone to error.
Application of ISO 9300 to flow-calibrated nozzles Using the previously quoted critical flow nozzle volume flow equation with the concept of a standard time or calibration factor, ts, the following equations are developed. For chosen standard conditions:
1
tRTost 1/2
t~ = q,,s = A,CsC,sZs \ M s /
(RTo×I u2
(4)
where the subscript x indicates a parameter under conditions of the flow measurement in the nozzles. To convert a nozzle calibration to volume flow with different gas flow conditions, the following relation applies:
1C×C,xZ×(MsTo×l 1/2 qvx - t~ CsC,s Zs \Mx Tos/
(5)
(6)
is the same as the ratio of the relative densities (sometimes referred to as specific gravities) of different gases. This term becomes unity if the nozzle calibration gas and the gas being measured have the same composition. It should be noted that the difference in properties of dry air and atmospheric air (which contains water vapour) must be taken into consideration. In many practical applications, where nozzles are used to determine flow at conditions close to the nozzle calibration conditions, the approximate expression shown below is often more than satisfactory.
1 iMs T×lU2 (7)
This simplified equation contains parameters which can usually be determined relatively easily. This equation
(8)
t~,Tn \Mn TJ J
Tmt
t 2 [Pn
Pm \minTs/
n
tsn \Tnl
J
(9)
The ratio of molecular weights (or relative densities) at the meter is the same as at the nozzles, so that factor can be brought outside the summation. Meter accuracy tests are conducted by running the meter under test at a constant flow rate using one or more calibrated nozzles in parallel and measuring the time taken for the meter to pass a chosen quantity of gas. The volume actually passed by the meter can be calculated as below.
Trn( Ms / 1'2
Vm=tVpm\mmT~J
The ratio
MJM×
Pm n
where n refers to the nozzle number. The equation can be rewritten to reduce calculation time as below: q,.,,~
qvx = A,C×C,xZ, \ M× /
t,
q~m
(3)
For other conditions:
qvx =
also assumes that the pipe sizing is large enough that the static and stagnation temperatures and pressures respectively are essentially the same, which is the case for nozzle throat to pipe diameter ratios of 0.3 or greater at atmospheric pressure. The calibration of gas meters is usually achieved by connecting the outlet of the meter under test via pipe work to the inlet(s) of one or more nozzles in parallel. This arrangement effectively ensures that the flow rate of the meter under test is kept constant if the inlet pressure to the meter is kept constant. In the above arrangement the flows through each of the nozzles can be summed to determine the total flow through the meter under test. This summation can be carried out with virtually no increase in overall uncertainty, as the percentage uncertainty of each nozzle flow leads to the same percentage uncertainty in the total flow. To enable the summation of the flows, the flow through each of the nozzles must be corrected to some reference condition. For the accuracy testing of gas meters the most convenient reference point is the conditions prevailing at the meter under test. Thus the summation of the flows through a meter under test can be described by the following equation:
[nt,t"q
~n t~n \Tnn/ J
(10)
The volume actually passed by the meter is compared with the volume indicated by the meter for the same period to determine the meter error. It is usual to time an integral number of revolutions of the meter test dial and use this time as the total test time in the above equation. The determination of meter error thus becomes a comparison of actual and indicated volume flow rates.
Sonic nozzle bridge intercomparison The intercomparison of critical flow venturi nozzles allows the flow calibration of one nozzle to be transferred to another with the minimum increase in uncertainty. The technique relies on pipe work and critical flow venturi nozzles arranged in the gas flow equivalent of an electrical Wheatstone bridge. Sonic nozzles become the equivalent of electrical resistors
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P. H. Wright- The application of sonic nozzles in the gas industry and pressure and mass flow become the equivalent of voltage and electrical current respectively. A schematic diagram of a sonic nozzle bridge is shown in Figure 1. The downstream nozzles must have a larger capacity than the upstream nozzles to pass the larger volume flow resulting from the pressure drop across the upstream nozzles. The actual pressure drops across arms 1 and 2 (and the corresponding increase in volume flow) depend on the ratio of volume flow capacities of the nozzles in arms 1 and 3, and 2 and 4, respectively. The technique relies on a suitable choice of nozzles and the existence of sufficient total pressure drop to ensure critical flow in all the sonic nozzles. It should be noted that although single nozzles are shown in arms 1, 3 and 4 of the diagram, the arms could be made up from combinations of nozzles in parallel. The pressure differential between the inlets of the nozzles in arms 3 and 4 is very sensitive to changes in the volume flow rates of any of the nozzles in the bridge, particularly if the bridge is nearly 'balanced', that is, if the differential pressure Ap is small. Thus if a known combination of nozzles in (say) arm 2 is replaced by an unknown nozzle, the difference in flow can be determined with precision because of the sensitivity of the differential pressure measurement Ap to changes in the nozzle flows. The bridge technique works with best uncertainty if the flow rate of the unknown nozzle and the (total) flow rate of the calibrated nozzle(s) are within 5% or better of each other. Tests at the Australian National
~ Suppl.y
I. AFm
Arm 2
or
1 Unknown sonic nozzte
Reference sonic nozzte(s)
I
\ Arr~ 3
Arm 4
)
I
Exhaust
Figure l Sonic nozzle bridge for intercomparison of sonic nozzles 70
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Measurement Laboratory indicate that the bridge technique can be developed to allow intercomparisons to better than 0.01%~. Within the Gas & Fuel Engineering Services Department gas flow laboratory relatively simple apparatus has been used to calibrate nozzles with air flow rates up to 90 m 3 h -1 with less than 0.05% increase in uncertainty. This increase in uncertainty is added to the uncertainty of the reference nozzle(s). The bridge technique allows large critical flow nozzles to be calibrated against combinations of smaller nozzles in parallel. This means that nozzles which are outside the capacity range of available calibration facilities can be calibrated, traceable via the bridge technique back to the available calibration facility.
Practical sonic nozzle sequences Test stations for accuracy testing of large gas meters usually have a range of critical flow venturi nozzles which can be used in a variety of combinations to provide a wide range of available testing gas flows. As an example, a station with six nozzles in a binary sequence can provide 63 different flow rates, ranging from the flow of the smallest nozzle to the sum of the flows though all the nozzles. In large meter test stations, which may have 10 to 20 available nozzles, the calibration of the larger nozzles may cause difficulties because of the large facilities required for measurement of large flow rates. The original set of nozzles in the largest of the Gas & Fuel Corporation test stations were originally calibrated overseas, as there were no facilities of appropriate size and uncertainty in Australia. It was considered desirable to be able to provide calibration traceability to local measurement standards in the future, possibly by the bridge technique. A second set of nozzles was required, as the meter testing rig could not be out of use during the potentially timeconsuming recalibration. To use the bridge technique for calibrating large nozzles it is necessary to use two or more nozzles whose total flow is close to the nozzle to be calibrated. This implies that if nozzles in a calibration station are arranged in a binary sequence it will be necessary to create a separate 'dummy' set of nozzles to allow each nozzle to be calibrated against two of the next smaller size in parallel s . To reduce costs, the second set of nozzles for the Gas & Fuel Corporation large meter test facility was designed such that the sizing lent itself to simple application of the bridge calibration technique without the necessity for the manufacture of duplicate nozzles which would not be required for the test station. The sequence is such that at the high flow rate end of the sequence the flow rate of each nozzle is close to the sum of the flow rates of the next three smaller nozzles. This means that using the sonic nozzle bridge technique it should be feasible to pass upwards through the sequence calibrating each nozzle by comparison with the sum of the three below it. The smaller nozzles in the sequence would be calibrated directly using conventional flow calibration techniques, such as bell or piston provers. The flow rate ratio between nozzles is 1.839 to 1
P. H. Wright - The application of sonic nozzles in the gas industry for each nozzle to be the equivalent to the sum of the three next smaller nozzles in the sequence. Other choices for how many nozzles should be the equivalent of the next larger nozzle did not seem as practical. It is found that using two nozzles results in a large number of nozzles being required to cover the desired flow range of a test station. Using the summation of four (or more) nozzles requires a more cumbersome bridge and the steps between nozzles are not that different from the case of using three nozzles. The choice of a regular sequence of nozzles can also overcome another problem with the practical application of the bridge technique, namely the requirement of suitable capacity nozzles for the remaining arms of the bridge. The nozzle one size step up from the nozzle being calibrated can be used as the nozzle in the arm of the bridge downstream of the nozzle being calibrated. This downstream nozzle does not need to be calibrated for this application. The two nozzles used to provide the reference arms on the bridge (arms 1 and 3 in Figure 1) can be chosen from adjacent nozzles in the sequence not required on the measurement side of the bridge. Thus the bridge technique only requires the manufacture of one extra nozzle, one step larger than the largest one required for the meter test rig. The above technique assumes that the three smallest nozzles can be precisely calibrated against some reference standard and that there are at least eight nozzles in the sequence. The sequence can be chosen so that each of the larger nozzles is not exactly the sum of the flow rates of the next three smaller nozzles, so that the range of flow rates available will not be reduced by having exactly duplicate flows. Conclusions
Critical flow venturi nozzles have proved to be highly repeatable gas flow standards. The acceptance of critical flow nozzles as the preferred technique for the routine accuracy testing and certification of gas flow meters will be assisted by the publication of ISO 9300:1990 and the acknowledgement that the limiting factor in the uncertainty of the application of these nozzles is the uncertainty in the actual flow calibration of the nozzles. The equations provided in this paper will allow
the application of directly calibrated nozzles to gas meter testing within the framework of ISO 9300. The application of the bridge technique means that the precision of nozzle calibrations from small reference standards such as bell provers can be transferred to higher flows, without the necessity for larger standards. Acknowledgements
The author wishes to thank Thiam Wee Chua who carried out a great many tests on the sonic nozzle bridge and lan Dollery who carried out much of the uncertainty analysis in the applications of sonic nozzles. The author also wishes to thank the Gas & Fuel Corporation of Victoria for permission to publish this work. References
1 Wright, P. H. The application of sonic nozzlesto the automated accuracy testing of gas flow meters In 'Proc. International Conference on Flow Measurement', 20-23 August, Melbourne, Australia (1985) 152-156 2 Aschenbrenner,A. Ein Pr6fstandfiJr Grol3gasz~hlermit ~iberkritischen D~isenals Normalger~te (A test stand for large-scale gas meters, with supercritical nozzles as standard instrument) PTBBericht, PTB-Me-24October (1979) 3 Aschenbrenner,A. Calibration of the new test rig for large gas meters of the Physikalisch-Technische Bundesanstalt. In 'Proc. Flomeko Conference', D6sseldorf, VDI Berichte 768 (1989) 4 ISDO 9300: 1990(E) Measurement of gas flow by means of critical flow Venturi nozzles, International Organization for Standardization, Geneva (1990) 5 Caw,W. A. and Prowse, D. B. A proposed calibration hierarchy for gas flow In 'National Seminar on Flow Measurement in Australia', 9-10 March, National Measurement Laboratory, Sydney (1987) 6 Wright, P. H. Sonic nozzles as gas meter calibration standards In 'Proc. 1986 IICASymposiumon CustodyTransfer', Melbourne 27 February (1986) 7 Caw, W. A., Bryant, N. W. and Bell, G. A. Analogue of the Wheatstone Bridge using critical flow nozzles In 'Australasian Hydraulics and Fluid Mechanics Conference', Adelaide (1977) 605-607 8 Bignell, N. Measurements with a sonic-nozzle bridge In Proc. Australasian Instrumentation and Measurement Conference', Adelaide, 14-I 7 November (1989) 312-315 9 Schroyer,H. R. Sonic nozzles in distribution metering. Pipeline and Gas J. D137-D141, December (1975) 10 Wright, P. H. Automated calibration of critical flow reference nozzles In AustralasianInstrumentationand MeasurementConference, Adelaide, 14-17 November (1989) 238-242
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